Identifying and Analyzing Sepsis States: A Retrospective Study on Patients with Sepsis in ICUs
Chih-Hao Fang, Vikram Ravindra, Salma Akhter, Mohammad Adibuzzaman, Paul Griffin, Shankar Subramaniam, Ananth Grama
IIdentifying and Analyzing Sepsis States: ARetrospective Study on Patients with Sepsis in ICUs.
Chih-Hao Fang , Vikram Ravindra , Salma Akhter , Mohammad Adibuzzaman , PaulGriffin , Shankar Subramaniam , and Ananth Grama Department of Computer Science, Purdue University, West Lafayette, IN, USA Regenstrief Center for Healthcare Engineering, Purdue University, West Lafayette, IN, USA Department of Bioengineering, University of California, San Diego, La Jolla, CA, USA. * Correspondence and requests for materials should be addressed to Chih-Hao Fang (email: [email protected])or to Ananth Grama (email: [email protected])
ABSTRACT
Sepsis accounts for more than 50% of hospital deaths, and the associated cost ranks the highest among hospital admissionsin the US. Improved understanding of disease states, severity, and clinical markers has the potential to significantly improvepatient outcomes and reduce cost. We develop a computational framework that identifies disease states in sepsis using clinicalvariables and samples in the MIMIC-III database. We identify six distinct patient states in sepsis, each associated with differentmanifestations of organ dysfunction. We find that patients in different sepsis states are statistically significantly composed ofdistinct populations with disparate demographic and comorbidity profiles. Collectively, our framework provides a holistic view ofsepsis, and our findings provide the basis for future development of clinical trials and therapeutic strategies for sepsis.
Sepsis accounts for more than 50% of hospital deaths , and the cost of sepsis management ranks the highest among hospitaladmissions for all illnesses in the United States . Key factors in improving patients’ outcomes are the early diagnosis of sepsis,and subsequent timely and appropriate treatment actions. While significant progress has been made towards the former ,with recent development of the Sequential Organ Failure Assessment (SOFA or Quick-SOFA) measure outside the IntensiveCare Unit (ICU) , the latter continues to be a significant challenge . There have been a number of effortsaimed at classifying disorders that broadly comprise sepsis, which have resulted in categories such as Systemic InflammatoryResponse Syndrome (SIRS), severe sepsis, and septic shock. These, in turn, have resulted in treatment strategies with limitedsuccess. More recently, these categorizations have been abandoned, in favor of a more broadly accepted definition of sepsis as a‘life-threatening organ dysfunction caused by a dysregulated host response to infection’ . This dysfunction is characterized by aSOFA score of two points or more. Although SOFA score is a more comprehensive measure of the severity of health status of a r X i v : . [ q - b i o . Q M ] S e p atients with sepsis, and a good predictor of mortality , the diverse mechanisms underlying sepsis and how they map toSOFA scores are still not fully understood. This is in spite of significant efforts aimed at developing and deploying new andimproved treatments. As a result, current approaches to sepsis treatment are primarily guideline-based, as opposed to relying onclinicians’ decision-making capability, when presented with a patient’s unique set of clinical variables . MIMIC-III Clinical Database
Patient Cohort
Cohort Identification DataPreprocessing
Data Samples • Gender• Heart Rate• Lab Values
Data Preparation PhaseData Analysis Phase
Archetypal Analysis
DimensionReduction
Sepsis StateAnalysis
Feature SelectionComorbidity Profiles Extraction
Primary FunctionAnalysisEtiological Analysis A1 Resipiratory LiverKidneyInflammationCoagulationNervousCardiovascular A2 Resipiratory LiverKidneyInflammationCoagulationNervousCardiovascular A3 Resipiratory LiverKidneyInflammationCoagulationNervousCardiovascular A4 Resipiratory LiverKidneyInflammationCoagulationNervousCardiovascular A5 Resipiratory LiverKidneyInflammationCoagulationNervousCardiovascular A6 Resipiratory LiverKidneyInflammationCoagulationNervousCardiovascular
Figure4.
Primaryfunctionexpressionsforeachsepsisstate.theexpressionlevelofitscorrespondingbiomarkersweightedbytheconfidencelevel.Specifically,foreachprimaryfunction,wefirstlycalculatehowfaristheexpressionofthebiomarkerisfromtheboundaryofthenormalrangeforeachsepsisstate,called d i ,where i denotesthesepsisstate i .Wethennormalizeeach d i bydividingthemaximumofthedistanceacrosssepsisstates, i.e. , d i / max { d ,..., d K } .Sinceeachprimaryfunctionhasmultiplebiomarkers,wecouldcalculatethefinalexpressionoftheprimaryfunctionasasummationofthe d i / max { d ,..., d K } foreachbiomarker.However,eachbiomarkerhasdifferentconfidencelevelwiththelessertheconfidencelevelthelesstrustworthyitisincalculatingthefinalexpressionoftheprimaryfunction.Therefore,wedefinethefinalexpressionoftheprimaryfunctionasasummationofthe d i / max { d ,..., d K } foreachbiomarkerweightedbyitscorrespondingconfidencelevel.Wethennormalizethefinalvalueintotherangefrom0to10.Ifthevalueiscloseto10,itindicatesahigherexpressionoftheprimaryfunction,andviceversa.TheresultforeachsepsisstateisshowninFigure4.Inwhatfollows,wealsoprovideadetailedexaminationoftheexpressionlevelofthebiomarkersforeachprimaryfunction.Forconvenience,wegivegiveasummaryofwhichbiomarkersbelongtowhichprimaryfunctioninTable2. NervousSystemfunction:
GCSisthemostcommonlyusedmethodofbedsideassessmentofbraininjuryandlateritisalsousedforassessingtheconsciousnesslevelofcriticallyillpatients,suchassepsispatients. .GCSestimatescomaseveritybasedoneye,verbal,andmotorcriteria.Itclassifiesthepersonintomild(score=13–15),moderate(score=9–12),severe(score=3–8),andvegetativestate(scorelessthan3) .ThemeanvalueofGCSscoreinA1,A2,A3,A4,A5,andA6statesare12.56,12.24,13.96,10.67,11.20,and11.77respectively.Thus,thenon-MODSgroupiswithintherangeofmildstatewhereastheMODSgroupiswithintherangeofmoderatestate.Amongallsepsisstates,A3stateexhibitsthehighestconsciousnesslevelwhileA4sateexhibitsthelowestconsciousness.TherankingorderofthesepsisstatesforthemeanvalueofGCSscoreisA4>A5>A6>A1>A2>A3,which (a) (b)(c) (d) A1 A2 A3 A4 A5 A6
Archetype congestive heart failurecardiac arrhythmiasvalvular diseasepulmonary circulationperipheral vascularhypertensionparalysisother neurologicalchronic pulmonarydiabetes uncomplicateddiabetes complicatedhypothyroidismrenal failureliver diseasepeptic ulceraidslymphomametastatic cancersolid tumorrheumatoid arthritiscoagulopathyobesityweight lossfluid electrolyteblood loss anemiadeficiency anemiasalcohol abusedrug abusepsychosesdepression P r e m o r b i d S t a t u s Z-score -0.3-0.2-0.100.10.20.30.40.50.60.7
Figure5. (a)
Thepopulationdistributionforeachsepsisstatestratifiedbyage. (b)
Thepopulationdistributionforeachsepsisstatestratifiedbyweight. (c)
Thepopulationdistributionforeachsepsisstatestratifiedbypremorbidcount. (d) showninFigure5a.WefindthatwhiletheaverageageintheA1,A3,andtheA4statesareclosetotheaverageageinthiscohorttheaverageageintheA2,A5,andtheA6statesaresignificantlylowerthanthetheaverageage.Inthiscohort,theaverageageis64.57yearsandtheaverageageintheA1,A2,A3,A4,A5,andtheA6statesare64.66years,56.57years,64.85years,62.77years,51.57years,and54.28yearsrespectively.Notethatwhiletheageisnotanindependentparameterofthehealthoutcomes,wefindthatthetrendofincreasingaworseoutcomeinelderpeopleforseveresepsisstates.IntheMODSgroup,wenoticethattheA4statethatwasshowntobeassociatedwiththehighestmortalityisalsohasthehighestaverageage.Inthenon-MODSgroup,ontheotherhand,wefindthatthesepsisstatethatexhibitsnotableexpressionofinflammatoryresponse,namelytheA2state,isassociatedwithalowerage.ThedistributionforeachthesepsisstatestratifiedbyweightareshowninFigure5b. Wefindthatthedifferenceofthe
Figure 1: Illustration of proposed framework: The data preparation phase extracts 42 variables (demographic profiles, vitalsigns, laboratory tests, mechanical ventilation status of the patients, and the comorbidity profiles) from 16,546 distinct sepsispatients admitted to Beth Israel Deaconess Medical Center from the MIMIC-III database. In the data analysis phase, weuse archetypal analysis to find distinct states of sepsis. We then use a dimension reduction method (UMAP) to visualize theidentified sepsis states. For analyzing each state, a statistical test (MANOVA) is performed to validate that the clusters aresignificantly different from the distribution of the cohort as a whole, and the SOFA score, SIRS score, and mortality rateare calculated to characterize each sepsis state. In primary function analysis, selected features from archetypes are used toidentify the primary functions (namely, nervous system, inflammation and infection, liver function, kidney function, coagulation,respiratory function, and, cardiovascular function ) of each sepsis state. Finally, in etiological analysis, we perform z-scoreanalysis to find correlation between pre-existing comorbidity profiles (30 types) and sepsis states.A personalized decision process for sepsis must be capable of differentiating heterogeneous response from diverse groupsof patients, and understanding the etiology of disease to minimize errors and maximize treatment efficacy. With the goalof motivating research on such personalized decision processes, the Medical Information Mart for Intensive Care versionIII (MIMIC-III) database released de-identified clinical data from approximately 46,000 patients admitted to Beth Israel eaconess Medical Center in Boston, Massachusetts between 2001 and 2012. We use clinical variables in the MIMIC-IIIdatabase, along with a range of novel algorithmic and statistical constructs for our retrospective study of sepsis states andresponse (Figure 1).We first identify a patient cohort that satisfies the sepsis-3 criteria from five tertiary ICUs in Boston. This results in asample of 16,546 distinct patients with 20,944 ICU admissions. We then extract clinical variables for the cohort, includingdemographic data, vital signs, lab results, and other information such as the use of a ventilator, and the number of comorbiditiesbefore sepsis infection, to characterize the health status of the patients with sepsis during the ICU stay. We summarize thisdata in Table 1. We develop a mathematical framework that: (i) identifies distinct sepsis states using archetypal analysis; (ii)extracts significant sets of features from clinical variables to differentiate sepsis states and identifies associated biomarkers thatcan be mapped back to organ function(s); and (iii) analyzes relationships between sepsis states, demographic variables, andcomorbidities before infection.We demonstrate that our framework uncovers distinct sepsis states – each state characterized by a unique set of pathologicalresponses that can be mapped back to organ function(s), and an association between patient attributes and sepsis states. Ourframework provides a holistic view of the diverse set of conditions that comprise sepsis. Our analysis reveals six sepsis states– among these states, State 1 manifests a mild condition of sepsis, State 2 primarily represents inflammation and infectionwith evident signs of inflammatory responses, State 3 corresponds to the highest survival rate, but is typically associated withhyperoxia. The last three states show signs and symptoms of Multiple Organ Dysfunction Syndrome (MODS) with diversemanifestations of organ failures. We also find that patients with sepsis being categorized into these states manifest distinctdemographic profiles. Patients categorized as inflammation type or the second and third MODS type are at least eight yearsyounger than the average for the cohort; patients with the second type of MODS tend to be overweight, and the average weightof patients in the third type is 3.99 kilograms lower than the average cohort weight of 83.27 kilograms. Finally, these states alsomanifest distinct comorbidities profiles before infection. Patients with weight loss, alcohol abuse, or paralysis are more likelyto develop the inflammation type, patients with coagulopathy and liver disease are more likely to develop MODS types, patientsin the first MODS type are associated with solid tumors. Patients in the second MODS type are associated with depressionand other related conditions, such as drug and alcohol abuse, obesity, and peptic ulcer disease. Patients in the third MODStype are associated with valvular disease, pulmonary circulation, other neurological disorders, and rheumatoid arthritis. Theseresults provide a better understanding of the etiology and pathological process of sepsis, and guides design of clinical trials andtherapeutic strategies for future investigations. This is a retrospective study. Future studies that involve AI intervention or treatment guidelines would be in compliance with guidelines for AI clinicalresearch . able 1: Description of the cohort. Demographic Type or Unit Normal Range Mean (std) Value in Cohort
Age years N/A 64.5738 (16.665)Gender binary 1 = Female, 0 = Male 0.4396 (0.4963)
Vitals
HR bpm 60 - 100 87.208 (16.8358)SysBP mmHg ≤
120 119.9199 (20.3514)MeanBP mmHg 70 - 100 78.2144 (13.4891)DiaBP mmHg 80 57.1157 (13.3192)Temp Celsius 36.5 - 37.5 36.9062 (2.0132)RR bpm 12 - 20 20.2073 (5.1868)
Lab Values
GCS N/A 15 12.5734 (3.4482)SpO2 percent 95 - 100 96.9085 (2.6548)FiO2 fraction .21% inhaled from natural air 0.4604 (0.1834)Potassium mEq/L 3.5 - 5.0 4.0789 (0.5594)Sodium mEq/L 135 - 145 138.6876 (4.8859)Chloride mEq/L 96 - 106 104.7204 (6.2447)Glucose mg/dL 80 - 130 138.9572 (51.1809)BUN mg/dL 7 - 20 29.2462 (22.5642)Creatinine mg/dL 0.6 (0.5) -1.2 (1.1) males (females) 1.4886 (2.1624)Magnesium mg/dL 1.5 - 2.5 2.055 (0.3521)Calcium mg/dL 8.8 - 10.7 8.3136 (0.7982)Ionised Ca mmol/L 1.16 - 1.32 1.1315 (0.1219)CO2 mEq/L 23 - 29 25.822 (5.6583)SGOT u/L 5 - 40 155.6854 (583.5742)SGPT u/L 7 - 56 583.5742 (466.3519)Total Bilirubin mg/dL 0.1 - 1.2 2.4121 (5.1454)Albumin g/dL 3.4 - 5.4 3.0015 (0.6761)Hb g/dL 13.5 (12.0) - 17.5 (15.5) males (females) 10.3012 (1.7361)WBC × /L 4.5 - 11.0 12.2717 (8.2931)Platelets × /L 150 - 450 228.6988 (139.1926)aPTT s 30 - 40 37.8122 (19.3446)PT s 11 - 13.5 16.1932 (6.754)INR N/A ≤ Others
Weight kg N/A 83.2268 (24.6507)Mechvent binary 0 = False, 1 = True 0.3689 (0.4825)Comorbidity Count Integer 0 - 30 4.0059 (2.1703)
All of the normal ranges presented apply to adults. HR, Heart Rate; SysBP, Systolic Blood Pressure; MeanBP, Mean Blood Pressure; DiaBP, DiastolicBlood Pressure; Temp, Temperature; GCS, Glasgow Coma Scale; RR, Respiratory Rate; BUN, Blood Urea Nitrogen; SGOT, Serum Glutamic-OxaloaceticTransaminase; SGPT, Serum Glutamic Pyruvic Transaminase; Hb, Hemoglobin; WBC, White Blood Cells; PTT, Partial Thromboplastin Time; PT, ProthrombinTime; INR, International Normalized Ratio, Arterial BE, Arterial Base Excess.
Results
We pose the following important question: do there exist distinct states of sepsis with different clinical manifestations,recovery rates, demographic and pathological characteristics, and is it possible to identify these states from patient clinicalmeasurements?
We formulate this problem as one of finding archetypes (representatives of states) of sepsis, and developpowerful algorithms for solving this problem. A geometric interpretation of our approach is to view each patient as a pointin a high dimensional space of attributes, and archetypes as corners of a convex hull in this high dimensional space. Withinthis representation, each data point can be approximated as a linear combination of the archetypes. Since archetypes forma convex polytope, the coefficients in the linear combinations sum to one (convex combinations). To account for noise, theproblem of finding archetypes is relaxed from an exact convex hull problem, to one of finding an approximate convex hullwith a given number of corners (archetypes). Mathematically, this is formulated as a constrained optimization problem thatminimizes the squared error in representation of each data point as a linear mixture of archetypes. The optimal number ofarchetypes is determined by checking the reduction in the residual (of representations of all data points) and finding the point atwhich this residual drops significantly. This formulation has several advantages over traditional clustering techniques (e.g., k -means). Archetypes represent extremal or pure states – to this end, they have clear clinical interpretations. Second, eachconvex combination has a well-characterized interpretation as a mixture of pure states, thus avoiding negative coefficients (withassociated loss of interpretability) in other methods. Finally, descriptors of archetypes may themselves be processed to identifyclinical markers for the pure states. Using this procedure, we discover six distinct states in sepsis among our cohort. We characterize the statistical significance of each sepsis state based on the data points (patient records) mapped to thecorresponding archetype from the cohort. Since archetypes represent extreme sepsis states, in the rest of this discussion, we usethe terms “sepsis state" and “archetype" interchangeably. Each point is a mixture of sepsis states and we can assign the pointto the closest sepsis state (the corresponding archetype). A statistical interpretation of this formulation views data points asmixtures of samples from the six distinct multivariate distributions. To ascertain that these distributions are indeed distinct, weapply a statistical test, coupled with a dimension reduction technique to the data points. Specifically, we first validate that theprobability distributions corresponding to these groups are significantly different from the distribution of the cohort as a whole.We also test to ensure that the probability distribution of each group is significantly different from others, as characterizedby a multivariate analysis of variance (MANOVA) procedure. Two-sample testing is sensitive to homogeneity of covariancematrices from the compared populations. We use the Box test to compare variation in multivariate samples. We then use aHotelling T-Squared testing variant to compare the mean vectors from two populations. We note that covariance matricesand mean vectors from the compared pairs are significantly different, with a 95 % confidence interval. igure 2 shows a uniform manifold approximation and projection (UMAP) embedding of the data points, along with thearchetypes (represented by colors). Readers may note that archetypes (A1 through A6) do not appear as corners of the convexpolytope, since this is a two-dimensional embedding of a higher dimensional attribute space.Figure 2: Visualization (using low-dimensional UMAP embedding) of the six derived sepsis states. Colors represent differentsepsis states. Co-occurrence ( See section 4) analysis is used to compute the SOFA score, SIRS score, and mortality rateof each sepsis state. Based on these scores, we characterize states A1 (blue), A2 (orange), and A3 (green) as ‘moderatecondition’, ‘inflammation’, and ‘mild condition’, respectively, and we characterize states A4 (red), A5 (brown), and A6 (purple)as ‘Multiple Organ Dysfunction Syndrome (MODS)’.
We use the SOFA score, SIRS score, and mortality rate as measures to characterize sepsis states. We calculate the averageSOFA score and SIRS score for patients in each state. We also apply co-occurrence analysis (See Methods Section 4 for moredetails) to calculate the conditional probability of death, given a sepsis state. The average values of SOFA scores in states A1,A2, A3, A4, A5, and A6 are 6.34, 5.66, 3.99, 10.06, 8.54, and 7.99, respectively. The average values of SIRS scores in statesA1, A2, A3, A4, A5, and A6 are 1.62, 2.28, 1.39, 1.86, 1.74, and 1.76, respectively.Based on the SIRS criteria, a patient with SIRS score higher than two is diagnosed with sepsis infection (please see fulldiscussion in Appendix Section 5.2). This definition of sepsis is mainly focused on signs of inflammation exhibited by patients.We find that, among the sepsis states, only state A2 satisfied the SIRS criteria. Consequently, we identify state A2 as primarilyrepresenting inflammatory response. According to the sepsis-3 criteria , sepsis is defined as having a SOFA score higher thantwo, and the higher the score is, the more severe the condition is. It is reported that patients who developed Multiple Organ ysfunction Syndrome (MODS) display significantly higher mortality rate . We observe that the mortality rate, as wellas the SOFA scores of state A4, A5, and A6 are significantly higher than the other types. Thus, we hypothesize that the A4, A5,and A6 represent MODS with heterogeneous organ dysfunction. Compared to the MODS states, states A1 and A3 displaylower mortality rates and SOFA scores, with A3 having the lowest mortality rate and SOFA score. Therefore, we characterizestates A1 and A3 as ‘moderate condition’ and ‘mild condition’, respectively.A restrictive definition of sepsis has significant adverse implications for diagnosis and treatment. The SIRS metric has beencriticized for its inability to identify all possible host responses for sepsis since the SIRS criteria focuses solely on inflammatoryexcess; hence it is an inaccurate predictor for mortality. This diagnostic metric for sepsis was replaced by sepsis-2 , andeventually by sepsis-3. Sepsis-3 uses the SOFA score to characterize the health status of patients with sepsis. It has been shownto be a more accurate predictor of mortality , compared to SIRS and sepsis-2. Our results support the arguments against theSIRS metric, and reinforce the use of SOFA scores for severity of sepsis infections. As mentioned earlier, only state A2 in ourcohort qualified as a sepsis infection based on SIRS scores – leading to potentially inadequate care for other sepsis states. Ouranalysis demonstrates that SOFA scores correlate well with our identified states, and that the severity and mortality rate foridentified states correlates well with their SOFA sores. However, as we show in the rest of this study, SOFA score alone doesnot capture the diversity of sepsis states – motivating our multidimensional approach based on archetypal analysis. SGOT SGPT PT PaO PaO / FiO WBC Count Platelets Count Arterial Lactate
Comorbidity Count
Creatinine Weight PTT DiaBP Glucose
BUN
Age HR
GCS FiO Mechvent INR None
Figure 3: Visualization of the selected features (21 features in total) by Q j ( P K ) , Q (cid:48) j ( P K ) , and Variation test . Q j ( P K ) calculatesthe discriminative power of feature i for a given clustering as the ratio of inter-cluster inertia to the total inertia computed usingfeature i . Q (cid:48) j ( P K ) calculates the discriminative power of feature i as the ratio of inter-cluster inertia computed using feature i tototal inter-cluster inertia computed using all features. Variation test selects features that have the lowest probability of overlapacross clusters (please see Methods section 4 for more details). Note that there is a significant overlap between features chosenby these selection criteria. However, each criterion yields a distinct set of features significantly associated with different sepsisstates.In Section 2.1.3, we used the SOFA score, SIRS score, and mortality rate to characterize sepsis states and find that theSOFA score is a distinguishing feature of our sepsis states. However, SOFA score provides few insights into the subset of athological responses that are uniquely expressed in each sepsis state. This, in turn, reflects the unique expression of organfunctions that differentiate individual states. Specifically, two patients with similar SOFA scores may exhibit disparate signs oforgan dysfunction. It is possible to analyze the SOFA score for each organ system . However, only a few clinical variables areused to evaluate the SOFA score, and therefore SOFA scores do not provide accurate measures of the functional state of theorgan system. Once we identify sepsis states and corresponding data points (patient assignment to states), we can identify thecomplete set of clinical attributes that uniquely characterize each state; many of these attributes are not included in the SOFAscore computation. This allows us to develop a finer-grained characterization of overall clinical disposition associated witheach sepsis state.To identify discriminative attributes for each state, we have developed three criteria. The first two criteria are based onHuygens-Steiner theorem to measure the inertia ( i.e. , the tendency of a physical object to remain still, or continue in motion)of the points in Euclidean space. The third criterion finds the most distinct features across populations and prunes them foreach state. The first method, which we refer to as the Q j ( P K ) , calculates the discriminative power of feature i for a givenclustering as the ratio of inter-cluster inertia to the total inertia computed using feature i . Intuitively, this method quantifiesthe heterogeneity of feature i across clusters. The second method, which we refer to as Q (cid:48) j ( P K ) calculates the discriminativepower of feature i as the ratio of inter-cluster inertia computed using attribute i to total inter-cluster inertia computed using allattributes. Intuitively, this method computes the relative heterogeneity of feature i with respect to all other features. The thirdmethod uses a variation test that selects features that have the lowest probability of overlapping across clusters (please seemethod section 4 for more details). We find that although there is a considerable overlap of selected features between thesemethods, there are few features that are uniquely selected by the measures. We rank the features in terms of the number ofcriteria that select the particular feature, and extract the top 15 features based on this ranking. As shown in Figure 3, 8 features, i.e. , SGOT, SGPT, PT, PaO2, PaO2/FiO2, WBC Count, Platelets Count, and Arterial lactate, were selected by all three criteria;6 features, i.e. , Age, HR, GCS, FiO2, Mechvent, and INR , were selected by two; and 7 features, i.e. , Weight, PTT, DiaBP,Glucose, BUN, Creatinine and Comorbidity Count were selected by one. We use these features to analyze the primary profilesfor each sepsis state in the next section. Among the 21 features selected by our methods, 18 are the vitals and lab results that are known biomarkers of organ functions,or of other aspects of overall health. From this set of features, we identify associated primary health indicators, correspondingto the nervous system, inflammation and infection, liver function, kidney function, coagulation, respiratory function, andcardiovascular function . We refer to these seven as primary functions . We measure the overall expression of each of theseprimary functions for each sepsis state using the level of corresponding biomarkers, weighted by the confidence level. For sepsisstate i , we calculate distance d i between readings from the biomarkers to the boundary of the normal range for each primaryfunction. We then normalize each d i by dividing by the maximum of the distance across sepsis states, i.e. , d i / max { d , . . . , d K } .Since each primary function can be tested by more than one biomarker, each of which has a different confidence level, we define he final expression of the primary function as a summation of normalized distance. The final value is linearly normalized intothe range from 0 to 10, with higher values indicating higher expression of the primary function. The spider-plot of primaryfunctions affected in each sepsis states is shown in Figure 4. A1 Respiratory LiverKidneyInflammationCoagulationNervousCardiovascular A2 Respiratory LiverKidneyInflammationCoagulationNervousCardiovascular A3 Respiratory LiverKidneyInflammationCoagulationNervousCardiovascular A4 Respiratory LiverKidneyInflammationCoagulationNervousCardiovascular A5 Respiratory LiverKidneyInflammationCoagulationNervousCardiovascular A6 Respiratory LiverKidneyInflammationCoagulationNervousCardiovascular
Figure 4: Spider-plot of primary functions affected in each sepsis state (represented by corresponding colors). There are sevendifferent dimensions of primary function for each sepsis sate. The measured dimensions are nervous system, inflammation andinfection, liver function, kidney function, coagulation, respiratory function, and cardiovascular function , respectively. The scaleof each dimension ranges from 0 to 10, with higher values indicating higher affect on the primary function.We find that each sepsis state manifests distinct expressions of organ dysfunction. We provide a detailed examination of theexpression level of the biomarkers for each primary function next. We provide: (i) the biomarkers that are used in assessmentof organ function; (ii) the severity level of biomarkers to assess organ function, and (iii) the expressions of these biomarkers ineach sepsis state.
We use the Glasgow Coma Scale (GCS) to evaluate the state of the nervous system. GCS is commonly used for bedsideassessment of brain injury, and for assessing the consciousness level of critically ill patients, including those with sepsis .GCS estimates coma severity based on eye, verbal, and motor criteria, and classifies the patient into mild (score = 13 – 15),moderate (score = 9 – 12), severe (score = 3 – 8), and vegetative state (score less than 3) . We find that the average GCS scoresfor states A1 through A6 are 12.56, 12.24, 13.96, 10.67, 11.20, and 11.77, respectively. This indicates that the non-MODSstates – A1, A2, and A3, are mild GCS states, while the MODS states – A4, A5, and A6 states, are within the range of moderateGCS state. Among all of the sepsis states, state A3 displays the highest level of consciousness, while the A4 corresponds tothe lowest level of consciousness. The order of the GCS scores, SOFA scores, as well as mortality rate of sepsis states, areidentical, indicating that the GCS score is a good predictor of mortality for patients with sepsis, and that our method identifies epsis states consistent with the GCS assessment.
White Blood Cell (WBC) count, Heart Rate (HR), and platelet count are used to evaluate inflammation and infection responsein the body. Among these, WBC count and HR are also used in the SIRS criteria to characterize systemic inflammation . Inacute inflammatory conditions, an increase in HR is often observed . HR in sepsis increased when patients suffer fromhypovolemia and hypoperfusion. The WBC count increases from a normal value of 4.5 to 11.0 × /L to 15.0 to 20.0 × /L , with WBC levels higher than 11.0 defined as leukocytosis . While not considered in the SIRS criteria, the elevationof platelet count is an important indicator for inflammation and infection . Inflammatory conditions such as bacterialinfection, sepsis, malignancy, and tissue damage, motivate a reactive response that elevates platelet count, namely secondarythrombocytosis (platelet count higher than 500 × /L) .We find that leukocytosis and secondary thrombocytosis are observed in state A2. This state displays the highest averageWBC count, platelet count, and HR with an average of 20.70 × /L, 905.58 × /L, and 95.57, respectively. The averageWBC count in state A3 is within, but close to the maximum of the normal range (10.95 × /L). Slightly elevated WBC countis observed in states A1, A4, A5, and A6, with an average of 12.22 × /L, 13.12 × /L, 11.24 × /L, and 13.01 × /L, respectively. The average platelet counts in states A1, A3, A4, A5, and A6 are within the normal range, with averages of223.79 × /L, 229.67 × /L, 185.09 × /L, 189.93 × /L, and 194.64 × /L, respectively.In summary, states A1, A3, A4, A5, and A6 show few signs of inflammation. In contrast, state A2 reveals high inflammatoryresponse, as all the inflammatory biomarkers – WBC count, platelet count, and HR, are significantly elevated. SGOT, SGPT, and arterial lactate are used to characterize liver function. An increase in SGOT and SGPT levels indicatesdamage to the liver . In general, the severity of liver dysfunction can be classified as mild, moderate, or severe if elevation ofSGOT and SGPT levels is less than 5 times, 5-10 times, and 10-50 times the upper reference limit. In addition to SGOT andSGPT, arterial lactate is a biomarker for liver dysfunction . Arterial lactate is primarily cleared by the liver, with a smallamount of additional clearance by the kidneys . Thus, arterial lactate is elevated when liver function is compromised . In ahealthy body, the lactate level is usually less than two mmol/L. Patients with hyperlactatemia usually have lactate levels higherthan two mmol/L. Lactate levels higher than four mmol/L are considered to be in a severe state of hyperlactatemia .We find that non-MODS states – A1, A2, and A3, reveal mild liver damage, with only a mild increase in SGOT and SGPTlevels (less than 5 times the upper reference limit ), as well as a mild increase in arterial lactate. The average SGOT levels instates A1, A2, and A3 are 121.20 u/L, 115.25 u/L, and 97.13 u/L, respectively; the average levels of SGPT in states A1, A2,and A3 are 104.71 u/L, 103.37 u/L, and 81.68 u/L, respectively; and the average arterial lactate levels in states A1, A2, and A3are 2.04 mmol/L, 1.88 mmol/L, and 2.10 mmol/L, respectively. In contrast to non-MODS states, SGOT, SGPT, and arteriallactate are all in severe levels in MODS states – A4, A5, and A6. The average SGOT levels in states A4, A5, and A6 are 6.56 × u/L, 2.01 × u/L, and 7.66 × u/L, respectively; the average SGPT levels in states A4, A5, and A6 are 3.02 × /L, 6.39 × u/L, and 6.69 × u/L, respectively; and the average arterial lactate levels in states A4, A5, and A6 are 5.50mmol/L, 3.95 mmol/L, and 4.59 mmol/L, respectively. Not identified by our feature selection methods, but also a representativebiomarker, high levels of bilirubin are often associated with liver damage . Patients with sepsis having (i) bilirubin ≥ . A high level of bilirubin ( ≥ . In our study, the average bilirubin levels in states A4, A5, andA6 are 5.37 mg/dL, 3.37 mg/dL, and 4.56 mg/dL, respectively, indicating common occurrence of jaundice in MODS states.In summary, non-MODS states reveal mild liver damage, reflected in a mild increase in SGOT, SGPT, and arterial lactatelevels. In contrast, MODS states display severe liver dysfunction, with SGOT, SGPT, and arterial lactate all at severe levels.This is generally accompanied with jaundice. Finally, we note that state A6 potentially develops ischemic injury, since weobserve that: (i) both SGOT and SGPT are more than 50 times higher than the upper reference limit; and (ii) SGOT is greaterthan SGPT . We show in the next section that the development of ischemic injury is related to a set of comorbidities associatedwith state A6 before sepsis infection. Blood Urea Nitrogen (BUN) test and serum creatinine, identified by our feature selection methods, are common biomarkers ofAcute Kidney Injury (AKI) . AKI , defined as a sudden episode of kidney failure or kidney damage that happenswithin a few hours or a few days, is a common complication in sepsis patients. It is associated with high morbidity andmortality . BUN measures the amount of urea nitrogen in the blood. Urea nitrogen is removed from the blood by the kidneys;consequently, high BUN levels indicate potential kidney damage. A serum creatinine test provides an estimate of filtrationefficiency of kidneys (glomerular filtration rate). An increased level of creatinine in blood is indicative of potential impairedkidney function.We find that state A3 exhibits relatively better kidney function when compared to the other sepsis states since both serumcreatinine (1.02 mg/L) and BUN (24.96 mg/L), though slightly elevated, are the lowest. In the rest of the states, damage tokidneys is observed, with state A4 being the worst. The average levels of serum creatinine in states A1, A2, A4, A5, and A6 are1.489 mg/L, 1.450 mg/L, 2.05 mg/L, 2.0 mg/L, and 2.0 mg/L, respectively; and the BUN levels in states A1, A2, A4, A5, andA6 are 29.31 mg/L, 26.68 mg/L, 33.63 mg/L, 26.26 mg/L, and 29.35 mg/L, respectively.
Activated Partial Thromboplastin Time (aPTT), Prothrombin Time (PT), and International Normalized Ratio (INR) are identifiedby our feature selection methods. These are measures of coagulation function. Sepsis-associated coagulopathy (SAC) istypically diagnosed by PT prolongation or elevated INR, in conjunction with reduced platelet count . aPTT is also used as atest for coagulation in patients with sepsis . Increased aPTT and PT above normal values, and decreased platelet count elow normal value indicate long clotting time (DIC) and bleeding in sepsis patients .We find that in non-MODS states, aPTT is within the normal range, and that INR and PT are slightly elevated. The averageaPTT values in states A1, A2, and A3 are 37.78 s, 37.52 s, and 37.84 s, respectively; the average INR values in states A1, A2,and A3 are 1.51, 1.46, and 1.48, respectively; and the average PT values in states A1, A2, and A3 are 16.16 s, 15.91 s, and15.88s, respectively. In contrast to non-MODS states, an increase in values of INR, PT, and aPTT is observed in MODS states.The average aPTT values in states A4, A5, and A6 are 44.14 s, 41.61 s, and 43.14 s, respectively; the average INR values instates A4, A5, and A6 are 2.08, 2.49, and 2.96, respectively; and the PT values in states A4, A5, and A6 are 20.68 s, 21.92 s,and 25.93 s, respectively. We also examine the platelet count in these states. Although the average platelet count in all sepsisstates is within the normal range, a higher percentage of the cases with a platelet count below the normal range (150 × /L)are observed in MODS states. The percentage of cases with platelet count lower than normal from states A1 to A6 are 30%,0%, 27.7%, 44.9%, 40.3%, and 44.9%, respectively.In summary, nearly one-third of the cases in states A1 and A3 develop a mild condition of SAC or DIC, while more than40% of cases in the MODS group have worse SAC or DIC. Partial pressure of oxygen (PaO2), fraction of inspired oxygen (FiO2), ratio of the arterial partial pressure of oxygen to fractionof inspired oxygen (PaO2/FiO2), and the indication of the patient being assisted by mechanical ventilator, are identified byour feature selection methods. These are commonly used to measure respiratory function. Partial pressure of oxygen (PaO2)measures the pressure of oxygen dissolved in blood, and how well oxygen can move from the airspace of the lungs intothe blood. The fraction of inspired oxygen (FiO2) is defined as the concentration of oxygen that a person inhales. Patientsexperiencing difficulty in breathing are provided with oxygen-enriched air . Therefore, higher FiO2 is observed if therespiratory function is compromised. The ratio of arterial partial pressure of oxygen to fraction of inspired oxygen (PaO2/FiO2)is a known measure for the assessment of respiratory dysfunction , such as Acute Respiratory Distress Syndrome (ARDS) .Under the Berlin ARDS definition , patients with PaO2/FiO2 levels in the range of 200–300, 100–200, and less than 100 areclassified as mild, moderate, and severe ARDS. The SOFA metric also incorporates PaO2/FiO2 as a parameter in assessingrespiratory function . According to the SOFA score, a normal person has a PaO2/FiO2 ratio of approximately 500 and a patientwith PaO2/FiO2 ratio between 300 – 400, 200 – 300, 100 – 200, and less than 100 would have SOFA scores 1, 2, 3, and 4,respectively. Thus, a lower PaO2/FiO2 ratio indicates worse respiratory condition. Conversely, high PaO2/FiO2 ratio (PaO2 >300 mmHg) indicates that the lung is exposed to hyperoxia . Mechanical ventilators are often used in ICUs to assist orreplace spontaneous breathing, indicating compromised respiratory function.We find that patients in state A3 display excessive amounts of PaO2 and a slight increase in FiO2 (0.07 higher than thenormal value of 0.21, on average). This indicates that patients in state A3 are less prone to lung dysfunction, but that state A3manifests hyperoxia. The lower fraction of patients on ventilators in state A3 also indicates better lung function, compared toother states. The fraction of patients on a ventilator in state A3 is the lowest, at 0.09. The FiO2/PaO2 parameter also indicates hat state A3 does not develop ARDS. Distinct from state A3, respiratory functions are compromised to varying extents in otherstates. We find that both PaO2 and FiO2 in states A1, A2, A4, A5, and A6 are slightly elevated. The average values of PaO2 instates A1, A2, A4, A5, and A6 are 20.83 mmHg, 21.77 mmHg, 26.95 mmHg, 20.98 mmHg, and 17.92 mmHg, respectively,and the average values of FiO2 in states A1, A2, A4, A5, and A6 are 0.46, 0.47, 0.52, 0.48, and 0.47, respectively. A higher rateof patients on ventilators is observed in states A1, A2, A4, A5, and A6, with the mean value of 0.37, 0.33 0.56, 0.50, and 0.41,respectively. We observe that states A1, A2, A4, A5, and A6 correspond to mild ARDS. The average values of FiO2/PaO2 instates A1, A2, A4, A5, and A6 are, respectively, 292.98 mmHg, 294.59 mmHg, 285.03 mmHg, 318.13 mmHg, and 301.8 5mmHg, which is close to the boundary of normal value of 300mmHg in the Berlin ARDS definition and close to SOFA score of2. We highlight that among these states, state A4, one of the MODS states that displays the highest SOFA score and mortalityrate, shows the highest FiO2, the lowest PaO2/FiO2, and the highest rate of ventilator use.In summary, states A1, A2, A4, A5, and A6 manifest mild respiratory dysfunction with state A4 being the worst. State A3shows better respiratory function, as the average value of FiO2, and rate of ventilator use is the lowest. According to both theBerlin ARDS definition and SOFA score, state A3 type does not manifest ARDS. However, state A3 manifests hyperoxia, sincethe average value of PaO2 in state A3 is higher than 300 mmHg. DiaBP, identified by our feature selection method, is a measure of potential hypotension and vasopressor use, and can beused to identify potential septic shock . Hypotension is generally defined as a systolic blood pressure of less than 90 mmHgor diastolic of less than 60 mm Hg. Severe hypotension can deprive the brain and other vital organs of oxygen and nutrients,leading to a life-threatening condition called shock. Patients with septic shock can be identified with a clinical construct ofsepsis with persisting hypotension requiring vasopressors to maintain mean arterial pressure (MAP) of 65 mmHg, and having aserum lactate level higher than two mmol/L despite adequate volume resuscitation .We observe that all sepsis states except A5 show lower blood pressure. The average DiaBP of state A5 is 60.46, and theaverage values of DiaBP in states A1, A2, A3, A4, and A6 are 57.07, 59.55, 58.31, 58.07, and 57.00, respectively. We alsofind that the dosage of vasopressin in MODS states is significantly higher than non-MODS states. The average dosage ofvasopressin in states A1, A2, and A3 are 0.06 mcg/kg/min, 0.08 mcg/kg/min, and 0.01 mcg/kg/min, respectively. In contrast,the average dosage of vasopressin in states A4, A5, and A6 are 0.26 mcg/kg/min, 0.13 mcg/kg/min, and 0.13 mcg/kg/min,respectively.In summary, non-MODS states show mild hypotension, while MODS states are potentially in septic shock, with state A4being the worst. It has been shown that the development of septic shock is an accurate predictor of mortality . Our resultsare consistent with these studies, since the severity of the septic shock in states A4, A5, and A6 is consistent with the mortalityrate – the severity level of the septic shock in states A4, A5, and A6 ranked the highest, second, and third, respectively, which isthe same order as the mortality rate. orrelation of demographic variables and comorbidities with sepsis states. (a) (b)(c) (d) A1 A2 A3 A4 A5 A6
Archetype congestive heart failurecardiac arrhythmiasvalvular diseasepulmonary circulationperipheral vascularhypertensionparalysisother neurologicalchronic pulmonarydiabetes uncomplicateddiabetes complicatedhypothyroidismrenal failureliver diseasepeptic ulceraidslymphomametastatic cancersolid tumorrheumatoid arthritiscoagulopathyobesityweight lossfluid electrolyteblood loss anemiadeficiency anemiasalcohol abusedrug abusepsychosesdepression P r e m o r b i d S t a t u s Z-score -0.3-0.2-0.100.10.20.30.40.50.60.7
Figure 5: (a)
The population distribution for each sepsis type stratified by age. (b)
The population distribution for each sepsistype stratified by weight. (c)
The population distribution for each sepsis type stratified by the number of comorbidities beforeinfection. (d)
Z-score analysis of the comorbidity profiles (row) of each sepsis type (column). Entries approaching red inintensity indicate that the comorbidity profiles are expressed in the corresponding sepsis states, and entries closer to blueindicate that the comorbidity profiles are suppressed in corresponding sepsis states.
Correlation of demographic variables and comorbidities with sepsis states.
Variations in patients’ demographics, such as gender, age, and medical comorbidities, present additional considerations forclassifying sepsis states . Our feature selection methods identify age, weight, and comorbidities, indicating that these attributesare strongly correlated with sepsis states. The distributions of sepsis states in terms of patient age are shown in Figure 5a. We observe that while the average ages ofpatient in states A1, A3, and A4 are close to the average age of the entire cohort, the average age patients in states A2, A5,and A6 are significantly lower than the average age of the entire cohort – the average age of the entire cohort is 64.57 years,and the average ages of states A1 to A6 are 64.66 years, 56.57 years, 64.85 years, 62.77 years, 51.57 years, and 54.28 years,respectively. Several studies have been shown that advanced age has been associated with worse outcomes . We also find
Figure 5: (a)
The population distribution for each sepsis type stratified by age. (b)
The population distribution for each sepsistype stratified by weight. (c)
The population distribution for each sepsis type stratified by the number of comorbidities beforeinfection. (d)
Z-score analysis of the comorbidity profiles (row) of each sepsis type (column). Entries approaching red inintensity indicate that the comorbidity profiles are expressed in the corresponding sepsis states, and entries closer to blueindicate that the comorbidity profiles are suppressed in corresponding sepsis states.Variations in patients’ demographics, such as gender, age, and medical comorbidities, present additional considerationsfor classifying sepsis states . Our feature selection methods identify age, weight, and comorbidities, indicating that theseattributes are strongly correlated with sepsis states. The distributions of sepsis states in terms of patient age are shown in Figure 5a. We observe that while the average ages ofpatient in states A1, A3, and A4 are close to the average age of the entire cohort, the average age patients in states A2, A5,and A6 are significantly lower than the average age of the entire cohort – the average age of the entire cohort is 64.57 years,and the average ages of states A1 to A6 are 64.66 years, 56.57 years, 64.85 years, 62.77 years, 51.57 years, and 54.28 years, espectively. Several studies have been shown that advanced age has been associated with worse outcomes . We also findthat worse outcomes are observed in older people for severe sepsis types. Specifically, in MODS states, we observe that stateA4, shown to be associated with the highest mortality, also has the highest average age. On the other hand, we observe that thesepsis state that demonstrates notable expression of inflammatory response, i.e.,
A2, is associated with lower average age.The distributions of sepsis states in terms of patient weight are shown in Figure 5b.We observe that the average weight ofthe entire cohort and the average weight of all sepsis states except A5 are within 4 percent. The average weight of patientsin state A5 is 7 percent higher than the average weight of the entire cohort. The average weight of the entire cohort is 83.27kilograms and the average weight of patients in states A1 to A6 is 83.29 kilograms, 84.95 kilograms, 79.28 kilograms, 85.18kilograms, 89.30 kilograms, and 82.31 kilograms, respectively.
We investigate the association of different comorbidity profiles with sepsis states. First, we construct distributions of sepsisstates by the total number of pre-existing comorbidities, shown in Figure 5c. We observe that, compared to non-MODS states,the MODS group has a higher number of comorbidities – the average comorbidity count for states A1 to A6 is 4.02, 3.08, 3.65,4.62, 4.29, and 4.28, respectively. The higher the number of comorbidities, the worse the outcomes of sepsis.Our results show clear association between comorbidities and patient outcomes. We next analyze the relationship betweenspecific comorbidity profiles and their association (positive or negative) with sepsis states. We use z-score as a measure ofdistance between observed condition (comorbidity) and its average over the entire cohort. If the z-score of a condition ispositive in a state, we note that the condition is expressed in the state; conversely, if the z-score is negative, the condition issuppressed in the state. To ensure that a diverse range of conditions is covered, a comprehensive set of comorbidity measures,30 types in all, are included in the z-score analysis (please see Table 5 in the appendix for more detail for each type).
Z-score analysis on non-MODS states.
As shown in Figure 5d, we find that none of the conditions are significantlydifferentially expressed from the overall cohort in state A1. This is explained by the fact that state A1 represents a mild sepsisstate. A slightly increased differential expression of comorbidities is observed in state A3. In state A2, the z-score of weightloss and alcohol abuse are significantly higher than other conditions, with values of 0.12 and 2.0, respectively. Other conditionsin this state with positive z-scores are paralysis and other neurological conditions, with values of 0.09 and 0.07, respectively. Itis known that alcohol abuse promotes intestinal inflammation and impairs the body’s ability to regulate inflammation .Therefore, positive association between alcohol abuse and sepsis state A2 is expected.
Z-score analysis on MODS states.
We observe strong association between MODS states and liver disease, as well ascoagulopathy. Damaged liver impairs the coagulation system . Therefore, we observe higher values of z-scores of liverdisease and coagulopathy in MODS states. The z-scores of liver disease in states A4, A5, and A6 are 0.79, 0.80, and 0.69,respectively, and the z-scores of coagulopathy in states A4, A5, and A6 are 0.28, 0.23, and 0.35, respectively. Individuals withpoor kidney health manifest fluid and electrolyte imbalances. We observe positive z-scores of fluid and electrolyte imbalances n MODS states to varying extents. The z-score of fluid and electrolyte imbalances in states A4, A5, and A6 are 0.23, 0.17, and0.06, respectively. Note that state A4 has the highest z-score for fluid and electrolyte imbalances among MODS states. In stateA4, a solid tumor is also observed as a significant comorbidity, with z-score of 0.15.In the MODS states, there are other comorbidities that are associated with specific states. In state A5, the z-score associatedwith depression is the second highest (0.45). Other conditions associated with depression including neurological disorders,peptic ulcers, alcohol abuse, drug abuse, and obesity , are associated with state A5. The z-scores of neurological disorders,peptic ulcer, alcohol abuse, and obesity in state A5 are 0.16, 0.25, 0.23, and 0.15, respectively. Depression is also associatedwith state A6. However, the associated disorders are different from those with state A5. Patients in state A6 exhibit associationwith drug abuse and rheumatoid arthritis. The z-scores of depression, drug abuse, neurological disorders, and rheumatoidarthritis in state A6 type are 0.28, 0.23, 0.29, and 0.13, respectively. Finally, valvular disease, pulmonary circulation, andneurological disorders are expressed in state A6 and hypothesized to cause ischemic injury . Ischemia is a restriction inblood supply to tissues, causing hypoxia. The existence of valvular disease and pulmonary circulation problems compromiseblood flow and carrying deoxygenated blood away from tissues, exacerbating pre-existing neurological disorders. The z-scoresof valvular disease and pulmonary circulation in state A5 are 0.12 and 0.17, respectively.
We present a computational framework to identify disease states in sepsis from 16,546 distinct patients admitted to Beth IsraelDeaconess Medical Center between 2001 and 2012, collected from the MIMIC-III database . We identified six sepsis states(moderate, inflammatory, mild, and MODS 1, 2, 3) based on the measurement of 42 variables (demographic profiles, vital signs,laboratory tests, mechanical ventilation status of the patients, and information on pre-existing clinical conditions) from thesesepsis patients.Our framework identified the most discriminating attributes for each sepsis state and showed that each state manifests aunique set of pathological responses, which correspond to different extents of organ dysfunction. These observations have twosignificant implications: (i) in contrast to the SOFA metric, our method identifies a larger number of attributes to provide acomprehensive view of sepsis symptoms, allowing for a more detailed diagnostic criterion; and (ii) it is possible to focus on asmaller set of attributes to differentiate sepsis symptoms, potentially reducing the associated diagnostic time and associatedcost. Our identification of three distinct MODS states associated with a higher mortality rate, provides insight into advancedmanagement of sepsis in ICU environments.We also analyzed the association of different demographics and comorbidity profiles with identified sepsis states. Ourresults revealed that these sepsis states are composed of distinct populations with different demographics and comorbidityprofiles, some of which have been supported in prior results. We find that a higher percentage of patients in MODS states haddeveloped liver disease before the onset of sepsis, validating that patients with liver disease are more prone to developing severesepsis . Patients with solid tumors may suffer from chronic advanced neoplasm and receive cancer chemotherapy, which eakens their immune system and disposes them to infective organisms, including multidrug-resistant organisms , leading tohigher mortality if sepsis develops . We find that solid tumors uniquely present in state A4 (highest mortality rate). Patientswith drug and alcohol abuse are found in state A5 (which manifests damage to the nervous system). A possible reason is thatpatients with drug abuse are more likely to lack self-consciousness, suffer from malnutrition, and cause self-induced injury,making them susceptible to injury and sepsis . Furthermore, patients with alcohol abuse are more likely to develop livercirrhosis, leading to the development of sepsis with severe outcomes . Patients with peptic ulcers can develop perforationand peritonitis, which can lead to sepsis with severe outcomes. These patients are also over-represented in state A5 . Patientswith Rheumatoid Arthritis are more likely to develop severe sepsis due to the use of cytokine antagonists, such as DMARD(Disease Modifying Anti-Rheumatoid Drug) and NSAIDs (Non-Steroidal Anti-Inflammatory Drug). This masks symptoms ofsevere infection, leading to the delay of diagnosis of sepsis . We find that patients in state A6, in which liver and coagulationsystems are primarily affected, had rheumatoid arthritis as a pre-existing condition. Valvular heart disease patients developseptic shock due to bacterial endocarditis, and mortality in infective endocarditis remains high . These patients are alsoover-represented in state A6 (third in mortality rate).There are other results from our analyses that are new and merit further investigation. Patients with paralysis, weight loss,or other neurological conditions are over-represented in state A2, and patients with AIDS are over-represented in state A3. Wenote that our results imply correlations, not causation. For instance, a damaged liver impairs the coagulation system. Therefore,patients with coagulopathy are found in states A4, A5, and A6. However, the development of coagulopathy might not be theindependent cause of severe sepsis or septic shock.Although we used the most distinguishing attributes to analyze organ function, other attributes, including Arterial bloodgas (ABG), electrolytes, albumin, shock index, and hemoglobin, are also crucial in analyzing various aspects of the healthstatus of sepsis patients. We also investigated these variables and found that these variables provide significant insight intopatients’ health status in different sepsis states; many of which are consistent with current literature. However, there are a fewcases that are at odds with the current literature. We highlight a few cases here, and refer readers to the detailed descriptionin the supplementary results section: Analyses of other variables 5.1. Metabolic acidosis often occurs in sepsis patients withorgan failure , and metabolic alkalosis has been noticed in sepsis patients . We also find that a higher percentage ofmetabolic acidosis occurs in MODS types. However, we observe fewer cases of metabolic alkalosis in our cohort. We alsofind that Arterial BE is a significant predictor of metabolic acidosis for sepsis patients. Hypocalcemia , measured by theconcentration of ionized calcium or serum calcium in the body, might be observed in critically ill patients, especially in thosewith sepsis , and is reported to be associated with increased severity of illness and increased mortality . We findthat low ionized calcium concentrations coincide with worse outcomes, while low serum calcium concentrations do not.We note that magnesium sulfate is often administered to patients with severe sepsis and has observed beneficial effects ,and that albumin, in addition to crystalloids, is often used for initial resuscitation and subsequent intravascular volumereplacement in patients with sepsis and septic shock . However, the administration of magnesium sulfate is not discussed nd implemented in current sepsis guidelines , and the benefits of albumin for resuscitation for patients with sepsis remainscontroversial . Based on our identified sepsis states, future development of clinical trials may focus on analyzing therole of magnesium and albumin administration in different sepsis states.Finally, by comparing the SIRS scores, SOFA scores, and mortality rates across the states, we confirm that the SIRS metriconly identifies a subset of sepsis states . Furthermore, our results show that the SOFA metric covers a broader spectrum ofdisease states and is a more accurate predictor of mortality for sepsis patients .Overall, our framework provides new insight into understanding the complex states of sepsis. By analyzing the relationshipbetween the pre-existing comorbidities and sepsis states, one can anticipate the severity of outcomes and devise suitabletherapeutic strategies for individual patients. Future research could focus on designing clinical trials to further analyse the statesbased on the pathophysiology and disease progression to establish more specific treatment guidelines for different sepsis states. Patient cohort and data preprocessing.
We use the Medical Information Mart for Intensive Care version III (MIMIC-III) database to collect samples from five distinctICUs located in Boston, Massachusetts. The sample criteria for cohort selection are: (i) patients over 18 years of age at time ofICU admission who did not withdraw from treatment, and whose mortality status was recorded; and (ii) patients who satisfiedsepsis-3 criteria , i.e., SOFA score ≥
2. The resulting cohort includes 16,546 distinct patients with 20,944 admissions in ICUs.Outliers and errors were checked and the corrected and the k-nearest neighbor algorithm was used as an imputation method tofill missing values . Clinical variables associated with the patients are demographic, vital signs, lab values, severity measuressuch as SIRS and SOFA scores, and other information relating to the use of a ventilator and number of comorbidities beforesepsis infection. We also track whether the patient survived for 48 hours, and extract history of 30 types of comorbidities before infection, as supplementary variables.
Archetypal analysis.
Archetypal analysis views each point in a dataset as a mixture (convex combination) of “pure types”, or “archetypes”. Theconvexity constraint here implies that in contrast to traditional clustering techniques that aim to identify “typical” representatives,archetypal analysis aims to identify “extremal” points in the dataset. The archetypes are themselves mixtures (convexcombinations) of the points in the data set. Archetypes can be learned by minimizing the squared error in representing eachpoint as a mixture of archetypes. Specifically, let x , . . . , x n be the data points in R m . The problem is to find a set of archetypes { z , . . . , z K } so that each archetype z k is a convex combination of the data points, i.e., ∑ nj = β k j x j , with the constraints of: (i) β k j ≥ ∀ j ; and (ii) ∑ nj = β k j = x i can be best approximated by a convexcombination of the archetypes, i.e. , ∑ Kk = α ik z k , with the constraints: (i) α ik ≥ ∀ i ; and (ii) ∑ pk = α ik = e can then define the following optimization problem:min { α ik , β kj } n ∑ i = (cid:13)(cid:13)(cid:13)(cid:13)(cid:13) x i − p ∑ k = α ik n ∑ j = β k j x j (cid:13)(cid:13)(cid:13)(cid:13)(cid:13) , (1)and the archetype problem is to find α ’s and β ’s to minimize the objective 1 subject to the aforementioned constraints. Thisproblem can be solved using general-purpose constrained nonlinear least squares methods , the alternating minimizingalgorithm , or the projected gradient procedure . The learned archetypes (for K >1) form a convex hull of the data set suchthat all of the points can be well-represented as a convex mixture of the archetypes. In our study, we treat patient measurementsas the point set and find the archetypes for our cohort. These archetypes represent the extreme states in sepsis, derived from ourcohort, and each patient can be viewed as a convex combination of the extreme sepsis states. Comparing mean vectors from two populations . We use Two-sample Hotelling’s T tests to characterize significant differences between the mean vectors of two multivariatedistributions (in reality, datasets drawn from these distributions). Two-sample Hotelling’s T tests are sensitive to violations ofthe assumption of equal variances and covariances . Different approximation of the sample variance is needed when thecovariance matrices of the two populations are significantly different. We use Box’s M test for significant differences betweencovariance matrices. Testing homogeneity of covariance matrices : Box’s M Test . Consider a sample set { x , . . . , x n } in R m sampled from population Θ and a sample set { x , . . . , x n } in R m sampled frompopulation Θ . Assuming that the sample sizes n and n are sufficiently large, Box’s M Test tests the null hypothesis thatthe population covariance matrices are equal, i.e. , H : Σ = Σ . Let S and S be the sample covariance matrices from thepopulations Θ and Θ , where each S j is based on n j independent observations, we define the pool variance S pooled as follows: S pooled = n + n − ( n − ) S + ( n − ) S , and the value of M is given by: M = ( n + n − ) ln | S pooled | − (( n − ) ln | S | + ( n − ) ln | S | ) . Then, M ( − c ) has an approximate χ d f -distribution, where: c = m + m − ( m + )( n + n − ) (cid:18) n − + n − − n + n − (cid:19) , d f = m ( m + )( n + n − ) . he null hypothesis H is rejected when M ( − c ) > χ d f ( α ) (or p-value < α ) . Testing homogeneity of mean vectors : Hotelling’s T-Squared test.
We test the equality of vector means from populations Θ and Θ . The null hypothesis is that the population means are equal, i.e., H : µ = µ . If Box’s M test indicates that the two covariance matrices are not significantly different, we can assume Σ = Σ and: T = ( ¯ x − ¯ x ) (cid:124) (cid:18) ( n + n ) S pooled (cid:19) − ( ¯ x − ¯ x ) . If Box’s M test concludes that Σ (cid:54) = Σ , T = ( ¯ x − ¯ x ) (cid:124) (cid:18) n S + n S (cid:19) − ( ¯ x − ¯ x ) In either case, T approximates chi-square distribution with m degrees of freedom, i.e., χ m . The null hypothesis is rejectedwhen T > χ m ( α ) (or p-value < α ) . Low-dimensional embeddings of dataset.
We use Uniform Manifold Approximation and Projection (UMAP) to compute a mapping from a dataset X = { x , . . . , x n } in R m to its corresponding lower-dimensional representation Y = { y , . . . , y n } in R d that preserves as much of the local and theglobal structure from the original space. UMAP assumes that the dataset X is uniformly drawn from a Riemannian manifold M .With this assumption, the goal is to reconstruct M and to find a mapping from M into R d . To do so, UMAP first approximatesthe manifold and finds a fuzzy simplicial set that captures all topological properties of the manifold M . Similarly, given acurrent lower-dimensional representation in Y (cid:48) of the data X in R m , it can also construct a fuzzy simplicial set from Y (cid:48) . Havingthe two fuzzy simplicial sets, one constructed from X and the other constructed from Y (cid:48) , UMAP then measures how good Y (cid:48) isas a representation of X using cross-entropy C of two fuzzy sets: C (( A , µ ) , ( A , υ )) = ∑ a ∈ A (cid:18) µ ( a ) log (cid:18) µ ( a ) υ ( a ) (cid:19) + ( − µ ( a )) log (cid:18) − µ ( a ) − υ ( a ) (cid:19)(cid:19) The above objective function can be minimized using first-order optimization methods or second-order meth-ods . Feature selection methods.
Quality-index based approach.
Given a set S = { x , . . . , x N } of N points in R m that is partitioned as P K = { C , . . . , C K } , where for each cluster pair C i , C j , ≤ i , j , ≤ K and i (cid:54) = j , C i (cid:84) C j = Φ , define g k to be the mean values of the instances in cluster C k , g be the average values ver all the instances in S , the total inertia T = ∑ Ni = d ( x i , g ) measures the dispersion of the points in the set S , where d ( x i , x i (cid:48) ) = ∑ mj = ( x i j − x i (cid:48) j ) is the squared Euclidean distance. According to Huygens-Steiner Theorem, the total inertia T can be decomposed into inter-cluster inertia B and within-cluster inertia W : T = B + W = K ∑ k = d ( g k , g ) + K ∑ k = I ( C k )= K ∑ k = d ( g k , g ) + K ∑ k = ∑ i ∈ C k d ( x i , g ) Here, inter-cluster inertia B measures the separation between the clusters, I ( C k ) is the inertia for cluster C k , and the within-clusterinertia W is the summation of the inertia of the clusters that measures the heterogeneity within the clusters. Variable quality.
The quality index is given by the ratio of the homogeneity value of each cluster and the correspondinghomogeneity value associated with the partition P = S . This can be interpreted as the gap between the null hypothesis, i.e., partition into one cluster, and partition into k clusters. We can use the quality index at each variable (in our case, patient feature) j to find the importance of the features. Given a set of points S partitioned by P K , the null hypothesis is that the total inertia ofthe system is T j . Since the partition P K is given, the total inertia of the system is fixed at T j and the optimal strategy of assigningclusters is to select minimal within-cluster inertia, W j . This leads to the following ratio as a measure of variable quality: Q j ( P k ) = B j T j = − W j T j , W j = ∑ i ∈ C k ( x i j − g k j ) , T j = N ∑ i = ( x i j − g j ) . Alternatively, since the partition P K is given, we can ignore the variability of within-cluster inertia in the variable qualitymeasure. That is, we only consider how each variable contributes to the total inter-cluster inertia: Q (cid:48) j ( P k ) = B j ∑ pi = B i . In our study, we use both Q j ( P K ) and Q (cid:48) j ( P K ) variable quality measures for feature selection. We also include a third featureselection criteria based on a variation test. Variation test.
Given a partition P K = { C , . . . , C K } of a set of points S , we can regard the points in cluster C i as being sampled from a distinctmultivariate probability distribution Θ i . To find the j -th feature that can distinguish the clusters, there exist at least two pairsof marginal distributions such that the difference of the mean value at the j -th feature sampled from the compared marginal istributions is larger than some threshold θ with probability 1 − δ , where δ is sufficiently small. We set θ = σ i j whencomparing clusters C i and C l ( l (cid:54) = i ) and collect the union of the variables from each case as the selected features. Althoughthis feature selection method treats each dimension independently, we find that the selected features are similar to those usingquality-index based approaches. See section supplementary 5.3 for a detailed comparison. Co-occurrence analysis . Let A be a random variable that maps sepsis states a , . . . , a K to binary values that indicate the presence of an event in interest.Let S be the sample set S = { ( a i , y lj ) , . . . , ( a iN , y ljN ) } of size N sampled from the joint probability distribution Pr ( A , Y ) . We cancharacterize the information in S by its sufficient statistics n i j = | ( a i , y lj ) ∈ S | , which measures the frequency of co-occurrence of a i and y j . We partition S into subsets S i based on the output of the random variable A . The sample set S i represents an empiricaldistribution n j | i over Y l , where n j | i = n i j / n i and n i is defined as the cardinality of S i . Here, n j | i measures the frequency of anoutcome of interest, conditioned on the presence of the sepsis state i . Z-score analysis.
The event of interest may be universally present in all sepsis states. In this case, n j | i ≈ n j | i (cid:48) for all ( i , i (cid:48) ) pairs. Specifically, n j | i is agnostic of the presence of the sepsis state i and n j | i is approximately equal to n j / | S | computed over the entire population.We aim to assess whether the event of interest is uniquely expressed or suppressed in a certain sepsis state. We compute thecorresponding Z-score : z i j = w i j − µσ , where µ = n j / | S | is the mean value over the entire population, σ is its corresponding standard deviation, and w i j is the referencepoint, i.e., n j | i . Here, z i j measures how far the the reference point w i j is from population mean for the sepsis state i . If z i j ispositive, w i j is expressed in sepsis state i , and vice versa. Acknowledgements
The authors thank Dr. Poching DeLaurentis and Dr. Ping Huang for initial discussions.
Data Availability
The MIMIC-III database is freely available. Our source code for data extraction builds on the AI clinician and will be madeavailable in the public domain along with implementations of all other methods.
Author contributions statement
Conceptualization, C.H.F., V.R.; Formal Analysis: C.H.F., V.R. S.A., A.G.; Investigation, C.H.F., V.R. S.A., M.A., A.G.; DataCuration, C.H.F.; Writing – Original Draft, C.H.F., A.G.; Writing – Review & Editing, C.H.F., V.R., S.A., M.A., P.G., S.S., and .G., Visualization, C.H.F.; All authors have read and approve the manuscript.
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Supplementary Material
Arterial blood gas (ABG).
ABG is a blood test that assesses the gas exchange and acid-base balance of the body. It is anessential marker for critical patients admitted to ICUs. Arterial PH, PaO2, PaCO2, HCO3, and Arterial base excess are the maincomponents of ABG. The presence of acidosis (arterial PH less than 7.35) or alkalosis (arterial PH higher than 7.45) is assessedby measuring arterial PH in the blood . Combined with arterial pH and PaCO2, one can measure the existence of respiratoryacidosis or respiratory alkalosis in the body. Respiratory acidosis occurs when PaCO2 is higher than 45 mmHg, with an arterialPH less than 7.35. Respiratory alkalosis occurs when PaCO2 is less than 35 mmHg, with an arterial PH higher than 7.45.Combined with arterial PH and HCO3, one can measure the existence of metabolic acidosis or metabolic alkalosis. Metabolicacidosis occurs when HCO3 is less than 22 mEq/L, with an arterial PH less than 7.35. Metabolic alkalosis occurs when HCO3is higher than 28 mmHg, with an arterial PH higher than 7.45. Among four types of acid-base disorders (respiratory acidosis,respiratory alkalosis, metabolic acidosis, and metabolic alkalosis ), metabolic acidosis is common in sepsis patients with organfailure . Metabolic alkalosis has been noted in sepsis patients . In our cohort, we find that the average values of arterialPH and HCO3 in MODS states are lower than non-MODS states, indicating that a higher portion of patients with metabolicacidosis is observed in MODS states. The average values of arterial PH for states A1 through A6 are 7.39, 7.40, 7.39, 7.35, 7.37,and 7.36, respectively. The average values of HCO3 for states A1 through A6 are 24.68, 25.06, 24.47, 22.79, 23.08, and 21.93,respectively. The percentage of patients with metabolic acidosis in states A1 through A6 are 8.7%, 6.6%, 6.7%, 22.8%, 16.4%,and 20.5%, respectively. On the other hand, we observe fewer cases of metabolic alkalosis in our cohort. The percentage ofpatients with metabolic alkalosis in states A1 through A6 are 4.5%, 6.2%, 3.9%, 4.7%, 2.6%, and 1.1%, respectively. Arterial base excess (Arterial BE).
Arterial BE reflects the metabolic component of the acid-base balance. Arterial BEmeasures the amount of H+ required to return the blood PH to normal when PaCO2 is within the normal range, with thenormal range from -2 to +2. The base excess increases in metabolic alkalosis and decreases (or becomes negative) in metabolicacidosis. Metabolic acidosis is common in sepsis patients with organ failure , and metabolic alkalosis can also occur insepsis patients . In our study, we find that the average value of arterial BE in MODS states is negative, indicating an inclinationtowards metabolic acidosis in MODS states. The average values of arterial BE for states A1 through A6 are 0.35, 0.80, 0.37,-1.9, -1.94, and -2.5, respectively, and the percentage of patients with metabolic acidosis in states A1 through A6 are 8.7%,6.6%, 6.7%, 22.8%, 16.4%, and 20.5%, respectively. Therefore, arterial BE is an important predictor of metabolic acidosis forsepsis patients. Albumin.
Albumin is one of the essential proteins, with a normal range of 3.4 to 5.4 g/dl. Albumin is responsible for plasmacolloid osmotic pressure, acting as a major binding protein for endogenous and exogenous compounds (drugs), with antioxidantand anti-inflammatory properties, and operates as a buffer to balance acid-base status of the body . A lower albumin level(Hypoalbuminemia) is often observed when: (i) patients have nutritional deficiencies ; (ii) patients develop chronic liver isease, advanced hepatic cirrhosis, or end-stage renal disease ; or (iii) an inflammation is present . Albumin, in additionto crystalloids, is often used for initial resuscitation and subsequent intravascular volume replacement in patients with sepsisand septic shock . Although albumin administration is widely used in the management of sepsis, the benefit of the use ofalbumin for resuscitation in this population remains controversial – while several meta-analyses have shown that theadministration of albumin in ICU patients has beneficial effects on health outcomes , other studies have showncontradictory results . However, the results are less conclusive when the included studies have differing experimentaldesign and comparison groups. As a result, albumin administration is suggested with weak confidence . In our study, wefind hypoalbuminemia in all sepsis states, and the albumin level in various sepsis states is not significantly different. Futuredevelopment of clinical trials may focus on comparing the effects of albumin administration on the health outcomes for differentsepsis states. Hemoglobin (Hb).
The normal range of hemoglobin for males and females is 13.5 to 17.5 grams per deciliter and 12.0 to 15.5grams per deciliter, respectively. A lower hemoglobin level in the body indicates a low red blood cell (RBC) count (Anemia).Anemia is common in sepsis due to inflammation, liver and renal impairment, and cancer . RBC transfusion is stronglyrecommended for patients with sepsis when hemoglobin concentration falls to less than 7.0 g/dL in adults in the absence ofextenuating circumstances, such as myocardial ischemia, severe hypoxemia, or acute hemorrhage . We find that the averageHb values in all sepsis states are lower than the normal range, with A2 (Inflammation state) having the lowest Hb values. Theaverage Hb values for states A1 through A6 are 10.30, 9.49, 10.49, 10.42, 10.90, and 10.75, respectively. Shock index (SI).
Shock index (SI) is a bedside assessment defined as heart rate (HR) divided by systolic blood pressure(SysBP), with a normal range of 0.5 to 0.7 in healthy adults . SI is suggested as a measure in the triage and management ofcritically ill patients. Its use is also suggested as a predictor of clinical outcomes, such as the serum lactate level in the body,the risk of mortality, and other markers of morbidity . However, a retrospective database review shows that SIdoes not correlate with the mortality rate in emergency room patients . Our results support this claim. We find that SI is nothighly associated with worse outcomes. While the MODS states display higher SI than A1 and A3 states, A2 (Inflammationstate) displays the highest SI, which is the state associated with lower SOFA score and mortality rate. The average SI values forstates A1 through A6 are 0.75, 0.81, 0.72, 0.77, 0.79, and 0.77, respectively. Furthermore, SI is not an independent predictor ofhyperlactatemia (serum lactate ≥ Ionized calcium.
In health, serum ionized calcium concentration is maintained between approximately 1.16 and 1.32 mmol/L.Ionized hypocalcemia (ionized calcium levels < 1.16 mmol/L) are common in critically ill patients with sepsis, cardiac failure,pulmonary failure renal failure, post-surgery or burns . Recent studies show that low ionized calcium concentrationscoincide with increased severity of illness and increased mortality . We find that ionized hypocalcemia occurs in allsepsis states, and the average ionized calcium concentration in MODS states is lower than non-MODS states. The average onized calcium concentration for states A1 through A6 are 1.13, 1.13, 1.14, 1.08, 1.09, and 1.09, respectively.
Calcium.
The normal range of total serum calcium concentration is 8.8 mg/dL to 10.7 mg/dL. Hypocalcemia , definedas serum calcium concentration less than 8.8 mg/dL or serum ionized calcium concentration less than 4.7 mg/dL, is common incritically ill patients, especially in those with sepsis . We find that hypocalcemia occurs in all sepsis states. However, lowserum calcium concentrations do not coincide with the increased severity of illness and increased mortality. The serum calciumconcentrations for states A1 through A6 are 8.31, 8.39, 8.38, 8.50, 8.13, and 8.20, respectively.
Magnesium.
Magnesium is a vital element involved in various physiological processes and an essential cofactor inmore than 300 enzymes , with a normal range of 1.5 to 2.5 mEq/L in healthy adults. Hypomagnesemia (serum Mg levels < 1.5mEq/L) can occur in critically ill patients, including sepsis patients, and is associated with prolonged ICU stay, increased needfor mechanical ventilation, and increased mortality . In our study, we find that, in the average case, serum magnesiumlevels in all sepsis states are within the normal range. The average values of serum magnesium levels for states A1 throughA6 are 2.06, 2.07, 2.02, 2.10, 2.04, and 2.29, respectively. We note that recent studies have shown that the administrationof magnesium sulfate increases lactate clearance in critically ill patients with severe sepsis , improve cerebral perfusion inpatients with sepsis-associated encephalopathy (SAE) , and may be used to open up small vessels, to reduce organ failure forpatients with severe sepsis and septic shock . Future development of clinical trials may focus on comparing the effects of theadministration of magnesium sulfate on the health outcomes for different sepsis states. Chloride.
Chloride is an essential anion of the extracellular fluid, representing two-thirds of all negative charges in plasmaand accounting for nearly one-third of plasma tonicity . Normal Serum chloride concentrations range from 96 to 106. mEq/L.Abnormal chloride levels in the blood (hypo- and hyperchloremia) are observed in critically ill patients . However, evidenceon the effects of hypo- and hyperchloremia on the clinical outcomes, such as length of stay and mortality rate, are sparse .A recent study shows that hyperchloremia is not significantly related to an increased mortality rate, and hypochloremia isassociated with increased mortality in patients with severe sepsis or septic shock . Our results are consistent with thesefindings: we observe a higher percentage of hypochloremia in MODS groups, which are the groups associated with a highermortality rate. We also observe that hyperchloremia does not directly correlate with MODS groups. The percentage of patientswith hypochloremia for states A1 through A6 are 7%, 7%, 5%, 15%, 12%, and 10%, respectively, and the percentage of patientshyperchloremia for states A1 through A6 are 39%, 27%, 36%, 30%, 35%, and 35%, respectively. Future development ofclinical trials may focus on comparing the effects of chloride levels on clinical outcomes in different sepsis states. Sodium.
The normal sodium level in the blood is 135 to 145 mEq/L. Hypernatremia (serum sodium concentration > 145mEq/L ) is an uncommon but important electrolyte abnormality in ICU patients. Hypernatremia also occurs in sepsispatients, but only a few studies have investigated the effect of serum sodium levels on the clinical outcomes in sepsispatients. Studies have shown that patients admitted with hypernatremia are significantly more likely to have sepsis andthat hypernatremia is strongly associated with worse outcomes in sepsis . However, we notice that sepsis patients with ypernatremia only constitutes 7.3% in the cohort and that although we find that state A4 (the state with highest mortality rate)constitutes the highest portion of patients with hypernatremia, state A5 (the state with second-highest mortality rate) has alower portion of patients with hypernatremia than the cohort. The percentage of patients with hypernatremia for states A1through A6 are 7.3%, 8.1%, 4.1%, 10.8%, 4.5%, and 8.8%, respectively. Potassium.
Potassium is one of the electrolytes mostly present in intracellular fluid . The normal value of serum potassiumis 3.5 to 5.0 mEq/L. Potassium homeostasis is important for negative resting membrane potential, neuromuscular, and cardiacexcitability. Abnormal potassium has adverse effects on the heart: both hypo and hyperkalemia cause cardiac arrhythmia.Hypokalaemia also causes muscle paralysis, including respiratory muscles and GIT. Potassium abnormality can occur incritically ill patients in ICU due to organ derangement and some medications, and is associated with an increased complicationrate and mortality risk . Our study found that the average potassium levels do not vary across sepsis states and are withinthe normal range in our cohort. The average potassium concentration for states A1 through A6 are 4.08, 4.22, 4.14, 4.31, 4.06,and 4.34, respectively. Systemic Inflammatory Response Syndrome (SIRS).
Sepsis was first defined as a systemic inflammatory response syn-drome (SIRS) . SIRS is the clinical presentation of the host response to inflammation. It manifests in four symptoms,temperature ≥
38 degree Celsius or ≤
36 degree Celsius, respiratory rate ≥
20 breaths/minute or PaCO <
32 mm of Hg,heart rate >
90 beats/minute, white blood count > < or bands > . However, it was argued that SIRS is not an adequate measure, since a sepsis-relatedsymptom may be observed without infection. Due to its non-specific issue, the diagnostic metric of sepsis was first replaced bysepsis-2 , and finally changed to Sequential Organ Failure Assessment Score (SOFA). Sequential Organ Failure Assessment (SOFA) Score. SOFA measures the functionality of six organ systems – respiratory,coagulation, cardiovascular, neurological, liver, and renal, shown in Table 2, each of which is measured by PaO /FiO ratio,platelet count, mean arterial pressure (MAP), Glasgow coma score (GCS), bilirubin, and creatinine or urine output, respectively.Each system is assigned a score from 0 to 4. The worst condition represents the highest score. The range of the SOFA score is0-24. It has been shown that the SOFA score is a good predictor of mortality in intensive care units . We compare the top 15 features selected by (i) Q j ( P k ) method measuring the ratio of inter-cluster inertia at the i-th feature B i tothe total inertia at the i-th feature T i , (ii) Q (cid:48) j ( P k ) method measuring the ratio of the between-cluster inertia at i-th feature B i to the total between-cluster inertia ∑ pi = B i , (iii) and the feature that has a lower probability of overlapping between clusters.The selected features are shown in Table 3. We observe that the first five features selected by Q j ( P k ) and Q (cid:48) j ( P k ) are identical– SGOT, SGPT, PaO2/FiO2, PaO2, and Platelet Count, in the same order, except for PaO2 and Platelets. For the rest of thefeatures selected by Q j ( P k ) and Q (cid:48) j ( P k ) , PT, WBC Count, Arterial Lactate, Age, and HR were selected by both Q j ( P k ) and able 2: Sequential Organ Failure Assessment Score SOFA Respiratory Cardiovascular Nervous Hepatic Renal Coagulationscore PaO2/ FiO2ratio Mean ArterialPressure/vasopressors Glasgowcomascore Bilirubin,mg/dl Creatinine,mg/dl(or urineoutput) Platelets( × /mm ) ≥ ≥
70 mm/Hg 15 < < ≥ < <
70 mm/Hg 13 - 14 1.2 - 1.9 1.2 - 1.9 < <
300 dopamine ≤ < <
200 dopamine >
5, epinephrine ≤ ≤ <
500 ml/d) < <
100 dopamine >
15, epinephrine > > < > > < < Q j ( P k ) and Q (cid:48) j ( P k ) methods, and the features selected by variation test method. Method \Rank 1 2 3 4 5 Q j ( P k ) SGOT SGPT PaO2/FiO2 PaO2 Platelets Q (cid:48) j ( P k ) SGOT SGPT PaO2/FiO2 Platelets PaO2
Variation Test
SGOT SGPT PaO2/FiO2 Platelets PaO2
Method \Rank 6 7 8 9 10 Q j ( P k ) Arterial lactate FiO2 WBC Count INR Mechvent Q (cid:48) j ( P k ) Glucose Age PT HR PTT
Variation Test
Arterial lactate FiO2 PT INR Mechvent
Method \Rank 11 12 13 14 15 Q j ( P k ) PT GCS Age HR Comorbidity Count Q (cid:48) j ( P k ) WBC Count Weight BUN Arterial lactate DiaBP
Variation Test
WBC Count GCS Creatinine N/A N/A Q (cid:48) j ( P k ) . Among the 10 features mentioned above, 8 are selected by the variation test as well. We present a Venn diagram for theinclusion-exclusion comparison between Q j ( P k ) , Q (cid:48) j ( P k ) , and the variation test in Figure 3. We observe that the three methodsare largely consistent in selecting representative features from the clusters. .4 Additional Figures and Tables. (a) A1 G ende r A ge E li x hau s e r W e i gh t K g G C S HR S ys BP M ean BP D i a BP RR S p O T e m p C F i O P o t a ss i u m S od i u m C h l o r i de G l u c o s e B UNC r ea t i n i ne M agne s i u m C a l c i u m I on i s ed C a C O S GO T S G P TT o t a l B ili A l bu m i n H b W B CC oun t P l a t e l e t s C oun t P TT P T I NR A r t e r i a l P H P a O P a C O A r t e r i a l BEA r t e r i a l La c t a t e HC O M e c h v en t S ho ck I nde x P a O / F i O P e r c en t il e (b) A2 G ende r A ge E li x hau s e r W e i gh t K g G C S HR S ys BP M ean BP D i a BP RR S p O T e m p C F i O P o t a ss i u m S od i u m C h l o r i de G l u c o s e B UNC r ea t i n i ne M agne s i u m C a l c i u m I on i s ed C a C O S GO T S G P TT o t a l B ili A l bu m i n H b W B CC oun t P l a t e l e t s C oun t P TT P T I NR A r t e r i a l P H P a O P a C O A r t e r i a l BEA r t e r i a l La c t a t e HC O M e c h v en t S ho ck I nde x P a O / F i O P e r c en t il e (c) A3 G ende r A ge E li x hau s e r W e i gh t K g G C S HR S ys BP M ean BP D i a BP RR S p O T e m p C F i O P o t a ss i u m S od i u m C h l o r i de G l u c o s e B UNC r ea t i n i ne M agne s i u m C a l c i u m I on i s ed C a C O S GO T S G P TT o t a l B ili A l bu m i n H b W B CC oun t P l a t e l e t s C oun t P TT P T I NR A r t e r i a l P H P a O P a C O A r t e r i a l BEA r t e r i a l La c t a t e HC O M e c h v en t S ho ck I nde x P a O / F i O P e r c en t il e (d) A4 G ende r A ge E li x hau s e r W e i gh t K g G C S HR S ys BP M ean BP D i a BP RR S p O T e m p C F i O P o t a ss i u m S od i u m C h l o r i de G l u c o s e B UNC r ea t i n i ne M agne s i u m C a l c i u m I on i s ed C a C O S GO T S G P TT o t a l B ili A l bu m i n H b W B CC oun t P l a t e l e t s C oun t P TT P T I NR A r t e r i a l P H P a O P a C O A r t e r i a l BEA r t e r i a l La c t a t e HC O M e c h v en t S ho ck I nde x P a O / F i O P e r c en t il e (e) A5 G ende r A ge E li x hau s e r W e i gh t K g G C S HR S ys BP M ean BP D i a BP RR S p O T e m p C F i O P o t a ss i u m S od i u m C h l o r i de G l u c o s e B UNC r ea t i n i ne M agne s i u m C a l c i u m I on i s ed C a C O S GO T S G P TT o t a l B ili A l bu m i n H b W B CC oun t P l a t e l e t s C oun t P TT P T I NR A r t e r i a l P H P a O P a C O A r t e r i a l BEA r t e r i a l La c t a t e HC O M e c h v en t S ho ck I nde x P a O / F i O P e r c en t il e (f) A6 G ende r A ge E li x hau s e r W e i gh t K g G C S HR S ys BP M ean BP D i a BP RR S p O T e m p C F i O P o t a ss i u m S od i u m C h l o r i de G l u c o s e B UNC r ea t i n i ne M agne s i u m C a l c i u m I on i s ed C a C O S GO T S G P TT o t a l B ili A l bu m i n H b W B CC oun t P l a t e l e t s C oun t P TT P T I NR A r t e r i a l P H P a O P a C O A r t e r i a l BEA r t e r i a l La c t a t e HC O M e c h v en t S ho ck I nde x P a O / F i O P e r c en t il e Figure 6: Percentile value (y-axis) of each variable (x-axis) in an archetype, as compared to the overall cohort.
Figure 6: Percentile value (y-axis) of each variable (x-axis) in an archetype, as compared to the overall cohort. able 4: Statistics of the clinical variables for each sepsis state.
Demographic Type or Unit A1 Mean (std) A2 Mean (std) A3 Mean (std) A4 Mean (std) A5 Mean (std) A6 Mean (std)
Age years 64.663 (16.602) 56.5665 (18.7243) 64.8518 (17.2279) 62.7714 (16.2069) 51.574 (21.7017) 54.2832(22.129)Gender binary 0.4395 (0.4963) 0.3514 (0.4775) 0.4778 (0.4996) 0.4078 (0.4917) 0.4739 (0.5003) 0.5852(0.5003)
Vitals
HR bpm 87.1709 (16.7968) 95.5663 (18.356) 84.9405 (16.3634) 88.7297 (19.2053) 90.9378 (19.2497) 89.2824(19.3743)SysBP mmHg 119.8967 (20.3539) 121.4193 (19.5506) 120.7683 (19.9297) 119.37 (22.4043) 119.8301 (21.3859) 119.5795(20.9424)MeanBP mmHg 78.1903 (13.4654) 80.0547 (14.2412) 78.8656 (13.9104) 77.2155 (15.2942) 81.1584 (15.2533) 78.1294(13.3615)DiaBP mmHg 57.0701 (13.293) 59.554 (13.8632) 58.3062 (13.826) 58.0745 (15.1096) 60.4603 (15.3068) 56.9948(13.8887)Temp Celsius 36.9064 (1.7824) 37.3685 (11.044) 36.7529 (1.4197) 36.6214 (3.0829) 36.9874 (0.9774) 36.8557(0.941)RR bpm 20.2032 (5.1781) 21.885 (6.2891) 19.5003 (4.7369) 20.6665 (6.0007) 21.0097 (5.601) 20.8984(5.1881)
Lab Values
GCS N/A 12.562 (3.4477) 12.2389 (3.5298) 13.9572 (2.3921) 10.6749 (4.7609) 11.2034 (4.4437) 11.7657 (4.0345)SpO2 percent 96.9089 (2.642) 97.1831 (2.4756) 97.077 (2.1706) 95.9839 (4.7988) 96.231 (4.3131) 95.9966 (5.9411)FiO2 Fraction 0.463 (0.183) 0.4735 (0.1903) 0.2841 (0.0749) 0.5193 (0.2122) 0.4761 (0.217) 0.4661 (0.2163)Potassium mEq/L 4.0755 (0.5561) 4.2223 (0.5966) 4.1442 (0.6301) 4.3133 (0.7767) 4.0643 (0.6654) 4.3403 (0.6969)Sodium mEq/L 138.6984 (4.8889) 138.3988 (5.0606) 138.1455 (4.4043) 138.9389 (5.4767) 138.5481 (4.5309) 138.5624 (5.5003)Chloride mEq/L 104.7454 (6.2452) 103.4621 (5.855) 104.4564 (5.7471) 102.4878 (7.5266) 103.4479 (7.3862) 103.7934 (7.0719)Glucose mg/dl 139.0001 (51.0059) 133.4703 (44.9989) 137.6523 (55.9765) 150.8865 (77.058) 138.8868 (63.89) 120.5447 (38.2647)BUN mg/dl 29.3086 (22.6237) 24.962 (19.8349) 26.684 (20.6605) 33.6255 (20.5769) 26.2646 (17.4777) 29.3539 (18.5723)Creatinine mg/dl 1.4887 (2.1789) 1.0243 (0.8691) 1.499 (1.6191) 2.0458 (1.5894) 1.994 (1.8473) 2.0084 (1.9972)Magnesium mg/dl 2.0551 (0.3503) 2.0673 (0.3121) 2.0169 (0.3344) 2.1042 (0.3923) 2.0373 (0.4165) 2.2905 (1.0883)Calcium mg/dl 8.3114 (0.7968) 8.3944 (0.7641) 8.3835 (0.7654) 8.5005 (1.1839) 8.1258 (0.8741) 8.202 (0.8551)Ionised Ca mmol/L 1.1317 (0.1223) 1.1315 (0.0942) 1.1394 (0.1016) 1.0837 (0.1306) 1.0718 (0.11) 1.0935 (0.1253)CO2 mEq/L 25.8455 (5.6656) 26.4052 (5.4564) 24.8079 (4.6421) 24.1683 (6.8329) 24.6976 (6.4869) 23.2444 (6.0989)SGOT u/L 121.1987 (319.2254) 115.2526 (328.7376) 97.1299 (281.488) 6.56 × (1.49 × ) 2.01 × (1.76 × ) 7.66 × (1.43 × )SGPT u/L 104.709 (292.993) 103.3734 (292.2103) 81.6814 (254.6595) 3.02 × (1.20 × ) 6.39 × (1.52 × ) 6.69 × (1.15 × )Total Bilirubin mg/dL 2.4088 (5.1579) 1.9281 (4.4836) 1.9465 (4.2194) 5.3717 (5.7693) 3.3705 (2.1968) 4.5556 (6.3519)Albumin g/dL 2.9994 (0.6756) 2.8733 (0.6736) 3.195 (0.6969) 2.9661 (0.619) 3.0209 (0.685) 2.9535 (0.5675)Hb g/dL 10.3025 (1.733) 9.488 (1.5127) 10.4938 (1.8691) 10.42 (1.7506) 10.8988 (1.9639) 10.7478 (1.9296)WBC × /L 12.227 (8.2151) 20.698 (15.4674) 10.9535 (6.3327) 13.1239 (7.9441) 11.2392 (4.9433) 13.0102 (6.8857)Platelets × /L 223.7886 (126.0426) 905.5808 (158.9635) 229.6721 (130.2459) 185.0943 (121.6149) 189.9349 (104.536) 194.6217 (127.3292)aPTT s 37.7794 (19.3023) 37.5194 (18.7424) 37.839 (20.2669) 44.1421 (23.6432) 41.6113 (23.9075) 43.1402 (21.2096)PT s 16.1654 (6.6965) 15.9141 (5.0994) 15.8759 (6.3263) 20.6772 (10.9054) 21.9298 (11.9564) 25.9364 (19.0131)INR N/A 1.5081 (0.8252) 1.4644 (0.6116) 1.4806 (0.7861) 2.0823 (1.324) 2.4955 (2.0079) 2.9554 (2.8588)Arterial PH N/A 7.3905 (0.0741) 7.3987 (0.081) 7.3945 (0.0713) 7.3531 (0.1014) 7.3738 (0.095) 7.3579 (0.0957)PaO2 mmHg 120.8273 (64.1414) 121.7747 (60.9402) 381.0231 (79.3787) 126.9464 (72.8629 120.977 (70.0857) 117.9201 (50.4301)PaCO2 mmHg 41.9729 (10.832) 41.7772 (10.6985) 40.872 (8.6858) 41.2665 (11.7813) 39.2051 (10.6536) 39.862 (11.6424)Arterial BE mEq/L 0.3591 (5.0242) 0.7962 (5.2063) 0.367 (3.9529) -1.919 (6.6414) -1.9408 (5.8841) -2.4647 (6.6472)Arterial lactate mmol/L 2.0365 (1.6021) 1.877 (1.4591) 2.0957 (1.5675) 5.498 (5.3563) 3.9508 (3.9727) 4.581 (4.5874)HCO3 mEq/L 24.6844 (5.0834 25.0584 (4.9991) 24.4738 (4.7358) 22.7896 (6.1283) 23.0842 (5.6634) 21.9257 (5.7679)Shock Index bpm/mmHg 0.7483 (0.1962) 0.8057 (0.1997) 0.7223 (0.185) 0.7707 (0.2386) 0.7874 (0.2371) 0.7713 (0.2254)PaO2/FiO2 mmHg 292.9807 (172.172) 294.5925 (179.6651) 1.38 × (300.0487) 285.0333 (205.488) 318.1304 (272.0889) 301.8456 (164.0181) Others
Weight kg 83.2915 (24.6464) 81.9459 (24.443) 79.2817(22.7953) 85.1836(28.6976) 89.298 (35.9261) 82.3125 (24.2238)Mechvent binary 0.373 (0.4836) 0.3314 (0.4708) 0.0918(0.2888) 0.5627(0.4963) 0.5037 (0.5009) 0.4148 (0.4934)Comorbidity Count Integer 4.0159 (2.1709) 3.0843 (2.0466) 3.6575(2.0539) 4.6206(2.2385) 4.291 (2.0927) 4.2841 (1.9404) able 5: Definitions of Comorbidities.
Comorbidity ICD-9-CM Codes DRG Screen: Case Does Not Havethe Following Disorders (DRG):Congestive heart failure 398.91, 402.11, 402.91, 404.11, 404.13, 404.91,404.93,428.0–428.9 Cardiac a Cardiac arrhythmias 426.10, 426.11, 426.13, 426.2–426.53,426.6–426.89, 427.0, 427.2, 427.31,427.60,427.9, 785.0, V45.0, V53.3 Cardiac a Valvular disease 093.20–093.24, 394.0–397.1, 424.0–424.91,746.3–746.6,V42.2,V43.3 Cardiac a Pulmonary circulation disorders 416.0–416.9, 417.9 Cardiac a or COPDPeripheral vascular disorders 440.0–440.9, 441.2, 441.4, 441.7, 441.9,443.1–443.9, 447.1,557.1,557.9, V43.4 Peripheral vascular (130–131)Hypertension (combined)Hypertension, uncomplicatedHypertension, complicated 401.1, 401.9402.10, 402.90, 404.10, 404.90, 405.11, 405.19,405.91, 405.99 Hypertension (134)Hypertension (134) or cardiac a or renal a Paralysis 342.0–342.12, 342.9–344.9 Cerebrovascular (5, 14–17)Other neurological disorders 331.9, 332.0, 333.4,333.5,334.0–335.9,340,341.1–341.9,345.00–345.11,345.40–345.51, 345.80-345.91, 348.1,348.3, 780.3, 784.3 Nervous system (1–35)Chronic pulmonary disease 490–492.8, 493.00–493.91, 494, 495.0–505,506.4 COPD (88) or asthma (96–88)Diabetes, uncomplicated b b a Peptic ulcer disease excludingbleeding 531.70, 531.90, 532.70, 532.90, 533.70,533.90,534.70,534.90, V12.71 GI hemorrhage or ulcer (174–178)AIDS b a Metastatic cancer b a Solid tumor withoutmetastasis b a Rheumatoid arthritis/collagenvascular diseases 701.0, 710.0–710.9, 714.0–714.9,720.0–720.9, 725 Connective tissue (240–241)Coagulopathy 2860–2869, 287.1, 287.3–287.5 Coagulation (397)Obesity 278.0 Obesity procedure (288) or nutrition/metabolic (296–298)Weight loss 260–263.9 Nutrition/metabolic (296–298)Fluid and electrolyte disorders 276.0–276.9 Nutrition/metabolic (296–298)Blood loss anemia 2800 Anemia (395–396)Deficiency anemias 280.1–281.9, 285.9 Anemia (395–396)Alcohol abuse 291.1, 291.2, 291.5, 291.8, 291.9,303.90-303.93,305.00–305.03, V113 Alcohol or drug (433–437)Drug abuse 292.0, 292.82–292.89,292.9,304.00–304.93,305.20-305.93 Alcohol or drug (433–437)Psychoses 295.00–298.9, 299.10–299.11 Psychose (430)Depression 300.4, 301.12, 309.0, 309.1, 311 Depression (426)
ICD-9-CM, International Classification of Diseases, 9th Revision, Clinical Modification; DRG, diagnosis-related group; COPD, chronic obstructive pulmonarydisease; GI, gastrointestinal; AIDS, acquired immune deficiency syndrome; HIV, human immunodeficiency virus. a Definitions of DRG groups: Cardiac: DRGs 103–108, 110–112, 115–118, 120-127, 129, 132–133, 135-143; Renal: DRGs 302-305, 315–333; Liver: DRGs199-202, 205-208; Leukemia/lymphoma: DRGs 400-414, 473, 492; Cancer: DRGs 10, 11, 64, 82, 172, 173, 199, 203, 239, 257–260, 274, 275, 303, 318, 319,338, 344, 346, 347, 354, 355, 357, 363, 366, 367, 406–414. b A hierarchy was established between the following pairs of comorbidities: If both uncomplicated diabetes and complicated diabetes are present, count onlycomplicated diabetes. If both solid tumor without metastasis and metastatic cancer are present, count only metastatic cancer. ∗ This table is adopted from A., Steiner et al. ..