Henry C. Thode

Testing for normality

Plots, probability plots and regression tests tests using moments other tests for univariate normality goodness of fit tests testing for outliers in univariate samples power comparisons for univariate tests for normality testing for normalitywith censored data assessing multivariate normality testing for multivariate outliers testing for normal mixtures robust methods computational methods and issues. Appendices: data sets used in examples critical values for tests.

The Association Between Length of Emergency Department Boarding and Mortality

OBJECTIVES Emergency department (ED) boarding has been associated with several negative patient-oriented outcomes, from worse satisfaction to higher inpatient mortality rates. The current study evaluates the association between length of ED boarding and outcomes. The authors expected that prolonged ED boarding of admitted patients would be associated with higher mortality rates and longer hospital lengths of stay (LOS). METHODS This was a retrospective cohort study set at a suburban academic ED with an annual ED census of 90,000 visits. Consecutive patients admitted to the hospital from the ED and discharged between October 2005 and September 2008 were included. An electronic medical record (EMR) system was used to extract patient demographics, ED disposition (discharge, admit to floor), ED and hospital LOS, and in-hospital mortality. Boarding was defined as ED LOS 2 hours or more after decision for admission. Descriptive statistics were used to evaluate the association between length of ED boarding and hospital LOS, subsequent transfer to an intensive care unit (ICU), and mortality controlling for comorbidities. RESULTS There were 41,256 admissions from the ED. Mortality generally increased with increasing boarding time, from 2.5% in patients boarded less than 2 hours to 4.5% in patients boarding 12 hours or more (p < 0.001). Mean hospital LOS also showed an increase with boarding time (p < 0.001), from 5.6 days (SD ± 11.4 days) for those who stayed in the ED for less than 2 hours to 8.7 days (SD ± 16.3 days) for those who boarded for more than 24 hours. The increases were still apparent after adjustment for comorbid conditions and other factors. CONCLUSIONS Hospital mortality and hospital LOS are associated with length of ED boarding.

Gamma distribution model describes maturational curves for delta wave amplitude, cortical metabolic rate and synaptic density

We analyzed the available ontogenetic data (birth to 30 years of age) for: amplitude of delta EEG (DA) waves during sleep; cortical metabolic rate (CMR) measured with positron emission tomography; and synaptic density (SD) in frontal cortex. Each is at the adult level at birth, increases to about twice this level by 3 years of age, and then gradually falls back to the adult level over the next two decades. Statistical analyses revealed that individual gamma distribution models fit each data set as well as did the best ad hoc polynomial. A test of whether a single gamma distribution model could describe all three data sets gave good results for DA and CMR but the fit was unsatisfactory for SD. However, because so few data were available for SD, this test was not conclusive. We proposed the following model to account for these changes. First, cortical neurons are stimulated by birth to enter a proliferative state (PS) that creates many connections. Next, as a result of interactions in the PS, neurons are triggered into a transient organizational state (OS) in which they make enduring connections. The OS has a finite duration (minutes to years), and is characterized by high rates of information-processing and metabolism. Levels of CMR, SD and DA, therefore, are proportional to the number of neurons in the OS at any time. Thus, the cortex after birth duplicates, over a vastly greater time scale, the overproduction and regression of neural elements that occurs repeatedly in embryonic development. Finally, we discussed the implications of post-natal brain changes for normal and abnormal brain function. Mental disorders that have their onset after puberty (notably schizophrenia and manic-depressive psychoses) might be caused by errors in these late maturational processes. In addition to age of onset, this neurodevelopmental hypothesis might explain several other puzzling features of these subtle disorders.

Validation of the Wong‐Baker FACES Pain Rating Scale in Pediatric Emergency Department Patients

OBJECTIVES The Wong-Baker FACES Pain Rating Scale (WBS), used in children to rate pain severity, has been validated outside the emergency department (ED), mostly for chronic pain. The authors validated the WBS in children presenting to the ED with pain by identifying a corresponding mean value of the visual analog scale (VAS) for each face of the WBS and determined the relationship between the WBS and VAS. The hypothesis was that the pain severity ratings on the WBS would be highly correlated (Spearmans rho > 0.80) with those on a VAS. METHODS This was a prospective, observational study of children ages 8-17 years with pain presenting to a suburban, academic pediatric ED. Children rated their pain severity on a six-item ordinal faces scale (WBS) from none to worst and a 100-mm VAS from least to most. Analysis of variance (ANOVA) was used to compare mean VAS scores across the six ordinal categories. Spearmans correlation (rho) was used to measure agreement between the continuous and ordinal scales. RESULTS A total of 120 patients were assessed: the median age was 13 years (interquartile range [IQR] = 10-15 years), 50% were female, 78% were white, and six patients (5%) used a language other than English at home. The most commonly specified locations of pain were extremity (37%), abdomen (19%), and back/neck (11%). The mean VAS increased uniformly across WBS categories in increments of about 17 mm. ANOVA demonstrated significant differences in mean VAS across face groups. Post hoc testing demonstrated that each mean VAS was significantly different from every other mean VAS. Agreement between the WBS and VAS was excellent (rho = 0.90; 95% confidence interval [CI] = 0.86 to 0.93). There was no association between age, sex, or pain location with either pain score. CONCLUSIONS The VAS was found to have an excellent correlation in older children with acute pain in the ED and had a uniformly increasing relationship with WBS. This finding has implications for research on pain management using the WBS as an assessment tool.

Evaluation of a New Rapid Quantitative Immunoassay for Serum Myoglobin Versus CK-MB for Ruling Out Acute Myocardial Infarction in the Emergency Department

STUDY OBJECTIVE To compare the predictive values of serum myoglobin and creatine kinase (CK)-MB for ruling out acute myocardial infarction in the emergency department. DESIGN Prospective, observational study. SETTING University teaching hospital. PARTICIPANTS One hundred eighty nine consecutive patients aged 30 years and older who presented within 12 hours from onset of chest discomfort, dyspnea, syncope, congestive heart failure, symptomatic dysrhythmia, pulmonary edema, or epigastric pain were entered into the study. Patients with trauma or renal failure were excluded. INTERVENTIONS Standardized history and physical examination and blood sampling for serum myoglobin (S-Mgb) and CK-MB were done at the time of presentation (T0) and 1 hour later (T1). RESULTS Using World Health Organization criteria, 22 acute myocardial infarction patients were identified. Mean time from symptom onset to presentation was 3.2 hours. S-Mgb was more sensitive than CK-MB at T0 and T1, 55% versus 23% (P < .05) and 73% versus 41% (P < .05), respectively. Respective specificities of S-Mgb versus CK-MB were 98% versus 99% (P = NS) at T0 and 97% versus 99% (P = NS) at T1. Negative predictive values of S-Mgb versus CK-MB were 94% versus 91% (P = NS) at T0 and 96% versus 93% (P = NS) at T1. The S-Mgb assay yielded quantitative results allowing the difference between the T0 and T1 values to be analyzed. A difference of 40 or more ng/mL between T0 and T1 was considered positive. When using a positive result in either the T0 or T1 value or a difference between the two values of 40 or more ng/mL, the sensitivity of S-Mgb was 91% (P < .05 versus CK-MB), the specificity was 96% (P = NS versus CK-MB), and the negative predictive value was 99% (95% confidence interval for S-Mgb, 97.0 to 100 versus CK-MB, 95% confidence interval, 88.9 to 96.6). CONCLUSION In the first hour of presentation to the ED, the rapid quantitative assay for S-Mgb was statistically more sensitive than CK-MB and had an excellent negative predictive value for ruling out acute myocardial infarction in patients with typical or atypical symptoms. Due to the relatively small sample size, we could not exclude the possibility that differences in specificity might become statistically significant (beta error) with a larger sample size of acute myocardial infarction patients.

The association between transfer of emergency department boarders to inpatient hallways and mortality: a 4-year experience.

STUDY OBJECTIVE We developed and implemented an institutional protocol aimed at reducing crowding by admitting boarded patients to hospital inpatient hallways. We hypothesized that transfer of admitted patients from the emergency department (ED) to inpatient hallways would be feasible and not create patient harm. METHODS This was a retrospective cohort study in a suburban, academic ED with an annual census of 70,000. We studied consecutive patients admitted from our ED between January 2004 and January 2008. In 2001, a multidisciplinary team developed and implemented an institutional protocol in which admitted adult patients boarded in the ED were transferred to hospital inpatient hallways under select conditions. We extracted data from the electronic medical record system, measuring patient demographics, ED disposition (discharge, admit to floor, admit to hallway), ED length of stay, and inhospital mortality. We report ED length of stay, subsequent transfer to an ICU, and hospital mortality of patients admitted to standard and hallway inpatient beds. RESULTS Of 55,062 ED patients admitted, there were 1,798 deaths. Of all admissions, 2,042 (4%) went to a hallway; 53,020 went to a standard bed. Patients admitted to standard and hallway beds were similar in age (median [interquartile range] 55 years [37 to 72 years] and 54 years [41 to 70 years], respectively) and sex (48.2% and 50% female patients, respectively). The median (interquartile range) times from ED triage to actual admission in patients admitted to standard and hallway beds were 426 minutes (306 to 600 minutes) and 624 (439 to 895 minutes) minutes, respectively (P<.001). Median ED census at triage was lower for standard bed admissions than for hallway patients (44 [33 to 53] versus 50 [38 to 61], respectively, P<.001). Inhospital mortality rates were higher among patients admitted to standard beds (2.6%; 95% confidence interval [CI] 2.5% to 2.7%) than among patients admitted to hallway beds (1.1%; 95% CI 0.7% to 1.7%). ICU transfers were also higher in the standard bed admissions (6.7% [95% CI 6.5% to 6.9%] versus 2.5% [95% CI 1.9% to 3.3%]). CONCLUSION Transfer of ED-boarded admitted patients to an inpatient hallway occurs during high ED census and waiting times for admission but does not appears to result in patient harm.

Simulated percentage points for the null distribution of the likelihood ratio test for a mixture of two normals

We find the percentage points of the likelihood ratio test of the null hypothesis that a sample of n observations is from a normal distribution with unknown mean and variance against the alternative that the sample is from a mixture of two distinct normal distributions, each with unknown mean and unknown (but equal) variance. The mixing proportion pi is also unknown under the alternative hypothesis. For 2,500 samples of sizes n = 15, 20, 25, 40, 50, 70, 75, 80, 100, 150, 250, 500, and 1,000, we calculated the likelihood ratio statistic, and from these values estimated the percentage points of the null distributions. Our algorithm for the calculation of the maximum likelihood estimates of the unknown parameters included precautions against convergence of the maximization algorithm to a local rather than global maximum. Investigations for convergence to an asymptotic distribution indicated that convergence was very slow and that stability was not apparent for samples as large as 1,000. Comparisons of the percentage points to the commonly assumed chi-squared distribution with 2 degrees of freedom indicated that this assumption is too liberal; i.e., ones P-value is greater than that indicated by chi 2(2). We conclude then that one would need what is usually an unfeasibly large sample size (n greater than 1,000) for the use of large-sample approximations to be justified.

Comparison of Plain, Warmed, and Buffered Lidocaine for Anesthesia of Traumatic Wounds

STUDY OBJECTIVE To compare pain on infiltration, need for additional anesthesia, and pain on suturing in patients given plain, warm, and buffered lidocaine preparations before the suturing of traumatic wounds in the emergency department. DESIGN Randomized, prospective, single-blinded convenience sample. SETTING University hospital ED. PARTICIPANTS Patients with traumatic lacerations. Patients allergic to lidocaine and patients with abnormal mental status or altered pain sensorium were excluded. INTERVENTIONS All wounds were anesthetized by use of a standard injection technique. Wound margins were anesthetized with plain, buffered, or warm lidocaine in a randomized fashion. Pain of infiltration was recorded for each margin by means of a previously validated visual-analogue pain scale. RESULTS The main outcome parameter was pain of infiltration. Need for additional anesthesia and pain on suturing were secondary outcome parameters. We evaluated 45 patients. Pain on injection varied by the type of lidocaine (mean pain scores: plain, 8.2; buffered, 4.7 [P < .05 versus plain]; warm, 4.9 [P < .05 versus plain]). There was no significant difference between the mean pain scores of the groups given warm and buffered lidocaine (P = NS). Need for additional anesthesia and pain on suturing did not vary by the type of anesthesia. The order of injection was not found to influence results. Mean pain scores were not different for margins 1 and 2 in any of the groups (P = NS). CONCLUSION Both buffered and warmed lidocaine were as efficacious as plain lidocaine, and they had significantly less pain associated with infiltration than did plain lidocaine. In EDs with fluid warmers, warmed lidocaine may be the most convenient, well-tolerated, efficacious lidocaine preparation for anesthesia of traumatic wounds.

Correlation Among Clinical, Laboratory, and Hepatobiliary Scanning Findings in Patients With Suspected Acute Cholecystitis

STUDY OBJECTIVE To assess the ability of various clinical and laboratory parameters to predict the results of hepatobiliary scintigraphy (HBS) in patients with suspected acute cholecystitis. METHODS This was a retrospective chart review of all patients referred from the emergency department for an HBS in 1993 to exclude acute cholecystitis. The setting was a university-affiliated tertiary care hospital with an annual census of approximately 42,000. The participants were 100 consecutive patients who were seen in the ED and had an HBS and obtainable medical records. Medical records of all patients referred from the ED for an urgent HBS in 1993 were retrospectively reviewed for the following information: demographics, historical information, physical findings, laboratory findings, biliary scintigraphic findings, and surgical pathologic findings. Comparisons were made between patients with a positive or negative HBS. Sensitivities, specificities, and positive and negative predictive values were calculated for dichotomous variables with a positive HBS as a control standard. A separate analysis was performed for patients with pathologically confirmed acute cholecystitis. RESULTS Fifty-three patients had a positive HBS, and 47 had a negative HBS. A history of fever had a positive predictive value of 100% and a sensitivity of 14.6%. The presence of Murphys sign was both sensitive (97.2%) and highly predictive (93.3%) of a positive HBS yet was not documented in 35 cases. All other variables were not found to be helpful in predicting the results of HBS. Pathologic diagnoses were available in 44 patients. Of 40 patients with pathologically confirmed acute cholecystitis, fever and leukocytosis were absent at the time of presentation in 36 (90%) and 16 (40%) of the cases, respectively. Murphys sign was absent in 3 (10%) of 29 of these patients. A stepwise analysis failed to identify any combination of clinical variables that was associated with a higher probability of a positive HBS. CONCLUSION No single or combination of clinical or laboratory findings at the time of ED presentation identified all patients with a positive HBS. Murphys sign had the highest sensitivity and positive predictive value yet was poorly documented. Liberal use of biliary scintigraphy or ultrasound is encouraged to avoid underdiagnosis of acute cholecystitis.

Evaluation of American college of surgeons trauma triage criteria in a suburban and rural setting

In suburban and rural counties, patient transport to specialized facilities such as trauma centers may result in prolonged transport times with the resultant loss of ambulance coverage in the primary service area. We evaluated the American College of Surgeons trauma triage criteria as modified by New York State to determine the ability of these criteria to predict the need for trauma center care in victims of blunt traumatic injury. Blunt trauma patients were retrospectively identified through review of patient care reports for the presence either of mechanism or of physiological criteria for transport to a trauma center. Controls were randomly selected from patients with blunt trauma not meeting any of the criteria. Main outcome parameters were the emergency department (ED) disposition, length of hospital stay, need for intensive care unit (ICU) care, and major nonorthopedic operative interventions. There were 857 patients enrolled. The presence either of mechanism or of physiological criteria increased the likelihood of hospital admission (control, 11%; mechanism, 35%; and physiological, 33%). Relative to patients without any criteria, the presence of mechanism criteria alone did not identify patients who required a prolonged length of stay (67% vs 71%), intensive care unit services (13% vs 19%) or major nonorthopedic operative interventions (0.2% vs 1.6%). The presence of physiological criteria increased the likelihood of requiring all of these services. These comparisons held true for victims of motor vehicle accidents, pedestrians struck by motor vehicles, and people who fell from heights above ground level. Patients with physiologic criteria may benefit from transport directly to a trauma center. Because of the low need for operative intervention and ICU services, patients with no criteria or mechanism criteria at long distances from a trauma center may be initially evaluated at the closest hospital and transferred to a trauma center if hospitalization or ICU care is necessary. Further study to determine the predictive value of certain individual mechanism criteria is warranted.