Charles E. McCulloch

Maximum Likelihood Algorithms for Generalized Linear Mixed Models

Abstract Maximum likelihood algorithms are described for generalized linear mixed models. I show how to construct a Monte Carlo version of the EM algorithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate and improve the use of importance sampling ideas. Calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorithm as a framework to compare maximum likelihood to the “joint-maximization” or penalized quasi-likelihood methods and explain why the latter can perform poorly.

Functional status of elderly adults before and after initiation of dialysis.

BACKGROUND It is unclear whether functional status before dialysis is maintained after the initiation of this therapy in elderly patients with end-stage renal disease (ESRD). METHODS Using a national registry of patients undergoing dialysis, which was linked to a national registry of nursing home residents, we identified all 3702 nursing home residents in the United States who were starting treatment with dialysis between June 1998 and October 2000 and for whom at least one measurement of functional status was available before the initiation of dialysis. Functional status was measured by assessing the degree of dependence in seven activities of daily living (on the Minimum Data Set-Activities of Daily Living [MDS-ADL] scale of 0 to 28 points, with higher scores indicating greater functional difficulty). RESULTS The median MDS-ADL score increased from 12 during the 3 months before the initiation of dialysis to 16 during the 3 months after the initiation of dialysis. Three months after the initiation of dialysis, functional status had been maintained in 39% of nursing home residents, but by 12 months after the initiation of dialysis, 58% had died and predialysis functional status had been maintained in only 13%. In a random-effects model, the initiation of dialysis was associated with a sharp decline in functional status, indicated by an increase of 2.8 points in the MDS-ADL score (95% confidence interval [CI], 2.5 to 3.0); this decline was independent of age, sex, race, and functional-status trajectory before the initiation of dialysis. The decline in functional status associated with the initiation of dialysis remained substantial (1.7 points; 95% CI, 1.4 to 2.1), even after adjustment for the presence or absence of an accelerated functional decline during the 3-month period before the initiation of dialysis. CONCLUSIONS Among nursing home residents with ESRD, the initiation of dialysis is associated with a substantial and sustained decline in functional status.

Risk Factors for End-Stage Renal Disease: 25-Year Follow-up

BACKGROUND Few cohort studies have focused on risk factors for end-stage renal disease (ESRD). This investigation evaluated the prognostic value of several potential novel risk factors for ESRD after considering established risk factors. METHODS We studied 177 570 individuals from a large integrated health care delivery system in northern California who volunteered for health checkups between June 1, 1964, and August 31, 1973. Initiation of ESRD treatment was ascertained using US Renal Data System registry data through December 31, 2000. RESULTS A total of 842 cases of ESRD were observed during 5 275 957 person-years of follow-up. This comprehensive evaluation confirmed the importance of established risk factors, including the following: male sex, older age, proteinuria, diabetes mellitus, lower educational attainment, and African American race, as well as higher blood pressure, body mass index, and serum creatinine level. The 2 most potent risk factors were proteinuria and excess weight. For proteinuria, the adjusted hazard ratios (HRs) were 7.90 (95% confidence interval [CI], 5.35-11.67) for 3 to 4+ on urine dipstick, 3.59 (2.82-4.57) for 1 to 2+ on urine dipstick, and 2.37 (1.79-3.14) for trace vs negative on urine dipstick. For excess weight, the HRs were 4.39 (95% CI, 3.38-5.70) for class 2 to class 3 obesity, 3.11 (2.51-3.84) for class 1 obesity, and 1.65 (1.39-1.97) for overweight vs normal weight. Furthermore, several independent novel risk factors for ESRD were identified, including lower hemoglobin level (1.33 [1.08-1.63] for lowest vs highest quartile), higher serum uric acid level (2.14 [1.65-2.77] for highest vs lowest quartile), self-reported history of nocturia (1.36 [1.17-1.58]), and family history of kidney disease (HR, 1.40 [95% CI, 1.02-1.90]). CONCLUSIONS We confirmed the importance of established ESRD risk factors in this large cohort with broad sex and racial/ethnic representation. Lower hemoglobin level, higher serum uric acid level, self-reported history of nocturia, and family history of kidney disease are independent risk factors for ESRD.

Dialysis-requiring acute renal failure increases the risk of progressive chronic kidney disease

To determine whether acute renal failure (ARF) increases the long-term risk of progressive chronic kidney disease (CKD), we studied the outcome of patients whose initial kidney function was normal or near normal but who had an episode of dialysis-requiring ARF and did not develop end-stage renal disease within 30 days following hospital discharge. The study encompassed 556,090 adult members of Kaiser Permanente of Northern California hospitalized over an 8 year period, who had pre-admission estimated glomerular filtration rates (eGFR) equivalent to or greater than 45 ml/min/1.73 m(2) and who survived hospitalization. After controlling for potential confounders such as baseline level of eGFR and diabetes status, dialysis-requiring ARF was independently associated with a 28-fold increase in the risk of developing stage 4 or 5 CKD and more than a twofold increased risk of death. Our study shows that in a large, community-based cohort of patients with pre-existing normal or near normal kidney function, an episode of dialysis-requiring ARF was a strong independent risk factor for a long-term risk of progressive CKD and mortality.

The risk of acute renal failure in patients with chronic kidney disease.

Few studies have defined how the risk of hospital-acquired acute renal failure varies with the level of estimated glomerular filtration rate (GFR). It is also not clear whether common factors such as diabetes mellitus, hypertension and proteinuria increase the risk of nosocomial acute renal failure independent of GFR. To determine this we compared 1,746 hospitalized adult members of Kaiser Permanente Northern California who developed dialysis-requiring acute renal failure with 600,820 hospitalized members who did not. Patient GFR was estimated from the most recent outpatient serum creatinine measurement prior to admission. The adjusted odds ratios were significantly and progressively elevated from 1.95 to 40.07 for stage 3 through stage 5 patients (not yet on maintenance dialysis) compared to patients with estimated GFR in the stage 1 and 2 range. Similar associations were seen after controlling for inpatient risk factors. Pre-admission baseline diabetes mellitus, diagnosed hypertension and known proteinuria were also independent risk factors for acute kidney failure. Our study shows that the propensity to develop in-hospital acute kidney failure is another complication of chronic kidney disease whose risk markedly increases even in the upper half of stage 3 estimated GFR. Several common risk factors for chronic kidney disease also increase the peril of nosocomial acute kidney failure.

Aneurysm Growth Occurs at Region of Low Wall Shear Stress Patient-Specific Correlation of Hemodynamics and Growth in a Longitudinal Study

Background and Purpose— Evolution of intracranial aneurysmal disease is known to be related to hemodynamic forces acting on the vessel wall. Low wall shear stress (WSS) has been reported to have a negative effect on endothelial cells normal physiology and may be an important contributor to local remodeling of the arterial wall and to aneurysm growth and rupture. Methods— Seven patient-specific models of intracranial aneurysms were constructed using MR angiography data acquired at two different time points (mean 16.4±7.4 months between the two time points). Numeric simulations of the flow in the baseline geometries were performed to compute WSS distributions. The lumenal geometries constructed from the two time points were manually coregistered, and the radial displacement of the wall was calculated on a pixel-by-pixel basis. This displacement, corresponding to the local growth of the aneurysm, was compared to the time-averaged wall shear stress (WSSTA) through the cardiac cycle at that location. For statistical analysis, radial displacement was considered to be significant if it was larger than half of the MR pixel resolution (0.3 mm). Results— Mean WSSTA values obtained for the areas with a displacement smaller and greater than 0.3 mm were 2.55±3.6 and 0.76±1.5 Pa, respectively (P<0.001). A linear correlation analysis demonstrated a significant relationship between WSSTA and surface displacement (P<0.001). Conclusions— These results indicate that aneurysm growth is likely to occur in regions where the endothelial layer lining the vessel wall is exposed to abnormally low wall shear stress.

Nonrecovery of Kidney Function and Death after Acute on Chronic Renal Failure

BACKGROUND AND OBJECTIVES Relatively little is known about clinical outcomes, especially long-term outcomes, among patients who have chronic kidney disease (CKD) and experience superimposed acute renal failure (ARF; acute on chronic renal failure). DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS We tracked 39,805 members of an integrated health care delivery system in northern California who were hospitalized during 1996 through 2003 and had prehospitalization estimated GFR (eGFR) <45 ml/min per 1.73 m(2). Superimposed ARF was defined as having both a peak inpatient serum creatinine greater than the last outpatient serum creatinine by > or =50% and receipt of acute dialysis. RESULTS Overall, 26% of CKD patients who suffered superimposed ARF died during the index hospitalization. There was a high risk for developing ESRD within 30 d of hospital discharge that varied with preadmission renal function, being 42% among hospital survivors with baseline eGFR 30-44 ml/min per 1.73 m(2) and 63% among hospital survivors with baseline eGFR 15-29 ml/min per 1.73 m(2). Compared with patients who had CKD and did not experience superimposed ARF, those who did had a 30% higher long-term risk for death or ESRD. CONCLUSIONS In a large, community-based cohort of patients with CKD, an episode of superimposed dialysis-requiring ARF was associated with very high risk for nonrecovery of renal function. Dialysis-requiring ARF also seemed to be an independent risk factor for long-term risk for death or ESRD.

Temporal Changes in Incidence of Dialysis-Requiring AKI

The population epidemiology of AKI is not well described. Here, we analyzed data from the Nationwide Inpatient Sample, a nationally representative dataset, to identify cases of dialysis-requiring AKI using validated International Classification of Diseases, Ninth Revision (ICD-9) codes. From 2000 to 2009, the incidence of dialysis-requiring AKI increased from 222 to 533 cases per million person-years, averaging a 10% increase per year (incidence rate ratio=1.10, 95% CI=1.10-1.11 per year). Older age, male sex, and black race associated with higher incidence of dialysis-requiring AKI. The rapid increase in incidence was evident in all age, sex, and race subgroups examined. Temporal changes in the population distribution of age, race, and sex as well as trends of sepsis, acute heart failure, and receipt of cardiac catheterization and mechanical ventilation accounted for about one third of the observed increase in dialysis-requiring AKI among hospitalized patients. The total number of deaths associated with dialysis-requiring AKI rose from 18,000 in 2000 to nearly 39,000 in 2009. In conclusion, the incidence of dialysis-requiring AKI increased rapidly in all patient subgroups in the past decade in the United States, and the number of deaths associated with dialysis-requiring AKI more than doubled.

Epidemiology of reproductive disorders in dairy cattle: associations among host characteristics, disease and production

Logistic regression was used to investigate the effects of host characteristics, production and 23 veterinary diagnoses on the risks of 10 reproductive disorders. For each reproductive disease in each lactation record, all prior disease events in that lactation were examined as possible risk factors. To make an equal opportunity for risk-factor diseases to be counted as present in both cases and controls, a dummy days in milk (DIM) variable was assigned to control records. The assignment was random, but in proportion to the distribution of the DIM for the cases of that disease. The data set was based on 61 124 Finnish Ayrshire cows, from milk-recorded herds, who calved during 1983. Each cow was under observation for 2 days before calving to the following calving or to removal from the herd. Twenty percent of the cows were treated by a veterinarian for reproductive disorders. Lactational incidence rates (%) were: dystocia, 1.2; prolapsed uterus, 0.2; retained placenta, 4.4; early metritis, 2.3; silent heat, 4.9; cystic ovary, 6.8; prolapsed vagina, 0.1; late metritis, 1.1; other infertility, 2.1; abortion, 0.4. The risk of silent heat and other infertility decreased and the risk of dystocia (after the first calving), retained placenta and ovarian cyst increased with increased parity. Parity did not explain the incidences of the other reproductive disorders. The cows calving during September-February (the dark season) had higher risks of early metritis, silent heat, cyst and other infertility than those calving during the light season. Higher herd milk yield in the previous lactation increased the risks of retained placenta, early metritis and late metritis; higher herd yield in the current lactation increased risks of dystocia and of ovarian cyst. The risks of retained placenta, early metritis, silent heat, ovarian cyst, other fertility and abortion also increased with increased individual-cows milk yield. Most reproductive disorders were interrelated. Six non-reproductive disorders (non-parturient paresis, udder edema, indoor and outdoor hypomagnesemia, rumen acidosis and chronic mastitis) were not risk factors for any of the reproductive disorders. Of the other non-reproductive disorders, clinical parturient paresis was a risk factor for dystocia, prolapsed uterus, retained placenta, and early metritis; clinical ketosis was associated with silent heat, cystic ovary and other infertility; disorder of the abomasum, traumatic recticuloperitonitis, acute mastitis and foot or leg injury also contribited to early metritis. No disorders were protective.

Longitudinal risk of intracranial hemorrhage in patients with arteriovenous malformation of the brain within a defined population.

Background and Purpose— Accurate estimates for risk and rates of intracranial hemorrhage (ICH) in the natural course of patients harboring brain arteriovenous malformation (BAVM) are needed to provide a quantitative basis for planning clinical trials to evaluate interventional strategies and to help guide practice management. Methods— We identified patients with BAVM at the Kaiser Permanente Northern California health maintenance organization and documented their clinical course. The influences of age at diagnosis, gender, race–ethnicity, ICH at presentation, venous draining pattern, and BAVM size on ICH subsequent to presentation were studied using the multivariate Cox proportional hazards model and Kaplan–Meier curves. Results— We identified 790 patients with BAVM (51% female; 63% white; mean age±SD at diagnosis: 38±19 years) between 1961 and 2001. Patients who presented with ICH experienced a higher rate of subsequent ICH than those who presented without ICH under multivariate analysis (hazard ratio, 3.6; 95% CI, 1.1 to 11.9; P < 0.032). The effect was similar across race–ethnicity and gender. This difference in ICH rates was greatest in the first year (7% versus 3% per year) and converged over time. The effect of subsequent ICH on functional status was similar to that of the initial ICH. Conclusions— Presentation with ICH was the most important predictor of future ICH, confirming previous studies. Future ICH had similar impact on functional outcome as incident ICH. Intervention to prevent ICH would be of potentially greater benefit to patients presenting with ICH, although the advantage decreases over time.