We propose functional linear models for zero-inflated count data with a focus on the functional hurdle and functional zero-inflated Poisson (ZIP) models. Although the hurdle model assumes the counts come from a mixture of a degenerate distribution at zero and a zero-truncated Poisson distribution, the ZIP model considers a mixture of a degenerate distribution at zero and a standard Poisson distribution. We extend the generalized functional linear model framework with a functional predictor and multiple cross-sectional predictors to model counts generated by a mixture distribution. We propose an estimation procedure for functional hurdle and ZIP models, called penalized reconstruction, geared towards error-prone and sparsely observed longitudinal functional predictors. The approach relies on dimension reduction and pooling of information across subjects involving basis expansions and penalized maximum likelihood techniques. The developed functional hurdle model is applied to modeling hospitalizations within the first 2 years from initiation of dialysis, with a high percentage of zeros, in the Comprehensive Dialysis Study participants. Hospitalization counts are modeled as a function of sparse longitudinal measurements of serum albumin concentrations, patient demographics, and comorbidities. Simulation studies are used to study finite sample properties of the proposed method and include comparisons with an adaptation of standard principal components regression.

We propose a new weighted hurdle regression method for modeling count data, with particular interest in modeling cardiovascular events in patients on dialysis. Cardiovascular disease remains one of the leading causes of hospitalization and death in this population. Our aim is to jointly model the relationship/association between covariates and (i) the probability of cardiovascular events, a binary process, and (ii) the rate of events once the realization is positive-when the hurdle is crossed-using a zero-truncated Poisson distribution. When the observation period or follow-up time, from the start of dialysis, varies among individuals, the estimated probability of positive cardiovascular events during the study period will be biased. Furthermore, when the model contains covariates, then the estimated relationship between the covariates and the probability of cardiovascular events will also be biased. These challenges are addressed with the proposed weighted hurdle regression method. Estimation for the weighted hurdle regression model is a weighted likelihood approach, where standard maximum likelihood estimation can be utilized. The method is illustrated with data from the United States Renal Data System. Simulation studies show the ability of proposed method to successfully adjust for differential follow-up times and incorporate the effects of covariates in the weighting.

Clinical examination to determine the dry weight of patients on hemodialysis (HD) has been problematic, with studies showing discordance between physician assessment and objective measures of volume status.We studied the association between predialysis bioimpedance spectroscopy (BIS)-based estimates of fluid overload and postdialysis hypotension in 635 patients in the United States Renal Data System ACTIVE/ADIPOSE (A Cohort study To Investigate the Value of Exercise/Analyses Designed to Investigate the Paradox of Obesity and Survival in ESRD) study receiving HD in 2009-2011. We recorded predialysis and postdialysis weight and blood pressures over 3 consecutive HD sessions and performed BIS before a single session. Using a previously reported method of estimating normohydration weight, we estimated postdialysis fluid overload (FOpost ) in liters. We used logistic regression with extracellular water/total body water (ECW/TBW) or estimated FOpost as the primary predictor and 1 or more postdialysis systolic blood pressures less than 110 mmHg as the dependent variable. Models were adjusted for age, sex, race, ultrafiltration rate per kilogram of body weight, end-stage renal disease vintage, diabetes mellitus, heart failure, and albumin. Higher ECW/TBW was associated with lower odds of postdialysis hypotension (odds ratio [OR] 0.35, 95% confidence interval [CI] 0.15-0.84 per 0.1, P = 0.02). Every liter of FOpost was associated with lower adjusted odds of postdialysis hypotension (OR 0.86, 95% CI 0.79-0.95, P = 0.003). Prospective studies are needed to determine whether this application of BIS could improve current clinical efforts to minimize episodes of postdialysis hypotension without leading to volume overload.

Background

Few studies have examined the changes in lipoproteins over time and how inflammation is associated with lipoprotein concentrations among patients with end-stage renal disease on dialysis. One possible explanation for the association of low LDL cholesterol concentration and adverse outcomes is that inflammation reduces selected apolipoprotein concentrations.

Methods

Serum samples were collected from a subsample of patients enrolled into the Comprehensive Dialysis Study every 3 months for up to 1 year. We examined the relation between temporal patterns in levels of inflammatory markers and changes in apolipoproteins (apo) A1 and B and the apo B/A1 ratio using linear mixed effects modeling and adjusting for potential confounders.

Results

We enrolled 266 participants from 56 dialysis facilities. The mean age was 62 years, 45% were women and 26% were black. Apo A1 was lower among patients with higher Quetelet's (body mass) index (BMI), diabetes mellitus and atherosclerosis. Apo B was lower among older patients, patients with higher serum creatinine and patients with lower BMI. Over the course of a year, apo A1 changed inversely with serum concentrations of the acute phase proteins C-reactive protein (CRP) and α1 acid glycoprotein (α1AG), while apo B did not. Changes in α1AG were more strongly associated with changes in apolipoprotein concentrations than were changes in CRP; increases in α1AG were associated with decreases in apo A1 and increases in the apo B/A1 ratio.

Conclusions

Changes in inflammatory markers were associated with changes in apo A1, but not apo B over 1 year, suggesting that reductions in high-density lipoprotein cholesterol are associated with inflammation, either of which could mediate cardiovascular risk, but not supporting a hypothesis linking increased risk of low levels of apo B containing lipoproteins to the risk associated with inflammation.

Among patients on dialysis, cardiovascular disease and infection are leading causes of hospitalization and death. Although recent studies have found that the risk of cardiovascular events is higher after an infection-related hospitalization, studies have not fully elucidated how the risk of cardiovascular events changes over time for patients on dialysis. In this work, we characterize the dynamics of cardiovascular event risk trajectories for patients on dialysis while conditioning on survival status via multiple time indices: (1) time since the start of dialysis, (2) time since the pivotal initial infection-related hospitalization, and (3) the patient's age at the start of dialysis. This is achieved by using a new class of generalized multiple-index varying coefficient (GM-IVC) models. The proposed GM-IVC models utilize a multiplicative structure and one-dimensional varying coefficient functions along each time and age index to capture the cardiovascular risk dynamics before and after the initial infection-related hospitalization among the dynamic cohort of survivors. We develop a two-step estimation procedure for the GM-IVC models based on local maximum likelihood. We report new insights on the dynamics of cardiovascular events risk using the United States Renal Data System database, which collects data on nearly all patients with end-stage renal disease in the United States. Finally, simulation studies assess the performance of the proposed estimation procedures.

Background

A well-accepted definition of frailty includes measurements of physical performance, which may limit its clinical utility.

Study design

In a cross-sectional study, we compared prevalence and patient characteristics based on a frailty definition that uses self-reported function to the classic performance-based definition and developed a modified self-report-based definition.

Setting & participants

Prevalent adult patients receiving hemodialysis in 14 centers around San Francisco and Atlanta in 2009-2011.

Index tests

Self-report-based frailty definition in which a score lower than 75 on the Physical Function scale of the 36-Item Short Form Health Survey (SF-36) was substituted for gait speed and grip strength in the classic definition; modified self-report definition with optimized Physical Function score cutoff points derived in a development (one-half) cohort and validated in the other half.

Reference test

Performance-based frailty defined as 3 of the following: weight loss, weakness, exhaustion, low physical activity, and slow gait speed.

Results

387 (53%) patients were frail based on self-reported function, of whom 209 (29% of the cohort) met the performance-based definition. Only 23 (3%) met the performance-based definition of frailty only. The self-report definition had 90% sensitivity, 64% specificity, 54% positive predictive value, 93% negative predictive value, and 72.5% overall accuracy. Intracellular water per kilogram of body weight and serum albumin, prealbumin, and creatinine levels were highest among nonfrail individuals, intermediate among those who were frail by self-report, and lowest among those who also were frail by performance. Age, percentage of body fat, and C-reactive protein level followed an opposite pattern. The modified self-report definition had better accuracy (84%; 95% CI, 79%-89%) and superior specificity (88%) and positive predictive value (67%).

Limitations

Our study did not address prediction of outcomes.

Conclusions

Patients who meet the self-report-based but not the performance-based definition of frailty may represent an intermediate phenotype. A modified self-report definition can improve the accuracy of a questionnaire-based method of defining frailty.