Rejoinder: Time-dynamic profiling with application to hospital readmission among patients on dialysis.

Standard profiling analysis aims to evaluate medical providers, such as hospitals, nursing homes, or dialysis facilities, with respect to a patient outcome. The outcome, for instance, may be mortality, medical complications, or 30-day (unplanned) hospital readmission. Profiling analysis involves regression modeling of a patient outcome, adjusting for patient health status at baseline, and comparing each provider's outcome rate (e.g., 30-day readmission rate) to a normative standard (e.g., national "average"). Profiling methods exist mostly for non time-varying patient outcomes. However, for patients on dialysis, a unique population which requires continuous medical care, methodologies to monitor patient outcomes continuously over time are particularly relevant. Thus, we introduce a novel time-dynamic profiling (TDP) approach to assess the time-varying 30-day readmission rate. TDP is used to estimate, for the first time, the risk-standardized time-dynamic 30-day hospital readmission rate, throughout the time period that patients are on dialysis. We develop the framework for TDP by introducing the standardized dynamic readmission ratio as a function of time and a multilevel varying coefficient model with facility-specific time-varying effects. We propose estimation and inference procedures tailored to the problem of TDP and to overcome the challenge of high-dimensional parameters when examining thousands of dialysis facilities

Performance Characteristics of Profiling Methods and the Impact of Inadequate Case-mix Adjustment.

Profiling or evaluation of health care providers involves the application of statistical models to compare each provider's performance with respect to a patient outcome, such as unplanned 30-day hospital readmission, adjusted for patient case-mix characteristics. The nationally adopted method is based on random effects (RE) hierarchical logistic regression models. Although RE models are sensible for modeling hierarchical data, novel high dimensional fixed effects (FE) models have been proposed which may be well-suited for the objective of identifying sub-standard performance. However, there are limited comparative studies. Thus, we examine their relative performance, including the impact of inadequate case-mix adjustment

Functional linear models for zero-inflated count data with application to modeling hospitalizations in patients on dialysis

We propose functional linear models for zero-inflated count data with a focus on the functional hurdle and functional zero-inflated Poisson (ZIP) models. While 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 (PR), 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 two 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 (PCR)