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

• Published in: Statistics in medicine Vol. 33; no. 27; pp. 4825 - 4840
• Main Authors: Şentürk, Damla, Dalrymple, Lorien S., Nguyen, Danh V.
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 30.11.2014; Wiley Subscription Services, Inc
• Subjects: Albumins - analysis; Computer Simulation; Cross-Sectional Studies - methods; Data Interpretation, Statistical; end-stage renal disease; functional data analysis; Hemodialysis; Hospitalization; Humans; hurdle model; Kidney Failure, Chronic - blood; Kidney Failure, Chronic - therapy; Likelihood Functions; Linear Models; Medical statistics; Patients; Poisson Distribution; Renal Dialysis; Simulation; sparse longitudinal design; United States Renal Data System; zero-inflated Poisson model; United States Renal Data System; functional data analysis; hurdle model; end-stage renal disease; sparse longitudinal design; zero-inflated Poisson model
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.6241

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. Copyright © 2014 John Wiley & Sons, Ltd.