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

Damla Şentürk, Lorien Dalrymple, Danh V. Nguyen

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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 2years 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.

Original languageEnglish (US)
Pages (from-to)4825-4840
Number of pages16
JournalStatistics in Medicine
Volume33
Issue number27
DOIs
StatePublished - Nov 30 2014

Keywords

  • End-stage renal disease
  • Functional data analysis
  • Hurdle model
  • Sparse longitudinal design
  • United States Renal Data System
  • Zero-inflated Poisson model

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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