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Non-parametric frailty Cox models for hierarchical time-to-event data.

Authors
  • Gasperoni, Francesca1
  • Ieva, Francesca1
  • Paganoni, Anna Maria1
  • Jackson, Christopher H2
  • Sharples, Linda3
  • 1 MOX - Modelling and Scientific Computing, Department of Mathematics Politecnico di Milano, Piazza Leonardo Da Vinci 32, Milano 20123, Italy. , (Italy)
  • 2 MRC Biostatistics Unit, Cambridge Institute of Public Health, Forvie Site, Robinson Way, Cambridge Biomedical Campus, Cambridge CB2 0SR, UK.
  • 3 Department of Medical Statistics, London School of Hygiene & Tropical Medicine, Keppel Street, London WC1E 7HT, UK.
Type
Published Article
Journal
Biostatistics (Oxford, England)
Publication Date
Jul 01, 2020
Volume
21
Issue
3
Pages
531–544
Identifiers
DOI: 10.1093/biostatistics/kxy071
PMID: 30590499
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

We propose a novel model for hierarchical time-to-event data, for example, healthcare data in which patients are grouped by their healthcare provider. The most common model for this kind of data is the Cox proportional hazard model, with frailties that are common to patients in the same group and given a parametric distribution. We relax the parametric frailty assumption in this class of models by using a non-parametric discrete distribution. This improves the flexibility of the model by allowing very general frailty distributions and enables the data to be clustered into groups of healthcare providers with a similar frailty. A tailored Expectation-Maximization algorithm is proposed for estimating the model parameters, methods of model selection are compared, and the code is assessed in simulation studies. This model is particularly useful for administrative data in which there are a limited number of covariates available to explain the heterogeneity associated with the risk of the event. We apply the model to a clinical administrative database recording times to hospital readmission, and related covariates, for patients previously admitted once to hospital for heart failure, and we explore latent clustering structures among healthcare providers. © The Author 2018. Published by Oxford University Press.

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