A double-Cox model for non-proportional hazards survival analysis with frailty.

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  • Author(s): Begun A;Begun A; Kulinskaya E; Kulinskaya E; Ncube N; Ncube N
  • Source:
    Statistics in medicine [Stat Med] 2023 Aug 15; Vol. 42 (18), pp. 3114-3127. Date of Electronic Publication: 2023 May 15.
  • Publication Type:
    Journal Article; Research Support, Non-U.S. Gov't
  • Language:
    English
  • Additional Information
    • Source:
      Publisher: Wiley Country of Publication: England NLM ID: 8215016 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1097-0258 (Electronic) Linking ISSN: 02776715 NLM ISO Abbreviation: Stat Med Subsets: MEDLINE
    • Publication Information:
      Original Publication: Chichester ; New York : Wiley, c1982-
    • Subject Terms:
      Frailty* ; Diabetes Mellitus, Type 2*; Humans ; Proportional Hazards Models ; Likelihood Functions ; Survival Analysis
    • Abstract:
      The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we propose to parameterize the shape parameter of the baseline hazard function using the additional, separate Cox-regression term which depends on the vector of the covariates. This parametrization retains the general form of the hazard function over the strata and is similar to one in Devarajan and Ebrahimi (Comput Stat Data Anal. 2011;55:667-676) in the case of the Weibull distribution, but differs for other hazard functions. We call this model the double-Cox model. We formally introduce the double-Cox model with shared frailty and investigate, by simulation, the estimation bias and the coverage of the proposed point and interval estimation methods for the Gompertz and the Weibull baseline hazards. For real-life applications with low frailty variance and a large number of clusters, the marginal likelihood estimation is almost unbiased and the profile likelihood-based confidence intervals provide good coverage for all model parameters. We also compare the results from the over-parametrized double-Cox model to those from the standard Cox model with frailty in the case of the scale-only proportional hazards. The model is illustrated on an example of the survival after a diagnosis of type 2 diabetes mellitus. The R programs for fitting the double-Cox model are available on Github.
      (© 2023 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)
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    • Contributed Indexing:
      Keywords: Cox regression; marginal likelihood; parametric survival analysis; shape and scale modeling; shared frailty
    • Publication Date:
      Date Created: 20230516 Date Completed: 20230718 Latest Revision: 20240320
    • Publication Date:
      20240320
    • Accession Number:
      PMC10946853
    • Accession Number:
      10.1002/sim.9760
    • Accession Number:
      37190904