Partial orders with respect to continuous covariates and tests for the proportional hazards model

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    Abstract

    Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against ordered alternatives like monotone hazard ratio and monotone ratio of cumulative hazards. Here we propose a natural extension of these partial orders to the case of continuous and potentially time varying covariates, and develop tests for the proportional hazards assumption against such ordered alternatives. The work is motivated by applications in biomedicine and economics where covariate effects often decay over lifetime. The proposed tests do not make restrictive assumptions on the underlying regression model, and are applicable in the presence of time varying covariates, multiple covariates and frailty. Small sample performance and an application to real data highlight the use of the framework and methodology to identify and model the nature of departures from proportionality. © 2010 Elsevier B.V.
    Original languageEnglish
    Pages (from-to)243-261
    Number of pages19
    JournalJournal of Statistical Planning and Inference
    Volume141
    Issue number1
    DOIs
    Publication statusPublished - Jan 2011

    Keywords

    • two-sample tests
    • increasing hazard ratio
    • continuous covariate
    • proportional hazards
    • frailty
    • partial orders of lifetime distributions
    • time varying coefficients

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