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Keywords:

  • Cox regression;
  • goodness-of-fit;
  • grouped data models;
  • interval-grouped failure times;
  • martingale residuals;
  • multiplier processes

Abstract.  Epidemiology research often entails the analysis of failure times subject to grouping. In large cohorts interval grouping also offers a feasible choice of data reduction to actually facilitate an analysis of the data. Based on an underlying Cox proportional hazards model for the exact failure times one may deduce a grouped data version of this model which may then be used to analyse the data. The model bears a lot of resemblance to a generalized linear model, yet due to the nature of data one also needs to incorporate censoring. In the case of non-trivial censoring this precludes model checking procedures based on ordinary residuals as calculation of these requires knowledge of the censoring distribution. In this paper, we represent interval grouped data in a dynamical way using a counting process approach. This enables us to identify martingale residuals which can be computed without knowledge of the censoring distribution. We use these residuals to construct graphical as well as numerical model checking procedures. An example from epidemiology is provided.