Checking the Grouped Data Version of the Cox Model for Interval-grouped Survival Data

• Published in: Scandinavian journal of statistics Vol. 34; no. 2; pp. 405 - 418
• Main Authors: PIPPER, CHRISTIAN B., RITZ, CHRISTIAN
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.2007; Blackwell Publishing; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: Applications; Biostatistics; Censored data; Censorship; Conditional convergence; Covariance; Cox regression; Data models; Epidemiology; Exact sciences and technology; Failure analysis; General topics; Generalized linear models; goodness-of-fit; grouped data models; interval-grouped failure times; Kolmogorov Smirnov test; martingale residuals; Martingales; Mathematical models; Mathematics; Medical sciences; Modeling; multiplier processes; Multivariate analysis; Nonparametric inference; Parametric models; Probability and statistics; Sciences and techniques of general use; Statistical methods; Statistics; Studies; Survival analysis; Temporal data; Generalized linear model; Censored sample; Epidemiology; Linear model; Survival function; Failure analysis; grouped data models; Distribution function; Survival model; Cox regression; interval-grouped failure times; Survival data; Data analysis; martingale residuals; Grouped data; Martingale; goodness-of-fit; Survival; Data reduction; Statistical method; Counting process; Cox model; Failure time; multiplier processes; Graphic method; Application
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2006.00537.x

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.