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Diagnostic Measures for the Cox Regression Model with Missing Covariates
Hongtu Zhu1, Joseph G Ibrahim2, Ming-Hui Chen3
1Department of Biostatistics, University of North Carolina at Chapel Hill, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A. hzhu@bios.unc.edu.
Abstract:
This paper investigates diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for the Cox regression model. Our diagnostics include case-deletion measures, conditional martingale residuals, and score residuals. The Q-distance is proposed to examine the effects of deleting individual observations on the estimates of finite-dimensional and infinite-dimensional parameters. Conditional martingale residuals are used to construct goodness of fit statistics for testing possible misspecification of the model assumptions. A resampling method is developed to approximate the p-values of the goodness of fit statistics. Simulation studies are conducted to evaluate our methods, and a real data set is analyzed to illustrate their use.
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