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Several possible definitions of residuals are given for relative risk regression with time-varying covariates. Each such residual has a representation as an estimator of a stochastic integral with respect to the martingale arising from a subject's failure time counting process. Previously proposed residuals for individual study subjects and for specific time points are shown to be special cases of this definition, as are previously derived regression diagnostics. An illustration and various generalizations are also given.
Barlow et al. (Fri,) studied this question.