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A class of omnibus chi-squared goodness-of-fit tests is presented for the model, relating failure time to covariate values, proposed by Cox (1972). These tests are based on the expected and observed frequency that a data point, representing a failure with associated covariates, falls into one of L mutually exclusive categories. Different partitions of the space of covariate values and failure time will yield different tests. Certain partitions are suggested for the goodness-of-fit problems commonly encountered in clinical trials.
David Schoenfeld (1980) studied this question.