Marginal Distribution Plots for Proportional Hazards Models with Time-Dependent Covariates or Time-Varying Regression Coefficients
- 1 Department of Mathematical Sciences, SUNY, Binghamton, NY, USA
- 2 Department of Mathematical Sciences, SUNY, Binghamton, NY, USA
- 3 Department of Integrative Medicine, Mount Sinai Beth Israel, New York, NY, USA
Abstract
Given a sample of regression data from ( Y, Z ), a new diagnostic plotting method is proposed for checking the hypothesis H 0 : the data are from a given Cox model with the time-dependent covariates Z . It compares two estimates of the marginal distribution F Y of Y . One is an estimate of the modified expression of F Y under H 0 , based on a consistent estimate of the parameter under H 0 , and based on the baseline distribution of the data. The other is the Kaplan-Meier-estimator of F Y , together with its confidence band. The new plot, called the marginal distribution plot, can be viewed as a test for testing H 0 . The main advantage of the test over the existing residual tests is in the case that the data do not satisfy any Cox model or the Cox model is mis-specified. Then the new test is still valid, but not the residual tests and the residual tests often make type II error with a very large probability.
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