TITLE:
Marginal Distribution Plots for Proportional Hazards Models with Time-Dependent Covariates or Time-Varying Regression Coefficients
AUTHORS:
Qiqing Yu, Junyi Dong, George Wong
KEYWORDS:
Cox’s Model, Time-Dependent Covariate, Semi-Parametric Set-Up, Diagnostic Plot
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.1,
February
27,
2017
ABSTRACT: Given a sample of regression data from (Y, Z), a new diagnostic plotting method is proposed for checking the hypothesis H0: the data are from a given Cox model with the time-dependent covariates Z. It compares two estimates of the marginal distribution FY of Y. One is an estimate of the modified expression of FY under H0, based on a consistent estimate of the parameter under H0, and based on the baseline distribution of the data. The other is the Kaplan-Meier-estimator of FY, together with its confidence band. The new plot, called the marginal distribution plot, can be viewed as a test for testing H0. 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.