Goodness-of-fit test for the parametric proportional hazard regression model with interval-censored data

ABSTRACT Interval-censored data are common in medical research. Fully parametric models provide simple and efficient inference for the estimation of survival functions using interval-censored observations. Inference based on a parametric regression model requires the complete specification of the probability density function, and therefore, correctly specifying the model is crucial, while the regression diagnostic is a very important step. However, regression diagnostic methods for use with the interval-censored data have not been completely developed. Here, we developed a model-checking procedure based on the cumulative martingale residuals for the interval-censored observations. We employed the conditional expectation of residuals for the diagnostics, because the data showing the exact failure time cannot be obtained for the interval-censoring analyses, and developed the formal resampling-based supremum-type test and graphical model-checking techniques. A simulation study demonstrated an excellent performance of the proposed method during the detection of a misspecified functional form of covariates in the finite sample. Furthermore, we used this method for the analysis of the medical checkup data obtained in Japan.