Goodness-of-fit test for monotone proportional subdistribution hazards assumptions based on weighted residuals

Recently goodness-of-fit tests have been proposed for checking the proportional subdistribution hazards assumptions in the Fine and Gray regression model. Zhou, Fine, and Laird proposed weighted Schoenfeld-type residuals tests derived under an assumed model with specific form of time-varying regression coefficients. Li, Sheike, and Zhang proposed an omnibus test based on cumulative sums of Schoenfeld-type residuals. In this article, we extend the class of weighted residuals tests by allowing random weights of Schoenfeld-type residuals at ordered event times. In particular, it is demonstrated that weighted residuals tests using monotone weight functions of time are consistent against monotone proportional subdistribution hazards assumptions. Extensive Monte Carlo studies were conducted to evaluate the finite-sample performance of recent goodness-of-fit tests. Results from simulation studies show that weighted residuals tests using monotone random weight functions commonly used in non-proportional hazards regression settings tend to be more powerful for detecting monotone departures than other goodness-of-fit tests assuming no specific time-varying effect or misspecified time-varying effects. Two examples using real data are provided for illustrations. Copyright © 2016 John Wiley & Sons, Ltd.