Further results on the non‐parametric linear regression model in survival analysis

Abstract

This paper gives further developments of a non-parametric linear regression model in survival analysis. Three subjects are studied. First, martingale residuals, originally developed for the Cox model, are introduced for our linear model. Their theory is developed and they are shown to be useful for judging goodness of fit. The second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation. In particular, this is applied to judging whether the effect of a covariate disappears over time, a problem for which no formal test exists. The third subject is density type, or kernel, estimation of the regression functions themselves. This might give more direct information than the cumulative plots. The approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx, and by survival times of grafts in renal patients.