Proportional hazards regression for cancer studies.

There has been some recent work in the statistical literature for modeling the relationship between the size of cancers and probability of detecting metastasis, i.e., aggressive disease. Methods for assessing covariate effects in these studies are limited. In this article, we formulate the problem as assessing covariate effects on a right-censored variable subject to two types of sampling bias. The first is the length-biased sampling that is inherent in screening studies; the second is the two-phase design in which a fraction of tumors are measured. We construct estimation procedures for the proportional hazards model that account for these two sampling issues. In addition, a Nelson-Aalen type estimator is proposed as a summary statistic. Asymptotic results for the regression methodology are provided. The methods are illustrated by application to data from an observational cancer study as well as to simulated data.