Gene selection in microarray survival studies under possibly non-proportional hazards

Motivation: Univariate Cox regression (COX) is often used to select genes possibly linked to survival. With non-proportional hazards (NPH), COX could lead to under-or over-estimation of effects. The effect size measure c= P(T-1< T-0), i.e. the probability that a person randomly chosen from group G1 dies earlier than a person from G(0), is independent of the proportional hazards (PH) assumption. Here we consider its generalization to continuous data c' and investigate the suitability of c' for gene selection. Results: Under PH, c' is most efficiently estimated by COX. Under NPH, c' can be obtained by weighted Cox regression (WHE) or a novel method, concordance regression (CON). The least biased and most stable estimates were obtained by CON. We propose to use c' as summary measure of effect size to rank genes irrespective of different types of NPH and censoring patterns.