Using Cox's proportional hazards regression model in the presence of non-proportional hazards, i.e., with underlying time-dependent hazard ratios of prognostic factors, may lead to possibly biased estimates of the average hazard ratio and a reduction of the testing power of the corresponding estimates. This bias is a consequence of the combination of censoring and non-proportional hazards. Concordance regression, which is based on conditional logistic regression on risk pairs rather than risk sets, provides unbiased estimates of the average hazard ratio under censoring, even under non-proportional hazards. This average hazard ratio directly translates into an estimate of the concordance index, i. e., the probability that the event occurs earlier in group 1 compared to group 0, or into an estimate of the generalized concordance index, i. e., the probability than the event occurs earlier in an individual with a continuous covariable value of x+1 compared to an individual with a value of x. Concordance regression has been implemented in an R package concreg. For more information concerning concordance regression we refer to Dunkler et al. 2010. This paper shows how to apply the method for ranking genes by their association with survival irrespective of the assumption of proportional hazards.
Dunkler, D., Schemper, M., Heinze, G. (2010): "Gene selection in microarray survival studies under possibly non-proportional hazards", Bioinformatics 26, 784 - 790
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