A method for determining the optimum transform for covariates of the Cox model with application to 3680 cases of intraocular melanoma.

For most applications of the Cox Model, a simple exponential relationship is assumed between covariates of this model and relative force of mortality (lambda). A method has been developed to examine this relationship in detail for data sets that contain a sufficient number of deaths. This method was applied to 3680 cases of intraocular melanoma with 1178 deaths over 20 years of follow-up, using largest tumor dimension (LTD) as a predictor of tumor-related death. Results indicated that the transform lambda = exp[beta log LTD] provides a closer approximation to observed mortality for this data set than the more traditional lambda = exp [beta LTD]. Additional applications to mathematically generated data sets revealed a close correspondence between lambda estimated by this method and the lambda programmed into each data set.