In any applied setting, performing a proportional hazards regression analysis of survival data requires a number of critical decisions. It is likely that we will have data on more covariates than we can reasonably expect to include in the model, so we must decide on a method to select a subset. We must consider such issues as clinical importance and adjustment for confounding, as well as statistical significance. Once we have selected the subset, we must determine whether the model is “linear” in the continuous covariates and, if not, what transformations are suggested by the data and clinical considerations. Which interactions, if any, should be included in the model is another important decision. In this chapter, we discuss these and other practical model development issues.
The end use of the estimated regression model will most often be a summary presentation and interpretation of the factors that have influenced survival. This summary may take the form of a table of estimated hazard ratios and confidence intervals and/or estimated covariate–adjusted survival functions. Before this step can be taken, we must critically examine the estimated model for adherence to key assumptions (e.g., proportional hazards) and determine whether any subjects have an undue influence on the fitted model. In addition, we may calculate summary measures of goodness-of-fit to support our efforts at model assessment. Methods for model assessment are discussed ...