Stratification by stepwise regression, correspondence analysis and recursive partition: a comparison of three methods of analysis for survival data with covariates

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The problem of defining prognostic groups on the basis of censored survival times and covariates is central in medical biostatistics. Several methods have been proposed, but little is known about their relative advantages. Here three methods are discussed: Stepwise Regression, Correspondence Analysis and Recursive Partition. The approach is empirical in that the focus is on the performance on real data sets. Our example is discussed at length. We find that Stepwise Regression has the advantage of flexibility and economy of description, but is limited in discovering interactions and other complex features of the data. Correspondence Analysis is equally flexible, though less economical, and is very powerful in revealing unexpected features of the data: it is recommended as an exploratory tool. Recursive Partition is efficient in discovering interactions within large data sets and has the advantage of being the only method that produces clear descriptions in direct clinical terms; its flexibility, however, is limited, especially when the number of covariates is large relative to the number of individuals. Since no method is universally preferable, their joint use is recommended. A variety of criteria for ranking stratifications are proposed when a choice to be made.