Con dence Regions For The Equality OfTwo Survival

Often when comparing the survival rates of individuals given either of two treatments the analysis stops with a test of the hypothesis of no treatment diierence and perhaps a plot of the two survival functions. The hypothesis test is usually a comparison of the two survival curves over the entire observational period. An alternative approach to this problem is to provide an investigator with a conndence region for the set of times at which the survival rates of the two treatments are the same. We discuss how such conndence regions can be constructed in three situations. First, we construct conndence regions when there are no additional factors that need be adjusted for. Second, based on a proportional hazards model, we show how to construct the desired conndence regions adjusted for explanatory covariates that are not confounded with the two treatments. Lastly, we extended these results to allow for explanatory covariates that are confounded with treatment. These approaches are illustrated on retrospective data gathered to compare the survival rates of allogeneic and autologous bone marrow transplants for acute leukemia.