Two-Sample Test for Differences in Survival at a Fixed Time Point with Small Sample Sizes

• Activity Number: 321
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Michael Fay*+ and Michael Proschan and Erica H. Brittain
• Companies: National Institute of Allergy and Infectious Diseases and NIH and National Institute of Allergy and Infectious Diseases
• Keywords: clinical trials ; exact tests ; fixed-time survival ; Kalpan-Meier ; survival analysis

Abstract

Consider a two sample study where the primary endpoint is survival until a fixed pre-specified time. This endpoint is important for comparing two treatments for a serious disease, where the hazards could have very different patterns between the treatments, even under the null hypothesis. For example, patients on placebo typically get worse steadily, while patients on a new onerous treatment may have higher death rates immediately following treatment but then, if they survive treatment, are essentially cured. The logrank test is not appropriate for this situation, and typically we instead compare the Kaplan-Meier curves at the fixed time. We consider the small sample case, where asymptotic methods cannot be used. Assumptions for permutation tests are not met in this situation since the strong null of no differences between treatments at every time point is not appropriate. We develop a new test using the recently developed beta product confidence procedure for survival data on each treatment group. The test reduces to Fisher's exact test when there is no censoring, and is expected to bound (or approximately bound) the type I error rate when censoring is present.