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

• Activity Number: 489
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Michael Fay*+ and Michael A. Proschan and Erica Brittain
• Companies: National Institute of Allergy and Infectious Diseases and National Institute of Allergy and Infectious Diseases and National Institute of Allergy and Infectious Diseases
• Keywords: clinical trials ; exact tests ; fixed-time survival ; Kaplan-Meier ; survival analysis

Abstract

When comparing survival between a harsh treatment and a standard one, early treatment related failures can make logrank-type tests inappropriate. A better option is to compare survival at a pre-specified fixed time, representing a longer term survival. We develop a test and associated confidence intervals for the difference in survival at a fixed time. The methods are developed without relying on asymptotics, and all simulations and mathematical results suggest that the tests bound the type I error rate and confidence intervals provide at least nominal coverage with any independent censoring distribution. For the special case of no censoring, the one-sided p-value from the test is equivalent to Fisher's exact test p-value. The confidence intervals on the difference in survival match the test, so that if the 100(1-alpha)% confidence interval does not contain a difference of 0, then the test rejects at level alpha.