ABSTRACT
This chapter introduces some basic concepts regarding survival and hazard functions, which are commonly used in the analysis of time-to-event data. In practice, hypotheses of clinical interest are often involved in comparing median survival times, survival functions, and hazard rates. Formulas for sample size calculation based on hazard rates for median survival times and survival functions between treatment groups will be derived under an exponential model, which is the simplest parametric statistical model for time-to-event data. The chapter derives formulas for sample size calculation for testing equality, noninferiority/superiority, and equivalence in two-sample problems under the commonly used exponential model. It presents formulas for sample size calculation under Cox's proportional hazards model. The chapter also derives formulas for sample size estimation based on the weighted log-rank test and discusses some practical issues. Further research in sample size estimation based on a fixed alternative is an interesting but challenging topic for statisticians in the pharmaceutical industry.
