Journal of Data Science

Abstract: Early phase clinical trials may not have a known variation (σ) for the response variable. In the light of applying t-test statistics, several procedures were proposed to use the information gained from stage-I (pilot study) to adaptively re estimate the sample size for managing the overall hypothesis test. We are interested in choosing a reasonable stage-I sample size (m) towards achieving an accountable overall sample size (stage-I and later). Conditional on any specified m, this paper replaces σ by the estimated σ (from stage-I with sample size m) to use the conventional formula under normal distribution assumption to re-estimate an overall sample size. The estimated σ, re-estimated overall sample size and the collective information (stage-I and later) would be incorporated into a surrogate normal variable which undergoes hypothesis test based on standard normal distribution. We plot the actual type I&II error rates and the expected sample size against m in order to choose a good universal stage-I sample size (𝑚∗ ) to start