Master of Science / Department of Statistics / Christopher I. Vahl / Estimation of sample size is an important and critical procedure in the design of clinical trials. A trial with inadequate sample size may not produce a statistically significant result. On the other hand, having an unnecessarily large sample size will definitely increase the expenditure of resources and may cause a potential ethical problem due to the exposure of unnecessary number of human subjects to an inferior treatment. A poor estimate of the necessary sample size is often due to the limited information at the planning stage. Hence, the adjustment of the sample size mid-trial has become a popular strategy recently. In this work, we introduce two methods for sample size re-estimation for trials with a binary endpoint utilizing the interim information collected from the trial: a blinded method and a partially unblinded method. The blinded method recalculates the sample size based on the first stage’s overall event proportion, while the partially unblinded method performs the calculation based only on the control event proportion from the first stage. We performed simulation studies with different combinations of expected proportions based on fixed ratios of response rates. In this study, equal sample size per group was considered. The study shows that for both methods, the type I error rates were preserved satisfactorily.

The problem of this study was to determine the differences in experimentwise and comparisonwise Type I error rate among six multiple comparison procedures when applied to twenty-eight combinations of normally distributed data. These were the Least Significant Difference, the Fisher-protected Least Significant Difference, the Student Newman-Keuls Test, the Duncan Multiple Range Test, the Tukey Honestly Significant Difference, and the Scheffe Significant Difference. The Spjøtvoll-Stoline and Tukey—Kramer HSD modifications were used for unequal n conditions. A Monte Carlo simulation was used for twenty-eight combinations of k and n. The scores were normally distributed (µ=100; σ=10). Specified multiple comparison procedures were applied under two conditions: (a) all experiments and (b) experiments in which the F-ratio was significant (0.05). Error counts were maintained over 1000 repetitions. The FLSD held experimentwise Type I error rate to nominal alpha for the complete null hypothesis. The FLSD was more sensitive to sample mean differences than the HSD while protecting against experimentwise error. The unprotected LSD was the only procedure to yield comparisonwise Type I error rate at nominal alpha. The SNK and MRT error rates fell between the FLSD and HSD rates. The SSD error rate was the most conservative. Use of the harmonic mean of the two unequal sample n's (HSD-TK) yielded uniformly better results than use of the minimum n (HSD-SS). Bernhardson's formulas controlled the experimentwise Type I error rate of the LSD and MRT to nominal alpha, but pushed the HSD below the 0.95 confidence interval. Use of the unprotected HSD produced fewer significant departures from nominal alpha. The formulas had no effect on the SSD.