Designing clinical trials with uncertain estimates of variability
Rationale for the Thesis One of the most important steps in the design of a clinical trial is the estimation of the sample size. For example for a superiority trial, where the data are expected to take a Normal form, the sample size (to achieve a stated power) would be based on a given clinically meaningful difference and an estimate of the population variance. This estimate of the population variance is traditionally based on the assumption of a known sampling variance when in reality this is unknown and has to be estimated. The variance estimate would be derived from an earlier similarly designed study (or a combination from several previous studies) and its precision would depend on its degrees of freedom. There is a need therefore for methods to be developed to deal with the problem of estimating sample size with imprecisely estimated variances. Outcome of the Thesis This thesis provides solutions for the calculation of sample sizes that allow for the imprecision of the estimates used in the calculations. It also shows how the traditional formulae give sample sizes that are too small. The solutions given are for the calculation of sample sizes for different types of trial (superiority, non-inferiority, equivalence, bioequivalence and trials for a given precision) and different forms of data (Normal, binary and ordinal). For Normal data a solution that uses the non-central t-distribution is given, while for binary and ordinal data numerical methods are proposed. For non-inferiority and equivalence trials with a binary outcome it is demonstrated that simple Bayesian methods add value to calculations. Conclusions Standard sample size calculations are shown to have limitations. The main limitation being that no account is made of the imprecision of the estimates used in the calculations. Methods are described in this dissertation that account for these limitations. It is hoped the results would be useful to any researcher calculating a sample size for a prospective clinical study.