sample size

randomized trials

sample size calculation

historical data

type error

Clinical Trials

Background/Aims For single arm trials, a treatment is evaluated by comparing an outcome estimate to historically reported outcome estimates. Such a historically controlled trial is often analyzed as if the estimates from previous trials were known without variation and there is no trial-to-trial variation in their estimands. We develop a test of treatment efficacy and sample size calculation for historically controlled trials that considers these sources of variation. Methods We fit a Bayesian hierarchical model, providing a sample from the posterior predictive distribution of the outcome estimand of a new trial, which, along with the standard error of the estimate, can be used to calculate the probability that the estimate exceeds a threshold. We then calculate criteria for statistical significance as a function of the standard error of the new trial and calculate sample size as a function of difference to be detected. We apply these methods to clinical trials for amyotrophic lateral sclerosis using data from the placebo groups of 16 trials. Results We find that when attempting to detect the small to moderate effect sizes usually assumed in amyotrophic lateral sclerosis clinical trials, historically controlled trials would require a greater total number of patients than concurrently controlled trials, and only when an effect size is extraordinarily large is a historically controlled trial a reasonable alternative. We also show that utilizing patient level data for the prognostic covariates can reduce the sample size required for a historically controlled trial. Conclusion This article quantifies when historically controlled trials would not provide any sample size advantage, despite dispensing with a control group.

Design and analysis of a clinical trial using previous trials as historical control