Sample size is a quantity of immense strategic and ethical importance in treatment development. It is therefore surprising how many misconceptions there are among clinicians and statisticians regarding this topic. There are two parameters directly related to calculation of sample size: power and treatment effect. Let us first define the power of the trial.
Power is conditional probability that trial will be positive according to pre-defined criteria. It is conditional on sample size assumptions being correct. In most cases we get assumptions from prior data, from our, or a similar product. Here we must deal with many uncertainties: similarity between products and trial designs, impact of different time periods, and more. Other issues are uncertainty in observed treatment effect, and dose selection bias when applicable.
The usual convention is that power is fixed at 80% or 90% level. In my view there is no reason for this. Two real constraints are sample size (budget) and treatment effect. If budget is not a constraint, then power can be fixed at a desired level. However, given all uncertainties with assumptions one does not have to obsess with this.
It is far more important to evaluate the relationship between sample size and power, as illustrated in Figure 1. At smaller sample sizes power increases sharply. It then levels off, and at some point it becomes flat. Meaning, one keeps on investing in sample size with no gain. Larger sample sizes increase cost and time, and if there is little or no gain then sponsor starts experiencing diminishing returns. This is illustrated in Figure 2.
Uncertainty with assumptions should
not prevent us from doing thorough research when planning the study. Much greater assurance can be gained by incorporation of interim analyses, whether this will be done by stopping rules, sample size increase, or Bayesian updating. Finally, it is extremely important to look at the impact of sample size on the whole program, or even portfolio.
Authored by:
Zoran Antonijevic is Chief Scientific Officer at Bioforum. He held executive positions in Pharmaceutical Companies and CROs and designed more than 100 clinical trials in numerous therapeutic areas, many of which included adaptive designs. Zoran was a long-time Chair and leader of the DIA Adaptive Design Scientific Working Group. He has authored numerous papers and scientific presentations and was editor of books “Optimization of Pharmaceutical R&D Programs and Portfolios” and, together with Bob Beckman, “Platform Trials in Drug Development”.