To The Editor:—
We read with much interest the article of Riou et al. 1The authors concluded that the bimodal distribution of probability of survival strongly impacts hypothesis testing in randomized trials by overestimating power.
We would like to point out that statistical power depends only on the average probability of survival for each of the groups, 2not the distribution of the probability of survival (Ps), as the authors claim.
If we have understood the authors’ presentation, it appears that the reported results are a direct consequence of the assumptions that are used to construct their models, i.e. , “if a drug is thought to increase Ps by 10%, when Ps was below 0.50, it was increased by 10% of Ps, and when Ps was greater or equal to 0.50, it was increased by 10% of 1 − Ps.” Their model does not increase the mean Ps by a predictable amount. We illustrate the lack of dependence on a bimodal distribution with a simplified example (table 1) in which there are patients with probability of survival of only 0.2, 0.6, and 0.8 of differing proportions and the treatment increases survival by 0.05 (e.g. , from 0.2 to 0.25).
In the left-hand example of table 1, the distribution has most of the patients with a 0.6 chance of survival, while the right-hand example has a bimodal distribution of patient survival with very few patients in the middle range. Yet, since both examples have the same mean Ps with and without treatment, the power is the same.
We agree that the probabilities of survival would vary greatly in any given sample of trauma patients, between patients who face the greatest probability of mortality or survival regardless of the intervention. The effect size is necessarily minimal at the extremes of the survival probability continuum and can be larger in the middle of the distribution.
Evaluating efficacy in a randomized clinical trial requires the appropriate patient population in which the effect of the intervention can be observed. However, once the appropriate population has been identified, the mean Ps will provide the correct sample size calculations, irrespective of the distribution of probabilities.