We thanks Drs. Halim and McCulloch for their comment. They are correct in their calculation (table 1) but wrong in the use of this calculation. They made the hypothesis that the difference between groups (placebo and treated groups, for example) is a fixed proportion (here +10%), whatever the value of the probability of survival (Ps) is. This assumption cannot be correct from a clinical point of view. Indeed, if we look for a group of patients with a very low Ps (i.e. , 0.01), the calculation from Drs. Halim and McCulloch suggests that the Ps could be 0.16 in the treated group. In the same manner, if the Ps is very high (i.e. , 0.99), what could be the Ps in the treated group—more than 100%? In these two situations, those are not drug effects, but miracles.
We must recognize that in our study, 1we tested only one simple hypothesis, concerning the relationship between Ps in the treated group and Ps in the placebo group, and that several other types of relationships could be used. For example, one can test the hypothesis that the drug-related increase in Ps (i.e. , the drug effect) is more pronounced in the most severely injured patients (or the contrary). But, whatever the hypothesis used, it must be clinically relevant, and the one proposed by Drs. Halim and McCulloch is not.
We must remember that several factors influence the number of patients to be included:α risk, β risk, the difference expected between groups, and last, but not least, the value of mortality in the placebo group. Assuming an α and β risks of 0.05 and a 50% decrease in mortality in the treatment group, we need more patients if the mortality in the placebo group is 5% (n = 3,154) than if it is 50% (n = 106). In trauma patients, as we demonstrated in our study, 1the mean mortality does not represent anything because of the bimodal distribution.