Authors: Bruno Mario Cesana
Publish Date: 2015/10/21
Volume: 42, Issue: 1, Pages: 136-136
Abstract
It is well known that RCTs are based on a null hypothesis H0 of no difference and on an alternative hypothesis HA quantified on the “minimal clinical relevant difference δ” superiority RCTs or on the “maximal difference not clinically relevant” noninferiority and equivalence RCTs or better for continuous variables on the effect size δ divided by the variability of the investigated phenomenon σ Then after having fixed the significance level α = 005 two tailed usually and the pertinent statistical test it is possible to calculate the sample size to be reported in the paper 2 for having a satisfactory probability power 080 at least of rejecting H0 Of course if the HA is true with a larger difference effect size than the foreseen one the probability of rejecting H0 will be greater and vice versa if the true difference effect size is lowerThen according to the frequentist approach 3 it is expected that if the foreseen HA is “true” it will be demonstrated in about the 80 of the cases power correct rejection of a “false” H0 and in the remaining about 20 H0 will not be disproved β type II error Finally the probability of wrongly rejecting a “true” H0 α type I error is equal to the fixed significance level αA very frequent cause of “negative” RCTs is an overoptimistic HA often for having a lower number of patients to enrol into the RCTs indeed two “negative” trials see references 8 and 10 in 1 supposed a too high 20 decrease of the mortality in favour of the prone position vs the supine positionFinally it has to be said that researchers tend to wrongly interpret the significance value as the probability that the H0 is “true” instead of correctly the probability of having obtained the result only by chance In fact in order to calculate the probability that H0 is “true” one has to consider that the H0 and also the HA has “a priori” probability of being “true” ranging in theory from 000 to 100 So by multiplying the “a priori” probability of a “true” H0 by the “Bayes factor” that one can calculate from the significance p value 4 5 it is possible to obtain the “a posteriori” probability of H0 being true For example statistically significant p values of 005 decrease the “a priori” probability of 005 very unfavourable 050 equipoiselike or tossup and 095 very favourable to about 0013 0205 and 0831 respectively So the probability of a significant result can be sensibly used to critically consider the probability that H0 is actually “true”
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