Modeling schizophrenic behavior and testing drug efficacy using general mixture components

摘要

A critical idea in the statistical analysis of randomized experiments is that the validity of the significance level for any test-statistic is assured by finding the randomization distribution of that statistic under the null hypothesis. Once theexperiment has been designed and implemented, the randomization distribution is determined, but there is still complete freedom to choose the statistic. Since validity under the null hypothesis is certain for any statistic, the most powerful statisticshould be used to test for the equivalence of treatments, that is, the statistic that is most likely to detect true differences in the treatment conditions. Logically, this statistic should be one that reflects the scientific actions of the treatmentsbeing compared and not simply a convenient off-the-shelf one, such as the difference in mean outcomes between the treatment groups, even if the computational demands in calculating the scientifically relevant statistic are extreme relative to those ofcomputing the off-the-shelf-statistic. Clearly the costs and benefits of drug development are enormous relative to the costs of developing relevant software and subsequent calculations using modern computing equipment, and so it makes absolutely no senseto be concerned with the increase in computational burdens. Despite these facts, it is almost unheard of in the world of drug development to use scientifically powerful statistics this way. Perhaps this is due to a lack of awareness of the benefits ofdoing more sophisticated analyses among researchers. Consequently, we illustrate these critical points about validity and power using data from a randomized experiment comparing drugs for schizophrenic patients, where computing the scientific statisticrequires extensive use of Markov Chain Monte Carlo techniques to fit a model that reflects current understanding of components of schizophrenic behavior.