Robust Simulation for Decisional Problems Applied for Drug Testing

This paper is inspired from specific situations for the early phases of drugs testing. The particularity of the problem consists in the small dimension of the analyzed samples. For this reason, there is a presumption that the small dimension of samples affects the result of ANOVA statistical tests, when multiples groups have to be compared. Six dermatological treatments are tested on groups of ten patients each to test their effect on particular affections. In order to observe a difference between treatments an ANOVA technique is applied. The result suggests that no statistically significant difference can be observed between the six drugs. For objective reasons, despite the result of ANOVA, a hierarchy between drug’s variants must be established taking into account the general effect on the observed affections. The statistical inferential problem is converted into a decisional problem with weighted criteria of evaluation. The general decisional situation in which a set of alternatives are evaluated from the point of view of a set of criteria of evaluation is modeled and simulated. Then, the model is applied for the pharmaceutical problem. The robustness of the method of weighting the criteria of evaluation is studied using the empirical influence curve. Applying this method of ranking, one of the six creams is recommended as optimal with respect to all criteria of evaluation. The advantage of such an approach is that an inferential deadlock, due to the small number of data, can be surpassed. Computer implementations are made using Matlab.