The Identification of Risk Factors: the Control of the Significance Level in Multiple Comparisons

A common problem in statistical medical analyses is the identification of risk factors associated with a certain disease. The collected sampled data are used to assess simultaneously more hypotheses, each of which assesses the influence of one factor. It is well known that the simultaneous assessment of two or more hypotheses entails a rise in the probability of rejecting at least one of the true null partial hypotheses. In this paper the rise in this probability is approximately evaluated for different levels of dependance between factors by means of a permutation-based procedure. The paper also proposes a procedure which computes an adjusted p-value for each test of the partial hypotheses in such a way that the global hypothesis that none of the factors have influence is assessed at a prefixed significance level. A simulation study is performed to check the power of the proposed procedure