MultiTest V.1.2, a program to binomially combine independent tests and performance comparison with other related methods on proportional data

Background: Combining multiple independent tests, when all test the same hypothesis and in the same direction, has been the subject of several approaches. Besides the inappropriate (in this case) Bonferroni procedure, the Fisher's method has been widely used, in particular in population genetics. This last method has nevertheless been challenged by the SGM (symmetry around the geometric mean) and Stouffer's Z-transformed methods that are less sensitive to asymmetry and deviations from uniformity of the distribution of the partial P-values. Performances of these different procedures were never compared on proportional data such as those currently used in population genetics. Results: We present new software that implements a more recent method, the generalised binomial procedure, which tests for the deviation of the observed proportion of P-values lying under a chosen threshold from the expected proportion of such P-values under the null hypothesis. The respective performances of all available procedures were evaluated using simulated data under the null hypothesis with standard P-values distribution (differentiation tests). All procedures more or less behaved consistently with similar to 5% significant tests at alpha = 0.05. Then, linkage disequilibrium tests with increasing signal strength (rate of clonal reproduction), known to generate highly nonstandard P-value distributions are undertaken and finally real population genetics data are analysed. In these cases, all procedures appear, more or less equally, very conservative, though SGM seems slightly more conservative. Conclusion: Based on our results and those discussed in the literature we conclude that the generalised binomial and Stouffer's Z procedures should be preferred and Z when the number of tests is very small. The more conservative SGM might still be appropriate for meta-analyses when a strong publication bias in favour of significant results is expected to inflate type 2 error.