Multiplicity false discovery rate control

Statistical analysis should be appropriate to the types of outcome data collected and the number of genotypes nsed in the analysis. The handling of missing data should be clearly stated. Corrections for multiple comparisons (e.g., controlling for false discovery rates 36) should be performed if multiple statistical tests are carried out. 

Benjamini, Y., and Hochberg, Y. (1995) Controlling false discovery rate a practical and powerful approach to multiple testing. J R Statist Soc Br. 57, 289-300. 

Belief that a very small p-value for a predictor (for example, a biomarker) is more likely to occur with high predictive accuracy. The multiple testing problem must not be ignored, and the false discovery rate (FDR) controlled see also Chapter 6. 

Suppose that we wish to make inferences on the parameters 0i,i = 1,g, where 9i represents the logarithm of the ratio of the expression levels of gene i under normal and disease conditions. If the ith gene has no differential expression, then the ratio is 1 and hence 0 = 0. In testing the g hypotheses Ho, 0 = 0, / = 1,..., g, suppose we set R, = 1 if H0, is rejected and Ri = 0 otherwise. Then, for any multiple testing procedure, one could in theory provide a complete description of the joint distribution of the indicator variables R, ..., Rg as a function of 0i,..., 0g in the entire parameter space. This is impractical if g > 2. Different controls of the error rate control different aspects of this joint distribution, with the most popular being weak control of the familywise error rate (FWER), strong control of the familywise error rate, and control of the false discovery rate (FDR). 

Y. Benjamini and D. Yekutieh, The control of the false discovery rate in multiple tests under dependency. Ann Stat 29 1165-1188 (2001). 

Benyamini Y, Hochberg Y. 1995. Controlling the false discovery rate A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society Series B 57 289-300. 

Benjamini, Y. Hochberg, Y. (1995). Controlling the False Discovery Rate A practical and Powerful Approach to Multiple Testing. Journal of The Royal Statistical Society, Vol. Ser B 57, pp. 289-300. 

In the framework of a generalized linear model, linear model decompositions (contrasts) are done in the usual traditional way. For example, if one compares controls against each of the test compounds, this is an a priori linear contrast and sufficient degrees of freedom exist to avoid a multiple comparisons adjustment. However, if one also compares each compound to every other one, or against a deet positive control, then one is making more comparisons than allowed for with the degrees of freedom (the multiple comparisons scenario) and an adjustment, either on the test statistic or the p value, is needed. A Bonferroni adjustment is an example of an adjustment on the p value better methods exist—a contemporary one is to adjust for the false discovery rate. 

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