Parametric Control of Familywise Error Rates with Dependent P-Values

Many research areas require multiple outcomes. For example, neuropsychological hypotheses may not be testable using a single measure. Similarly, genetic researchers frequently examine multiple markers across the genome. Examining multiple hypotheses requires the use of multiple testing procedures (MTPs) to control Type I error. The application of MTPs is significant to public health researchers because of the danger of declaring false inferences. Researchers need MTPs to control such error while maintaining power to detect real effects. Two specific error rates include the familywise error rate (FWER) and the generalized FWER (k-FWER). We begin with an examination of ten FWER MTPs with respect to a key multiple testing issue, p-value dependence. This preliminary look illuminated the benefit of stepwise methods over single-step counterparts, the strengths and challenges of nonparametric, resampling-based methods, and the insufficiency of parametric methods in addressing p-value dependence. This dissertation continues with proposals for new, parametric, step-down (SD) MTPs that incorporate correlation information with the aim to control the FWER and k-FWER. By simulation studies and applications to a microarray data example, we compared these proposed methods against several existing MTPs, including the nonparametric SD minP and SD k-minP methods, considered here as the benchmark MTPs. The proposed FWER and k-FWER methods approximated the error and power of the comparison SD minP and SD k-minP methods more closely than the other parametric MTPs. The proposed FWER method demonstrated notable FWER control. The proposed k-FWER method exhibited a degree of error, suggesting the need for further refinement.