A pure likelihood approach to the analysis of genetic association data: an alternative to Bayesian and frequentist analysis.

Investigators performing genetic association studies grapple with how to measure strength of association evidence, choose sample size, and adjust for multiple testing. We apply the evidential paradigm (EP) to genetic association studies, highlighting its strengths. The EP uses likelihood ratios (LRs), as opposed to P-values or Bayes' factors, to measure strength of association evidence. We derive EP methodology to estimate sample size, adjust for multiple testing, and provide informative graphics for drawing inferences, as illustrated with a Rolandic Epilepsy (RE) fine-mapping study. We focus on controlling the probability of observing weak evidence for or against association (W) rather than type I errors (M). For example, for LR> or =32 representing strong evidence, at one locus with n=200 cases, n=200 controls, W=0.134, whereas M=0.005. For n=300 cases and controls, W=0.039 and M=0.004. These calculations are based on detecting an OR=1.5. Despite the common misconception, one is not tied to this planning value for analysis; rather one calculates the likelihood at all possible values to assess evidence for association. We provide methodology to adjust for multiple tests across m loci, which adjusts M and W for m. We do so for (a) single-stage designs, (b) two-stage designs, and (c) simultaneously controlling family-wise error rate (FWER) and W. Method (c) chooses larger sample sizes than (a) or (b), whereas (b) has smaller bounds on the FWER than (a). The EP, using our innovative graphical display, identifies important SNPs in elongator protein complex 4 (ELP4) associated with RE that may not have been identified using standard approaches.