Blindly Using Wald's Test Can Miss Rare Disease-Causal Variants in Case-Control Association Studies

There are four tests the likelihood ratio (LR) test, Wald's test, the score test and the exact test commonly employed in genetic association studies. On comparison of the four tests, we found that Wald's test, popular in genome-wide screens due to its low computational demands, exhibited a paradoxical behaviour in that the test statistic decreased as the effect size of the variant increased, resulting in a loss of power. The LR test always achieved the most significant P-values, followed by the exact test. We further examined the results in a real data set composed of high- and low-cholesterol subjects from the Dallas Heart Study (DHS). We also compared the single-variant LR test with two multi-variant analysis approaches the burden test and the C-alpha test in analysing the sequencing data by simulation. Our results call for caution in using Wald's test in genome-wide case-control association studies and suggest that the LR test is a better alternative in spite of its computational demands.