Keywords: precision medicine, single SNP detection, multiple comparison with the best, response profile, simultaneous confidence set, Additive Equality method
A companion diagnostic is a diagnostic test, co-developed with drugs, to provide information for the safe and effective use of the treatment. Most FDA-approved companion diagnostics follow “one drug, one SNP” pattern. In recent years, many statistical procedures have been proposed to identify the single best predictive SNP from a genome-wide dataset in two-arm randomized clinical trails. Most procedures are based on the p-value ordering to select the SNP with the smallest p-value. However, the p-value ordering is sensitive to the noise, and doesn’t necessarily correlate with the true ordering. Furthermore, to our best knowledge, no work has considered the response profiles of SNPs. The SNP with the smallest p-value would not be useful for a companion diagnostic unless its response profiles satisfy certain patterns. In this paper, we formulate the problem of identifying the single best predictive SNP in the framework of multiple comparison with the best (MCB) procedure. As a result, the parameter of interest is naturally the minimal difference in predictive ability between a given SNP and the best SNP excluding that given SNP, conditional on SNP response profiles satisfying desired patterns. The predictive ability for each SNP is quantified by differential treatment efficacy in different genotype subgroups. We then construct a simultaneous confidence set for the parameters of interest for each SNP while the expected number of parameters with false confidence interval coverage are well controlled. A best SNP is detected if the upper limit of its confidence interval is larger than the minimal clinically important difference (MCID), which indicates the given SNP has the most predictive ability. Or a set of equally best SNPs are detected if there exist other SNPs are not the best, but nevertheless are at least close to the best. Simulation studies show that the proposed method works well in the selection of either the best one SNP, or a set of equally best SNPs.