Selecting "significant" differentially expressed genes from the combined perspective of the null and the alternative
In the search for genes associated with disease, statistical analysis yields a key towards reproducible results. To avoid a plethora of type I errors, classical gene selection procedures strike a balance between magnitude and precision of observed effects in terms of p-values. Protecting false discovery rates recovers some power but still ranks genes according to classical p-values. In contrast, we propose a selection procedure driven by the concern to detect well-specified important alternatives. By summarizing evidence from the perspective of both the null and such an alternative hypothesis, genes line up in a substantially different order with different genes yielding powerful signals. A cutoff point for a measure of relative evidence which balances the standard p-value, p(0), with its counterpart, p(1), derived from the perspective of the target alternative, determines our gene selection. We find the cutoff point that maximizes an expected specific gain. This yields an optimal decision which exploits gene-specific variances and thus involves different type I and type II errors across genes. We show the dramatic impact of this alternative perspective on the detection of differentially expressed genes in hereditary breast cancer. Our analysis does not rely on parametric assumptions on the data.
alternative p-values balanced testing gene expression