Use of p-value plots to diagnose and remedy problems with statistical analysis of microarray data

Abstract

Microarray and RNA-sequencing technologies measure thousands of genes per biological sample. Because of the large number of genes, empirical distributions over genes for statistics computed over samples resolve properties of the data that can be exploited to define the expressed genes, diagnose problems with hypothesis tests, and even remedy some of these problems. The empirical distribution of the average expressions for genes was first used to partition the interrogated genes into two subsets, 'non-expressed' genes and 'expressed' genes. The p-values from tests for treatment effects were computed for both subsets and their empirical distributions were examined next. A plot of empirical distributions of p-values (p-value plot) indicated that the 'non-expressed' genes do not follow the anticipated null distribution, which implies that the p-values for expressed genes may also misrepresent their true significance. In simulations we were able to produce a similar departure from the null distribution with dye effects, suggesting that comparable confounding may account for the observed discrepancies. By using the empirical distribution of non-expressed genes as the null distribution, p-values for the expressed genes were adjusted with the goal of mitigating biases introduced by systematic distortions such as a dye effect. A plot of the empirical distribution for a statistic computed per endpoint provides a succinct visualization of the distributional properties, which can be compared to expected properties. Such comparisons are effective at identifying problems with analyses, and indicating adjustments that can be applied to generate more reliable lists of affected genes based on false-discovery criteria.