20 Multiple Testing

20.1 An example from genetics

We consider a gene expression dataset available from the Gene Expression Omnibus (GEO) database ( https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE7621). The corresponding paper was published with PLOS Genetics (https://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.0030098). In the experiment, substantia nigra tissue from postmortem brain of normal patients (9 of them) and Parkinson disease patients (16 of them) were used for RNA extraction and hybridization on Affymetrix microarrays. Both cohorts included males and females. (We only look at the first 50000 locuses for the sake of simplicity. Some the remaining ones have missing values.)

We perform a Student–Welch test for each gene/locus.

20.2 An example from meta-analysis

We use the dataset described in Table 3 of “Controlled low protein diets in chronic renal insufficiency” published in the BMJ in 1992 (https://www.bmj.com/content/304/6821/216.short).

20.2.1 Cochran–Mantel–Haenszel test

    Mantel-Haenszel chi-squared test with continuity correction

data:  dat
Mantel-Haenszel X-squared = 10.407, df = 1, p-value = 0.001255
alternative hypothesis: true common odds ratio is not equal to 1
95 percent confidence interval:
 0.3619622 0.7727168
sample estimates:
common odds ratio 

20.2.2 Combination tests

We can also take a multiple testing stance, applying a test to each contingency table, and then apply a combination test to the p-values. Here we use the Fisher and Simes combination tests (coded by hand, although they are available in some packages).

[1] 0.04301827
[1] 0.8229667