We consider usefulness of the second diagnostic test in medical diagnosis from the point of view of positive predictive value (PPV) and negative predictive value (NPV). We assume in this paper that medical diagnosis is given by the result of a single diagnostic test or group discussions of experts. We call the process the diagnostic test and consider the situation where an individual has chance to undergo two diagnostic tests. When the second diagnostic test is undertaken, two decision rules, Rule 1 and Rule 2, may be considered. Rule 1 is judge positive if the both tests are positive and negative otherwise. Rule 2 is judge negative if both tests are negative and positive otherwise. The test is called reasonable if, and only if it selects diseased person with higher probability than it does non-diseased persons. It is shown that when the first and second tests are reasonable, usefulness of the second test depends on one’s priority on PPV or NPV and whether one takes Rule 1 or Rule 2.
Enrichment analysis is an effective tool to interpret gene expression data generated by high throughput genomic analysis. Enrichment analysis can be applied to differential exon expression data generated by RNA-seq. However, the enrichment analysis based on differential exon expression introduced unknown exon number bias. Gene ontology terms related to the genes that have larger number of exons tend to be more significant in the enrichment analysis. To correct this exon number bias, we adopted two approaches. First approach is to apply non-central hypergeometric distribution to test significance of each term. Second approach is to count exon number instead of gene number. We confirmed that exon number bias had been adjusted by non-central hypergeometric distribution approach.
Under the assumptions of continuous distribution and homogeneous variance, we consider multiple comparison tests for comparing several treatments with a control in k sample models under a simple ordered restriction．Williams (1971) proposed a closed testing procedure based on t-tests similar to two-sample t-tests under assuming normality. We propose closed testing procedures based on tests of Batholomew (1959). The powers of the proposed tests are superior to Williams (1971). Furthermore nonparametric closed testing procedures are discussed based on ranks. The procedures proposed in this paper are also applicable for the models with unequal sample sizes.