Tests for Probability of A Reaction and Difference Between Reactions Where Treatment Increases Marker-Values of Particular Subjects but Decreases Others

PD-1 has a role in regulating the response of the immune system to the cells of the human body. Paris et al. reported that combination antiretroviral therapy did not change % CD4 + of PD-1 high CTLA-4 low CD127 high early/intermediated T cells of human immunodeficiency virus infected patients but increased the percent of the marker limited to initial CD4 counts <200 with Wilcoxon signed-rank test. We hypothesized that the treatment increased the marker value in patients whose initial marker value is less than a particular value and decreased the marker value in other patients and that the test misleadingly concluded that the treatment did not change the marker value. General subgroup analyses correctly estimate the statistical significance of such a reaction or difference between such reactions only when the reaction of both of subgroups or both difference between such subgroups is statistically significant. We propose Ishida’ t-test for paired samples that can correctly judge the probability without division of the group into subgroups, and Ishida’ t-test for unpaired samples that can correctly judge the statistical significance of the difference between such reactions. We also showed that many treatments cause such increase and decrease of marker values relating PD-1 of subjects.