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Usage of contingency tables 2×2 for estimation of the association between effects and outcomes in the longitudinal biomedical research (Doctor’s nonparametric test)


T. V. Feofanova– Ph.D. (Phys.-Math.), Leading Scientist, Laboratory Simulation of immunological Processes, Federal State Organization \"Institute of Immunology\" FMBA (Moscow). E-mail: T. A. Serova – Ph.D. (Biol.), Leading Scientist, Laboratory Immunological Research Methods, Scientific Research Institute of Vaccines and Sera by I.I. Mechnikov named, RAMS (Moscow). E-mail:

We offer new nonparametric criterion for the analysis of quantitative data of the two groups in dynamics (Doctor’s nonparametric test). The first group receives the external effect (EE) after the first survey (test group, EE+), the second group is control (EE-). We should estimate the association between the effect and the outcome for these groups. The live object has low, high and normal values of a quantitative index. External effect may decrease the low and increase the high values of the indicator. This is the negative outcome (negative dynamics, ND). External effect may increase the low and reduce the high values of the indicator. This is the positive result (positive dynamics, PD). So we make replacement of quantitative values of the indicator «before-after» in the qualitative indicator «type of dynamics». This is the Doctor’s data conversion. Then, all objects are divided into 4 groups: group 1 (EE+, PD, a – number of objects), group 2 (EE+, ND, b – number of objects), group 3 (EE–, PD, c – number of objects), group 4 (EE–, ND, d – number of objects). These groups are a 2×2 contingency table. We take the values of the groups (a, b, c, d) and estimate the association between EE+ and PD with the help of Fisher’s exact test. The results are presents in terms of the absolute risk difference (ARD) to have a positive dynamics of the indicator in two groups: ARD = a/(a+b) – c/(c+d). It is seen that the Doctor’s nonparametric test is a combination of the Doctor’s data conversion and Fisher’s exact test. We used this test to evaluate the two methods of laser therapy for patients with gastric ulcer. Our results: one of these methods demonstrates the detrimental effects on human lymphocytes, which regulate the immune response.


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