Post-Hoc Comparison Tests for Odds Ratios


The null hypothesis of homogeneity of odds ratio across the strata is testedby several tests. When the null hypothesis is rejected, means at least one ofthe odds ratios signicantly diers from others. Post hoc tests are used afterthe null hypothesis of equality of groups is rejected. Those tests aim to revealthe true dierences between groups. In this paper, we propose post-hoc pro-cedures that control familywise type-I error. These procedures provide thehomogeneous subsets that appear in the same homogeneous subset that arenot signicantly dierent. The suggested procedures are applied to severalCOVID-19 data sets.

DOI Code: 10.1285/i20705948v15n1p75

Keywords: 2x2 tables; common odds ratio; post-hoc compariso; homogeneity of odds ratios; COVID-19 data


Agresti, A. (2002). Categorical data analysis. John Wiley & Sons, New York.

Bonferroni, C. E. (1936). Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze, 8, 3-62.

Borenstein, M., Hedges, L. V., Higgins, J. P. T., Rothstein H. R. (2009). Introduction to meta-analysis. John Wiley & Sons, West Sussex.

Breslow, N. E., Day, N. E. (1980). The analysis of case-control studies. Statistical Methods in Cancer Research, 1.

Breslow, N. E. (1996). Statistics in epidemiology: The case-control study. Journal of the American Statistical Association, 91, 14-26.

Dunn, O. J. (1961). Multiple comparisons among means. Journal of the American Statistical Association, 56(293), 52-64.

Lawal, B. (2003). Categorical data analysis with SAS and SPSS applications. Lawrence Erlbaum Associates, Publishers, New Jersey.

Mantel N., Haenszel, W. (1959). Statistical aspects of the analysis of data from retrospective studies. Journal of the National Cancer Institute, 22, 719-748.

Perneger, T. V. (1998). What's wrong with Bonferroni adjustments. British Medical Journal, 316(7139), 1236-1238.

Ruan, Q., Yang, K., Wang, W., et al. (2020). Clinical predictors of mortality due to COVID-19 based on an analysis of data of 150 patients from Wuhan, China. Intensive Care Medicine, 46(5), 846-848.

Sidak, Z. (1967). Rectangular confidence regions for the means of multivariate normal distribu-

tions. Journal of the American Statistical Association, 62(318), 626-633.

Yusuf, S., Peto, R., Lewis, J., Colins R., Sleight, P. (1985). Beta blockade during and after myocardial infarction: An overview of randomized trials. Progress in Cardiovascular Disease, 27, 335-371.

Tarone, R. E. (1985). On heterogeneity tests based on efficient scores. Biometrika, 72(1), 91-95.

Wang, D., Yin, Y., Hu, C., et al. (2020). Clinical course and outcome of novel coronavirus COVID-19 infection in 107 patients discharged from the Wuhan Hospital. Critical Care, 24(188).

Woolf, B. (1955). On estimating the relation between blood group and disease. Annals of Human

Genetics, 19(4), 251-253.

Wu, C., Chen, X., Cai, Y., et al. (2020). Risk factors associated with acute respiratory distress syndrome and death in patients with coronavirus disease 2019 pneumonia in Wuhan, China. JAMA Internal Medicine.

Yuan, M., Yin, W., Tao, Z., et al. (2020). Association of radiologic findings with mortality of patients infected with 2019 novel coronavirus in Wuhan, China. PLoS ONE, 15(3), e0230548.

Zhou, F., Yu, T., Du, R., et al. (2020). Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: A retrospective cohort study. The Lancet, 395, 1054-1062.

Yang, X., Yu, Y., Xu, J., et al. (2020). Clinical course and outcomes of critically ill patients with SARS-CoV-2 pneumonia in Wuhan, China: A single-centered, retrospective, observational study. The Lancet Respiratory Medicine, 8, 475-481.

Full Text: pdf

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.