Bonferroni-Holm and permutation tests to compare health data: methodological and applicative issues

Statistical methodology is a powerful tool in the health research; however, there is wide accord that statistical methodologies are not usually used properly. In particular when multiple comparisons are needed, it is necessary to check the rate of false positive results and the potential inflation of type I errors. In this case, permutation testing methods are useful to check the simultaneous significance level and identify the most significant factors.

In this paper an application of permutation tests, in the medical context of Inflammatory Bowel Diseases, is performed. The main goal is to assess the existence of significant differences between Crohn's Disease (CD) and Ulcerative Colitis (UC). The Sequentially Rejective Multiple Test (Bonferroni-Holm procedure) is used to find which of the partial tests are effectively significant and solve the problem of the multiplicity control.

Applying Non-Parametric Combination (NPC) Test for partial and combined tests we conclude that Crohn's Disease patients and Ulcerative Colitis patients differ between them for most examined variables. UC patients compared with the CD patients, have a higher diagnosis age, not show smoking status, proportion of patients treated with immunosuppressants or with biological drugs is lower than the CD patients, even if the duration of such therapies is longer. CD patients have a higher rate of re-hospitalization. Diabetes is more present in the sub-population of UC patients. Analyzing the Charlson score we can highlight that UC patients have a more severe clinical situation than CD patients. Finally, CD patients are more frequently subject to surgery compared to UC. Appling of the Bonferroni Holm procedure, which provided adjusted p-values, we note that only nine of the examined variables are statistically significant: Smoking habit, Immunosuppressive therapy, Surgery, Biological Drug, Diabetes, Adverse Events, Re-hospitalization, Gender and Duration of Immunosoppressive Therapy. Therefore, we can conclude that these are the specific variables that can discriminate effectively the Crohn's Disease and Ulcerative Colitis groups.

We identified significant variables that discriminate the two groups, satisfying the multiplicity problem, in fact we can affirm that Smoking habit, Immunosuppressive therapy, Surgery, Biological Drug, Diabetes, Adverse Events, Hospitalization, Gender and Duration of Immunosoppressive Therapy are the effectively significant variables.