Hypothesis tests for multiple responses regression: effect of probiotics on addiction and binge eating disorder

Clinical trials are common in medical research where multiple non-Gaussian responses and time-dependent observations are frequent. The analysis of data from these studies requires statistical modeling techniques that take these characteristics into account. We propose a general strategy based on the Wald statistics to perform hypothesis tests like ANOVAs, MANOVAs and multiple comparison tests on regression and dispersion parameters of multivariate covariance generalized linear models (McGLMs). McGLMs provide a general statistical modeling framework for normal and non-normal multivariate data analysis along with a wide range of correlation structures. We design different simulation scenarios to verify the properties of the proposed tests. The results are promising showing that the proposed tests present the levels of confidence close to the specified one for all simulation study scenarios. Complementary to the proposal, we developed implementations in the R language to carry out the tests presented, the codes are available in the supplementary material. The proposal is motivated by the analysis of a clinical trial that aims to evaluate the effect of the use of probiotics in the control of addiction and binge eating disorder in patients undergoing bariatric surgery. The subjects were separated into two groups (placebo and treatment) and evaluated at three different times. The results indicate that addiction and binge eating disorder reduce over time, but there is no difference between groups at each time point.