Hypothesis tests for multiple responses regression: effect of probiotics on addiction and binge eating disorder (2208.00027v1)

Abstract: 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.

• The paper introduces a novel Wald test methodology within the McGLM framework for multivariate hypothesis testing in clinical settings.
• It demonstrates the framework's robustness through simulation studies with Normal, Poisson, and Bernoulli responses, highlighting power increases with sample sizes.
• The practical application on clinical trial data shows temporal improvements in addiction and binge eating symptoms, though no significant treatment effects were observed.

Hypothesis Tests for Multiple Responses Regression: Effect of Probiotics on Addiction and Binge Eating Disorder

Overview

The central endeavor of this research involves proposing a methodological framework to implement hypothesis tests for multivariate models, specifically focusing on the effects of probiotics on addiction and binge eating disorders in clinical settings. This paper extends the multivariate covariance generalized linear models (McGLMs) to develop hypothesis testing strategies such as ANOVA, MANOVA, and multiple comparison tests using Wald statistics.

McGLM Framework

The McGLM framework provides robust modeling for datasets with multiple non-Gaussian responses and time-dependent observations. It draws on the generalized Kronecker product to define a joint covariance structure across responses, allowing for flexible modeling of both mean and covariance structures in multivariate settings. The authors utilize this framework to address the statistical needs of clinical trials involving correlated responses and non-independent data points.

Wald Test Implementation

The Wald test is central to the proposed hypothesis testing strategy. It is applied to determine the significance of regression and dispersion parameters within the McGLM framework. The paper elaborates on constructing linear hypotheses, specifying the structure of the L matrix to conduct various hypothesis tests, such as those involving individual parameters, parameter sets, and equalities between parameters. Furthermore, the authors propose generating ANOVA and MANOVA tables tailored to type I, II, and III analyses and extend the methodology to multiple comparison tests.

Simulation Studies

Simulation studies are conducted across various scenarios—univariate and multivariate with Normal, Poisson, and Bernoulli distributions. These simulations gauge the power and characteristics of the Wald test in the proposed settings, examining sample sizes ranging from 50 to 1000. Results consistently show that the rejection rates of null hypotheses increase with sample size and divergence from the true parameter values, demonstrating the efficacy of the Wald test within McGLMs.

Practical Application

The clinical trial data analyzes the effectiveness of probiotics in controlling addiction and binge eating disorders post-bariatric surgery. The dataset comprises placebo and treatment groups evaluated over three time points. The McGLM framework, inclusive of both regression and dispersion parameters, effectively models this dataset, considering the correlation between observations collected from the same individual over time.

Type II multivariate analysis of variance highlights significant temporal effects, without significant differences between treatment groups. This temporal change suggests a reduction in addiction and binge eating disorder symptoms over time, with no discernible effect attributable to the probiotic treatment.

Conclusion

This paper delivers a comprehensive framework for conducting hypothesis tests in multivariate settings with McGLMs using the Wald test. The simulation results substantiate the reliability and power of the method, while the practical application to clinical trial data illustrates its efficacy in real-world settings. Future directions include exploring additional statistical tests and procedures to enhance the utility and flexibility of the proposed framework within the landscape of multivariate analysis in clinical research.