Multiple-response logistic regression modeling with application to an analysis of cirrhosis liver disease data

In practical data analysis, individual measurements usually include two or more responses, and some statistical correlations often exist between the responses. Especially in medical data analysis, observations are often binary responses. A class of multi-response logistic regression model based on a joint modeling approach is investigated in this paper, and an application to a group data of primary biliary cirrhosis diseases is considered. Firstly, we propose a new class of multi-response logistic distribution and investigate its statistical properties. Secondly, a multi-response logistic regression model is constructed using a latent variable model and multi-variate logistic error distribution. Furthermore, the parameter estimation method of the model is provided by applying the monte carlo expectation maximization (MCEM) algorithm and the multiple imputation method. Finally, numerical simulations and comparative predictions on a test set are performed to validate the finite sample performance of the proposed model, and the model is applied to a cirrhosis disease dataset for analysis. Copyright © 2024 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.