Longitudinal joint modelling of binary and continuous outcomes: A comparison of bridge and normal distributions

Abstract

Background: Longitudinal joint models consider the variation caused by repeated measurements over time as well as the association between the response variables. In the case of combining binary and continuous response variables using generalized linear mixed models, integrating over a normally distributed random intercept in the binary logistic regression sub-model does not yield a closed form. In this paper, we assessed the impact of assuming a Bridge distribution for the random intercept in the binary logistic regression submodel and compared the results to that of a normal distribution. Method: The response variables are combined through correlated random intercepts. The random intercept in the continuous outcome submodel follows a normal distribution. The random intercept in the binary outcome submodel follows a normal or Bridge distribution. The estimations were carried out using a likelihood-based approach in direct and conditional joint modelling approaches. To illustrate the performance of the models, a simulation study was conducted. Results: Based on the simulation results and regardless of the joint modelling approach, the models with a Bridge distribution for the random intercept of the binary outcome resulted in a slightly more accurate estimation and better performance. Conclusion: Our study revealed that even if the random intercept of binary logistic regression is normally distributed, assuming a Bridge distribution in the model leads to in more accurate results.