Quantile Probit Copula Model for Association in Paired Study Data

• Activity Number: 158 - Statistical Methods for High-Dimensional Data in Health Care and Medical Research
• Type: Topic-Contributed
• Date/Time: Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Roberta De Vito* and Isabella Grabsky and Barbara Engelhardt
• Companies: Brown University and Harvard University and Princeton University
• Keywords: probit; copula; quantile; joint

Abstract

Adopting joint modeling methods for different outcomes is essential to gain insight from high-dimensional correlated data. This type of data leads to two key challenges: a) the relationship between the outcomes, which relies crucially on the model used for the joint analysis, and b) the effects of any possible covariates on each outcome. To meet these two challenges, we develop the Bayesian Bivariate Quantile probit model (BaBiQ), a new joint modeling approach focused on a copula probit model. Our model is able to capture two critical features: a) the association between the two different binary outcomes, b) the complex relationship between the covariates and each outcome by modeling the conditional quantile function. We assess our method's operating characteristics by simulation studies, and we present an application to the Fragile Family Study data, a longitudinal study that includes information about both mothers and their children. We clarify the benefit of using our model for better accuracy of the outcomes' association. Moreover, we determine the need to account for quantile effects in joint modeling to obtain reliable results.