A Bayesian Local Gaussian-Copula Allocation Model for Bivariate Discrete-Time First-Event Data With Time-Dependent...

Bivariate first-event outcomes arise in longitudinal biomedical studies when two clinically related events are assessed on a shared visit schedule. We propose a Bayesian local Gaussian-copula allocation model for bivariate discrete-time first-event data with baseline and time-dependent covariates. Two outcome-specific working discrete-time decrement models define interval-specific working decrement probabilities and thereby generate marginal survival coordinates on the common interval grid. Among subjects jointly at risk at the start of an interval, a Gaussian copula is used locally to allocate probability mass across four terminal outcomes: no event, event 1 only, event 2 only, and same-interval co-occurrence. The Gaussian copula accommodates negative local dependence, independence, and positive local dependence. We consider constant, unstructured interval-specific, and hierarchical shrinkage specifications for the dependence parameter, and compare them with frequentist and Bayesian odds-ratio benchmarks on the observed-probability scale. Because the native copula-model coefficients act on the working decrement scale, observed-scale covariate effects are summarized by Kullback-Leibler projection. In simulations, the Gaussian-copula models were competitive with odds-ratio benchmarks for observed-scale covariate-effect estimation; the hierarchical model provided a regularized alternative to unstructured interval-specific dependence. We illustrate the method using National Health and Aging Trends Study data on first onset of mobility help and self-care help. The application gave broadly similar observed-scale covariate-effect conclusions across the odds-ratio, constant Gaussian-copula, and hierarchical Gaussian-copula models.