Abstract

Previous studies indicate that retention on an opioid agonist treatment (OAT) can reduce the mortality risk of people with opioid use disorder. To account for the dynamic nature of OAT use, we considered an extended Cox proportional hazards model to account for treatment history through a time-dependent stratification variable. As OAT use is a time-dependent internal covariate, conventional likelihood / partial likelihood based methods do not directly apply, and an estimating function based procedure for estimating model parameters is proposed. As the model makes explicit use of the time-dependent internal covariate, estimating survival probabilities based on the model is no longer feasible. With the aim of obtaining such probabilities, we considered an alternative Cox proportional hazards model, where the internal covariate is replaced with a latent random variable, in which its distribution depends on the entire history of the covariate process. Upon modelling the OAT usage process, we predict the latent variable based on an individual's observed history, and use the conditional score approach to derive unbiased estimating equations for the parameters of interest. The resulting procedure serves as an alternative to traditional joint modelling that requires strong parametric assumptions, and can be computationally intensive. The methods are illustrated using an administrative dataset capturing OAT dispensations and deaths in British Columbia, Canada. This is joint work with Joan Hu (SFU) and Bohdan Nosyk (St. Paul's Hospital and SFU).