Due to its rich collection of information over time, administrative databases have become a popular data source to conduct population-based health research. Motivated by estimating the long-term exposure effect of an opioid agonist treatment (OAT) on mortality risk, this dissertation develops methodology to estimate effects of internal covariates in a hazard regression model. Since an internal covariate obstructs the conventional relationship between the hazard and survivor functions, this not only invalidates likelihood methods to infer model parameters, but also makes survival probabilities redundant. We review two general approaches to overcome challenges brought on by internal covariates: avoid all inference procedures that rely on the survivor function, or somehow rectify the relationship between the hazard and survivor functions. We conduct a preliminary analysis with the administrative service utilization records, in which we summarize internal covariates with either one-jump processes, functional principal scores, or a model based summary. We demonstrate how this approach greatly reduces the computational complexity that currently plagues traditional joint models, and is capable of providing survival predictions. Our results not only reveal the OAT dispensation effect to be time-varying, but younger individuals receive the greatest protective effect of OAT against mortality, despite having lower OAT dispensation rates relative to older individuals. To account for the dynamic nature exhibited within the OAT dispensation process, a generalized Cox regression model is proposed using a time-dependent stratification variable to summarize lifetime service utilization in presence of other potential covariates. Since conventional likelihood inference methods are inapplicable, we present an estimating function based procedure for estimating model parameters, and provide a testing procedure for updating the stratification levels. The proposed approach is examined both asymptotically through modern empirical process theory, and numerically via simulation. Our analysis shows the effect on mortality risk decreases in successive OAT attempts, in which two risk classes based on an individual's treatment episode number are established: (i) 1-3 OAT episodes, and (ii) 4+ OAT episodes. We revisit our modelling from the preliminary analysis to address the apparent bias upon directly replacing an internal covariate process with a model based summary. We extend the conditional score approach of Tsiatis and Davidian (2001) by allowing for potential autocorrelation within an internal covariate process. Through a simulation study, we show that our proposed method is able to produce consistent estimates, whereas naively ignoring the autocorrelation within the data underestimates the true effect. We additionally address confounding by age within our data application by weighting birth generation specific estimates by their relative group size. This procedure up-weights contributions made by younger individuals, and produces an overall protective treatment effect against mortality. Since the conventional relationship between the hazard and survivor functions is held intact, the proposed method is also capable of producing model based survival predictions. We then extend our developed methodology to allow an internal covariate to be multivariate. Specifically, we estimate the effect of a multivariate internal covariate process on the mortality hazard function, and extend the conditional score approach in hopes of obtaining survival predictions; in which the latter approach requires us to account for potential correlation over time and between covariates. In the context of our data application, we extract the OAT dispensation indicator, OAT type, and dosage level from the OAT dispensation process, and our modelling suggests that buprenorphine has the greatest protective effect against mortality among different OAT types. Although the proposed research is motivated within the context of opioid use disorder management through health service utilization records, we anticipate the methodology to have broad applications, and the proposed methods are intuitive and simple to implement.
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Thesis advisor: Hu, Joan
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