UC San Diego

In chapter 1 we study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival dataset as well as the linked surveillance, epidemiology, and end results-Medicare database for prediction of mortality in early stage prostate cancer patients using high-dimensional claims codes.

In chapter 2 we propose a new flexible method for survival prediction: DeepHazard, a neural network for time-varying risks. Prognostic models in survival analysis are aimed at understanding the relationship between patients’ covariates and the distribution of survival time. Traditionally, semiparametric models, such as the Cox model, have been assumed. These often rely on strong proportionality assumptions of the hazard that might be violated in practice. Moreover, they do not often include covariates' information updated over time. Our approach is tailored for a wide range of continuous hazards forms, with the only restriction of being additive in time. A flexible implementation, allowing different optimization methods, along with any norm penalty, is developed. Numerical examples illustrate that our approach outperforms existing state-of-the-art methodology in terms of predictive capability evaluated through the C-index metric. The same is revealed on the popular real datasets as METABRIC, GBSG, ACTG and PBC.

In chapter 3 we consider the conditional treatment effect for competing risks data in observational studies. While it is described as a constant difference between the hazard functions given the covariates, we do not assume the additive hazards model in order to adjust for the covariates. We derive the efficient score for the treatment effect using modern semiparametric theory, as well as two doubly robust scores with respect to both the assumed propensity score for treatment and the censoring model, and the outcome models for the competing risks. We provide the asymptotic distributions of the estimators when the two sets of working models are both correct, or when only one of them is correct. We study the inference based on these estimators using simulation. The estimators are applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of midlife drinking behavior on late life cognitive outcomes.

In chapter 4 we consider doubly robust estimation of the causal hazard ratio in observational studies. The treatment effect of interest, described as the constant ratio between the hazard functions of thetwo potential outcomes, is parametrized by the Marginal Structural Cox Model. Under the assumption of no unmeasured confounders, causal methods, as Cox-IPW, have been developed for estimation of the treatment effect of interest. However no doubly robust methods have been proposed under the Marginal Structural Cox model. We develop an AIPW estimator for this popular model that is both model and rate-doubly robust with respect to the treatment assignment model and the conditional outcome model. The proposed estimator is applied to the data from a cohort of Japanese men in Hawaii followed since 1960s in order to study the effect of mid-life alcohol exposure on overall death.