Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Epidemiology & Biostatistics

First Advisor

Nandita Mitra

Second Advisor

Dylan Small


Unmeasured confounding is a common concern when clinical and health services researchers attempt to estimate a treatment effect using observational data or randomized studies with non-perfect compliance. To address this concern, instrumental variable (IV) methods, such as two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI), have been widely adopted. In many clinical studies of binary and survival outcomes, 2SRI has been accepted as the method of choice over 2SPS but a compelling theoretical rationale has not been postulated.

First, We directly compare the bias in the causal hazard ratio estimated by these two IV methods. Under the potential outcome and principal stratification framework, we derive closed form solutions for asymptotic bias in estimating the causal hazard ratio among compliers for both the 2SPS and 2SRI methods by assuming survival time follows the Weibull distribution with random censoring. When there is no unmeasured confounding and no always takers, our analytic results show that 2SRI is generally asymptotically unbiased but 2SPS is not. However, when there is substantial unmeasured confounding, 2SPS performs better than 2SRI with respect to bias under certain scenarios. We use extensive simulation studies to confirm the analytic results from our closed-form solutions. We apply these two methods to prostate cancer treatment data from SEER-Medicare and compare these 2SRI and 2SPS estimates to results from two published randomized trials.

Next, we propose a novel two-stage structural modeling framework to understanding the bias in estimating the conditional treatment effect for 2SPS and 2SRI when the outcome is binary, count or time to event. Under this framework, we demonstrate that the bias in 2SPS and 2SRI estimators can be reframed to mirror the problem of omitted variables in non-linear models. We demonstrate that only when the influence of the unmeasured covariates on the treatment is proportional to their effect on the outcome that 2SRI estimates are generally unbiased for logit and Cox models. We also propose a novel dissimilarity metric to quantify the difference in these effects and demonstrate that with increasing dissimilarity, the bias of 2SRI increases in magnitude. We investigate these methods using simulation studies and data from an observational study of perinatal care for premature infants.

Last, we extend Heller and Venkatraman's covariate adjusted conditional log rank test by using the propensity score method. We introduce the propensity score to balance the distribution of covariates among treatment groups and reduce the dimensionality of covariates to fit the conditional log rank test. We perform the simulation to assess the performance of this new method and covariates adjusted Cox model and score test.

Available for download on Friday, June 22, 2018

Included in

Biostatistics Commons