Sensitivity Analysis of Unmeasured Confounding in Causal Inference based on Exponential Tilting and Super Learner
Causal inference under the potential outcome framework relies on the strongly ignorable treatment assumption. This assumption is usually unverifiable, and therefore we will never know if there is unmeasured confounding. Unmeasured confounding is one of the fundamental challenges in causal inference. Sensitivity studies are often used to address this issue and evaluate how sensitive a causal estimate is to the unmeasured confounder. In this dissertation, we propose a new sensitivity analysis method to evaluate the impact of the unmeasured confounder by combining ideas of the doubly robust estimator, the exponential tilt method, and the super learner algorithm for both binary and continuous outcomes in chapters 2 and 3, respectively. Compared to other existing methods of sensitivity analysis that parameterize the unmeasured confounder as a latent variable in the working models, the exponential tilting method does not impose any restrictions on the structure or models of the unmeasured confounders. Therefore, the unmeasured confounder could be continuous, binary, or categorical, and could be univariate or multivariate. In order to reduce the modeling bias of traditional parametric methods, we propose incorporating the super learner machine learn-vi ing algorithm to perform nonparametric model estimation and the corresponding sensitivity analysis. In addition, we employ the data-driven trimming method to handle the estimated extreme propensity scores that can hamper the performance of the proposed doubly robust estimator. Furthermore, most existing sensitivity analysis methods require multivariate sensitivity parameters, which makes it more difficult and subjective to specify a reasonable range of the sensitivity parameters in practice. However, the new method has a univariate sensitivity parameter with a nice and simple interpretation of log-odds ratios and deviation in the conditional means of the outcomes for binary and continuous outcomes respectively. This makes choosing a range for the sensitivity parameter easier for the application. The simulation studies demonstrate the effectiveness of the proposed method.