Topics In Statistical Inference For Treatment Effects

This thesis unites three papers discussing different approaches for estimating treatment effects, either in observational study or randomized trial. The first paper presents an approach to sensitivity analysis for the instrumental variable(IV) method, which examines the sensitivity of inferences to violations of IV validity. Our approach is based on extending the Anderson-Rubin test and is robust to weak IVs. The second paper presents a unified \proglang{R} software \pkg{ivmodel} for analyzing instrumental variables with one endogenous variable. The package implements a general class of estimators, $k$-class estimators, and two confidence intervals that are fully robust to weak instruments. The package also provides power formulas. The sensitivity analysis discussed in the first paper is also included in the package. The third paper uses Hidden Markov Model to estimate the dynamic effects of lottery-based incentives towards patient's healthy behavior every day. The data is collected from randomized clinical trials.