The instrumental variable (IV) method is an approach to estimating a causal relationship in the presence of unmeasured confounders. A central concern in most studies using the IV method is that the IV is not perfectly valid in the sense that it is correlated with unmeasured confounders. This project will contribute to improved methodology for using the IV method. The project will develop a new, more interpretable sensitivity analysis for IV studies that is calibrated to observed covariates. A new way of designing IV studies to make the study less sensitive to the proposed IV being invalid (i.e., correlated with unmeasured confounders) also will be developed. The approach will involve setting up a matched comparison between a group of subjects with a high level of the IV and a group of subjects with a low level of the IV in such a way that the IV is a strong predictor of the treatment that is received in the two groups. Finally, a new IV method for studies with binary outcomes will be developed that is easier to implement and more robust than existing methods.
A main goal of many empirical studies in the social sciences is to provide evidence about the effects caused by policies or treatments. For practical and/or ethical reasons, most such studies are observational rather than randomized studies. A central difficulty for observational studies is that because treatments were not randomly assigned, the subjects receiving different treatments may not be comparable so differing outcomes after treatment may not be effects caused by the treatment. The instrumental variable (IV) method is an approach for estimating a causal relationship that can overcome unmeasured confounding. The basic idea is to use an "instrumental" variable to extract variation in the treatment that is unrelated to the unmeasured confounders, and then use this variation to estimate the causal effect of the treatment on the outcome. This project will provide ways to better assess sensitivity of results from using the IV methods to concerns that the proposed IV is related to unmeasured confounders (and thus not a valid IV), and better ways to make use of an IV when the outcome of the study is a binary variable. The project also will develop and disseminate freely available software for implementing the new methods. By offering rigorous analysis in complex setting otherwise not suited for experimentation, improved methodology for observational studies has the potential to lead to improved policies and practices of both public and private institutions.
,’’ was to develop improved methods for using IVs. My project made several contributions to IV methods. One direction of my project was to develop improved IV methods for nonlinear outcomes, such as censored survival outcomes and binary outcomes. In Nie, Cheng and Small (2011, Biometrics), we developed a nonparametric IV method for survival outcomes that is more efficient than the standardly used IV method for survival outcomes. In Cai, Small and Ten Have (2011, Statistics in Medicine), we derived formulas for the asymptotic biases of commonly used IV estimators for binary outcomes and provided guidance on which estimator is best for which situation. In Cai, Hennessy, Flory, Sha, Ten Have and Small (2012), we conducted a simulation study of IV methods for binary outcomes and studied an application of IV methods to estimating the effect of bezafibrate on diabetes incidence. In Okui, Small, Tan and Robins (2012, Statistica Sinica), we developed a doubly robust IV method that provides consistent estimates when either the model relating the outcome to the treatment and covariates or the model relating the IV to the covariates is correctly specified. Another direction of my project was to develop methods for making IV studies less sensitive to bias by making the IV stronger. The strength of an IV refers to how strongly the IV is associated with the treatment. In Baiocchi, Small, Lorch and Rosenbaum (2010, Journal of the American Statistical Association), we showed that we could build a stronger IV on a subset of the original data and that a study conducted with this subset of the data with a stronger IV is less sensitive to unobserved biases than the original study. To build the stronger IV, we used nonbipartite matching to pair subjects who are far apart on their IV but near on their covariates. In Lorch, Baiocchi, Ahlberg and Small (2012, Pediatrics), we applied this methodology of near-far matching to study the effect of a premature baby being delivered in a high volume, high technology neonatal intensive care unit (NICU) vs. a lower level NICU using the excess travel time the mother lived from the nearest high level NICU compared to the nearest lower level NICU as an IV. We found that high level NICUs provide a substantial benefit. In Baiocchi, Small, Yang, Polsky and Groeneveld (2012, Health Services and Outcomes Research Methodology), we further developed the near-far matching method for building a stronger IV and applied the method to study the effectiveness of carotid arterial stents with cerebral protection (CAS) versus carotid endarterectomy (CEA) for the treatment of carotid stenosis. In Zubizarreta, Small, Goyal, Lorch and Rosenbaum (2013, Annals of Applied Statistics), we developed a new, more powerful method of near-far matching. Instead of using nonbipartite matching based on a network algorithm, we used integer programming techniques, thereby obtaining a wealth of new tools not previously available for nonbipartite matching including fine and near-fine balance for several nominal variables, forced near balance on means of covariates and optimal subsetting. In Goyal, Zubizarreta, Small and Lorch (2013), we applied this integer programming method of near-far matching to study the effect of length of stay in the hospital for late pre-term babies (babies born at 34-36 weeks) on the chance that the baby would need to be rapidly readmitted to the hospital, using hour of birth as an IV. Another direction of my project was to develop improved sensitivity analysis methods for IV studies and other observational studies. In Hsu, Lorch and Small (2012, Health Services and Outcomes Research Methodology), we studied the sensitivity of IV method estimates when only aggregate level (e.g., zip code or census tract) information is available on socioeconomic characteristics of people in the study. In Hsu and Small (submitted), we developed methods of calibrating sensitivity analyses to observed covariates, making the sensitivity analyses more interpretable. The broader impact of this project was that it developed improved methodology for using IVs in observational studies. Observational studies using IVs play an important role in improving policies and practices of public and private institutions. The project also applied the developed methodology to several health economics and health services studies. Additionally, the project supported several Ph.D. students and provided mentoring for these students to develop careers in statistical methods for observational studies.
