ABSTRACT
Overt Bias and Bias Due to Omitted Variables . . . . . . 47 2.1.4 Instrumental Variables: NICU Example Revisited . . . . . . . . . 48
2.2 Sources of Instruments in Comparative Effectiveness Research Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.3 IV Assumptions and Estimation for Binary IV and Binary Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.3.1 Framework and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.3.2 Two-Stage Least Squares (Wald) Estimator . . . . . . . . . . . . . . . 59 2.3.3 More Efficient Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.3.4 Estimation with Observed Covariates . . . . . . . . . . . . . . . . . . 61 2.3.5 Robust Standard Errors for 2SLS . . . . . . . . . . . . . . . . . . . . . . 63 2.3.6 Example: Analysis of NICU Study . . . . . . . . . . . . . . . . . . . . . 63
2.4 Understanding the Treatment Effect That IV Estimates . . . . . . . . . . . 64 2.4.1 Relationship between Average Treatment Effect for
Compliers and Average Treatment Effect for the Whole Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.4.2 Characterizing the Compliers . . . . . . . . . . . . . . . . . . . . . . . . 65 2.4.3 Understanding the IV Estimate When Compliance Status
Is Not Deterministic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.5 Assessing the IV Assumptions and Sensitivity Analysis for Violations of Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.5.1 Assessing the IV Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 68 2.5.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.6 Weak Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2.7 Binary Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.7.1 Two-Stage Residual Inclusion . . . . . . . . . . . . . . . . . . . . . . . . 79 2.7.2 Bivariate Probit Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2.7.3 Matching-Based Estimator: Effect Ratio . . . . . . . . . . . . . . . . . 80
2.8 Multinomial, Survival, and Distributional Outcomes . . . . . . . . . . . . 81 2.8.1 Multinomial Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.8.2 Survival Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.8.3 Effect of Treatment on Distribution of Outcomes . . . . . . . . . . 84
2.9 Study Design IV and Multiple IVs . . . . . . . . . . . . . . . . . . . . . . . . . . 87 2.9.1 Study Design IV: Near-Far Matching . . . . . . . . . . . . . . . . . . . 87 2.9.2 Multilevel and Continuous IVs . . . . . . . . . . . . . . . . . . . . . . . 89 2.9.3 Multiple IVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
2.10 Multilevel and Continuously Valued Treatments . . . . . . . . . . . . . . . 91 2.11 IV Methods for Mediation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 93 2.12 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
ABSTRACT Comparative effectiveness seeks to determine the causal effect of one treatment versus another on health outcomes. Often, it is not ethically or practically possible to conduct a perfectly randomized experiment and instead an observational study must be used. A major difficulty with observational studies is that there might be unmeasured confounding, that is, unmeasured covariates that differ between the treatment and control groups before the treatment and that are associated with the outcome. Instrumental variables analysis is a method for controlling for unmeasured confounding. Instrumental variables analysis requires the measurement of a valid instrumental variable, which is a variable that is independent of the unmeasured confounding and encourages a subject to take one treatment level versus another, while having no effect on the outcome beyond its encouragement of a certain treatment level. This chapter discusses the types of causal effects that can be estimated by instrumental variables analysis; the assumptions needed for instrumental variables analysis to provide valid estimates of causal effects and sensitivity analysis for those assumptions; methods of estimation of causal effects using instrumental variables; and sources of instrumental variables in comparative effectiveness research studies.
