Abstract
Health scientists often use observational data to estimate treatment effects when controlled experiments are not feasible. A limitation of observational research is non-random selection of subjects into different treatments, potentially leading to selection bias. The two commonly used solutions to this problem—covariate adjustment and fully parametric models—are limited by strong and untestable assumptions. Instrumental variables (IV) estimation can be a viable alternative. In this paper, I review examples of the application of IV in the health sciences, I show how the IV estimator works, I discuss the factors that affect its performance, I review how the interpretation of the IV estimator changes when treatment effects vary by individual, and consider the application of IV to nonlinear models.
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Notes
The generalized IV model can be estimated using the \({\tt{ivregress}}\) command in the statistical software program Stata (version 10).
Errors drawn from U[ − 10,10] can take on any one of 21 different integer values: \(-10, -9, -8, \ldots, -1, 0, 1, \ldots, 8, 9, 10,\) each occurring with equal probability (=1/21). Subjects with the same values of D, F and age can therefore have health outcomes that differ by as much as 20 units.
As Davidson and MacKinnon (2004, pp. 456, 476) note, one could improve estimator precision by dividing observations on H i and \(\user2{x}_{i}(\varvec{\beta})\) by the square root of the observation’s error variance. The error variance in the Poisson case is equal to its conditional mean, while the error variance in the logit case is simply the variance of a Bernoulli distributed random variable: p i (1 − p i ) where \(p_{i}=\frac{{\rm exp}(\beta_{0}+\beta_{1}D_{i}+\user2{W_{i}}^{\prime}\varvec{\gamma})} {1+{\rm exp}(\beta_{0}+\beta_{1}D_{i}+\user2{W_{i}}^{\prime}\varvec{\gamma})}.\)
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Acknowledgments
Grootendorst acknowledges support from the Premier’s Research Excellence Award and the research program into the Social and Economic Dimensions of an Aging Population centered at McMaster University that is primarily funded by the Social Sciences and Humanities Research Council of Canada (SSHRC) and which has received additional support from Statistics Canada. Grootendorst thanks an anonymous referee for helpful suggestions.
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Grootendorst, P. A review of instrumental variables estimation of treatment effects in the applied health sciences. Health Serv Outcomes Res Method 7, 159–179 (2007). https://doi.org/10.1007/s10742-007-0023-6
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DOI: https://doi.org/10.1007/s10742-007-0023-6