Abstract
Estimating the causal effect of an active ingredient in a randomized treatment may be complicated when participants receive heterogeneous doses of the active ingredient. For example, homeless veterans with mental illness were randomized to receive either case management only, or case management plus special access to a Section 8 housing voucher. However, a quarter of those randomized to the housing voucher group did not actually use the voucher, while a few of those randomized to case management actually used a housing voucher. Our goal is to estimate the causal effect of the proposed active ingredient (i.e., using a housing voucher), as opposed to the effect of being randomized to the active ingredient. The proposed instrumental variable methodology assumes that the outcome is proportional to the dose of the active ingredient and tests the significance of the instrumental variable estimate using a permutation test such as the Hodges–Lehman aligned rank statistic proposed by Rosenbaum for pair-matched data (Rosenbaum, Observational studies, 2002; The design of observational studies, 2010). This method removes unmeasured confounding when the assumptions of monotonicity and the exclusion restrictions hold; however, in practice these assumptions may not hold perfectly. Consequently, we extend and strengthen this approach by incorporating optimal full matching on the propensity to use the active ingredient, to further reduce bias and variability in the IV estimation.
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Acknowledgments
We are grateful to the Columbia Center for Homelessness Prevention Studies and the Program Evaluation Unit in the Bureau of Epidemiology Services in the New York City Department of Health and Mental Hygiene for their support and to Paul Rosenbaum for his helpful suggestions.
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Marcus, S.M., Weaver, J., Lim, S. et al. Assessing the causal effect of Section 8 housing vouchers as the active ingredient for decreasing homelessness in veterans with mental illness. Health Serv Outcomes Res Method 12, 273–287 (2012). https://doi.org/10.1007/s10742-012-0100-3
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DOI: https://doi.org/10.1007/s10742-012-0100-3