What is better: propensity score matching or instrumental variables? How about both?
That is basically what is proposed using a near/far matching approach as described in Baiocchi et al. (2012). In this paper, they use a two step approach to examine the causal affect of adopting a new treatment–carotid arterial stents (CAS)–versus and older treatment–carotid endarterectomy (CEA)–for the treatment of cartioid stenosis.
The first stage matches HRRs so that characteristics are as similar as possible, but use of the treatment of interest are as different as possible. To make this occur, an optimal nonbipartite matching algorithm was using. To maximize the influence of the “instrument” (i.e., use of the intervention in the area), some HRRs are removed from the analysis. This approach increases the strength of the instrument, but limits the generalizability as some regions are removed from the analysis. On to some of the technical details.
An optimal nonbipartite matching then divides the 2N HRRs into nonoverlapping pairs of two HRRs in such a way that the sum of the discrepancies within the N pairs is minimized. That is, two HRRs in the same pair are as similar as possible in their covariates while also being quite different in their utilization of CAS. In order to get the best covariate balance between the two groups, and at the same time achieve good separation in the instrument…some of the HRRs must be removed from the analysis. We do this in an optimal way by using “sinks” see Lu et al. (2001). To remove e HRRs, e sinks are added to the data set before matching, where each sink is at zero discrepancy to each HRR and at infinite discrepancy to all other sinks. This yields a (2N + e) × (2N + e) discrepancy matrix. An optimal match will pair e HRRs to the e sinks in such a way as to minimize the total of the remaining discrepancies within N − e/2 pairs of 2N − e HRRs; that is, the best possible choice of e HRRs is removed”
In the second step, individuals are matched using bipartite match between paired HRRs more versus less likely to adopt CAS. Here, a propensity score match could be used. In the study of interest, the authors use the package optmatch in R to where match quality relies on the Mahalanobis distance and with the function fullmatch(). This second step makes sure that individuals are matched on observed covariates, but their region of interest (i.e., the interest) is sufficiently different in CAS treatment propensity.
Why use this approach? One reason is that the analysis is easy: once the matching occurs a simple t-test is all that is needed. Further, the approach can help increase the strength of weak instruments but can only do so with a loss of generalizability.
The drawback of this approach is that the matching algorithm is complex. Plus—as mentioned above—the generalizability is lower. In the study of interest, half of HRRs were removed from the analysis to maintain covariate balance. Further, you still need a good instrument as this approach can help but not totally solve the issue of a weak instrument.
- Baiocchi M, Small DS, Yang L, Polsky D, Groeneveld PW. Near/far matching: a study design approach to instrumental variables. Health Services and Outcomes Research Methodology. 2012 Dec 1;12(4):237-53.