Instrumental variable estimation has been traditionally used in economics and the social sciences. Jamie Robins and I wrote a paper that 1) summarized the method in a way that ties together previous work from statistics, econometrics and epidemiology, and 2) presented new insights and formal results in its appendix:
- Hernán MA, Robins JM. Instruments for causal inference: An epidemiologist’s dream? Epidemiology 2006; 17:360-372
Relatedly, see also our proposal about how to report instrumental variable analyses. Our papers emphasize that valid instrumental variable estimation requires not only the 3 instrumental conditions (that is, having a valid instrument), but also a fourth condition to be chosen between homogeneity or monotonicity.
Before 1994, all instrumental variable estimates implicitly relied on homogeneity, which is generally an implausible assumption. With the shift to monotonicity after the mid-1990s, many authors thought the problem was solved. However, Sonja Swanson demonstrated empirically that monotonicity is unlikely to hold in many applications:
- Swanson SA, Miller M, Robins JM, Hernán MA. Definition and evaluation of the monotonicity condition for preference-based instruments. Epidemiology 2015; 26:414-420. PMCID: PMC4669963
And even if the 3 instrumental conditions plus monotonicity held true, the interpretation of the instrumental variable estimates wouldn’t be straightforward:
- Swanson SA, Hernán MA. Think globally, act globally: An epidemiologist’s perspective on instrumental variable estimation. Statistical Science 2014; 29(3): 371-374. PMCID: PMC4285626
- Swanson SA, Hernán MA. The challenging interpretation of instrumental variable estimates under monotonicity. International Journal of Epidemiology 2017 (in press).
Further, there are additional, less known problems that can introduce substantial bias:
- Swanson SA, Miller M, Robins JM, Hernán MA. Selecting on treatment: a pervasive form of bias in instrumental variable analysis. American Journal of Epidemiology 2015; 181(3):191-197.
All of the above is becoming increasingly relevant for health researchers because of the emergence of Mendelian randomization, a form of instrumental variable estimation that proposes genetic variants as instruments. Unfortunately, some researchers are unfamiliar with the shortcomings of instrumental variable estimation and believe that Mendelian randomization results are as robust as those from randomized trials. Bear in mind that, despite its unfortunate name, Mendelian randomization is just another form of observational research. We explain here:
- Swanson SA, Tiemeier H, Ikram MA, Hernán MA. Nature as a trialist? Deconstructing the analogy between Mendelian randomization and randomized trials. Epidemiology 2017; 28(5):653-659. PMCID: PMC5552969
These criticisms have been countered by arguing that the goal of Mendelian randomization is not to quantify the causal effect, but just to determine whether the causal effect is null. But, as we argue here, this retreat into the null doesn’t quite work:
- Swanson SA, Labrecque J, Hernán MA. Causal null hypotheses of sustained treatment strategies: What can be tested with an instrumental variable? European Journal of Epidemiology 2018; 33(8): 723-728.
A way to free ourselves from the fourth condition (homogeneity or monotonicity) is to renounce to the calculation of point estimates of causal effect. Rather, we can use instrumental variables to obtain upper and lower bounds for the causal effect, that is, to partially identify the effect. Here is a review of methods for partial identification and an application to a randomized trial :
- Swanson SA, Hernán MA, Miller M, Robins JM, Richardson T. Partial identification of the average treatment effect using instrumental variables: : Review of methods for binary instruments, treatments, and outcomes. Journal of the American Statistical Association 2018; 113(522):933-947.
- Swanson SA, Holme Ø, Løberg M, Kalager M, Bretthauer M, Hoff G, Aas E, Hernán MA. Bounding the per-protocol effect in randomized trials: an application to colorectal cancer screening. Trials 2015; 16:541.