Instrumental Variables

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:

Relatedly, see this proposal about how to report instrumental variable analyses. We 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:

And even if the 3 instrumental conditions plus monotonicity held true, the interpretation of the instrumental variable estimates wouldn’t be straightforward:

Further, there are additional, less known problems that can introduce substantial bias:

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:

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 their 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.

Finally, the elephant in the room for conventional instrumental variable methodology is that it cannot be used for time-varying treatments, that is, treatment that may take different values over time for the same individual. This is not a minor limitation because many, if not most, treatments are time-varying. We are currently tackling this issue and helping extend instrumental variable estimation to time-varying treatments:

  • Shi J, Swanson SA, Kraft P, Rosner B, De Vivo I, Hernán MA. Mendelian randomization with repeated measures of a time-varying exposure: an application of structural mean models. Epidemiology 2022; 33(1):84-94. Epidemiology 2022; 33(1):84-94.
  • Shi J, Swanson SA, Kraft P, Rosner B, De Vivo I, Hernán MA. Instrumental variable estimation for a time-varying treatment and a time-to-event outcome via structural nested cumulative failure time models. BMC Medical Research Methodology 2021; 21(1):258.