Editorial: observational studies, time-dependent confounding, and marginal structural models.

ARTHRITIS & RHEUMATOLOGY Vol. 67, No. 3, March 2015, pp 609–611 DOI 10.1002/art.38931 © 2015, American College of Rheumatology EDITORIAL Observational Studies, Time-Dependent Confounding, and Marginal Structural Models Charles E. McCulloch Observational studies have an undeniable role in medical research and often have significant advan- tages over randomized trials (1), such as broader gener- alizability. But, we regularly want to use observational studies to draw causal conclusions about the ability of interventions to prevent and treat disease, which can be problematic. In companion articles published in this issue of Arthritis & Rheumatology, Yang, Lapane, and coworkers (2,3) consider the causal impact of glucosamine/chondroitin and nonsteroidal antiinflam- matory drugs (NSAIDs) on knee osteoarthritis (OA), based on data from the Osteoarthritis Initiative (OAI), a longitudinal observational study. They use a statistical technique called “marginal structural models” with the goal of strengthening their ability to infer causation. This is becoming a more common approach to address- ing issues of confounding in observational studies. When should this technique be used, and what are its advan- tages and disadvantages? It is well understood that a key threat to drawing causal conclusions from observational studies is con- founding. For example, a history of knee surgery could easily be associated with both NSAID use and OA, and failure to account for differences in rates of knee surgery in comparing users and nonusers of NSAIDs could lead to biased estimates of the causal effect of NSAIDs. Fortunately, multiple regression analysis is in the statis- tical toolkit of virtually any medical researcher and can, in a wide variety of situations, adjust for or control for the effects of history of knee surgery to reduce or eliminate the effects of confounding. But what about a variable such as inflammation? Inflammation could also easily be associated with both NSAID use and OA. The conventional wisdom is that we should not adjust or control for inflammation be- cause it may be one of the paths by which NSAIDs could work to reduce OA. If we adjusted or controlled for it by multiple regression, we might be removing or reducing the true causal effect of NSAIDs on OA that occurs through reduced inflammation. So, variables such as inflammation (called mediator or intermediate vari- ables) should not be adjusted or controlled for (4). So far, so good. We should adjust for confounders but not intermediate variables. Unfortunately, it is possible for a variable to be both a confounder and an intermediate variable in a longitudinal study. For example, inflammation during the first year of a study (between baseline and year 1) could cause higher NSAID use at the year 1 visit. So, it is a confounder during year 1, and we should adjust for it. NSAID use might then lead to reductions in inflam- mation between year 1 and 2 and be associated with lower rates of OA. So, it is an intermediate variable during year 2, and we should not adjust for it. Variables that are simultaneously confounders and intermediate variables are known as “time-dependent confounders.” The technique of marginal structural models sets out to solve this dilemma by accounting for the associ- ation of inflammation and NSAID use not by adjusting for it in a regression model but instead by using weight- ing methods. The basic idea is to weight the data to break the association between the time-dependent con- founder and the outcome. Continuing the hypothetical inflammation example, suppose that there are 50 partic- ipants with no inflammation during year 1, 10% (or n ⫽ 5) of whom reported NSAID use at year 1, and 100 participants with inflammation during year 1, 20% (or n ⫽ 20) of whom report NSAID use at year 1. The weighting used in marginal structural models is called “inverse probability of treatment” weighting. So, in the no inflammation group, those who took NSAIDs are weighted by 10 (from 1/0.1 ⫽ 10) and those who did not take NSAIDs are weighted by 1.11 (from 1/0.9 ⫽ 1.11). Thus, the 5 participants in the no inflammation group who took NSAIDs are essentially inflated (by the Charles E. McCulloch, PhD: University of California, San Francisco. Address correspondence to Charles E. McCulloch, PhD, Department of Epidemiology and Biostatistics, University of Califor- nia, San Francisco, Box 0560, San Francisco, CA 94143-0560. E-mail: Charles.McCulloch@ucsf.edu. Submitted for publication October 15, 2014; accepted Octo- ber 23, 2014.