Letter to the editor
Bias introduced by conditioning on an intermediate variable: Comment on the article by Zhang et al
Article first published online: 6 MAY 2011
Copyright © 2011 by the American College of Rheumatology
Arthritis Care & Research
Volume 63, Issue 5, page 784, May 2011
How to Cite
Zhu, Y. (2011), Bias introduced by conditioning on an intermediate variable: Comment on the article by Zhang et al. Arthritis Care Res, 63: 784. doi: 10.1002/acr.20443
- Issue published online: 6 MAY 2011
- Article first published online: 6 MAY 2011
- Accepted manuscript online: 26 JAN 2011 03:24PM EST
To the Editors:
I read with great interest the article by Zhang et al published recently in Arthritis Care & Research (Zhang Y, Niu J, Felson DT, Choi HK, Nevitt M, Neogi T. Methodologic challenges in studying risk factors for progression of knee osteoarthritis. Arthritis Care Res [Hoboken] 2010;62:1527–32). In the article, the authors discussed several potential mechanisms that could bias the effect estimate of a particular risk factor on progression of radiographic knee ostearthrithis (OA). One mechanism, which would tend to bias the effect toward the null, is conditioning on a collider (or a common effect as described in the article).
I would like to propose another potential explanation for this paradoxical phenomenon. Assuming that a risk factor could not cause knees to have a Kellgren/Lawrence (K/L) grade of 3 or 4 without first having a K/L grade of 2 or 3, and there is neither a confounding factor nor collider, the relation of the risk factor (X) to radiographic OA progression (Y; i.e., K/L grade 3 or 4) among knees with preexisting radiographic knee OA (Z; i.e., K/L grade 2 or 3) could be depicted using the following causal diagram: X Y. A box surrounding Z indicates conditioning on Z as we only study the knees with preexisting radiographic OA. In this case, conditioning on Z, an intermediate variable on the causal pathway between X and Y, blocks the path between X and Y when it contains no collider, i.e., conditioning on preexisting radiographic knee OA would completely eliminate the effect of risk factor X on radiographic knee OA progression (Rothman K, Greeland S, Lash T. Modern epidemiology. 3rd ed. Philadelphia: Lippincott Williams & Wilkins; 2008. p. 183–209).
Such findings, however, do not imply that the risk factor X is not a cause of radiographic OA progression, but rather that we are unable to evaluate that relation using the information typically collected in OA studies. In fact, if the investigators could manipulate the risk factor X, for example by performing bariatric surgery causing weight loss at the time when OA already exists, the causal relationship between that specific risk factor X (in this example body mass index) and radiographic OA progression could be accurately evaluated. Given that most risk factors that have been evaluated for radiographic knee OA are chronic in nature, they are likely present long before the occurrence of radiographic OA. Therefore, the causal diagram proposed above and consequently the bias introduced by conditioning on an intermediate variable will probably hold in most situations.
Yanyan Zhu PhD*, * Boston University School of Medicine, Boston, Massachusetts.