American Journal of Epidemiology Advance Access originally published online on January 29, 2008
American Journal of Epidemiology 2008 167(5):530-531; doi:10.1093/aje/kwm358
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PRACTICE OF EPIDEMIOLOGY |
Pischon et al. Respond to "Variable Selection versus Shrinkage in Control of Confounders"
From the Department of Epidemiology, German Institute of Human Nutrition Potsdam-Rehbrücke, Nuthetal, Germany
Correspondence to Dr. Tobias Pischon, Department of Epidemiology, German Institute of Human Nutrition Potsdam-Rehbrücke, Arthur-Scheunert-Allee 114–116, 14558 Nuthetal, Germany (e-mail: pischon{at}dife.de).
Received for publication October 24, 2007. Accepted for publication November 7, 2007.
We read with great interest Dr. Greenland's invited commentary (1) about variable selection to control for confounding in observational studies. We agree with Dr. Greenland that the identification of confounders should be based primarily on background knowledge and not on significance testing. However, our proposed method (2) is not meant primarily as a variable selection procedure. Currently, relative risk estimates are commonly presented from nested models with increasing complexity of covariate use (3). This is not caused predominantly by the uncertainty of selecting the proper model, but rather by the interest to quantify the relative effect of adjustment for specific covariates on risk estimates. For example, relative risks from a multivariate model for a specific nutrient might be compared with those from a model with additional adjustment for other nutrients or foods to evaluate the relative importance of confounding by other dietary characteristics (3). Another potential application is the situation where it may be more likely that a covariate reflects a potential mediator rather than a confounder. Although such type of analysis requires several assumptions and careful interpretation, the comparison of models without and with adjustment for potentially intermediate variables might be informative to quantify the change in a beta coefficient when these covariates are taken into account (4). As pointed out by Dr. Greenland, the precision of the impact of a covariate on the incidence rate ratio in a given regression model may depend on sample size and measurement error. Our method allows deriving a confidence interval for the ratio of incidence rate ratios and is therefore an important tool for more precisely analyzing and interpreting results from Cox proportional hazards models (2).
As reviewed by Dr. Greenland, inclusion of all measured potential confounders as covariates may be a desirable approach to avoid the complexities of variable selection, and shrinkage methods have been proposed to obtain unbiased results when following this strategy in the case of collinearity or sparse data (1). However, the example that Dr. Greenland presents in table 1 (1) illustrates that the additional inclusion of 85 food items using the shrinkage method to 35 nutrients within a conditional logistic regression model had little effect on the point estimates for most nutrients, while the confidence intervals for all nutrients presented largely increased. The rationale of selecting 35 nutrients out of hundreds of potential nutrients and nonnutritive food constituents remains unknown, but it seems clear from this example that the pure availability of food and nutrient intake values should not guide covariate selection. Rather, such selection should be driven by a priori hypotheses and should be limited to plausible covariates, as it is the case for other epidemiologic questions. In addition, when using the prior-data method, we find that the degree of shrinkage seems somewhat arbitrary. Finally, shrinkage adds complexity to the regression models, thus further complicating the biologic interpretation of the coefficients provided in table 1. Therefore, despite advances in methodology, the decisions involved in the definition of the confounder structure, as well as the statistical penalty for added covariates in terms of loss of precision, are problems epidemiologists still face in the current millennium.
Note: With great sadness we report the loss of our colleague Dr. Kurt Hoffmann. He died shortly after acceptance of our article by the Journal, without having the opportunity to read Dr. Greenland's comment.
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ACKNOWLEDGMENTS |
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Conflict of interest: none declared.
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References |
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 TOP References |
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- Greenland S. Variable selection versus shrinkage in the control of multiple confounders. Am J Epidemiol (2008) 167:523–9.
[Abstract/Free Full Text] - Hoffmann K, Pischon T, Schulz M, et al. A statistical test for the equality of differently adjusted incidence rate ratios. Am J Epidemiol (2008) 167:517–22.
[Abstract/Free Full Text] - Schulze MB, Schulz M, Heidemann C, et al. Fiber and magnesium intake and incidence of type 2 diabetes: a prospective study and meta-analysis. Arch Intern Med (2007) 167:956–65.
[Abstract/Free Full Text] - Petersen ML, Sinisi SE, van der Laan MJ. Estimation of direct causal effects. Epidemiology (2006) 17:276–84.[CrossRef][Web of Science][Medline]
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Related articles in Am. J. Epidemiol.:
- A Statistical Test for the Equality of Differently Adjusted Incidence Rate Ratios
- Kurt Hoffmann, Tobias Pischon, Mandy Schulz, Matthias B. Schulze, Jennifer Ray, and Heiner Boeing
Am. J. Epidemiol. 2008 167: 517-522.[Abstract] [FREE Full Text]
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