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EDUCATION AND DEBATE: Muhammad Mamdani, Kathy Sykora, Ping Li, Sharon-Lise T Normand, David L Streiner, Peter C Austin, Paula A Rochon, and Geoffrey M Anderson Reader's guide to critical appraisal of cohort studies: 2. Assessing potential for confounding BMJ 2005; 330: 960-962 [Full text]

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Adding an operational definition to confounding

James M O'Brien   (26 April 2005)

assessing differences in distribution

Richard Goldstein   (4 May 2005)

Adding an operational definition to confounding 26 April 2005
James M O'Brien, Assistant Professor, Division of Pulmonary, Critical Care and Sleep Medicine The Ohio State University Medical Center, 201 Davis HLRI, 473 West 12th Avenue, Columbus, OH 43210 Send response to journal: Re: Adding an operational definition to confounding	Mamdani et al. did an excellent job providing an introduction to confounding. However, I feel they should have been clear that they were explaining confounders as defined by the classical criteria. By the operational definition, a confounding variable is one that appreciably changes the association between the explanatory and outcome variables. This is particularly important for dichotomous outcomes. As an example, in a hypothetical study of lung cancer, smoking and gender, investigators report the following data1: MALE:   Smoking Lung Cancer   No Yes Total No 90 75 165 Yes 10 25 35 Total 100 100 200 Odds Ratio = 3.0 FEMALE:   Smoking Lung Cancer   No Yes Total No 50 25 75 Yes 50 75 125 Total 100 100 200 Odds Ratio = 3.0 By the “classic” definition (and that provided by Mamdani et al.), gender is not a confounder in the relationship between smoking and lung cancer. This is because there are the same proportion of smokers in both males and females. However, if one pools the data across gender, the following results are seen: BOTH GENDERS:   Smoking Lung Cancer   No Yes Total No 140 100 240 Yes 60 100 160 Total 200 200 400 Odds Ratio = 2.3 The crude odds ratio (2.3) is 22% lower than the OR adjusted for gender, even though gender does not meet the classic definition of confounding. Using the classic definition, gender would not be included in a risk-adjusting model to measures the independent association between smoking and lung cancer. Propensity scores are a method to try to account for differences between individuals in the comparative groups using multiple covariates. However, an explanation of the operational definition of confounding provides for greater risk-adjustment and completes the explanation of confounding. References: 1. Hauck WW, Neuhaus JM, Kalbfleisch JD, Anderson S. 1991. A consequence of omitted covariates when estimating odds ratios. J Clin Epidemiol, 44(1): 77-81. Competing interests: None declared
assessing differences in distribution 4 May 2005
Richard Goldstein, consulting statistician Brighton, MA USA 02135 Send response to journal: Re: assessing differences in distribution	On p. 960 of their article, the authors correctly note that a potential confounder that only differs in variation can still be a confounder. However, when they present their suggestion on how to assess differences, they only present a statistic (the standardized difference) that will not show a problem if the difference is primarily in the variability of the distribution. Since the authors, correctly, do not like standard tests of statistical significance, presumably they have something in mind other than a test of whether the variances are equal. I would be interested in knowing what they have in mind for this situation. Competing interests: None declared