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A consequence of omitted covariates when estimating odds ratios
W W Hauck1, J M Neuhaus, J D Kalbfleisch
1Department of Epidemiology and Biostatistics, University of California, San Franciso 94143-0560.
Abstract:
In the epidemiologic literature, one finds three criteria for confounding, which we will call the classical (marginal), operational (change-in-estimate) and conditional criteria. We define mavericks to be covariates that satisfy the operational criterion, but not the classical criterion. We present what is known about the problems of mavericks for estimating odds ratios and clarify the interpretation of odds ratios. Key results are: (1) omitting mavericks biases odds ratios towards 1; (2) omitting mavericks cannot artificially introduce an effect in contrast to omitting classical confounders; (3) the operational criterion for confounding corresponds to the conditional criterion when estimating odds ratios, but for relative risks, there are no mavericks (i.e. the classical and operational criterion correspond); and (4) the interpretation of odds ratios obtained from standard methods is that of comparing proportions, not of individual risk.
Insights
Mavericks, covariates meeting the operational but not classical confounding criteria, bias odds ratios toward 1 when omitted. Unlike classical confounders, omitting mavericks does not create artificial effects, clarifying odds ratio interpretation.
Area of Science:
- Epidemiology
- Biostatistics
Background:
- Confounding is a critical concept in epidemiologic research, with established criteria for identification.
- Three criteria for confounding exist: classical (marginal), operational (change-in-estimate), and conditional.
- Mavericks are covariates satisfying the operational criterion but not the classical one.
Purpose of the Study:
- To define and investigate 'mavericks' in epidemiologic studies.
- To clarify the impact of mavericks on estimating odds ratios and their interpretation.
- To differentiate the behavior of mavericks from classical confounders.
Main Methods:
- Review of epidemiologic literature on confounding criteria.
- Theoretical analysis of the effect of omitting mavericks on odds ratio estimation.
- Comparison of confounding criteria for odds ratios versus relative risks.
Main Results:
- Omitting mavericks biases odds ratios towards 1.
- Omitting mavericks does not artificially introduce an effect, unlike omitting classical confounders.
- For odds ratios, the operational criterion aligns with the conditional criterion; for relative risks, they correspond to the classical and operational criteria.
Conclusions:
- Mavericks present unique challenges in odds ratio estimation.
- Understanding mavericks is crucial for accurate interpretation of odds ratios as comparisons of proportions, not individual risks.
- The distinction between odds ratios and relative risks is highlighted concerning maverick covariates.