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On quantifying the magnitude of confounding.

ABSTRACT: When estimating the association between an exposure and outcome, a simple approach to quantifying the amount of confounding by a factor, Z, is to compare estimates of the exposure-outcome association with and without adjustment for Z. This approach is widely believed to be problematic due to the nonlinearity of some exposure-effect measures. When the expected value of the outcome is modeled as a nonlinear function of the exposure, the adjusted and unadjusted exposure effects can differ even in the absence of confounding (Greenland , Robins, and Pearl, 1999); we call this the nonlinearity effect. In this paper, we propose a corrected measure of confounding that does not include the nonlinearity effect. The performances of the simple and corrected estimates of confounding are assessed in simulations and illustrated using a study of risk factors for low birth-weight infants. We conclude that the simple estimate of confounding is adequate or even preferred in settings where the nonlinearity effect is very small. In settings with a sizable nonlinearity effect, the corrected estimate of confounding has improved performance.

SUBMITTER: Janes H

PROVIDER: S-EPMC2883302 | biostudies-literature | 2010 Jul

REPOSITORIES: biostudies-literature

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On quantifying the magnitude of confounding.

Janes Holly H Dominici Francesca F Zeger Scott S

Biostatistics (Oxford, England) 20100304 3

When estimating the association between an exposure and outcome, a simple approach to quantifying the amount of confounding by a factor, Z, is to compare estimates of the exposure-outcome association with and without adjustment for Z. This approach is widely believed to be problematic due to the nonlinearity of some exposure-effect measures. When the expected value of the outcome is modeled as a nonlinear function of the exposure, the adjusted and unadjusted exposure effects can differ even in t ...[more]

PMID: 20203259

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Project description:BackgroundConfounding bias is a common concern in epidemiological research. Its presence is often determined by comparing exposure effects between univariable- and multivariable regression models, using an arbitrary threshold of a 10% difference to indicate confounding bias. However, many clinical researchers are not aware that the use of this change-in-estimate criterion may lead to wrong conclusions when applied to logistic regression coefficients. This is due to a statistical phenomenon called noncollapsibility, which manifests itself in logistic regression models. This paper aims to clarify the role of noncollapsibility in logistic regression and to provide guidance in determining the presence of confounding bias.MethodsA Monte Carlo simulation study was designed to uncover patterns of confounding bias and noncollapsibility effects in logistic regression. An empirical data example was used to illustrate the inability of the change-in-estimate criterion to distinguish confounding bias from noncollapsibility effects.ResultsThe simulation study showed that, depending on the sign and magnitude of the confounding bias and the noncollapsibility effect, the difference between the effect estimates from univariable- and multivariable regression models may underestimate or overestimate the magnitude of the confounding bias. Because of the noncollapsibility effect, multivariable regression analysis and inverse probability weighting provided different but valid estimates of the confounder-adjusted exposure effect. In our data example, confounding bias was underestimated by the change in estimate due to the presence of a noncollapsibility effect.ConclusionIn logistic regression, the difference between the univariable- and multivariable effect estimate might not only reflect confounding bias but also a noncollapsibility effect. Ideally, the set of confounders is determined at the study design phase and based on subject matter knowledge. To quantify confounding bias, one could compare the unadjusted exposure effect estimate and the estimate from an inverse probability weighted model.

Project description:Genetic selection programs have driven development of most lactation models, to estimate the magnitude of animals' productive capacity from sampled milk production data. There has been less attention to management and research applications, where it may also be important to quantify the shape of lactation curves, and predict future daily milk production for incomplete lactations since residuals between predicted and actual daily production can be used to quantify the response to an intervention. A model may decrease the confounding effects of lactation stage, parity, breed, and possibly other factors depending on how the model is constructed and used, thus increasing the power of statistical analyses. Models with a mechanistic derivation may allow direct inference about biology from fitted production data. The MilkBot(®) lactation model is derived from abstract suppositions about growth of udder capacity. This permits inference about shape of the lactation curve directly from parameter values, but not direct conclusions about physiology. Individual parameters relate to the overall scale of the lactation, the ramp , or rate of growth around parturition, decay describing the senescence of productive capacity (inversely related to persistence ), and the relatively insignificant time offset between calving and the physiological start of milk secretion. A proprietary algorithm was used to fit monthly test data from two parity groups in 21 randomly selected herds, and results displayed in box-and-whisker charts and Z-test tables. Fitted curves are constrained by the MilkBot(®) equation to a single peak that blends into an exponential decline in late lactation. This is seen as an abstraction of productive capacity, with actual daily production higher or lower due to random error plus short-term environmental effects. The four MilkBot(®) parameters, and metrics calculated directly from them including fitting error, peak milk and cumulative production, can be used to describe and compare individual lactations or groups of lactations. There is considerable intra-herd and inter-herd variability in scale, ramp, decay, RMSE, peak milk, and cumulative production, suggesting that management and environment have significant influence on both shape and magnitude of normal lactation curves.

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On quantifying the magnitude of confounding.

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On quantifying the magnitude of confounding.

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