An efficient design strategy for logistic regression using outcome- and covariate-dependent pooling of biospecimens prior to assay

Gamma models for estimating the odds ratio for a skewed biomarker measured in pools and subject to errors

Measuring a biomarker in pooled samples from multiple cases or controls can lead to cost-effective estimation of a covariate-adjusted odds ratio, particularly for expensive assays. But pooled measurements may be affected by assay-related measurement error (ME) and/or pooling-related processing error (PE), which can induce bias if ignored. Building on recently developed methods for a normal biomarker subject to additive errors, we present two related estimators for a right-skewed biomarker subject to multiplicative errors: one based on logistic regression and the other based on a Gamma discriminant function model. Applied to a reproductive health dataset with a right-skewed cytokine measured in pools of size 1 and 2, both methods suggest no association with spontaneous abortion. The fitted models indicate little ME but fairly severe PE, the latter of which is much too large to ignore. Simulations mimicking these data with a non-unity odds ratio confirm validity of the estimators and illustrate how PE can detract from pooling-related gains in statistical efficiency. These methods address a key issue associated with the homogeneous pools study design and should facilitate valid odds ratio estimation at a lower cost in a wide range of scenarios.

Logistic regression with a continuous exposure measured in pools and subject to errors

In a multivariable logistic regression setting where measuring a continuous exposure requires an expensive assay, a design in which the biomarker is measured in pooled samples from multiple subjects can be very cost effective. A logistic regression model for poolwise data is available, but validity requires that the assay yields the precise mean exposure for members of each pool. To account for errors, we assume the assay returns the true mean exposure plus a measurement error (ME) and/or a processing error (PE). We pursue likelihood-based inference for a binary health-related outcome modeled by logistic regression coupled with a normal linear model relating individual-level exposure to covariates and assuming that the ME and PE components are independent and normally distributed regardless of pool size. We compare this approach with a discriminant function-based alternative, and we demonstrate the potential value of incorporating replicates into the study design. Applied to a reproductive health dataset with pools of size 2 along with individual samples and replicates, the model fit with both ME and PE had a lower AIC than a model accounting for ME only. Relative to ignoring errors, this model suggested a somewhat higher (though still nonsignificant) adjusted log-odds ratio associating the cytokine MCP-1 with risk of spontaneous abortion. Simulations modeled after these data confirm validity of the methods, demonstrate how ME and particularly PE can reduce the efficiency advantage of a pooling design, and highlight the value of replicates in improving stability when both errors are present.

Lipid and Creatinine Adjustment to Evaluate Health Effects of Environmental Exposures

PURPOSE OF REVIEW

Urine- and serum-based biomarkers are useful for assessing individuals' exposure to environmental factors. However, variations in urinary creatinine (a measure of dilution) or serum lipid levels, if not adequately corrected for, can directly impact biomarker concentrations and bias exposure-disease association measures.

RECENT FINDINGS

Recent methodological literature has considered the complex relationships between creatinine or serum lipid levels, exposure biomarkers, outcomes, and other potentially relevant factors using directed acyclic graphs and simulation studies. The optimal measures of urinary dilution and serum lipids have also been investigated. Existing evidence supports the use of covariate-adjusted standardization plus creatinine adjustment for urinary biomarkers and standardization plus serum lipid adjustment for lipophilic, serum-based biomarkers. It is unclear which urinary dilution measure is best, but all serum lipid measures performed similarly. Future research should assess methods for pooled biomarkers and for studying diseases and exposures that affect creatinine or serum lipids directly.