A general framework for the regression analysis of pooled biomarker assessments

Additive partially linear model for pooled biomonitoring data

Human biomonitoring involves monitoring human health by measuring the accumulation of harmful chemicals, typically in specimens like blood samples. The high cost of chemical analysis has led researchers to adopt a cost-effective approach. This approach physically combines specimens and subsequently analyzes the concentration of toxic substances within the merged pools. Consequently, there arises a need for innovative regression techniques to effectively interpret these aggregated measurements. To address this need, a new regression framework is proposed by extending the additive partially linear model (APLM) to accommodate the pooling context. The APLM is well-known for its versatility in capturing the complex association between outcomes and covariates, which is particularly valuable in assessing the complex interplay between chemical bioaccumulation and potential risk factors. Consistent estimators of the APLM are obtained through an iterative process that disaggregates information from the pooled observations. The performance is evaluated through simulations and an environmental health study focused on brominated flame retardants using data from the National Health and Nutrition Examination Survey.

Assessing disparities in Americans' exposure to PCBs and PBDEs based on NHANES pooled biomonitoring data

The National Health and Nutrition Examination Survey (NHANES) has been continuously biomonitoring Americans' exposure to two families of harmful environmental chemicals: polychlorinated biphenyls (PCBs) and polybrominated diphenyl ethers (PBDEs). However, biomonitoring these chemicals is expensive. To save cost, in 2005, NHANES resorted to pooled biomonitoring; i.e., amalgamating individual specimens to form a pool and measuring chemical levels from pools. Despite being publicly available, these pooled data gain limited applications in health studies. Among the few studies using these data, racial/age disparities were detected, but there is no control for confounding effects. These disadvantages are due to the complexity of pooled measurements and a dearth of statistical tools. Herein, we developed a regression-based method to unzip pooled measurements, which facilitated a comprehensive assessment of disparities in exposure to these chemicals. We found increasing dependence of PCBs on age and income, whereas PBDEs were the highest among adolescents and seniors and were elevated among the low-income population. In addition, Hispanics had the lowest PCBs and PBDEs among all demographic groups after controlling for potential confounders. These findings can guide the development of population-specific interventions to promote environmental justice. Moreover, both chemical levels declined throughout the period, indicating the effectiveness of existing regulatory policies.

Varying-coefficient regression analysis for pooled biomonitoring

Human biomonitoring involves measuring the accumulation of contaminants in biological specimens (such as blood or urine) to assess individuals' exposure to environmental contamination. Due to the expensive cost of a single assay, the method of pooling has become increasingly common in environmental studies. The implementation of pooling starts by physically mixing specimens into pools, and then measures pooled specimens for the concentration of contaminants. An important task is to reconstruct individual-level statistical characteristics based on pooled measurements. In this article, we propose to use the varying-coefficient regression model for individual-level biomonitoring and provide methods to estimate the varying coefficients based on different types of pooled data. Asymptotic properties of the estimators are presented. We illustrate our methodology via simulation and with application to pooled biomonitoring of a brominated flame retardant provided by the National Health and Nutrition Examination Survey (NHANES).

Local polynomial regression for pooled response data

We propose local polynomial estimators for the conditional mean of a continuous response when only pooled response data are collected under different pooling designs. Asymptotic properties of these estimators are investigated and compared. Extensive simulation studies are carried out to compare finite sample performance of the proposed estimators under various model settings and pooling strategies. We apply the proposed local polynomial regression methods to two real-life applications to illustrate practical implementation and performance of the estimators for the mean function.

Formulas and Web Application for Designing a Biospecimen Pooling Study to Compare Group Means

BACKGROUND

When research focuses on biomarker assessment in settings where per-assay costs are high relative to per-subject costs, a biospecimen pooling study design can be extremely cost-effective. However, designing a study to maximize cost savings is complicated by the fact that pooled measurements are typically subject to processing error, inducing additional variability caused by combining biospecimens, and may also be affected by assay-related measurement error.

METHODS

We provide formulas and an interactive web application (hereafter called app) for designing a pooling study to compare group means. Power and sample size formulas are justified by Central Limit Theorem arguments that make no distributional assumptions on the biomarker. Errors can be assumed mean-0 additive or mean-1 multiplicative, the latter being well-suited for skewed biomarkers.

RESULTS

User inputs for the app include usual power parameters as well as per-assay and per-subject costs and information about the errors: which are present, whether they are additive or multiplicative, and their variances. The app generates plots revealing the optimal pool size, required number of assays, cost savings, and sensitivity to the hard-to-predict processing error variance.

CONCLUSIONS

These tools should aid in the design and deployment of pooling studies powered to detect group mean differences while minimizing total study costs.

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.