A Discriminant Function Approach to Adjust for Processing and Measurement Error When a Biomarker is Assayed in Pooled Samples

Comparison of strategies to efficiently combine repeated urine samples in biomarker-based studies

BACKGROUND

In biomarker-based studies, collecting repeated biospecimens per participant can decrease measurement error, particularly for biomarkers displaying high within-subject variability. Guidelines to combine such repeated biospecimens do not exist.

AIMS

To compare the efficiency of several designs relying on repeated biospecimens to estimate exposure over 7 days.

METHODS

We quantified triclosan and bisphenol A (BPA) in all urine voids (N = 427) collected over seven days from eight individuals. We estimated the volume-weighted concentrations for all urine samples collected during a week and compared these gold standards with the concentrations obtained for equal-volume pools (standardized or not for urine dilution), unequal-volume pools (based on sample volume or creatinine concentration), and for the mean of the creatinine-standardized concentrations measured in each spot sample.

RESULTS

For both chemicals, correlations with gold standards were similar for equal- and unequal-volume pooling designs. Only for BPA, correlation coefficients were markedly lower after standardization for specific gravity or creatinine of concentrations estimated in equal-volume pools. Averaging BPA creatinine-standardized concentrations measured in each spot sample led also to lower correlations with gold standards compared to those obtained for unstandardized pooling designs.

CONCLUSION

For BPA and triclosan, considering individual urine sample volume or creatinine concentrations when pooling is unnecessary because equal-volume pool adequately estimates concentrations in gold standards. Standardization for specific gravity or creatinine of the concentrations assessed in equal-volume pool as well as averaging creatinine-standardized concentrations measured in each individual spot sample are not suitable for BPA. These results provide a practical framework on how to combine repeated biospecimens in epidemiological studies.

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.

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.