# Statistical methods for biomarker data pooled from multiple nested case-control studies

## TL;DR

This paper introduces new statistical methods for calibrating and pooling biomarker data from multiple nested case-control studies, improving the accuracy of disease association estimates across diverse datasets.

## Contribution

It proposes a two-stage and two aggregated calibration methods, with the full calibration method being optimal for bias reduction in pooled biomarker analyses.

## Key findings

- Full calibration minimizes bias in effect estimates.
- Two-stage and full calibration methods yield similar effect estimates.
- Full calibration provides more accurate pooled biomarker-disease associations.

## Abstract

Pooling biomarker data across multiple studies allows for examination of a wider exposure range than generally possible in individual studies, evaluation of population subgroups and disease subtypes with more statistical power, and more precise estimation of biomarker-disease associations. However, biomarker measurements often require calibration to a reference assay prior to pooling due to assay and laboratory variability across studies. We propose several methods for calibrating and combining biomarker data from nested case-control studies when reference assay data are obtained from a subset of controls in each contributing study. Specifically, we describe a two-stage method and two aggregated methods, named the internalized and full calibration methods, to evaluate the main effect of the biomarker exposure on disease risk and whether that association is modified by a potential covariate. The internalized method uses the reference laboratory measurement in the analysis when available and otherwise uses the calibrated measurement. The full calibration method uses calibrated biomarker measurements for all subjects, even those with reference laboratory measurements. Our results demonstrate that the full calibration method is the preferred aggregated approach to minimize bias in point estimates regardless of the inclusion of an interaction term in the model. We also observe that the two-stage and full calibration methods provide similar effect and variance estimates, but that the variance estimates for these two methods are slightly larger than those from the internalized approach. As an illustrative example, we apply the methods in a pooling project of nested case-control studies to evaluate (i) the association between circulating vitamin D levels and risk of stroke, and (ii) how BMI modifies the association between circulating vitamin D levels and cardiovascular disease.