A Bayesian Modeling Approach to Optimize Longitudinal Biomarker Sampling Schedules Using Hormonal Data

Optimal schedules for longitudinal biomarker sampling are specific to the individual biomarkers and study aims. We present a Bayesian modeling approach for evaluating intraindividual, interindividual, and population-level biomarker variation in order to optimize precision in parameter estimates and inform biomarker sampling decisions.

We apply Bayesian linear and nonlinear mixed-effects models to estimate individual- and population-level parameters of longitudinal hormone data from 35 pubertal girls. Starting with first morning void measures of urinary testosterone and C-peptide collected across a two-year timespan, we downsample these longitudinal data systematically to evaluate precision in parameter estimates from nine sampling frequencies: annual, biannual (6-month), and quarterly (3-month) intervals with one, two, and three repeated samples per interval.

Standard errors and credible intervals of individual- and population-level parameter estimates as well as the overall residual errors from our applied models indicate that specific dimensions of sampling frequency have distinct impacts on model parameters across different levels. Collectively, metrics of model fit, precision, and uncertainty indicate that more data are not always better, as we do not find parameter estimates to improve directly with increasing total sample size across models. Notably, we identify optimal sampling thresholds beyond which individual parameter estimates become less precise with additional measures.

The data, code, and results from these analyses provide tools for Bayesian model building, evaluation, and sampling decisions. Specific biomarker features impact precision in distinct ways, and our hormone modeling example showcases sampling analysis methods that are applicable to a broad range of biological data.