# Optimization of Serum and Salivary Cortisol Interpolation for Time-Dependent Modeling Frameworks in Healthy Adult Males

## TL;DR

This study finds that using second- and third-degree polynomial models can accurately estimate cortisol levels over 24 hours from less frequent sampling in healthy adult males.

## Contribution

The study introduces optimized polynomial interpolation methods for cortisol data to reduce sampling frequency without losing accuracy.

## Key findings

- Second- and third-degree polynomial models best fit salivary cortisol data.
- Interpolated cortisol estimates matched observed data in 24-hour output.
- Polynomial interpolation allows flexible sampling frequencies for cortisol analysis.

## Abstract

Cortisol is an important marker of hypothalamic-pituitary-adrenal function and follows robust circadian and diurnal rhythms. However, biomarker sampling protocols can be labor-intensive and cost-prohibitive. Objectives: Explore analytical approaches that can handle differing biological sampling frequencies to maximize these data in more detailed and time-dependent analyses. Methods: Healthy adult males [N = 8; 26.1 (±3.1) years; 176.4 (±8.6) cm; 73.1 (±12.0) kg)] completed two 24 h admissions: one at rest and one including a high-intensity exercise session on the cycle ergometer. Serum and salivary cortisol were sampled every 60 and 120 min, respectively. Six alternative sampling profiles were defined by downsampling from the observed data and creating two intermittent sampling profiles. A polynomial (1–6 degrees) validation process was performed, and interpolation was conducted to match the observed data. Model fit and performance were assessed using the coefficient of determination (R2) and the root mean square error (RMSE), as well as an examination of the equivalence, via two one-sided t-tests (TOST), of 24 h cortisol output between the observed and interpolated data. Results: Mean serum cortisol output was higher than salivary cortisol (p < 0.001), and no effect was observed for condition (p = 0.61). Second- and third-degree polynomial regressions were determined to be the optimal models for fitting salivary. TOST tests determined that serum data and estimated 24 h output from these models (with interpolation) provided statistically similar estimates to the observed data (p < 0.05). Conclusions: Second- and third-degree polynomial fits of salivary and serum cortisol provide a reasonable means for interpolation without introducing bias into estimates of 24 h output. This allows researchers to sample biomarkers at biologically relevant frequencies and subsequently match necessary sampling frequencies during the data processing stage of various machine learning workflows.