Use of a non-linear spline regression to model time-varying fluctuations in mammary-secretion element concentrations of periparturient mares in Michigan, USA

Abstract

A study was designed to model the fluctuations of nine specific element concentrations in mammary secretions from periparturient mares over time. During the 1992 foaling season, serial samples of mammary secretions were collected from all 18 pregnant Arabian mares at the Michigan State University equine teaching and research center. Non-linear regression techniques were used to model the relationship between element concentration in mammary secretions and days from foaling (which connected two separate sigmoid curves with a spline function); indicator variables were included for mare and mare parity. Element concentrations in mammary secretions varied significantly during the periparturient period in mares. Both time trends and individual variability explained a significant portion of the variation in these element concentrations. Multiparous mares had lower concentrations of K and Zn, but higher concentrations of Na. Substantial serial and spatial correlation were detected in spite of modeling efforts to avoid the problem. As a result, p-values obtained for parameter estimates were likely biased toward zero. Nonetheless, results of this analysis indicate that monitoring changes in mammary-secretion element concentrations might reasonably be used as a predictor of impending parturition in the mare. In addition, these results suggest that element concentrations warrant attention in the development of neonatal milk-replacement therapies. This study demonstrates that non-linear regression can be used successfully to model time-series data in animal-health management. This approach should be considered by investigators facing similar analytical challenges.