Performance evaluation of different computational methods to estimate Wood's lactation curve by nonlinear mixed-effects models

Abstract

Nonlinear mixed-effects models allow modeling repeated measures over time. The fixed effects of these models allow incorporating covariates, whereas the random effects reflect the multiple sources of heterogeneity and correlation between and within the units. To estimate the parameters of these models, it is necessary to use iterative processes, which can be done through different approaches, some of which are applied by the statistical software SAS. In this work, through simulation, we studied the performance of the estimators of a Wood’s incomplete gamma function, obtained through three different methods: linearization method through a Taylor series expansion on the empirical best linear unbiased predictor of random effects, applied by the NLINMIX macro, and expansion around the expected value of random effects, applied by both the NLINMIX macro and the NLMIXED procedure. We also investigated the impact of an incorrect specification of the covariance matrix for random errors. The linearization method through a Taylor series expansion on the empirical best linear unbiased predictor of random effects, applied by the NLINMIX macro, provided estimators with good performance, approximately normally distributed and with biases lower than those obtained with the other methods, even when the covariance matrix for random errors was incorrectly specified.