The geometry of the lactation curve based on Wood's equation: a two-step prediction

Lactation records from cows of the southwestern Paraná state, Brazil, form the dataset of this study. We applied the information-theoretic approach to evaluate the ability of the nonlinear Wood, Brody, Dijkstra, and Gamma functions to fit to these data by employing a two-step technique based on nonlinear mixed-effects models and generalized linear mixed-effects models. Wood's equation was fitted with the combination of a first-order autoregressive correlation structure and a variance function to account for heteroscedasticity. This version was the best choice to mimic lactation records. Some geometric attributes of Wood's model were deduced, mainly the ascending specific rate from parturition to peak milk yield and the descending specific rate as a measure of the lactation persistence of the milk yield at peak production. Breed and parity order of the cows were assumed as fixed effects to obtain a reliable model fitting process. Regardless of breed, first-order parity cows had greater persistency than their older counterparts, and the greater the ascending rate of milk yield from the parturition to the peak, the sharper the decrease in milk yield post-peak; therefore, the rates (absolute values) of ascending and descending phases correlated positively. Nonetheless, the actual estimated values of the descending phase rates are negative. Wood's equation was flexible enough to mimic either concave- and convex-shaped lactation profiles. The correlations between both peak milk yield and random estimates for ß with total milk yield per lactation were positive. However, peak milk yield might not be the only variable used for ranking cows; the total milk yield integrates all information of the lactation profile through the estimated parameters of Wood's equation.(AU)

Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements.

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to assess association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. When a nonlinear mixed-effects model is used to fit the longitudinal trajectories, the existing estimation strategies based on likelihood approximations have been shown to exhibit some computational efficiency problems (De la Cruz et al., 2011). In this article we consider a Bayesian estimation procedure for the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. The proposed prior structure allows for the implementation of an MCMC sampler. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to assess the importance of modelling correlated errors and quantify the consequences of model misspecification.