Abstract #198

# 198
A framework for conducting nonlinear meta-analysis in the dairy sciences.
Luis E. Moraes*1, 1The Ohio State University, Columbus, OH.

A framework for conducting meta-analysis based on linear mixed-effects model has been available to the dairy science community for almost 2 decades (St-Pierre, 2001; J. Dairy Sci. 84:741–755). However, statistical methods used when nonlinear models are developed with literature data are extremely heterogeneous. Methods that ignore the underlying structure of meta-analytic databases are frequently used. For instance, ignoring study effects can result in parameter estimates that are severely biased. Further, not accounting for potential heterogeneous errors across studies violates the assumption of homogeneous error variance. Although nonlinear mixed models provide a framework for introducing random effects into nonlinear models, meta-analytic designs are often sparse, with a narrow range of measurements for independent variables within studies. Consequently, dairy scientists have been frequently challenged with model convergence issues and have often ignored study effects or selected overly simplistic covariance structures. The objective of this study was to propose a general framework to conduct meta-analysis with nonlinear functional forms. A Bayesian hierarchical modeling approach is proposed and ideas borrowed from Empirical Bayes are utilized to increase the practicality and generality of the approach. In particular, a 2-step model fitting is proposed. Initially, weighted nonlinear least squares are used to obtain pooled estimates of model parameters. On the second step, a hierarchical model is used to introduce between study variability in the parameters of the nonlinear model. The connection between the 2 steps is that pooled estimates from the first step are used as hyperparameters for the prior distribution of the mean population parameters in the second step. Strategies to improve computational efficiency and numerical stability are also proposed within our framework, for instance, constructing the model for the between-study variability using Cholesky factors. Two examples with meta-analysis recently conducted on ruminant nutrition will be used to describe the framework, interpret results, and illustrate the use of software.

Key Words: nonlinear, meta-analysis, Bayesian