Invited review: A review of some commonly used meta-analysis methods in dairy science research

Meta-analyses have become increasingly common, providing meaningful summaries of cumulative knowledge in the dairy science literature. Some of the corresponding meta-analytic techniques have been developed by knowledgeable dairy scientists, some of which predate tractable likelihood-based random or mixed effects model meta-analytic techniques and associated software developed by statisticians. This review compares various meta-analytic techniques on aggregate data (i.e., study-specific treatment effect or slope estimates and their standard errors) generated from simulated data involving regression, completely randomized designs (CRD), and Latin square design scenarios. In all cases, meta-estimates generated from the analysis of individual performance data (IPD), using the same statistical model as that used to simulate the data, were considered to be gold-standard references for meta-estimates derived from various meta-analysis strategies on aggregate data. In all cases, likelihood-based techniques outperformed techniques developed by dairy scientists for meta-estimate proximity to corresponding IPD estimates. An extensive simulation study comparing meta-analytic techniques within a CRD framework indicated that these advantages widen with increasing study heterogeneity in effect sizes, smaller number of experimental replicates (i.e., cows) per treatment per study, and lower within-study variability; nevertheless, the impact of meta-analytic methods on estimated standard errors of these meta-estimates were rather trivial. To best utilize aggregate data from Latin square studies in meta-analyses, a concerted effort is required to recover standard errors of mean differences rather than the standard errors of the means themselves. Perhaps the most compelling reason for choosing likelihood-based methods for meta-analysis is their ability to provide reliable prediction intervals on effect sizes, noting that these intervals are currently under-reported in the dairy science literature. Compared with the reporting of meta-estimates and their standard errors, prediction intervals provide a far more appropriate indication of uncertainty on treatment effects in future studies and should be greater emphasized in extension or outreach efforts. Although R software packages such as metafor are readily available for likelihood-based methods, both SAS and R code for linear mixed models can be readily modified to facilitate these analyses as demonstrated extensively in the supplemental materials of this review.