Revisiting Meta-analytic Strategies for Latin Square Designs

Meta-analyses studies continue to be published within the Journal of Dairy Science (JDS), with much of the corresponding analysis techniques developed in some landmark JDS papers. These techniques have served the JDS research community reasonably well with respect to the estimation of overall treatment effects or slopes and their standard errors in completely randomized designs (CRD). I recently published a simulation study in JDS that demonstrated these techniques to be less suitable compared to more proper and widely used (outside JDS) likelihood-based techniques developed by statisticians. Most importantly, these methods can be used to provide prediction intervals (PI) on treatment effects. These PI are rarely reported in JDS but should be of critical relevance to extension efforts as they best reflect a plausible range of treatment effects within any one commercial environment or future study. It is rather straightforward to apply R and SAS mixed model software to conduct a proper meta-analyses for CRD. However, a current conundrum with respect to adapting these techniques to Latin square (LS) designs is the extraction of standard errors of mean differences (SED). That is, only standard errors of the means (SEM), rather than SED, are typically reported in JDS studies. With random blocking factors (e.g., cows), SEM are functions of several variance components whereas SED are functions of only the estimated residual variance (MSE) in LS designs; hence, it is challenging to use SEM to derive SED. It has been previously demonstrated by Larry Madden’s group that treatment mean separation based on, for example, Tukey’s test can be used to derive SED. Nevertheless, I demonstrate using simulation that this strategy has limited effectiveness if only a few (i.e., 2-4) treatments are compared within component studies as is typical in JDS. Other potential strategies involve using P-values for contrasts (e.g., orthogonal polynomial, 2 x 2 factorial) to backsolve for MSE/SED; however, that also invokes various challenges as I will share. Hence, reporting SED or estimated variance components might be routinely encouraged in future JDS papers to facilitate more reliable meta-estimates and PI in subsequent meta-analyses. However, feedback as to how to best include past/current studies would be welcome.