Multi-treatment (“network”) meta-analysis in agriculture

Meta-analysis, the methodology for analyzing the results from multiple studies, has grown tremendously in popularity since being first proposed by Smith and Glass in 1977. Although most meta-analyses involve a single effect size from each study (e.g., a mean difference for two treatments or a log-odds ratio), there are often multiple treatments of interest across the network of studies. Multi-treatment or network meta-analysis (NMA) can be used for simultaneously analyzing the results from all the treatments simultaneously. With this approach, correlations of treatment effects are automatically taken into account (when an appropriate model is used), and more studies may be included in the analysis because individual studies need not contain all of the treatments of interest. In fact, NMA is typically performed for sparse study-by-treatment classifications, allowing for the combination of direct and indirect evidence of treatment effects.

NMA can be based on contrasts with a baseline treatment from each study or directly on treatment arms from each study, with the estimation of contrasts performed after the model fit. The contrast-based approach is more popular, overall, especially in medical research, thanks to the statistical work and advocacy by Lu, Ades, and colleagues. Piepho, Williams and Madden showed that the results are very similar for contrast- and arm-based methods, and equivalent under some circumstances, if the appropriate mixed model is chosen. Equivalence requires, among other things, the use of a fixed main effect of study (trial) in the model. Arm-based methods are much easier to perform with standard mixed-model software, and are straight- forward to expand for incorporation of effects of moderator-variables (study-level covariates) on the response variable.

In the plant and agricultural sciences, arm-based NMA is most common. Original observations are usually not available, so the analysis is almost always based on the summary results (e.g., means) for each treatment in each study (with weights based on the within-study variances). The most extensive use of NMA probably has been in the estimation of the effects of chemical treatments (fungicides) in controlling the most economically important disease of wheat in the world, Fusarium head blight. There are now over 300 studies in the database, with over 25 different treatments, with response variables for disease severity, toxin concentration in harvested wheat grain, and yield. The mixed-model arm-based NMA is demonstrated for this dataset, and methods are proposed to determine if treatment effects are stable over the 19 years of the investigation.