Comparison of statistical models in a meta-analysis of fungicide treatments for the control of citrus black spot caused by Phyllosticta citricarpa
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Meta-analysis has been recognised as a powerful method to synthetize existing published data from different studies through a formal statistical analysis. Several statistical models have been proposed to evaluate the effectiveness of treatments against plant diseases using meta-analysis, but the sensitivity of the estimated treatment effects to the model chosen has not been investigated in detail in the context of plant pathology. In this paper, four different statistical models were defined to analyse fungicide control trials with binary outcomes. These models were used to conduct a meta-analysis on the effectiveness of fungicide treatments against citrus black spot, a fungal disease caused by the quarantine pathogen Phyllosticta citricarpa. The models differed in the assumption made on the variability of the treatment effect (constant or variable between experimental plots) and in the method used for parameter estimation (classical or Bayesian). Odds ratios were estimated for two groups of fungicides, copper compounds and dithiocarbamates, widely applied for CBS control using each model in turn. Classical and Bayesian statistical models led to similar results, but the estimated treatment effectiveness and their associated levels of uncertainty were sensitive to the assumption made about the variability of the treatment effect. Estimated odds ratios were different depending on whether the treatment effect was assumed to be constant or variable between experimental plots. The size of the confidence intervals was underestimated when the treatment effect was assumed constant while it was variable in reality. Because of the strong between-plot variability, the 90 % percentiles of the odds ratios were much higher than the point estimates, and this result revealed that, in some plots, treatment effectiveness could be much lower than expected. Based on our results, we conclude that it is not sufficient to calculate point estimates of odds ratio when the between-plot variability of the treatment effect is strong and that, in such case, it is recommended to compute the predictive distributions of the odds ratio.