A. L. Mila and
H. K. Ngugi
First author: Department of Plant Pathology, North Carolina State University, Campus Box 7405, Raleigh 27606; and second author: Department of Plant Pathology, Pennsylvania State University, Fruit Research & Extension Center, Biglerville 17307.
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Bayesian statistical methods are used for meta-analysis in many disciplines, including medicine, molecular biology, and engineering, but have not yet been applied for quantitative synthesis of plant pathology studies. In this paper, we illustrate the key concepts of Bayesian statistics and outline the differences between Bayesian and classical (frequentist) methods in the way parameters describing population attributes are considered. We then describe a Bayesian approach to meta-analysis and present a plant pathological example based on studies evaluating the efficacy of plant protection products that induce systemic acquired resistance for the management of fire blight of apple. In a simple random-effects model assuming a normal distribution of effect sizes and no prior information (i.e., a noninformative prior), the results of the Bayesian meta-analysis are similar to those obtained with classical methods. Implementing the same model with a Student's t distribution and a noninformative prior for the effect sizes, instead of a normal distribution, yields similar results for all but acibenzolar-S-methyl (Actigard) which was evaluated only in seven studies in this example. Whereas both the classical (P = 0.28) and the Bayesian analysis with a noninformative prior (95% credibility interval [CRI] for the log response ratio: –0.63 to 0.08) indicate a nonsignificant effect for Actigard, specifying a t distribution resulted in a significant, albeit variable, effect for this product (CRI: –0.73 to –0.10). These results confirm the sensitivity of the analytical outcome (i.e., the posterior distribution) to the choice of prior in Bayesian meta-analyses involving a limited number of studies. We review some pertinent literature on more advanced topics, including modeling of among-study heterogeneity, publication bias, analyses involving a limited number of studies, and methods for dealing with missing data, and show how these issues can be approached in a Bayesian framework. Bayesian meta-analysis can readily include information not easily incorporated in classical methods, and allow for a full evaluation of competing models. Given the power and flexibility of Bayesian methods, we expect them to become widely adopted for meta-analysis of plant pathology studies.
acibenzolar-S-methyl, Apogee, Erwinia amylovora, harpin protein, Messenger, prohexadione-calcium, systemic acquired resistance.
© 2011 The American Phytopathological Society