We compare leading statistical methods to combine information from independent similar studies using random effects model. One of the oldest methods is that of Cochran (1954). The method of Paule and Mandel (1982) was developed to determine the consensus value of a measurand from interlaboratory studies. The methods of DerSimonian and Laird(1986) was developed to combine information from clinical trials. Rukhin et al. (2000) show that the Paule and Mandel estimate is optimal in the sense of being the restricted maximum likelihood estimate under normality. We show that normality is not needed. The method of Paule and Mandel is universally optimal in generalized (weighted) least-squares theory. We show that all three methods are special cases one theorem. The method of Paule and Mandel is iterative. One reason for the popularity of the method of DerSimonian and Laird is that it is non-iterative. The common theorem that links the three methods suggests a second non-interative method. We include it in the pool for comparison. We compare the methods of Cochran, DerSimonian and Laird, and the second non-iterative method proposed here against the optimal method of Paule and Mandel using six data sets from interlaboratory evaluations. We cannot think of a good reason for not using the optimal methods of Paule and Mandel to combine information from independent similar studies using random effects model. However, if one must use a non-iterative method, the second non-iterative method proposed here approximates the optimal method of Paule and Mandel better than the method of DerSimonian and Laird.
Citation: Journal of Quality Technology
Pub Type: Journals
clinical trials, heteroscedastic, interlaboratory evaluations, Meta-analysis, restricted maximum likelihood, unbalanced, uncertainty, variance components