Optimising a coordinate ascent algorithm for the meta-analysis of test accuracy studies

Meta-analysis may be used to summarise a test’s accuracy. Often the sensitivity and specificity are the measures of interest and as these are correlated a bivariate random effects model is commonly used to fit the data. This model has five parameters and it may be optimised using a Newton-Raphson based algorithm providing adequate initial values of the parameters are identified. Numerical methods may be used to estimate robust initial values but estimating these is computationally expensive and it is not clear whether they provide a significant advantage over closed form methods in terms of reducing bias, mean square error, average relative error, and coverage probability. Here we consider six closed form methods for estimating the initial values of the parameters for a co-ordinate ascent algorithm used to fit the bivariate model and compare them with numerically derived robust initial values. Using simulation studies we demonstrate that all the closed form methods lead to a reduction in computation time of around 80% and rank higher overall across the metrics when compared with the robust initial values method. Although no initial values estimator dominated the others across all parameters and metrics, the two-step Hedges-Olkin estimator ranked highest overall across the different scenarios.