Studies in the Combination of Bioassay Results

The usual method of combining potency ratios (by a weighted mean of the log potencies, the weights being inversely proportional to the estimated variances) gives a bias towards the nominal potency. A first order approximation to this bias is obtained, using asymptotic expansions. Monte Carlo studies in situations with high degrees of freedom for estimation of error in individual assays confirm this theoretical approximation and show also that the x2 heterogeneity statistic may be biased downwards, whereas a recently proposed maximum likelihood (ML) estimator appears to be approximately unbiased and to yield a heterogeneity statistic closely following the x2 distribution. Further Monte Carlo studies, in situations with low degrees of freedom, reveal a tendency for the asymptotic theory to become unreliable, especially in cases where values of g, the familiar assay quantity, are large.