A comparison of statistical methods for combining relative bioactivities from parallel line bioassays

Abstract

This paper compares the ordinary unweighted average, weighted average, and maximum likelihood methods for estimating a common bioactivity from multiple parallel line bioassays. Some of these or similar methods are also used in meta-analysis. Based on a simulation study, these methods are assessed by comparing coverage probabilities of the true relative bioactivity and the length of the confidence intervals computed for these methods. The ordinary unweighted average method outperforms all statistical methods by consistently giving the best coverage probability but with somewhat wider confidence intervals. The weighted average methods give good coverage and smaller confidence intervals when combining homogeneous bioactivities. For heterogeneous bioactivities, these methods work well when a liberal significance level for testing homogeneity of bioactivities is used. The maximum likelihood methods gave good coverage when homogeneous bioactivities were considered. Overall, the preferred methods are the ordinary unweighted average and two weighted average methods that were specifically developed for bioassays.

Jointly pooling aggregated effect sizes and their standard errors from studies with continuous clinical outcomes

“…For meta‐analyses with a very small number of studies, our approach can still be improved by implementing the appropriate degrees of freedom when the between‐study variance is estimated zero. This would also be true for the other conservative methods (Mzolo et al., 2013 ).…”

“…The conservative coverage probabilities are explained by the incorrect use of the degrees of freedom in the t ‐quantile. The estimates for the between‐study variance frequently vanishes, which would imply that the degrees of freedom for the estimated standard error of the pooled effect size is much closer to the sum of all the degrees of freedom in the meta‐analysis study (Cochran, 1954 ; Mzolo et al., 2013 ). In that case, a normal quantile is warranted or one could update the degrees of freedom in the t ‐quantile.…”

“…In the presence of heterogeneous effect sizes ($$\tau ^{2}>0$$), the precision of the pooled estimator $$\hat{\theta }_{DL}$$ depends on the number of studies and confidence intervals based on normal quantiles lead to an undercoverage. This has been well‐established in the work of Cochran (Cochran, 1954), who proposed to use the t ‐distribution with $$m-1$$ degrees of freedom instead of the normal distribution, in particular in the presence of heterogeneity (see also Mzolo et al., 2013). Higher degrees of freedom should be used when no heterogeneity in the effect sizes is present (Cochran, 1954).…”

A bivariate likelihood approach for estimation of a pooled continuous effect size from a heteroscedastic meta-analysis study

“…Note that it has been more common in literature to use the normal quantile instead of the quantile of the t-distribution (Brockwell and Gordon, 2007;Thorlund et al, 2011;Jackson et al, 2010), but we believe that DerSimonian and Laird were not explicit on this topic (DerSimonian and Laird, 1986) and therefore did not rule out our preferred choice. We believe that our choice is in line with the work of Cochran (Cochran, 1954), who proposed to use the t-distribution with m − 1 degrees of freedom instead of the normal distribution, in particular in the presence of heterogeneity (see also Mzolo et al (2013)). The use of this t-distribution is common when the corrected standard error of Hartung-Knapp-Sidik-Jonkman is used (Sidik and Jonkman, 2005) .…”