## Likelihood-based estimators for meta-regression analyses of standardised differences of means

In this seminar we present the distribution for standardized difference of means (SMD) estimators under the assumption that the data is sampled from a normal distribution which includes a normally distributed random effect component. This distribution, a rescaled non-central t and which is not conditional on the random effect, can then be used to create maximum likelihood estimators (MLEs) where our main focus is on the meta-regression setting. Additionally, we explore the use of normalization transformations on the SMD estimates that can be used to obtain MLEs based on approximate normal densities which may reduce the computational effort required for estimation. An advantage of our approaches is that they do not require individual studies to consist of large sample sizes which is commonly assumed to be the case. We also highlight how simple these estimates and associated confidence intervals are to obtain using existing functionality within the R statistical package. Examples from the scientific literature are considered and we also present some simulation studies that compare these MLE estimators with other common approaches. Despite this being on-going work, some excellent simulation results point to the future availability of useful estimators for meta-regression analysis of SMDs.

This presentations is based on joint work between Luke Prendergast, Bob Staudte and Michael Malloy.