Statistical methods for meta-analysis

A meta-analysis is a statistical analysis method which synthesises the results of multiple trials into a single result. Rather than focusing on one of the individual trials' conclusions, a meta-analysis can describe in a concise manner the body of evidence. If the meta-analysis is created using studies with low risk of bias, the results of a meta-analysis are considered to be the highest standard of evidence. However, the quality of the meta-analysis is also dependent on the statistical method used for modelling the data. Many factors can lead to bias, invalidity or misinterpretation of the results of the meta-analysis. This thesis presents a statistical investigation of two such areas: subgroup meta-analysis and sequential meta-analysis.

The first area, subgroup meta-analysis, relates to ecological bias in aggregate data subgroup meta-analysis. Ecological bias is a type of bias caused by the ecological level of a subgroup which modifies the effect of treatment on outcome. Ecological bias may lead to confounding that biases the assessment of subgroup and treatment effect interactions, depending on the analysis method used. This thesis proposes a new method for subgroup meta-analysis using linear mixed models. The method is used for estimating effect modification of treatment by subgroup while correcting for ecological bias. This method fills gaps where the existing methods fall short.

The second area, sequential meta-analysis, is concerned with the validity of statistical results when a meta-analysis is updated sequentially. Updating a meta-analysis will increase the risk of finding a false-positive. If properly planned in advance using a group sequential design, the inflation of type-I-error may be removed. Trial Sequential Analysis is a software package developed in Java to adapt the group sequential designs originally created for single trials to meta-analyses. A new version of the software is presented with multiple extensions. New features include updated methods for sample size calculation, a framework for prospective meta-analysis, binding and non-binding futility boundaries for both one- or two-sided designs, and an extended library for calculating inference. A software package for the statistical software language R is presented.

A further problem considered within sequential meta-analysis is a specific type of bias. Conditional bias due to a decision to continue a meta-analysis happens when new studies are motivated by earlier information, e.g. the results of a promising but not definitive meta-analysis. If the new studies are combined with the promising meta-analysis this results in an upwards bias of the point estimate. Inspired by the adjustment estimators developed for group sequential methods for single trials, this thesis presents an estimator for updating meta-analyses adjusting for the conditional bias from decision making.