Hat Matrix Meta-analysis

The nodes correspond to the treatments and the edges show which treatments are directly compared.

Hat matrix meta-analysis. W hen we perform meta-analyses of clinical trials or other types of intervention studies we usually estimate the true effect size of one specific treatment. The results of an NMA depend critically on the quality of evidence being pooled. We start with the projection matrix in a two-step network meta-analysis model called the H matrix which is analogous to the hat matrix in a linear regression model.

It describes the influence each response value has on each fitted value. 1 summarizing effect size estimates across studies 2 characterizing and 3 explaining the variability in the effect sizes. We develop a method to translate H entries to proportion contributions based on the observation that the rows of H can be interpreted as flow networks where a stream is defined.

The results of an NMA depend critically on the quality of evidence being pooled. In the first step a pairwise meta-analysis is performed across each edge using the adjusted weights these account for correlations due to multi-arm trials. Removing these study sets did not change the overall trends and conclusions for the yield.

The three major goals of meta-analysis include. Let n be the number of different treatments nodes vertices in a network and let m be the number of existing comparisons edges between the treatments. This auxiliary function can be used to derive various hat matrices from a network meta-analysis object.

The diagonal elements of the projection matrix are the leverages which describe the influence each. Where H XXT X 1XT is an n nmatrix which puts the hat on y and is therefore. Metaanalysis has evolved to a core method for summarizing evidence from multiple studies in medicine and healthcare.

If there are only two-arm studies m is equal. Meta-analysis plays an important role in summarizing and synthesizing scientific evidence derived from multiple studies. In assessing the validity of an NMA it is therefore important to know the proportion contributions of each direct treatment comparison to each network treatment effect.