Influence Diagnostics for Meta-Analysis of Individual Patient Data Using Generalized Linear Mixed Models

In meta-analysis, generalized linear mixed models (GLMMs) are usually used when heterogeneity is present and individual patient data (IPD) are available, while accepting binary, discrete as well as continuous response variables. In the present paper some measures of influence diagnostics based on log-likelihood are suggested and discussed. A known measure is approximated to get a simpler form, for which the information matrix is no more necessary. The performance of the proposed measure is assessed through a diagnostic analysis on simulated data reproducing a possible meta-analytical context of IPD with influential outliers. The proposed measure is showed to work well and to have a form similar to the gradient statistic, recently introduced.