**Doctor**: Theodoros Evrenoglou

**Title:** Dealing with sparse data in network meta-analysis

**Supervisor**: Anna Chaimani

**Doctoral school**: ED 393 Epidemiology and Biomedical Information Sciences, Université Paris Cité

**Date of thesis defense: **30/11/2022

**Jury: **Tim Fried, Stefan Michiels, Nicky Welton, Georgia Salanti, Raphaël Porcher, Anna Chaimani

**Summary:**

In meta-analysis, the issue of sparse data can be defined as either the case where the studied outcome is rare across a set of available studies or as the case where there are only a few studies available. In both of those cases of sparsity the standard inverse-variance (IV) approach which is used for either pairwise or network meta-analysis can be problematic. This arises from the fact that in such cases the standard normal assumptions made by the conventional IV model are invalid and thus the summary effect estimates can be biased.

This thesis aims to deal with sparse data through three different projects.

The aim of the first project was to deal with the problem of rare events in NMA of binary data. An approach of penalizing the likelihood function has been previously proposed for bias reduction in the analysis of individual studies with rare events. To improve the accuracy and the precision of the NMA estimates in the presence of rare events, the first project aimed to extend the penalized likelihood approach to the context of NMA. The latter took place at first for the common-effect NMA model that uses logistic regression. The common-effect model was extended to a random-effects model by using a two-stage approach that incorporates the heterogeneity parameter through a multiplicative term. The performance of the PL-NMA model was evaluated through a simulation study of in total 33 scenarios where the method was also compared with 10 other NMA approaches in terms of various measures such as bias and coverage probability. The simulations suggested that the PL-NMA approach performs consistently well across all tested scenarios and most often results in smaller bias than the other NMA methods.

The second project of this thesis aimed to facilitate the estimation of summary intervention effects for rare outcomes in the context of Covid-19 pandemic. The COVID-NMA initiative is a living 3 evidence synthesis platform that provides public access to the most up-to-date information with respect to the effects of the different Covid-19 interventions. Rare events are quite frequent in the COVID-NMA database. For example, across 432 RCTs with hospitalized patients in the database the median risk for the outcome of serious adverse events is only 8%. To facilitate the analysis of COVID-NMA data the metaCOVID application was built. This is a freely available RShiny application that allows all the end-users of the COVID-NMA platform to perform complex types of analysis through a user-friendly environment. metaCOVID deals with rare events by allowing the replacement of the IV model with other more suitable models for sparse data such as the Mantel-Haenszel or the PL-NMA model.

The third project addressed the issue of sparse networks in NMA. This is the case of networks that contain a limited number of direct comparisons and very few studies to inform them. Results from such networks are accompanied with substantial uncertainty not only in NMA estimates but also in the plausibility of the underlying NMA assumptions. A Bayesian framework was proposed to allow sharing information between two networks that pertain to different subgroups of the population. Specifically, the results from a subgroup with a lot of direct evidence forming a ‘dense’ network were used to create informative priors for the relative effects of the target subgroup forming a sparse network. This is a two-stage approach where at the first-stage the results of the dense network are extrapolated to the sparse network using a NMA model which uses a location parameter that shifts the distribution of the relative effects to make them applicable to the target population. At the second-stage, the predictions of these results are used as prior information for the sparse network. The location parameter is informed either through the data or using expert opinion. The two-stage approach was found to result in more precise and robust estimates of the final NMA estimates.