arXiv subjects
Publications and source records attributed to Gerta Rücker.
We show that the covariance matrix of the treatment effect estimates in a network meta-analysis can be obtained without matrix inversion using a geometric series of diffusion matrices. This property extends to the hat matrix and provides a connection between parameter estimation in regression analysis and random walks on the network graph. We also provide a number of visualization tools implemented in R.
A key output of network meta-analysis (NMA) is the relative ranking of treatments; nevertheless, it has attracted substantial criticism. Existing ranking methods often lack clear interpretability and fail to adequately account for uncertainty, over-emphasizing small differences in treatment effects. We propose a novel framework to estimate treatment hierarchies in NMA using a probabilistic model, focusing on a clinically relevant treatment-choice criterion (TCC). Initially, we formulate a mathematical expression to define a TCC based on smallest worthwhile differences (SWD), converting NMA relative treatment effects into treatment preference format. This data is then synthesized using a probabilistic ranking model, assigning each treatment a latent 'ability' parameter, representing its propensity to yield clinically important and beneficial true treatment effects relative to the rest of the treatments in the network. Parameter estimation relies on the maximum likelihood theory, with standard errors derived asymptotically from Fisher's information matrix. To facilitate the use of our methods, we launched the R package mtrank. We applied our method to two clinical datasets: one comparing 18 antidepressants for major depression and another comparing 6 antihypertensives for the incidence of diabetes. Our approach provided robust, interpretable treatment hierarchies that account for a concrete TCC. We further examined the agreement between the proposed method and existing ranking metrics in 153 published networks, concluding that the degree of agreement depends on the precision of the NMA estimates. Our framework offers a valuable alternative for NMA treatment ranking, mitigating over-interpretation of minor differences. This enables more reliable and clinically meaningful treatment hierarchies.
Network Meta-Analysis (NMA) plays a pivotal role in synthesizing evidence from various sources and comparing multiple interventions. At its core, NMA relies on integrating both direct evidence from head-to-head comparisons and indirect evidence from different paths that link treatments through common comparators. A key aspect is evaluating consistency between direct and indirect sources. Existing methods to detect inconsistency, although widely used, have limitations. For example, they do not account for differences within indirect sources or cannot estimate inconsistency when direct evidence is absent. In this paper, we introduce a path-based approach that explores all sources of evidence without separating direct and indirect. We introduce a measure based on the square of differences to quantitatively capture inconsistency, and propose a Netpath plot to visualize inconsistencies between various paths. We provide an implementation of our path-based method within the netmeta R package. Via application to fictional and real-world examples, we show that our method is able to detect and visualize inconsistency between multiple paths of evidence that would otherwise be masked by considering all indirect sources together. The path-based approach therefore provides a more comprehensive evaluation of inconsistency within a network of treatments.
Network meta-analysis (NMA) is an extension of pairwise meta-analysis which facilitates the estimation of relative effects for multiple competing treatments. A hierarchy of treatments is a useful output of an NMA. Treatment hierarchies are produced using ranking metrics. Common ranking metrics include the Surface Under the Cumulative RAnking curve (SUCRA) and P-scores, which are the frequentist analogue to SUCRAs. Both metrics consider the size and uncertainty of the estimated treatment effects, with larger values indicating a more preferred treatment. Although SUCRAs and P-scores themselves consider uncertainty, treatment hierarchies produced by these ranking metrics are typically reported without a measure of certainty, which might be misleading to practitioners. We propose a new metric, Precision of Treatment Hierarchy (POTH), which quantifies the certainty in producing a treatment hierarchy from SUCRAs or P-scores. The metric connects three statistical quantities: The variance of the SUCRA values, the variance of the mean rank of each treatment, and the average variance of the distribution of individual ranks for each treatment. POTH provides a single, interpretable value which quantifies the degree of certainty in producing a treatment hierarchy. We show how the metric can be adapted to apply to subsets of treatments in a network, for example, to quantify the certainty in the hierarchy of the top three treatments. We calculate POTH for a database of NMAs to investigate its empirical properties, and we demonstrate its use on three published networks.
Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta-analysis (NMA) is an active area of research. We extend this to the contributions of paths to NMA estimates. We present a general framework, based on the path-design matrix, that describes the problem of finding path contributions as a linear equation. The resulting solutions may have negative coefficients. We show that two known approaches, called shortestpath and randomwalk, are special solutions of this equation, and both meet an optimization criterion, as they minimize the sum of absolute path contributions. In general, there is an infinite space of solutions, which can be identified using the generalized inverse (Moore-Penrose pseudoinverse). We consider two further special approaches. For complex networks we find that shortestpath is superior with respect to run time and variability, compared to the other approaches, and is thus recommended in practice. The path-weights framework also has the potential to answer more general research questions in network meta-analysis.
Network meta-analysis (NMA) is widely used in evidence synthesis to estimate the effects of several competing interventions for a given clinical condition. One of the challenges is that it is not possible in disconnected networks. Component network meta-analysis (CNMA) allows technically 'reconnecting' a disconnected network with multicomponent interventions. The additive CNMA model assumes that the effect of any multicomponent intervention is the additive sum of its components. This assumption can be relaxed by adding interaction component terms, which improves the goodness of fit but decreases the network connectivity. Model selection aims at finding the model with a reasonable balance between the goodness of fit and connectivity (selected CNMA model). We aim to introduce a forward model selection strategy for CNMA models and to investigate the performance of CNMA models for connected and disconnected networks. We applied the methods to a real Cochrane review dataset and simulated data with additive, mildly, or strongly violated intervention effects. We started with connected networks, and we artificially constructed disconnected networks. We compared the results of the additive and the selected CNMAs from each connected and disconnected network with the NMA using the mean squared error and coverage probability. CNMA models provide good performance for connected networks and can be an alternative to standard NMA if additivity holds. On the contrary, model selection does not perform well for disconnected networks, and we recommend conducting separate analyses of subnetworks.
Network meta-analysis (NMA) is a central tool for evidence synthesis in clinical research. The results of an NMA depend critically on the quality of evidence being pooled. 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. The construction of proportion contributions is based on the observation that each row of the hat matrix represents a so-called 'evidence flow network' for each treatment comparison. However, the existing algorithm used to calculate these values is associated with ambiguity according to the selection of paths. In this work we present a novel analogy between NMA and random walks. We use this analogy to derive closed-form expressions for the proportion contributions. A random walk on a graph is a stochastic process that describes a succession of random 'hops' between vertices which are connected by an edge. The weight of an edge relates to the probability that the walker moves along that edge. We use the graph representation of NMA to construct the transition matrix for a random walk on the network of evidence. We show that the net number of times a walker crosses each edge of the network is related to the evidence flow network. By then defining a random walk on the directed evidence flow network, we derive analytically the matrix of proportion contributions. The random-walk approach, in addition to being computationally more efficient, has none of the associated ambiguity of the existing algorithm.
This is a comment to an article by Laakso, Matthias and Jahn (arXiv:2008.11933).