The impact of covariance priors on arm‐based Bayesian network meta‐analyses with binary outcomes

Abstract

Bayesian analyses with the arm‐based (AB) network meta‐analysis (NMA) model require researchers to specify a prior distribution for the covariance matrix of the treatment‐specific event rates in a transformed scale, for example, the treatment‐specific log‐odds when a logit transformation is used. The commonly used conjugate prior for the covariance matrix, the inverse‐Wishart (IW) distribution, has several limitations. For example, although the IW distribution is often described as noninformative or weakly informative, it may in fact provide strong information when some variance components are small (eg, when the standard deviation of study‐specific log‐odds of a treatment is smaller than 1/2), as is common in NMAs with binary outcomes. In addition, the IW prior generally leads to underestimation of correlations between treatment‐specific log‐odds, which are critical for borrowing strength across treatment arms to estimate treatment effects efficiently and to reduce potential bias. Alternatively, several separation strategies (ie, separate priors on variances and correlations) can be considered. To study the IW prior's impact on NMA results and compare it with separation strategies, we did simulation studies under different missing‐treatment mechanisms. A separation strategy with appropriate priors for the correlation matrix and variances performs better than the IW prior, and should be recommended as the default vague prior in the AB NMA approach. Finally, we reanalyzed three case studies and illustrated the importance, when performing AB‐NMA, of sensitivity analyses with different prior specifications on variances.

A historical review of publication bias

“…Methods for evaluating PB in this setting have typically taken a contrast-based approach, while an arm-based approach has been increasingly studied as an alternative. [170][171][172][173] As such, additional considerations need to be accounted for including correlations between treatments in multiarm studies, different selection mechanisms for different study designs or treatment contrasts, and the inclusion of indirect evidence. While efforts have been made to visualize NMAs using funnel graphs, 174 displaying indirect comparisons for the purpose of assessing symmetry is difficult, and extending graph-based methods to an NMA framework remains challenging.…”

“…Methods for evaluating PB in this setting have typically taken a contrast‐based approach, while an arm‐based approach has been increasingly studied as an alternative 170‐173 . As such, additional considerations need to be accounted for including correlations between treatments in multiarm studies, different selection mechanisms for different study designs or treatment contrasts, and the inclusion of indirect evidence.…”

Application of network meta-analysis in the field of physical activity and health promotion

“…White et al 38 concluded that both arm-based and contrast-based models are suitable for NMA but pointed out that using random study intercepts requires a strong rationale, while models with fixed study intercepts are useful because they can be implemented with either a contrast-based or arm-based model. Wang et al 40 observed that a separation strategy with appropriate priors for the correlation matrix and variances performs better than strategies employing the inverse—Wishart priors used in the original arm-based NMA and can therefore reduce potential biases. Recently, Ma et al 41 and Lian et al 42 have extended arm-based NMA to simultaneously compare multiple diagnostic tests in which absolute measures, such as sensitivities and specificities, are of primary interest.…”

A variance shrinkage method improves arm-based Bayesian network meta-analysis

“…16 Descriptive statistics of these 42 networks (Figure 1) show that nearly 40% of treatments in these NMAs are included in four or fewer clinical studies, which can lead to overestimation of variances of relevant treatment effects in the AB approach if noninformative priors are used. 17 To overcome this problem, both the AB and CB approaches often make additional assumptions. For example, in the CB model, Dias et al.…”

“…16 This phenomenon may produce difficulties in accurately estimating correlations among treatments in the AB approach. 17 In the CB approach, it may cause variances of certain contrasts to be overestimated. 9 Second, the number of clinical studies involving each treatment is limited.…”