Pattern-mixture model in network meta-analysis of binary missing outcome data: one-stage or two-stage approach?

Loukia M Spineli,Chrysostomos Kalyvas,Katerina Papadimitropoulou

doi:10.1186/s12874-020-01205-6

Abstract

BackgroundTrials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The performance of the one-stage and the two-stage approaches has been documented extensively in the literature. However, little is known about how these approaches behave in the presence of missing outcome data (MOD), which are ubiquitous in clinical trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis using Bayesian methods to handle MOD appropriately.MethodsWe used 29 published networks to empirically compare the two approaches concerning the relative treatment effects of several competing interventions and the between-trial variance (τ2), while considering the extent and level of balance of MOD in the included trials. We additionally conducted a simulation study to compare the competing approaches regarding the bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and τ2 in the presence of moderate and large MOD.ResultsThe empirical study did not reveal any systematic bias between the compared approaches regarding the log OR, but showed systematically larger uncertainty around the log OR under the one-stage approach for networks with at least one small trial or low event risk and moderate MOD. For these networks, the simulation study revealed that the bias in log OR for comparisons with the reference intervention in the network was relatively higher in the two-stage approach. Contrariwise, the bias in log OR for the remaining comparisons was relatively higher in the one-stage approach. Overall, bias increased for large MOD. For these networks, the empirical results revealed slightly higher τ2 estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and τ2 when compared with the two-stage approach for large MOD.ConclusionsDue to considerable bias in the log ORs overall, especially for large MOD, none of the competing approaches was superior. Until a more competent model is developed, the researchers may prefer the one-stage approach to handle MOD, while acknowledging its limitations.

Highlights

Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively
Posterior mean or median For the ‘susceptible’ networks, one-stage and two-stage PM approaches overall agreed concerning the posterior mean of within-trial log odds ratios (OR) (CCC: 0.99) and the posterior mean of network meta-analysis (NMA) log ORs (CCC: 0.99) across the different scenarios of missing outcome data (MOD) (Fig. 1 a, first and second panel)
An agreement could be inferred for the posterior median of τ2 (CCC: 0.90), except for four networks with moderate and balanced MOD whose τ2 estimates were found to be higher under the one-stage PM approach (Fig. 1 a, third panel)

Summary

Introduction

Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. To address aggregate binary missing participant outcome data (MOD) in pairwise and network metaanalysis, the researchers usually resort to simple datahandling approaches, such as exclusion or imputation. Both approaches are popular due to their simplicity [1,2,3], yet notorious for the implausibility of their assumptions. The pattern-mixture model is the most commonly described model in the methodological literature for pairwise and network meta-analysis to address binary MOD [4,5,6,7] It consists of two parts: a model for the outcome conditional on being missing or observed and a model for the probability of MOD [8]. Under the Bayesian framework, IMOR is commonly assigned a normal prior distribution in the logarithmic scale with mean and variance indicating our on average prior belief and uncertainty about the missingness mechanism, respectively [4, 6]

Methods

Results

Discussion

Conclusion