Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta-analysis

Abstract

Missing outcome data are commonly encountered in randomized controlled trials and hence may need to be addressed in a meta-analysis of multiple trials. A common and simple approach to deal with missing data is to restrict analysis to individuals for whom the outcome was obtained (complete case analysis). However, estimated treatment effects from complete case analyses are potentially biased if informative missing data are ignored. We develop methods for estimating meta-analytic summary treatment effects for continuous outcomes in the presence of missing data for some of the individuals within the trials. We build on a method previously developed for binary outcomes, which quantifies the degree of departure from a missing at random assumption via the informative missingness odds ratio. Our new model quantifies the degree of departure from missing at random using either an informative missingness difference of means or an informative missingness ratio of means, both of which relate the mean value of the missing outcome data to that of the observed data. We propose estimating the treatment effects, adjusted for informative missingness, and their standard errors by a Taylor series approximation and by a Monte Carlo method. We apply the methodology to examples of both pairwise and network meta-analysis with multi-arm trials.

Keywords: informative missing; mixed treatment comparison; sensitivity analysis.

Figure 1

Network plot for comparison of antidepressants. Nodes are weighted according to the number of studies including the respective interventions. Edges are weighted according to the inverse variance of the direct treatment effect estimates for the respective comparisons.

Figure 2

Comparison of Monte Carlo and Taylor approximation for computing the posterior mean and standard error of the three effect sizes (MR, SMD, and ln RoM) for the MIR 003‐21 study assuming a bivariate distribution for IMDoM. Solid line refers to the Taylor series approximation and the dotted line to Monte Carlo sampling.

Figure 3

Comparison of Monte Carlo and Taylor approximation of computing the posterior mean and standard error of the three effect sizes (MR, SMD, and ln RoM) for the MIR 003‐21 study assuming a bivariate distribution for IMRoM. Solid line refers to the Taylor series approximation and the dotted line to Monte Carlo sampling.

Figure 4

Forest plot of mitrazapine studies under various IMRoM assumptions when the effect size is MD (random‐effects models).

Figure 5

Plots of the three summary relative treatment effects of mirtazapine (MD, SMD, and ln RoM) Random‐effects meta‐analysis for various σ _λ values under the IMDoM assumption (panel a) and the IMRoM assumption (panel b).

Figure 6

Antidepressants network: plots of the cumulative ranking curves. Solid line corresponds to the MAR assumption and dashed line IMDoM λN(0, 3²). The effect size considered is SMD.