HANDLING MISSING DATA IN META-ANALYSIS OF INDIVIDUAL PARTICIPANT DATA WITH MIXED OUTCOMES

Purpose:

Meta-analysis of individual participant data (IPD) is increasingly utilized for combining data from both randomized trials and observational studies. However, an important concern in IPD meta-analysis is that outcomes are often partially or completely missing for some studies. This paper aims to: i) present a multivariate Bayesian hierarchical model for addressing the missing data, the between-study heterogeneity and multiple mixed outcomes (continuous and discrete); ii) compare the relative performance of the Bayesian approach with alternative, simpler methods such as multiple imputation (MI) and complete-case analysis.

Method:

We use a simulation study to assess the relative performance of alternative strategies for dealing with the missing data across different settings in IPD meta-analysis.  For example, we consider scenarios which differ according to: number of studies, level of between-study heterogeneity, proportion of missing data, missingness predictors (e.g. covariates vs outcomes), and missingness mechanisms including missing at random (MAR) and missing not at random (MNAR). We report performance in terms of bias, root mean square error (rMSE), and confidence interval (CI) coverage for estimating treatment effects on both continuous and binary outcomes. To illustrate these approaches, we consider a meta-analysis of randomized controlled trials comparing the effectiveness of implantable cardiac devices to treat heart failure, with missing binary and continuous outcomes (mortality, functional and quality of life endpoints).

Result:

Under ideal circumstances, for example, 20 studies, low between-study heterogeneity and MAR conditional on observed covariates, both MI and the Bayesian joint model provided unbiased estimates and CI coverage close to the nominal level (95%). With increased levels of missing data, strong correlation between outcomes, and each outcome being MAR conditional on the other endpoint, the Bayesian joint model provided estimates relatively closer to the true values and better CI coverage than MI methods (Figure 1). When data were MNAR (but the methods assumed MAR) the Bayesian model still provided estimates less biased than MI. In the case-study, inferences about the effectiveness of alternative heart failure devices differed according to method.

Conclusion:

The Bayesian approach performed well across a wide range of settings, and provides an appropriate tool for jointly handling the missing data, between-study heterogeneity, and correlated mixed outcomes in IPD meta-analysis.

Figure 1. Full-data; Complete-cases; MI without the other outcome; MI including the other outcome; Bayesian model.