Imputation methods for missing outcome data in meta-analysis of clinical trials

Abstract

Background: Missing outcome data from randomized trials lead to greater uncertainty and possible bias in estimating the effect of an experimental treatment. An intention-to-treat analysis should take account of all randomized participants even if they have missing observations.

Purpose: To review and develop imputation methods for missing outcome data in meta-analysis of clinical trials with binary outcomes.

Methods: We review some common strategies, such as simple imputation of positive or negative outcomes, and develop a general approach involving ;informative missingness odds ratios' (IMORs). We describe several choices for weighting studies in the meta-analysis, and illustrate methods using a meta-analysis of trials of haloperidol for schizophrenia.

Results: IMORs describe the relationship between the unknown risk among missing participants and the known risk among observed participants. They are allowed to differ between treatment groups and across trials. Application of IMORs and other methods to the haloperidol trials reveals the overall conclusion to be robust to different assumptions about the missing data.

Limitations: The methods are based on summary data from each trial (number of observed positive outcomes, number of observed negative outcomes and number of missing outcomes) for each intervention group. This limits the options for analysis, and greater flexibility would be available with individual participant data.

Conclusions: We propose that available reasons for missingness be used to determine appropriate IMORs. We also recommend a strategy for undertaking sensitivity analyses, in which the IMORs are varied over plausible ranges.

Figure 1

Some possible scenarios for missing data. Arrows indicate causal effects. Missing completely at random: (a) outcome and missingness are unrelated and not dependent on any other variables; (b) missingness is ‘random’, but outcome may be dependent on other variables. Missing at random: (c) different variables are responsible for outcomes and for missingness; (d) the same variables are responsible for outcomes and for missingness, but can be incorporated into the analysis; Informatively missing: (e) the same variables are responsible for outcomes and for missingness, but cannot be incorporated into the analysis; (f) missingness depends directly on the unobserved outcome

Figure 2

Meta-analysis (assuming a common effect) of available case analyses (ACA) from each of the haloperidol trials

Figure 3

L’Abbé plot providing graphical representation of the proposed sensitivity analysis strategy, representing risks to be applied to missing participants. The dotted line represents absence of a treatment effect. The open circle corresponds to a experimental group risk of 0.46, and a control group risk of 0.21, reflecting the overall risks among the haloperidol trials. Filled circles represent combinations of IMORs of 2,1/2 (nearest to the open circle); 3,1/3; 4,1/4; and 5;1/5 (nearest to the corner). In this example, points above the dotted line represent superiority of haloperidol, and points below represent superiority of placebo. Note that choosing larger IMORs (with their reciprocals) leads to traveling along curved paths towards the corners. The corners reflect four of the imputation strategies described earlier, where IMORs are combinations of 0 and ∞