Abstract
Background
Trials with binary outcomes can be synthesised using within-trial exact likelihood or approximate normal likelihood in one-stage or two-stage approaches, respectively. The advantages of the one-stage over the two-stage approach have been documented extensively in the literature. Little is known how these approaches behave in the presence of missing outcome data (MOD) which are ubiquitous in trials. In this work, we compare the one-stage versus two-stage approach via a pattern-mixture model in the network meta-analysis Bayesian framework to handle MOD appropriately.
Methods
We used 29 published networks to empirically compare the two approaches with respect to the relative treatment effects of several competing interventions and the between-trial variance (
{\tau }^{2}
). We categorised the networks according to the extent and balance of MOD in the included trials. To complement the empirical study, we conducted a simulation study to compare the competing approaches regarding bias and width of the 95% credible interval of the (summary) log odds ratios (OR) and
{\tau }^{2}
in the presence of moderate and large MOD.
Results
The 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. Furthermore, in these networks, the empirical results revealed slightly higher
{\tau }^{2}
estimates under the one-stage approach irrespective of the extent of MOD. The one-stage approach also led to less precise log OR and
{\tau }^{2}
when compared with the two-stage approach for large MOD.
Conclusions
Due 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.
Estimation of population mean in two– stage sampling under a deterministic response mechanism in the presence of non-response
