Underreporting in mixed treatment comparisons meta-analysis for Poisson data

Mixed treatment comparisons meta-analysis has become a popular methodology because of its ability to use separate trials to make comparisons about parameters, even when the parameters have not been directly compared. We consider a mixed treatment comparisons meta-analysis problem when analyzing Poisson data allowing for counts that are potentially underreported. Previously proposed methods do not allow for the presence of underreporting. Here, we illustrate how a constant underreporting rate for all treatments has no effect on relative risk comparisons; however, when the reporting rate changes with treatment, ignoring the underreporting can lead to considerable bias. We propose an approach that accounts for the underreporting and corrects for the bias.