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Authors: Mauro Bernardi, Paolo Caraceni, Roberta J. Navickis, Mahlon M. Wilkes
Journal: Hepatology (2014)

We previously reported a novel meta-analysis examining the effects of albumin infusion in patients undergoing large-volume paracentesis.1 Seventeen randomized trials with 1,225 total patients were included. Reductions were demonstrated in postparacentesis circulatory dysfunction, hyponatremia, and mortality resulting from albumin infusion. The meta-analysis was subsequently cited as a basis for a new recommendation to administer albumin with large-volume paracentesis in the 2012 Practice Guideline of the American Association for the Study of Liver Diseases.2 Using our data, Chen et al. performed a trial sequential analysis. Since the cumulative z-score curves for hyponatremia and mortality were not observed to cross the monitoring boundaries, they questioned the robustness of our meta-analytic findings with respect to those two endpoints. However, they misapplied trial sequential analysis, and their conclusions are not valid. Trial sequential analysis has been proposed as a tool to adjust the results of cumulative meta-analyses for multiple testing.3, 4 Cumulative meta-analysis involves sequentially adding new trials as they become available and may allow firm conclusions about the effectiveness of interventions to be drawn earlier than otherwise.5 Nevertheless, if approached within a frequentist framework, cumulative meta-analysis may typically entail repetitive hypothesis tests as new trials are added and consequent increased chance of false-positive results. Importantly, our meta-analysis was not a cumulative meta-analysis, and our hypothesis tests were performed only once. Hence, adjustment for multiple testing by trial sequential analysis is unnecessary in our case.6, 7 Furthermore, trial sequential analysis has been criticized as "moving the goal post" without addressing key issues such as underinclusiveness and systematic error and has never been widely adopted.8 Nonetheless, since our meta-analysis was comparatively large, we were surprised by an analysis suggesting insufficient evidence for two of our endpoints. We therefore sought to replicate their analysis independently. We used Trial Sequential Analysis software v. 0.99 and standard a priori assumptions of a 25% relative risk reduction, 30% control group event rate, 80% statistical power, and an α level for significance of 0.05.4,6,7,10,11 Figure 1 shows the cumulative z-score curves for postparacentesis circulatory dysfunction, hyponatremia, and mortality all crossing the monitoring boundaries. Thus, even by the more stringent criteria of trial sequential analysis, the findings of our meta-analysis were affirmed. Also included in Fig. 1 are results of two additional eligible randomized trials published after our meta-analysis.12, 13 Both trials further strengthened the evidence supporting the conclusions of our meta-analysis. Chen et al. neglected to specify the assumptions of their analysis. They also wrongly indicated 1.8 as the conventional critical value for statistical significance. The correct value is 1.96, corresponding to the number of standard deviations on either side of the mean that encompass 95% of normally distributed observations. As in sample size computations for clinical trials, information size in trial sequential analysis is highly sensitive to assumptions.4 Sufficiently low assumed effect size and/or control group event rate can potentially "move the goal post" beyond the reach of any meta-analysis.3 This may explain the discordance between Fig. 1 and the analysis presented by Chen et al. Our meta-analysis was conducted by rigorous established methodology, and newer evidence supports its results. While not designed for application to a meta-analysis such as ours, trial sequential analysis in our hands also confirms our findings. Mauro Bernardi, M.D.1 Paolo Caraceni, M.D.1 Roberta J. Navickis, Ph.D.2 Mahlon M. Wilkes, Ph.D.2 1Department of Medical and Surgical Sciences University of Bologna Bologna, Italy 2Hygeia Associates Grass Valley, CA, USA