One mean to rule them all? The arithmetic mean based egg reduction rate can be misleading when estimating anthelminthic drug efficacy in clinical trials

Animal and human helminth infections are highly prevalent around the world, with only few anthelminthic drugs available. The anthelminthic drug performance is expressed by the cure rate and the egg reduction rate. However, which kind of mean should be used to calculate the egg reduction rate remains a controversial issue. We visualized the distributions of egg counts of different helminth species in 7 randomized controlled trials and asked a panel of experts about their opinion on the egg burden and drug efficacy of two different treatments. Simultaneously, we calculated infection intensities and egg reduction rates using different types of means: arithmetic, geometric, trimmed, winsorized and Hölder means. Finally, we calculated the agreement between expert opinion and the different means. We generated 23 different trial arm pairs, which were judged by 49 experts. Among all investigated means, the arithmetic mean showed poorest performance with only 64% agreement with expert opinion (bootstrap confidence interval: 60-68). Highest agreement of 94% (CI: 86-96) was reached by the Hölder mean M0.2, followed by the geometric mean (91%, CI: 85-94). Winsorized and trimmed means showed a rather poor performance (e.g. winsorization with 0.1 cut-off showed 85% agreement, CI: 78-87), but they performed reasonably well after excluding treatment arms with a small number of patients. In clinical trials with moderate sample size, the currently recommended arithmetic mean does not necessarily rank anthelminthic efficacies in the same order as might be obtained from expert evaluation of the same data. Estimates based on the arithmetic mean should always be reported together with an estimate, which is more robust to outliers, e.g. the geometric mean.