Statistical Issues and Lessons Learned from COVID-19 Clinical Trials with Lopinavir-Ritonavir and Remdesivir
Authors: Yin Guosheng , Zhang Chenyang , Jin Huaqing 
Published: June 2020

AbstractBackgroundSince the outbreak of the novel coronavirus disease 2019 (COVID-19) in December 2019, it has rapidly spread in more than 200 countries or territories with over 8 million confirmed cases and 440,000 deaths by June 17, 2020. Recently, three randomized clinical trials on COVID-19 treatments were completed, one for lopinavir-ritonavir and two for remdesivir. One trial reported that remdesivir was superior to placebo in shortening the time to recovery, while the other two showed no benefit of the treatment under investigation. However, several statistical issues in the original design and analysis of the three trials are identified, which might shed doubts on their findings and the conclusions should be evaluated with cautions.ObjectiveFrom statistical perspectives, we identify several issues in the design and analysis of three COVID-19 trials and reanalyze the data from the cumulative incidence curves in the three trials using more appropriate statistical methods.MethodsThe lopinavir-ritonavir trial enrolled 39 additional patients due to insignificant results after the sample size reached the planned number, which led to inflation of the type I error rate. The remdesivir trial of Wang et al. failed to reach the planned sample size due to a lack of eligible patients, while the bootstrap method was used to predict the quantity of clinical interest conditionally and unconditionally if the trial had continued to reach the originally planned sample size. Moreover, we used a terminal (or cure) rate model and a model-free metric known as the restricted mean survival time or the restricted mean time to improvement (RMTI) in this context to analyze the reconstructed data due to the existence of death as competing risk and a terminal event. The remdesivir trial of Beigel et al. reported the median recovery time of the remdesivir and placebo groups and the rate ratio for recovery, while both quantities depend on a particular time point representing local information. We reanalyzed the data to report other percentiles of the time to recovery and adopted the bootstrap method and permutation test to construct the confidence intervals as well as the P values. The restricted mean time to recovery (RMTR) was also computed as a global and robust measure for efficacy.ResultsFor the lopinavir-ritonavir trial, with the increase of sample size from 160 to 199, the type I error rate was inflated from 0.05 to 0.071. The difference of terminal rates was −8.74% (95% CI [-21.04, 3.55]; P=.16) and the hazards ratio (HR) adjusted for terminal rates was 1.05 (95% CI [0.78, 1.42]; P=.74), indicating no significant difference. The difference of RMTIs between the two groups evaluated at day 28 was −1.67 days (95% CI [-3.62, 0.28]; P=.09) in favor of lopinavir-ritonavir but not statistically significant. For the remdesivir trial of Wang et al., the difference of terminal rates was −0.89% (95% CI [-2.84, 1.06]; P=.19) and the HR adjusted for terminal rates was 0.92 (95% CI [0.63, 1.35]; P=.67). The difference of RMTIs at day 28 was −0.89 day (95% CI [-2.84, 1.06]; P=.37). The planned sample size was 453, yet only 236 patients were enrolled. The conditional prediction shows that the HR estimates would reach statistical significance if the target sample size had been maintained, and both conditional and unconditional prediction delivered significant HR results if the trial had continued to double the target sample size. For the remdesivir trial of Beigel et al., the difference of RMTRs between the remdesivir and placebo groups up to day 30 was −2.7 days (95% CI [-4.0, −1.2]; P<.001), confirming the superiority of remdesivir. The difference in recovery time at the 25th percentile (95% CI [-3, 0]; P=.65) was insignificant, while the differences manifested to be statistically significant at larger percentiles.ConclusionsBased on the statistical issues and lessons learned from the recent three clinical trials on COVID-19 treatments, we suggest more appropriate approaches for the design and analysis for ongoing and future COVID-19 trials.