Statistical Issues and Lessons Learned From COVID-19 Clinical Trials With Lopinavir-Ritonavir and Remdesivir

Abstract

Background: Recently, three randomized clinical trials on coronavirus disease (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.

Objective: The aim of this paper is to, from a statistical perspective, identify several key 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.

Methods: The 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, and 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) to analyze the reconstructed data. 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 use the restricted mean time to recovery (RMTR) as a global and robust measure for efficacy.

Results: For 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 RMTIs between the two groups evaluated at day 28 was -1.67 days (95% CI -3.62 to 0.28; P=.09) in favor of lopinavir-ritonavir but not statistically significant. For the remdesivir trial of Wang et al, the difference of RMTIs at day 28 was -0.89 days (95% CI -2.84 to 1.06; P=.37). The planned sample size was 453, yet only 236 patients were enrolled. The conditional prediction shows that the hazard ratio estimates would reach statistical significance if the target sample size had been maintained. For the remdesivir trial of Beigel et al, the difference of RMTRs between the remdesivir and placebo groups at day 30 was -2.7 days (95% CI -4.0 to -1.2; P<.001), confirming the superiority of remdesivir. The difference in the recovery time at the 25th percentile (95% CI -3 to 0; P=.65) was insignificant, while the differences became more statistically significant at larger percentiles.

Conclusions: Based 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 of ongoing and future COVID-19 trials.

Keywords: COVID-19; coronavirus; cure rate model; restricted mean survival time; sample size adjustment; terminal event; type I error rate.

Figure 1

The restricted mean time to improvement corresponding to the area under the curves for the lopinavir-ritonavir group and the standard care group evaluated at days 7, 14, and 28 in Cao et al [12].

Figure 2

The restricted mean time to improvement corresponding to the area under the curves for the remdesivir group and the placebo group evaluated at days 7, 14, and 28 in Wang et al [13].