Competing risk events in antimalarial drug trials in uncomplicated Plasmodium falciparum malaria: a WorldWide Antimalarial Resistance Network individual participant data meta-analysis

Abstract

Background: Therapeutic efficacy studies in uncomplicated Plasmodium falciparum malaria are confounded by new infections, which constitute competing risk events since they can potentially preclude/pre-empt the detection of subsequent recrudescence of persistent, sub-microscopic primary infections.

Methods: Antimalarial studies typically report the risk of recrudescence derived using the Kaplan-Meier (K-M) method, which considers new infections acquired during the follow-up period as censored. Cumulative Incidence Function (CIF) provides an alternative approach for handling new infections, which accounts for them as a competing risk event. The complement of the estimate derived using the K-M method (1 minus K-M), and the CIF were used to derive the risk of recrudescence at the end of the follow-up period using data from studies collated in the WorldWide Antimalarial Resistance Network data repository. Absolute differences in the failure estimates derived using these two methods were quantified. In comparative studies, the equality of two K-M curves was assessed using the log-rank test, and the equality of CIFs using Gray's k-sample test (both at 5% level of significance). Two different regression modelling strategies for recrudescence were considered: cause-specific Cox model and Fine and Gray's sub-distributional hazard model.

Results: Data were available from 92 studies (233 treatment arms, 31,379 patients) conducted between 1996 and 2014. At the end of follow-up, the median absolute overestimation in the estimated risk of cumulative recrudescence by using 1 minus K-M approach was 0.04% (interquartile range (IQR): 0.00-0.27%, Range: 0.00-3.60%). The overestimation was correlated positively with the proportion of patients with recrudescence [Pearson's correlation coefficient (ρ): 0.38, 95% Confidence Interval (CI) 0.30-0.46] or new infection [ρ: 0.43; 95% CI 0.35-0.54]. In three study arms, the point estimates of failure were greater than 10% (the WHO threshold for withdrawing antimalarials) when the K-M method was used, but remained below 10% when using the CIF approach, but the 95% confidence interval included this threshold.

Conclusions: The 1 minus K-M method resulted in a marginal overestimation of recrudescence that became increasingly pronounced as antimalarial efficacy declined, particularly when the observed proportion of new infection was high. The CIF approach provides an alternative approach for derivation of failure estimates in antimalarial trials, particularly in high transmission settings.

Keywords: Competing risk event; Plasmodium falciparum; Treatment efficacy study.

Fig. 1

Situational competitiveness of newly emergent infections. Adapted from White-2002 [44]. The blue line represents a hypothetical drug concentration of partner component, the green and red lines represent scenarios for parasite burden versus time profiles following treatment for an infection where all the parasites are completely killed resulting in cure (green) and an infection where parasites are initially killed by high drug levels but with drug levels below the minimum inhibitory concentration (MIC), net parasite growth results in subsequent recrudescence (red). The orange line represents parasite-time profiles for a new infection. The left y-axis is for parasite density, and the right y-axis shows drug levels at hypothetical units. The vertical dotted line is the administrative end of the study follow-up. The horizontal dotted line represents the microscopic limit of detection for parasites. a Parasite population from a new inoculation out-competes the parasite population which caused the disease thus precluding recrudescence. In this situation, new infection is a biologically competing risk event. b In this situation new infection can be thought of as biologically competing risk event which doesn’t prevent recrudescence being observed. c The parasite population which caused the disease is completely eliminated. Here, new infection is not a competing event. d In this situation, the parasite population which caused the disease and which is derived from a novel inoculation appear at the same time

Fig. 2

The observed proportion of recurrence events in the studies included. The distribution of observed proportion of recrudescences, new infections and indeterminate outcomes from 233 study arms included in the analysis

Fig. 3

The overestimation of derived failure by 1 minus Kaplan–Meier method compared to the Cumulative Incidence Function. The overestimation $\left({\widehat{F}}_{\mathit{KM}}\left(t\right)-{\widehat{F}}_{\mathit{CIF}}\left(t\right)\right)$ of cumulative recrudescence (top panel) and new infection (bottom panel) by using the Kaplan–Meier method plotted against observed proportion of recrudescence and proportion of new infections respectively. Estimates presented are at the end of the study follow-up. The grey trend line is a smoothed estimator obtained from local polynomial regression fitting, shown together with 95% confidence interval (outer dotted lines) for the overall data. AL artemether–lumefantrine, ASAQ artesunate–amodiaquine, DP dihydroartemisinin–piperaquine, ASMQ artesunate–mefloquine. Data are shown from the study arms where at least one recrudescence and at least one competing risk event were observed and from those arms where the number of patients at risk > 25 on the last day of the study follow-up

Fig. 4

Predicted risk of recrudescence from cause-specific Cox model and sub-distribution hazard model. The graph was generated using the regression coefficients presented in Table 5 and the estimate of baseline hazard obtained from the respective sub-distribution and cause-specific hazard model (for a 3 year old child). The cumulative baseline sub-distribution hazard on day 28 from Fine and Gray’s model was 0.006; the cumulative baseline hazard on day 28 from the cause-specific Cox model was 0.003. The vertical dotted line represents the parasitaemia of 100,000/µL for the child described in the main text. On day 28, the predicted risk of recrudescence for this patient was 16.15%, 4.76% and 4.28% using the cause-specific Cox model. The corresponding figures were 10.72%, 4.76% and 4.28% with the Fine and Gray’s sub-distribution hazard model. AL artemether–lumefantrine, ASAQ artesunate–amodiaquine, DP dihydroartemisinin–piperaquine