The aim of this work was to pool the results from five randomized clinical trials comparing the efficacy of anti-malarial drugs based on the same repeated observation-time design but with partially overlapping treatment arms, in order to improve the estimated treatment effects and their corresponding variances. Among the five studies, one was discarded (study #2) as it was not connected to the other ones, whereas the four remaining studies (studies # 1,3,4,5) were analysed with a mixed ordinal logistic model incorporating a between-subject heterogeneity variance model. This approach can be considered as an extension of the multi-treatment approach of Jansen et al.
], which was limited to a binary response at a single time point (day 28) or, an alternative to a recent work carried by Dakin et al.
], where the outcome was continuous. Results concerning the unconnected study are just mentioned for the sake of completeness, as they were not part of the global analysis: they showed that the combination ASMQ was more effective than AQSP. In the global analysis, the best model was M3 with a random individual effect, in which the residual variance was a function of explanatory covariates. Modeling the subject residual variance appeared to improve the model ability to fit the data by reducing heterogeneity within the analysed trials. Based on model M3, DHPP was significantly more efficacious than ASAQ, whereas ASCD appeared less efficacious than ASSP, AMLM and DHPP, the latter difference being significant. These results slightly differ from the results of our previous work [5
], in which no significant treatment difference was found. Therefore, taking into consideration both the ordinal type of the WHO criteria and the results at the repeated visits seems to increase the power for finding a difference, if any.
Regarding the categorical outcome, LCF is symptomatic, whereas LPF is not. It remains possible that a patient with LPF become symptomatic beyond day 28. However, the protocol was designed to separate the two endpoints when performing a 28-day treatment evaluation. The clinical implications of LPF and LCF on day 28 seem to be quite different. Moreover, the more recent WHO document [24
] maintains the four treatment outcomes.
In the present study, analyses were based on the observed treatment responses between day 14 and day 28 (due to the absence of ETF), and the contribution of each observed category was evaluated. Pooling randomized clinical trials raises the issue of heterogeneity between studies. However, all studies included in this analysis were based on the same population of children, within the same age range and in the same geographic area. These studies had the same design and were run by the same investigators and field workers over the years. Mixed treatment comparison (MTC) meta-analysis faces several limits leading to the possibility of biased estimates. Comparing treatment arms using indirect comparisons apparently exposes to the loss of the benefits of randomization. However, it is partially preserved using adjusted comparisons with possibly less biased differences towards positive results, according to Song et al.
]. A study random effect was not considered in the models as the number of studies was too small. None of the study fixed effects was significant, but including them in the model allowed for a correlation between the treatment arms within a single study, which kept part of the randomisation process. Missing responses represent a frequent issue in anti-malarials trials, usually carried out in field conditions. The absence of a patient during a scheduled visit could be due either to an earlier treatment failure leading to another treatment, which could be considered as missing at random (MAR), according to Rubin [26
], or a lost to follow-up considered as missing completely at random (MCAR) or an exclusion due to some protocol violation, considered as missing not at random (MNAR). In order to explore the internal validity of our results, a sensitivity analysis was carried out in which missing responses were imputed according to different scenarii, including the worst scenario where missing responses were imputed as failures. None of the evaluations carried out before day 14 (i.e. days 1, 2, 3, and 7) was considered because early treatment failure (ETF, for days 1 to 3) and late failure between day 7 and day 13 were not observed. In addition the whole purpose for WHO to extend the follow up beyond day 14 up to day 28 was to study the long term efficacy of anti-malarial drugs following an acute episode. Each of the 3 categories ACPR, LCF, LPF on days 14, 21 and 28, according to the 2003 WHO protocol, was observed. On the observed data, one subject cannot be LPF or LCF without being ACPR at least on day 14. When the outcome of a subject is classified as LPF or LCF, the next outcome is missing since the evaluation of drug efficacy is terminated for that particular patient and an alternative treatment is necessary because of ethical consideration. Therefore, outcomes are not strictly speaking repeated. Modeling repeated observations over time can been achieved either using a conditional model, where the outcome at time t is modelled according to the previous outcomes, or using a marginal model, where the individual outcomes are modelled in relation to a mean outcome at each time- point, the time dependency reflecting this memory effect acting on the categorical response. As the main objective of the present work was to pool the results of different multi- arm trials, the latter approach was adopted, which could be directly related to recent advances in meta-analysis developments [27
]. Analyses with incomplete (PP) and complete outcomes (imputation approach) were performed by imputing missing outcomes on days 14, 21 and 28. The results were then compared to check for biases (Table ). The results remained similar in all approaches. It is now common in anti-malarial drug trials to distinguish between new infections and recrudescence by PCR, although, from the pragmatic point of view, one might expect that an optimal treatment of an acute episode would protect the patients from new infection in the weeks following the episode, in areas without a large variability in parasite phenotype. In case of unevenly distributed missing categories at different times and/or treatment arms, difficulties in adjusting the proposed models could occur. The main difficulty was related either to a too small number or an absence of failure categories over time after PCR correction. This could be considered as extreme category outcomes, for which the clog- log link can be more adapted than the logit link in the fitting process. When the missing responses were imputed as previously described except for the cases of PCR-detected new infections where the missing observations were imputed ACPR, the analyses using the Gibbs sampler failed to converge.
Sensitivity analysis: Estimated effects in the PP data set and the imputed data sets
From the clinical standpoint, it is worth noting that the present data set concerned the use of highly efficacious anti-malarial combination drugs, thus explaining the absence of the ETF category. AMLM is already an alternative to ASAQ in Cameroon. Both ASAQ and AMLM treatments are recommended by the WHO, based on several published trials, comparing different subsets of the treatments listed in the present analysis [28
]. The results of the present analysis complete the previous meta-analysis based on a binary outcome at a fixed time point, where it was concluded that AMLM appeared to be the most effective drug with no treatment failure due to recrudescence, closely followed by DHPP. However, the previous analysis did not take into account the individual repeated measurements.
DHPP showed a higher efficacy as compared to the reference treatment ASAQ in all tested models, whereas ASCD appeared less efficacious than ASAQ. AMLM did not differ significantly in efficacy from ASAQ. It should be remembered that the present analysis discarded study #2, as it was unconnected to others, increasing the power for comparison between the remaining treatment arms. The final result is in agreement with the meta-analysis conducted by Sinclair et al.
], which was based on the binary outcome on Day 28. In that study, both DHPP and ASMQ appeared more efficacious than AMLM. ASMQ, which is not recommended by the WHO in Africa at present, although it is the first-line treatment in Southeast Asia, was not connected to the other treatment arms in the analysed network of randomised trials, and could only be compared to AQSP, showing a significantly higher efficacy. Treatment failure may have several origins including individual pharmacokinetic and pharmacodynamic variations and intensity of transmission. For instance, as CD has a shorter half-life than the other drugs, new infections could occur more easily than with other drugs, which explains why in a non PCR-corrected data analysis ASCD appears less effective. While a 100% full success rate (ACPR) represents the optimal target when treating acute malaria, it is worth noting that incorporating the information about the other intermediary states and the absence of parasitaemia appear to be of importance, at least from the public health standpoint to limit the burden of circulating parasites. Taking into account these intermediary outcomes could more adequately participate in the evaluation of different public health policies for malaria control in parallel to other validated interventions, such as the distribution of insecticide-impregnated bednets, environmental drainage and other mosquito control measures.