Estimating intervention effectiveness in trials of malaria interventions with contamination.

BACKGROUND: In cluster randomized trials (CRTs) or stepped wedge cluster randomized trials (SWCRTs) of malaria interventions, mosquito movement leads to contamination between trial arms unless buffer zones separate the clusters. Contamination can be accounted for in the analysis, yielding an estimate of the contamination range, the distance over which contamination measurably biases the effectiveness. METHODS: A previously described analysis for CRTs is extended to SWCRTs and estimates of effectiveness are provided as a function of intervention coverage. The methods are applied to two SWCRTs of malaria interventions, the SolarMal trial on the impact of mass trapping of mosquitoes with odor-baited traps and the AvecNet trial on the effect of adding pyriproxyfen to long-lasting insecticidal nets. RESULTS: For the SolarMal trial, the contamination range was estimated to be 146 m ([Formula: see text] credible interval [Formula: see text] km), together with a [Formula: see text] ([Formula: see text] credible interval [Formula: see text]) reduction of Plasmodium infection, compared to the [Formula: see text] reduction estimated without accounting for contamination. The estimated effectiveness had an approximately linear relationship with coverage. For the AvecNet trial, estimated contamination effects were minimal, with insufficient data from the cluster boundary regions to estimate the effectiveness as a function of coverage. CONCLUSIONS: The contamination range in these trials of malaria interventions is much less than the distances Anopheles mosquitoes can fly. An appropriate analysis makes buffer zones unnecessary, enabling the design of more cost-efficient trials. Estimation of the contamination range requires information from the cluster boundary regions and trials should be designed to collect this.

Analysis of contamination in cluster randomized trials of malaria interventions.

BACKGROUND: In cluster randomized trials (CRTs) of interventions against malaria, mosquito movement between households ultimately leads to contamination between intervention and control arms, unless they are separated by wide buffer zones. METHODS: This paper proposes a method for adjusting estimates of intervention effectiveness for contamination and for estimating a contamination range between intervention arms, the distance over which contamination measurably biases the estimate of effectiveness. A sigmoid function is fitted to malaria prevalence or incidence data as a function of the distance of households to the intervention boundary, stratified by intervention status and including a random effect for the clustering. The method is evaluated in a simulation study, corresponding to a range of rural settings with varying intervention effectiveness and contamination range, and applied to a CRT of insecticide treated nets in Ghana. RESULTS: The simulations indicate that the method leads to approximately unbiased estimates of effectiveness. Precision decreases with increasing mosquito movement, but the contamination range is much smaller than the maximum distance traveled by mosquitoes. For the method to provide precise and approximately unbiased estimates, at least 50% of the households should be at distances greater than the estimated contamination range from the discordant intervention arm. CONCLUSIONS: A sigmoid approach provides an appropriate analysis for a CRT in the presence of contamination. Outcome data from boundary zones should not be discarded but used to provide estimates of the contamination range. This gives an alternative to "fried egg" designs, which use large clusters (increasing costs) and exclude buffer zones to avoid bias.

Spatial Effects of Permethrin-Impregnated Bed Nets on Child Mortality: 26 Years on, a Spatial Reanalysis of a Cluster Randomized Trial.

In addition to the direct effect of insecticide-treated nets (ITNs), there has been evidence for spatial indirect effects. Spatial analyses in cluster randomized trials (CRTs) are rare, but a large-scale CRT from 1993 was one of the first to conduct a spatial analysis of ITNs in CRTs. We revisit these data by applying a broader range of contemporary spatial methods to further explore spatial spillover. We conducted three analyses: 1) exploratory spatial analysis, considering spatial patterns and spillover in the data; 2) spatial modeling, estimating the intervention effect considering spatial effects; and 3) analysis of distance-based spillover and interaction with the intervention, characterizing the functional distance over which the spillover effect was present. There were consistent indications of spatial patterns from the exploratory analysis. Bed nets were associated with a 17% reduction in all-cause mortality for children aged 6-59 months, and the intervention estimate remained robust when allowing for the spatial structure of the data. There was strong evidence of a spatial spillover effect: for every additional 100 m that a control household was from an intervention household (and vice versa), the standardized mortality ratio (SMR) increased by 1.7% (SMR 1.017, 95% credible interval 1.006-1.026). Despite evidence of a spatial spillover effect, the conclusions of the trial remain unaffected by spatial model specifications. Use of ITNs was clearly beneficial for individuals, and there was compelling evidence that they provide an indirect benefit to individuals living nearby. This article demonstrates the extra utility that spatial methods can provide when analyzing a CRT.

Modeling the impact of sterile males on an Aedes aegypti population with optimal control.

We use partial differential equations to describe the dynamics of an Aedes aegypti mosquito population on an island, and the effects of a sterile male release. The model includes mosquito movement and an Allee effect to capture extinction events. We apply optimal control theory to identify the release strategy that eliminates the mosquitoes most rapidly, conditional on a limited availability of sterile males. The optimal solution for a single location is to initially release a substantial number of mosquitoes and to subsequently release fewer sterile males proportionally to the decreasing female population. The optimal solution for the whole island is intractable given a constraint on the total daily release of sterile males. The best approximation to the spatial optimal control strategy is to focus on the high mosquito density areas first and then move outwards (in both directions along the periphery of the island), until all areas have been covered, retaining throughout sufficient release intensity to prevent reintroduction in the already cleared areas.