Background
When testing new malaria control interventions, cluster randomized trials (CRTs) are often the study design of choice, because the intervention is either assigned at the household level, or contamination effects are anticipated between the households [
1]. With malaria, most transmission happens during the night when
Anopheles mosquitoes bite and people are in their home. Movement of mosquitoes while searching for human hosts or oviposition sites is therefore the main cause of contamination in trials of mosquito control interventions against malaria. Whereas this is a challenge in field trials, the practical consequence is that intervention has a beneficial community effect on individuals living close by. To prevent this effect from biasing trial estimates of efficacy towards the null, clusters are usually chosen as geographically contiguous areas of households.
Since contamination may still arise at the cluster boundaries and hence bias trial results, malaria trials are often designed by choosing well separated clusters or enforcing separation by defining buffer zones around each cluster [
2‐
7]. Ideally, buffer size might be determined using estimates of the range of the contamination [
8], but very broad buffers are often used since other information is rarely available. In such trials, entire clusters receive the intervention, but only data from cluster cores are analyzed. This allows a standard analytical approach [
2] but at the cost of enrolling very large populations. Spatial separation may increase heterogeneity between clusters, and the cluster cores may be unrepresentative of the whole population if clusters correspond to natural units such as villages.
Estimating the spatial contamination is of scientific interest [
9‐
13] because protection of people living nearby is an important property of an intervention. Secondary analyses of several CRTs of malaria interventions have estimated contamination effects using linear models with terms measuring the distance between observations from one arm of the study to the nearest observation from the other study arm [
10,
14‐
16]. These analyses all found evidence of spatial effects and tended to demonstrate the importance of accounting for contamination in estimating unbiased effects of the intervention. Nevertheless, these linear models cannot simultaneously provide closed-form estimates of the range over which the contamination is relevant while adjusting the estimate of effectiveness for the contamination. The authors recently demonstrated that this can be achieved with a sigmoid random effects model for the analysis of CRTs of malaria interventions with contamination arising from mosquito movement [
9].
Stepped wedge cluster randomized trials (SWCRTs) [
2,
17,
18] are a modification of CRTs in which the intervention is introduced progressively to all clusters in random order. To gain a better understanding of the effect of contamination in SWCRTs, the proposed model for CRTs [
9] is extended to analyze SWCRTs. It is then shown how the measurable contamination between trial arms (a quantity termed contamination range) leads to an estimate of the effective intervention coverage for each household and how this relates to the intervention effectiveness. These methods are applied to two SWCRTs of malaria interventions; the SolarMal trial assessing the effect of mass trapping with solar-powered odor-baited mosquito traps on Rusinga island, Kenya [
19‐
21], and the AvecNet trial investigating the effect of adding pyriproxyfen to long-lasting insecticidal nets in Burkina Faso [
22,
23].
Discussion
In CRTs or SWCRTs of malaria interventions, contamination between the trial arms arises because of mosquito movement. In a conventional analysis this may bias effectiveness estimates, but this can be corrected with an appropriate analysis, such as a Bayesian hierarchical model with a sigmoid function for effectiveness as a function of distance to the nearest discordant household, that was recently proposed for CRTs [
9]. This model yields a closed-form contamination range that quantifies the contamination arising from mosquito movement between trial arms, and adjusts the main estimate of effectiveness for contamination, eliminating the need for buffer zones.
The proposed analytical approach is tailor-made for malaria interventions where transmission can be geolocated to the host’s primary residence, and the main source of contamination between clusters arises from dispersal of adult female
Anopheles mosquitoes, for which the proposed model, corresponding to mosquito dispersion by diffusion [
27,
28] is a reasonable approximation. In nature dispersal will vary between sites, within sites and by season, and depends on the extent and spatial distribution of aquatic habitats, households and alternative blood sources [
29], as well as wind strength and direction and obstacles in the environment. For both interventions considered here, with effects mainly depending on mosquito densities, contamination was considered to be symmetrical. The intervention may protect nearby nonusers, while users with many nearby nonusers have reduced intervention effects. With this model, a difference between homogeneously distributed and clustered interventions on the overall intervention effect is not distinguishable [
29]. The same modelling approach might be applied where the intervention itself is designed to be dispersed by mosquitoes (for instance sterile insect techniques) and even with human-side interventions such as mass drug administration or mass vaccination, though in the latter cases contamination is less important relative to the overall efficacy since more of the impact is due to the direct effect of individual protection. Contamination also arises in CRTs of many other health interventions, but where transmission is not by night-biting mosquitoes the geometry is likely to be more complicated. For instance, where the intervention is behavioural and the primary source of contamination is social (and hence non-spatial), or with directly transmitted infections or those transmitted by less mobile and day biting
Aedes mosquitoes (where infections often acquired at workplaces or schools, making geographically congruent clusters less desirable), different models of contamination are needed. In any given trial, the appropriateness and fit of the chosen contamination model should be carefully evaluated.
In this work, the sigmoid model is applied to two SWCRTs, the SolarMal and AvecNet trials. SWCRTs can be inferior in terms of power or bias compared to parallel designs and might be vulnerable to imprecision caused by temporal trends in underlying disease rates [
3,
30] but may be required because of logistical, practical or financial constraints [
1,
31] (for example, in the SolarMal trial an objective was to assess whether interruption of transmission would occur at complete coverage [
20]). Because of the changing boundaries, the analysis of contamination effects in SWCRTs is more complicated, but in principle SWCRT data could be used to analyze changing patterns of contamination in time and place. At the same time, it is unclear how the imbalance between arms affects the precision and bias of the resulting estimates.
A reanalysis of the SolarMal trial yielded a slightly higher estimate of effectiveness than was reported in the original trial analysis [
21], but with less precision. Adding a random effect for the households increased the estimate of effectiveness with reasonably wide credible intervals. Also for the AvecNet trial, the reduction in incidence of clinical malaria in children was higher than in the original analysis [
23], with only slightly less precision. The contamination range was consistently around 140 m in the SolarMal trial and around 100 m in the AvecNet trial, which is much less than the maximal distance
Anopheles mosquitoes can fly [
8,
32].
The SolarMal trial was conducted in a small, densely populated area and had many small clusters. The AvecNet trial, in contrast, was conducted in a much larger area, with a population density 10 times lower than that in the SolarMal trial (around 50 people per km
\(^2\) compared to more than 500 people per km
\(^2\)). The settlement patterns where these trials were conducted are also different: in the region where the SolarMal trial took place around Lake Victoria, households are scattered, while the area where the AvecNet trial was conducted has villages with tight aggregations of houses, typical of the West African Sahel. These factors affect the percentage of households in core, the percentage of households unaffected by the contamination across cluster boundaries, where a balance is needed for the proposed analysis to yield unbiased and precise estimates. In the AvecNet trial, a subset of children was chosen from each village, to allow for clusters to be chosen as administrative units. This resulted in a high percentage of households in core, though this number is not comparable to the SolarMal trial, because only the distance to the household of the nearest discordant child was calculated. Informed by a previous simulation study [
9], it is assumed that with so little information from the boundary regions, the contamination range cannot be estimated reliably and the proposed model is not working.
Like AvecNet, many trials define clusters based on administrative units with cluster boundaries passing through uninhabited areas. However, for contamination effects to be estimable, the trial must be designed to collect information from the boundary zones where contamination is likely. If cluster boundaries can pass through inhabited areas, as in the SolarMal trial, equal-population clusters can be assigned giving a more balanced design with optimal power, therefore requiring fewer participants. When there is contamination there is also empirical information about every level of local coverage from within either a CRT or SWCRT, even without universal overall coverage. This enables extension of the analysis using kernel density estimation to infer from the contamination range how effectiveness depends on intervention coverage. These estimates could be used to support allocation decisions when interventions are deployed, but where resource constraints mean universal coverage is not achievable.
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