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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 (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$95\%$$\end{document}    95  %credible interval    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$[0.052,\,0.923]$$\end{document}    [  0.052  ,    0.923  ] km), together with a    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$31.9\%$$\end{document}    31.9  %(   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$95\%$$\end{document}    95  %credible interval    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$[15.3,\,45.8]\%$$\end{document}    [  15.3  ,    45.8  ]  %) reduction of  Plasmodium  infection, compared to the    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$30.0\%$$\end{document}    30.0  %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.

Estimating intervention effectiveness in trials of malaria interventions with contamination