Incentivizing appropriate malaria case management in the private sector: a study protocol for two linked cluster randomized controlled trials to evaluate provider- and client-focused interventions in western Kenya and Lagos, Nigeria

Table 3 Estimated power in Nigeria and Kenya

	Estimated power in Nigeria		Estimated power in Kenya
Primary outcome comparison	4-arm design with a total of 48 clusters (alpha = 0.05/3 = 0.0167)		3-arm design with a total of 40 clusters (alpha = 0.05/2 = 0.025)
Primary outcome comparison	Expected effect size	Power	Expected effect size	Power
Combined incentives (PD + CD) vs. control	68% (PD + CD) − 21% (control) = 47 percentage points	100%	23% (PD + CD) − 7% (control) = 16 percentage points	99.1%
Combined incentives (PD + CD) vs. provider-incentives (PD)	68% (PD + CD) − 24% (PD) = 44 percentage points	100%	NA	NA
Combined incentives (PD + CD) vs. Client-incentives (CD)	68% (PD + CD) − 38% (CD) = 30 percentage points	98.8%	23% (PD + CD) − 12% (CD) = 11 percentage points	80.2%

Expected effect size, change in percentage of ACTs taken by clients with a positive test. Since our outcome is a composite measure of testing rates and adherence to the test result, our sample size calculations accounted for the fact that not everyone who we interview will have taken an ACT. For Nigeria, power was calculated based on 12 clusters per arm for a total of 48 clusters. For Kenya, power was calculated based on 13 clusters per arm. In practice an additional cluster will be available in the control arm in Kenya, for a total of 14 clusters in this arm, for a total of 40 clusters

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