Outcome variable
The outcome variable for the study was appropriate treatment-defined as a drug seller prescribing and dispensing age appropriate medication to children less than five years old with symptoms of pneumonia, uncomplicated malaria and non-bloody diarrhoea in the right dose, frequency and duration for the right indication as per the standard iCCM treatment guidelines 27.

2.5 Data analysis

To assess the effectiveness of peer supervision among drug sellers on appropriate treatment of children less than five years of age with pneumonia symptoms, uncomplicated malaria and non-bloody diarrhoea, interrupted time series for multiple group analysis was conducted29. The ITSA method was the preferred choice for this this study because it was not possible to randomise peer supervision (the intervention)30. In addition we wanted to cater for policy shifts if they occurred during the study period-a major strength of using interrupted time series31. Consideration was made in using interrupted time series since the study had six data points before and six data points after introduction of peer supervision which are considered a minimum for reliable results32,33.
The mean with the corresponding standard deviation and median number of visits by DDIs and peer supervisors was computed. Then, the percentage of appropriately treated children by drug seller by month by district was calculated by dividing the total number of appropriately treated children for a given childhood illness by the total number of children presenting with symptoms of that particular illness multiplied by 100. Results were then aggregated at district level by month covering both the pre-intervention and intervention period and used to show the trend of appropriate treatment in both districts for both periods.
This was followed by fitting the multiple group ITSA model (Equation 1). In the final step, the Cumby-Huizinga test was used to test for autocorrelation. The model was re-run by specifying the lag order accounting for autocorrelation. Data from the sick child registers was entered in Epi Data (www.epidata.dk), exported to excel for cleaning and coding. Data analysis was done using STATA version 15 (Stata Corp, College Station, TX, 2015).The ITSA model is as follows;
\(y_{t}=\ \beta_{0}+\beta_{1}T_{t}+\beta_{2}X_{t}+\beta_{3}X_{t}T_{t}+\ \beta_{4}Z+\beta_{5}ZT_{t}+\ \beta_{6}ZX_{t}+\ \beta_{7}ZX_{t}T_{t}+\ \epsilon_{t}\)..(Equation 1)
The names and definitions of all variables used in this model are listed in table 1.
The ITSA uses ordinary least squares (OLS) approaches to estimate the effects of the intervention (peer supervision) on appropriate treatment for multiple treatment (intervention) periods. The ITSA model accounts for auto correlation among equally spaced observation data by comparison for the lag order for which auto correlation is assumed to be present. The estimated coefficients from the model together with their standard errors are reported.