Estimating economies of scale and learning-by-doing effects in a health systems strengthening intervention

Abstract It can be challenging to evaluate efficiencies for interventions strengthening health systems, for a variety of reasons. As part of a program review of The Challenge Initiative (TCI) that took place in 2020, we explored whether economies of scale and learning-by-doing effects existed for the health systems strengthening portion of the project, utilizing audited expenditure data and validated reported outcomes. TCI is a project that partnered with local governments in low- and middle-income countries to deliver interventions for family planning; it is relatively unique in terms of both its activities and in how its expenditures and outcomes were tracked. Using TCI data, we estimated a cost function, evaluating economies of scale using as output measures both the number of geographies that joined the project over time and the population of women of reproductive age in those geographies over time, allowing for complex effects by including levels, squared and cubic formulations of the output variables. We also evaluated whether learning-by-doing effects obtained by examining coefficients of time-related variables. Results suggested that while initially there were diseconomies of scale when output was measured using number of geographies, the TCI program began to experience economies of scale as the number expanded, with significant economies of scale experienced beginning at the mean number of geographies. When output was measured using population of women of reproductive age, economies of scale existed throughout. We did not find econometric evidence of learning-by-doing effects. Competing Interest Statement The authors have declared no competing interest. Funding Statement The research in this paper was funded by the Bill and Melinda Gates Foundation (INV-016714). Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Data Availability All data produced in the present study are available upon reasonable request to the authors