Characterising the scale-up and performance of antiretroviral therapy programmes in sub-Saharan Africa: an observational study using growth curves.

Objectives: The rate of change in key health indicators (eg, intervention coverage) is an understudied area of health system performance. Rates of change in health services indicators can augment traditional measures that solely involve the absolute level of performance in those indicators. Growth curves are a class of mathematical models that can parameterise dynamic phenomena and estimate rates of change summarising these phenomena; however, they are not commonly used in global health. We sought to characterise the changes over time in antiretroviral therapy (ART) coverage in sub-Saharan Africa using growth curve models.

Design: This was a retrospective observational study. We used publicly available data on ART coverage levels from 2000 to 2017 in 42 sub-Saharan African countries. We developed two ordinary differential equations models, the Gompertz and logistic growth models, that allowed for the estimation of summary parameters related to scale-up and rates of change in ART coverage. We fitted non-linear regressions for the two models, assessed goodness of fit using the Bayesian information criterion (BIC), and ranked countries based on their estimated performance drawn from the fitted model parameters.

Results: We extracted country performance in rates of scale-up of ART coverage, which ranged from ≤2.5 percentage points per year (South Sudan, Sudan, and Madagascar) to ≥8.0 percentage points per year (Benin, Zimbabwe and Namibia), using the Gompertz model. Based on BIC, the Gompertz model provided a better fit than the logistic growth model for most countries studied.

Conclusions: Growth curve models can provide benchmarks to assess country performance in ART coverage evolution. They could be a useful approach that yields summary metrics for synthesising country performance in scaling up key health services.