Bigelow Benjamin, Verguet Stéphane
Independent Researcher, Arlington, Virginia, USA.
Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, Massachusetts, USA
BMJ Open. 2020 Sep 28;10(9):e034973. doi: 10.1136/bmjopen-2019-034973.
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.
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.
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.
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.
关键健康指标（如干预覆盖率）的变化率是卫生系统绩效中一个研究不足的领域。卫生服务指标的变化率可以补充那些仅涉及这些指标绝对绩效水平的传统衡量方法。增长曲线是一类数学模型，它可以对动态现象进行参数化，并估计总结这些现象的变化率；然而，它们在全球卫生领域并不常用。我们试图使用增长曲线模型来描述撒哈拉以南非洲地区抗逆转录病毒疗法（ART）覆盖率随时间的变化情况。
这是一项回顾性观察研究。我们使用了2000年至2017年42个撒哈拉以南非洲国家公开可用的ART覆盖率数据。我们开发了两个常微分方程模型，即冈珀茨模型和逻辑增长模型，用于估计与ART覆盖率扩大规模和变化率相关的汇总参数。我们对这两个模型进行了非线性回归，使用贝叶斯信息准则（BIC）评估拟合优度，并根据从拟合模型参数中得出的估计绩效对各国进行排名。
我们使用冈珀茨模型提取了各国在ART覆盖率扩大规模方面的表现，范围从每年≤2.5个百分点（南苏丹、苏丹和马达加斯加）到≥8.0个百分点（贝宁、津巴布韦和纳米比亚）。基于BIC，对于大多数所研究的国家，冈珀茨模型比逻辑增长模型拟合得更好。
增长曲线模型可以为评估各国在ART覆盖率演变方面的表现提供基准。它们可能是一种有用的方法，能够得出汇总指标，以综合各国在扩大关键卫生服务规模方面的表现。
