This paper presents two approaches to smoothing time trends in prevalence and estimating the underlying incidence of remissible infections. In the first approach, we use second order segmented polynomials to smooth a curve in a bounded domain. In the second, incidence is modeled instead and the prevalence is reconstructed using the recovery rate which is assumed to be known. In both approaches, the number of knots and their positions are estimated, resulting in non-linear regressions. Akaike Information Criterion is used for model selection. The method is illustrated with Syphilis and Gonorrhea prevalence smoothing and incidence trend estimation in Guinea-Bissau and South Africa, respectively.

中文翻译：

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梅毒和淋病流行和发病趋势估计的二阶分段多项式：在 Spectrum 几内亚比绍和南非数据中的应用

本文提出了两种方法来平滑流行率的时间趋势和估计可缓解感染的潜在发病率。在第一种方法中，我们使用二阶分段多项式来平滑有界域中的曲线。在第二种情况下，改为对发病率进行建模，并使用假定已知的恢复率重建流行率。在这两种方法中，都会估计结的数量及其位置，从而导致非线性回归。Akaike Information Criterion 用于模型选择。该方法分别通过几内亚比绍和南非的梅毒和淋病流行率平滑和发病趋势估计来说明。