Several demographic and health indicators, including the total fertility rate (TFR) and modern contraceptive use rate (mCPR), evolve similarly over time, characterized by a transition between stable states. Existing approaches for estimation or projection of transitions in multiple populations have successfully used parametric functions to capture the relation between the rate of change of an indicator and its level. However, incorrect parametric forms may result in bias or incorrect coverage in long-term projections. We propose a new class of models to capture demographic transitions in multiple populations. Our proposal, the B-spline Transition Model (BTM), models the relationship between the rate of change of an indicator and its level using B-splines, allowing for data-adaptive estimation of transition functions. Bayesian hierarchical models are used to share information on the transition function between populations. We apply the BTM to estimate and project country-level TFR and mCPR and compare the results against those from extant parametric models. For TFR, BTM projections have generally lower error than the comparison model. For mCPR, while results are comparable between BTM and a parametric approach, the B-spline model generally improves out-of-sample predictions. The case studies suggest that the BTM may be considered for demographic applications

翻译：多项人口与健康指标，包括总和生育率（TFR）和现代避孕措施使用率（mCPR），随时间呈现出相似的演变模式，其特征为稳定状态之间的转变。现有用于估计或预测多个人群转变过程的方法已成功采用参数化函数来捕捉指标变化率与其水平之间的关系。然而，不正确的参数形式可能导致长期预测出现偏差或覆盖范围不准确。我们提出一类新的模型来捕捉多个人群的人口转变过程。我们提出的B样条转变模型（BTM）使用B样条对指标变化率与其水平之间的关系进行建模，从而实现对转变函数的数据自适应估计。通过贝叶斯分层模型在人群间共享转变函数信息。我们将BTM应用于国家层面TFR和mCPR的估计与预测，并将结果与现有参数化模型进行比较。对于TFR，BTM预测的误差普遍低于对比模型。对于mCPR，虽然BTM与参数化方法的结果具有可比性，但B样条模型通常能改进样本外预测效果。案例研究表明，BTM可考虑应用于人口学领域。