Nonlinear Fractional Polynomials for Estimating Long-Term Persistence of Induced Anti-HPV Antibodies: A Hierarchical Bayesian Approach

When the true relationship between a covariate and an outcome is nonlinear, one should use a nonlinear mean structure that can take this pattern into account. In this article, the fractional polynomial modeling framework, which assumes a prespecified set of powers, is extended to a nonlinear fractional polynomial framework (NLFP). Inferences are drawn in a Bayesian fashion. The proposed modeling paradigm is applied to predict the long-term persistence of vaccine-induced anti-HPV antibodies. In addition, the subject-specific posterior probability to be above a threshold value at a given time is calculated. The model is compared with a power-law model using the deviance information criterion (DIC). The newly proposed model is found to fit better than the power-law model. A sensitivity analysis was conducted, from which a relative independence of the results from the prior distribution of the power was observed. Supplementary materials for this article are available online.

当协变量与结局变量间的真实关联呈非线性时，应采用能够适配该关联模式的非线性均值结构。本文将预设幂次集合的分数多项式建模框架拓展至非线性分数多项式建模框架（NLFP），并采用贝叶斯推断范式开展统计推断。本研究将所提出的建模范式应用于预测疫苗诱导的抗人乳头瘤病毒（HPV）抗体的长期留存情况；此外，还计算了每名个体在给定时间点其抗体水平高于设定阈值的后验概率。本研究采用偏差信息准则（DIC），将所提模型与幂律模型进行对比，结果显示新型模型的拟合效果优于幂律模型。本研究同时开展了敏感性分析，结果表明模型结果与幂次的先验分布相对独立。本文的补充材料可在线获取。