Nonlinear Fractional Polynomials for Estimating Long-Term Persistence of Induced Anti-HPV Antibodies: A Hierarchical Bayesian Approach
Datasets usually provide raw data for analysis. This raw data often comes in spreadsheet form, but can be any collection of data, on which analysis can be performed.
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.