Non-linear 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 non-linear, one should use a non-linear mean structure that can take this pattern into account. In this paper, the fractional polynomial modeling framework, which assumes a pre-specified set of powers, is extended to a non-linear 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.