Abstract
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.
Highlights
Human papillomavirus (HPV) infection is a necessary cause of cervical cancer
Using the non-linear fractional polynomial framework (NLFP), we observe from the lower panels that the proportion of subjects who are above the threshold value was 99.7% (389 out of 390 subjects) for anti-HPV-16 antibodies, while it was 99.5% (388 out of 390 subjects) for anti-HPV-18 antibodies over 50 years
We proposed an extension of the fractional polynomial model discussed by Aregay et al (2013) to non-linear fractional polynomial using a hierarchical Bayesian model
Summary
Human papillomavirus (HPV) infection is a necessary cause of cervical cancer. Even though 90% of the HPV infections are cleared within two years (Goldstein et al, 2009), persistent infection will lead to the development of cervical cancer and other anogenital cancers (Ho et al, 1998). Aregay et al (2013) showed that the power-law model of Fraser et al (2007) and David et al (2009) can be formulated using fractional polynomial (FP), which is a data-driven method to predict long-term persistence and to estimate the time point above a given threshold. The method is applied to predict the long-term persistence of vaccine-induced anti-HPV-16 and anti-HPV-18 antibodies, as well as to predict the proportion of subjects above a threshold value. The data set used encompasses 390 healthy women who received the HPV-16/18 AS04-adjuvanted vaccine (Cervarix) They were enrolled in the initial multi-center study (HPV-001, NCT00689741) and took part in a follow-up study for three additional years (HPV-007, NCT00120848). It can be seen that the decline in the antibody level was higher in the first few months followed by a moderate decrease until the end of the follow-up period
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