Model-Based Estimates of Long-Term Persistence of Induced HPV Antibodies: A Flexible Subject-Specific Approach

Abstract In infectious diseases, it is important to predict the long-term persistence of vaccine-induced antibodies and to estimate the time points where the individual titers are below the threshold value for protection. This article focuses on HPV-16/18, and uses a so-called fractional-polynomial model to this effect, derived in a data-driven fashion. Initially, model selection was done from among the second- and first-order fractional polynomials on the one hand and from the linear mixed model on the other. According to a functional selection procedure, the first-order fractional polynomial was selected. Apart from the fractional polynomial model, we also fitted a power-law model, which is a special case of the fractional polynomial model. Both models were compared using Akaike's information criterion. Over the observation period, the fractional polynomials fitted the data better than the power-law model; this, of course, does not imply that it fits best over the long run, and hence, caution ought to be used when prediction is of interest. Therefore, we point out that the persistence of the anti-HPV responses induced by these vaccines can only be ascertained empirically by long-term follow-up analysis. Key Words: Akaike's information criterionFractional polynomial modelFunctional selection procedurePower-law model ACKNOWLEDGMENTS The authors gratefully acknowledge support from IAP research Network P6/03 of the Belgian Government (Belgian Science Policy). They also thank the study participants and clinical investigators from the Phase IIb primary efficacy study (NCT00689741). Finally, they thank the laboratory personnel for their contribution in performing the assays.