Approximate maximum likelihood estimation in cure models using aggregated data, with application to HPV vaccine completion

Research into vaccine hesitancy is a critical component of the public health enterprise, as rates of communicable diseases preventable by routine childhood immunization have been increasing in recent years. It is therefore important to estimate proportions of "never-vaccinators" in various subgroups of the population in order to successfully target interventions to improve childhood vaccination rates. However, due to privacy issues, it may be difficult to obtain individual patient data (IPD) needed to perform the appropriate time-to-event analyses: state-level immunization information services may only be willing to share aggregated data with researchers. We propose statistical methodology for the analysis of aggregated survival data that can accommodate a cured fraction based on a polynomial approximation of the mixture cure model log-likelihood function relying only on summary statistics. We study the performance of the method through simulation studies and apply it to a real-world data set from a study examining reminder/recall approaches to improve human papillomavirus (HPV) vaccination uptake. The proposed methods may be generalized for use when there is interest in fitting complex likelihood-based models but IPD is unavailable due to data privacy or other concerns.