Estimation of summary protective efficacy using a frailty mixture model for recurrent event time data.

Area of Science:

• Biostatistics
• Epidemiology
• Clinical Trials

Background:

• Recurrent event time data analysis presents challenges including within-subject event dependence, between-subject heterogeneity, and non-susceptible populations.
• Accurate estimation of vaccine protective efficacy is vital, particularly in infectious disease clinical trials with recurrent events.

Purpose of the Study:

• To propose a novel two-part frailty mixture model for recurrent event time data.
• To simultaneously address event dependence, heterogeneity in event rates, and the presence of a nonsusceptible fraction.
• To provide a unified measure for summary protective efficacy, combining 'all-or-none' and 'leaky' vaccine action models.

Main Methods:

• A two-part frailty mixture model was developed to analyze recurrent event time data.
• Model parameters were estimated using the expectation-maximization (EM) algorithm.
• Variances were calculated using Louis's formula for the EM algorithm, and summary protective efficacy was estimated using the delta method.

Main Results:

• The proposed model successfully accommodates within-subject event dependence, between-subject heterogeneity, and nonsusceptible fractions.
• Simulation studies demonstrated the performance of the proposed estimation approach.
• Reanalysis of malaria prophylaxis trial data from Ghana was conducted.

Conclusions:

• The developed two-part frailty mixture model offers a robust framework for analyzing recurrent event time data in complex scenarios.
• The model provides a unified measure of summary protective efficacy, enhancing the interpretation of vaccine effectiveness.
• The methodology is applicable to various infectious disease clinical trials and observational studies involving recurrent events.