Parametric overdispersed frailty models for current status data

Frailty models have a prominent place in survival analysis to model univariate and multivariate time‐to‐event data, often complicated by the presence of different types of censoring. In recent years, frailty modeling gained popularity in infectious disease epidemiology to quantify unobserved heterogeneity using Type I interval‐censored serological data or current status data. In a multivariate setting, frailty models prove useful to assess the association between infection times related to multiple distinct infections acquired by the same individual. In addition to dependence among individual infection times, overdispersion can arise when the observed variability in the data exceeds the one implied by the model. In this article, we discuss parametric overdispersed frailty models for time‐to‐event data under Type I interval‐censoring, building upon the work by Molenberghs et al. (2010) and Hens et al. (2009). The proposed methodology is illustrated using bivariate serological data on hepatitis A and B from Flanders, Belgium anno 1993–1994. Furthermore, the relationship between individual heterogeneity and overdispersion at a stratum‐specific level is studied through simulations. Although it is important to account for overdispersion, one should be cautious when modeling both individual heterogeneity and overdispersion based on current status data as model selection is hampered by the loss of information due to censoring.