Identifiability and model misspecification for modelling recurrent infections using routine health care data

For infectious diseases where people can experience multiple infections during their lifetime, the time between observed infections in individuals (or "time to recurrence") can provide valuable information on infection and transmission dynamics. Routinely collected data, such as electronic health records, are a potential source of time to recurrence data. However, they are challenging to analyse because patients can drop out of the data set in a way that is not visible to the data collection process. Standard epidemiological approaches, such as parametric survival analysis with imputation, cannot be applied to such data. In this study, we explored the feasibility of interrogating routinely collected time to recurrence data by calibrating mechanistic transmission models with explicit dropout mechanisms. We identified model structures and parameter regimes where the method could precisely and accurately estimate important epidemiological quantities. Application of our method to real data of malaria infections routinely collected in Papua, Indonesia, was able to estimate the forces of infection for different malaria species, the rate of dropout and recrudescence for Plasmodium falciparum, and the probability of treatment success. Our method has the potential to increase the value of existing and new data sets for informing public health research.