Fitting dynamic measles models to subnational case notification data from Ethiopia: Methodological challenges and key considerations

In many settings, ongoing measles transmission is maintained due to pockets of un- or under-vaccinated individuals even if the critical vaccination threshold is reached nationwide. Therefore, assessing the underlying gaps in measles susceptibility within a population is essential for vaccination programs and measles control efforts. Recently, there have been increased efforts to use geospatial and small area methods to estimate subnational measles vaccination coverage in high-burden settings, such as in Ethiopia. However, the distribution of remaining susceptible individuals, either unvaccinated or having never previously been infected, across age groups and subnational geographies is unknown. In this study, we developed a dynamic transmission model that incorporates geospatial estimates of routine measles vaccination coverage, available data on supplemental immunization activities, and reported cases to estimate measles incidence and susceptibility across time, age, and space. We use gridded population estimates and subnational estimates of routine and supplemental measles vaccination coverage. To account for mixing between age-groups, we used a synthetic contact matrix, and travel times via a friction surface were used in a modified gravity model to account for spatial movement. We explored model fitting using Ethiopia as a case study. To address data-related and statistical challenges, we investigated a range of model parameterization and possible fitting algorithms. The approach with the best performance was a model fitted to case notifications adjusted for case ascertainment by using maximum likelihood estimation with block coordinate descent. This strategy was chosen because many data observations (and likely presence of unquantified uncertainty) yielded a steep likelihood surface, which was challenging to fit using Bayesian approaches. We ran sensitivity analyses to explore variations in vaccine effectiveness and compared patterns of susceptibility across space, time, and age. Substantial heterogeneity in reported measles cases as well as susceptibility persists across ages and second-administrative units. These methods and estimates could contribute towards tailored subnational and local planning to reduce preventable measles burden. However, computational and data challenges would need to be addressed for these methods to be applied on a large scale.Author summary: Estimates of subnational measles susceptibility are critical for planning targeted immunization interventions. In this study, we used subnational case notifications available from Ethiopia from 2013 to 2019 as a case study to fit dynamic transmission models of measles with various reporting structures. After exploring biases inherent in these case data, we used various model fitting approaches to consider how best to include these case data in transmission models. Following our investigations, we used a deterministic optimization algorithm via block coordinate descent to fit bootstrapped models with different reporting structures (i.e., single reporting rate and region-specific reporting rates) and conducted a sensitivity analysis across multiple vaccine effectiveness values. We discussed various considerations that need to be made when fitting dynamic transmission models broadly to subnational case notification data based on their inherent biases. These include:accounting for sporadic temporal case reporting,fitting models to biased and variable case notifications despite their certainty based on statistical calculations,considering how best to estimate parameters that may be collinear (i.e., transmission probabilities and reporting rates),accounting for various reporting mechanisms and how they may contribute to under-reporting, andexploring implications related to assumptions on vaccine effectiveness.