Estimating fine age structure and time trends in human contact patterns from coarse contact data: The Bayesian rate consistency model

Since the emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), large-scale social contact surveys are now longitudinally measuring the fundamental changes in human interactions in the face of the pandemic and non-pharmaceutical interventions. Here, we present a model-based Bayesian approach that can reconstruct contact patterns at 1-year resolution even when the age of the contacts is reported coarsely by 5 or 10-year age bands. This innovation is rooted in population-level consistency constraints in how contacts between groups must add up, which prompts us to call the approach presented here the Bayesian rate consistency model. The model can also quantify time trends and adjust for reporting fatigue emerging in longitudinal surveys through the use of computationally efficient Hilbert Space Gaussian process priors. We illustrate estimation accuracy on simulated data as well as social contact data from Europe and Africa for which the exact age of contacts is reported, and then apply the model to social contact data with coarse information on the age of contacts that were collected in Germany during the COVID-19 pandemic from April to June 2020 across five longitudinal survey waves. We estimate the fine age structure in social contacts during the early stages of the pandemic and demonstrate that social contact intensities rebounded in an age-structured, non-homogeneous manner. The Bayesian rate consistency model provides a model-based, non-parametric, computationally tractable approach for estimating the fine structure and longitudinal trends in social contacts and is applicable to contemporary survey data with coarsely reported age of contacts as long as the exact age of survey participants is reported.Author summary: The transmission of respiratory infectious diseases occurs during close social contacts. Hence, measuring the intensity and patterns in social contacts leads to a better understanding of disease spread and provides essential data to estimate central quantities such as the reproduction number in real-time. Unlike pre-pandemic surveys, which largely recorded contacts’ age in one-year age intervals, most COVID-era studies only recorded the age of contacts in broad age categories to facilitate reporting. Some studies allowed participants to report an estimate for the total number of contacts for which they could not remember age and gender information. Many studies were partially longitudinal, which introduced the issue of reporting fatigue. Thus, directly applying existing statistical methods for estimating social contact matrices may result in losing age detail and confounded estimates. To this end, we develop a model-based approach which estimates fine-age contact patterns from coarse-age data by exploiting particular constraints that must hold mathematically in closed populations. The model can also adjust for the confounding effects of aggregate contact reporting and reporting fatigue and estimate the time trends in social contact dynamics. We hope this statistical model is a useful addition to the global pandemic preparedness toolkit to reconstruct the fine structure of social contact patterns and measure real-time effective reproduction numbers with greater precision.