Cohort-based smoothing methods for age-specific contact rates

Abstract

The use of social contact rates is widespread in infectious disease modeling since it has been shown that they are key driving forces of important epidemiological parameters. Quantification of contact patterns is crucial to parametrize dynamic transmission models and to provide insights on the (basic) reproduction number. Information on social interactions, can (for instance) be obtained from population-based contact surveys, such as the European Commission project POLYMOD. Estimation of age-specific contact rates from these studies is often done using a piecewise constant approach or bivariate smoothing techniques. For the latter, typically, smoothing is done in the dimensions of the respondent’s and contact’s age. We propose a new flexible strategy based on a smoothing constrained approach - taking into account the reciprocal nature of contacts - where the contact rates are assumed smooth from a cohort perspective as well as from the age distribution of contacts. This is achieved by smoothing over the diagonal components (including all subdiagonals) of the social contact matrix. This approach is supported by the fact that people age with time and thus motivates smoothly varying contact rates from a cohort angle. Two approaches that allow for smoothing of social contact data over cohorts are proposed namely, (1) reordering of the diagonal components of the social contact matrix; and (2) reordering of the penalty matrix associated with the diagonal components. Parameter estimation is done in the likelihood framework by using constrained penalized iterative reweighted least squares (C-PIRLS), under Poisson and negative Binomial distributional assumptions for the observed contacts. A simulation study underlines the benefits of cohort-based smoothing based on two scalar measures of performance. Finally, the proposed methods are illustrated on the Belgian POLYMOD data of 2006. Code to reproduce the results of the article can be downloaded on this Github repository https://github.com/oswaldogressani/Cohort_smoothing.