Cohort-based Smoothing Methods for Age-specific Contact Rates

Abstract

The use of social contact rates is widespread in infectious disease modelling, since it is known that they provide proxies of crucial determinants of epidemiological and disease transmission parameters. Information on social contact rates can, for example, be obtained from a population-based contact diary survey, such as the POLYMOD study. Estimation of age-specific contact rates from these studies is often done using bivariate smoothing techniques. Typically, smoothing is done in the dimensions of the respondents and contacts age. In this paper, we introduce 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 contact rates should vary smoothly by cohorts. Two approaches that allow for smoothing of social contact data over cohorts are proposed: (1) reordening of the diagonal components of the social contact rate matrix; and (2) reordening of the penalty matrix associated with the diagonal components. Parameter estimation is done using constrained penalized iterative reweighted least squares. A simulation study is presented to compare methods. The proposed methods are illustrated on the Belgian POLYMOD data of 2006.