Vandendijck Yannick, Gressani Oswaldo, Faes Christel, Camarda Carlo G, Hens Niel
Interuniversity Institute for Biostatistics and Statistical Bioinformatics (I-BioStat), Data Science Institute, Hasselt University, Hasselt, Belgium.
French Institute for Demographic Studies (INED), Aubervilliers, France.
Biostatistics. 2024 Apr 15;25(2):521-540. doi: 10.1093/biostatistics/kxad005.
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 parameterize dynamic transmission models and to provide insights on the (basic) reproduction number. Information on social interactions can 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, smoothness is introduced in the dimensions of the respondent's and contact's age (i.e., the rows and columns of the social contact matrix). We propose a smoothing constrained approach-taking into account the reciprocal nature of contacts-introducing smoothness over the diagonal (including all subdiagonals) of the social contact matrix. This modeling approach is justified assuming that when people age their contact behavior changes smoothly. We call this smoothing from a cohort perspective. Two approaches that allow for smoothing over social contact matrix diagonals are proposed, namely (i) reordering of the diagonal components of the contact matrix and (ii) reordering of the penalty matrix ensuring smoothness over the contact matrix diagonals. Parameter estimation is done in the likelihood framework by using constrained penalized iterative reweighted least squares. A simulation study underlines the benefits of cohort-based smoothing. 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.
社交接触率在传染病建模中广泛应用，因为研究表明它们是重要流行病学参数的关键驱动因素。接触模式的量化对于参数化动态传播模型以及深入了解（基本）再生数至关重要。关于社交互动的信息可从基于人群的接触调查中获取，例如欧盟委员会的POLYMOD项目。通常使用分段常数法或双变量平滑技术从这些研究中估计特定年龄的接触率。对于后者，通常在受访者年龄和接触对象年龄维度（即社交接触矩阵的行和列）引入平滑性。我们提出一种平滑约束方法——考虑到接触的相互性——在社交接触矩阵的对角线上（包括所有次对角线）引入平滑性。假设人们随着年龄增长其接触行为会平稳变化，这种建模方法是合理的。我们将此称为从队列角度进行平滑。提出了两种允许在社交接触矩阵对角线上进行平滑的方法，即（i）对接触矩阵的对角线元素进行重新排序，以及（ii）对惩罚矩阵进行重新排序以确保在接触矩阵对角线上的平滑性。通过使用约束惩罚迭代加权最小二乘法在似然框架中进行参数估计。一项模拟研究强调了基于队列平滑的益处。最后，在2006年比利时POLYMOD数据上展示了所提出的方法。可从这个GitHub仓库https://github.com/oswaldogressani/Cohort_smoothing下载重现本文结果的代码。
