Penalized composite link mixed models for two-dimensional count data

Mortality data provide valuable information for the study of the spatial distribution of mortality risk, in disciplines such as spatial epidemiology, medical demography, and public health. However, they are often available in an aggregated form over irregular geographical units, hindering the visualization of the underlying mortality risk and the detection of meaningful patterns. Also, it could be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked with potential risk factors — in a posterior correlation analysis — that are usually measured in a different spatial resolution than mortality data. In this paper, we propose the use of the penalized composite link model and its representation as a mixed model to deal with these issues. This model takes into account the nature of mortality rates by incorporating the population size at the finest resolution, and allows the creation of mortality maps at a desirable scale, reducing the visual bias resulting from the spatial aggregation within original units. We illustrate our proposal with the analysis of several datasets related with deaths by respiratory diseases, cardiovascular diseases, and lung cancer.Acknowledgements: The first and second authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness grants MTM2011-28285-C02-02 and MTM2014-52184. The third author acknowledges financial support from the Basque Government through the BERC 2014-2017 program and by the Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323