Penalized composite link models for aggregated spatial count data: A mixed model approach

Abstract

Mortality data provide valuable information for the study of the spatial distribution of mortality risk, in disciplines such as spatial epidemiology and public health. However, they are frequently available in an aggregated form over irregular geographical units, hindering the visualization of the underlying mortality risk. Also, it can be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked to potential risk factors that are usually measured in a different spatial resolution. In this paper, we propose the use of the penalized composite link model and its mixed model representation. This model considers the nature of mortality rates by incorporating the population size at the finest resolution, and allows the creation of mortality maps at a finer scale, thus reducing the visual bias resulting from the spatial aggregation within original units. We also extend the model by considering individual random effects at the aggregated scale, in order to take into account the overdispersion. We illustrate our novel proposal using two datasets: female deaths by lung cancer in Indiana, USA, and male lip cancer incidence in Scotland counties. We also compare the performance of our proposal with the area-to-point Poisson kriging approach.

Relating ultrasonic vocalizations from a pair of rats to individual behavior: A composite link model approach

“…Given that the USV rate varied widely between pairs, a mixed modeling approach could be an interesting future extension of our work. For mixed modeling approaches for CLM, see Ayma, Durbán, Lee, and Eilers () and Douma ().…”

Modeling latent spatio-temporal disease incidence using penalized composite link models

“…Once the ST-PCLM defined in (6) is in the GLMM framework, it is possible to estimate its parameters. This estimation procedure was presented by [ 20 ] in a spatial disaggregation context, and it involves two interrelated stages: (a) estimation of fixed coefficients and random effects ( β and α ); and (b) estimation of smoothing parameters (λ 1 , λ 2 , and λ 3 ). The penalized quasi-likelihood (PQL) methods of [ 32 ] are used for stage (a), and the restricted (or residual) maximum likelihood (REML, [ 32 , 33 ]) is used for stage (b) as a numerical optimization criterion for smoothing parameter selection.…”

“…The penalized quasi-likelihood (PQL) methods of [ 32 ] are used for stage (a), and the restricted (or residual) maximum likelihood (REML, [ 32 , 33 ]) is used for stage (b) as a numerical optimization criterion for smoothing parameter selection. Technical details are provided in [ 20 ] and, thus, we only describe here the necessary results.…”

“…We can find several techniques that allow the spatial disaggregation of health data. For example, the use of an interpolation process from empirical Bayes estimates [ 17 ], (generalized) Poisson kriging methods [ 18 ], log-Gaussian Cox processes [ 19 ], and spatial composite link mixed models [ 20 ] have been suggested to produce a continuous smooth surface (across the study area) from regional health data. However, as far as we know, there is no appropriate model to address the problem of disaggregation of health data in both space and time (although there are some works about spatio-temporal disaggregation in a Gaussian context; see, for example, [ 21 – 25 ]).…”

How to estimate mortality trends from grouped vital statistics

“…In a one-dimensional setting it has been found to model age-specific grouped data, 11 outperforming kernel density estimator and spline interpolation methods in the presence of open-ended intervals especially, 15 and data suffering from digit preferences 16 . In two- or three-dimensional settings it has been applied to aggregated spatial counts 17 and to fertility rates grouped by age, time and birth order 18 . The methodology was also explored in a Bayesian framework 19 .…”