Spline smoothing in Bayesian disease mapping

MacNab, Ying C.

doi:10.1002/env.876

Cited by 35 publications

(45 citation statements)

References 30 publications

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“…Inclusion of the spline smoothing appeared to have reduced the need for 'local spatial' smoothing, as the spatial priors did not offer notably improved fit over the non-spatial prior. Similar results were also seen in [20].…”

Section: Discussion and Future Researchsupporting

confidence: 92%

“…the penalty matrices) and on the random effects variances so that the corresponding penalty is proportional to the negative logarithm of the prior density, often named the smoothing prior [10,11,13,19]. More recently, the use of smoothing spline and P-spline for spatiotemporal modelling of rates within the context of Bayesian disease mapping has been presented in MacNab and Gustafson [20]. The study presents hierarchical Bayes formulation of B-spline, P-spline, and smoothing spline, explores the connections among them and sheds light on their smoothing capabilities with respect to disease mapping.…”

Section: Introductionmentioning

confidence: 99%

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Regression B‐spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

MacNab

Gustafson

2007

Statistics in Medicine

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In the context of Bayesian disease mapping, recent literature presents generalized linear mixed models that engender spatial smoothing. The methods assume spatially varying random effects as a route to partially pooling data and 'borrowing strength' in small-area estimation. When spatiotemporal disease rates are available for sequential risk mapping of several time periods, the 'smoothing' issue may be explored by considering spatial smoothing, temporal smoothing and spatiotemporal interaction. In this paper, these considerations are motivated and explored through development of a Bayesian semiparametric disease mapping model framework which facilitates temporal smoothing of rates and relative risks via regression B-splines with mixed-effect representation of coefficients. Specifically, we develop spatial priors such as multivariate Gaussian Markov random fields and non-spatial priors such as unstructured multivariate Gaussian distributions and illustrate how time trends in small-area relative risks may be explored by splines which vary in either a spatially structured or unstructured manner. In particular, we show that with suitable prior specifications for the random effects ensemble, small-area relative risk trends may be fit by 'spatially varying' or randomly varying B-splines. A recently developed Bayesian hierarchical model selection criterion, the deviance information criterion, is used to assess the trade-off between goodness-of-fit and smoothness and to select the number of knots. The methodological development aims to provide reliable information about the patterns (both over space and time) of disease risks and to quantify uncertainty. The study offers a disease and health outcome surveillance methodology for flexible and efficient exploration and assessment of emerging risk trends and clustering. The methods are motivated and illustrated through a Bayesian analysis of adverse medical events (also known as iatrogenic injuries) among hospitalized elderly patients in British Columbia, Canada.

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Section: Discussion and Future Researchsupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Regression B‐spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

MacNab

Gustafson

2007

Statistics in Medicine

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“…As presented in MacNab and Gustafson [33], one may consider placing spatial priors (such as the MCARs presented in Section 4.2) on the random intercepts and spline coefficients of the spatiotemporal models for spatially varying B-splines [33,34]. For example, for model (18) + (19) and denoting …”

Section: Joint Component Modelling Of Spatiotemporal Rates: Shared Comentioning

confidence: 98%

“…In particular, recently developed multivariate CAR models [31][32][33][34], which enable us to account for and estimate crosscomponent correlation, may be considered for JM of the non-fatal and fatal outcomes:…”

Section: Joint Modelling Of Spatial Rates: Bivariate Car Modelsmentioning

confidence: 99%

Mapping disability‐adjusted life years: a Bayesian hierarchical model framework for burden of disease and injury assessment

MacNab

2007

Statistics in Medicine

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This paper presents a Bayesian disability-adjusted life year (DALY) methodology for spatial and spatiotemporal analyses of disease and/or injury burden. A Bayesian disease mapping model framework, which blends together spatial modelling, shared-component modelling (SCM), temporal modelling, ecological modelling, and non-linear modelling, is developed for small-area DALY estimation and inference. In particular, we develop a model framework that enables SCM as well as multivariate CAR modelling of non-fatal and fatal disease or injury rates and facilitates spline smoothing for non-linear modelling of temporal rate and risk trends. Using British Columbia (Canada) hospital admission-separation data and vital statistics mortality data on non-fatal and fatal road traffic injuries to male population age 20-39 for year 1991-2000 and for 84 local health areas and 16 health service delivery areas, spatial and spatiotemporal estimation and inference on years of life lost due to premature death, years lived with disability, and DALYs are presented. Fully Bayesian estimation and inference, with Markov chain Monte Carlo implementation, are illustrated. We present a methodological framework within which the DALY and the Bayesian disease mapping methodologies interface and intersect. Its development brings the relative importance of premature mortality and disability into the assessment of community health and health needs in order to provide reliable information and evidence for community-based public health surveillance and evaluation, disease and injury prevention, and resource provision.

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“…[2][3][4][5][6][7] Such models aim to cope with various types of drawbacks that could lead to a misspecification, for example:…”

Section: Introductionmentioning

confidence: 99%

Semiparametric M-quantile regression for count data

Dreassi

Ranalli

Salvati

2014

Stat Methods Med Res

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Lung cancer incidence over 2005-2010 for 326 Local Authority Districts in England is investigated by ecological regression. Motivated from mis-specification of a Negative Binomial additive model, a semiparametric Negative Binomial M-quantile regression model is introduced. The additive part relates to those univariate or bivariate smoothing components, which are included in the model to capture nonlinearities in the predictor or to account for spatial dependence. All such components are estimated using penalized splines. The results show the capability of the semiparametric Negative Binomial M-quantile regression model to handle data with a strong spatial structure.

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Spline smoothing in Bayesian disease mapping

Cited by 35 publications

References 30 publications

Regression B‐spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

Regression B‐spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

Mapping disability‐adjusted life years: a Bayesian hierarchical model framework for burden of disease and injury assessment

Semiparametric M-quantile regression for count data

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