Fernandez–Steel Skew Normal Conditional Autoregressive (FSSN CAR) Model in Stan for Spatial Data

Rantini, Dwi; Iriawan, Nur; Irhamah,

doi:10.3390/sym13040545

Cited by 4 publications

(4 citation statements)

References 41 publications

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“…In addition, Allard and Naveau [ 25 ] and Zareifard and Jafari Khaledi [ 26 ] introduced a skew-normal spatial random field based on Domınguez-Molina et al [ 27 ] and Palacios and Steel [ 28 ], respectively, for point referenced data. Other skewed spatial distributions are the skew-normal by Rantini et al [ 29 ] and Fernández and Steel [ 30 ].…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa

Ayalew

Manda

Cai

2021

IJERPH

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Despite making significant progress in tackling its HIV epidemic, South Africa, with 7.7 million people living with HIV, still has the biggest HIV epidemic in the world. The Government, in collaboration with developmental partners and agencies, has been strengthening its responses to the HIV epidemic to better target the delivery of HIV care, treatment strategies and prevention services. Population-based household HIV surveys have, over time, contributed to the country’s efforts in monitoring and understanding the magnitude and heterogeneity of the HIV epidemic. Local-level monitoring of progress made against HIV and AIDS is increasingly needed for decision making. Previous studies have provided evidence of substantial subnational variation in the HIV epidemic. Using HIV prevalence data from the 2016 South African Demographic and Health Survey, we compare three spatial smoothing models, namely, the intrinsically conditionally autoregressive normal, Laplace and skew-t (ICAR-normal, ICAR-Laplace and ICAR-skew-t) in the estimation of the HIV prevalence across 52 districts in South Africa. The parameters of the resulting models are estimated using Bayesian approaches. The skewness parameter for the ICAR-skew-t model was not statistically significant, suggesting the absence of skewness in the HIV prevalence data. Based on the deviance information criterion (DIC) model selection, the ICAR-normal and ICAR-Laplace had DIC values of 291.3 and 315, respectively, which were lower than that of the ICAR-skewed t (348.1). However, based on the model adequacy criterion using the conditional predictive ordinates (CPO), the ICAR-skew-t distribution had the lowest CPO value. Thus, the ICAR-skew-t was the best spatial smoothing model for the estimation of HIV prevalence in our study.

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Section: Introductionmentioning

confidence: 99%

A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa

Ayalew

Manda

Cai

2021

IJERPH

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“…Comparison of these models with the standard ICAR-normal and ICAR double exponential/Laplace models using DIC and CPO values indicates that the model that assumed ICAR-skew-normal distribution is the best model in terms of its predictive capacity. A similar study that used Fernandez-Steel skew normal (FSSN) CAR model also suggested better predictive performance as compared to its CAR-normal counterpart (Rantini et al, 2021). This model is used for generating the final estimates of HIV prevalence by district in South Africa.…”

Section: Discussionmentioning

confidence: 90%

Flexible Bayesian hierarchical spatial modelling in disease mapping.

Ayalew

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The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis is to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considers the skew-normal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considers non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model are evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD work shows the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.

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“…Comparison of these models with the standard ICAR-normal and ICAR double exponential/Laplace models using DIC and CPO values indicates that the model that assumed ICAR-skew-normal distribution is the best model in terms of its predictive capacity. And a similar study that used Fernandez-Steel skew normal (FSSN) CAR model also suggested better predictive performance as compared to its CAR-normal counterpart (Rantini et al, 2021). This model is used for generating the final estimates of HIV prevalence by district in South Africa.…”

Section: Mapping District Hiv Prevalence In South Africamentioning

confidence: 91%

“…In addition, Allard & Naveau (2007) and Zareifard & Khaledi (2013) introduced a skew-normal spatial random field based on Dominguez-Molina et al (2003) and Palacios & Steel (2006), respectively, for point referenced data. Other skewed spatial distributions are the skew-normal by Rantini et al (2021) and (Fernández & Steel, 1998).…”

Section: Introductionmentioning

confidence: 99%

Flexible Bayesian hierarchical spatial modeling in disease mapping.

Ayalew

View full text Add to dashboard Cite

The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis was to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considered the skewnormal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considered non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model were evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD has shown the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.

show abstract

Fernandez–Steel Skew Normal Conditional Autoregressive (FSSN CAR) Model in Stan for Spatial Data

Cited by 4 publications

References 41 publications

A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa

A Comparison of Bayesian Spatial Models for HIV Mapping in South Africa

Flexible Bayesian hierarchical spatial modelling in disease mapping.

Flexible Bayesian hierarchical spatial modeling in disease mapping.

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