Joint Quantile Regression for Spatial Data

Xu, Chen; Tokdar, Surya T.

doi:10.1111/rssb.12467

Cited by 6 publications

(8 citation statements)

References 70 publications

(86 reference statements)

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“…in (16), respectively. Various random effects such as splines for non-linear effects of covariates and is included through functions { } 1 =1 in (15) and { } 2 =1 in ( 16), respectively.…”

Section: Model Specificationmentioning

confidence: 98%

“…However, we advocate the use of INLA over MCMC for practical disease mapping due to its computational advantages. Spatial quantile regression is widely used with applications ranging from modeling of wildfire risk 16 to studying healthy life years expectancy 20 to economics 17 . In 21 , a Bayesian multiple quantile regression method is proposed for linear models, and they used the working likelihood instead of the likelihood of the generating distribution.…”

Section: Introductionmentioning

confidence: 99%

“…The main difference to our work is that we consider joint quantile regression with two diseases, instead of a single one. In joint quantile regression, one can model spatial dependence through a Gaussian or t-copula process of the quantile levels 16 , which could provide certain benefits for cases with heavy-tailed spatial data. One of the approaches to spatial quantile regression is to use the Asymmetric Laplace Process (ALP) for modeling the data 17 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Joint Quantile Disease Mapping with Application to Malaria and G6PD Deficiency

Alahmadi¹,

Rue²,

Niekerk³

2022

Preprint

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Statistical analysis based on quantile regression methods is more comprehensive, flexible, and less sensitive to outliers when compared to mean regression methods.When the link between different diseases are of interest, joint disease mapping is useful for measuring directional correlation between them. Most studies study this link through multiple correlated mean regressions. In this paper we propose a joint quantile regression framework for multiple diseases where different quantile levels can be considered. We are motivated by the theorized link between the presence of Malaria and the gene deficiency G6PD, where medical scientist have anecdotally discovered a possible link between high levels of G6PD and lower than expected levels of Malaria initially pointing towards the occurrence of G6PD inhibiting the occurrence of Malaria. This link cannot be investigated with mean regressions and thus the need for flexible joint quantile regression in a disease mapping framework.Our joint quantile disease mapping model can be used for linear and non-linear effects of covariates by stochastic splines, since we define it as a latent Gaussian model.We perform Bayesian inference of this model using the INLA framework embedded in the R software package INLA. Finally, we illustrate the applicability of model by analyzing the malaria and G6PD deficiency incidences in 21 African countries using linked quantiles of different levels.

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“…in (16), respectively. Various random effects such as splines for non-linear effects of covariates and is included through functions { } 1 =1 in (15) and { } 2 =1 in ( 16), respectively.…”

Section: Model Specificationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Joint Quantile Disease Mapping with Application to Malaria and G6PD Deficiency

Alahmadi¹,

Rue²,

Niekerk³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Quantile regression: Quantile regression has been extended to the spatial case by Hallin et al (2009). The spatial dependence has been modelled by copulas in a Bayesian statistical-based setting (Chen and Tokdar 2021).…”

Section: Spatial Modelsmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

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Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users’ needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

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“…Since then quantile regression has been widely used, also in Bayesian spatial analysis by Reich et al [ 15 ]. Moreover, spatial quantile regression is widely used with other applications ranging from modelling of wildfire risk [ 16 ] to studying healthy life years expectancy [ 17 ] to economics [ 18 ]. In most works, however, the response variable is assumed to be continuously distributed and the asymmetric Laplace distribution (ALD) likelihood [ 19 ] is used to model the quantiles, irrespective of the data-generating distribution.…”

Section: Introductionmentioning

confidence: 99%

Joint quantile disease mapping with application to malaria and G6PD deficiency

Alahmadi,

van Niekerk,

Padellini

et al. 2024

R. Soc. open sci.

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Statistical analysis based on quantile methods is more comprehensive, flexible and less sensitive to outliers when compared to mean methods. Joint disease mapping is useful for inferring correlation between different diseases. Most studies investigate this link through multiple correlated mean regressions. We propose a joint quantile regression framework for multiple diseases where different quantile levels can be considered. We are motivated by the theorized link between the presence of malaria and the gene deficiency G6PD, where medical scientists have anecdotally discovered a possible link between high levels of G6PD and lower than expected levels of malaria initially pointing towards the occurrence of G6PD inhibiting the occurrence of malaria. Thus, the need for flexible joint quantile regression in a disease mapping framework arises. Our model can be used for linear and nonlinear effects of covariates by stochastic splines since we define it as a latent Gaussian model. We perform Bayesian inference using the R integrated nested Laplace approximation, suitable even for large datasets. Finally, we illustrate the model’s applicability by considering data from 21 countries, although better data are needed to prove a significant relationship. The proposed methodology offers a framework for future studies of interrelated disease phenomena.

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Joint Quantile Regression for Spatial Data

Cited by 6 publications

References 70 publications

Joint Quantile Disease Mapping with Application to Malaria and G6PD Deficiency

Joint Quantile Disease Mapping with Application to Malaria and G6PD Deficiency

A review of predictive uncertainty estimation with machine learning

Joint quantile disease mapping with application to malaria and G6PD deficiency

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