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Hierarchical models for the analysis of spatial health surveys with missing information at individual and areal level
No full textStatistics are used to draw conclusions from a population of interest, based on a representative sample. Surveys are a frequent example of a sample, where people, sampled from
the population, answer questions or fill out a questionnaire. The distribution of certain
characteristics (e.g. age, sex, socioeconomic status) between sample and population may
differ. In order to account for this difference, a survey weight is assigned to every person
in the sample.
When conducting a survey, some respondents do not want to or are unable to answer
certain questions. This introduces incomplete data when analyzing the survey. It is
important for researchers to deal with the missing data in a correct way, in order to
avoid biased estimates. Therefore, an assumption has to be made for the reason why
someone did not respond to the question of interest. We distinguish three possibilities:
(1) the missingness is completely random (MCAR), (2) the missingness depends solely
on the observed measurements, independent of the unobserved measurements (MAR)
and (3) the missingness depends on both the observed and unobserved measurements
(MNAR)(Rubin, 1976).
In this thesis, we investigate models which can correctly analyse survey data with
missing observations. Furthermore, we account for the spatial context of the data. Estimates are provided at the level of “small areas” (e.g. districts, counties, provinces). The
measurements of areas which are close to each other are assumed to be more alike than
those of areas which are more distant. The goal of this thesis is to develop methodology
which can analyse these three types of data simultaneously.
In Chapter 2, the impact of missing data in health surveys was evaluated when estimating area-specific prevalences. The methods described by Mercer et al. (2014) and
Vandendijck et al. (2016) served as a foundation, and vary from the unweighted mean in
the frequentist framework to the unit-specific spatial random effects model in the Bayesian framework. To account for missing observations in the analysis, a new missingness weight
was defined. The inclusion of this missingness weight can correct for distributional shifts,
caused by missing data. An extensive simulation study showed that unbiased estimates
for the prevalence were yielded under the MCAR and MAR assumption. However, under
the MNAR assumption the missingness weight did not have enough support to account
for the missing data, as expected. Furthermore, we define a new weight smoothing model,
which can model the survey design and the missing data in a flexible, non-linear way. This
model produced the best results when a strong spatial effect is present in the data. The
2001 Belgian Health Interview Survey (HIS) was used as an application. The perceived
health of respondents was investigated using the proposed models for the 43 administrative
districts.
Chapter 3 further extended these weight smoothing models by adding covariate information. The analysis was carried out under the MAR assumption. The 2013 Florida
Behavioral Risk Factor Surveillance System (BRFSS) was used as an example. The proportion of inhabitants without health insurance coverage was the outcome of interest for
the 67 counties. The income of the inhabitants was incorporated in the weight smoothing
model as a covariate on the one hand and by means of a subgroup analysis on the other
hand. Finally, the direct standardized rate was determined, which corrects for risk factors
and allows us to directly compare the results from different counties.
Due to economical or practical reasons, it might occur that not every area is included in
the survey. As such, it is more difficult to produce unbiased estimates for the areas missing
in the sample. In Chapter 4, methods were introduced to cope with the lack of information
in these unsampled areas. Again, the methods from Mercer et al. (2014) were used as a
foundation in the analysis. The simulation study showed that the results remained stable if
about 75% of the intended areas were included in the survey. Furthermore, a strong spatial
effect in the data implied that the results remained stable longer as more areas were missing
from the survey. Next, we demonstrated a new methodology to improve the estimates for
non-sampled areas, using census data about certain population characteristics. While this
method had no effect on the results of the sampled areas, the results for the non-sampled
areas greatly improved, given that the support for these areas was strong enough. Lastly,
this new methodology was applied to the 2008 Mozambique Poverty and Social Impact
Analysis (PSIA) survey, where the proportion of school attendance was investigated for
the 125 districts.
Finally, in Chapter 5, the performance of several multivariate methods were compared
in order to model two outcome variables. Since these two outcome variables can be
correlated, it is important to include this correlation when constructing the model. Four
spatial multivariate models were considered in this chapter. The correlated random effects models produced the best results, highlighting the importance of including the correlation
structure between the two outcome variables in the analysis. This was illustrated using
the 2013 Florida BRFSS survey, where the prevalences of asthma and COPD were jointly
estimated.models produced the best results, highlighting the importance of including the correlation
structure between the two outcome variables in the analysis. This was illustrated using
the 2013 Florida BRFSS survey, where the prevalences of asthma and COPD were jointly
estimated. meten bij het schatten van gebiedsspecifieke prevalenties. Hierbij werd er verder gebouwd
op methodologie die reeds werd beschreven door Mercer et al. (2014) en Vandendijck et al.
(2016). Deze modellen variëren van het ongewogen gemiddelde uit het frequentistische
kader tot een persoonsgebonden spatiaal random effect model binnen het Bayesiaanse kader. Om de ontbrekende gegevens mee in rekening te nemen bij de analyse werd een nieuw
“missingness-”gewicht gedefinieerd. Door dit gewicht mee in de modellen op te nemen,
kunnen eventuele verschuivingen in verdeling door de ontbrekende data gecorrigeerd worden. Uit een uitgebreide simulatiestudie volgde dat onder de MCAR- en MAR-assumptie
correcte schattingen werden verkregen voor de prevalenties. In het MNAR-scenario had,
zoals verwacht, het nieuwe missingess-gewicht echter niet genoeg draagkracht om de ontbrekende data op te vangen. Bovendien definiëren we een nieuw weight smoothing model
waarbij het design van de studie en de ontbrekende gegevens op een flexibele, niet-lineaire
manier apart werden gemodelleerd. Dit model presteerde het beste wanneer er een sterk
spatiaal effect in de data aanwezig was. Als toepassing werd in dit hoofdstuk de Belgische
gezondheidsenquête (HIS) uit 2001 gebruikt. Hierbij werd de waargenomen gezondheid
van ondervraagden onderzocht aan de hand van de voorgestelde modellen voor de 43
administratieve arrondissementen.
Hoofdstuk 3 ging verder in op deze modellen en breidde deze nog verder uit door een
verklarende variabele in het weight smoothing model toe te voegen. De analyse gebeurde
onder de MAR-assumptie. Hierbij werd de Florida Behavioral Risk Factor Surveillance
System (BRFSS) enquête uit 2013 ter illustratie gebruikt. Het percentage inwoners zonder
ziekteverzekering werd als uitkomstvariabele onderzocht binnen de 67 provincies in Florida.
In de analyse met het weight smoothing model werd het inkomen van de ondervraagde
personen mee in rekening genomen, enerzijds als verklarende variabele, anderzijds met
behulp van een subgroepanalyse. Tenslotte berekenen we met behulp van het flexibele
weight smoothing model de direct standardized rate, waardoor we kunnen corrigeren voor
risicofactoren en de gebieden rechtstreeks met elkaar kunnen vergelijken.
Uit economische of praktische overwegingen kan het voorkomen dat niet ieder gebied
in de populatie mee in rekening genomen worden in de enquête. Hierdoor wordt het
moeilijker om een correcte schatting te geven voor die ontbrekende gebieden. In Hoofdstuk
4 werden methodes onderzocht om het gebrek aan informatie in deze gebieden op te
vangen. Opnieuw werden de modellen gebruikt uit Mercer et al. (2014) als basis gebruikt
in de analyse. Uit een simulatiestudie bleek dat de resultaten stabiel bleven indien ongeveer
75% van de beoogde gebieden in de steekproef werden opgenomen. Verder zorgde een
sterk spatiaal effect in de data ervoor dat de geschatte parameters langer stabiel blijven
naarmate meer gebieden uit de steekproef zouden ontbreken. Vervolgens demonstreerde
we een nieuwe methodologie om betere schattingen te krijgen voor de niet-bevraagde gebieden door gebruik te maken van algemene populatiedata over karakteristieken van de
populatie. Hoewel deze werkwijze geen effect had op de gebieden in de steekproef, was
er een sterke verbetering zichtbaar voor de niet-bevraagde gebieden, mits het draagvlak
sterk genoeg was. Tenslotte werd deze nieuwe methodologie toegepast op de Poverty and
Social Impact Analysis (PSIA) enquête uit 2008, uitgevoerd in Mozambique. De variabele
die hierbij werd onderzocht was de schoolaanwezigheid binnen 125 districten.
Tenslotte werden in Hoofdstuk 5 methodes vergeleken om twee uitkomsten tegelijkertijd te modelleren. Aangezien deze twee uitkomstvariabelen gecorreleerd kunnen zijn, is
het belangrijk om deze parameter mee in rekening te nemen bij het opstellen van het model. Vier spatiale multivariate modellen werden opgesteld en vergeleken. Het gecorreleerd
random effect model presteerde hierbij het beste, waardoor het belang werd getoond om
de correlatiestructuur tussen beide uitkomstvariabelen mee in rekening te nemen bij de
analyse. Dit werd geïllustreerd aan de hand van de Florida BRFSS studie uit 2013 waarbij
de prevalenties van astma en chronische obstructieve longziekte werden geschat
Hierarchical models for the analysis of spatial health surveys with missing information at individual and areal level
No full textStatistics are used to draw conclusions from a population of interest, based on a representative sample. Surveys are a frequent example of a sample, where people, sampled from
the population, answer questions or fill out a questionnaire. The distribution of certain
characteristics (e.g. age, sex, socioeconomic status) between sample and population may
differ. In order to account for this difference, a survey weight is assigned to every person
in the sample.
When conducting a survey, some respondents do not want to or are unable to answer
certain questions. This introduces incomplete data when analyzing the survey. It is
important for researchers to deal with the missing data in a correct way, in order to
avoid biased estimates. Therefore, an assumption has to be made for the reason why
someone did not respond to the question of interest. We distinguish three possibilities:
(1) the missingness is completely random (MCAR), (2) the missingness depends solely
on the observed measurements, independent of the unobserved measurements (MAR)
and (3) the missingness depends on both the observed and unobserved measurements
(MNAR)(Rubin, 1976).
In this thesis, we investigate models which can correctly analyse survey data with
missing observations. Furthermore, we account for the spatial context of the data. Estimates are provided at the level of “small areas” (e.g. districts, counties, provinces). The
measurements of areas which are close to each other are assumed to be more alike than
those of areas which are more distant. The goal of this thesis is to develop methodology
which can analyse these three types of data simultaneously.
In Chapter 2, the impact of missing data in health surveys was evaluated when estimating area-specific prevalences. The methods described by Mercer et al. (2014) and
Vandendijck et al. (2016) served as a foundation, and vary from the unweighted mean in
the frequentist framework to the unit-specific spatial random effects model in the Bayesian framework. To account for missing observations in the analysis, a new missingness weight
was defined. The inclusion of this missingness weight can correct for distributional shifts,
caused by missing data. An extensive simulation study showed that unbiased estimates
for the prevalence were yielded under the MCAR and MAR assumption. However, under
the MNAR assumption the missingness weight did not have enough support to account
for the missing data, as expected. Furthermore, we define a new weight smoothing model,
which can model the survey design and the missing data in a flexible, non-linear way. This
model produced the best results when a strong spatial effect is present in the data. The
2001 Belgian Health Interview Survey (HIS) was used as an application. The perceived
health of respondents was investigated using the proposed models for the 43 administrative
districts.
Chapter 3 further extended these weight smoothing models by adding covariate information. The analysis was carried out under the MAR assumption. The 2013 Florida
Behavioral Risk Factor Surveillance System (BRFSS) was used as an example. The proportion of inhabitants without health insurance coverage was the outcome of interest for
the 67 counties. The income of the inhabitants was incorporated in the weight smoothing
model as a covariate on the one hand and by means of a subgroup analysis on the other
hand. Finally, the direct standardized rate was determined, which corrects for risk factors
and allows us to directly compare the results from different counties.
Due to economical or practical reasons, it might occur that not every area is included in
the survey. As such, it is more difficult to produce unbiased estimates for the areas missing
in the sample. In Chapter 4, methods were introduced to cope with the lack of information
in these unsampled areas. Again, the methods from Mercer et al. (2014) were used as a
foundation in the analysis. The simulation study showed that the results remained stable if
about 75% of the intended areas were included in the survey. Furthermore, a strong spatial
effect in the data implied that the results remained stable longer as more areas were missing
from the survey. Next, we demonstrated a new methodology to improve the estimates for
non-sampled areas, using census data about certain population characteristics. While this
method had no effect on the results of the sampled areas, the results for the non-sampled
areas greatly improved, given that the support for these areas was strong enough. Lastly,
this new methodology was applied to the 2008 Mozambique Poverty and Social Impact
Analysis (PSIA) survey, where the proportion of school attendance was investigated for
the 125 districts.
Finally, in Chapter 5, the performance of several multivariate methods were compared
in order to model two outcome variables. Since these two outcome variables can be
correlated, it is important to include this correlation when constructing the model. Four
spatial multivariate models were considered in this chapter. The correlated random effects models produced the best results, highlighting the importance of including the correlation
structure between the two outcome variables in the analysis. This was illustrated using
the 2013 Florida BRFSS survey, where the prevalences of asthma and COPD were jointly
estimated.models produced the best results, highlighting the importance of including the correlation
structure between the two outcome variables in the analysis. This was illustrated using
the 2013 Florida BRFSS survey, where the prevalences of asthma and COPD were jointly
estimated. meten bij het schatten van gebiedsspecifieke prevalenties. Hierbij werd er verder gebouwd
op methodologie die reeds werd beschreven door Mercer et al. (2014) en Vandendijck et al.
(2016). Deze modellen variëren van het ongewogen gemiddelde uit het frequentistische
kader tot een persoonsgebonden spatiaal random effect model binnen het Bayesiaanse kader. Om de ontbrekende gegevens mee in rekening te nemen bij de analyse werd een nieuw
“missingness-”gewicht gedefinieerd. Door dit gewicht mee in de modellen op te nemen,
kunnen eventuele verschuivingen in verdeling door de ontbrekende data gecorrigeerd worden. Uit een uitgebreide simulatiestudie volgde dat onder de MCAR- en MAR-assumptie
correcte schattingen werden verkregen voor de prevalenties. In het MNAR-scenario had,
zoals verwacht, het nieuwe missingess-gewicht echter niet genoeg draagkracht om de ontbrekende data op te vangen. Bovendien definiëren we een nieuw weight smoothing model
waarbij het design van de studie en de ontbrekende gegevens op een flexibele, niet-lineaire
manier apart werden gemodelleerd. Dit model presteerde het beste wanneer er een sterk
spatiaal effect in de data aanwezig was. Als toepassing werd in dit hoofdstuk de Belgische
gezondheidsenquête (HIS) uit 2001 gebruikt. Hierbij werd de waargenomen gezondheid
van ondervraagden onderzocht aan de hand van de voorgestelde modellen voor de 43
administratieve arrondissementen.
Hoofdstuk 3 ging verder in op deze modellen en breidde deze nog verder uit door een
verklarende variabele in het weight smoothing model toe te voegen. De analyse gebeurde
onder de MAR-assumptie. Hierbij werd de Florida Behavioral Risk Factor Surveillance
System (BRFSS) enquête uit 2013 ter illustratie gebruikt. Het percentage inwoners zonder
ziekteverzekering werd als uitkomstvariabele onderzocht binnen de 67 provincies in Florida.
In de analyse met het weight smoothing model werd het inkomen van de ondervraagde
personen mee in rekening genomen, enerzijds als verklarende variabele, anderzijds met
behulp van een subgroepanalyse. Tenslotte berekenen we met behulp van het flexibele
weight smoothing model de direct standardized rate, waardoor we kunnen corrigeren voor
risicofactoren en de gebieden rechtstreeks met elkaar kunnen vergelijken.
Uit economische of praktische overwegingen kan het voorkomen dat niet ieder gebied
in de populatie mee in rekening genomen worden in de enquête. Hierdoor wordt het
moeilijker om een correcte schatting te geven voor die ontbrekende gebieden. In Hoofdstuk
4 werden methodes onderzocht om het gebrek aan informatie in deze gebieden op te
vangen. Opnieuw werden de modellen gebruikt uit Mercer et al. (2014) als basis gebruikt
in de analyse. Uit een simulatiestudie bleek dat de resultaten stabiel bleven indien ongeveer
75% van de beoogde gebieden in de steekproef werden opgenomen. Verder zorgde een
sterk spatiaal effect in de data ervoor dat de geschatte parameters langer stabiel blijven
naarmate meer gebieden uit de steekproef zouden ontbreken. Vervolgens demonstreerde
we een nieuwe methodologie om betere schattingen te krijgen voor de niet-bevraagde gebieden door gebruik te maken van algemene populatiedata over karakteristieken van de
populatie. Hoewel deze werkwijze geen effect had op de gebieden in de steekproef, was
er een sterke verbetering zichtbaar voor de niet-bevraagde gebieden, mits het draagvlak
sterk genoeg was. Tenslotte werd deze nieuwe methodologie toegepast op de Poverty and
Social Impact Analysis (PSIA) enquête uit 2008, uitgevoerd in Mozambique. De variabele
die hierbij werd onderzocht was de schoolaanwezigheid binnen 125 districten.
Tenslotte werden in Hoofdstuk 5 methodes vergeleken om twee uitkomsten tegelijkertijd te modelleren. Aangezien deze twee uitkomstvariabelen gecorreleerd kunnen zijn, is
het belangrijk om deze parameter mee in rekening te nemen bij het opstellen van het model. Vier spatiale multivariate modellen werden opgesteld en vergeleken. Het gecorreleerd
random effect model presteerde hierbij het beste, waardoor het belang werd getoond om
de correlatiestructuur tussen beide uitkomstvariabelen mee in rekening te nemen bij de
analyse. Dit werd geïllustreerd aan de hand van de Florida BRFSS studie uit 2013 waarbij
de prevalenties van astma en chronische obstructieve longziekte werden geschat
Spatial Modelling to Inform Public Health Based on Health Surveys: Impact of Unsampled Areas at Lower Geographical Scale
No full textSmall area estimation is an important tool to provide area-specific estimates of population characteristics for governmental organizations in the context of education, public health and care. However, many demographic and health surveys are unrepresentative at a small geographical level, as often areas at a lower level are not included in the sample due to financial or logistical reasons. In this paper, we investigated (1) the effect of these unsampled areas on a variety of design-based and hierarchical model-based estimates and (2) the benefits of using auxiliary information in the estimation process by means of an extensive simulation study. The results showed the benefits of hierarchical spatial smoothing models towards obtaining more reliable estimates for areas at the lowest geographical level in case a spatial trend is present in the data. Furthermore, the importance of auxiliary information was highlighted, especially for geographical areas that were not included in the sample. Methods are illustrated on the 2008 Mozambique Poverty and Social Impact Analysis survey, with interest in the district-specific prevalence of school attendance
Impact of Income on Small Area Low Birth Weight Incidence Using Multiscale Models
No full textLow birth weight (LBW) is an important public health issue in the US as well as worldwide. The two main causes of LBW are premature birth and fetal growth restriction. Socio-economic status, as measured by family income has been correlated with LBW incidence at both the individual and population levels. In this paper, we investigate the impact of household income on LBW incidence at different geographical levels. To show this, we choose to examine
LBW incidences collected from the state of Georgia, in the US, at both the county and public health (PH) district. The data at the PH district are an aggregation of the data at the county
level nested within the PH district. A spatial scaling effect is induced during data aggregation from the county to the PH level. To address the scaling effect issue, we applied a shared multiscale model that jointly models the data at two levels via a shared correlated random effect. To assess the benefit of using the shared multiscale model, we compare it with an independent multiscale model which ignores the scale effect. Applying the shared multiscale model for the Georgia LBW incidence, we have found that income has a negative impact at both the county and PH levels. On the other hand, the independent multiscale model shows that income has a negative impact only at the county level. Hence, if the scale effect is not properly accommodated in the model, a different interpretation of the findings could result.The authors would like to acknowledge support from the National Institutes of Health via grant R01CA172805. The third author also acknowledges support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy)
Spatial smoothing models to deal with the complex sampling design and nonresponse in the Florida BRFSS survey
No full textPublic health and governmental organizations have acknowledged the importance of obtaining information of various characteristics for small areas, such as counties. Spatial smoothing models have been developed to gain reliable information on the geographical distribution of the outcome of interest. When the geographical analysis is based on survey data, two issues pose challenges: (1) the complex design of the survey and (2) the presence of missing data due to non-response. We investigate the influence of missing data and the adjustment thereof in the context of the 2013 Florida Behavioral Risk Factor Surveillance System (BRFSS) health survey. We focus on the application and comparison of the Hajek ratio estimator and two model-based approaches for estimation of the spatial trend of the prevalence of having no health insurance coverage. The model-based methods are compared using the Deviance Information Criterion which show the benefits of modeling the weights as flexibly as possible. Methods are extended towards subgroup analyses and the estimation of area-specific standardized rates, where household incomes was identified as an important factor to include in the analysis. 1Support from the National Institutes of Health is ac- knowledged [award number 1. National Institutes of Health R01CA172805]. Support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) is grate- fully acknowledged. For the analyses we used the in- frastructure of the VSC - Flemish Supercomputer Center, funded by the Hercules Foundation and the Flemish Gov- ernment - department EWI
Spatially-dependent Bayesian Model Selection for Disease Mapping
Full text linkIn disease mapping where predictor effects are to be modeled, it is often the case that sets of predictors are fixed, and the aim is to choose between fixed model sets. Model selection methods, both Bayesian model selection and Bayesian model averaging, are approaches within the Bayesian paradigm for achieving this aim. In the spatial context, model selection could have a spatial component in the sense that some models may be more appropriate for certain areas of a study region than others. In this work, we examine the use of spatially referenced Bayesian model averaging and Bayesian model selection via a large-scale simulation study accompanied by a small-scale case study. Our results suggest that BMS performs well when a strong regression signature is found
Comparing INLA and OpenBUGS for hierarchical Poisson modeling in disease mapping.
No full textThe recently developed R package INLA (Integrated Nested Laplace Approximation) is becoming a more widely used package for Bayesian inference. The INLA software has been promoted as a fast alternative to MCMC for disease mapping applications. Here, we compare the INLA package to the MCMC approach by way of the BRugs package in R, which calls OpenBUGS. We focus on the Poisson data model commonly used for disease mapping. Ultimately, INLA is a computationally efficient way of implementing Bayesian methods and returns nearly identical estimates for fixed parameters in comparison to OpenBUGS, but falls short in recovering the true estimates for the random effects, their precisions, and model goodness of fit measures under the default settings. We assumed default settings for ground truth parameters, and through altering these default settings in our simulation study, we were able to recover estimates comparable to those produced in OpenBUGS under the same assumptions
Multiscale Measurement Error Models for Aggregated Small Area Health Data
No full textSpatial data are often aggregated from a finer (smaller) to a coarser (larger) geographical level. The process of data aggregation induces a scaling effect which smoothes the variation in the data. To address the scaling problem, multiscale models that link the convolution models at different scale levels via the shared random effect have been proposed. One of the main goals in aggregated health data is to investigate the relationship between predictors and an outcome at different geographical levels. In this paper, we extend multiscale models to examine whether a predictor effect at a finer level hold true at a coarser level. To adjust for predictor uncertainty due to aggregation, we applied measurement error models in the framework of multiscale approach. To assess the benefit of using multiscale measurement error models, we compare the performance of multiscale models with and without measurement error in both real and simulated data. We found that ignoring the measurement error in multiscale models underestimates the regression coefficient, while it overestimates the variance of the spatially structured random effect. On the other hand, accounting for the measurement error in multiscale models provides a better model fit and unbiased parameter estimates
Space-time variation of respiratory cancers in South Carolina: a flexible multivariate mixture modeling approach to risk estimation
No full textPurpose: Many types of cancer have an underlying spatiotemporal distribution. Spatiotemporal mixture modeling can offer a flexible approach to risk estimation via the inclusion of latent variables. Methods: In this article, we examine the application and benefits of using four different spatiotemporal mixture modeling methods in the modeling of cancer of the lung and bronchus as well as "other" respiratory cancer incidences in the state of South Carolina. Results: Of the methods tested, no single method outperforms the other methods; which method is best depends on the cancer under consideration. The lung and bronchus cancer incidence outcome is best described by the univariate modeling formulation, whereas the "other" respiratory cancer incidence outcome is best described by the multivariate modeling formulation. Conclusions: Spatiotemporal multivariate mixture methods can aid in the modeling of cancers with small and sparse incidences when including information from a related, more common type of cancer. (C) 2016 Elsevier Inc. All rights reserved.This research was supported in part by funding under grant NIH R01CA172805
Bayesian model selection methods in modeling small area colon cancer incidence
No full textPurpose: Many types of cancer have an underlying spatial incidence distribution. Spatial model selection methods can be useful when determining the linear predictor that best describes incidence outcomes. Methods: In this article, we examine the applications and benefits of using two different types of spatial model selection techniques, Bayesian model selection and Bayesian model averaging, in relation to colon cancer incidence in the state of Georgia, United States. Results: Both methods produce useful results that lead to the determination that median household income and percent African American population are important predictors of colon cancer incidence in the Northern counties of the state, whereas percent persons below poverty level and percent African American population are important in the Southern counties. Conclusions: Of the two presented methods, Bayesian model selection appears to provide more succinct results, but applying the two in combination offers even more useful information into the spatial preferences of the alternative linear predictors. (C) 2016 Elsevier Inc. All rights reserved.This research was supported in part by funding under grant NIH R01CA172805
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