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Evaluation of the performance of smoothing functions in generalized additive models for spatial variation in disease.

ABSTRACT: Generalized additive models (GAMs) with bivariate smoothing functions have been applied to estimate spatial variation in risk for many types of cancers. Only a handful of studies have evaluated the performance of smoothing functions applied in GAMs with regard to different geographical areas of elevated risk and different risk levels. This study evaluates the ability of different smoothing functions to detect overall spatial variation of risk and elevated risk in diverse geographical areas at various risk levels using a simulation study. We created five scenarios with different true risk area shapes (circle, triangle, linear) in a square study region. We applied four different smoothing functions in the GAMs, including two types of thin plate regression splines (TPRS) and two versions of locally weighted scatterplot smoothing (loess). We tested the null hypothesis of constant risk and detected areas of elevated risk using analysis of deviance with permutation methods and assessed the performance of the smoothing methods based on the spatial detection rate, sensitivity, accuracy, precision, power, and false-positive rate. The results showed that all methods had a higher sensitivity and a consistently moderate-to-high accuracy rate when the true disease risk was higher. The models generally performed better in detecting elevated risk areas than detecting overall spatial variation. One of the loess methods had the highest precision in detecting overall spatial variation across scenarios and outperformed the other methods in detecting a linear elevated risk area. The TPRS methods outperformed loess in detecting elevated risk in two circular areas.

SUBMITTER: Siangphoe U

PROVIDER: S-EPMC4415687 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Evaluation of the performance of smoothing functions in generalized additive models for spatial variation in disease.

Siangphoe Umaporn U Wheeler David C DC

Cancer informatics 20150429 Suppl 2

Generalized additive models (GAMs) with bivariate smoothing functions have been applied to estimate spatial variation in risk for many types of cancers. Only a handful of studies have evaluated the performance of smoothing functions applied in GAMs with regard to different geographical areas of elevated risk and different risk levels. This study evaluates the ability of different smoothing functions to detect overall spatial variation of risk and elevated risk in diverse geographical areas at va ...[more]

PMID: 25983545

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Project description:BACKGROUND:Many methods of spatial smoothing have been developed, for both point data as well as areal data. In Bayesian spatial models, this is achieved by purposefully designed prior(s) or smoothing functions which smooth estimates towards a local or global mean. Smoothing is important for several reasons, not least of all because it increases predictive robustness and reduces uncertainty of the estimates. Despite the benefits of smoothing, this attribute is all but ignored when it comes to model selection. Traditional goodness-of-fit measures focus on model fit and model parsimony, but neglect "goodness-of-smoothing", and are therefore not necessarily good indicators of model performance. Comparing spatial models while taking into account the degree of spatial smoothing is not straightforward because smoothing and model fit can be viewed as opposing goals. Over- and under-smoothing of spatial data are genuine concerns, but have received very little attention in the literature. METHODS:This paper demonstrates the problem with spatial model selection based solely on goodness-of-fit by proposing several methods for quantifying the degree of smoothing. Several commonly used spatial models are fit to real data, and subsequently compared using the goodness-of-fit and goodness-of-smoothing statistics. RESULTS:The proposed goodness-of-smoothing statistics show substantial agreement in the task of model selection, and tend to avoid models that over- or under-smooth. Conversely, the traditional goodness-of-fit criteria often don't agree, and can lead to poor model choice. In particular, the well-known deviance information criterion tended to select under-smoothed models. CONCLUSIONS:Some of the goodness-of-smoothing methods may be improved with modifications and better guidelines for their interpretation. However, these proposed goodness-of-smoothing methods offer researchers a solution to spatial model selection which is easy to implement. Moreover, they highlight the danger in relying on goodness-of-fit measures when comparing spatial models.

Project description:BackgroundA common, important problem in spatial epidemiology is measuring and identifying variation in disease risk across a study region. In application of statistical methods, the problem has two parts. First, spatial variation in risk must be detected across the study region and, second, areas of increased or decreased risk must be correctly identified. The location of such areas may give clues to environmental sources of exposure and disease etiology. One statistical method applicable in spatial epidemiologic settings is a generalized additive model (GAM) which can be applied with a bivariate LOESS smoother to account for geographic location as a possible predictor of disease status. A natural hypothesis when applying this method is whether residential location of subjects is associated with the outcome, i.e. is the smoothing term necessary? Permutation tests are a reasonable hypothesis testing method and provide adequate power under a simple alternative hypothesis. These tests have yet to be compared to other spatial statistics.ResultsThis research uses simulated point data generated under three alternative hypotheses to evaluate the properties of the permutation methods and compare them to the popular spatial scan statistic in a case-control setting. Case 1 was a single circular cluster centered in a circular study region. The spatial scan statistic had the highest power though the GAM method estimates did not fall far behind. Case 2 was a single point source located at the center of a circular cluster and Case 3 was a line source at the center of the horizontal axis of a square study region. Each had linearly decreasing logodds with distance from the point. The GAM methods outperformed the scan statistic in Cases 2 and 3. Comparing sensitivity, measured as the proportion of the exposure source correctly identified as high or low risk, the GAM methods outperformed the scan statistic in all three Cases.ConclusionsThe GAM permutation testing methods provide a regression-based alternative to the spatial scan statistic. Across all hypotheses examined in this research, the GAM methods had competing or greater power estimates and sensitivities exceeding that of the spatial scan statistic.

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Evaluation of the performance of smoothing functions in generalized additive models for spatial variation in disease.

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Evaluation of the performance of smoothing functions in generalized additive models for spatial variation in disease.

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