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.

Spatial analyses of ALS incidence in Denmark over three decades

“…Regions with greater population distributions would smooth data from a smaller geographic area than regions with sparse populations. Previous simulation studies evaluated the type I error rate and power of several GAM hypothesis testing methods and showed that GAMs performed well for analyzing spatial patterns of various shape and sizes including non-circular clusters (43–48).…”

Data Imputation and Body Weight Variability Calculation Using Linear and Nonlinear Methods in Data Collected From Digital Smart Scales: Simulation and Validation Study

“…LOESS regressions were conducted with the stats package in R [ 58 ]. It employs quadratic polynomial models on a moving collection of data points (termed a neighborhood ) in a TS [ 59 ]. The size of the neighborhood is user defined and referred to as the span of the LOESS model, with greater spans creating more smooth trends because of using a wider collection of surrounding data points, whereas shorter spans resulting in closer fitting to the data.…”

The timing of geographic power

“…[30][31][32] We used GAMs because of their flexibility, computational efficiency, power, and sensitivity to detect areas of elevated disease risks. 30,[33][34][35] In each risk situation we used the residential locations at the time of study enrollment, s i , to model the log-odds of disease as log…”

“…Forms of smoothers that have been used previously in spatial analyses include the locally weighted scatterplot smoothing (LOESS), 36 and the thin plate regression spline (TPRS). 35,37,38 For this study f (s i ) in Equation (2) is the estimate of the spatial log-odds at location s i using TPRS. A thin plate spline (TPS) is a type of regression that estimates a smooth function of multiple predictor variables and the response variable.…”

“…The TPS approach includes a "wiggliness" penalty term of predictors in the least square objective function which allows for knot-free locations. 32,35 A TPRS, an extension of the TPS, truncates the space of the "wiggly" components of the TPS, which further reduces the computational cost. The objective function for TPRS fitting is…”