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Dupont, Emiko; Wood, Simon N.; Augustin, Nicole H.
doi: 10.1111/biom.13656pmid: 35258102
In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modeling forestry data to assess the effect of temperature on tree health. Reliable inference is difficult as results depend on whether or not spatial effects are included in the model. We propose a novel approach, spatial+, for dealing with spatial confounding when the covariate of interest is spatially dependent but not fully determined by spatial location. Using a thin plate spline model formulation we see that, in this case, the bias in covariate effect estimates is a direct result of spatial smoothing. Spatial+ reduces the sensitivity of the estimates to smoothing by replacing the covariates by their residuals after spatial dependence has been regressed away. Through asymptotic analysis we show that spatial+ avoids the bias problems of the spatial model. This is also demonstrated in a simulation study. Spatial+ is straightforward to implement using existing software and, as the response variable is the same as that of the spatial model, standard model selection criteria can be used for comparisons. A major advantage of the method is also that it extends to models with non‐Gaussian response distributions. Finally, while our results are derived in a thin plate spline setting, the spatial+ methodology transfers easily to other spatial model formulations.
doi: 10.1111/biom.13655pmid: 35712896
I congratulate Dupont, Wood, and Augustin (DWA hereon) for providing an easy‐to‐implement method for estimation in the presence of spatial confounding, and for addressing some of the complicated aspects on the topic. I discuss conceptual and operational issues that are fundamental to inference in spatial settings: (i) the target quantity and its interpretability, (ii) the nonspatial aspect of covariates and their relative spatial scales, and (iii) the impact of spatial smoothing. While DWA provide some insights on these issues, I believe that the audience might benefit from a deeper discussion.
Dupont, Emiko; Wood, Simon N.; Augustin, Nicole H.
doi: 10.1111/biom.13653pmid: 35363888
In this rejoinder, we set out some of the main points that we took from the discussions of our paper “Spatial+: A novel approach to spatial confounding.” The comments provided by the discussants include excellent questions and suggestions for extensions and improvements to spatial+. The discussions also highlight the growing interest in understanding spatial confounding, underpinned by the many recent contributions to the literature on this topic.
German, Christopher A.; Sinsheimer, Janet S.; Zhou, Jin; Zhou, Hua
doi: 10.1111/biom.13506pmid: 34142722
The availability of vast amounts of longitudinal data from electronic health records (EHRs) and personal wearable devices opens the door to numerous new research questions. In many studies, individual variability of a longitudinal outcome is as important as the mean. Blood pressure fluctuations, glycemic variations, and mood swings are prime examples where it is critical to identify factors that affect the within‐individual variability. We propose a scalable method, within‐subject variance estimator by robust regression (WiSER), for the estimation and inference of the effects of both time‐varying and time‐invariant predictors on within‐subject variance. It is robust against the misspecification of the conditional distribution of responses or the distribution of random effects. It shows similar performance as the correctly specified likelihood methods but is 103 ∼ 105 times faster. The estimation algorithm scales linearly in the total number of observations, making it applicable to massive longitudinal data sets. The effectiveness of WiSER is evaluated in extensive simulation studies. Its broad applicability is illustrated using the accelerometry data from the Women's Health Study and a clinical trial for longitudinal diabetes care.
Wang, Dewei; Mou, Xichen; Liu, Yan
doi: 10.1111/biom.13516pmid: 34190334
Human biomonitoring involves measuring the accumulation of contaminants in biological specimens (such as blood or urine) to assess individuals' exposure to environmental contamination. Due to the expensive cost of a single assay, the method of pooling has become increasingly common in environmental studies. The implementation of pooling starts by physically mixing specimens into pools, and then measures pooled specimens for the concentration of contaminants. An important task is to reconstruct individual‐level statistical characteristics based on pooled measurements. In this article, we propose to use the varying‐coefficient regression model for individual‐level biomonitoring and provide methods to estimate the varying coefficients based on different types of pooled data. Asymptotic properties of the estimators are presented. We illustrate our methodology via simulation and with application to pooled biomonitoring of a brominated flame retardant provided by the National Health and Nutrition Examination Survey (NHANES).
Chen, Heng; Heitjan, Daniel F.
doi: 10.1111/biom.13532pmid: 34297356
The ISNI (index of sensitivity to local nonignorability) method quantifies local sensitivity of parametric inferences to nonignorable missingness in an outcome variable. Here we extend ISNI to the situations where both outcomes and predictors can be missing and where the missingness mechanism can be either parametric or semi‐parametric. We define the quantity MinNI (minimum nonignorability) to be an approximation to the norm of the smallest value of the transformed nonignorability that gives a nonnegligible displacement of the estimate of the parameter of interest. We illustrate our method in a complete data set from which we synthetically delete observations according to various patterns. We then apply the method to real‐data examples involving the normal linear model and conditional logistic regression.
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