Spatially Varying Coefficient Inequalities: Evaluating How the Impact of Patient Characteristics on Breast Cancer Survival Varies by Location.
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ABSTRACT:
SUBMITTER: Hsieh JC
PROVIDER: S-EPMC4857928 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. To specifically account for these two features, SVCM includes a measurement model with multiple varying coefficient functions, a jumping surface model for each varying coefficient function, and a functional principal component model. We develop a three-stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations. The estimation procedure includes a fast multiscale adaptive estimation and testing procedure to independently estimate each varying coefficient function, while preserving its edges among different piecewise-smooth regions. We systematically investigate the asymptotic properties (e.g., consistency and asymptotic normality) of the multiscale adaptive parameter estimates. We also establish the uniform convergence rate of the estimated spatial covariance function and its associated eigenvalues and eigenfunctions. Our Monte Carlo simulation and real data analysis have confirmed the excellent performance of SVCM.
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Project description:Varying coefficient models have been widely used in longitudinal data analysis, nonlinear time series, survival analysis, and so on. They are natural non-parametric extensions of the classical linear models in many contexts, keeping good interpretability and allowing us to explore the dynamic nature of the model. Recently, penalized estimators have been used for fitting varying-coefficient models for high-dimensional data. In this paper, we propose a new computationally attractive algorithm called IVIS for fitting varying-coefficient models in ultra-high dimensions. The algorithm first fits a gSCAD penalized varying-coefficient model using a subset of covariates selected by a new varying-coefficient independence screening (VIS) technique. The sure screening property is established for VIS. The proposed algorithm then iterates between a greedy conditional VIS step and a gSCAD penalized fitting step. Simulation and a real data analysis demonstrate that IVIS has very competitive performance for moderate sample size and high dimension.
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Project description:The wetlands in the Prairie Pothole Region and in the Great Plains are notorious for their sensitivity to weather variability. These wetlands have been the focus of considerable attention because of their ecological importance and because of the expected impact of climate change. Few models in the literature, however, take into account spatial variation in the importance of wetland drivers. This is surprising given the importance spatial heterogeneity in geomorphology and climatic conditions have in the region. In this paper, I use spatially-varying coefficients to assess the variation in ecological drivers in a number of ponds observed over a 50-year period (1961-2012). I included the number of ponds observed the year before on a log scale, the log of total precipitation, and mean maximum temperature during the four previous seasons as explanatory variables. I also included a temporal component to capture change in the number of ponds due to anthropogenic disturbance. Overall, fall and spring precipitation were most important in pond abundance in the west, whereas winter and summer precipitation were the most important drivers in the east. The ponds in the east of the survey area were also more dependent on pond abundance during the previous year than those in the west. Spring temperature during the previous season influenced pond abundance; while the temperature during the other seasons had a limited effect. The ponds in the southwestern part of the survey area have been increasing independently of climatic conditions, whereas the ponds in the northeast have been steadily declining. My results underline the importance of accounting the spatial heterogeneity in environmental drivers, when working at large spatial scales. In light of my results, I also argue that assessing the impacts of climate change on wetland abundance in the spring, without more accurate climatic forecasting, will be difficult.
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Project description:BackgroundAn increasing number of studies have identified spatial differences in colorectal cancer survival. However, little is known about the spatially varying effects of predictors in survival prediction modeling studies of colorectal cancer that have focused on estimating the absolute survival risk for patients from a wide range of populations. This study aimed to demonstrate the spatially varying effects of predictors of survival for nonmetastatic colorectal cancer patients.MethodsPatients diagnosed with nonmetastatic colorectal cancer from 2004 to 2013 who were followed up through the end of 2013 were extracted from the Surveillance Epidemiology End Results registry (Patients: 128061). The log-rank test and the restricted mean survival time were used to evaluate survival outcome differences among spatial clusters corresponding to a widely used clinical predictor: stage determined by AJCC 7th edition staging system. The heterogeneity test, which is used in meta-analyses, revealed the spatially varying effects of single predictors. Then, considering the above predictors in a standard survival prediction model based on spatially clustered data, the spatially varying coefficients of these models revealed that some covariate effects may not be constant across the geographic regions of the study. Then, two types of survival prediction models (a statistical model and a machine learning model) were built; these models considered the predictors and enabled survival prediction for patients from a wide range of geographic regions.ResultsBased on univariate and multivariate analysis, some prognostic factors, such as "TNM stage", "tumor size" and "age at diagnosis," have significant spatially varying effects among different regions. When considering these spatially varying effects, machine learning models have fewer assumption constraints (such as proportional hazard assumptions) and better predictive performance compared with statistical models. Upon comparing the concordance indexes of these two models, the machine learning model was found to be more accurate (0.898[0.895,0.902]) than the statistical model (0.732 [0.726, 0.738]).ConclusionsBased on this study, it's recommended that the spatially varying effect of predictors should be considered when building survival prediction models involving large-scale and multicenter research data. Machine learning models that are not limited by the requirement of a statistical hypothesis are promising alternative models.
| S-EPMC6225720 | biostudies-literature
Project description:Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We develop several statistical inference procedures for MVCM and systematically study their theoretical properties. We first establish the weak convergence of the local linear estimate of coefficient functions, as well as its asymptotic bias and variance, and then we derive asymptotic bias and mean integrated squared error of smoothed individual functions and their uniform convergence rate. We establish the uniform convergence rate of the estimated covariance function of the individual functions and its associated eigenvalue and eigenfunctions. We propose a global test for linear hypotheses of varying coefficient functions, and derive its asymptotic distribution under the null hypothesis. We also propose a simultaneous confidence band for each individual effect curve. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply MVCM to investigate the development of white matter diffusivities along the genu tract of the corpus callosum in a clinical study of neurodevelopment.
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Project description:By allowing the regression coefficients to change with certain covariates, the class of varying coefficient models offers a flexible approach to modeling nonlinearity and interactions between covariates. This paper proposes a novel estimation procedure for the varying coefficient models based on local ranks. The new procedure provides a highly efficient and robust alternative to the local linear least squares method, and can be conveniently implemented using existing R software package. Theoretical analysis and numerical simulations both reveal that the gain of the local rank estimator over the local linear least squares estimator, measured by the asymptotic mean squared error or the asymptotic mean integrated squared error, can be substantial. In the normal error case, the asymptotic relative efficiency for estimating both the coefficient functions and the derivative of the coefficient functions is above 96%; even in the worst case scenarios, the asymptotic relative efficiency has a lower bound 88.96% for estimating the coefficient functions, and a lower bound 89.91% for estimating their derivatives. The new estimator may achieve the nonparametric convergence rate even when the local linear least squares method fails due to infinite random error variance. We establish the large sample theory of the proposed procedure by utilizing results from generalized U-statistics, whose kernel function may depend on the sample size. We also extend a resampling approach, which perturbs the objective function repeatedly, to the generalized U-statistics setting; and demonstrate that it can accurately estimate the asymptotic covariance matrix.
| S-EPMC2908045 | biostudies-literature
Project description:Large spatial datasets with many spatial covariates have become ubiquitous in many fields in recent years. A question of interest is to identify which covariates are likely to influence a spatial response, and whether and how the effects of these covariates vary across space, including potential abrupt changes from region to region. To solve this question, a new efficient regularized spatially clustered coefficient (RSCC) regression approach is proposed, which could achieve variable selection and identify latent spatially heterogeneous covariate effects with clustered patterns simultaneously. By carefully designing the regularization term of RSCC as a chain graph guided fusion penalty plus a group lasso penalty, the RSCC model is computationally efficient for large spatial datasets while still achieving the theoretical guarantees for estimation. RSCC also adopts the idea of adaptive learning to allow for adaptive weights and adaptive graphs in its regularization terms and further improves the estimation performance. RSCC is applied to study the acceptance of COVID-19 vaccines using county-level data in the United States and discover the determinants of vaccination acceptance with varying effects across counties, revealing important within-state and across-state spatially clustered patterns of covariates effects.
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Project description:Analyzing the large-scale survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) Program may help guide the management of cancer. Detecting and characterizing the time-varying effects of factors collected at the time of diagnosis could reveal important and useful patterns. However, fitting a time-varying effect model by maximizing the partial likelihood with such large-scale survival data is not feasible with most existing software. Moreover, estimating time-varying coefficients using spline based approaches requires a moderate number of knots, which may lead to unstable estimation and over-fitting issues. To resolve these issues, adding a penalty term greatly aids estimation. The selection of penalty smoothing parameters is difficult in this time-varying setting, as traditional ways like using Akaike information criterion do not work, while cross-validation methods have a heavy computational burden, leading to unstable selections. We propose modified information criteria to determine the smoothing parameter and a parallelized Newton-based algorithm for estimation. We conduct simulations to evaluate the performance of the proposed method. We find that penalization with the smoothing parameter chosen by a modified information criteria is effective at reducing the mean squared error of the estimated time-varying coefficients. Compared to a number of alternatives, we find that the estimates of the variance derived from Bayesian considerations have the best coverage rates of confidence intervals. We apply the method to SEER head-and-neck, colon, prostate, and pancreatic cancer data and detect the time-varying nature of various risk factors.
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Project description:Recently, massive functional data have been widely collected over space across a set of grid points in various imaging studies. It is interesting to correlate functional data with various clinical variables, such as age and gender, in order to address scientific questions of interest. The aim of this article is to develop a single-index varying coefficient (SIVC) model for establishing a varying association between functional responses (e.g., image) and a set of covariates. It enjoys several unique features of both varying-coefficient and single-index models. An estimation procedure is developed to estimate varying coefficient functions, the index function, and the covariance function of individual functions. The optimal integration of information across different grid points is systematically delineated and the asymptotic properties (e.g., consistency and convergence rate) of all estimators are examined. Simulation studies are conducted to assess the finite-sample performance of the proposed estimation procedure. Furthermore, our real data analysis of a white matter tract dataset obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study confirms the advantage and accuracy of SIVC model over the popular varying coefficient model.
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Project description:In this work, we present a computationally efficient image-derived volume mesh generation approach for vasculatures that implements spatially varying patient-specific wall thickness with a novel inward extrusion of the wall surface mesh. Multi-domain vascular meshes with arbitrary numbers, locations, and patterns of both iliac bifurcations and thrombi can be obtained without the need to specify features or landmark points as input. In addition, the mesh output is coordinate-frame independent and independent of the image grid resolution with high dimensional accuracy and mesh quality, devoid of errors typically found in off-the-shelf image-based model generation workflows. The absence of deformable template models or Cartesian grid-based methods enables the present approach to be sufficiently robust to handle aneurysmatic geometries with highly irregular shapes, arterial branches nearly parallel to the image plane, and variable wall thickness. The assessment of the methodology was based on i) estimation of the surface reconstruction accuracy, ii) validation of the output mesh using an aneurysm phantom, and iii) benchmarking the volume mesh quality against other frameworks. For the phantom image dataset (pixel size 0.105 mm; slice spacing 0.7 mm; and mean wall thickness 1.401±0.120 mm), the average wall thickness in the mesh was 1.459±0.123 mm. The absolute error in average wall thickness was 0.060±0.036 mm, or about 8.6% of the largest image grid spacing (0.7 mm) and 4.36% of the actual mean wall thickness. Mesh quality metrics and the ability to reproduce regional variations of wall thickness were found superior to similar alternative frameworks.
| S-EPMC4492838 | biostudies-literature