Competing risks model for clustered data based on the subdistribution hazards with spatial random effects

In some applications, the clustered survival data are arranged spatially such as clinical centers or geographical regions. Incorporating spatial variation in these data not only can improve the accuracy and efficiency of the parameter estimation, but it also investigates the spatial patterns of survivorship for identifying high-risk areas. Competing risks in survival data concern a situation where there is more than one cause of failure, but only the occurrence of the first one is observable. In this paper, we considered Bayesian subdistribution hazard regression models with spatial random effects for the clustered HIV/AIDS data. An intrinsic conditional autoregressive (ICAR) distribution was employed to model the areal spatial random effects. Comparison among competing models was performed by the deviance information criterion. We illustrated the gains of our model through application to the HIV/AIDS data and the simulation studies.KEYWORDS: Competing risks, subdistribution hazard, cumulative incidence function, spatial random effect, Markov chain Monte Carlo     

空间回归模型选择的反思

空间计量经济学存在两种最基本的模型:空间滞后模型和空间误差模型,这里旨在重新思考和探讨这两种空间回归模型的选择,结论为:Moran’s I指数可以用来判断回归模型后的残差是否存在空间依赖性;在实证分析中,采用拉格朗日乘子检验判断两种模型优劣是最常见的做法。然而,该检验仅仅是基于统计推断而忽略了理论基础,因此,可能导致选择错误的模型;在实证分析中,空间误差模型经常被选择性遗忘,而该模型的适用性较空间滞后模型更为广泛;实证分析大多缺乏空间回归模型设定的探讨,Anselin提出三个统计量,并且,如果模型设定正确,应该遵从Wald统计量>Log likelihood统计量>LM统计量的排列顺序。     

The Implications of Using Messy Data to Estimate Production-Frontier-Based Technical Efficiency Measures

An empirical study of efficiency at the plant level, requiring production and financial data, was done using frontier function specifications. It is not evident from the implementation of the production-frontier models that different methodologies will consistently flag the same observations as being efficient or inefficient. As a result, outlier diagnostics for individual observations and for subsets of observations are used to achieve a relative index of influentiality within the spectrum of efficiency. These outlier diagnostic tests consistently flag the same subset of efficient and inefficient observations as the frontier models and additionally clarify ranking discrepancies among the frontier model specifications.     

Identification of local clusters for count data: a model-based Moran's I test

We set out I_DR as a loglinear-model-based Moran's I test for Poisson count data that resembles the Moran's I residual test for Gaussian data. We evaluate its type I and type II error probabilities via simulations, and demonstrate its utility via a case study. When population sizes are heterogeneous, I_DR is effective in detecting local clusters by local association terms with an acceptable type I error probability. When used in conjunction with local spatial association terms in loglinear models, I_DR can also indicate the existence of first-order global cluster that can hardly be removed by local spatial association terms. In this situation, I_DR should not be directly applied for local cluster detection. In the case study of St. Louis homicides, we bridge loglinear model methods for parameter estimation to exploratory data analysis, so that a uniform association term can be defined with spatially varied contributions among spatial neighbors. The method makes use of exploratory tools such as Moran's I scatter plots and residual plots to evaluate the magnitude of deviance residuals, and it is effective to model the shape, the elevation and the magnitude of a local cluster in the model-based test.     

A Case Study for Modelling Cancer Incidence Using Bayesian Spatio‐Temporal Models

Researchers familiar with spatial models are aware of the challenge of choosing the level of spatial aggregation. Few studies have been published on the investigation of temporal aggregation and its impact on inferences regarding disease outcome in space–time analyses. We perform a case study for modelling individual disease outcomes using several Bayesian hierarchical spatio‐temporal models, while taking into account the possible impact of spatial and temporal aggregation. Using longitudinal breast cancer data from South East Queensland, Australia, we consider both parametric and non‐parametric formulations for temporal effects at various levels of aggregation. Two temporal smoothness priors are considered separately; each is modelled with fixed effects for the covariates and an intrinsic conditional autoregressive prior for the spatial random effects. Our case study reveals that different model formulations produce considerably different model performances. For this particular dataset, a classical parametric formulation that assumes a linear time trend produces the best fit among the five models considered. Different aggregation levels of temporal random effects were found to have little impact on model goodness‐of‐fit and estimation of fixed effects.     

Hierarchical Bayesian bivariate disease mapping: analysis of children and adults asthma visits to hospital

In spatial epidemiology, detecting areas with high ratio of disease is important as it may lead to identifying risk factors associated with disease. This in turn may lead to further epidemiological investigations into the nature of disease. Disease mapping studies have been widely performed with considering only one disease in the estimated models. Simultaneous modelling of different diseases can also be a valuable tool both from the epidemiological and also from the statistical point of view. In particular, when we have several measurements recorded at each spatial location, one can consider multivariate models in order to handle the dependence among the multivariate components and the spatial dependence between locations. In this paper, spatial models that use multivariate conditionally autoregressive smoothing across the spatial dimension are considered. We study the patterns of incidence ratios and identify areas with consistently high ratio estimates as areas for further investigation. A hierarchical Bayesian approach using Markov chain Monte Carlo techniques is employed to simultaneously examine spatial trends of asthma visits by children and adults to hospital in the province of Manitoba, Canada, during 2000–2010.     

Semiparametric Proportional Odds Models for Spatially Correlated Survival Data

The last decade has witnessed major developments in Geographical Information Systems (GIS) technology resulting in the need for statisticians to develop models that account for spatial clustering and variation. In public health settings, epidemiologists and health-care professionals are interested in discerning spatial patterns in survival data that might exist among the counties. This paper develops a Bayesian hierarchical model for capturing spatial heterogeneity within the framework of proportional odds. This is deemed more appropriate when a substantial percentage of subjects enjoy prolonged survival. We discuss the implementation issues of our models, perform comparisons among competing models and illustrate with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute, paying particular attention to the underlying spatial story.     

Least squares variogram fitting by spatial subsampling

Summary. Least squares methods are popular for fitting valid variogram models to spatial data. The paper proposes a new least squares method based on spatial subsampling for variogram model fitting. We show that the method proposed is statistically efficient among a class of least squares methods, including the generalized least squares method. Further, it is computationally much simpler than the generalized least squares method. The method produces valid variogram estimators under very mild regularity conditions on the underlying random field and may be applied with different choices of the generic variogram estimator without analytical calculation. An extension of the method proposed to a class of spatial regression models is illustrated with a real data example. Results from a simulation study on finite sample properties of the method are also reported.     

Multistage sampling for latent variable models

I consider the design of multistage sampling schemes for epidemiologic studies involving latent variable models, with surrogate measurements of the latent variables on a subset of subjects. Such models arise in various situations: when detailed exposure measurements are combined with variables that can be used to assign exposures to unmeasured subjects; when biomarkers are obtained to assess an unobserved pathophysiologic process; or when additional information is to be obtained on confounding or modifying variables. In such situations, it may be possible to stratify the subsample on data available for all subjects in the main study, such as outcomes, exposure predictors, or geographic locations. Three circumstances where analytic calculations of the optimal design are possible are considered: (i) when all variables are binary; (ii) when all are normally distributed; and (iii) when the latent variable and its measurement are normally distributed, but the outcome is binary. In each of these cases, it is often possible to considerably improve the cost efficiency of the design by appropriate selection of the sampling fractions. More complex situations arise when the data are spatially distributed: the spatial correlation can be exploited to improve exposure assignment for unmeasured locations using available measurements on neighboring locations; some approaches for informative selection of the measurement sample using location and/or exposure predictor data are considered.     

Finite sample power of Cliff–Ord-type tests for spatial disturbance correlation in linear regression

The paper considers tests against autocorrelation among the disturbances in linear regression models that can be expressed as ratios of quadratic forms. It shows that such tests are, in general, not unbiased and that power can even drop to zero for certain regressors and spatial weight matrices. Whether or not this can happen is however easily diagnosed for given regressors and for given spatial weights.     

Comparison of predictions by kriging and spatial autoregressive models

In geostatistics, the prediction of unknown quantities at given locations is commonly made by the kriging technique. In addition to the kriging technique for modeling regular lattice spatial data, the spatial autoregressive models can also be used. In this article, the spatial autoregressive model and the kriging technique are introduced. We extend prediction method proposed by Basu and Reinsel for SAR(2,1) model. Then, using a simulation study and real data, we compare prediction accuracy of the spatial autoregressive models with that of the kriging prediction. The results of simulation study show that predictions made by the autoregressive models are good competitor for the kriging method.     

A close look at the spatial structure implied by the CAR and SAR models

Modeling spatial interactions that arise in spatially referenced data is commonly done by incorporating the spatial dependence into the covariance structure either explicitly or implicitly via an autoregressive model. In the case of lattice (regional summary) data, two common autoregressive models used are the conditional autoregressive model (CAR) and the simultaneously autoregressive model (SAR). Both of these models produce spatial dependence in the covariance structure as a function of a neighbor matrix W and often a fixed unknown spatial correlation parameter. This paper examines in detail the correlation structures implied by these models as applied to an irregular lattice in an attempt to demonstrate their many counterintuitive or impractical results. A data example is used for illustration where US statewide average SAT verbal scores are modeled and examined for spatial structure using different spatial models.     

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Summary.  Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models , where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.     

Two-stage generalized moment method approach for bidimensional random coefficient autoregressive models

ABSTRACT

A two-dimensionally indexed random coefficients autoregressive models (2D ? RCAR) and the corresponding statistical inference are important tools for the analysis of spatial lattice data. The study of such models is motivated by their second-order properties that are similar to those of 2D ? (G)ARCH which play an important role in spatial econometrics. In this article, we study the asymptotic properties of two-stage generalized moment method (2S ? GMM) under general asymptotic framework for 2D ? RCA models. So, the efficiency, strong consistency, the asymptotic normality, and hypothesis tests of 2S ? GMM estimation are derived. A simulation experiment is presented to highlight the theoretical results.     

时变空间权重矩阵面板数据模型稳健LM检验有效性研究

空间权重矩阵是描述个体间空间关系的重要工具,通常基于个体间的地理距离构造不随时间而改变的空间权重矩阵。然而,当个体间的空间关系源自经济/社会/贸易距离或人口流动性/气候等特征时,空间权重矩阵本质上可能将随时间而改变。由此,本研究提出时变空间权重矩阵面板数据模型的稳健LM检验。大量Monte Carlo模拟结果显示：从检验水平和功效角度来看,基于误设的非时变空间权重矩阵的稳健LM检验存在较大偏差,但是基于时变空间权重矩阵的稳健LM检验能够有效地识别面板数据中的空间关系类型。尤其是,在时间较长和个体较多等情况下,时变空间权重矩阵的稳健LM检验功效更高。     

From distance sampling to spatial capture–recapture

Distance sampling and capture–recapture are the two most widely used wildlife abundance estimation methods. capture–recapture methods have only recently incorporated models for spatial distribution and there is an increasing tendency for distance sampling methods to incorporated spatial models rather than to rely on partly design-based spatial inference. In this overview we show how spatial models are central to modern distance sampling and that spatial capture–recapture models arise as an extension of distance sampling methods. Depending on the type of data recorded, they can be viewed as particular kinds of hierarchical binary regression, Poisson regression, survival or time-to-event models, with individuals’ locations as latent variables and a spatial model as the latent variable distribution. Incorporation of spatial models in these two methods provides new opportunities for drawing explicitly spatial inferences. Areas of likely future development include more sophisticated spatial and spatio-temporal modelling of individuals’ locations and movements, new methods for integrating spatial capture–recapture and other kinds of ecological survey data, and methods for dealing with the recapture uncertainty that often arise when “capture” consists of detection by a remote device like a camera trap or microphone.     

BAYESIAN PREDICTION FOR SPATIAL GENERALISED LINEAR MIXED MODELS WITH CLOSED SKEW NORMAL LATENT VARIABLES

Spatial generalised linear mixed models are used commonly for modelling non‐Gaussian discrete spatial responses. In these models, the spatial correlation structure of data is modelled by spatial latent variables. Most users are satisfied with using a normal distribution for these variables, but in many applications it is unclear whether or not the normal assumption holds. This assumption is relaxed in the present work, using a closed skew normal distribution for the spatial latent variables, which is more flexible and includes normal and skew normal distributions. The parameter estimates and spatial predictions are calculated using the Markov Chain Monte Carlo method. Finally, the performance of the proposed model is analysed via two simulation studies, followed by a case study in which practical aspects are dealt with. The proposed model appears to give a smaller cross‐validation mean square error of the spatial prediction than the normal prior in modelling the temperature data set.     

Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.     

中国企业对外直接投资速度空间关联性研究

在微观上探明企业对外直接投资速度的空间特征是理解我国对外直接投资快速增长的重要因素，本文通过匹配《中国工业企业数据库》和《境外投资企业（机构）名录》构建企业对外直接投资速度及其空间关联变量指标进行微观实证研究。研究发现：①企业对外直接投资速度不仅存在直接正向空间关联性，而且存在通过抵消企业低管理效率不利影响的间接正向空间关联性；②企业对外直接投资速度的空间关联性仅存在于邻省之间，并不存在于非邻省之间；③企业对外直接投资速度的邻省空间关联性存在异质性，对发达国家进行投资的企业并不存在这种关联性。研究结果意味着在制定对外直接投资促进政策时应充分考虑空间协调性，发挥空间关联的积极作用。     

基础设施投资效率的空间溢出与门限效应研究

利用数据包络分析（DEA）估计了中国31个省份1999—2006年基础设施投资的相对效率,并以此代表各地区基础设施投资的成效,进而分析其对经济增长的贡献是否存在空间溢出和门限效应。采用普通面板回归、空间面板回归和门限面板回归这三种基于面板数据的回归模型进行实证分析后发现：基础设施投资效率对本地区和相邻地区的经济增长均有显著促进作用,并且随着经济规模的扩大,基础设施投资效率对经济增长的促进作用也有所提高,即证实了空间溢出和门限效应的存在。