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     

Non-stationary partition modeling of geostatistical data for malaria risk mapping

The most common assumption in geostatistical modeling of malaria is stationarity, that is spatial correlation is a function of the separation vector between locations. However, local factors (environmental or human-related activities) may influence geographical dependence in malaria transmission differently at different locations, introducing non-stationarity. Ignoring this characteristic in malaria spatial modeling may lead to inaccurate estimates of the standard errors for both the covariate effects and the predictions. In this paper, a model based on random Voronoi tessellation that takes into account non-stationarity was developed. In particular, the spatial domain was partitioned into sub-regions (tiles), a stationary spatial process was assumed within each tile and between-tile correlation was taken into account. The number and configuration of the sub-regions are treated as random parameters in the model and inference is made using reversible jump Markov chain Monte Carlo simulation. This methodology was applied to analyze malaria survey data from Mali and to produce a country-level smooth map of malaria risk.     

A model for analyzing spatially correlated binary data clustered in uncorrelated lattices

In recent years, the spatial lattice data has been a motivating issue for researches. Modeling of binary variables observed at locations on a spatial lattice has been sufficiently investigated and the autologistic model is a popular tool for analyzing these data. But, there are many situations where binary responses are clustered in several uncorrelated lattices, and only a few studies were found to investigate the modeling of binary data distributed in such spatial structure. Besides, due to spatial dependency in data exact likelihood analyses is not possible. Bayesian inference, for the autologistic function due to intractability of its normalizing-constant, often has limitations and difficulties. In this study, spatially correlated binary data clustered in uncorrelated lattices are modeled via autologistic regression and IBF (inverse Bayes formulas) sampler with help of introducing latent variables, is extended for posterior analysis and parameter estimation. The proposed methodology is illustrated using simulated and real observations.     

Estimation in an empirical bayes model for longitudinal and cross‐sectionally clustered binary data

Some studies generate data that can be grouped into clusters in more than one way. Consider for instance a smoking prevention study in which responses on smoking status are collected over several years in a cohort of students from a number of different schools. This yields longitudinal data, also cross‐sectionaliy clustered in schools. The authors present a model for analyzing binary data of this type, combining generalized estimating equations and estimation of random effects to address the longitudinal and cross‐sectional dependence, respectively. The estimation procedure for this model is discussed, as are the results of a simulation study used to investigate the properties of its estimates. An illustration using data from a smoking prevention trial is given.     

Non parametric space-time modeling of SO2 in presence of many missing data

Given pollution measurement from a network of monitoring sites in the area of a city and over an extended period of time, an important problem is to identify the spatial and temporal structure of the data. In this paper we focus on the identification and estimate of a statistical non parametric model to analyse the SO₂ in the city of Padua, where data are collected by some fixed stations and some mobile stations moving without any specific rule in different new locations. The impact of the use of mobile stations is that for each location there are times when data was not collected. Assuming temporal stationarity and spatial isotropy for the residuals of an additive model for the logarithm of SO₂ concentration, we estimate the semivariogram using a kernel-type estimator. Attempts are made to avoid the assumption of spatial isotropy. Bootstrap confidence bands are obtained for the spatial component of the additive model that is a deterministic function which defines the spatial structure. Finally, an example is proposed to design an optimal network for the mobiles monitoring stations in a fixed future time, given all the information available.     

Optimal Estimator for Logistic Model with Distribution‐free Random Intercept

Logistic models with a random intercept are prevalent in medical and social research where clustered and longitudinal data are often collected. Traditionally, the random intercept in these models is assumed to follow some parametric distribution such as the normal distribution. However, such an assumption inevitably raises concerns about model misspecification and misleading inference conclusions, especially when there is dependence between the random intercept and model covariates. To protect against such issues, we use a semiparametric approach to develop a computationally simple and consistent estimator where the random intercept is distribution‐free. The estimator is revealed to be optimal and achieve the efficiency bound without the need to postulate or estimate any latent variable distributions. We further characterize other general mixed models where such an optimal estimator exists.     

Semiparametric transformation models with random effects for clustered doubly censored data

For right-censored data, Zeng et al. [Semiparametirc transformation modes with random effects for clustered data. Statist Sin. 2008;18:355–377] proposed a class of semiparametric transformation models with random effects to formulate the effects of possibly time-dependent covariates on clustered failure times. In this article, we demonstrate that the approach of Zeng et al. can be extended to analyse clustered doubly censored data. The asymptotic properties of the nonparametric maximum likelihood estimators of the model parameters are derived. A simulation study is conducted to investigate the performance of the proposed estimators.     

A New Method for Statistical Multidimensional Unfolding

ABSTRACT

Consider the problem of estimating the positions of a set of targets in a multidimensional Euclidean space from distances reported by a number of observers when the observers do not know their own positions in the space. Each observer reports the distance from the observer to each target plus a random error. This statistical problem is the basic model for the various forms of what is called multidimensional unfolding in the psychometric literature. Multidimensional unfolding methodology as developed in the field of cognitive psychology is basically a statistical estimation problem where the data structure is a set of measures that are monotonic functions of Euclidean distances between a number of observers and targets in a multidimensional space. The new method presented in this article deals with estimating the target locations and the observer positions when the observations are functions of the squared distances between observers and targets observed with an additive random error in a two-dimensional space. The method provides robust estimates of the target locations in a multidimensional space for the parametric structure of the data generating model presented in the article. The method also yields estimates of the orientation of the coordinate system and the mean and variances of the observer locations. The mean and the variances are not estimated by standard unfolding methods which yield targets maps that are invariant to a rotation of the coordinate system. The data is transformed so that the nonlinearity due to the squared observer locations is removed. The sampling properties of the estimates are derived from the asymptotic variances of the additive errors of a maximum likelihood factor analysis of the sample covariance matrix of the transformed data augmented with bootstrapping. The robustness of the new method is tested using artificial data. The method is applied to a 2001 survey data set from Turkey to provide a real data example.     

Modeling proportions and marginal counts simultaneously for clustered multinomial data with random cluster sizes

Clustered multinomial data with random cluster sizes commonly appear in health, environmental and ecological studies. Traditional approaches for analyzing clustered multinomial data contemplate two assumptions. One of these assumptions is that cluster sizes are fixed, whereas the other demands cluster sizes to be positive. Randomness of the cluster sizes may be the determinant of the within-cluster correlation and between-cluster variation. We propose a baseline-category mixed model for clustered multinomial data with random cluster sizes based on Poisson mixed models. Our orthodox best linear unbiased predictor approach to this model depends only on the moment structure of unobserved distribution-free random effects. Our approach also consolidates the marginal and conditional modeling interpretations. Unlike the traditional methods, our approach can accommodate both random and zero cluster sizes. Two real-life multinomial data examples, crime data and food contamination data, are used to manifest our proposed methodology.     

Bayesian spatial quantile regression for areal count data,with application on substitute care placements in Texas

Quantile regression (QR) allows one to model the effect of covariates across the entire response distribution, rather than only at the mean, but QR methods have been almost exclusively applied to continuous response variables and without considering spatial effects. Of the few studies that have performed QR on count data, none have included random spatial effects, which is an integral facet of the Bayesian spatial QR model for areal counts that we propose. Additionally, we introduce a simplifying alternative to the response variable transformation currently employed in the QR for counts literature. The efficacy of the proposed model is demonstrated via simulation study and on a real data application from the Texas Department of Family and Protective Services (TDFPS). Our model outperforms a comparable non-spatial model in both instances, as evidenced by the deviance information criterion (DIC) and coverage probabilities. With the TDFPS data, we identify one of four covariates, along with the intercept, as having a nonconstant effect across the response distribution.     

Analysis of spatial frailty models by a weighted estimating equation

Spatially correlated survival data are frequently observed in ecological and epidemiological studies. An assumption in the clustered survival models is inter-cluster independence, which may not be adequate to model the dependence in spatial settings. For survival data, the likelihood function based on a spatial frailty may be complicated. In this paper, we develop a weighted estimating equation for spatially right-censored data. Some large sample properties for the estimate are developed. We also conduct simulations to compare estimation performance with other methods. A data set from a study of forest decline in Wisconsin is used to illustrate the proposed method.     

Two-scale spatial models for binary data

A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified, and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the background. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian–Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence–absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted.     

Generalized confidence intervals for the process capability indices in general random effect model with balanced data

In this paper, we consider the interval estimation problem on the process capability indices in general random effect model with balanced data. The confidence intervals for three commonly used process capability indices are developed by using the concept of generalized confidence interval. Furthermore, some simulation results on the coverage probability and expected value of the generalized lower confidence limits are reported. The simulation results indicate that the proposed confidence intervals do provide quite satisfactory coverage probabilities.     

Gaussian Markov random field spatial models in GAMLSS

This paper describes the modelling and fitting of Gaussian Markov random field spatial components within a Generalized AdditiveModel for Location, Scale and Shape (GAMLSS) model. This allows modelling of any or all the parameters of the distribution for the response variable using explanatory variables and spatial effects. The response variable distribution is allowed to be a non-exponential family distribution. A new package developed in R to achieve this is presented. We use Gaussian Markov random fields to model the spatial effect in Munich rent data and explore some features and characteristics of the data. The potential of using spatial analysis within GAMLSS is discussed. We argue that the flexibility of parametric distributions, ability to model all the parameters of the distribution and diagnostic tools of GAMLSS provide an ideal environment for modelling spatial features of data.     

Spatial bootstrapped microeconometrics: Forecasting for out-of-sample geo-locations in big data

Spatial econometric models estimated on the big geo-located point data have at least two problems: limited computational capabilities and inefficient forecasting for the new out-of-sample geo-points. This is because of spatial weights matrix W defined for in-sample observations only and the computational complexity. Machine learning models suffer the same when using kriging for predictions; thus this problem still remains unsolved. The paper presents a novel methodology for estimating spatial models on big data and predicting in new locations. The approach uses bootstrap and tessellation to calibrate both model and space. The best bootstrapped model is selected with the PAM (Partitioning Around Medoids) algorithm by classifying the regression coefficients jointly in a nonindependent manner. Voronoi polygons for the geo-points used in the best model allow for a representative space division. New out-of-sample points are assigned to tessellation tiles and linked to the spatial weights matrix as a replacement for an original point what makes feasible usage of calibrated spatial models as a forecasting tool for new locations. There is no trade-off between forecast quality and computational efficiency in this approach. An empirical example illustrates a model for business locations and firms' profitability.     

An alternative to confidence intervals constructed after a Hausman pretest in panel data

Consider panel data modelled by a linear random intercept model that includes a time‐varying covariate. Suppose that our aim is to construct a confidence interval for the slope parameter. Commonly, a Hausman pretest is used to decide whether this confidence interval is constructed using the random effects model or the fixed effects model. This post‐model‐selection confidence interval has the attractive features that it (a) is relatively short when the random effects model is correct and (b) reduces to the confidence interval based on the fixed effects model when the data and the random effects model are highly discordant. However, this confidence interval has the drawbacks that (i) its endpoints are discontinuous functions of the data and (ii) its minimum coverage can be far below its nominal coverage probability. We construct a new confidence interval that possesses these attractive features, but does not suffer from these drawbacks. This new confidence interval provides an intermediate between the post‐model‐selection confidence interval and the confidence interval obtained by always using the fixed effects model. The endpoints of the new confidence interval are smooth functions of the Hausman test statistic, whereas the endpoints of the post‐model‐selection confidence interval are discontinuous functions of this statistic.     

An extended Gaussian max-stable process model for spatial extremes

The extremes of environmental processes are often of interest due to the damage that can be caused by extreme levels of the processes. These processes are often spatial in nature and modelling the extremes jointly at many locations can be important. In this paper, an extension of the Gaussian max-stable process is developed, enabling data from a number of locations to be modelled under a more flexible framework than in previous applications. The model is applied to annual maximum rainfall data from five sites in South-West England. For estimation we employ a pairwise likelihood within a Bayesian analysis, incorporating informative prior information.     

A Spatial-temporal Model for Temperature with Seasonal Variance

We propose a spatial-temporal stochastic model for daily average surface temperature data. First, we build a model for a single spatial location, independently on the spatial information. The model includes trend, seasonality, and mean reversion, together with a seasonally dependent variance of the residuals. The spatial dependency is modelled by a Gaussian random field. Empirical fitting to data collected in 16 measurement stations in Lithuania over more than 40 years shows that our model captures the seasonality in the autocorrelation of the squared residuals, a property of temperature data already observed by other authors. We demonstrate through examples that our spatial-temporal model is applicable for prediction and classification.     

Nonparametric modeling of clustered customer survival data

We incorporate a random clustering effect into the nonparametric version of Cox Proportional Hazards model to characterize clustered survival data. The simulation studies provide evidence that clustered survival data can be better characterized through a nonparametric model. Predictive accuracy of the nonparametric model is affected by number of clusters and distribution of the random component accounting for clustering effect. As the functional form of the covariate departs from linearity, the nonparametric model is becoming more advantageous over the parametric counterpart. Finally, nonparametric is better than parametric model when data are highly heterogenous and/or there is misspecification error.     

MODELLING TRUNCATED AND CLUSTERED COUNT DATA

Count response data often exhibit departures from the assumptions of standard Poisson generalized linear models. In particular, cluster level correlation of the data and truncation at zero are two common characteristics of such data. This paper describes a random components truncated Poisson model that can be applied to clustered and zero‐truncated count data. Residual maximum likelihood method estimators for the parameters of this model are developed and their use is illustrated using a dataset of non‐zero counts of sheets with edge‐strain defects in iron sheets produced by the Mobarekeh Steel Complex, Iran. The paper also reports on a small‐scale simulation study that supports the estimation procedure.