A generalized estimating equations approach for spatially correlated binary data: applications to the analysis of neuroimaging data.

This paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects. This approach is useful when the scientific focus is on modeling the marginal mean structure. Proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters. Generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed. The use of semivariogram models for parameterizing the correlation structure is discussed, and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation. The methodology is illustrated with neuroimaging data collected as part of the National Institute of Neurological Disorders and Stroke (NINDS) Stroke Data Bank. A simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies.

[1]  Sunil Narumalani,et al.  Aquatic macrophyte modeling using GIS and logistic multiple regression , 1997 .

[2]  J. C. Price.  Calibration of satellite radiometers and the comparison of vegetation indices , 1987 .

[3]  Stuart F. Biggar,et al.  In-flight radiometric calibration of Landsat-5 Thematic Mapper from 1984 to the present , 1993, Defense, Security, and Sensing.

[4]  A. Mollié,et al.  Empirical Bayes estimates of cancer mortality rates using spatial models. , 1991, Statistics in medicine.

[5]  M. H. Quenouille.  Problems in Plane Sampling , 1949 .

[6]  L. Ryan,et al.  The Analysis of Multiple Correlated Binary Outcomes: Application to Rodent Teratology Experiments , 1989 .

[7]  L. Zhao,et al.  Correlated binary regression using a quadratic exponential model , 1990 .

[8]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[9]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[10]  Joseph J. Luczkovich,et al.  Multispectral change vector analysis for monitoring coastal marine environments , 1992 .

[11]  K Y Liang,et al.  Longitudinal data analysis for discrete and continuous outcomes. , 1986, Biometrics.

[12]  Daniel B Hier,et al.  The Stroke Data Bank: design, methods, and baseline characteristics. , 1988, Stroke.

[13]  M. M. Spencer,et al.  Atmospheric model for correction of spacecraft data. , 1973 .

[14]  J. Keith Ord,et al.  Spatial Processes Models and Applications , 1981 .

[15]  N. Cressie,et al.  Spatial Modeling of Regional Variables , 1993 .

[16]  Philip J. Howarth,et al.  Change-detection accuracy assessment using SPOT multispectral imagery of the rural-urban fringe☆ , 1989 .

[17]  D. Clayton,et al.  Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. , 1987, Biometrics.

[18]  S. Rambal,et al.  Identifying spatial patterns of Mediterranean landscapes from geostatistical analysis of remotely-sensed data , 1994 .

[19]  M. Piedmonte,et al.  A Method for Generating High-Dimensional Multivariate Binary Variates , 1991 .

[20]  K. Rutchey,et al.  Inland Wetland Change Detection in the Everglades Water Conservation Area 2A Using a Time Series of Normalized Remotely Sensed Data , 1995 .

[21]  S. Zeger,et al.  Multivariate Regression Analyses for Categorical Data , 1992 .

[22]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[23]  A. Pack,et al.  The prevalence of overhanging margins in posterior amalgam restorations and periodontal consequences. , 1990, Journal of clinical periodontology.

[24]  P. Albert,et al.  Models for longitudinal data: a generalized estimating equation approach. , 1988, Biometrics.

[25]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[26]  G. Christakos.  On the Problem of Permissible Covariance and Variogram Models , 1984 .

[27]  William J. Volchok,et al.  Radiometric scene normalization using pseudoinvariant features , 1988 .

[28]  Ashbindu Singh,et al.  Review Article Digital change detection techniques using remotely-sensed data , 1989 .

[29]  David A. Pyke,et al.  Shrub dieback in a semiarid ecosystem : The integration of remote sensing and geographic information systems for detecting vegetation change , 1992 .

[30]  P. Diggle.  An approach to the analysis of repeated measurements. , 1988, Biometrics.

[31]  P. S. Chavez,et al.  Automatic detection of vegetation changes in the southwestern United States using remotely sensed images , 1994 .

[32]  P. Chavez.  Image-Based Atmospheric Corrections - Revisited and Improved , 1996 .

[33]  Fangju Wang,et al.  A knowledge-based vision system for detecting land changes at urban fringes , 1993, IEEE Trans. Geosci. Remote. Sens..

[34]  S. Zeger.  A regression model for time series of counts , 1988 .

[35]  R. Itami,et al.  GIS-based habitat modeling using logistic multiple regression : a study of the Mt. Graham red squirrel , 1991 .

[36]  E. Ising.  Beitrag zur Theorie des Ferromagnetismus , 1925 .

[37]  Kenneth C. McGwire,et al.  Spatial structure, sampling design and scale in remotely-sensed imagery of a California savanna woodland , 1993 .

[38]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[39]  J. R. Jensen,et al.  Inland wetland change detection using aircraft MSS data , 1987 .

[40]  D. Muchoney,et al.  Change detection for monitoring forest defoliation , 1994 .

[41]  R. Prentice,et al.  Correlated binary regression with covariates specific to each binary observation. , 1988, Biometrics.