Identifying Pediatric Cancer Clusters in Florida Using Log-Linear Models and Generalized Lasso Penalties

REFERENCES

• Akaike, H. (1974), A New Look at the Statistical Model Identification, IEEE Transactions on Automatic Control, 19, 716–723.
   Web of Science ®Google Scholar
• Amin, R., Bohnert, A., Holmes, L., Rajasekaran, A., Assanasen, C. (2010), Epidemiologic Mapping of Florida Childhood Cancer Clusters, Pediatric Blood & Cancer, 54, 511–518.
   PubMed Web of Science ®Google Scholar
• Anderson, C., Lee, D., Dean, M. (2013), Identifying Clusters in Bayesian Disease Mapping,”technical report, arXiv:1311.0660. Available at http://arxiv.org/abs/1311.0660v1
   Google Scholar
• Andrews, D.F., Mallows, C.L. (1974), Scale Mixtures of Normal Distributions, Journal of the Royal Statistical Society, Series B, 36, 99–102.
   Google Scholar
• Banerjee, S., Gelfand, A.E., and Carlin, B.P. (2004), Hierarchical Modeling and Analysis For Spatial Data, Boca Raton, FL: CRC Press.
   Google Scholar
• Besag, J., Newell, J. (1991), The Detection of Clusters in Rare Diseases, Journal of the Royal Statistical Society, Series A, 154, 143–155.
   Google Scholar
• Bivand, R., Altman, M., Anselin, L. (2014). spdep: Spatial Dependence: Weighting Schemes, Statistics and Models, R package version 0.5-77. Available at http://cran.r-project.org/web/packages/spdep/index.html
   Google Scholar
• Bregman, L. (1967), The Relaxation Method of Finding the Common Points of Convex Sets and Its Application to the Solution of Problems in Convex Optimization, USSR Computational Mathematics and Mathematical Physics, 7, 200–217.
   Google Scholar
• Charras-Garrido, M., Abrial, D., De Goër, J., Dachian, S., Peyrard, N. (2012), Classification Method for Disease Risk Mapping Based on Discrete Hidden Markov Random Fields, Biostatistics, 13, 241–255.
   PubMed Web of Science ®Google Scholar
• Chen, X., Lin, Q., Kim, S., Carbonell, J.G., Xing, E.P. (2012), Smoothing Proximal Gradient Method for General Structured Sparse Regression, The Annals of Applied Statistics, 6, 719–752.
   Web of Science ®Google Scholar
• Damien, P., Wakefield, J., Walker, S.G. (1999), Gibbs Sampling for Bayesian Non-Conjugate and Hierarchical Models by Using Auxiliary Variables, Journal of the Royal Statistical Society, Series B, 61, 331–344.
   Google Scholar
• Diggle, P.J., Chetwynd, A.G. (1991), Second-Order Analysis of Spatial Clustering for Inhomogeneous Populations, Biometrics, 47, 1155–1163.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., Höfling, H., Tibshirani, R. (2007), Pathwise Coordinate Optimization, The Annals of Applied Statistics, 1, 302–332.
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., Tibshirani, R. (2010), Regularization Paths for Generalized Linear Models via Coordinate Descent, Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Goldstein, T., Osher, S. (2009), The Split Bregman Method for l1-Regularized Problems, SIAM Journal of Imaging Sciences, 2, 323–343.
   Web of Science ®Google Scholar
• Gómez-Rubio, V., Ferrándiz-Ferragud, J., Lopez-Quílez, A. (2005), Detecting Clusters of Disease With R, Journal of Geographical Systems, 7, 189–206.
   Google Scholar
• Goujon-Bellec, S., Demoury, C., Guyot-Goubin, A., Hémon, D., Clavel, J. (2011), Detection of Clusters of a Rare Disease Over a Large Territory: Performance of Cluster Detection Methods, International Journal of Health Geographics, 10, 53.
   PubMed Web of Science ®Google Scholar
• Green, P.J., Richardson, S. (2002), Hidden Markov Models and Disease Mapping, Journal of the American Statistical Association, 97, 1055–1070.
   Web of Science ®Google Scholar
• Heinzl, F., Tutz, G. (2014), Clustering in Linear-Mixed Models With a Group Fused Lasso Penalty, Biometrical Journal, 56, 44–68.
   PubMed Web of Science ®Google Scholar
• Knorr-Held, L., Raßer, G. (2000), Bayesian Detection of Clusters and Discontinuities in Disease Maps, Biometrics, 56, 13–21.
   PubMed Web of Science ®Google Scholar
• Krishnapuram, B., Carin, L., Figueiredo, M.A., Hartemink, A.J. (2005), Sparse Multinomial Logistic Regression: Fast Algorithms and Generalization Bounds, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 957–968.
   PubMed Web of Science ®Google Scholar
• Kulldorff, M. (1997), A Spatial Scan Statistic, Communications in Statistics—Theory and Methods, 26, 1481–1496.
   Web of Science ®Google Scholar
• Kulldorff, M., Nagarwalla, N. (1995), Spatial Disease Clusters: Detection and Inference, Statistics in Medicine, 14, 799–810.
   PubMed Web of Science ®Google Scholar
• Kulldorff, M., Tango, T., Park, P.J. (2003), Power Comparisons for Disease Clustering Tests, Computational Statistics and Data Analysis, 42, 665–684.
   Web of Science ®Google Scholar
• Kyung, M., Gill, J., Ghosh, M., Casella, G. (2010), Penalized Regression, Standard Errors, and Bayesian Lassos, Bayesian Analysis, 5, 369–411.
   Web of Science ®Google Scholar
• Matthews, B.W. (1975), Comparison of the Predicted and Observed Secondary Structure of t4 Phage Lysozyme, Biochimica et Biophysica Acta (BBA)-Protein Structure, 405, 442–451.
   PubMed Web of Science ®Google Scholar
• Moraga, P., Montes, F. (2011), Detection of Spatial Disease Clusters With Lisa Functions, Statistics in Medicine, 30, 1057–1071.
   PubMed Web of Science ®Google Scholar
• Morton-Jones, T., Diggle, P., Elliott, P. (1999), Investigation of Excess Environmental Risk Around Putative Sources: Stone’s Test With Covariate Adjustment, Statistics in Medicine, 18, 189–197.
   PubMed Web of Science ®Google Scholar
• Neter, J., Kutner, M.H., Nachtsheim, C.J., and Wasserman, W. (1996), Applied Linear Statistical Models (Vol. 1), Chicago, IL: Irwin.
   Google Scholar
• Openshaw, S., Charlton, M., Wymer, C., Craft, A. (1987), A Mark 1 Geographical Analysis Machine for the Automated Analysis of Point Data Sets, International Journal of Geographical Information System, 1, 335–358.
   Google Scholar
• Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W. (2005), An Iterative Regularization Method for Total Variation-Based Image Restoration, Multiscale Modeling and Simulation, 4, 460–489.
   Web of Science ®Google Scholar
• Potthoff, R.F., Whittinghill, M. (1966a), Testing for Homogeneity: I. The Binomial and Multinomial Distributions, Biometrika, 53, 167–182.
   PubMed Web of Science ®Google Scholar
• ——— (1966b), Testing for Homogeneity: II. The Poisson Distribution, Biometrika, 183–190.
   PubMed Web of Science ®Google Scholar
• Rinaldo, A. (2009), Properties and Refinements of the Fused Lasso, The Annals of Statistics, 37, 2922–2952.
   Web of Science ®Google Scholar
• Rue, H., and Held, L. (2005), Gaussian Markov Random Fields: Theory and Applications, Boca Raton, FL: CRC Press.
   Google Scholar
• Stone, R.A. (1988), Investigations of Excess Environmental Risks Around Putative Sources: Statistical Problems and a Proposed Test, Statistics in Medicine, 7, 649–660.
   PubMed Web of Science ®Google Scholar
• Tango, T. (1995), A Class of Tests for Detecting ‘General’ and ‘Focused’ Clustering of Rare Diseases, Statistics in Medicine, 14, 2323–2334.
   PubMed Web of Science ®Google Scholar
• Tango, T., Takahashi, K. (2005), A Flexibly Shaped Spatial Scan Statistic for Detecting Clusters, International Journal of Health Geographics, 4, 11.
   PubMedGoogle Scholar
• Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., Knight, K. (2005), Sparsity and Smoothness via the Fused Lasso, Journal of the Royal Statistical Society, Series B, 67, 91–108.
   Google Scholar
• Tibshirani, R., Wang, P. (2008), Spatial Smoothing and Hot Spot Detection for CGH Data Using the Fused Lasso, Biostatistics, 9, 18–29.
   PubMed Web of Science ®Google Scholar
• Tibshirani, R.J., Taylor, J., . (2012), Degrees of Freedom in Lasso Problems, The Annals of Statistics, 40, 1198–1232.
   Web of Science ®Google Scholar
• Wakefield, J., Kim, A. (2013), A Bayesian Model for Cluster Detection, Biostatistics, 14, 752–765.
   PubMed Web of Science ®Google Scholar
• Waller, L.A., Hill, E.G., Rudd, R.A. (2006), The Geography of Power: Statistical Performance of Tests of Clusters and Clustering in Heterogeneous Populations, Statistics in Medicine, 25, 853–865.
   PubMed Web of Science ®Google Scholar
• Weinstock, M.A. (1981), A Generalised Scan Statistic Test for the Detection of Clusters, International Journal of Epidemiology, 10, 289–293.
   PubMed Web of Science ®Google Scholar
• Whittemore, A.S., Friend, N., Brown, B.W., Holly, E.A. (1987), A Test to Detect Clusters of Disease, Biometrika, 74, 631–635.
   Web of Science ®Google Scholar
• Witten, D.M., Tibshirani, R. (2011), scout: Implements the Scout Method for Covariance-Regularized Regression, R package version 1.0.3. Available at http://cran.r-project.org/web/packages/scout/index.html
   Google Scholar
• Zou, H., Hastie, T., Tibshirani, R. (2007), On the “Degrees of Freedom” of the Lasso, The Annals of Statistics, 35, 2173–2192.
   Web of Science ®Google Scholar