We present a methodology for constructing a short-term event risk score in heart failure patients from an ensemble predictor, using bootstrap samples, two different classification rules, logistic regression and linear discriminant analysis for mixed data, continuous or categorical, and random selection of explanatory variables to build individual predictors. We define a measure of the importance of each variable in the score and an event risk measure by an odds-ratio. Moreover, we establish a property of linear discriminant analysis for mixed data. This methodology is applied to EPHESUS trial patients on whom biological, clinical and medical history variables were measured.
Levy, W.C., Mozaffarian, D., Linker, D.T., et al. (2006) The Seattle Heart Failure Model: Prediction of Survival in Heart Failure. Circulation, 113, 1424-1433. https://doi.org/10.1161/CIRCULATIONAHA.105.584102
Ketchum, E.S., Dickstein, K., Kjekshus, J., et al. (2014) The Seattle Post Myocardial Infarction Model (SPIM): Prediction of Mortality after Acute Myocardial Infarction with Left Ventricular Dysfunction. European Heart Journal: Acute Cardiovascular Care, 3, 46-55. https://doi.org/10.1177/2048872613502283
Pitt, B., Remme, W., Zannad, F., et al. (2003) Eplerenone, a Selective Aldosterone Blocker, in Patients with Left Ventricular Dysfunction after Myocardial Infarction. New England Journal of Medicine, 348, 1309-1321. https://doi.org/10.1056/NEJMoa030207
Duarte, K., Monnez, J.M., Albuisson, E., Pitt, B., Zannad, F. and Rossignol, P. (2015) Prognostic Value of Estimated Plasma Volume in Heart Failure. JACC: Heart Failure, 3, 886-893. https://doi.org/10.1016/j.jchf.2015.06.014
Cockcroft, D.W. and Gault, H. (1976) Prediction of Creatinine Clearance from Serum Creatinine. Nephron, 16, 31-41. https://doi.org/10.1159/000180580
Levey, A.S., Coresh, J., Balk, E., et al. (2003) National Kidney Foundation Practice Guidelines for Chronic Kidney Disease: Evaluation, Classification, and Stratification. Annals of Internal Medicine, 139, 137-147. https://doi.org/10.7326/0003-4819-139-2-200307150-00013
Levey, A.S., Stevens, L.A., Schmid, C.H., et al. (2009) A New Equation to Estimate Glomerular Filtration Rate. Annals of Internal Medicine, 150, 604-612. https://doi.org/10.7326/0003-4819-150-9-200905050-00006
Lebart, L., Morineau, A. and Warwick, K. (1984) Multivariate Descriptive Statistical Analysis: Correspondence Analysis and Related Techniques for Large Matrices. Wiley, New York.
Escofier, B. and Pagès, J. (1990) Multiple Factor Analysis. Computational Statistics and Data Analysis, 18, 121-140. https://doi.org/10.1016/0167-9473(94)90135-X
Pagès, J. (2004) Analyse Factorielle de Données Mixtes. Revue de Statistique Appliquée, 52, 93-111.
Saporta, G. (1977) Une Méthode et un Programme d’Analyse Discriminante sur Variables Qualitatives. Analyse des Données et Informatique, Inria, 201-210.
Rotella, F. and Borne, P. (1995) Théorie et Pratique du Calcul Matriciel. Editions Technip.
Carroll, J.D. (1968) A Generalization of Canonical Correlation Analysis to Three or More Sets of Variables. Proceedings of the 76th Annual Convention of the American Psychological Association, Washington DC, 227-228.
Friedman, J.H. and Meulman, J.J. (2004) Clustering Objects on Subsets of Attributes (with Discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66, 815-849. https://doi.org/10.1111/j.1467-9868.2004.02059.x
Gower, J.C. (1971) A General Coefficient of Similarity and Some of its Properties. Biometrics, 27, 857-871. https://doi.org/10.2307/2528823
Genuer, R. and Poggi, J.M. (2017) Arbres CART et Forêts Aléatoires, Importance et Sélection de Variables. https://arxiv.org/pdf/1610.08203v2.pdf
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning. Springer, New York. https://doi.org/10.1007/978-0-387-84858-7
Efron, B. and Tibshirani, R.J. (1994) An Introduction to the Bootstrap. CRC Press, Boca Raton.
Breiman, L. (1996) Bagging Predictors. Machine Learning, 24, 123-140. https://doi.org/10.1007/BF00058655
In Lee, K. and Koval, J.J. (1997) Determination of the Best Significance Level in Forward Stepwise Logistic Regression. Communications in Statistics-Simulation and Computation, 26, 559-575. https://doi.org/10.1080/03610919708813397
Wang, Q., Koval, J.J., Mills, C.A. and Lee, K.I.D. (2007) Determination of the Selection Statistics and Best Significance Level in Backward Stepwise Logistic Regression. Communications in Statistics-Simulation and Computation, 37, 62-72. https://doi.org/10.1080/03610910701723625
Bendel, R.B. and Afifi, A.A. (1977) Comparison of Stopping Rules in Forward “Stepwise” Regression. Journal of the American Statistical Association, 72, 46-53.
Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58, 267-288. http://www.jstor.org/stable/2346178
Breiman, L. (2001) Random Forests. Machine Learning, 45, 5-35. https://doi.org/10.1023/A:1010933404324
Song, L., Langfelder, P. and Horvath, S. (2013) Random Generalized Linear Model: A Highly Accurate and Interpretable Ensemble Predictor. BMC Bioinformatics, 14, 5. https://doi.org/10.1186/1471-2105-14-5
Akaike, H. (1998) Information Theory and an Extension of the Maximum Likelihood Principle. In: Parzen, E., Tanabe, K. and Kitagawa, G., Eds., Selected Papers of Hirotugu Akaike, Springer Series in Statistics (Perspectives in Statistics), Springer, New York, 199-213.
Schwarz, G. (1978) Estimating the Dimension of a Model. The Annals of Statistics, 6, 461-464. https://doi.org/10.1214/aos/1176344136
Tufféry, S. (2015) Modélisation Prédictive et Apprentissage Statistique avec R. Editions Technip.
Breiman, L. (1996) Out-of-Bag Estimation. https://www.stat.berkeley.edu/~breiman/OOBestimation.pdf
Dixon, W.J. (1960) Simplified Estimation from Censored Normal Samples. The Annals of Mathematical Statistics, 31, 385-391. https://doi.org/10.1214/aoms/1177705900
Royston, P. and Sauerbrei, W. (2007) Multivariable Modeling with Cubic Regression Splines: A Principled Approach. Stata Journal, 7, 45-70.
Oza, N.C. and Russell, S. (2001) Online Bagging and Boosting. Proceedings of Eighth International Workshop on Artificial Intelligence and Statistics, Key West, 4-7 January 2001, 105-112.
Duarte, K., Monnez, J.M. and Albuisson, E. (2018) Sequential Linear Regression with Online Standardized Data. PLoS ONE, 13, e0191186. https://doi.org/10.1371/journal.pone.0191186
Monnez, J.M. (2018) Online Logistic Regression Process with Online Standardized Data.