Preface to First Edition - lib

ANALYSIS USING R 171R> avg predictions 0.5, "glaucoma",+ "normal"))R> predtab predtabpredictions glaucoma normalglaucoma 77 16normal 21 82Thus, an honest estimate of the probability of a glaucoma prediction whenthe patient is actually suffering from glaucoma isR> round(predtab[1,1] / colSums(predtab)[1] * 100)glaucoma79per cent. ForR> round(predtab[2,2] / colSums(predtab)[2] * 100)normal84per cent of normal eyes, the ensemble does not predict a glaucomateous damage.Although we are mainly interested in a predictor, i.e., a black box machinefor predicting glaucoma is our main focus, the nature of the black box mightbe interesting as well. From the classification tree analysis shown above weexpect to see a relationship between the volume above the reference plane(varg) and the estimated conditional probability of suffering from glaucoma.A graphical approach is sufficient here and we simply plot the observed valuesof varg against the averages of the estimated glaucoma probability (such plotshave been used by Breiman, 2001b, Garczarek and Weihs, 2003, for example).In addition, we construct such a plot for another covariate as well, namelyvari, the volume above the reference plane measured in the inferior part ofthe optic nerve head only. Figure 9.5 shows that the initial split of 0.209mm 3for varg (see Figure 9.4) corresponds to the ensemble predictions rather well.The bagging procedure is a special case of a more general approach calledrandom forest (Breiman, 2001a). The package randomForest (Breiman et al.,2009) can be used to compute such ensembles viaR> library("randomForest")R> rf table(predict(rf), GlaucomaM$Class)glaucoma normalglaucoma 80 12normal 18 86© 2010 by Taylor and Francis Group, LLC