An Introduction to Recursive Partitioning Using the ... - Mayo Clinic

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7 Regression 28 7.1 Denition : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 28 7.2 Example: Consumer Report Auto data (cont.) : : : : : : : : : : : : 29 7.3 Example: Stage C prostate cancer (anova method) : : : : : : : : : : 33 8 Poisson regression 35 8.1 Denition : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 35 8.2 Improving the method : : : : : : : : : : : : : : : : : : : : : : : : : : 36 8.3 Example: solder data : : : : : : : : : : : : : : : : : : : : : : : : : : : 37 8.4 Example: Stage C prostate cancer (survival method) : : : : : : : : 41 9 Plotting options 46 10 Other functions 49 11 Relation to other programs 50 11.1 CART : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 50 11.2 Tree : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 51 12 Source 52 2
24 patients revived / 144 not revived H HHHHHHHH X 1 =1 22 / 13 H HHHH X 1 =2, 3 or 4 2 / 131 H HHHH X 2 =1 20/5 X 2 =2 or 3 2/8 X 3 =1 2/31 X 3 =2 or 3 0 / 100 Figure 1: Revival data 1 Introduction This document is an update of a technical report written several years ago at Stanford [5], and is intended to give a short overview of the methods found in the rpart routines, which implement many of the ideas found in the CART (Classication and Regression Trees) book and programs of Breiman, Friedman, Olshen and Stone [1]. Because CART is the trademarked name of a particular software implementation of these ideas, and tree has been used for the S-plus routines of Clark and Pregibon[2] a dierent acronym | Recursive PARTitioning or rpart | was chosen. The rpart programs build classication or regression models of a very general structure using a two stage procedure; the resulting models can be represented as binary trees. An example is some preliminary data gathered at Stanford on revival of cardiac arrest patients by paramedics. The goal is to predict which patients are revivable in the eld on the basis of fourteen variables known at or near the time of paramedic arrival, e.g., sex, age, time from arrest to rst care, etc. Since some patients who are not revived on site are later successfully resuscitated at the hospital, early identication of these \recalcitrant" cases is of considerable clinical interest. The resultant model separated the patients into four groups as shown in gure 1, where X 1 = initial heart rhythm 1= VF/VT, 2=EMD, 3=Asystole, 4=Other X 2 = initial response to debrillation 3
Page 1: An Introduction to Recursive Partit
Page 5 and 6: (x) (A) True class of an observatio
Page 7 and 8: Impurity 0.0 0.2 0.4 0.6 Gini crite
Page 9 and 10: in which case ~ i = iL P i j jL j
Page 11 and 12: 2) grade2.5 85 40 Prog ( 0.4706 0.5
Page 13 and 14: 4.2 Cross-validation Cross-validati
Page 15 and 16: x.7>0.5 | x.3>0.5 x.4
Page 17 and 18: so and seriously overts the data. I
Page 19 and 20: Variables actually used in tree con
Page 21 and 22: formula: the model formula, as in l
Page 23 and 24: Country:dghij | Country:dghij | Muc
Page 25 and 26: probabilities: 0.3103 0.2069 0.3966
Page 27 and 28: parms=list(prior=c(.65,.35))) > fit
Page 29 and 30: The prediction error for a new obse
Page 31 and 32: The rst split on displacement parti
Page 33 and 34: R-square 0.0 0.2 0.4 0.6 0.8 1.0
Page 35 and 36: 7) g2>13.2 45 10.580 0.6222 14) g2>
Page 37 and 38: One might expect this phenomenon to
Page 39 and 40: Call: rpart(formula = skips ~ Openi
Page 41 and 42: The use.n=T option species that num
Page 43 and 44: grade
Page 45 and 46: Prob Progression 0.0 0.2 0.4 0.6 0.
Page 47 and 48: grade11.845 No (20/11) Prog (3/6) N
Page 49 and 50: Endpoint = progstat No | (92/54) gr
Page 51 and 52: 11.2 Tree The user interface to rpa

An Introduction to Recursive Partitioning Using the ... - Mayo Clinic

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