DATA SET1;
INFILE 'c:\courses\st557\sas\bpd.dat';
INPUT SEX 1 YOB 2-3 APGAR 4-5 GEST 6-8
BWT 9-12 AGSYM 13-14 AGVEN 15-17
INTUB 18-21 VENTL 22-25
LOWO2 26-30 MEDO2 31-34
HIO2 35-38 SURV 39 DSURV 40-44
RDS 45 BPDHI 46-47;
/* This program uses the TREEDISC
macro in SAS to apply a CHAID
algorithm to the BPD data. This
code is stored in the file
chaidbpd.sas
*/
/* First set some graphics options */
/* To print postscipt files in UNIX */
/*
goptions cback=white ctext=black
targetdevice=ps300 rotate=landscape;
*/
/* To print postscript files from Windows */
goptions cback=white ctext=black
device=WIN target=ps
rotate=landscape ;
IF BPDHI>20 THEN BPD=1; ELSE BPD=2;
LABEL YOB
APGAR
GEST
BWT
AGSYM
=
=
=
=
=
YEAR OF BIRTH
APGAR SCORE
GESTATIONAL AGE (WEEKSx10)
BIRTH WEIGHT (GRAMS)
AGE AT ONSET OF
RESPIRATORY SYMPTOMS (HRSx10)
AGVEN = AGE WHEN VENTILATORY
ASSISTANCE BEGAN (HRS)
INTUB = DURATION OF ENDOTRACHEAL
INTUBATION (HRS)
VENTL = DURATION OF ASSISTED
VENTILATION (HRS)
1228
1227
/* Establish formats for
classification variables */
LOWO2
MEDO2
HIO2
SURV
DSURV
=
=
=
=
=
EXPOSURE TO 22-39% OXYGEN (HRS)
EXPOSURE TO 40-79% OXYGEN (HRS)
EXPOSURE TO 80-100% OXYGEN (HRS)
SURVIVAL AS OF 5/1/1975
DURATION OF SURVIVAL AS
OF 5/1/75 (HRS)
RDS = SEVERITY OF RDS
BPDHI = BPD ASSESSMENT
BPD = BPD INDICATOR;
/* Retain only babies who lived at
least 72 hours */
PROC FORMAT; VALUE SEX 0 = 'FEMALE'
1 = 'MALE';
VALUE SURV 0 = 'DEAD'
1 = 'ALIVE';
VALUE RDS 0 = 'NONE'
1 = 'SLIGHT'
2 = 'MODERATE'
3 = 'SUBSTANTIAL'
4 = 'SEVERE'
5 = 'VERY SEVERE';
VALUE BPD 1 = 'YES'
2 = 'NO';
IF(DSURV > 72);
run;
1229
1230
/* Load in the xmacros file */
/* Draw the tree on one page */
%inc 'c:\courses\st557\sas\xmacro.sas';
%treedisc(intree=trd, draw=graphics);
/* Load in the TREEDISC macro */
/* Draw a larger tree on several
pages */
%inc 'c:\courses\st557\sas\treedisc.sas';
goptions cback=white ctext=black
device=WIN target=ps rotate=portrait;
/* Compute a
incidence
levels of
and other
%treedisc(intree=trd,
draw=graphics, pos=120 120);
tree for predicting BPD
from exposure to elevated
oxygen, use of ventilation,
explanatory variables*/
%treedisc(data=set1, depvar=bpd, nominal=rds:,
ordinal=ventl: lowo2: medo2: hio2:,
outtree=trd, options=noformat,
trace=long);
1231
All infants
BPD:78
no BPD:170
Med O2 < 157 hrs
BPD:21
no BPD:152
157
Summary:
H@HH
@@HHH
@@ HHHH
@@ HHHH
HH
@
Med O2 450
BPD:22
no BPD:18
Low O2 < 170 hrs
BPD:5
no BPD:14
@
High O2 > 90 hrs
BPD:3
no BPD:0
P@PPP
@@ PPPPP
PPPP
@
PPPP
@@
PPP
@
PP
High O2 35 hrs
BPD:2
no BPD:78
36
High O2 159
BPD:7
no BPD:64
1232
@@
@
Med O2 > 450 hrs
BPD:35
no BPD:0
Low O2 > 170 hrs
BPD:17
no BPD:4
@@
High O2 90 hrs
BPD:2
no BPD:14
Keep exposure to the medium O levels
below 450 hours
When exposure to the medium O levels is between 157 and 450 hours, keep
{ exposure to low O levels
below 170 hours
{ exposure to high O levels
below 90 hours
When exposure to the medium level of
oxygen is below 157 hours, keep exposure to high O levels below 160 hours
2
2
2
2
2
High O2 > 160 hrs
BPD:12
no BPD:10
1233
1234
The Algorithm:
Classication and Regression Trees
(Cart)
Brieman, et al. (1984),
Classicaiton and Regression
Trees, Wadsworth.
CART software sold by Salford Systems, CA.
Available in the SAS data mining package
Chambers and Hastie (1992), Statistical Models in S, (Chapter 9),
Wadsworth.
Tree( ) and related functions in Splus.
All cases
@
@
@@
@@
X7 18.3
1235
Deviance
@@
@
DevianceLeft
@@
X7 > 18.3
Build a larger tree than you really
need and prune it back
{ cross validation
{ validation sample
Can have
{ continuous variables
{ nominal (categorical) variabales
Missing data?
1236
For a discrete response (at the k-th
node):
I
Deviance = 2nk iX=1
Pik log(Pik )
Determination of a split:
@@
Binary Splits
@@
@
DevianceRight
Choose
(i) an explanatory variable
(ii) boundary (or cut point)
that maximizes the change in deviance
deviance = deviance
(devianceLeft + devianceRight)
1237
where Pik is the proportion of cases at
the k-th node in the i-th response category.
For a continuous response (at the k-th
node):
n
Deviance = jX=1k (yjk yk)2
1238
Stop splitting if
node deviance is less than some fraction
of root node deviance (say < 1%).
number of cases at the node is too
small (say < 10 cases).
Use mindev and minsize in
tree.control ( )
Prune the tree:
Crossvalidation
Validation sample
# Use the tree function in Splus to
# build a classification tree. This
# file is stored as bpdtree.ssc
#
#
#
#
#
#
#
Use the bpdsp3.dat data file which
does not have missing values. The tree
function in Splus cannot handle missing
values. The APGAR score variable was
not included because it contained too
many missing values. The tree is pruned
with the prune function in Splus
# Enter the data as a matrix
treec.dat <- matrix(scan("c:/courses/st557/splus/b
ncol=17,byrow=T)
# Select the columns to be used in the
# analysis and define row and column labels
ID<-treec.dat[,1]
1240
1239
# Create a data frame and a factor
treec.dat<-data.frame(treec.dat)
treec.dat$BPD<-as.factor(treec.dat$BPD)
# Compute the classification tree and put
# it in the file trees.out
treec.dat <- treec.dat[, c(2:12,15,17)]
dimnames(treec.dat)<-list(ID,c("Sex","Year",
"Gage","Bweight","AgeSYM","AgeVEN",
"Intub","Ventl","LowO2",
"MedO2","HiO2","RDS","BPD"))
ftree <- formula(factor(BPD)~Sex+Year+Gage+Bweight
AgeSYM+AgeVEN+Intub+Ventl+
LowO2+MedO2+HiO2+RDS)
trees.out<-tree(ftree,treec.dat)
# Print a summary description of the tree
summary(trees.out)
# Print a description of what happens at
# each node of the tree
print(trees.out)
1241
#
#
#
#
#
#
# Display the tree. Unix users should
# first use the motif( ) function to open
# a graphics window.
plot(trees.out)
text(trees.out)
Use crossvalidation provided by the
cv.tree function to determine how to
prune the tree. You should run this
several times, because different
random grouping of cases can yield
very different results in small samples
trees.cv <- cv.tree(trees.out, FUN=prune.tree)
plot(trees.cv)
# The following crossvalidation of the
# misclassification rates only works if
# the response is a factor.
trees.cv <- cv.tree(trees.out, FUN=prune.misclass)
plot(trees.cv)
# Plot misclassification rates for simple
# resubstitution. This is not a good way
# to decide how much to prune.
1242
tree.mis<-prune.misclass(trees.out)
plot(tree.mis)
# The resulting plot suggests that the tree
# should be pruned at about 6 nodes
# Display the pruned tree
treep.out <- prune.tree(tree = trees.out, best=6)
summary(treep.out)
plot(treep.out)
text(treep.out)
Description of the tree created for
the BPD data. Each line provides the
information for one node in the tree.
The information is presented in the
following order:
[1] node number
[2] decision rule for going left
at this node
[3] Number of sample cases that
reached this node
[4] value of the deviance
[5] average value for the response:
in this case it is the
proportion of babies with
BPD at this node
[6] An * denotes a terminal node
1243
node), split, n, deviance, yval
* denotes terminal node
5) HiO2>159.5 23 5.6520 0.56520
10) MedO2<71.5 17 4.1180 0.41180
20) Gage<342.5 10 2.4000 0.60000
40) Year<67.5 5 0.8000 0.80000 *
41) Year>67.5 5 1.2000 0.40000 *
21) Gage>342.5 7 0.8571 0.14290 *
11) MedO2>71.5 6 0.0000 1.00000 *
3) MedO2>183 60 7.6500 0.85000
6) Ventl<220.5 13 3.2310 0.46150
12) HiO2<26.5 8 0.8750 0.12500 *
13) HiO2>26.5 5 0.0000 1.00000 *
7) Ventl>220.5 47 1.9150 0.95740
14) Intub<430.5 14 1.7140 0.85710
28) Gage<330 5 1.2000 0.60000 *
29) Gage>330 9 0.0000 1.00000 *
15) Intub>430.5 33 0.0000 1.00000 *
1) root 242 52.5000 0.31820
2) MedO2<183 182 22.2900 0.14290
4) HiO2<159.5 159 11.9400 0.08176
8) LowO2<527.5 146 6.6640 0.04795
16) Ventl<146 106 0.0000 0.00000 *
17) Ventl>146 40 5.7750 0.17500
34) MedO2<158 35 3.5430 0.11430
68) Bweight<2239.5 28 0.9643 0.03571
136) Year<69.5 5 0.8000 0.20000 *
137) Year>69.5 23 0.0000 0.00000 *
69) Bweight>2239.5 7 1.7140 0.42860 *
35) MedO2>158 5 1.2000 0.60000 *
9) LowO2>527.5 13 3.2310 0.46150
18) Gage<305 6 0.0000 0.00000 *
19) Gage>305 7 0.8571 0.85710 *
1244
1245
100.0
19.0
15.0
8.5
7.9
6.7
5.7
3.3
LowO2<527.5
MedO2<71.5
0.12501.0000
Gage<342.5
Ventl<146
Gage<305 Year<67.5
1.0000
MedO2<158
Bweight<2239.5
0.80000.40000.1429
0.0000
Year<69.5
0.60000.00000.8571
0.20000.00000.4286
280
240
Ventl<220.5
HiO2<26.5 Gage<330
Intub<430.5
0.60001.00001.0000
220
HiO2<159.5
260
deviance
300
320
340
MedO2<183
|
5
10
15
size
1246
1247
-Inf
19.0
15.0
8.5
7.9
6.7
5.7
3.3
-Inf
42.0
2.3
2.0
1.3
1.0
0.0
-Inf
200
40
50
60
misclass
300
250
deviance
70
350
100.0
5
10
15
5
10
size
15
size
1248
42.0
2.3
2.0
1.3
1.0
0.0
1249
-Inf
60
HiO2<159.5
50
HiO2<45.5
1
LowO2<247
1
1
Ventl<146
0
40
misclass
70
MedO2<183
|
0
5
10
0
15
size
1250
1251
Summary
Do not exceed 160 hours of exposure to the high oxygen levels
Do not exceed 183 hours of exposure to the medium oxygen
levels
Do not exceed 528 hours of exposure to the lower oxygen levels
Do not ventilate for more than
146 hours
1252