4 MAKING S COMPOSE LAT
E
XTABLES
The EXAMPLE Study
Protocolxyz–001
February 4, 2003
Proportion
0.0
0.2
0.4
0.6
0.8
1.0
l
l
l
l
l
l
c
6
2
=5.33,  P = 0.502
c
2
2
=2.38,  P = 0.304
c
1
2
=0.02,  P = 0.885
1  
2  
3  
4  
female  
Histologic Stage
Ludwig Criteria  
sex  
spiders  
l
l
l
l
l
l
Proportions Stratified by drug
l
l
D−penicillamine
placebo
not randomized
Figure 6:
Proportions of patients in various categories of baseline variables, strat-
ified by drug. Pearson χ
2
test results are given.
31
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4 MAKING S COMPOSE LAT
E
XTABLES
The EXAMPLE Study
Protocolxyz–001
February 4, 2003
Serum Bilirubin , 
mg
dl
0
5
10
15
20
D−penicillamine 
placebo 
not randomized 
l
l
l
F
2, 415
=0.03,  P = 0.97
Albumin , 
gm
dl
2.5
3.0
3.5
4.0
D−penicillamine 
placebo 
not randomized 
l
l
l
F
2, 415
=2.1,  P =0.12
Prothrombin Time , 
sec.
10
11
12
13
D−penicillamine 
placebo 
not randomized 
l
l
l
F
2, 413
=0.23,  P = 0.8
Age
30
40
50
60
70
D−penicillamine 
placebo 
not randomized 
l
l
l
F
2, 415
=6.1,  P = 0.0024
Figure 7:
Box-percentile plots for continuous baseline variables in prostate cancer
trial. 0.90, 0.75, 0.50, and0.25 coverage intervals are shown. The solid circle depicts
the mean and the vertical line the median. Kruskal-Wallis tests are also shown.
32
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4 MAKING S COMPOSE LAT
E
XTABLES
The EXAMPLE Study
Protocolxyz–001
February 4, 2003
attach(prostate)
stage ← factor(stage, 3:4, c("Stage 3","Stage 4"))
s6 ← summary(stage ∼ rx + age + wt + pf + hx + sbp + dbp + ekg +
hg + sz + sg + ap + bm,
method=’reverse’, overall=TRUE, test=TRUE)
options(digits=2)
w ← latex(s6, size=’smaller[3]’, outer.size=’smaller’, Nsize=’smaller’,
long=TRUE, prmsd=TRUE, msdsize=’smaller’,
middle.bold=TRUE, ctable=TRUE)
#Table10
#smaller :from relsize LaTeX style
#long=TRUE :put first category on a row by itself
#prmsd=TRUE:print means and S.D.
setpdf(f6a, h=7)
plot(s6, which=’categorical’, cex=.8)
#Figure8
Key(-.02, 1)
dev.off()
setpdf(f6b, h=7)
plot(s6, which=’continuous’)
#Figure9
dev.off()
#-----------------------------------------------------------------------
#Final examples usecross-classifications on possibly more than one
#independent variable. Thesummary function with method=’cross’ produces
#a data frame containing the cross-classifications. This data frameis
#suitable for multi-panel trellis displays.
bone ← factor(bm, 0:1, c("no mets","bone mets"))
s7 ← summary(ap>1 ∼ sz + bone, method=’cross’)
options(digits=3)
print(s7, twoway=F)
s7
#sameas print(s7)
w ← latex(s7)
#Makes7.tex for Figure11
33
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4 MAKING S COMPOSE LAT
E
XTABLES
The EXAMPLE Study
Protocolxyz–001
February 4, 2003
library(lattice)
#S-Plus: trellis (automatically attached)
setpdf(f7, h=6, w=6, trellis=T)
#Figure10
Dotplot(sz ∼ S | bone, data=s7,
#s7 is name of summary stats
xlab="Fraction ap>1", ylab="Quartile of Tumor Size")
#Dotplot is Hmiscversion of dotplot in lattice (S-Plus trellis)
dev.off()
summary(age ∼ stage, method=’cross’)
summary(age ∼ stage, fun=quantile, method=’cross’)
summary(age ∼ stage, fun=function(x) c(Mean=mean(x), Median=median(x)),
method=’cross’)
summary(cbind(age,ap) ∼ stage + bone,
fun=function(y) apply(y, 2, quantile, c(.25,.75)),
method=’cross’)
options(digits=2)
summary(log(ap) ∼ sz + bone,
fun=function(y) c(Mean=mean(y), quantile(y)),
method=’cross’)
34
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Table10:DescriptiveStatisticsbystage
N
Stage3
Stage4
Combined
TestStatistic
N=289
N=213
N=502
rx
502
2χ3
placebo
26%(74)
25%(53)
25%(127)
0.2mgestrogen
25%(73)
24%(51)
25%(124)
1.0mgestrogen
25%(71)
26%(55)
25%(126)
5.0mgestrogen
25%(71)
25%(54)
25%(125)
AgeinYears
501
70.073.076.0(71.8±6.7)
69.073.076.0
(71.0±7.6)
70.073.076.0(71.5±7.1)
2F1,499=0.2,P=0.657
WeightIndex=wt(kg)-ht(cm)+200
500
9199109(100±13)
8997105(97±14)
9098107
(99±13)
2F1,498=5.4,P=0.021
pf
502
2χ3
normalactivity
93%(268)
85%(182)
90%(450)
inbed<50%daytime
6%(18)
9%(19)
7%(37)
inbed>50%daytime
1%(3)
5%(10)
3%(13)
confinedtobed
0%(0)
1%(2)
0%(2)
HistoryofCardiovascularDisease
502
46%(134)
37%(79)
42%(213)
2χ1
SystolicBloodPressure/10
502
13.014.016.0(14.4±2.6)
13.014.016.0
(14.3±2.2)
13.014.016.0(14.4±2.4)
2F1,500=0.01,P=0.907
DiastolicBloodPressure/10
502
7.08.09.0
(8.2±1.6)
7.08.09.0
(8.1±1.3)
7.08.09.0(8.1±1.5)
2F1,500=0.43,P=0.511
ekg
494
2χ6
normal
35%(98)
33%(70)
34%(168)
benign
5%(14)
4%(9)
5%(23)
rhythmicdisturb&electrolytech
8%(22)
14%(29)
10%(51)
heartblockorconductiondef
6%(17)
4%(9)
5%(26)
heartstrain
30%(85)
31%(65)
30%(150)
oldMI
17%(47)
13%(28)
15%(75)
recentMI
0%(1)
0%(0)
0%(1)
SerumHemoglobin
g/100ml
502
12.513.814.9(13.7±1.8)
11.813.414.6
(13.1±2.1)
12.313.714.7(13.4±2.0)
2F1,500=11,P<0.001
SizeofPrimaryTumor
2cm
497
4816(12±11)
71726
(18±13)
51121(15±12)
2F1,495=39,P<0.001
CombinedIndexofStageandHist.Grade
491
8.09.09.0
(9.1±1.3)
11.012.013.0
(12.0±1.5)
9.010.011.0
(10.3±2.0)
2F1,489=605,P<0.001
SerumProstaticAcidPhosphatase
502
0.400.500.70
(0.66±1.75)
1.604.2020.00
(27.80±93.29)
0.500.702.97
(12.18±62.17)
2F1,500=802,P<0.001
BoneMetastases
502
0%(1)
38%(81)
16%(82)
2χ1
¯abcrepresentthelowerquartilea,themedianb,andtheupperquartilecforcontinuousvariables.x±srepresentsX±1SD.Nisthenumberof
1non–missingvalues.Numbersafterpercentsarefrequencies.Testsused:Pearsontest;Wilcoxontest
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4 MAKING S COMPOSE LAT
E
XTABLES
The EXAMPLE Study
Protocolxyz–001
February 4, 2003
Proportion
0.0
0.2
0.4
0.6
0.8
1.0
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
c
3
2=0.22,  P=0.97
c
3
2=11,  P=0.012
c
1
2=4.3,  P=0.038
c
6
2=6.7,  P=0.35
c
1
2=127,  P<0.001
placebo  
0.2 mg estrogen  
1.0 mg estrogen  
5.0 mg estrogen  
normal activity  
in bed < 50% daytime  
in bed > 50% daytime  
confined to bed  
normal  
benign  
rhythmic disturb & electrolyte ch  
heart block or conduction def  
heart strain  
old MI  
recent MI  
rx  
pf  
History of Cardiovascular Disease  
ekg  
Bone Metastases  
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
Proportions Stratified by stage
l
l
Stage 3
Stage 4
Combined
Figure 8:
Distribution of categorical baseline variables in prostate cancer trial
36
4 MAKING S COMPOSE LAT
E
XTABLES
The EXAMPLE Study
Protocolxyz–001
February 4, 2003
Age in Years
55
60
65
70
75
80
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 499
=0.2,  P=0.66
Weight Index = wt(kg)−ht(cm)+200
80
90
100
110
120
130
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 498
=5.4,  P=0.021
Systolic Blood Pressure/10
10
12
14
16
18
20
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 500
=0.01,  P=0.9
Diastolic Blood Pressure/10
6
7
8
9
10
11
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 500
=0.43,  P=0.51
Serum Hemoglobin , 
g
100ml
10
12
14
16
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 500
=11,  P<0.001
Size of Primary Tumor , 
cm
2
0
10
20
30
40
50
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 495
=39,  P<0.001
Combined Index of Stage and Hist. Grade
6
8
10
12
14
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 489
=605,  P<0.001
Serum Prostatic Acid Phosphatase
0
50
100
150
200
250
[
[
[
Stage 3  
Stage 4  
Combined  
l
l
l
]
]
]
F
1, 500
=802,  P<0.001
Figure 9:
Quartiles of continuous variables in prostate cancer trial. x–axes are
scaled to the lowest 0.025 and highest 0.975 quantiles over all groups for each
variable.
37
5 HANDLING SPECIAL VARIABLES
4.3 Data Displays from Cross–Classifying Variables
The final examples use cross–classification on possibly more than one inde-
pendent variable. The summary function with
method=’cross’
produces a
data frame containing the cross–classifications. This data frame is suitable
for multi-panel trellis displays although if marginal statistics are not needed,
the Hmisc
summarize
function is better. The first example in this series was
LAT
E
X’ed to create Table11 (the code is listed above).
Table 11: Fraction of ap > 1 by sz, bone
Size of Primary Tumor
cm
2
no mets
bone mets
Total
N
ap > 1
N
ap > 1
N
ap > 1
[0,5)
105
0.248
5
0.8
110
0.273
[5,11)
119
0.21
17
0.765
136
0.279
[11,21)
103
0.301
19
0.947
122
0.402
[21,69]
88
0.5
41
0.902
129
0.628
Missing
5
0.4
0
5
0.4
Total
420
0.305
82
0.878
502
0.398
There is no
plot
method for
method=’cross’
tables, but you can use Trellis
graphics on the data frame that is created by
summary
(see code above). For
thispurpose, the
Hmiscsummarize
function might be better than
summary.formula
for producing the needed aggregated data.
5 Handling Special Variables
5.1 Multiple Choice Variables
Clinical reports frequuently must summarize “checklist” or multiple–choice
variables. Such variables are typically listed on a case report form using one
of two methods:
1. Specify up to three primary presenting symptoms:
38
5 HANDLING SPECIAL VARIABLES
Fraction ap>1
Quartile of Tumor Size
l
l
l
l
l
l
[ 0, 6)
[ 6,12)
[12,22)
[22,69]
NA
ALL
0.2
0.4
0.6
0.8
no mets
l
l
l
l
l
bone mets
l
l
l
l
l
l
ALL
Figure 10:
Proportion of patients with acid phosphatase exceeding 1.0, cross–
classified by tumor size and bone metastasis
39
5 HANDLING SPECIAL VARIABLES
_________ ________ ________
Here the respondent writes in up to three symptom codes from a list
of perhaps 15 integer codes defined below the question.
2. Check symptoms that are present:
headache
__
stomach ache __
hangnail __
back pain __
neck ache
__
wheezing __
When such data are processed, either a series of three categorical variables
or 6 binary variables is created. In what follows we assume that the binary
variables are coded as numeric 0/1 or as character variables with values
(ignoring case) of
’yes’
and
’present’
denoting a positive response. In
composing a report, we usually want to consider all of these component
variables under the umbrella of
’Presenting Symptoms’
.If using presenting
symptoms as stratification (independent) variables, we will want to know an
outcome statistic computed separately for those subjects having headache,
those having stomach ache, etc. These categories will overlap for some sub-
jects. When summarizing presenting symptoms stratified by treatment, we
will want to know the proportion of subjects in each treatment group having
headache, the proportion having stomach ache, etc., with the proportions
summing to > 1.0 if any subject had more than one symptom.
The Hmisc
summary.formula
function can handle multiple choice / checklist
variables after they are combinedintoa matrix. The Hmisc
mChoice
function
will take as input a series of categorical vector variables (using the first input
format above), and make a matrix with the number of columns equal to the
number of choices that were actually selected in the data
7
. This new matrix
consists of logical
T/F
values. You can also give
summary.formula
amatrix
you create, if using input format two above. The elements of this matrix
need to be numeric with values 0 and 1, logical
F/T
,or character with values
(ignoring case) of
’yes’
or
’present’
.
Here is an example of the use of
mChoice
from its help file.
> options(digits=3)
> set.seed(173)
7
There is also an option tocreate a column for
’none’
for subjects for whom no choices
were selected. The input variables need not have the same levels. A master list of cate-
gories is constructed by findingalluniquecategories in the levels of all variables combined,
preserving the order of levels for the factor variables.
40
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