Bonnie LaFleur
Department of Biostatistics bonnie.lafleur@vanderbilt.edu

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Miscellaneous review of graphics and data collection/display.
Paper 1:
Enhanced tumor formation in cyclin D1 x transforming growth factor beta1 double transgenic mice with characterization by magnetic resonance imaging.
Cancer Res. 2004 Feb 15;64(4):1315-22.
Paper 2:
Neuroblastomas of infancy exhibit a characteristic ganglioside pattern. Cancer 2001 Feb. 15;
91(4): 785-793.
Paper 3:
MeCP2 mutations in children with and without the phenotype of Rett syndrome. Neurology 2001;
56: 1486-1495 .

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Useful for counts or proportions, not for means
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Need to make sure that the standard error, if shown, is the correct standard error for proportions, and whether or not standard error or standard deviation is what you want to show.

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Percent of type 1 in each group is 25,
27.4, 73
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What is the standard error?
By definition the standard error is a way to express how close to the real value we are getting using a random sample instead of the whole population.
100
90
80
70
30
20
10
0
60
50
40
Group Group Group
1 2 3
Type 1
Type 2

se
 p ( 1
 p )
N
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Can see that this is dependent on N
What does this mean for our example?

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For our example (20.4) we calculate the standard error for two different sample sizes se ( p )

( 0 .
204 )( 0 .
796 ) 4

0 .
201

20 .
1 %
 se ( p )

( 0 .
204 )( 0 .
796 ) / 20

0 .
090

9 %
So, our estimate of the true percentage has lower sampling fluctuation with higher sample sizes

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The main use of standard errors, from a statistical sense, is to calculate 95% confidence intervals for our estimate: p ± 1.96(se)
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For n=4: (-19%, 60%)
For n=20: (3%, 38%)

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Bar charts should be used for proportions
(or percentages) or counts … not means
Correct standard error bars need to be shown, if at all (show standard deviation instead),
MUCH more important to include sample sizes with bar charts than either standard error or standard deviation, since once p and the sample size are given the standard deviation and/or standard error are easily calculated.

N=568 N=574 N=522
NIH Sponsered Human Studies
Non-Gender Specific
Non-Gender Specific Including Women
Analyzed by Gender
N=568
1.0
0.8
0.6
0.4
0.2
0.0
1993 1995
YEAR
1997 1998

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Dot here is the median (can also include the mean as a bar)
Ends of the “ box ” are the 1 st and 3 rd quartiles
“ hinges ” are the interquartile range,
1.5 x quartiles (never exceed the data)

Plots to display multiple events over time

Data: Things to avoid when creating a dataset to be used in statistical packages
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Character variables must be in the same case and consistent
Don ’ t mix characters with data that should be numeric
Date formats should be consistent
No summary computations in middle of spreadsheet
Differentiate between missing values and
“ zero ’ s ” , “ below detection ” , etc.

Date of Blood CD4 CD4 % HIV VL
1/14/1998
10/16/1998
7/15/1997
10/14/1997
3/3/1998
12/14/1998
8/17/1999
2/7/2000
1/23/1997
6/16/1997
1/20/1998
2/3/1998
9/15/1998
5/16/2000
11/25/1997
4/28/1998
11/24/1998
4/14/1999
1/10/2000
3/26/1997
10-6-98 (lab date)
431
2
627
589
430
1736
1061
897
841
842
0
759
829
829
28 <10000
950
942
1966
1997
920
1462 not CHIP Patient
28
27
39
42
34
35
<20
20670
86569
<400
20-50
<20
32
25
53
42
32
39
47
0
31.9
36
36
133585
<400
452
452
4471
2885
6400
40500
26,310
72,617
<20
37
1
1120
315703 (9-16-98)
HAART start date VZV ser
CMV ser
VZV
RCF
03/03/98
03/03/98
03/03/98
03/03/98
03/03/98
03/04/98
9/15/98
9/15/98
9/15/98
9/15/98 no therapy
12/21/98
12/21/98
12/21/98
12/21/98
12/21/99 no HAART pos pos pos pos.
pos pos pos pos pos pos pos pos pos pos pos.
pos.
pos pos pos pos neg neg.
neg.
neg.
neg pos pos pos pos pos pos pos pos pos pos pos
5.4
<1
>8
3.7
<1
ND
6.2
<1
>8
5.5
>8
>8
1.3
<1
3.8
ND
6.2
<1
5.18
>8
CMV
RCF
<1
<1
ND
ND
ND
ND
ND
ND
ND
ND
ND
<1
ND
ND
<1
1.5
1
<1
<1
1.85

Mean vs. DTaP
Hep B
7
8
5
6
3
4
1
2
9
10
11 birth PT
14
8
5
6
18
9
16
35
5
49
63
6 M PT
34
17
29
33
8
16
32
11
18
14
4
7 M PT
30
15
52
68
27
14
68
10
15
19
6
12
13
14
DTaP
7
8
5
6
3
4
1
2
9
10
11 birth PT
11
4
7
9
9
20
9
9
5
10
17
6 M PT
4
3
2
4
7
17
27
29
8
7
48
8
11
30
11
10
29
7 M PT
64
25
9
10
57
10
23
31
8
32
32
4
9
27
20.72727
0.069793
19.63636
0.665387
29.45455
0.552718
0.142732
8.5
17.57143
24.35714

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Basic question was whether cyclin
D1/TGF 1 double transgenic mice are different from cyclin D1 single transgenic mice on a variety of outcomes:
•
Tumor incidence
•
•
•
Tumor multiplicity
Tumor burden
Cellular and molecular changes

The data were categorical, plus there were some zero (and very small) cell counts so we had to use nonparametric tests.

block age
1231
1243
1239
1247
1259
1024
1251
1034
1235
1026
1263
1223
1019
1015
1017
1028
1='Wild Type'
2='Alb-TGFB'
3='LFABP-Cyclin D1'
4='Double Transgenic'
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6 type score cytomegaly nuclear DPM nodularity lesions
1 0 0 0 0 0
1
1
1
2
0
1
0
0
0
0
1
1
3
3
2
3
2
2
1
2
4
4
3
4
4
1
2
4
1
1
1
3
1
6
6
3
4
6
0
1
2
1
0
1
1
0
2
1
1
1
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
2
3
1
3
2

type cytomegaly
Frequency ‚
Percent ‚
Row Pct ‚
Col Pct ‚ 0‚ 1‚ 2‚ Total
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
Wild Type ‚ 2 ‚ 2 ‚ 0 ‚ 4
‚ 12.50 ‚ 12.50 ‚ 0.00 ‚ 25.00
‚ 50.00 ‚ 50.00 ‚ 0.00 ‚
‚ 40.00 ‚ 25.00 ‚ 0.00 ‚
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
Alb-TGFB ‚ 2 ‚ 1 ‚ 1 ‚ 4
‚ 12.50 ‚ 6.25 ‚ 6.25 ‚ 25.00
‚ 50.00 ‚ 25.00 ‚ 25.00 ‚
‚ 40.00 ‚ 12.50 ‚ 33.33 ‚
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
LFABP-Cyclin D1 ‚ 1 ‚ 3 ‚ 0 ‚ 4
‚ 6.25 ‚ 18.75 ‚ 0.00 ‚ 25.00
‚ 25.00 ‚ 75.00 ‚ 0.00 ‚
‚ 20.00 ‚ 37.50 ‚ 0.00 ‚
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
Double Transgeni ‚ 0 ‚ 2 ‚ 2 ‚ 4 c ‚ 0.00 ‚ 12.50 ‚ 12.50 ‚ 25.00
‚ 0.00 ‚ 50.00 ‚ 50.00 ‚
‚ 0.00 ‚ 25.00 ‚ 66.67 ‚
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ
Total 5 8 3 16
31.25 50.00 18.75 100.00

Statistics for Table of type by cytomegaly
Statistic DF Value Prob
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Chi-Square 6 6.8667 0.3334
Likelihood Ratio Chi-Square 6 8.8589 0.1817
Mantel-Haenszel Chi-Square 1 3.4839 0.0620
Phi Coefficient 0.6551
Contingency Coefficient 0.5480
Cramer's V 0.4632
WARNING: 100% of the cells have expected counts less
than 5. Chi-Square may not be a valid test.
Statistics for Table of type by cytomegaly
Fisher's Exact Test
______________________________________
Table Probability (P) 0.0024
Pr <= P 0.4390

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First, we graphically examined the data
Note that the times are not equal for the two groups (or for any two samples)
We grouped into time intervals for the analysis
•
•
•
•
0-20 days
21-40 days
41-60 days
> 60 days

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
First, we graphically examined the data
Note that the times are not equal for the two groups (or for any two samples)
We grouped into time intervals for the analysis
•
•
•
•
0-20 days
21-40 days
41-60 days
> 60 days

Obs vol mouse tumno group day
1 993.65 B119 1 2 1
2 1017.52 B119 2 2 1
3 921.01 B119 1 2 11
4 878.19 B119 2 2 11
5 131.29 B120 1 2 1
6 248.32 B120 1 2 22
7 312.06 B120 1 2 37
8 1611.53 BH130 1 2 1
9 1447.34 BH130 1 2 16
10 1474.50 BH130 2 2 16
11 685.10 BH130 1 2 35
12 59.63 F4410 1 2 1
13 185.63 F4410 1 2 59
14 102.95 F4410 2 2 59
15 348.20 F4410 3 2 59
16 32.50 F4411 1 2 1
17 52.35 F4411 2 2 1
18 322.24 F4411 1 2 43
19 279.02 F4411 2 2 43
20 108.44 F446 1 2 1
21 14.80 F446 2 2 1
22 52.38 F446 1 2 43
23 363.50 F446 1 2 101
24 490.00 F446 2 2 101

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First, we graphically examined the data
Note that the times are not equal for the two groups (or for any two samples)
We grouped into time intervals for the analysis
•
•
•
•
0-20 days
21-40 days
41-60 days
> 60 days

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We then used an analysis that accounts for repeated measures on a single mouse, and looked at the difference over time
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F daygp 3 12 0.42 0.7422
group 1 7 1.36 0.2812
group*daygp 3 39 0.96 0.4233

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There is no difference in genotype and cytomegaly (though if we use a sum of all the tumor histopathology variable scores we do see a difference between the double transgenic group and all the other genotypes).
There was no difference in tumor volume between the double transgenic and the
Cyclin D1 genotype.

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In typical embryonic development ganglioside expression shifts from the fetal b pathway to the adult a pathway.
Neuroblastomas in infants is different
(biologically and clinically) than those found in older children
The main question is whether the ganglioside pathway is different between these two types of neuroblastomas.

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68 confirmed neuroblastoma samples that were either diagnosed by urinary HVA and VMA at either 3 weeks or 6 months of age (n=25), or presented clinically during study period (n=43). Information was collected on age at sample, time until disease progression, stage, and some other clinical information that was not discussed in this paper.

First, lets look at the plot of the data that looks at the
% of b pathway gangliosides

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We probably could have used a ttest (comparing two normal means) or analysis of variance (comparing more than two normal means)
But, there was some indication that the distributions of these % b gangliosides was non-normal, so we decided to use the Wilcoxon-rank sum test.

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Survival analysis is used to compare
“ time-to-event ” between groups. In this case we are looking at time until some clinical adverse event.
We need to use specialized statistic tests because we have “ censoring ” in the data.
Censoring is when you have incomplete data due to loss-to-follow-up or no event up until the end of study.

> 60% B Predominance
< 60 % B Predominance
0 10 20 30 40 50 60
Time (months)
70 80 90 100 110 120

Test of Equality over Strata
Pr >
Test Chi-Square DF Chi-Square
Log-Rank 7.4102 1 0.0065
Wilcoxon 6.1856 1 0.0129

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The distribution in % b pathway ganglioside production is different in children ≥ 1 year of age that present clinically compared with group that is screened (3 weeks or 6 months of age)
This fit their paradigm that neuroblastomas in older children are different than younger children

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There is a difference in the event free survival distributions between those patients with ≥ 60% b pathway gangliosides and those with
< 60 % b pathway gangliosides.
The group with ≥ 60% b pathway gangliosides had longer event free survival.

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This study wanted to examine the association between MeCP2 gene mutations and Rett syndrome (a neurodevelopmental disorder)
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More specifically, whether a particular pattern of mutation, X-inactivation, along with clinical features differ among mutation types

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Here we are looking at 5 mutations
•
•
•
•
•
MBD nonsense
Nonsense between MBD and TRD
TRD nonsense
TRD missense
C-terminal deletions
And scores of 5 clinical parameters (head growth, seizures, scoliosis and motor skills/ability to walk)
The scores were all measured on an ordinal scale

REDUCED GENOTYPE and PHENOTYPE DATA
Obs MUTATION HV MOTOR SIEZURE SCOL HCIRC TOT AGE SUBJECT
1 1 3 3 2.5 0 3.0 11.5 6.0 1
2 1 1 2 0.0 1 3.0 7.0 10.0 2
3 1 0 3 2.0 1 3.0 9.0 18.0 3
4 1 1 3 0.0 0 3.0 7.0 3.0 4
5 1 2 1 2.0 2 3.0 10.0 19.0 5
6 1 0 1 0.0 0 3.0 4.0 6.0 6
7 1 2 3 0.0 0 3.0 8.0 2.0 7
8 1 0 2 0.0 0 3.0 5.0 6.0 8
9 1 3 3 1.0 3 3.0 13.0 8.0 9
10 1 3 0 0.0 0 3.0 6.0 9.0 10
11 1 2 2 3.0 0 2.0 9.0 8.0 11
12 1 0 3 1.0 1 3.0 8.0 6.0 12
13 1 0 3 0.0 3 1.0 7.0 21.0 13
14 1 3 1 0.0 0 3.0 7.0 6.0 14
15 1 0 2 0.0 2 2.0 6.0 13.0 15
16 1 0 3 2.5 0 3.0 8.5 4.0 16
17 1 2 3 1.0 3 3.0 12.0 9.0 17
18 1 2 2 1.0 2 3.0 10.0 9.0 18
19 2 0 3 1.0 2 3.0 9.0 34.0 19
20 2 2 2 1.0 1 3.0 9.0 6.0 20
21 2 2 3 2.0 1 3.0 11.0 8.0 21
22 2 3 3 1.0 0 3.0 10.0 4.0 22
23 2 3 3 1.0 2 3.0 12.0 4.0 23
24 3 1 0 0.0 0 1.5 2.5 5.0 24

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Since the severity scores were ordinal, we viewed them as continuous (and normally distributed)
We used ANOVA and looked at differences between the mean scores for each of the mutation groups

Analysis Of Parameter Estimates
Standard Wald 95% Confidence Chi-
Parameter DF Estimate Error Limits Square Pr > ChiSq
Intercept 1 1.4000 0.3298 0.7536 2.0464 18.02 <.0001
MUTATION 1 1 1.3778 0.3728 0.6470 2.1085 13.66 0.0002
MUTATION 2 1 1.6000 0.4664 0.6858 2.5142 11.77 0.0006
MUTATION 3 1 0.5286 0.4318 -0.3178 1.3750 1.50 0.2210
MUTATION 4 1 0.2250 0.4947 -0.7447 1.1947 0.21 0.6493
MUTATION 5 0 0.0000 0.0000 0.0000 0.0000 . .
Scale 1 0.7375 0.0835 0.5907 0.9208
NOTE: The scale parameter was estimated by maximum likelihood.
LR Statistics For Type 3 Analysis
Chi-
Source DF Square Pr > ChiSq
MUTATION 4 18.94 0.0008

Contrast Results
Chi-
Contrast DF Square Pr > ChiSq Type
1 vs 2 1 0.35 0.5520 LR
1 vs 3 1 6.17 0.0130 LR
1 vs 4 1 7.27 0.0070 LR
1 vs 5 1 11.71 0.0006 LR
2 vs 3 1 5.72 0.0168 LR
2 vs 4 1 7.05 0.0079 LR
2 vs 5 1 10.28 0.0013 LR
3 vs 4 1 0.43 0.5125 LR
3 vs 5 1 1.47 0.2253 LR
4 vs 5 1 0.21 0.6497 LR

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Is a combination of analysis of variance and regression
The main aim is to see if the regression lines in two or more groups are different
In this study, we wanted to see if two of the mutations differed in their regression of clinical severity and X-inactivation (% of one allele active); can be stated as the covariance of mutations on the regression of clinical severity on X-inactivation.

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Is the straight line relationship between clinical score and severity the same for the two mutations (missense in MBD and nonsense between MBD and TRD versus
TRD missense and nonsense and Cterminal deletions)?
Do the clinical severity scores for the two mutations differ after adjusting for Xinactivation pattern?

Total Score by % X-Inactivation
10
9
8
7
6
5
14
13
12
11
2
1
0
4
3
40
P-value for intercepts < 0.0001
50 60
P-value for slope = 0.006
70
% X-INACTIVATION
80 90 Group 2
Group 1

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There was an a statistically significant difference in many of the mutations with respect to head circumference data as well as when a summary of all clinical features
There was a statistically significant difference in clinical severity score between the two mutation groups, as well as a difference in slopes between severity score and x-inactivation between the two mutation groups
Both of these findings confirmed, and described,
MeCP2 mutations causative in Rhett syndrome

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Suggested readings
•
Creating More Effective Graphs by
Naomi B. Robbins
•
Statistical Analysis and Data Display by
Heiberger and Holland
•
Introduction to Biostatistics by Bernard
Rosner