Design of Case-Control Studies of Longevity

1
Design of Case-Control Studies of Longevity

• J. Dai, L. Li, S. Kim, B. Kimball, S. M.
  Jazwinski, J. Arnold for the
• Georgia Centenarian Study

2
Georgia Centenarian Study Project 3 Preliminary
Model
Food Habit
Hemoglobin
Nutrition
Albumin
Handgrip
Blood Chemistry
DAFS
Functional Capacity/ Performance
Physical Exam
EPESE
PPME
Age
Subject Characteristics
Gender
OARS _ADL
Race
Self
Depression
Living
OARS _IADL
Functional Evaluation
Neuropsych Function
Proxy_GDS
Self_GDS
OARS _ADL
Proxy
OARS _IADL
SIB
FOME
COWAT
HANDTAP
SIMILA
BDS
MMSE
GDRS
Safety
3
Online Access to GCSDB

• http//qa.genetics.uga.edu
• Data release plan at Web site
• Reference Dai et al., Bioinformation 1 214-219
  (2006)
• Also find by googling Centenarian database.

4
Sample Size Problem for 2 x 2 x 2 Table

• What are the sample sizes needed to detect an
  association between longevity and single
  nucleotide polymorphisms (SNPs) in joint
  collaborations involving participants in the
  International Consortium of Centenarians?
• Subjects are stratified by race and age to
  examine gene by environment interactions.
• Subjects are scored for SNPs with two alleles
  denoted A and a.

5
SNP Data on Cases / Controls by Race
Centenarians
Young Controls
Ca
Am
Ca
Am
a
b
A
l
e
f
n
c
d
a
L - l
g
h
N - n
k
L - k
L
m
N - m
N
6
SNP Data on Cases / Controls by Race, Continued

• L and N are fixed in advance
• L Centenarians
• N Young Controls
• Ca Caucasian
• Am African-American
• A One allele in SNP
• a Other allele in SNP

7
Mode I
Centenarians
Young Controls
Ca
Am
Ca
Am
P1
P2
A
p
P5
P6
r
P3
P4
a
1 - p
P7
P8
1 - r
q
1 - q
1
s
1 - s
1
8
Odds Ratios (ORs) as Measures of Association with
SNPs
Association with race
r2 P5 P8P6 P7
r1 P1 P4P2 P3
Association with longevity
rC P1 P7P3 P5
rAM P2 P8P4 P6
9
Relations of Odds Ratios

• There are only two independent odds ratios
• r1 rCr2 rAM

10
Sample Size Problem for 2 x 2 x 2 Table

• Fix significance level, a
• Fix power, 1 - b
• Fix marginal frequencies p, q, r, s
• Fix odds ratios rA , rC
• Determine minimal sample size L and N for exact
  test.

11
Kinds of Associations

• Alleles with longevity and race
• Alleles with each other
• Genotypes with longevity and race
• Genotypes with each other

12
Exact Test of Association (LN 326)
13
SNP Data on Cases / Controls by Race for SNP 18
Exon 1 of LASS1
Centenarians
Young Controls
Ca
Am
Ca
Am
132
18
A
92
44
136
150
30
18
a
48
24
36
60
162
36
116
80
198
196
14
Probabilities on Cases / Controls by Race for
LASS1
Centenarians
Young Controls
Ca
Am
Ca
Am
.6667
.0909
A
.7576
.4694
.2245
.6939
.0909
.1515
a
.2424
.1224
.1837
.3061
.8182
.1818
1.00
.5918
.4082
1.00
15
SNP Data on Cases / Controls by Race for SNP 18
Exon 1 of LASS1
Centenarians
Young Controls
Ca
Am
Ca
Am
132
18
A
92
44
136
150
18
30
a
48
24
36
60
162
36
116
80
198
196
16
Expected on Cases / Controls by Race for SNP 18
in Exon 1 of LASS1
Centenarians
Young Controls
Ca
Am
Ca
Am
150
A
80.49
136
122.73
27.27
55.52
39.27
8.73
a
48
35.51
24.49
60
162
36
116
80
196
198
17
(O - E)2/E on Cases / Controls by Race for LASS1
Centenarians
Young Controls
Ca
Am
Ca
Am
.70
3.15
A
.2273
1.65
2.39
.2704
9.84
2.19
a
.7727
3.73
5.41
.7296
.8182
.1818
15.88
.5918
.4082
13.18
X2 15.88 13.18 29.06
18
Association for Exon 1 - LASS1 - SNP18

• X2 29.06
• df 2 because we lose 4 df from the margins
• Significance level 0.05
• C 5.99
• We conclude there is an association
• There is actually an association of A with
  longevity, although this requires more
  calculations.

19
Odds Ratios (ORs) as Measures of Association with
SNPs - SNP18
Association with race
r2 92364424
r1 132181830
3.14
4.4
Association with longevity
rC 132243092
rAM 18361844
1.15
0.82
20
Minimal L needed as ln rCA increases for SNP 17
21
Extrapolation to other studies

• Take the information on effect sizes on 15 SNPs
  in the GCS selected in part by such power
  calculations
• Extrapolate to other Centenarian studies in
  proposed collaborations to increase the power to
  detect effects, i.e., alleles on age.

22
Log odds used for power studies (L 99 N 100
GA)
23
Probabilities on Cases / Controls by Race for
LASS1 Promoter(-718) 16 GA
Centenarians
Young Controls
Ca
Am
Ca
Am
.1003
.0968
A
.1970
.1148
.2551
.1403
.1164
.6866
a
.8030
.5575
.1875
.7449
.7869
.2132
1.00
.6723
.3277
1.00
244
473
24
Probabilities on Cases / Controls by Race for
LASS1 Promoter(-718) 16 LA
Centenarians
Young Controls
Ca
Am
Ca
Am
.1247
.0723
A
.1970
.1827
.2551
.0724
.0741
.0733
.7289
a
.8030
.6716
.7449
.8536
.1464
1.00
.8543
1.00
.1457
280
597
25
Probabilities on Cases / Controls by Race for
LASS1 Promoter(-718) 16 JP/OK
Centenarians
Young Controls
Ja
Ok
Ja
Ok
.1069
.0901
A
.1970
.1736
.0815
.2551
.1034
.6996
a
.8030
.6597
.0852
.7449
.8065
.1935
1.00
.8333
.1667
1.00
310
600
26
Probabilities on Cases / Controls by Race for
LASS1 Promoter(-718) 16 KO/JP
Centenarians
Young Controls
Ko
Ja
Ko
Ja
.0187
.1783
A
.1970
.0385
.2166
.2551
.5029
.3001
a
.8030
.2922
.4527
.7449
.3188
.6812
1.00
.3307
.6693
1.00
747
367
27
Exact Power at least
28
Conclusion

• Current study sizes adequate to test for
  association in APOE, HRAS1, LASS1 SNPs 6, 10, and
  16.
• Association with race is the major confounding
  issue.
• Solving the sample size problem for the 2 x 2 x 2
  table can provide guidance in the choice of SNPs
  informative about ORs.