Case-only Power Analysis
The discordance between the case-control sub-phenotype analysis and the case-only
analysis can be reconciled in terms of statistical power. To illustrate, we evaluated the
power under each analysis scenario using the genetic power calculator for the analysis
of discreet traits in case-control studies (pngu.mgh.harvard.edu/~purcell/gpc/cc2.html).
The following parameters were used in the two different analysis scenarios:
Parameter
Case-control
Case-only
Risk allele frequency (A)
0.08
0.129
Prevalence of lupus renal1
0.00003
0.00003
Genotype relative risk Aa
2.0
2.0
Genotype relative risk AA
3.0
3.0
D-prime
0.9
0.9
Marker allele frequency (B)
0.08
0.08
Number of cases
380
380
Control:case ratio
3
2
Type 1 error rate
0.05
0.05
Power
0.80
0.99
1Prevalence
of lupus renal estimated by: Prevalence of SLE in European Americans
(EA) = 0.0001; Prevalence of renal in EA SLE = 0.3; Prevalence of lupus renal =
0.0001 x 0.3 = 0.00003 [1]
In the case-control analysis using the assumptions in the table above and using the
general 2 degree of freedom test (BB vs. Bb vs. bb) our study would have 99% power to
detect a relative risk of 2.0 for the heterozygote. However, in the case-only analysis
where our “case” (SLE patients with renal) to “control” (SLE patients without renal) ratio
was reduced to 2 and the prevalence of the C allele was increased to 12.9%
(Supplementary Table 2), we would need at least 559 cases and 1118 controls to detect
to detect an effect with OR 2.0 at 99% power. This suggests that our inability to
replicate a significant effect for SLE sub-phenotypes in the case-only analysis was likely
due to reduced statistical power resulting from a decreased sample size.
Note that these calculations were done using the details of the renal subset as it had the
smallest sample size, but certainly, given the slightly smaller effect size but slightly
larger sample, these results can be generalized to the analyses of hematologic traits as
well.
Supplementary Table 1. Imputation results of SLE associated SNPs reported in other
studies.
SNP
Study
BP
NPRX
INFO
A1
A2
F_A
F_U
CHISQ
P
OR
rs2327832
rs6920220
rs13192841
rs12527282
rs10499194
rs6922466
[2]
[3-5]
[2]
[2]
[3]
[2]
138014761
138048197
138008907
138008945
138044330
138486623
5
4
5
5
5
5
0.999
0.985
0.981
0.981
0.982
0.986
C
A
A
T
T
G
A
G
G
C
C
A
0.2459
0.2494
0.2629
0.2629
0.2651
0.2278
0.2135
0.2144
0.2765
0.2765
0.2768
0.2348
4.433
5.134
0.6639
0.6639
0.4902
0.1941
0.03525
0.02346
0.4152
0.4152
0.4838
0.6595
1.202
1.218
0.933
0.933
0.942
0.961
Observed SNPs are shown in italicized font
BP = base pair position on chromosome 6, build 36
NPRX - number of proxy SNPs used to impute
INFO - score of accuracy of imputation
A1/A2 - allele 1 or 2
F_A/F_U - allele frequency in affected/unaffected
Supplementary Table 2. Conditional analysis of clinical traits (Case:Case Analysis)
SLE Cases Conditioned on:
CG
GG
Positive:Negative
Positive:Negative
OR
95% C.I.
P-value
49:40
330:416
1.54
0.99-2.40
0.0543
88:56
661:537
1.28
0.90-1.82
0.17
33:111
209:989
1.41
0.93-2.13
0.11
a
Renal
b
Hematology
c
Renal or Hematology
a
SLE Cases positive or negative for renal
SLE Cases positive or negative for hematologic manifestations
c SLE Cases positive or negative for either renal or hematologic manifestations
b
.
Supplementary Table 3. Grouping of each SLE criteria into clusters
R2 within group
R2 within next
closest group
Malar Rash
0.55
0.004
Photosensitivity
0.45
0.03
Oral Ulcers
0.43
0.01
Renal
0.33
0.02
Hematologic
0.46
0.03
Immunologic
0.52
0.003
Arthritis
0.57
0.01
Serositis
0.57
0.01
4
Neurologic
1.00
0.004
5
Discoid rash
1.00
0.01
Cluster
1
2
Sub-Phenotype
3
Supplemental References
1.
Wallace, D.J., The Clinical Presentation of Systemic Lupus Erythematosus, in
Dubois' Lupus Erythematosus, D.J. Wallace and B.H. Hahn, Editors. 2007,
Lippincott Williams & Wilkins: Philadelphia. p. 638-646.
2.
Musone, S.L., et al., Multiple polymorphisms in the TNFAIP3 region are
independently associated with systemic lupus erythematosus. Nat Genet, 2008.
3.
Plenge, R.M., et al., Two independent alleles at 6q23 associated with risk of
rheumatoid arthritis. Nat Genet, 2007. 39(12): p. 1477-82.
4.
Thomson, W., et al., Rheumatoid arthritis association at 6q23. Nat Genet, 2007.
39(12): p. 1431-3.
5.
Genome-wide association study of 14,000 cases of seven common diseases and
3,000 shared controls. Nature, 2007. 447(7145): p. 661-78.