GPC: Genetics power calculator for linear trend association...

In GeneticsDesign: Functions for designing genetics studies

Description

Genetics power calculator for linear trend association studies.

Usage

  GPC(pA, pD, RRAa, RRAA, r2, pB, 
              nCase=500, ratio=1, alpha=0.05, quiet=FALSE)
  GPC.default(pA, pD, RRAa, RRAA, Dprime, pB, 
              nCase=500, ratio=1, alpha=0.05, quiet=FALSE)

Arguments

pA	High risk allele frequency (A).
pD	Disease prevalence.
RRAa	Genotype relative risk (Aa) = RR(Aa|aa)=Pr(D|Aa)/Pr(D|aa).
RRAA	Genotype relative risk (AA) = RR(AA|aa)=Pr(D|AA)/Pr(D|aa).
r2	LD measure. Assume that D > 0.
Dprime	LD measure.
pB	Marker allele frequency (B).
nCase	Number of cases.
ratio	Control:case ratio = nControl/nCase.
alpha	User-defined type I error rate.
quiet	Print some intermediate results if quiet=FALSE.

Details

The power is for the test that disease is associated with a marker, given high risk allele frequency (A), disease prevalence, genotype relative risk (Aa), genotype relative risk (AA), LD measure (D' or r^2), marker allele frequency (B), number of cases, control:case ratio, and probability of the Type I error. The linear trend test (Cochran 1954; Armitage 1955) is used.

Value

power	The estimated power for the association test.
ncp	Non-centrality parameter.
mat.para	A matrix of case-control parameters, including number of cases, number of controls, high risk allele frequency, prevalence, genotypic relative risk (Aa), genotypic relative risk (AA), genotypic risk for aa (baseline).
mat.B	A matrix of marker locus B parameters, including marker allele frequency, linkage disequilibrium (D'), penetrance at marker genotype bb, penetrance at marker genotype Bb, penetrance at marker genotype BB, genotypic odds ratio Bb, genotypic odds ratio BB.
mat.aFreq	A 2 by 2 matrix of expected allele frequencies Pr(B|D), Pr(b|D), Pr(B|non D), Pr(b|non D).
mat.gFreq	A 3 by 2 matrix of expected genotype frequencies Pr(BB|D), Pr(Bb|D), Pr(bb|D), Pr(BB|non D), Pr(Bb|non D), Pr(bb|non D).
mat.stat	Power estimates for a sequence of Type I errors.

Author(s)

Weiliang Qiu [e-mail], Ross Lazarus [e-mail]

References

Armitage, P. (1955) Tests for linear trends in proportions and frequencies. Biometrics, 11, 375-386.

Cochran, W.G. (1954) Some methods for strengthening the common chi-squared tests. Biometrics, 10, 417-451.

Gordon D, Finch SJ, Nothnagel M, Ott J (2002) Power and sample size calculations for case-control genetic association tests when errors are present: application to single nucleotide polymorphisms. Hum. Hered., 54:22-33.

Gordon D, Haynes C, Blumenfeld J, Finch SJ (2005) PAWE-3D: visualizing Power for Association With Error in case/control genetic studies of complex traits. Bioinformatics, 21:3935-3937.

Purcell S, Cherny SS, Sham PC. (2003). Genetic Power Calculator: design of linkage and association genetic mapping studies of complex traits. Bioinformatics, 19(1):149-150.

Sham P. (1998). Statistics in Human Genetics. Arnold Applications of Statistics.

Examples

  res1<-GPC(pA=0.05, pD=0.1, RRAa=1.414, RRAA=2, r2=0.9, pB=0.06, 
                   nCase=500, ratio=1, alpha=0.05, quiet=FALSE)

  res2<-GPC.default(pA=0.05, pD=0.1, RRAa=1.414, RRAA=2, Dprime=0.9, pB=0.06, 
                   nCase=500, ratio=1, alpha=0.05, quiet=FALSE)

Example output

 Case-control parameters>>
                                         [,1]
Number of cases                  500.00000000
Number of controls               500.00000000
High risk allele frequency (A)     0.05000000
Prevalence                         0.10000000
Genotypic relative risk Aa         1.41400000
Genotypic relative risk AA         2.00000000
Genotypic risk for aa (baseline)   0.09598495

 Marker locus B>>
                                       [,1]
High risk allele frequency (B)   0.06000000
Linkage disequilibrium (D')      0.99723021
Penetrance at marker genotype bb 0.09599596
Penetrance at marker genotype Bb 0.12902094
Penetrance at marker genotype BB 0.17344738
Genotypic odds ratio Bb          1.39498627
Genotypic odds ratio BB          1.97612611

 Expected allele frequencies>>
        Case    Control
B 0.07901192 0.05788756
b 0.92098808 0.94211244

 Expected genotype frequencies>>
          Case    Control
BB 0.006244106 0.00330621
Bb 0.145535624 0.10916271
bb 0.848220271 0.88753108

 Case-control statistics>>
 Alpha      Power
 0.100 0.58900688
 0.050 0.46393515
 0.010 0.23992694
 0.001 0.07762229
 0.050 0.46393515

 power (alpha= 0.05 )= 0.4639352  ncp= 3.494199 
Warning message:
In Dprime.fun2(r2, pA, pB) :
  r2 =  0.9  > upper bound of r2 =  0.824561403508772 . r2 is changed to floor(tmpr2*100)/100!


 Case-control parameters>>
                                         [,1]
Number of cases                  500.00000000
Number of controls               500.00000000
High risk allele frequency (A)     0.05000000
Prevalence                         0.10000000
Genotypic relative risk Aa         1.41400000
Genotypic relative risk AA         2.00000000
Genotypic risk for aa (baseline)   0.09598495

 Marker locus B>>
                                       [,1]
High risk allele frequency (B)   0.06000000
Linkage disequilibrium (D')      0.90000000
Penetrance at marker genotype bb 0.09638274
Penetrance at marker genotype Bb 0.12624798
Penetrance at marker genotype BB 0.16539976
Genotypic odds ratio Bb          1.35463248
Genotypic odds ratio BB          1.85798248

 Expected allele frequencies>>
        Case    Control
B 0.07715825 0.05809353
b 0.92284175 0.94190647

 Expected genotype frequencies>>
          Case     Control
BB 0.005954391 0.003338401
Bb 0.142407718 0.109510254
bb 0.851637891 0.887151345

 Case-control statistics>>
 Alpha      Power
 0.100 0.52110203
 0.050 0.39631201
 0.010 0.18968278
 0.001 0.05549084
 0.050 0.39631201

 power (alpha= 0.05 )= 0.396312  ncp= 2.878885 

GeneticsDesign documentation built on April 28, 2020, 6:25 p.m.