# 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

 ```1 2 3 4``` ``` 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 [email protected], Ross Lazarus [email protected]

## 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

 ```1 2 3 4 5``` ``` 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
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
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 May 2, 2018, 2:37 a.m.