The genpwr package performs power and sample size calculations for genetic association studies, considering the impact of mis-specification of the genetic model. The user can specify the true genetic model, such as additive, dominant, and recessive, which represents the actual relationship between genotype and the outcome. The user also specifies a “Test” model, which indicates how the genetic effect will be coded for statistical testing. Options for test models include: additive, dominant, recessive and 2 degree of freedom (also called genotypic) tests.

The genpwr package allows the user to perform calculations for:

Binary (case/control) or continuous outcome variables.

Tests of gene and gene x environment interactions including both continuous and categorical environmental measurements.

genpwr is capable of calculating:

sample size

detectable effect size (or odds ratio in the case of a binary outcome variable)

power

provided that two of the three above variables are entered into the appropriate genpwr function.

In addition to specifying of the three above variables (power, sample size, effect size), input variables include:

Minor Allele Frequency

Type 1 error rate, or “Alpha”

“True” model type (recessive, dominant, additive)

“Test” model type (recessive, dominant, additive, 2 degree of freedom)

- For binary outcomes / logistic regression models, either:
- Case rate
The number of controls per case

For continuous outcomes / linear regression models, the population standard deviation of the outcome.

Assuming an environmental exposure interaction term is to be tested:

Population prevalence of environmental exposure for categorical environment variables or the standard deviation of the environmental exposure for continuous environment variables.

Environmental exposure odds ratio (or effect size in the case of linear regression models)

Environmental exposure / genetic variant interaction term odds ratio (or effect size in the case of linear regression models)

To install the package, first, you need to install the devtools package. You can do this from CRAN. Invoke R and then type:

`install.packages("devtools")`

Next, load the devtools package:

`library(devtools)`

Install the package.

`install_github("camillemmoore/Power_Genetics", subdir="genpwr")`

Load the package.

`library(genpwr)`

We calculate power to detect an odds ratio of 3 in a case control study with 400 subjects, including 80 cases and 320 controls (case rate of 20%) over a range of minor allele frequencies from 0.18 to 0.25. We calculate power for all possible combinations of true and test models, assuming an alpha of 0.05.

For a power calculation with a binary outcome and no gene/environment interaction, we use the following inputs:

```
pw <- genpwr.calc(calc = "power", model = "logistic", ge.interaction = NULL,
N=400, Case.Rate=0.2, k=NULL,
MAF=seq(0.18, 0.25, 0.01), OR=c(3),Alpha=0.05,
True.Model=c("Dominant", "Recessive", "Additive"),
Test.Model=c("Dominant", "Recessive", "Additive", "2df"))
```

We look to see what the resulting data frame looks like:

```
head(pw)
#> Test.Model True.Model MAF OR N_total N_cases N_controls Case.Rate
#> 1 Dominant Dominant 0.18 3 400 80 320 0.2
#> 3 Dominant Additive 0.18 3 400 80 320 0.2
#> 5 Dominant Recessive 0.18 3 400 80 320 0.2
#> 7 Dominant Dominant 0.19 3 400 80 320 0.2
#> 9 Dominant Additive 0.19 3 400 80 320 0.2
#> 11 Dominant Recessive 0.19 3 400 80 320 0.2
#> Power_at_Alpha_0.05
#> 1 0.98985513
#> 3 0.99730560
#> 5 0.08137351
#> 7 0.99040997
#> 9 0.99769410
#> 11 0.08615138
```

We then use the plotting function to plot these results

`power.plot(pw)`

A model with a continuous outcome can also be calculated:

```
pw <- genpwr.calc(calc = "power", model = "linear",
N=40, sd_y=4, k=NULL,
MAF=seq(0.18, 0.25, 0.01), ES=c(3),Alpha=0.05,
True.Model=c("Dominant", "Recessive", "Additive"),
Test.Model=c("Dominant", "Recessive", "Additive", "2df"))
```

```
ss <- genpwr.calc(calc = "ss", model = "logistic", ge.interaction = NULL,
OR=4, Case.Rate=0.4, k=NULL,
MAF=seq(0.3, 0.4, 0.02), Power=0.8, Alpha=0.05,
True.Model=c("Dominant", "Recessive", "Additive"),
Test.Model=c("Dominant", "Recessive", "Additive", "2df"))
```

Plot:

`ss.plot(ss)`

```
or <- genpwr.calc(calc = "es", model = "logistic", ge.interaction = NULL,
N=1000, Case.Rate=0.4, k=NULL,
MAF=seq(0.30, 0.4, 0.02), Power=0.4, Alpha=0.05,
True.Model="All", Test.Model="All")
```

`or.plot(or)`

```
pec <- genpwr.calc(calc = "power", model = "logistic",
ge.interaction = "binary",
N=500, Case.Rate=0.3, MAF=seq(0.2,0.4,0.02), OR_G=3,
OR_E=3.5, OR_GE=4, P_e = 0.4,
Alpha=0.05, True.Model='All', Test.Model='All')
```

`power.plot(pec)`

Other options are available.

- linear model for continuous outcomes

```
pec <- genpwr.calc(calc = "power", model = "linear",
ge.interaction = "binary",
N=50, sd_y=3, MAF=seq(0.2,0.34,0.02), ES_G=3,
ES_E=1.5, ES_GE=2, P_e = 0.4,
Alpha=0.05, True.Model='All', Test.Model='All')
```

- continuous environment measurement

```
pec <- genpwr.calc(calc = "power", model = "logistic",
ge.interaction = "continuous",
N=500, Case.Rate=0.3, MAF=seq(0.25,0.31,0.02), OR_G=3,
OR_E=3.5, OR_GE=4, sd_e = 4,
Alpha=0.05, True.Model='All', Test.Model='All')
```

```
sse <- genpwr.calc(calc = "ss", model = "logistic", ge.interaction = "binary",
Power=0.5, Case.Rate=0.4, MAF=seq(0.3,0.4,0.05), OR_G=1.5,
OR_E=1.3, OR_GE=1.2, P_e = 0.4,
Alpha=0.05, True.Model="All", Test.Model="All")
```

`ss.plot(sse)`