Introduction to genpwr

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:

genpwr is capable of calculating:

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:

Assuming an environmental exposure interaction term is to be tested:

Install genpwr

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)

Examples

Power Calculation for a Case Control Study

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"))

Sample Size Calculation for a Case Control Study

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)

Detectable Odds Ratio Calculation for a Case Control Study

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)

Power Calculation for a Case Control Study with a Gene x Environment Interaction

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.

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')
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')

Sample Size Calculation for a Case Control Study with a Gene x Environment Interaction

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)