| Title: | Power Calculations Under Genetic Model Misspecification |
| Version: | 1.0.4 |
| Description: | Power and sample size calculations for genetic association studies allowing for misspecification of the model of genetic susceptibility. "Hum Hered. 2019;84(6):256-271.<doi:10.1159/000508558>. Epub 2020 Jul 28." Power and/or sample size can be calculated for logistic (case/control study design) and linear (continuous phenotype) regression models, using additive, dominant, recessive or degree of freedom coding of the genetic covariate while assuming a true dominant, recessive or additive genetic effect. In addition, power and sample size calculations can be performed for gene by environment interactions. These methods are extensions of Gauderman (2002) <doi:10.1093/aje/155.5.478> and Gauderman (2002) <doi:10.1002/sim.973> and are described in: Moore CM, Jacobson S, Fingerlin TE. Power and Sample Size Calculations for Genetic Association Studies in the Presence of Genetic Model Misspecification. American Society of Human Genetics. October 2018, San Diego. |
| Depends: | R (≥ 3.5.0) |
| License: | GPL-3 |
| Imports: | ggplot2, nleqslv, MASS, stats, utils |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.1 |
| Suggests: | knitr, rmarkdown |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2021-03-30 14:57:52 UTC; jacobsons |
| Author: | Camille Moore [aut, cre], Sean Jacobson [aut] |
| Maintainer: | Camille Moore <moorec@njhealth.org> |
| Repository: | CRAN |
| Date/Publication: | 2021-03-31 00:00:07 UTC |
Function to output X matrices used in calculation of MLE's for linear outcome with logistic environment interaction
Description
Returns X matrices used in calculation of MLE's for linear outcome with logistic environment interaction
Usage
X_mat_returner(mod, reduced = F)
Arguments
mod |
type of model |
reduced |
logical, indicates whether the X matrix will be used for a reduced model |
Value
A matrix to be used in MLE calculation for linear outcome with logistic environment interaction
Examples
X_mat_returner(mod = "Dominant")
Function to output X matrices used in calculation of MLE's for linear outcome with linear environment interaction
Description
Function to output X matrices used in calculation of MLE's for linear outcome with linear environment interaction
Usage
X_mat_returner_lle(mod)
Arguments
mod |
type of model |
Value
A probability vector to be used in MLE calculation for linear outcome with linear environment interaction
Examples
X_mat_returner_lle("Dominant")
Function to Calculate t matrix for logistic outcome with binary environment interaction in additive model
Description
Calculates the t matrix for logistic outcome with binary environment interaction in additive model
Usage
add.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)
Arguments
MAF |
Vector of minor allele frequencies |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
OR_E |
Vector of environmental odds ratios to detect |
OR_G |
Vector of genetic odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
Value
t matrix for all combinations of environment/outcome
Examples
add.fun.t(MAF = 0.1, P_e = 0.2, Case.Rate = 0.5,
OR_G = 1.5, OR_E = 2, OR_GE = 1.8)
Additive Model Function
Description
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "Additive"
Usage
add.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
Arguments
like |
Expected log likelihood |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
True.Model |
A vector object specifying the true underlying genetic model(s): 'Dominant', 'Additive', or 'Recessive' |
risk_allele |
Logical: If OR > 1, the allele is classified as a "risk allele" |
Value
: The odds ratios and their corresponding genetic model(s)
Examples
add.or.function(like=-0.57162, Case.Rate=0.3, P_AA=0.5625, P_AB=0.375,
P_BB=0.0625, True.Model="Additive", risk_allele=TRUE)
Function to Calculate Additive Log Likelihood for a Logistic Regression Model
Description
Calculates the log likelihood for a given set of logistic regression coefficients under an additive genetic model.
Usage
additive.ll(beta, t)
Arguments
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
Value
The log likelihood.
Examples
additive.ll(c(-0.3793525, -1.1395417),
rbind(c(0.2339079, 0.05665039, 0.009441731),
c(0.3285921, 0.31834961, 0.053058269)))
Function to Calculate Additive Log Likelihood for a Linear Regression Model
Description
Calculates the log likelihood for a given set of linear regression coefficients under an additive genetic model.
Usage
additive.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
Arguments
beta |
Vector of linear regression coefficients. |
m |
Minor allele frequency. |
es |
Vector of effect sizes with two elements, (mean AB - mean AA) and (mean BB - mean AA). |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
Value
The log likelihood.
Examples
additive.ll.linear(beta = c(-0.03, 0.3), m = 0.1, es = c(0,3),
sd_y_x_model = 0.9918669, sd_y_x_truth = 0.9544108)
Function to convert to numeric with scientific notation containing the "." character
Description
convert to numeric with scientific notation containing the "." character
Usage
as.numeric2(char)
Arguments
char |
string to be converted to numeric |
Value
a number
Examples
as.numeric2("2e.2")
Function to Calculate Log Likelihood for a Logistic Regression Model
Description
Convenience function to calculate the log likelihood of a specified model.
Usage
calc.like(beta, t, model)
Arguments
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
model |
The genetic model in the logistic regression: "Dominant", "Additive", "Recessive", "2df" or "null" |
Value
The log likelihood.
Examples
t <- rbind(c(0.2967437, 0.1806723, 0.02258404),
c(0.3432563, 0.1393277, 0.01741596))
calc.like(logistic.mles(t, "Dominant"), t, model="Dominant")
Function to Calculate Log Likelihood for a Linear Regression Model
Description
Convenience function to calculate the log likelihood of a specified model.
Usage
calc.like.linear(beta, m, es_ab, es_bb, sd_y_x_model, sd_y_x_truth, model)
Arguments
beta |
Vector of linear regression coefficients. |
m |
Minor allele frequency. |
es_ab |
effect size for mean AB - mean AA |
es_bb |
effect size for mean BB - mean AA |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
model |
The genetic model in the linear regression: "Dominant", "Additive", "Recessive", "2df" or "null" |
Value
The log likelihood.
Examples
calc.like.linear(beta = c(0.0000000, 0.1578947), m = 0.1, es_ab = 0, es_bb = 3,
sd_y_x_model = 0.9980797, sd_y_x_truth = 0.9544108, model = "Dominant")
Function to calculate the standard deviation of y given x for linear models with logistic environment interaction
Description
Returns the standard deviation of y given x for linear models with logistic environment interaction
Usage
calc.like.linear.log.envir.interaction(
beta_hat,
MAF,
P_e,
ES_G,
ES_E,
ES_GE,
sd_y_x_truth,
sd_y_x_model,
Test.Model,
True.Model,
reduced = F
)
Arguments
beta_hat |
Effect sizes from MLE |
MAF |
Minor allele Frequency |
P_e |
Population prevalence of logistic environmental factor |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
sd_y_x_truth |
Standard deviation of y for the true model |
sd_y_x_model |
Standard deviation of y for the test model |
Test.Model |
Test model |
True.Model |
True model |
reduced |
logical, indicates whether the X matrix will be used for a reduced model |
Value
The standard deviation of y given x for linear models with logistic environment interaction
Examples
beta_hat = linear.mles.log.envir.interaction(MAF = 0.1, P_e = 0.2,
ES_G = 1.2, ES_E = 1.3, ES_GE = 2,
Test.Model = "Dominant", True.Model = "Additive")
calc.like.linear.log.envir.interaction(beta_hat = beta_hat,
MAF = 0.1, P_e = 0.2, ES_G = 1.2, ES_E = 1.3,
ES_GE = 2, sd_y_x_truth = 9.947945, sd_y_x_model = 9.949468,
True.Model = "Additive", Test.Model="Dominant")
Function to Calculate 2df Log Likelihood for a Logistic Regression Model
Description
Calculates the log likelihood for a given set of logistic regression coefficients under an unspecificed/2df genetic model.
Usage
df2.ll(beta, t)
Arguments
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
Value
The log likelihood.
Examples
df2.ll(c(-0.3793525, -1.1395417),
rbind(c(0.2339079, 0.05665039, 0.009441731),
c(0.3285921, 0.31834961, 0.053058269)))
Function to Calculate 2 Degree of Freedom Log Likelihood for a Linear Regression Model
Description
Calculates the log likelihood for a given set of linear regression coefficients under a the 2df model.
Usage
df2.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
Arguments
beta |
Vector of linear regression coefficients. |
m |
Minor allele frequency. |
es |
Vector of effect sizes with two elements, (mean AB - mean AA) and (mean BB - mean AA). |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
Value
The log likelihood.
Examples
df2.ll.linear(beta = c(0, 0, 3), m = 0.1, es = c(0,3),
sd_y_x_model = 0.9544108, sd_y_x_truth = 0.9544108)
Function to Calculate t matrix for logistic outcome with binary environment interaction in dominant model
Description
Calculates the t matrix for logistic outcome with binary environment interaction in dominant model
Usage
dom.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)
Arguments
MAF |
Vector of minor allele frequencies |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
OR_E |
Vector of environmental odds ratios to detect |
OR_G |
Vector of genetic odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
Value
t matrix for all combinations of environment/outcome
Examples
dom.fun.t(MAF = 0.1, P_e = 0.2, Case.Rate = 0.5,
OR_G = 1.5, OR_E = 2, OR_GE = 1.8)
Dominant Model Function
Description
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "Dominant"
Usage
dom.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
Arguments
like |
Expected log likelihood |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
True.Model |
A vector object specifying the true underlying genetic model(s): 'Dominant', 'Additive', or 'Recessive' |
risk_allele |
Logical: If OR > 1, the allele is classified as a "risk allele" |
Value
: The odds ratios and their corresponding genetic model(s)
Examples
dom.or.function(like=-0.57162, Case.Rate=0.3, P_AA=0.5625, P_AB=0.375,
P_BB=0.0625, True.Model="Dominant", risk_allele=TRUE)
Function to Calculate Dominant Log Likelihood for a Logistic Regression Model
Description
Calculates the log likelihood for a given set of logistic regression coefficients under a dominant genetic model.
Usage
dominant.ll(beta, t)
Arguments
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
Value
The log likelihood.
Examples
dominant.ll(c(-0.3793525, -1.1395417),
rbind(c(0.2339079, 0.05665039, 0.009441731),
c(0.3285921, 0.31834961, 0.053058269)))
Function to Calculate Dominant Log Likelihood for a Linear Regression Model
Description
Calculates the log likelihood for a given set of linear regression coefficients under a dominant genetic model.
Usage
dominant.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
Arguments
beta |
Vector of linear regression coefficients. |
m |
Minor allele frequency. |
es |
Vector of effect sizes with two elements, (mean AB - mean AA) and (mean BB - mean AA). |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
Value
The log likelihood.
Examples
dominant.ll.linear(beta = c(0.0000000, 0.1578947), m = 0.1, es = c(0,3),
sd_y_x_model = 0.9980797, sd_y_x_truth = 0.9544108)
Function to Calculate Effect Size for Linear Models
Description
Calculates the detectable effect size/regression coefficient, at a given sample size, N, and power, with type 1 error rate, Alpha
Usage
es.calc.linear(
power = NULL,
N = NULL,
MAF = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
power |
Vector of the desired power(s) |
N |
Vector of the desired sample size(s) |
MAF |
Vector of minor allele frequencies |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
es <- es.calc.linear(N=1000,power=0.8,
MAF=0.1, sd_y = 1, Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Calculate Expected Log Likelihood for a Single Genotype
Description
Calculates the expected log likelihood for a single genotype given the true and estimated mean and standard deviation for the outcome.
Usage
expected.linear.ll(mean_truth, mean_model, sd_y_x_truth, sd_y_x_model)
Arguments
mean_truth |
Mean of the outcome given X(predictors/genotype) under the true model. |
mean_model |
Mean of the outcome given X(predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
Value
The log likelihood.
Examples
expected.linear.ll(mean_truth = 0, mean_model = 0.03,
sd_y_x_model = 1, sd_y_x_truth = 0.9544108)
Function to Calculate Expected Log Likelihood for a Single Genotype with linear environment interaction
Description
Calculates the expected log likelihood for a single genotype with linear environment interaction given the true and estimated mean and standard deviation for the outcome.
Usage
expected.linear.ll.lin.env(sd_y_x_model)
Arguments
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
Value
The log likelihood.
Examples
expected.linear.ll.lin.env(4.309354)
Dominant probability finding function
Description
Operates within add.or.function to find probability of disease in a dominant truth given AB or BB, additive test model
Usage
find.prob.dom(x, P_AA, P_AB, P_BB, cr, like)
Arguments
x |
Probability of disease given AB or BB |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
cr |
proportion of cases in the sample (cases/(cases + controls)). |
like |
Expected log likelihood |
Value
: The "a" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions
Examples
find.prob.dom(0.1510677, 0.5625, 0.375, 0.0625, 0.3, -0.57162)
Recessive probability finding function
Description
Operates within add.or.function to find probability of disease in a recessive truth given AB or BB, additive test model
Usage
find.prob.rec(x, P_AA, P_AB, P_BB, cr, like)
Arguments
x |
Probability of disease given AB or BB |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
cr |
proportion of cases in the sample (cases/(cases + controls)). |
like |
Expected log likelihood |
Value
: The "a" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions
Examples
find.prob.rec(0.7072381, 0.5625, 0.375, 0.0625, 0.3, -0.6005743)
Function to Calculate Power for Linear Models with logistic environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
genpwr.calc(
calc,
model,
ge.interaction = NULL,
N = NULL,
Power = NULL,
MAF = NULL,
Alpha = 0.05,
P_e = NULL,
sd_e = NULL,
sd_y = NULL,
Case.Rate = NULL,
k = NULL,
OR = NULL,
OR_G = NULL,
OR_E = NULL,
OR_GE = NULL,
risk_allele = TRUE,
ES = NULL,
ES_G = NULL,
ES_E = NULL,
ES_GE = NULL,
R2 = NULL,
R2_G = NULL,
R2_E = NULL,
R2_GE = NULL,
True.Model = "All",
Test.Model = "All"
)
Arguments
calc |
What kind of calculation to perform? sample size ("ss"), power ("power"), or effect size ("es") |
model |
Distribution of the outcome variable? ("logistic" or "linear") |
ge.interaction |
If no environment interaction, should be NULL, otherwise should be "logistic" or "linear" |
N |
Vector of the desired sample size(s) |
Power |
Vector of the desired power(s) |
MAF |
Vector of minor allele frequencies |
Alpha |
the desired type 1 error rate(s) |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
sd_e |
Standard deviation of the environmental variable |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Case.Rate |
Case Rate of the outcome in the population (ignoring genotype). Either Case.Rate_x or Case.Rate must be specified. |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
OR |
Vector of genetic odds ratios to detect in absence of environmental odds ratios |
OR_G |
Vector of genetic odds ratios to detect |
OR_E |
Vector of environmental odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
risk_allele |
Logical: If OR > 1, the allele is classified as a "risk allele" |
ES |
Vector of effect sizes (difference in means) to detect. Either ES or R2 must be specified. |
ES_G |
Vector of genetic effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_E |
Vector of environmental effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_GE |
Vector of genetic/environment interaction effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2 |
Vector of R-squared values to detect. Either ES or R2 must be specified. |
R2_G |
Vector of genetic R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_E |
Vector of environmental R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_GE |
Vector of genetic/environment interaction R-squared values Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
pw <- genpwr.calc(calc = "power", model = "logistic", ge.interaction = "continuous",
N=100, OR_G=2, OR_E=1.4, OR_GE=c(1.5, 2),
sd_e = 1.1, MAF=0.1, Case.Rate = 0.3, Alpha=0.05,
True.Model="All", Test.Model=c("Dominant", "Recessive"))
Function to generate integrand for mle for cases
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
integrand_funct_case(x1, x2)
Arguments
x1 |
"true" part of model |
x2 |
"test" part of model |
Value
a function to be used as the integrand for the mle
Examples
integrand_funct_case(-1.462531 + 1*0.1823216,
-1.462531 + 1*0.1823216)
Function to generate integrand for mle for controls
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
integrand_funct_control(x1, x2)
Arguments
x1 |
"true" part of model |
x2 |
"test" part of model |
Value
a function to be used as the integrand for the mle
Examples
integrand_funct_control(-1.462531 + 1*0.1823216,
-1.462531 + 1*0.1823216)
Function to calculate MLE's for linear models
Description
Finds the maximum likelihood estimates for a given MAF under the specified genetic model and effect size.
Usage
linear.mles(m, es_ab, es_bb, model)
Arguments
m |
minor allele frequency |
es_ab |
effect size for mean AB - mean AA |
es_bb |
effect size for mean BB - mean AA |
model |
The assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive', '2df' |
Value
A vector of linear regression model coefficients.
Examples
linear.mles(m = 0.1, es_ab = 0, es_bb = 3, model = "Dominant")
Function to calculate the standard deviation of y given x for linear models with linear environment interaction
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
linear.mles.lin.envir.interaction(
MAF,
beta0,
ES_G,
ES_E,
ES_GE,
Test.Model,
True.Model
)
Arguments
MAF |
Minor allele Frequency |
beta0 |
baseline value for the outcome |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
Test.Model |
Test Model |
True.Model |
True Model |
Value
The standard deviation of y given x for linear models with linear environment interaction
Examples
linear.mles.lin.envir.interaction(MAF = 0.28, ES_G = 0.5, beta0 = -0.28,
ES_E = 1.6, ES_GE = 1.4, Test.Model = "Dominant", True.Model = "Additive")
Function to calculate the standard deviation of y given x for linear models with linear environment interaction for the reduced model without GxE interaction
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
linear.mles.lin.envir.interaction_reduced(
MAF,
beta0,
ES_G,
ES_E,
ES_GE,
Test.Model,
True.Model
)
Arguments
MAF |
Minor allele Frequency |
beta0 |
baseline value for the outcome |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
Test.Model |
Test Model |
True.Model |
True Model |
Value
The standard deviation of y given x for linear models with linear environment interaction
Examples
linear.mles.lin.envir.interaction_reduced(MAF = 0.28, ES_G = 0.5, beta0 = -0.28,
ES_E = 1.6, ES_GE = 1.4, Test.Model = "Dominant", True.Model = "Additive")
Function to calculate the standard deviation of y given x for linear models with logistic environment interaction
Description
Returns the standard deviation of y given x for linear models with logistic environment interaction
Usage
linear.mles.log.envir.interaction(
MAF,
P_e,
ES_G,
ES_E,
ES_GE,
Test.Model,
True.Model,
reduced = F
)
Arguments
MAF |
Minor allele Frequency |
P_e |
Population prevalence of logistic environmental factor |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
Test.Model |
Test model |
True.Model |
True model |
reduced |
logical, indicates whether the X matrix will be used for a reduced model |
Value
The standard deviation of y given x for linear models with logistic environment interaction
Examples
linear.mles.log.envir.interaction(MAF = 0.1, P_e = 0.2,
ES_G = 1.2, ES_E = 1.3, ES_GE = 2,
Test.Model = "Dominant", True.Model = "Additive")
Function to calculate the standard deviation of y given x for linear models with linear environment interaction
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
linear.outcome.lin.envir.interaction.sds(
MAF,
sd_e,
beta0,
ES_G,
ES_E,
ES_GE,
mod,
True.Model,
sd_y
)
Arguments
MAF |
Minor allele Frequency |
sd_e |
Standard deviation of linear environmental factor |
beta0 |
baseline value for the outcome |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
mod |
Test model |
True.Model |
True model |
sd_y |
Standard deviation of y |
Value
The standard deviation of y given x for linear models with linear environment interaction
Examples
linear.outcome.lin.envir.interaction.sds(MAF = 0.28, beta0 = -0.28,
sd_y = 5, sd_e = 1, ES_G = 0.5, ES_E = 1.6, ES_GE = 1.4,
mod = "Dominant", True.Model = "Additive")
Function to calculate the standard deviation of y given x for linear models with linear environment interaction
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
linear.outcome.lin.envir.interaction.sds_reduced(
MAF,
sd_e,
beta0,
ES_G,
ES_E,
ES_GE,
mod,
True.Model,
sd_y
)
Arguments
MAF |
Minor allele Frequency |
sd_e |
Standard deviation of linear environmental factor |
beta0 |
baseline value for the outcome |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
mod |
Test model |
True.Model |
True model |
sd_y |
Standard deviation of y |
Value
The standard deviation of y given x for linear models with linear environment interaction
Examples
linear.outcome.lin.envir.interaction.sds_reduced(MAF = 0.28, beta0 = -0.28,
sd_y = 5, sd_e = 1, ES_G = 0.5, ES_E = 1.6,
ES_GE = 1.4, mod = "Dominant", True.Model = "Additive")
Function to calculate the standard deviation of y given x for linear models with logistic environment interaction
Description
Returns the standard deviation of y given x for linear models with logistic environment interaction
Usage
linear.outcome.log.envir.interaction.sds(
MAF,
P_e,
ES_G,
ES_E,
ES_GE,
mod,
True.Model,
sd_y,
reduced = F
)
Arguments
MAF |
Minor allele Frequency |
P_e |
Population prevalence of logistic environmental factor |
ES_G |
Genetic Effect size |
ES_E |
Environment Effect size |
ES_GE |
Environment x Genetic interaction Effect size |
mod |
Test model |
True.Model |
True model |
sd_y |
Standard deviation of y |
reduced |
logical, indicates whether the X matrix will be used for a reduced model |
Value
The standard deviation of y given x for linear models with logistic environment interaction
Examples
linear.outcome.log.envir.interaction.sds(MAF = 0.1, P_e = 0.2, sd_y = 10,
ES_G = 1.2, ES_E = 1.3, ES_GE = 2, mod = "Dominant", True.Model = "Additive")
Functions to Calculate Residual SD for Normal/Continuous Outcomes Function to calculate the standard deviation of y given x for linear models
Description
Functions to Calculate Residual SD for Normal/Continuous Outcomes Function to calculate the standard deviation of y given x for linear models
Usage
linear.sds(m, es_ab, es_bb, sd_y, model)
Arguments
m |
minor allele frequency |
es_ab |
effect size for mean AB - mean AA |
es_bb |
effect size for mean BB - mean AA |
sd_y |
the standard deviation of y in the overall population. |
model |
The assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive', '2df' |
Value
A vector of linear regression model coefficients.
Examples
linear.sds(m = 0.1, es_ab = 0, es_bb = 3, sd_y = 1, model = "Dominant")
Function to calculate MLE's for logistic models with logistic environment interaction
Description
Finds the maximum likelihood estimates for a given 2x3 table under the specified genetic model.
Usage
ll.ge.logistic(t, N = NULL, power = NULL, Alpha, mod)
Arguments
t |
A 2x6 table of the joint probabilities of disease, genotype, and environment. Rows are case vs. control and columns are genotypes. |
N |
Sample size |
power |
Power |
Alpha |
Alpha |
mod |
Test model |
Value
A vector of logistic regression model coefficients.
Examples
t <- rbind(c(0.2870353, 0.07833006, 0.00435167, 0.09946088, 0.029199878, 0.0016222154),
c(0.3609647, 0.06566994, 0.00364833, 0.06253912, 0.006800122, 0.0003777846))
ll.ge.logistic(t, N = 200, Alpha = 0.05, mod = "Dominant")
Function to output log likelihood for logistic outcome with linear environment variables
Description
Returns the standard deviation of y given x for linear models with linear environment interaction
Usage
ll.ge.logistic.lin.envir(
sd_e,
N = NULL,
MAF,
power = NULL,
beta0,
OR_G,
OR_E,
OR_GE,
Alpha,
True.Model,
Test.Model
)
Arguments
sd_e |
Standard deviation of the environmental variable |
N |
desired sample size |
MAF |
Vector of minor allele frequencies |
power |
desired power |
beta0 |
the beta0 coefficient in the logistic model |
OR_G |
Vector of genetic odds ratios to detect |
OR_E |
Vector of environmental odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
a function to be used as the integrand for the mle
Examples
ll.ge.logistic.lin.envir(sd_e = 1, MAF = 0.2, N = 30, beta0 = -1.462531, OR_G = 1.1,
OR_E = 1.2, OR_GE = 1.5, Alpha = 0.05, True.Model = "Dominant", Test.Model = "Dominant")
Function to return log likelihood function for specified model type
Description
Convenience function to return log likelihood function for specified model type
Usage
ll.linear.selector(model)
Arguments
model |
The genetic model in the linear regression: "Dominant", "Additive", "Recessive", "2df" or "null" |
Value
Log likelihood function for specified model type
Examples
ll.linear.selector("Dominant")
Zero finding function
Description
Finds the zeros of a function af. Alternative to uniroot, designed specifically to work with the genpwr package. Finds multiple zeros if a function has more than one in the given range.
Usage
ll_zero_finder2(af, ii = 6, lower = 0, upper = 1, qdelta = 27)
Arguments
af |
The function for which to find the zero(s) |
ii |
Number of iterations. The more iterations, the more accuracy. It is recommended that ii be at least 4. |
lower |
Lower limit of region in which to find the zero |
upper |
Upper limit of region in which to find the zero |
qdelta |
Factor for finding intervals over which the function is close to zero |
Value
Points over the given interval at which the given function is approximately equal to zero
Examples
ll_zero_finder2(function(x) (x-0.5)^2 - 0.1)
ll_zero_finder2(function(x) 8*x^3 - 11.2*x^2 + 4.56*x - 0.476)
Function to calculate MLE's for logistic models
Description
Finds the maximum likelihood estimates for a given 2x3 table under the specified genetic model.
Usage
logistic.mles(t, model)
Arguments
t |
A 2x3 table of the joint probabilities of disease and genotype. Rows are case vs. control and columns are genotypes. |
model |
The assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' |
Value
A vector of logistic regression model coefficients.
Examples
logistic.mles(rbind(c(0.2967437, 0.1806723, 0.02258404),
c(0.3432563, 0.1393277, 0.01741596)), "Dominant")
Logit Function
Description
Calculates the logit of a specified value.
Usage
logit(x, min = 0, max = 1)
Arguments
x |
a number between 0 and 1. |
min |
minimum |
max |
maximum |
Value
The logit of x.
Examples
logit(0.5)
Function to Determine Non-Centrality Parameter of the Chi-squared distribution
Description
This function is set to 0 and solved for x, the non-centrality parameter to determine the sample size in ss.calc
Usage
ncp.search(x, power, Alpha, df)
Arguments
x |
the non-centrality parameter |
power |
the desired power |
Alpha |
the desired type 1 error rate |
df |
the degrees of freedom for the likelihood ratio test |
Value
numeric value of the function
Examples
ncp.search(x = 7.848861, pow = 0.8, Alpha = 0.05, df=1)
Function to Calculate Null Log Likelihood for a Logistic Regression Model
Description
Calculates the log likelihood for a given set of logistic regression coefficients under the null.
Usage
null.ll(t)
Arguments
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
Value
The log likelihood.
Examples
null.ll(rbind(c(0.2339079, 0.05665039, 0.009441731),
c(0.3285921, 0.31834961, 0.053058269)))
Function to Calculate Expected Null Log Likelihood for a Linear Regression Model
Description
Calculates the expected log likelihood for a given set of linear regression coefficients under the null.
Usage
null.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
Arguments
beta |
Vector of linear regression coefficients. |
m |
Minor allele frequency. |
es |
Vector of effect sizes with two elements, (mean AB - mean AA) and (mean BB - mean AA). |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
Value
The log likelihood.
Examples
null.ll.linear(beta = 0.03, m = 0.1, es = c(0,3),
sd_y_x_model = 1, sd_y_x_truth = 0.9544108)
Odds Ratio Function
Description
Calculates the odds ratio for a given power, at a given sample size, N, with type 1 error rate, Alpha
Usage
odds_ratio_function(
N = NULL,
Case.Rate = NULL,
k = NULL,
MAF = NULL,
power = NULL,
risk_allele = TRUE,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
Case.Rate |
Vector of the proportion(s) of cases in the sample (cases/(cases + controls)). Either k or Case.Rate must be specified. |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
MAF |
Vector of minor allele frequencies |
power |
Vector of powers to detect |
risk_allele |
Logical: If OR > 1, the allele is classified as a "risk allele" |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector vector the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the odds ratios for all combinations of the specified parameters
Examples
or <- odds_ratio_function(N=c(100), Case.Rate=0.3,
k=NULL, MAF= 0.25, power=0.8,
Alpha = 0.05, risk_allele = TRUE, True.Model = 'All', Test.Model = 'All')
2df Model Function
Description
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "2df"
Usage
or.function.2df(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
Arguments
like |
Expected log likelihood |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
True.Model |
A vector object specifying the true underlying genetic model(s): 'Dominant', 'Additive', or 'Recessive' |
risk_allele |
Logical: If OR > 1, the allele is classified as a "risk allele" |
Value
: The odds ratios and their corresponding genetic model(s)
Examples
or.function.2df(like=-0.5626909, Case.Rate=0.3, P_AA=0.5625,
P_AB=0.375, P_BB=0.0625, True.Model="Recessive", risk_allele=TRUE)
Function to Plot Odds Ratio Results
Description
Plot the power results by MAF, Power, Alpha or N
Usage
or.plot(
data = NULL,
x = "MAF",
panel.by = "True.Model",
y_limit = NULL,
y_log = F,
return_gg = F,
linear.effect.measure = "ES",
select.Alpha = NULL,
select.power = NULL,
select.ES = NULL,
select.N = NULL,
select.MAF = NULL,
select.Case.Rate = NULL,
select.SD = NULL,
select.True.Model = NULL,
select.Test.Model = NULL
)
Arguments
data |
The data frame result from |
x |
The desired variable on the y axis: "MAF", "OR", "Alpha", or "N_total" |
panel.by |
A grouping variable to panel the graphs by: "True.Model", "MAF", "Power", "Alpha", or "N_total" |
y_limit |
An object specifying the minimum and maximum of the y-axis (eg c(0,4)) default is NULL, which allows the limits to be picked automatically |
y_log |
Logical, specifying whether the y axis should be logarithmic. Default is F |
return_gg |
Logical, specifying whether to return the ggplot object instead of printing out the plot |
linear.effect.measure |
Should the graphs indicate ES values, or R2 values? (default ES) |
select.Alpha |
Only produce graphs for the specified Alpha level(s). |
select.power |
Only produce graphs for the specified Power(s). |
select.ES |
Only produce graphs for the specified effect sizes(s). |
select.N |
Only produce graphs for the specified sample size(s). |
select.MAF |
Only produce graphs for the specified minor allele frequency(ies). |
select.Case.Rate |
Only produce graphs for the specified case rate(s). |
select.SD |
Only produce graphs for the specified standard deviation(s). |
select.True.Model |
Only produce graphs for the specified true genetic model(s): "Additive", "Dominant", "Recessive". |
select.Test.Model |
Only produce graphs for the specified testing model(s): "Additive", "Dominant", "Recessive", "2df". |
Value
A series of plots with power on the Y axis.
Examples
or <- odds_ratio_function(N=1000, Case.Rate=0.5, k=NULL,
MAF=seq(0.3, 0.32, 0.01), power=0.8,Alpha=0.05,
True.Model=c("Dominant", "Recessive"), Test.Model=c("Dominant", "Recessive"))
or.plot(data=or, x='MAF')
Odds ratio calculation
Description
Calculates odds ratio for given parameters. Used by the function odds_ratio_function.
Usage
or_calc(a, b, c, d, e, f, mod, risk_allele)
Arguments
a |
The probability of a case given homogeneity for the major allele |
b |
The probability of a case given heterozygosity |
c |
The probability of a case given homogeneity for the minor allele |
d |
The probability of a control given homogeneity for the major allele |
e |
The probability of a control given heterozygosity |
f |
The probability of a control given homogeneity for the minor allele#' |
mod |
The model to be used (eg "Dominant", "Recessive", etc) |
risk_allele |
Is this allele a risk allele? use T or F |
Value
Odds ratio
Examples
or_calc(a = 0.3649185, b = 0.12797197, c = 0.007109554,
d= 0.4450815, e= 0.05202803, f = 0.002890446,
mod = "Dominant", risk_allele = TRUE)
Function to output probability vector used in calculation of MLE's for linear outcome with logistic environment interaction
Description
Returns probability vector used in calculation of MLE's for linear outcome with logistic environment interaction
Usage
p_vec_returner(MAF, P_e)
Arguments
MAF |
Minor allele frequency |
P_e |
Population prevalence of logistic environmental factor |
Value
A probability vector to be used in MLE calculation for linear outcome with logistic environment interaction
Examples
p_vec_returner(MAF = 0.1, P_e = 0.2)
Function to output probability vector used in calculation of MLE's for linear outcome with linear environment interaction
Description
Returns probability vector used in calculation of MLE's for linear outcome with linear environment interaction
Usage
p_vec_returner_lin_env(MAF)
Arguments
MAF |
Minor Allele Frequency |
Value
A probability vector to be used in MLE calculation for linear outcome with linear environment interaction
Examples
p_vec_returner_lin_env(0.1)
Function to Calculate Power
Description
Calculates the power to detect an odds ratio, OR, at a given sample size, N, with type 1 error rate, Alpha
Usage
power.calc(
N = NULL,
Case.Rate = NULL,
k = NULL,
MAF = NULL,
OR = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
Case.Rate |
Vector of the proportion(s) of cases in the sample (cases/(cases + controls)). Either k or Case.Rate must be specified. |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
MAF |
Vector of minor allele frequencies |
OR |
Vector of odds ratios to detect |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, OR, Power, etc)
Examples
pw <- power.calc(N=2000, Case.Rate=0.5, k=NULL,
MAF=0.2, OR=1.5,Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Calculate Power for Linear Models
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
power.calc.linear(
N = NULL,
MAF = NULL,
ES = NULL,
R2 = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
MAF |
Vector of minor allele frequencies |
ES |
Vector of effect sizes (difference in means) to detect. Either ES or R2 must be specified. |
R2 |
Vector of R-squared values to detect. Either ES or R2 must be specified. |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive1', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
pw <- power.calc.linear(N=1000,
MAF=0.1, ES=3,sd_y = 1,Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Plot Power Results
Description
Plot the power results by MAF, OR, Alpha or N
Usage
power.plot(
data = NULL,
x = "MAF",
panel.by = "True.Model",
y_limit = NULL,
y_log = F,
return_gg = F,
linear.effect.measure = "ES",
select.Alpha = NULL,
select.OR = NULL,
select.ES = NULL,
select.N = NULL,
select.MAF = NULL,
select.Case.Rate = NULL,
select.SD = NULL,
select.True.Model = NULL,
select.Test.Model = NULL
)
Arguments
data |
The data frame result from |
x |
The desired variable on the y axis: "MAF", "OR", "Alpha", or "N_total" |
panel.by |
A grouping variable to panel the graphs by: "True.Model", "MAF", "OR", "Alpha", or "N_total" |
y_limit |
An object specifying the minimum and maximum of the y-axis (eg c(0,4)) default is NULL, which allows the limits to be picked automatically |
y_log |
Logical, specifying whether the y axis should be logarithmic. Default is F |
return_gg |
Logical, specifying whether to return the ggplot object instead of printing out the plot |
linear.effect.measure |
Should the graphs indicate ES values, or R2 values? (default ES) |
select.Alpha |
Only produce graphs for the specified Alpha level(s). |
select.OR |
Only produce graphs for the specified odds ratio(s). |
select.ES |
Only produce graphs for the specified effect sizes(s). |
select.N |
Only produce graphs for the specified sample size(s). |
select.MAF |
Only produce graphs for the specified minor allele frequency(ies). |
select.Case.Rate |
Only produce graphs for the specified case rate(s). |
select.SD |
Only produce graphs for the specified standard deviation(s). |
select.True.Model |
Only produce graphs for the specified true genetic model(s): "Additive", "Dominant", "Recessive". |
select.Test.Model |
Only produce graphs for the specified testing model(s): "Additive", "Dominant", "Recessive", "2df". |
Value
A series of plots with power on the Y axis.
Examples
pw <- power.calc(N=1000, Case.Rate=c(0.5), k=NULL,
MAF=seq(0.15, 0.2, 0.01), OR=1.5,Alpha=c(0.05),
True.Model='All', Test.Model='All')
Function to Calculate Power for Logistic Models with Environment Interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
power_envir.calc(
N = NULL,
Case.Rate = NULL,
k = NULL,
MAF = NULL,
OR_G = NULL,
OR_E = NULL,
OR_GE = NULL,
P_e = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
MAF |
Vector of minor allele frequencies |
OR_G |
Vector of genetic odds ratios to detect |
OR_E |
Vector of environmental odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive1', 'Additive2', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
pw <- power_envir.calc(P_e = 0.2, MAF = 0.1, N = 200, Case.Rate = 0.5, Alpha = 0.05,
OR_G = 1.5, OR_E = 2, OR_GE = 1.8, Test.Model = "All", True.Model = "All")
Function to Calculate Power for Linear Models with logistic environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
power_envir.calc.linear_outcome(
N = NULL,
MAF = NULL,
ES_G = NULL,
ES_E = NULL,
ES_GE = NULL,
P_e = NULL,
R2_G = NULL,
R2_E = NULL,
R2_GE = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
MAF |
Vector of minor allele frequencies |
ES_G |
Vector of genetic effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_E |
Vector of environmental effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_GE |
Vector of genetic/environment interaction effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
R2_G |
Vector of genetic R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_E |
Vector of environmental R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_GE |
Vector of genetic/environment interaction R-squared valuesEither ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
pw <- power_envir.calc.linear_outcome(N=100, ES_G = 1.2, ES_E = 1.3,
ES_GE = 2, Alpha = 0.05, MAF = 0.2, P_e = 0.2,
sd_y = 10, True.Model = "All", Test.Model = "All")
Function to Calculate Power for Linear Models with linear environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
power_linear_envir.calc.linear_outcome(
N = NULL,
MAF = NULL,
ES_G = NULL,
ES_E = NULL,
ES_GE = NULL,
sd_e = NULL,
R2_G = NULL,
R2_E = NULL,
R2_GE = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
MAF |
Vector of minor allele frequencies |
ES_G |
Vector of genetic effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_E |
Vector of environmental effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_GE |
Vector of genetic/environment interaction effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
sd_e |
Standard deviation of the environmental variable |
R2_G |
Vector of genetic R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_E |
Vector of environmental R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_GE |
Vector of genetic/environment interaction R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
pw <- power_linear_envir.calc.linear_outcome(N=1000,
ES_G=0.5, ES_E=1.6, ES_GE=1.4,
sd_e = 1, MAF=0.28,
sd_y = 5,Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Calculate Power for Linear Models with logistic environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
power_linear_envir.calc.logistic_outcome(
N = NULL,
MAF = NULL,
OR_G = NULL,
OR_E = NULL,
OR_GE = NULL,
sd_e = NULL,
Case.Rate = NULL,
k = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
N |
Vector of the desired sample size(s) |
MAF |
Vector of minor allele frequencies |
OR_G |
Vector of genetic odds ratios to detect |
OR_E |
Vector of environmental odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
sd_e |
Standard deviation of the environmental variable |
Case.Rate |
Standard deviation of the outcome in the population (ignoring genotype). Either Case.Rate_x or Case.Rate must be specified. |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
pw <- power_linear_envir.calc.logistic_outcome(N=30,
OR_G=1.1, OR_E=1.2, OR_GE=1.5,
sd_e = 1, MAF=0.2, Case.Rate = 0.2,
Alpha=0.05, True.Model="All", Test.Model="All")
Function to Solve Quadratic Equations
Description
Finds the positive root of a quadratic equation ax^2 + bx + c .
Usage
quad_roots(a, b, c)
Arguments
a |
the coefficient for x^2 |
b |
the coefficient for x |
c |
the constant |
Value
The positive root of the quadratic equation ax^2 + bx + c
Examples
pw<-power.calc(N=c(1000,2000), Case.Rate=c(0.5),
k=NULL, MAF=seq(0.05, 0.1, 0.01), OR=c(3,4),
Alpha=c(0.05), True.Model='All', Test.Model='All')
Function to Calculate t matrix for logistic outcome with binary environment interaction in recessive model
Description
Calculates the t matrix for logistic outcome with binary environment interaction in recessive model
Usage
rec.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)
Arguments
MAF |
Vector of minor allele frequencies |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
OR_E |
Vector of environmental odds ratios to detect |
OR_G |
Vector of genetic odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
Value
t matrix for all combinations of environment/outcome
Examples
rec.fun.t(MAF = 0.1, P_e = 0.2, Case.Rate = 0.5,
OR_G = 1.5, OR_E = 2, OR_GE = 1.8)
Recessive Model Function
Description
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "Recessive"
Usage
rec.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
Arguments
like |
Expected log likelihood |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
True.Model |
A vector object specifying the true underlying genetic model(s): 'Dominant', 'Additive', or 'Recessive' |
risk_allele |
Logical: If OR > 1, the allele is classified as a "risk allele" |
Value
: The odds ratios and their corresponding genetic model(s)
Examples
rec.or.function(like=-0.57162, Case.Rate=0.3, P_AA=0.5625, P_AB=0.375,
P_BB=0.0625, True.Model="Recessive", risk_allele=TRUE)
Function to Calculate Recessive Log Likelihood for a Logistic Regression Model
Description
Calculates the log likelihood for a given set of logistic regression coefficients under a recessive genetic model.
Usage
recessive.ll(beta, t)
Arguments
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
Value
The log likelihood.
Examples
recessive.ll(c(-0.3793525, -1.1395417),
rbind(c(0.2339079, 0.05665039, 0.009441731),
c(0.3285921, 0.31834961, 0.053058269)))
Function to Calculate Recessive Log Likelihood for a Linear Regression Model
Description
Calculates the log likelihood for a given set of linear regression coefficients under a recessive genetic model.
Usage
recessive.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
Arguments
beta |
Vector of linear regression coefficients. |
m |
Minor allele frequency. |
es |
Vector of effect sizes with two elements, (mean AB - mean AA) and (mean BB - mean AA). |
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
sd_y_x_truth |
The standard deviation of Y given X (predictors/genotype) given genotype under the true model. |
Value
The log likelihood.
Examples
recessive.ll.linear(beta = c(0, 3), m = 0.1, es = c(0,3),
sd_y_x_model = 0.9544108, sd_y_x_truth = 0.9544108)
Binomial coefficient calculation
Description
Operates within add.or.function to solve for 'a' when 'b' is known in an additive model
Usage
solve_a(b, cr, P_AA, P_AB, P_BB)
Arguments
b |
The "b" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions |
cr |
proportion of cases in the sample (cases/(cases + controls)). |
P_AA |
Probability the allele is homozygous for the major allele |
P_AB |
Probability the allele is heterozygous |
P_BB |
Probability the allele is homozygous for the minor allele |
Value
: The "a" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions
Examples
solve_a(0.1493558, 0.3, 0.5625, 0.375, 0.062)
Function to Calculate Sample Size
Description
Calculates the necessary sample size to achieve the specified level of power to detect an odds ratio, OR, with type 1 error rate, Alpha
Usage
ss.calc(
power = 0.8,
Case.Rate = NULL,
k = NULL,
MAF = NULL,
OR = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
power |
Vector of the desired power(s) |
Case.Rate |
Vector of the proportion(s) of cases in the sample (cases/(cases + controls)). Either k or Case.Rate must be specified. |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
MAF |
Vector of minor allele frequencies |
OR |
Vector of odds ratios to detect |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the total number of subjects required for all combinations of the specified parameters (Case.Rate, OR, Power, etc)
Examples
ss <- ss.calc(power=0.8, Case.Rate=0.5, k=NULL,
MAF=0.1, OR=3,Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Calculate Sample Size in Linear Models
Description
Calculates the necessary sample size to acheive the specified level of power to detect an effect size, ES or R2 value, with type 1 error rate, Alpha
Usage
ss.calc.linear(
power = 0.8,
MAF = NULL,
ES = NULL,
R2 = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
power |
Vector of the desired power(s) |
MAF |
Vector of minor allele frequencies |
ES |
Vector of effect sizes (difference in means) to detect. Either ES or R2 must be specified. |
R2 |
Vector of R-squared values to detect. Either ES or R2 must be specified. |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the total number of subjects required for all combinations of the specified parameters
Examples
ss <- ss.calc.linear(power=0.8,MAF=0.1,
ES=3, R2=NULL, sd_y = 1,Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Plot Sample Size Results
Description
Plot the sample size results by MAF, OR, Alpha or Power
Usage
ss.plot(
data = NULL,
x = "MAF",
panel.by = "True.Model",
y_limit = NULL,
y_log = F,
return_gg = F,
linear.effect.measure = "ES",
select.Alpha = NULL,
select.OR = NULL,
select.ES = NULL,
select.Power = NULL,
select.MAF = NULL,
select.Case.Rate = NULL,
select.SD = NULL,
select.True.Model = NULL,
select.Test.Model = NULL
)
Arguments
data |
The data frame result from |
x |
The desired variable on the y axis: "MAF", "OR", "ES","Alpha", or "Power" |
panel.by |
A grouping variable to panel the graphs by: "True.Model", "MAF", "OR", "Alpha", or "Power" |
y_limit |
An object specifying the minimum and maximum of the y-axis (eg c(0,4)) default is NULL, which allows the limits to be picked automatically |
y_log |
Logical, specifying whether the y axis should be logarithmic. Default is F |
return_gg |
Logical, specifying whether to return the ggplot object instead of printing out the plot |
linear.effect.measure |
Should the graphs indicate ES values, or R2 values? (default ES) |
select.Alpha |
Only produce graphs for the specified Alpha level(s). |
select.OR |
Only produce graphs for the specified odds ratio(s). |
select.ES |
Only produce graphs for the specified effect size(s). |
select.Power |
Only produce graphs for the specified power(s). |
select.MAF |
Only produce graphs for the specified minor allele frequency(ies). |
select.Case.Rate |
Only produce graphs for the specified case rate(s). |
select.SD |
Only produce graphs for the specified standard deviation(s). |
select.True.Model |
Only produce graphs for the specified true genetic model(s): "Additive", "Dominant", "Recessive". |
select.Test.Model |
Only produce graphs for the specified testing model(s): "Additive", "Dominant", "Recessive", "2df". |
Value
A series of plots with sample size on the Y axis.
Examples
ss <- ss.calc(power=0.8, Case.Rate=c(0.5), k=NULL,
MAF=seq(0.01, 0.05, 0.01), OR=c(4),Alpha=c(0.05),
True.Model='All', Test.Model='All')
ss.plot(data=ss, x='MAF',panel.by='OR')
Function to Calculate Power for Logistic Models with Environment Interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
ss_envir.calc(
power = 0.8,
Case.Rate = NULL,
k = NULL,
MAF = NULL,
OR_G = NULL,
OR_E = NULL,
OR_GE = NULL,
P_e = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
power |
Vector of the desired power(s) |
Case.Rate |
proportion of cases in the sample (cases/(cases + controls)). |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
MAF |
Vector of minor allele frequencies |
OR_G |
Vector of genetic odds ratios to detect |
OR_E |
Vector of environmental odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive1', 'Additive2', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
ssc <- ss_envir.calc(P_e = 0.2, MAF = 0.1, power = 0.6, Case.Rate = 0.5, Alpha = 0.05,
OR_G = 1.5, OR_E = 2, OR_GE = 1.8, Test.Model = "All", True.Model = "All")
Function to Calculate Power for Linear Models with logistic environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
ss_envir.calc.linear_outcome(
pow = NULL,
MAF = NULL,
ES_G = NULL,
ES_E = NULL,
ES_GE = NULL,
P_e = NULL,
R2_G = NULL,
R2_E = NULL,
R2_GE = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
pow |
Vector of the desired power(s) |
MAF |
Vector of minor allele frequencies |
ES_G |
Vector of genetic effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_E |
Vector of environmental effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_GE |
Vector of genetic/environment interaction effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
P_e |
Vector of proportions of the population with exposure to the environmental effect |
R2_G |
Vector of genetic R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_E |
Vector of environmental R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_GE |
Vector of genetic/environment interaction R-squared values Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
ss_envir.calc.linear_outcome(pow=0.8, ES_G = 1.2, ES_E = 1.3,
ES_GE = 2, Alpha = 0.05, MAF = 0.1, P_e = 0.2,
sd_y = 10, True.Model = "All", Test.Model = "All")
Function to Calculate Power for Linear Models with linear environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
ss_linear_envir.calc.linear_outcome(
pow = NULL,
MAF = NULL,
ES_G = NULL,
ES_E = NULL,
ES_GE = NULL,
sd_e = NULL,
R2_G = NULL,
R2_E = NULL,
R2_GE = NULL,
sd_y = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
pow |
Vector of the desired power(s) |
MAF |
Vector of minor allele frequencies |
ES_G |
Vector of genetic effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_E |
Vector of environmental effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
ES_GE |
Vector of genetic/environment interaction effect sizes (difference in means) to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
sd_e |
Standard deviation of the environmental variable |
R2_G |
Vector of genetic R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_E |
Vector of environmental R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
R2_GE |
Vector of genetic/environment interaction R-squared values to detect. Either ES_G, ES_E, and ES_EG or R2_G, R2_E, and R2_EG must be specified. |
sd_y |
Standard deviation of the outcome in the population (ignoring genotype). Either sd_y_x or sd_y must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
ss_linear_envir.calc.linear_outcome(pow = 0.8,
ES_G=0.5, ES_E=1.6, ES_GE=1.4,
sd_e = 1, MAF=0.28,
sd_y = 5,Alpha=0.05,
True.Model='All', Test.Model='All')
Function to Calculate Sample Size for Linear Models with logistic environment interaction
Description
Calculates the power to detect an difference in means/effect size/regression coefficient, at a given sample size, N, with type 1 error rate, Alpha
Usage
ss_linear_envir.calc.logistic_outcome(
power = NULL,
MAF = NULL,
OR_G = NULL,
OR_E = NULL,
OR_GE = NULL,
sd_e = NULL,
Case.Rate = NULL,
k = NULL,
Alpha = 0.05,
True.Model = "All",
Test.Model = "All"
)
Arguments
power |
Vector of the desired power(s) |
MAF |
Vector of minor allele frequencies |
OR_G |
Vector of genetic odds ratios to detect |
OR_E |
Vector of environmental odds ratios to detect |
OR_GE |
Vector of genetic/environmental interaction odds ratios to detect |
sd_e |
Standard deviation of the environmental variable |
Case.Rate |
Standard deviation of the outcome in the population (ignoring genotype). Either Case.Rate_x or Case.Rate must be specified. |
k |
Vector of the number of controls per case. Either k or Case.Rate must be specified. |
Alpha |
the desired type 1 error rate(s) |
True.Model |
A vector specifying the true underlying genetic model(s): 'Dominant', 'Additive', 'Recessive' or 'All' |
Test.Model |
A vector specifying the assumed genetic model(s) used in testing: 'Dominant', 'Additive', 'Recessive' or 'All' |
Value
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
Examples
ss <- ss_linear_envir.calc.logistic_outcome(power=0.8,
OR_G=1.1, OR_E=1.2, OR_GE=1.5,
sd_e = 1, MAF=0.2, Case.Rate = 0.2,
Alpha=0.05, True.Model="All", Test.Model="All")
Zero finder
Description
Finds zeros of multinomial functions using the nleqslv package
Usage
zero_finder_nleqslv(
afun,
veclength,
tol = 0.4,
x.start.vals = NULL,
upper.lim = Inf
)
Arguments
afun |
The function to find zeros |
veclength |
The dimension of the system of equations |
tol |
The range within which to set start values for the function to use to find zeros |
x.start.vals |
Optional user defined start values |
upper.lim |
to be used if there is to be an upper limit to the solution |
Value
Predicted zeros of the given equation
Examples
afun <- function(x) {
y <- numeric(2)
y[1] <- x[1]^2 + x[2]^2 - 1
y[2] <- exp(x[1]-1) + x[2]^3 - 1.1
y
}
zero_finder_nleqslv(afun, veclength = 2)