| Title: | Power Calculations Under Genetic Model Misspecification |
|---|---|
| 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. |
| Authors: | Camille Moore [aut, cre], Sean Jacobson [aut] |
| Maintainer: | Camille Moore <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.4 |
| Built: | 2024-12-16 07:00:33 UTC |
| Source: | CRAN |
Calculates the t matrix for logistic outcome with binary environment interaction in additive model
add.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)add.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)
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)). |
t matrix for all combinations of environment/outcome
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)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)
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "Additive"
add.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)add.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
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" |
: The odds ratios and their corresponding genetic model(s)
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)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)
Calculates the log likelihood for a given set of logistic regression coefficients under an additive genetic model.
additive.ll(beta, t)additive.ll(beta, t)
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
The log likelihood.
additive.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))additive.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))
Calculates the log likelihood for a given set of linear regression coefficients under an additive genetic model.
additive.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)additive.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
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. |
The log likelihood.
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)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)
convert to numeric with scientific notation containing the "." character
as.numeric2(char)as.numeric2(char)
char |
string to be converted to numeric |
a number
as.numeric2("2e.2")as.numeric2("2e.2")
Convenience function to calculate the log likelihood of a specified model.
calc.like(beta, t, model)calc.like(beta, t, model)
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" |
The log likelihood.
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")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")
Convenience function to calculate the log likelihood of a specified model.
calc.like.linear(beta, m, es_ab, es_bb, sd_y_x_model, sd_y_x_truth, model)calc.like.linear(beta, m, es_ab, es_bb, sd_y_x_model, sd_y_x_truth, model)
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" |
The log likelihood.
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")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")
Returns the standard deviation of y given x for linear models with logistic environment interaction
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 )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 )
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 |
The standard deviation of y given x for linear models with logistic environment interaction
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")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")
Calculates the log likelihood for a given set of logistic regression coefficients under an unspecificed/2df genetic model.
df2.ll(beta, t)df2.ll(beta, t)
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
The log likelihood.
df2.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))df2.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))
Calculates the log likelihood for a given set of linear regression coefficients under a the 2df model.
df2.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)df2.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
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. |
The log likelihood.
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)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)
Calculates the t matrix for logistic outcome with binary environment interaction in dominant model
dom.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)dom.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)
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)). |
t matrix for all combinations of environment/outcome
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)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)
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "Dominant"
dom.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)dom.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
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" |
: The odds ratios and their corresponding genetic model(s)
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)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)
Calculates the log likelihood for a given set of logistic regression coefficients under a dominant genetic model.
dominant.ll(beta, t)dominant.ll(beta, t)
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
The log likelihood.
dominant.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))dominant.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))
Calculates the log likelihood for a given set of linear regression coefficients under a dominant genetic model.
dominant.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)dominant.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
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. |
The log likelihood.
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)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)
Calculates the detectable effect size/regression coefficient, at a given sample size, N, and power, with type 1 error rate, Alpha
es.calc.linear( power = NULL, N = NULL, MAF = NULL, sd_y = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )es.calc.linear( power = NULL, N = NULL, MAF = NULL, sd_y = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
es <- es.calc.linear(N=1000,power=0.8, MAF=0.1, sd_y = 1, Alpha=0.05, True.Model='All', Test.Model='All')es <- es.calc.linear(N=1000,power=0.8, MAF=0.1, sd_y = 1, Alpha=0.05, True.Model='All', Test.Model='All')
Calculates the expected log likelihood for a single genotype given the true and estimated mean and standard deviation for the outcome.
expected.linear.ll(mean_truth, mean_model, sd_y_x_truth, sd_y_x_model)expected.linear.ll(mean_truth, mean_model, sd_y_x_truth, sd_y_x_model)
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. |
The log likelihood.
expected.linear.ll(mean_truth = 0, mean_model = 0.03, sd_y_x_model = 1, sd_y_x_truth = 0.9544108)expected.linear.ll(mean_truth = 0, mean_model = 0.03, sd_y_x_model = 1, sd_y_x_truth = 0.9544108)
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.
expected.linear.ll.lin.env(sd_y_x_model)expected.linear.ll.lin.env(sd_y_x_model)
sd_y_x_model |
The standard deviation of Y (the outcome) given X (predictors/genotype) under the test model. |
The log likelihood.
expected.linear.ll.lin.env(4.309354)expected.linear.ll.lin.env(4.309354)
Operates within add.or.function to find probability of disease in a dominant truth given AB or BB, additive test model
find.prob.dom(x, P_AA, P_AB, P_BB, cr, like)find.prob.dom(x, P_AA, P_AB, P_BB, cr, like)
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 |
: The "a" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions
find.prob.dom(0.1510677, 0.5625, 0.375, 0.0625, 0.3, -0.57162)find.prob.dom(0.1510677, 0.5625, 0.375, 0.0625, 0.3, -0.57162)
Operates within add.or.function to find probability of disease in a recessive truth given AB or BB, additive test model
find.prob.rec(x, P_AA, P_AB, P_BB, cr, like)find.prob.rec(x, P_AA, P_AB, P_BB, cr, like)
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 |
: The "a" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions
find.prob.rec(0.7072381, 0.5625, 0.375, 0.0625, 0.3, -0.6005743)find.prob.rec(0.7072381, 0.5625, 0.375, 0.0625, 0.3, -0.6005743)
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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"))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"))
Returns the standard deviation of y given x for linear models with linear environment interaction
integrand_funct_case(x1, x2)integrand_funct_case(x1, x2)
x1 |
"true" part of model |
x2 |
"test" part of model |
a function to be used as the integrand for the mle
integrand_funct_case(-1.462531 + 1*0.1823216, -1.462531 + 1*0.1823216)integrand_funct_case(-1.462531 + 1*0.1823216, -1.462531 + 1*0.1823216)
Returns the standard deviation of y given x for linear models with linear environment interaction
integrand_funct_control(x1, x2)integrand_funct_control(x1, x2)
x1 |
"true" part of model |
x2 |
"test" part of model |
a function to be used as the integrand for the mle
integrand_funct_control(-1.462531 + 1*0.1823216, -1.462531 + 1*0.1823216)integrand_funct_control(-1.462531 + 1*0.1823216, -1.462531 + 1*0.1823216)
Finds the maximum likelihood estimates for a given MAF under the specified genetic model and effect size.
linear.mles(m, es_ab, es_bb, model)linear.mles(m, es_ab, es_bb, model)
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' |
A vector of linear regression model coefficients.
linear.mles(m = 0.1, es_ab = 0, es_bb = 3, model = "Dominant")linear.mles(m = 0.1, es_ab = 0, es_bb = 3, model = "Dominant")
Returns the standard deviation of y given x for linear models with linear environment interaction
linear.mles.lin.envir.interaction( MAF, beta0, ES_G, ES_E, ES_GE, Test.Model, True.Model )linear.mles.lin.envir.interaction( MAF, beta0, ES_G, ES_E, ES_GE, Test.Model, True.Model )
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 |
The standard deviation of y given x for linear models with linear environment interaction
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")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")
Returns the standard deviation of y given x for linear models with linear environment interaction
linear.mles.lin.envir.interaction_reduced( MAF, beta0, ES_G, ES_E, ES_GE, Test.Model, True.Model )linear.mles.lin.envir.interaction_reduced( MAF, beta0, ES_G, ES_E, ES_GE, Test.Model, True.Model )
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 |
The standard deviation of y given x for linear models with linear environment interaction
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")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")
Returns the standard deviation of y given x for linear models with logistic environment interaction
linear.mles.log.envir.interaction( MAF, P_e, ES_G, ES_E, ES_GE, Test.Model, True.Model, reduced = F )linear.mles.log.envir.interaction( MAF, P_e, ES_G, ES_E, ES_GE, Test.Model, True.Model, reduced = F )
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 |
The standard deviation of y given x for linear models with logistic environment interaction
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")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")
Returns the standard deviation of y given x for linear models with linear environment interaction
linear.outcome.lin.envir.interaction.sds( MAF, sd_e, beta0, ES_G, ES_E, ES_GE, mod, True.Model, sd_y )linear.outcome.lin.envir.interaction.sds( MAF, sd_e, beta0, ES_G, ES_E, ES_GE, mod, True.Model, sd_y )
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 |
The standard deviation of y given x for linear models with linear environment interaction
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")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")
Returns the standard deviation of y given x for linear models with linear environment interaction
linear.outcome.lin.envir.interaction.sds_reduced( MAF, sd_e, beta0, ES_G, ES_E, ES_GE, mod, True.Model, sd_y )linear.outcome.lin.envir.interaction.sds_reduced( MAF, sd_e, beta0, ES_G, ES_E, ES_GE, mod, True.Model, sd_y )
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 |
The standard deviation of y given x for linear models with linear environment interaction
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")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")
Returns the standard deviation of y given x for linear models with logistic environment interaction
linear.outcome.log.envir.interaction.sds( MAF, P_e, ES_G, ES_E, ES_GE, mod, True.Model, sd_y, reduced = F )linear.outcome.log.envir.interaction.sds( MAF, P_e, ES_G, ES_E, ES_GE, mod, True.Model, sd_y, reduced = F )
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 |
The standard deviation of y given x for linear models with logistic environment interaction
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")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
linear.sds(m, es_ab, es_bb, sd_y, model)linear.sds(m, es_ab, es_bb, sd_y, model)
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' |
A vector of linear regression model coefficients.
linear.sds(m = 0.1, es_ab = 0, es_bb = 3, sd_y = 1, model = "Dominant")linear.sds(m = 0.1, es_ab = 0, es_bb = 3, sd_y = 1, model = "Dominant")
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.
ll_zero_finder2(af, ii = 6, lower = 0, upper = 1, qdelta = 27)ll_zero_finder2(af, ii = 6, lower = 0, upper = 1, qdelta = 27)
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 |
Points over the given interval at which the given function is approximately equal to zero
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)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)
Finds the maximum likelihood estimates for a given 2x3 table under the specified genetic model.
ll.ge.logistic(t, N = NULL, power = NULL, Alpha, mod)ll.ge.logistic(t, N = NULL, power = NULL, Alpha, mod)
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 |
A vector of logistic regression model coefficients.
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")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")
Returns the standard deviation of y given x for linear models with linear environment interaction
ll.ge.logistic.lin.envir( sd_e, N = NULL, MAF, power = NULL, beta0, OR_G, OR_E, OR_GE, Alpha, True.Model, Test.Model )ll.ge.logistic.lin.envir( sd_e, N = NULL, MAF, power = NULL, beta0, OR_G, OR_E, OR_GE, Alpha, True.Model, Test.Model )
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' |
a function to be used as the integrand for the mle
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")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")
Convenience function to return log likelihood function for specified model type
ll.linear.selector(model)ll.linear.selector(model)
model |
The genetic model in the linear regression: "Dominant", "Additive", "Recessive", "2df" or "null" |
Log likelihood function for specified model type
ll.linear.selector("Dominant")ll.linear.selector("Dominant")
Finds the maximum likelihood estimates for a given 2x3 table under the specified genetic model.
logistic.mles(t, model)logistic.mles(t, model)
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' |
A vector of logistic regression model coefficients.
logistic.mles(rbind(c(0.2967437, 0.1806723, 0.02258404), c(0.3432563, 0.1393277, 0.01741596)), "Dominant")logistic.mles(rbind(c(0.2967437, 0.1806723, 0.02258404), c(0.3432563, 0.1393277, 0.01741596)), "Dominant")
Calculates the logit of a specified value.
logit(x, min = 0, max = 1)logit(x, min = 0, max = 1)
x |
a number between 0 and 1. |
min |
minimum |
max |
maximum |
The logit of x.
logit(0.5)logit(0.5)
This function is set to 0 and solved for x, the non-centrality parameter to determine the sample size in ss.calc
ncp.search(x, power, Alpha, df)ncp.search(x, power, Alpha, df)
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 |
numeric value of the function
ncp.search(x = 7.848861, pow = 0.8, Alpha = 0.05, df=1)ncp.search(x = 7.848861, pow = 0.8, Alpha = 0.05, df=1)
Calculates the log likelihood for a given set of logistic regression coefficients under the null.
null.ll(t)null.ll(t)
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
The log likelihood.
null.ll(rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))null.ll(rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))
Calculates the expected log likelihood for a given set of linear regression coefficients under the null.
null.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)null.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
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. |
The log likelihood.
null.ll.linear(beta = 0.03, m = 0.1, es = c(0,3), sd_y_x_model = 1, sd_y_x_truth = 0.9544108)null.ll.linear(beta = 0.03, m = 0.1, es = c(0,3), sd_y_x_model = 1, sd_y_x_truth = 0.9544108)
Calculates the odds ratio for a given power, at a given sample size, N, with type 1 error rate, Alpha
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" )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" )
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' |
A data frame including the odds ratios for all combinations of the specified parameters
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')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')
Calculates odds ratio for given parameters. Used by the function odds_ratio_function.
or_calc(a, b, c, d, e, f, mod, risk_allele)or_calc(a, b, c, d, e, f, mod, risk_allele)
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 |
Odds ratio
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)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)
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "2df"
or.function.2df(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)or.function.2df(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
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" |
: The odds ratios and their corresponding genetic model(s)
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)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)
Plot the power results by MAF, Power, Alpha or N
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 )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 )
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". |
A series of plots with power on the Y axis.
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')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')
Returns probability vector used in calculation of MLE's for linear outcome with logistic environment interaction
p_vec_returner(MAF, P_e)p_vec_returner(MAF, P_e)
MAF |
Minor allele frequency |
P_e |
Population prevalence of logistic environmental factor |
A probability vector to be used in MLE calculation for linear outcome with logistic environment interaction
p_vec_returner(MAF = 0.1, P_e = 0.2)p_vec_returner(MAF = 0.1, P_e = 0.2)
Returns probability vector used in calculation of MLE's for linear outcome with linear environment interaction
p_vec_returner_lin_env(MAF)p_vec_returner_lin_env(MAF)
MAF |
Minor Allele Frequency |
A probability vector to be used in MLE calculation for linear outcome with linear environment interaction
p_vec_returner_lin_env(0.1)p_vec_returner_lin_env(0.1)
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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")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")
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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")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")
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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')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')
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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")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")
Calculates the power to detect an odds ratio, OR, at a given sample size, N, with type 1 error rate, Alpha
power.calc( N = NULL, Case.Rate = NULL, k = NULL, MAF = NULL, OR = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )power.calc( N = NULL, Case.Rate = NULL, k = NULL, MAF = NULL, OR = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, OR, Power, etc)
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')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')
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
power.calc.linear( N = NULL, MAF = NULL, ES = NULL, R2 = NULL, sd_y = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )power.calc.linear( N = NULL, MAF = NULL, ES = NULL, R2 = NULL, sd_y = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
pw <- power.calc.linear(N=1000, MAF=0.1, ES=3,sd_y = 1,Alpha=0.05, True.Model='All', Test.Model='All')pw <- power.calc.linear(N=1000, MAF=0.1, ES=3,sd_y = 1,Alpha=0.05, True.Model='All', Test.Model='All')
Plot the power results by MAF, OR, Alpha or N
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 )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 )
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". |
A series of plots with power on the Y axis.
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')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')
Finds the positive root of a quadratic equation ax^2 + bx + c .
quad_roots(a, b, c)quad_roots(a, b, c)
a |
the coefficient for x^2 |
b |
the coefficient for x |
c |
the constant |
The positive root of the quadratic equation ax^2 + bx + c
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')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')
Calculates the t matrix for logistic outcome with binary environment interaction in recessive model
rec.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)rec.fun.t(MAF, P_e, OR_E, OR_G, OR_GE, Case.Rate)
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)). |
t matrix for all combinations of environment/outcome
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)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)
Operates within odds_ratio_function to calculate odds ratios for a Test.Model of "Recessive"
rec.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)rec.or.function(like, Case.Rate, P_AA, P_AB, P_BB, True.Model, risk_allele)
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" |
: The odds ratios and their corresponding genetic model(s)
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)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)
Calculates the log likelihood for a given set of logistic regression coefficients under a recessive genetic model.
recessive.ll(beta, t)recessive.ll(beta, t)
beta |
Vector of logistic regression coefficients. |
t |
A 2x3 table of joint probabilities of disease and genotype. Rows = case vs. control, columns=genotype. |
The log likelihood.
recessive.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))recessive.ll(c(-0.3793525, -1.1395417), rbind(c(0.2339079, 0.05665039, 0.009441731), c(0.3285921, 0.31834961, 0.053058269)))
Calculates the log likelihood for a given set of linear regression coefficients under a recessive genetic model.
recessive.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)recessive.ll.linear(beta, m, es, sd_y_x_model, sd_y_x_truth)
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. |
The log likelihood.
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)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)
Operates within add.or.function to solve for 'a' when 'b' is known in an additive model
solve_a(b, cr, P_AA, P_AB, P_BB)solve_a(b, cr, P_AA, P_AB, P_BB)
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 |
: The "a" in the binomial function ax^2 + bx + c that arises in solution for the additive OR functions
solve_a(0.1493558, 0.3, 0.5625, 0.375, 0.062)solve_a(0.1493558, 0.3, 0.5625, 0.375, 0.062)
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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")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")
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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")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")
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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')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')
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
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" )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" )
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' |
A data frame including the power for all combinations of the specified parameters (Case.Rate, ES, Power, etc)
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")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")
Calculates the necessary sample size to achieve the specified level of power to detect an odds ratio, OR, with type 1 error rate, Alpha
ss.calc( power = 0.8, Case.Rate = NULL, k = NULL, MAF = NULL, OR = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )ss.calc( power = 0.8, Case.Rate = NULL, k = NULL, MAF = NULL, OR = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )
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' |
A data frame including the total number of subjects required for all combinations of the specified parameters (Case.Rate, OR, Power, etc)
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')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')
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
ss.calc.linear( power = 0.8, MAF = NULL, ES = NULL, R2 = NULL, sd_y = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )ss.calc.linear( power = 0.8, MAF = NULL, ES = NULL, R2 = NULL, sd_y = NULL, Alpha = 0.05, True.Model = "All", Test.Model = "All" )
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' |
A data frame including the total number of subjects required for all combinations of the specified parameters
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')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')
Plot the sample size results by MAF, OR, Alpha or Power
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 )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 )
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". |
A series of plots with sample size on the Y axis.
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')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')
Returns X matrices used in calculation of MLE's for linear outcome with logistic environment interaction
X_mat_returner(mod, reduced = F)X_mat_returner(mod, reduced = F)
mod |
type of model |
reduced |
logical, indicates whether the X matrix will be used for a reduced model |
A matrix to be used in MLE calculation for linear outcome with logistic environment interaction
X_mat_returner(mod = "Dominant")X_mat_returner(mod = "Dominant")
Function to output X matrices used in calculation of MLE's for linear outcome with linear environment interaction
X_mat_returner_lle(mod)X_mat_returner_lle(mod)
mod |
type of model |
A probability vector to be used in MLE calculation for linear outcome with linear environment interaction
X_mat_returner_lle("Dominant")X_mat_returner_lle("Dominant")
Finds zeros of multinomial functions using the nleqslv package
zero_finder_nleqslv( afun, veclength, tol = 0.4, x.start.vals = NULL, upper.lim = Inf )zero_finder_nleqslv( afun, veclength, tol = 0.4, x.start.vals = NULL, upper.lim = Inf )
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 |
Predicted zeros of the given equation
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)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)