example_with_crossover {LEGIT}

Simulated example of a 2 way interaction GxE model with crossover point.

Description

Simulated example of a 2 way interaction GxE model with crossover point (where G and E are latent variables).

g_j \sim Binomial(n=1,p=.30)

j = 1, 2, 3, 4

e_l \sim 10 Beta(\alpha,\beta))

l = 1, 2, 3

g = .30g_1 + .10g_2 + .20g_3 + .40g_4

e = .45e_1 + .35e_2 + .2e_3

\mu = coef[1] + coef[2]e + coef[3]ge

y \sim Normal(\mu=\mu,\sigma=\code{sigma}) if logit=FALSE

y \sim Binomial(n=1,p=logit(\mu)) if logit=TRUE

Usage

example_with_crossover(
  N,
  sigma = 1,
  c = 0,
  coef_main = c(0, 1, 2),
  coef_G = c(0.3, 0.1, 0.2, 0.4),
  coef_E = c(0.45, 0.35, 0.2),
  logit = FALSE,
  seed = NULL,
  beta_param = c(2, 2)
)

Arguments

N

Sample size.

sigma

Standard deviation of the gaussian noise (if logit=FALSE).

c

crossover point

coef_main

Coefficients of the main model, must be a vector of size 3 for intercept, E main effect and GxE effect (Default = c(0,1,2)).

coef_G

Coefficients of the 4 genes, must be a vector of size 4 (Default = c(.30, .10, .20, .40)).

coef_E

Coefficients of the 3 environments, must be a vector of size 3 (Default = c(.45, .35, .2)).

logit

If TRUE, the outcome is transformed to binary with a logit link.

seed

RNG seed.

beta_param

Vector of size two for the parameters of the beta distribution of the environmental variables (Default = c(2,2)).

Value

Returns a list containing, in the following order: data.frame with the observed outcome (with noise) and the true outcome (without noise), data.frame of the genetic variants (G), data.frame of the environments (E), vector of the true genetic coefficients, vector of the true environmental coefficients, vector of the true main model coefficients, the crossover point.

Examples

## Examples
# Diathesis Stress WEAK
ex_dia = example_with_crossover(250, c=10, coef_main = c(3,1,2), sigma=1)
# Diathesis Stress STRONG
ex_dia_s = example_with_crossover(250, c=10, coef_main = c(3,0,2), sigma=1)
# Differential Susceptibility WEAK
ex_ds = example_with_crossover(250, c=5, coef_main = c(3+5,1,2), sigma=1)
# Differential Susceptibility STRONG
ex_ds_s = example_with_crossover(250, c=5, coef_main = c(3+5,0,2), sigma=1)