CGEInfo {GEInfo}

CGEInfo and GEsgMCP approaches with fixed tunings

Description

Realize to estimate CGEInfo and GEsgMCP approaches at fixed tunings.

Usage

CGEInfo(
  E,
  G,
  Y,
  family,
  lam1,
  lam2,
  xi = 6,
  epsilon = 0,
  max.it = 500,
  thresh = 0.001,
  S_G = NULL,
  S_GE = NULL
)

Arguments

E

Observed matrix of E variables, of dimensions n x q.

G

Observed matrix of G variables, of dimensions n x p.

Y

Response variable of length n. Quantitative for family="gaussian", or family="poisson" (non-negative count). For family="binomial" should be a factor with two levels.

family

Model type: one of ("gaussian", "binomial", "poisson").

lam1

A user supplied lambda1.

lam2

A user supplied lambda2.

xi

Tuning parameter of MCP penalty. Default is 6.

epsilon

Tuning parameter of Ridge penalty which shrinks the coefficients of variables having prior information. Default is 0.

max.it

Maximum number of iterations (total across entire path). Default is 500.

thresh

Convergence threshold for group coordinate descent algorithm. The algorithm iterates until the change for each coefficient is less than thresh. Default is 1e-3.

S_G

A user supplied vector, denoting the subscript of G variables which have prior information. Default is NULL.

S_GE

A user supplied matrix, denoting the subscript of G-E interactions which have prior information. The first and second columns of S_GE represent the subscript of G variable and the subscript of E variable, respectively. For example, S_GE = matrix( c(1, 2), ncol = 2), which indicates that the 1st G and the 2nd E variables have an interaction effect on Y. Default is NULL. If both S_G and S_GE are NULL, no prior information is incorporated in the model, in which case function CGEInfo realizes GEsgMCP approach.

Value

An object of class "GEInfo" is returned, which is a list including the estimation results at fixed tunings.

a

Coefficient vector of length q for E variables.

b

Coefficient vector of length (q+1)p for W (G variables and G-E interactions).

beta

Coefficient vector of length p for G variables.

gamma

Coefficient matrix of dimensions p*q for G-E interactions.

alpha

Intercept.

coef

A coefficient vector of length (q+1)*(p+1), including the estimates for \alpha (intercept), a (coefficients for all E variables), and b (coefficients for all G variables and G-E interactions).

References

Wang X, Xu Y, and Ma S. (2019). Identifying gene-environment interactions incorporating prior information. Statistics in medicine, 38(9): 1620-1633. doi: 10.1002/sim.8064

Examples

n <- 30; p <- 5; q <- 2
E <- MASS::mvrnorm(n, rep(0,q), diag(q))
G <- MASS::mvrnorm(n, rep(0,p), diag(p))
W <- matW(E, G)
alpha <- 0; a <- seq(0.4, 0.6, length=q);
beta <- c(seq(0.2, 0.5, length=3),rep(0, p-3))  # coefficients of G variables
vector.gamma <- c(0.8, 0.5, 0, 0)
gamma <- matrix(c(vector.gamma, rep(0, p*q - length(vector.gamma))), nrow=p, byrow=TRUE)
mat.b.gamma <- cbind(beta, gamma)
b <- as.vector (t(mat.b.gamma))              # coefficients of G and G-E interactions
Y <- alpha + E %*% a + W %*% b + rnorm (n, 0, 0.5)
S_G <- c(1)
S_GE <- cbind(c(1), c(1))
fit1 <- CGEInfo(E, G, Y,family='gaussian', S_G=S_G, S_GE=S_GE,lam1=0.4,lam2=0.4)