CoefEst {BVSNLP}

Coefficient estimation for a specific set of covariates

Description

This function estimates coefficient vector for a given set of covariates in a logistic regression and Cox proportional hazard models. It uses the inverse moment nonlocal prior (iMOM) for non zero coefficients.

Usage

CoefEst(
  X,
  resp,
  mod_cols,
  nlptype = "piMOM",
  tau,
  r,
  family = c("logistic", "survival")
)

Arguments

X

The design matrix. It is assumed that the preprocessing steps have been done on this matrix. It is recommended that to use the output of PreProcess function of the package. Also note that the X should NOT have a vector of $1$'s as the first column. If the coefficients of a selected model by bvs is to be estimated, it is highly recommended that the design matrix that is one of the outputs of the bvs function and is reported as des_mat to be used here.

resp

For logistic regression models, this variable is the binary response vector. For Cox proportional hazard models this is a two column matrix where the first column contains the survival time vector and the second column is the censoring status for each observation.

mod_cols

A vector of column indices of the design matrix, representing the selected model.

nlptype

Determines the type of nonlocal prior that is used in the analyses. It can be "piMOM" for product inverse moment prior, or "pMOM" for product moment prior. The default is set to piMOM prior.

tau

Hyperparameter tau of the iMOM prior.

r

Hyperparameter r of the iMOM prior.

family

Determines the type of data analysis. logistic is for binary outcome and logistic regression model whereas, survival represents survival outcomes and the Cox proportional hazard model.

Value

It returns the vector of coefficients for the given model.

Author(s)

Amir Nikooienejad

References

Nikooienejad, A., Wang, W., and Johnson, V. E. (2016). Bayesian variable selection for binary outcomes in high dimensional genomic studies using non-local priors. Bioinformatics, 32(9), 1338-1345.

Nikooienejad, A., Wang, W., & Johnson, V. E. (2020). Bayesian variable selection for survival data using inverse moment priors. Annals of Applied Statistics, 14(2), 809-828.

See Also

ModProb

Examples

### Simulating Survival Data
n <- 400
p <- 1000
lambda <- 0.8
cens_rate <- 0.27
set.seed(123)
Sigma <- diag(p)
full <- matrix(c(rep(0.5, p*p)), ncol=p)
Sigma <- full + 0.5*Sigma
cholS <- chol(Sigma)
Beta <- c(-1.8, 1.2, -1.7, 1.4, -1.4, 1.3)
X = matrix(rnorm(n*p), ncol=p)
X = X%*%cholS
X <- scale(X)
beta <- numeric(p)
beta[c(1:length(Beta))] <- Beta
XB <- X%*%beta
uvector <- -log(runif(n));
times <- uvector/(lambda*exp(XB))
cens_time <- quantile(times,1-cens_rate)
status <- as.numeric(times < cens_time)
TS <- cbind(times,status)

### Estimating coeffcients of the true model and an arbitrary hyper
### parameter for the iMOM prior density
mod <- c(1:6)
coef <- CoefEst(X, TS, mod, tau = 1.8, r = 2, family = "survival")
coef