HyperSelect {BVSNLP}

Hyperparameter selection for iMOM prior density

Description

This function finds data specific hyperparameters for inverse moment prior density so that the overlap between the iMOM prior and null MLE density is 1/\sqrt p. In this algorithm r is always chosen to be equal to 1 and tau is found based on the mentioned overlap.

Usage

HyperSelect(
  X,
  resp,
  eff_size = 0.7,
  nlptype = "piMOM",
  iter = 10000,
  mod_prior = c("unif", "beta"),
  family = c("logistic", "survival")
)

Arguments

X

The design matrix. NA's should be removed and columns be scaled. It is recommended that the PreProcess function is run first and its output used for this argument. The columns are genes and rows represent the observations. The column names are used as gene names.

resp

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

eff_size

This is the expected effect size in the model for a standardized design matrix, which is basically the coefficient value that is expected to occur the most based on some prior knowledge.

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.

iter

The number of iteration needed to simulate from null model in order to approximate the null MLE density.

mod_prior

Type of prior used for model space. uniform is for uniform binomial and beta is for beta binomial prior. In the former case, both hyper parameters in the beta prior are equal to 1 but in the latter case those two hyper parameters are chosen as explained in the reference papers.

family

Determines the type of data analysis. logistic is for binary outcome data where logistic regression modeling is used whereas survival is for survival outcome data using Cox proportional hazard model.

Value

It returns a list having following object:

tau

The hyperparameter for iMOM prior density function, calculated using the proposed algorithm for the given dataset.

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 nonlocal priors. Bioinformatics, 32(9), 1338-1345.

Johnson, V. E., and Rossell, D. (2010). On the use of nonlocal prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(2), 143-170.

Examples

### Simulating Logistic Regression Data
n <- 20
p <- 100
set.seed(321)
Sigma <- diag(p)
full <- matrix(c(rep(0.5, p * p)), ncol = p)
Sigma <- full + 0.5 * Sigma
cholS <- chol(Sigma)
Beta <- c(1, 1.8, 2.5)
X = matrix(rnorm(n*p, 1, 2), ncol = p)
X = X%*%cholS
beta <- numeric(p)
beta[c(1:length(Beta))] <- Beta
XB <- X%*%beta
probs <- as.vector(exp(XB)/(1+exp(XB)))
y <- rbinom(n,1,probs)
colnames(X) <- paste("gene_",c(1:p),sep="")
Xout <- PreProcess(X)
XX <- Xout$X
hparam <- HyperSelect(XX, y, iter = 1000, mod_prior = "beta",
                      family = "logistic")

hparam$tau