# Non-parallel version of Bayesian variable selector for survival data using nonlocal priors This function performs Bayesian variable selection for survival data in a non-parallel fashion. It runs modified S5 algorithm to search the model space but since this is only on one CPU, the number of visited models will not be large and therefore is NOT recommended for high dimensional datasets. This function is called by `bvs` function in a parllel fashion and therefore that function is recommended to be used. ```r cox_bvs(exmat, cur_cols, nf, tau, r, nlptype, a, b, d, L, J, temps) ``` ## Arguments - `exmat`: An extended matrix where the first two columns are survival times and status, respectively and the rest is the design matrix which is produced by `PreProcess` function. - `cur_cols`: A vector containing indices of the initial model for variable selector to start the S5 algorithm from. Note that the first `nf` indices are `1` to `nf` where `nf` is the number of fixed covariates that do not enter the selection procedure. - `nf`: The number of fixed covariates that do not enter the selection procedure. - `tau`: The paramter `tau` of the iMOM prior. - `r`: The paramter `r` of the iMOM prior. - `nlptype`: Determines the type of nonlocal prior that is used in the analyses. `0` is for piMOM and `1` is for pMOM. - `a`: The first parameter in beta distribution used as prior on model size. This parameter is equal to 1 when uinform-binomial prior is used. - `b`: The second paramter in beta distribution used as prior on model size. This parameter is equal to 1 when uinform-binomial prior is used. - `d`: This is the number of candidate covariates picked from top variables with highest utility function value and used in S5 algorithm. - `L`: Number of temperatures in S5 algorithm. - `J`: Number of iterations at each temperature in S5 algorithm. - `temps`: Vector of temperatuers used in S5 algorithm. ## Returns It returns a list containing following objects: - **max_model**: A `1` by `p` binary vector showing the selected model with maximum probability. `1` means a specific variable is selected. - **hash_key**: A column vector indicating the generated key for each model that is used to track visited models and growing dictionary. - **max_prob**: The unnormalized probability of the model with highest posterior probability. - **all_probs**: A vector containing unnormalized probabilities of all visited models. - **vis_covs_list**: A list containing the covariates in each visited model in the stochastic search process. ## Examples ```r ### Initializing the parameters n <- 100 p <- 40 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 sur_times <- rexp(n,exp(XB)) cens_times <- rexp(n,0.2) times <- pmin(sur_times,cens_times) status <- as.numeric(sur_times <= cens_times) exmat <- cbind(times,status,X) L <- 10; J <- 10 d <- 2 * ceiling(log(p)) temps <- seq(3, 1, length.out = L) tau <- 0.5; r <- 1; a <- 6; b <- p-a nlptype <- 0 ### PiMOM nonlocal prior cur_cols <- c(1,2,3) ### Starting model for the search algorithm nf <- 0 ### No fixed columns ### Running the Function coxout <- cox_bvs(exmat,cur_cols,nf,tau,r,nlptype,a,b,d,L,J,temps) ### The number of visited model for this specific run: length(coxout$hash_key) ### The selected model: which(coxout$max_model>0) ### The unnormalized probability of the selected model: coxout$max_prob ``` ## References Nikooienejad, A., Wang, W., and Johnson, V. E. (2017). Bayesian Variable Selection in High Dimensional Survival Time Cancer Genomic Datasets using Nonlocal Priors. arXiv preprint, arXiv:1712.02964. Shin, M., Bhattacharya, A., and Johnson, V. E. (2017). Scalable Bayesian variable selection using nonlocal prior densities in ultrahigh dimensional settings. Statistica Sinica. Johnson, V. E., and Rossell, D. (2010). On the use of non-local prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(2), 143-170. ## See Also `bvs` ## Author(s) Amir Nikooienejad

cox_bvs function