dat {springer}

simulated data for demonstrating the usage of springer

Description

Simulated gene expression data for demonstrating the usage of springer.

Usage

data("dat")

Format

The dat file consists of five components: e, g, y, clin and coeff. The coefficients are the true values of parameters used for generating Y.

Details

The data model for generating Y

Consider a longitudinal case study with n subjects and k_i measurements over time for the ith subject (i=1,\ldots,n). Let Y_{ij} be the response of the jth observation for the ith subject (i=1,\ldots,n, j=1,\ldots,k_i), X_{ij}=(X_{ij1},...,X_{ijp})^\top be a p-dimensional vector of covariates denoting p genetic factors, E_{ij}=(E_{ij1},...,E_{ijq})^\top be a q-dimensional environmental factor and Clin_{ij}=(Clin_{ij1},...,Clin_{ijt})^\top be a t-dimensional clinical factor. There is time dependence among measurements on the same subject, but we assume that the measurements between different subjects are independent. The model we used for hierarchical variable selection for gene–environment interactions is given as:

Y_{ij}= \alpha_0 + \sum_{m=1}^{t}\theta_m Clin_{ijm} + \sum_{u=1}^{q}\alpha_u E_{iju} + \sum_{v=1}^{p}(\gamma_v X_{ijv} + \sum_{u=1}^{q}h_{uv} E_{iju} X_{ijv})+\epsilon_{ij},

where \alpha_{0} is the intercept and the marginal density of Y_{ij} belongs to a canonical exponential family defined in Liang and Zeger (1986). Define \eta_v=(\gamma_v, h_{1v}, ..., h_{qv})^\top, which is a vector of length q+1 and Z_{ijv}=(X_{ijv}, E_{ij1}X_{ijv}, ..., E_{ijq}X_{ijv})^\top, which contains the main genetic effect of the vth SNP from the jth measurement on the ith subject and its interactions with all the q environmental factors. The model can be written as:

Y_{ij}= \alpha_0 + \sum_{m=1}^{t}\theta_m Clin_{ijm} + \sum_{u=1}^{q}\alpha_u E_{iju} + \sum_{v=1}^{p}\eta_v^\top Z_{ijv}+\epsilon_{ij},

where Z_{ijv} is the vth genetic factor and its interactions with the q environment factors for the jth measurement on the ith subject, and \eta_{v} is the corresponding coefficient vector of length 1+q. The random error \epsilon_{i}=(\epsilon_{i1},...,\epsilon_{ik_i})^{T}, which is assumed to follow a multivariate normal distribution with \Sigma_i as the covariance matrix for the repeated measurements of the ith subject among the k_i time points.

See Also

springer