# wbysuni: Posterior univariate estimates of AFT model with weibull... In afthd: Accelerated Failure Time for High Dimensional Data with MCMC

## Description

Provides posterior estimates of AFT model with weibull distribution using MCMC for univariate in high dimensional gene expression data. It also deals covariates with missing values.

## Usage

 `1` ```wbysuni(m, n, STime, Event, nc, ni, data) ```

## Arguments

 `m` Starting column number of covariates of study from high dimensional entered data. `n` Ending column number of covariates of study from high dimensional entered data. `STime` name of survival time in data `Event` name of event status in data. 0 is for censored and 1 for occurrence of event. `nc` number of markov chain. `ni` number of iteration for MCMC. `data` High dimensional gene expression data that contains event status, survival time and and set of covariates.

## Details

This function deals covariates (in data) with missing values. Missing value in any column (covariate) is replaced by mean of that particular covariate. AFT model is log-linear regression model for survival time T_{1}, T_{2},..,T_{n}. i.e.,

log(T_i)= x_i'β +σε_i ;~ε_i \sim F_ε (.)~which~is~iid

Where F_ε is known cdf which is defined on real line. Here, when baseline distribution is extreme value then T follows weibull distribution. To make interpretation of regression coefficients simpler, using extreme value distribution with median 0. So using weibull distribution that leads to AFT model when

T \sim Weib(√{τ},log(2)\exp(-x'β √{τ}))

## Value

Data frame is containing posterior estimates (Coef, SD, Credible Interval, Rhat, n.eff) of regression coefficient for covariates and deviance. Result shows together for all covariates chosen from column m to n.

## Author(s)

Atanu Bhattacharjee, Gajendra Kumar Vishwakarma and Pragya Kumari

## References

Prabhash et al(2016) <doi:10.21307/stattrans-2016-046>

 ```1 2 3 4``` ```## data(hdata) wbysuni(9,13,STime="os",Event="death",1,10,hdata) ## ```