wbysmv {afthd} R Documentation

## Posterior multivariate estimates of AFT model with weibull distribution using MCMC.

### Description

Provides estimate of AFT model with weibull distribution using MCMC for multivariable (maximum 5 covariates of column at a time) in high dimensional gene expression data. It also deals covariates with missing values.

### Usage

wbysmv(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'\beta +\sigma\epsilon_i ;~\epsilon_i \sim F_\epsilon (.)~which~is~iid

Where  F_\epsilon  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(\sqrt{\tau},log(2)\exp(-x'\beta \sqrt{\tau}))

### Value

Data frame is containing mean, sd, n.eff, Rhat and credible intervals for beta's, sigma, alpha, tau and deviance of the model for the chosen covariates. beta is for intercept and others are for covariates (which is/are chosen as columns in data). sigma is the scale parameter of the distribution. alpha is shape parameter of the distribution.

### Author(s)

Atanu Bhattacharjee, Gajendra Kumar Vishwakarma and Pragya Kumari

### References

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

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