aftbybmv {afthd} R Documentation

## Bayesian multivariate analysis of parametric AFT model with minimum deviance (DIC) among weibull, log normal and log logistic distribution.

### Description

Provides better estimates (which has minimum deviance(DIC) ) for survival data among weibull, log normal and log logistic distribution of parametric AFT model using MCMC for multivariable (maximum 5 at a time) in high dimensional data.

### Usage

aftbybmv(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 in data. 0 is for censored and 1 for occurrence of event. nc number of MCMC chain. ni number of MCMC iteration to update the outcome. 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

i.e.,

T_i \sim AFT(F_\epsilon ,\beta,\tau|x_i)

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}))

When baseline distribution is normal then T follows log normal distribution.

 T \sim LN(x'\beta,1/\tau)

When baseline distribution is logistic then T follows log logistic distribution.

 T \sim Log-Logis(x'\beta,\sqrt{\tau)}

### Value

Data frame is containing posterior estimates mean, sd, credible intervals, n.eff and Rhat for beta's, sigma, tau and deviance of the model for the selected covariates. beta's of regression coefficient of the model. beta is for intercept and others are for covariates (which is/are chosen order as columns in data). 'sigma' is the scale parameter of the distribution. DIC is the estimate of expected predictive error (so lower deviance denotes better estimation).

### 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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