survregVB {survregVB}R Documentation

Variational Bayesian Analysis of Survival Data Using a Log-Logistic Accelerated Failure Time Model

Description

Applies a mean-field Variational Bayes (VB) algorithm to infer the parameters of an accelerated failure time (AFT) survival model with right-censored survival times following a log-logistic distribution.

Usage

survregVB(
  formula,
  data,
  alpha_0,
  omega_0,
  mu_0,
  v_0,
  lambda_0,
  eta_0,
  na.action,
  cluster,
  max_iteration = 100,
  threshold = 1e-04
)

Arguments

formula

A formula object, with the response on the left of a ~ operator, and the covariates on the right. The response must be a survival object of type right, as returned by the Surv function.

data

A data.frame in which to interpret the variables named in the formula and cluster arguments.

alpha_0

The shape hyperparameter \alpha_0 of the prior distribution of the scale parameter, b.

omega_0

The shape hyperparameter \omega_0 of the prior distribution of the scale parameter, b.

mu_0

Hyperparameter \mu_0, a vector of means, of the prior distribution of the vector of coefficients, \beta.

v_0

The precision (inverse variance) hyperparameter v_0, of the prior distribution of the vector of coefficients, \beta.

lambda_0

The shape hyperparameter \lambda_0 of the prior distribution of the frailty variance, \sigma_\gamma^2.

eta_0

The scale hyperparameter \eta_0 of the prior distribution of the frailty variance, \sigma_\gamma^2.

na.action

A missing-data filter function, applied to the model.frame, after any subset argument has been used. (Default:options()$na.action).

cluster

An optional variable which clusters the observations to introduce shared frailty for correlated survival data.

max_iteration

The maximum number of iterations for the variational inference optimization. If reached, iteration stops. (Default:100)

threshold

The convergence threshold for the evidence based lower bound (ELBO) optimization. If the difference between the current and previous ELBO's is smaller than this threshold, iteration stops. (Default:0.0001)

Details

The goal of survregVB is to maximize the evidence lower bound (ELBO) to approximate posterior distributions of the AFT model parameters using the VB algorithms with and without shared frailty proposed in Xian et al. (2024) doi:10.1007/s11222-023-10365-6 and doi:10.48550/ARXIV.2408.00177 respectively.

Value

An object of class survregVB.

References

Xian, C., Souza, C. P. E. de, He, W., Rodrigues, F. F., & Tian, R. (2024). "Variational Bayesian analysis of survival data using a log-logistic accelerated failure time model." Statistics and Computing, 34(2). https://doi.org/10.1007/s11222-023-10365-6

Xian, C., Souza, C. P. E. de, He, W., Rodrigues, F. F., & Tian, R. (2024). "Fast variational bayesian inference for correlated survival data: An application to invasive mechanical ventilation duration analysis." https://doi.org/10.48550/ARXIV.2408.00177

See Also

survregVB.object

Examples

# Data frame containing survival data
fit <- survregVB(
  formula = survival::Surv(time, infect) ~ trt + fev,
  data = dnase,
  alpha_0 = 501,
  omega_0 = 500,
  mu_0 = c(4.4, 0.25, 0.04),
  v_0 = 1,
  max_iteration = 100,
  threshold = 0.0005
)
summary(fit)

# Call the survregVB function with shared frailty
fit2 <- survregVB(
  formula = survival::Surv(Time.15, delta.15) ~ x1 + x2,
  data = simulation_frailty,
  alpha_0 = 3,
  omega_0 = 2,
  mu_0 = c(0, 0, 0),
  v_0 = 0.1,
  lambda_0 = 3,
  eta_0 = 2,
  cluster = cluster,
  max_iteration = 100,
  threshold = 0.01
)
summary(fit2)

[Package survregVB version 0.0.1 Index]