bayesics (version 2.0.2)

survfit_b: Create survival curves

Description

Use the semi-parametric piecewise exponential survival model to fit a survival curve to one or more samples

Usage

survfit_b(formula, data, prior_shape, prior_rate, max_n_time_bins, n_time_bins)

Value

Object of class survfit_b with the following:

• posterior_parameters An n_time_binsx2 matrix whose columns provide shapes and rates of the gamma posterior distribution of each of the piecewise hazard rates.

• intervals An n_time_binsx2 matrix whose columns provide the start and endpoints of each time bin. If comparing multiple samples, a list of such matrices will be provided.

• marginal_likelihood

• data

If comparing multiple samples, each group will have a list of posterior_parameters and intervals.

Arguments

formula

Either Surv(time,event) ~ group for multiple groups, or else Surv(time,event) ~ 1 to make inference on a single population. The event variable must equal 1 if the event occurred and 0 if right censored. Currently right censoring is the only type of censoring allowed.

data

A data frame in which the variables specified in the formula will be found.

prior_shape

The shape parameter used in the gamma priors for the hazard rates

prior_rate

The rate parameter used in the gamma priors for the hazard rates

max_n_time_bins

integer. Maximum number of time bins, or "pieces", of the hazard function to be evaluated via Bayes factors. Ignored if n_time_bins is provided.

n_time_bins

Number of time bins used for hazard ratio. For a more data-driven approach, leave this argument missing and provide max_n_time_bins.

Details

The approach proposed by Qing et al. (2023) models the survival curve by way of piecewise exponential curves. That is, the hazard function is a piecewise function. The prior on the hazard within each "piece", or equivalently the rate of the exponential distribution, is a conjugate gamma distribution. Unless specified, the prior shape and rate for each piece is the posterior under the assumption that the data follow a single exponential distribution.

Unless prespecified by the user, the number of breaks in the hazard function is determined by Bayes factors, which can be quickly computed analytically.

If more than one population is being compared, then as before Bayes factors will be used to determine the number of breaks in each group's hazard function, and then Bayes factors will be used to compare the hypothesis that each group has a separate survival function vs. the null hypothesis that all groups share the same survival function.

References

Qing Y, Thall PF, Yuan Y. A Bayesian piecewise exponential phase II design for monitoring a time-to-event endpoint. Pharm Stat. 2023 Jan;22(1):34-44. doi: 10.1002/pst.2256. Epub 2022

Examples

# \donttest{
# Single population
set.seed(2025)
N = 300
test_data = 
  data.frame(outcome = 
               rweibull(N,2,5))
test_data$observed = 
  ifelse(test_data$outcome >= 7, 0, 1)
test_data$outcome =
  ifelse(dplyr::near(test_data$observed,1), test_data$outcome, 7)
fit1 = 
  survfit_b(Surv(test_data$outcome,
                 test_data$observed) ~ 1)
fit1
plot(fit1)

# Multiple populations
set.seed(2025)
N = 300
test_data = 
  data.frame(outcome = 
               c(rweibull(2*N/3,2,5),
                 rweibull(N/3,2,10)),
             x1 = rep(letters[1:3],each = N/3))
test_data$observed = 
  ifelse(test_data$outcome >= 9, 0, 1)
test_data$outcome =
  ifelse(dplyr::near(test_data$observed,1), test_data$outcome, 9)
fit2 =
  survfit_b(Surv(outcome,
                 observed) ~ x1,
            data = test_data)
fit2
plot(fit2)
# }