R/sim-plots.R
approx_mvn_at_time.RdConverts a multivariate normal distribution for Weibull parameters (or a mixture of these distributions) into an approximate beta distribution for the survival probability at a specific time point. This is particularly useful for visualizing survival probabilities in sweet spot plots
approx_mvn_at_time(x, time)A vector of distributional objects that must be either multivariate normal distributions or mixtures of multivariate normal distributions. For Weibull models, these represent distributions of the log(shape) and log(scale) parameters.
A numeric value specifying survival time at which to calculate the survival probability.
A vector of beta distributional (or mixture of beta distributional) objects approximating the survival probabilities at the specified time point. If the input is a mixture distribution, the output will be a mixture of beta distributions with the same weights.
The function performs the following steps:
For each multivariate normal distribution, it generates 10,000 samples of the Weibull parameters
Calculates the corresponding survival probabilities at the specified time using the Weibull survival function
Fits a beta distribution to match the mean and variance of these survival probabilities
For mixture distributions, it performs this approximation for each component and creates a new mixture with the same weights
The conversion uses the relationship between Weibull parameters and survival probability: S(t) = exp(-(t*exp(log_scale))^exp(log_shape)).
library(distributional)
# Create a multivariate normal distribution for Weibull parameters
# (log(shape), log(scale))
mvn_dist <- dist_multivariate_normal(
mu = list(c(0, -1)), # log(shape) = 0, log(scale) = -1
sigma = list(matrix(c(0.1, 0, 0, 0.1), nrow = 2))
)
# Approximate as beta distribution for survival at time t=12
beta_approx <- approx_mvn_at_time(mvn_dist, time = 12)