log_gamma_mixture

Computes the logarithm of the probability density function and cumulative density function per observation for each observation under a Gamma mixture model.

A fully Bayesian approach in order to estimate a general family of cure rate models under the presence of covariates, see Papastamoulis and Milienos (2024) <doi:10.1007/s11749-024-00942-w> and Papastamoulis and Milienos (2024b) <doi:10.48550/arXiv.2409.10221>. The promotion time can be modelled (a) parametrically using typical distributional assumptions for time to event data (including the Weibull, Exponential, Gompertz, log-Logistic distributions), or (b) semiparametrically using finite mixtures of distributions. In both cases, user-defined families of distributions are allowed under some specific requirements. Posterior inference is carried out by constructing a Metropolis-coupled Markov chain Monte Carlo (MCMC) sampler, which combines Gibbs sampling for the latent cure indicators and Metropolis-Hastings steps with Langevin diffusion dynamics for parameter updates. The main MCMC algorithm is embedded within a parallel tempering scheme by considering heated versions of the target posterior distribution.

Panagiotis Papastamoulis

bayesCureRateModel

Bayesian Cure Rate Modeling for Time-to-Event Data

Fotios Milienos

log_gamma_mixture function

<dl> <dt>y</dt>
<dd>observed data</dd> <dt>a1</dt>
<dd>vector containing the shape parameters of each Gamma mixture component</dd> <dt>a2</dt>
<dd>vector containing the rate parameters of each Gamma mixture component</dd> <dt>p</dt>
<dd>vector of mixing proportions</dd> <dt>c_under</dt>
<dd>threshold for underflows.</dd></dl>

Arguments

Author

PDF and CDF of a Gamma mixture distribution — log_gamma_mixture

<dl>

 <dt>y</dt>
<dd>observed data</dd>

 <dt>a1</dt>
<dd>vector containing the shape parameters of each Gamma mixture component</dd>

 <dt>a2</dt>
<dd>vector containing the rate parameters of each Gamma mixture component</dd>

 <dt>p</dt>
<dd>vector of mixing proportions</dd>

 <dt>c_under</dt>
<dd>threshold for underflows.</dd>

</dl>

log_gamma_mixture: PDF and CDF of a Gamma mixture distribution

Description

Usage

Value

Arguments

Author

Examples