log_gamma

Computes the pdf and cdf of the Gamma distribution.

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 function

<dl> <dt>y</dt>
<dd>observed data</dd> <dt>a1</dt>
<dd>shape parameter</dd> <dt>a2</dt>
<dd>rate parameter</dd> <dt>c_under</dt>
<dd>A small positive value corresponding to the underflow threshold, e.g. c_under = 1e-9.</dd></dl>

Arguments

Author

PDF and CDF of the Gamma distribution — log_gamma

<dl>

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

 <dt>a1</dt>
<dd>shape parameter</dd>

 <dt>a2</dt>
<dd>rate parameter</dd>

 <dt>c_under</dt>
<dd>A small positive value corresponding to the underflow threshold, e.g. c_under = 1e-9.</dd>

</dl>

log_gamma: PDF and CDF of the Gamma distribution

Description

Usage

Value

Arguments

Author

See Also

Examples