omega_star_cluster

Calculates parameter \(\omega^*\) of \(q^*(b)\) to optimize the evidence
based lower bound (ELBO) in <code>survregVB.frailty.fit</code>.

Implements Bayesian inference in accelerated failure time (AFT) models for
right-censored survival times assuming a log-logistic distribution. Details of the
variational Bayes algorithms, with and without shared frailty, are described in
Xian et al. (2024) <doi:10.1007/s11222-023-10365-6> and
Xian et al. (2024) <doi:10.48550/arXiv.2408.00177>, respectively.

Alison Zhang

survregVB

Variational Bayesian Analysis of Survival Data

Chengqian Xian

omega_star_cluster function

<dl><dt>y</dt>
<dd>A vector of observed log-transformed survival times.</dd>
<dt>X</dt>
<dd>A design matrix including covariates with first column of ones
to represent the intercept.</dd>
<dt>delta</dt>
<dd>A binary vector indicating right censoring.</dd>
<dt>omega_0</dt>
<dd>The shape hyperparameter \(\omega_0\) of the prior
distribution of the scale parameter, b.</dd>
<dt>mu</dt>
<dd>Parameter \(\mu^*\) of \(q^*(\beta)\), a vector of means.</dd>
<dt>tau</dt>
<dd>Parameter \(\tau^*\) of \(q^*(\gamma_i)\), a vector of
means.</dd>
<dt>expectation_b</dt>
<dd>The expected value of b.</dd>
<dt>cluster</dt>
<dd>A numeric vector indicating the cluster assignment for
each observation.</dd></dl>

Arguments

Calculates parameter \(\omega^*\) of \(q^*(b)\) to optimize the evidence
based lower bound (ELBO) in survregVB.frailty.fit. — omega_star_cluster

<dl>

<dt>y</dt>
<dd>A vector of observed log-transformed survival times.</dd>


<dt>X</dt>
<dd>A design matrix including covariates with first column of ones
to represent the intercept.</dd>


<dt>delta</dt>
<dd>A binary vector indicating right censoring.</dd>


<dt>omega_0</dt>
<dd>The shape hyperparameter \(\omega_0\) of the prior
distribution of the scale parameter, b.</dd>


<dt>mu</dt>
<dd>Parameter \(\mu^*\) of \(q^*(\beta)\), a vector of means.</dd>


<dt>tau</dt>
<dd>Parameter \(\tau^*\) of \(q^*(\gamma_i)\), a vector of
means.</dd>


<dt>expectation_b</dt>
<dd>The expected value of b.</dd>


<dt>cluster</dt>
<dd>A numeric vector indicating the cluster assignment for
each observation.</dd>

</dl>

omega_star_cluster: Calculates parameter \(\omega^\) of \(q^(b)\) to optimize the evidence based lower bound (ELBO) in `survregVB.frailty.fit`.

Description

Usage

Value

Arguments

See Also