tau_star

Calculates parameter \(\tau^*_i\) of \(q^*(\gamma_i)\) for
\(i=1,...,K\) clusters 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

tau_star 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>alpha</dt>
<dd>The shape parameter \(\alpha^*\) of \(q^*(b)\).</dd>
<dt>omega</dt>
<dd>The scale parameter \(\omega^*\) of \(q^*(b)\).</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>sigma</dt>
<dd>Parameter \(\sigma^{2*}_i\) of \(q^*(\gamma_i)\), a
vector of variance.</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 \(\tau^*_i\) of \(q^*(\gamma_i)\) for
\(i=1,...,K\) clusters to optimize the evidence based lower bound
(ELBO) in survregVB.frailty.fit. — tau_star

<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>alpha</dt>
<dd>The shape parameter \(\alpha^*\) of \(q^*(b)\).</dd>


<dt>omega</dt>
<dd>The scale parameter \(\omega^*\) of \(q^*(b)\).</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>sigma</dt>
<dd>Parameter \(\sigma^{2*}_i\) of \(q^*(\gamma_i)\), a
vector of variance.</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>

Calculates parameter \(\tau^*_i\) of \(q^*(\gamma_i)\) for
\(i=1,...,K\) clusters to optimize the evidence based lower bound
(ELBO) in <code>survregVB.frailty.fit</code>.

tau_star: Calculates parameter \(\tau^_i\) of \(q^(\gamma_i)\) for \(i=1,...,K\) clusters to optimize the evidence based lower bound (ELBO) in `survregVB.frailty.fit`.

Description

Usage

Value

Arguments

See Also