ic_bayes | R Documentation |

Fits a Bayesian regression model for interval censored data. Can fit a proportional hazards, proportional odds or accelerated failure time model.

```
ic_bayes(
formula,
data,
logPriorFxn = function(x) return(0),
model = "ph",
dist = "weibull",
weights = NULL,
controls = bayesControls(),
useMCores = F
)
```

`formula` |
Regression formula. Response must be a |

`data` |
Dataset |

`logPriorFxn` |
An R function that computes the log prior |

`model` |
What type of model to fit. Current choices are " |

`dist` |
What baseline parametric distribution to use. See details for current choices |

`weights` |
vector of case weights. Not standardized; see details |

`controls` |
Control parameters passed to samplers |

`useMCores` |
Should multiple cores be used? Each core is used to run a single chain. |

Currently supported distributions choices are "exponential", "weibull", "gamma", "lnorm", "loglogistic" and "generalgamma" (i.e. generalized gamma distribution).

The `logPriorFxn`

should take in the a vector of values corresponding to *all*
the parameters of the model (baseline parameters first, regression parameters second) and returns the
log prior, calculated up to an additive constant. Default behavior is to use a flat prior.
See examples for an example of using the log prior function.

Sampling is done by a single MH block updater on all the parameters.
See `?bayesControls`

for more details.

Response variable should either be of the form `cbind(l, u)`

or `Surv(l, u, type = 'interval2')`

,
where `l`

and `u`

are the lower and upper ends of the interval known to contain the event of interest.
Uncensored data can be included by setting `l == u`

, right censored data can be included by setting
`u == Inf`

or `u == NA`

and left censored data can be included by setting `l == 0`

.

Does not allow uncensored data points at t = 0 (i.e. `l == u == 0`

), as this will
lead to a degenerate estimator for most parametric families. Unlike the current implementation
of survival's `survreg`

, does allow left side of intervals of positive length to 0 and
right side to be `Inf`

.

In regards to weights, they are not standardized. This means that if weight[i] = 2, this is the equivalent to having two observations with the same values as subject i.

For numeric stability, if abs(right - left) < 10^-6, observation are considered uncensored rather than interval censored with an extremely small interval.

Clifford Anderson-Bergman

```
data(miceData)
flat_prior_model <- ic_bayes(cbind(l, u) ~ grp, data = miceData)
# Default behavior is flat prior
priorFxn <- function(pars){
ans <- 0
ans <- ans + dnorm(pars[1], log = TRUE)
ans <- ans + dnorm(pars[3], sd = 0.25, log = TRUE)
}
# Prior function puts N(0,1) prior on baseline shape parameter (first parameter)
# flat prior on baseline scale parameter (second parameter)
# and N(0,0.25) on regression parameter (third parameter)
inform_prior_fit <- ic_bayes(cbind(l, u) ~ grp,
data = miceData,
logPriorFxn = priorFxn)
summary(flat_prior_model)
summary(inform_prior_fit)
# Note tight prior on the regression pulls posterior mean toward 0
```

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