# dic.fit: Fits a log-normal, gamma, or Weibull model to doubly interval... In nickreich/coarseDataTools: A Collection of Functions to Help with Analysis of Coarsely Observed Data

## Description

`dic.fit` fits a parametric accelerated failure time model to survival data. It was developed with the application to estimating incubation periods of infectious diseases in mind but is applicable to many general problems. The data can be a mixture of doubly interval-censored, single interval-censored or exact observations from a single univariate distribution. Currently, three distributions are supported: log-normal, gamma, and Weibull. (The Erlang distribution is supported in the `dic.fit.mcmc` function, which implements an MCMC version of this code.) We use a consistent (par1, par2) notation for each distribution, they map in the following manner:

Log-normal(meanlog=par1, sdlog=par2)

Gamma(shape=par1, scale=par2)

Weibull(shape=par1, scale=par2)

Standard errors of parameters can be computed using closed-form asymptotic formulae or using a bootstrap routine for log-normal and gamma models. Currently, bootstrap SEs are the only option for the gamma models, which do not have a closed form for the percentiles. `dic.fit()` calculates asymptotic SEs by default, or whenever the `n.boots` option is set to 0. To compute bootstrap SEs, just set `n.boots` to be greater than zero. `dic.fit.mcmc` also allows for Markov Chain Monte Carlo fitting of these three parametric models and Erlang models as well.

## Usage

 ```1 2 3 4 5 6``` ``` dic.fit(dat, start.par2 = log(2), opt.method = "L-BFGS-B", par1.int = c(log(0.5), log(13)), par2.int = c(log(1.01), log(log(5))), ptiles = c(0.05, 0.95, 0.99), dist = "L", n.boots = 0, ...) ```

## Arguments

 `dat` a matrix with columns named "EL", "ER", "SL", "SR", corresponding to the left (L) and right (R) endpoints of the windows of possible exposure (E) and symptom onset (S). Also, a "type" column must be specified and have entries with 0, 1, or 2, corresponding to doubly interval-censored, single interval-censored or exact observations, respsectively. `start.par2` starting value for 2nd parameter of desired distribtution `opt.method` method used by optim `par1.int` the log-scale interval of possible median values (in the same units as the observations in dat). Narrowing this interval can help speed up convergence of the algorithm, but care must be taken so that possible values are not excluded or that the maximization does not return a value at an endpoint of this interval. `par2.int` the log-scale interval of possible dispersion values `ptiles` percentiles of interest `dist` what distribution to use to fit the data. Default "L" for log-normal. "G" for gamma, and "W" for Weibull. `n.boots` number of bootstrap resamples (0 means that asymptotic results are desired) `...` additional options passed to optim

## Value

a cd.fit S4 object.

## References

Reich NG et al. Statistics in Medicine. Estimating incubation periods with coarse data. 2009. http://www3.interscience.wiley.com/journal/122507367/abstract

`cd.fit`, `dic.fit.mcmc`

## Examples

 ```1 2``` ```data(fluA.inc.per) dic.fit(fluA.inc.per, dist="L") ```

nickreich/coarseDataTools documentation built on May 23, 2017, 2:46 p.m.