# ConvertWeibull: Transformation of survreg output for the Weibull distribution In SurvRegCensCov: Weibull Regression for a Right-Censored Endpoint with Interval-Censored Covariate

## Description

Transforms output from `survreg` using the Weibull distribution to a more natural parameterization. See details and the vignette for more information.

## Usage

 `1` ```ConvertWeibull(model, conf.level = 0.95) ```

## Arguments

 `model` A `survreg` model, with `dist = "weibull"`. `conf.level` Confidence level used to produce two-sided 1-α/2 confidence intervals for the hazard and event time ratios.

## Details

The `survreg` function fits a Weibull accelerated failure time model of the form

log t = μ + α^T Z + σ W,

where Z is a matrix of covariates, and W has the extreme value distribution, μ is the intercept, α is a vector of parameters for each of the covariates, and σ is the scale. The usual parameterization of the model, however, is defined by hazard function

h(t|Z) = γ λ t^{γ - 1} exp(β^T Z).

The transformation is as follows: γ = 1/σ, λ = exp(-μ/σ), and β=-α/σ, and estimates of the standard errors can be found using the delta method.

The Weibull distribution has the advantage of having two separate interpretations. The first, via proportional hazards, leads to a hazard ratio, defined by exp β. The second, of accelerated failure times, leads to an event time ratio (also known as an acceleration factor), defined by exp (-β/γ).

Further details regarding the transformations of the parameters and their standard errors can be found in Klein and Moeschberger (2003, Chapter 12). An explanation of event time ratios for the accelerated failure time interpretation of the model can be found in Carroll (2003). A general overview can be found in the `vignette("weibull")` of this package.

## Value

 `vars` A matrix containing the values of the transformed parameters and their standard errors `HR` A matrix containing the hazard ratios for the covariates, and 1 - `conf.level` / 2 confidence intervals. `ETR` A matrix containing the event time ratios for the covariates, and 1 - `conf.level` / 2 confidence intervals.

## Author(s)

Sarah R. Haile, [email protected]

## References

Carroll, K. (2003). On the use and utility of the Weibull model in the analysis of survival data. Controlled Clinical Trials, 24, 682–701.

Klein, J. and Moeschberger, M. (2003). Survival analysis: techniques for censored and truncated data. 2nd edition, Springer.

This function is used by `WeibullReg`.

## Examples

 ```1 2``` ```data(larynx) ConvertWeibull(survreg(Surv(time, death) ~ stage + age, larynx), conf.level = 0.95) ```

### Example output

```Loading required package: survival
\$vars
Estimate          SE
lambda 0.007627474 0.008061303
gamma  1.095136383 0.132267441
stage  0.514452319 0.138619731
age    0.023847800 0.014373668

\$HR
HR        LB       UB
stage 1.672722 1.2747660 2.194912
age   1.024134 0.9956853 1.053396

\$ETR
ETR        LB        UB
stage 0.6251517 0.4857836 0.8045035
age   0.9784593 0.9533024 1.0042801
```

SurvRegCensCov documentation built on May 30, 2017, 3:32 a.m.