# flexsurv: Flexible parametric models for time-to-event data

### Description

flexsurv: Flexible parametric models for time-to-event data, including the generalized gamma, the generalized F and the Royston-Parmar spline model.

### Details

`flexsurvreg`

fits parametric models for time-to-event
(survival) data. Data may be right-censored or left-truncated.
Several built-in parametric distributions are available. Any
user-defined parametric model can also be employed by supplying a list
with basic information about the distribution, including the density
and probability functions.

Covariates can be included using a linear model on any parameter of the distribution, log-transformed to the real line if necessary. This typically defines an accelerated failure time or proportional hazards model, depending on the distribution and parameter.

`flexsurvspline`

fits the flexible survival model of
Royston and Parmar (2002) in which the log cumulative hazard is
modelled as a natural cubic spline function of log time, including a
linear term for covariates. Alternative proportional odds or probit
parameterisations are available.

Output from the models can be presented as survivor, cumulative
hazard and hazard functions (`summary.flexsurvreg`

).
These can be plotted against nonparametric estimates
(`plot.flexsurvreg`

) to assess goodness-of-fit.

Distribution (“dpqr”) functions for the generalized gamma and F distributions are
given in `GenGamma`

, `GenF`

(preferred
parameterisations) and `GenGamma.orig`

,
`GenF.orig`

(original parameterisations).

`flexsurv`

also includes the standard Gompertz distribution
with unrestricted shape parameter, see `Gompertz`

.

### Related R packages

`flexsurv`

was written to encourage the use of flexible
distributions to account for model uncertainty in survival analysis,
initially the three-parameter generalized gamma, four-parameter
generalized F and the Royston-Parmar spline
model. However it was straightforward to modularise the design of the
code to accept any generic parametric distribution.

`survreg`

from the survival package, the
recommended R package for survival analysis, supports two-parameter
location-scale parametric models.

The eha package includes functions `phreg`

and
`aftreg`

for parametric survival modelling under a
variety of distributions and proportional hazards or accelerated
failure time parameterisations.

Other facilities for generic maximum likelihood model fitting exist,
for example `fitdistr`

in the MASS package.
`flexsurvreg`

is intended to provide typical outputs and
summaries of interest to survival analysts, particularly in medical
applications. Feature requests along these lines are welcome.

Note that if an R package provides density and probability functions
for a parametric distribution, it can then be used easily in
`flexsurvreg`

. For instance, several “reliability”
distributions used in industrial statistics are available in the
VGAM package. Please report unexplained inconsistencies in
results between flexsurv and other software.

### Author(s)

Christopher Jackson chris.jackson@mrc-bsu.cam.ac.uk

### References

Royston, P. and Parmar, M. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 21(1):2175-2197.

Cox, C. (2008). The generalized *F* distribution: An umbrella for
parametric survival analysis. Statistics in Medicine 27:4301-4312.

Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine 26:4252-4374