*! version 1.0.0 03oct2014

help staft also see: staft postestimation

Title

staft -- Flexible parametric accelerated failure time models

Syntax

staft [varlist] [if] [in] [, options]

Model
bknots(numlist) boundary knots for baseline

bknotstvc(knots list) boundary knots for time-dependent effects

df(#) degrees of freedom for baseline function

dftvc(df_list) degrees of freedom for each time-dependent effect

knots(numlist) knot locations for baseline

knotstvc(numlist) knot locations for time-dependent effects

knscale(scale) scale for user-defined knots (default scale is time)

noorthog do not use orthogonal transformation of splines variables

tvc(varlist) varlist of time varying effects

Reporting
eform exponentiate coefficients of first ml equation

level(#) set confidence level; default is level(95)

showinitial display output from initial value model fits

Maximization options
search(string) search option to pass to ml

initmat(matrix_name) matrix of initial values to pass to ml

copy parameters in the initial values matrix are entered by position

skip any parameters found in initial values matrix but not in model are skipped

nolog suppress display of log-likelihood iteration log

maximize_options control the maximization process; seldom used

You must stset your data before using stgenreg; see [ST] stset.

fweights, iweights, and pweights may be specified using stset; [ST] stset.

Factor variables are not currently supported.

Description

staft fits flexible parametric accelerated failure time models, using restricted cubic splines. Time-dependent effects can be included.
staft can be used with single- or multiple-record or single- or multiple-failure st data.

The model is parametrised as follows,

S(t|X) = S_{0}(t exp(-X beta))

Consider the log cumulative hazard function of a Weibull distribution,

log H(t|X) = log lambda + gamma log(t)

we then incorporate our linear predictor

log H(t|X) = log lambda + gamma log(t exp(-X beta))

and expand log(t exp(-X beta)) into our spline basis functions.

See stpm2 for the flexible parametric models in a proportional hazards metric (Royston-Parmar models).

See [ST] streg for other (standard) parametric survival models.

Options

Model

bknots(knotslist) knotslist is a two-element numlist giving
the boundary knots. By default these are located at the minimum and maximum
of the uncensored survival times. They are specified on the scale defined
by knscale().

bknotstvc(knotslist) knotslist gives the boundary knots for
any time-dependent effects. By default these are the same as for the bknots
option. They are specified on the scale defined by knscale().

For example,

bknotstvc(x1 0.01 10 x2 0.01 8)

df(#) specifies the degrees of freedom for the restricted
cubic spline function used for the baseline function. # must be between
1 and 10, but usually a value between 1 and 4 is sufficient, with 3 being the
default. The knots() option is not applicable if the df() option
is specified. The knots are placed at the following centiles of the
distribution of the uncensored log survival times:

df knots Centile positions

1 0 (no knots)
2 1 50
3 2 33 67
4 3 25 50 75
5 4 20 40 60 80
6 5 17 33 50 67 83
7 6 14 29 43 57 71 86
8 7 12.5 25 37.5 50 62.5 75 87.5
9 8 11.1 22.2 33.3 44.4 55.6 66.7 77.8 88.9
10 9 10 20 30 40 50 60 70 80 90

Note that these are interior knots and there are also boundary knots
placed at the minimum and maximum of the distribution of uncensored survival
times.

dftvc(df_list) gives the degrees of freedom for time-dependent effects
in df_list. The potential degrees of freedom are listed under the
df() option. With 1 degree of freedom a linear effect of log time is fitted.
If there is more than one time-dependent effect and different degress of freedom
are requested for each time-dependent effect then the following syntax applies:

dftvc(x1:3 x2:2 1)

This will use 3 degrees of freedom for x1, 2 degrees of freedom for
x2 and 1 degree of freedom for all remaining time-dependent effects.

knots(# [# ...]) specifies knot locations for the baseline distribution
function, as opposed to the default locations set by df(). Note that
the locations of the knots are placed on the scale defined by knscale.
However, the scale used by the restricted cubic spline function is always
log time. Default knot positions are determined by the df() option.

knotstvc(knotslist) defines numlist knotslist as the location
of the interior knots for time-dependent effects. If different knots
are required for different time-dependent effects the option is
specified, for example, as follows:

knotstvc(x1 1 2 3 x2 1.5 3.5)

knscale(scale) sets the scale on which user-defined knots are specified.
knscale(time) denotes the original time scale, knscale(log) the
log time scale and knscale(centile) specifies that the knots
are taken to be centile positions in the distribution of the uncensored log
survival times. The default is knscale(time).

noorthog suppresses orthogonal transformation of spline variables.

tvc(varlist) gives the name of the variables that are time-dependent.
Time-dependent effects are fitted using restricted cubic splines.
The degrees of freedom are specified using the dftvc() option.

Reporting

eform exponentiate the coefficients of the first ml equation.

level(#) specifies the confidence level, as a percentage, for confidence intervals.
The default is level(95) or as set by set level.

showinitial displays the models fitted to obtain initial values for staft, which includes an
AFT Weibull model using streg, and a null stpm2 model.

Maximization

maximize_options; difficult, technique(algorithm_spec),
iterate(#), [no]log, trace, gradient,
showstep, hessian, shownrtolerance, tolerance(#),
ltolerance(#) gtolerance(#), nrtolerance(#),
nonrtolerance, from(init_specs); see [R] maximize. These
options are seldom used, but the difficult option may be useful if there
are convergence problems.

Example

Setup

webuse brcancer

stset rectime, failure(censrec = 1) scale(365.25)

Fit AFT model with 3 degrees of freedom for the spline function.

staft hormon, df(3)

Author

Michael J. Crowther

Department of Medical Epidemiology and Biostatistics

Karolinska Institutet

E-mail: michael.crowther@ki.se

Please report any errors you may find.

References

Crowther MJ, Royston P, Clements M. A flexible parametric accelerated failure time model. https://arxiv.org/abs/2006.06807

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

P. Royston, P.C. Lambert. Flexible parametric survival analysis in Stata: Beyond the Cox model StataPress, 2011

Also see

Online: staft postestimation, stpm2, [ST] streg