help for stsurvimputePatrick Royston

Impute censored survival times

Syntax

stsurvimpute
[varlist]
[if] [in]
[, options]

df(#) baseline degrees of freedom for stpm2 (Royston-Parmar models)

generate(newvar [,replace]) creates new variable containing observed and imputed survival times

llogistic imputes using log-logistic distribution

lnormal imputes using lognormal distribution

scale(scalename) specifies the scale on which the Royston-Parmar model is
to be fitted

seed(#) sets random number seed

truncate(#) truncate survival distribution at #

uniform(varname) uses varname to supply uniformly distributed random numbers

weibull imputes using Weibull distribution

stpm2_options additional options for stpm2

Weights are not allowed. Note that stsurvimpute requires stpm2
to be installed - it can be downloaded from the SSC archive (see help on ssc).

Description

stsurvimpute singly imputes censored observation-times using a parametric
survival model. Available basic parametric models are Weibull, log-logistic
and lognormal; also supported are Royston-Parmar flexible
parametric models, implemented by stpm2. Variables in
varlist constitute a prognostic model that is used for predicting
individual imputed survival times. Such a model should make
the imputations more accurate than using only the overall distribution.

Options

df(#) specifies the degrees of freedom for Royston-Parmar models.
When # > 1 Royston-Parmar models are used to impute censored
survival times, and the baseline distribution function is approximated
by a restricted cubic spline with # degrees of freedom.
If # = 1 then a Weibull, log-logistic or lognormal distribution
is assumed. Further options controlling Royston-Parmar
models are available (see stpm2).

generate(newvar [, replace]) creates a new variable
newvar containing observed
and imputed survival times. replace allows newvar to be replaced
with new data. replace may not be abbreviated.

llogistic imputes assuming a log-logistic distribution.
llogistic is equivalent to df(1) scale(odds).

lnormal imputes assuming a lognormal distribution. lnormal
is equivalent to df(1) scale(normal).

scale(scalename) specifies on which scale the survival model is to be
fitted. scalename can be hazard, odds or normal.

seed(#) sets the random number seed before random uniform values
are generated.

truncate(#) truncates the survival distribution at #. The default
# is 1, meaning that the entire survival distribution is used for imputation.
With, for example, truncate(0.8) the longest (but less probable)
survival times, for which the survival probability is in the range 0.2 to 0.0,
are not imputed. Only the range 0.2 to 1 of the survival distribution is
used for imputation. The result is shorter and perhaps more realistic extreme
imputed survival times.

uniform(varname) uses varname to supply
uniformly distributed random numbers. By default
the numbers are created internally. If the unif() option is used, the
seed() option is ignored.

weibull imputes assuming a Weibull distribution.
weibull is equivalent to df(1) scale(hazard).

stpm2_options are options for stpm2.

Remarks

Royston, Parmar & Altman (2008) present an example of imputing right-censored
survival times in kidney cancer. The aim is to be able to use familiar and
informative graphs such as scatter plots and dotplots to illustrate the
relationship between the outcome and treatments, covariates, prognostic
scores etc in an informative manner. Note that because the imputation
of censored observations is heavily model-dependent, one cannot validly do
linear regression or the like of the complete and imputed times on
covariates.

Royston et al (2008) use the lognormal distribution in their analysis,
and that is the default provided by stsurvimpute. However,
stsurvimpute provides many other distributional models which
may fit the data better than the lognormal, and so give more
appropriate imputations. Choosing between the various models
can be done using the Akaike Information Criterion, as discussed
by Royston & Parmar (2002) - see also Royston (2001) and
help on stpm2.

An important point to remember when inspecting imputed survival
times is that their distribution is based on extrapolation
of the modelled survival distribution into the future, on the
assumption that all individuals will eventually experience the
event of interest. In many cases the assumption is false - there
is a 'cured fraction' who will never experience the event.
The consequence is that in many instances unrealistic survival
times will be imputed, particularly when a large proportion of
the times are censored. The higher the censoring proportion, the
less information is present on the right-hand tail of the survival
distribution and the more 'wild' the imputed times are likely
to be.

Examples

. stsurvimpute x1 x2 x3, gen(t_imputed) weibull

. stsurvimpute age sex stage, gen(t_imputed) llogistic

. stsurvimpute, scale(normal) df(3) gen(t_imputed) truncate(0.8) seed(101)

Author

Patrick Royston, MRC Clinical Trials Unit, London.

pr@ctu.mrc.ac.uk

References

P. C. Lambert and P. Royston. 2009. Further development of flexible parametric
models for survival analysis. Stata Journal, in press.

P. Royston. 2001. Flexible alternatives to the Cox model, and more.
Stata Journal 1: 1-28.

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

P. Royston, M. K. B. Parmar and D. G. Altman. 2008.
Visualizing length of survival in time-to-event studies:
a complement to Kaplan–Meier plots.
Journal of the National Cancer Institute 100: 1-6.

Also see

On-line: help for stpm2.