**[ST] stcrreg** -- Competing-risks regression

__Syntax__

__stcrr__**eg** [*indepvars*] [*if*] [*in*]**,** __comp__**ete(***crvar*[**==***numlist*]**)** [*options*]

*options* Description
-------------------------------------------------------------------------
Model
* __comp__**ete(***crvar*[**==***numlist*]**)** specify competing-risks event(s)
**tvc(***tvarlist***)** time-varying covariates
**texp(***exp***)** multiplier for time-varying covariates;
default is **texp(_t)**
__off__**set(***varname***)** include *varname* in model with coefficient
constrained to 1
__const__**raints(***constraints***)** apply specified linear constraints
__col__**linear** keep collinear variables

SE/Robust
**vce(***vcetype***)** *vcetype* may be __r__**obust**, __cl__**uster** *clustvar*,
__boot__**strap**, or __jack__**knife**
__noadj__**ust** do not use standard degree-of-freedom
adjustment

Reporting
__l__**evel(***#***)** set confidence level; default is **level(95)**
**noshr** report coefficients, not subhazard ratios
__nosh__**ow** do not show st setting information
__nohead__**er** suppress header from coefficient table
**notable** suppress coefficient table
**nodisplay** suppress output; iteration log is still
displayed
__nocnsr__**eport** do not display constraints
*display_options* control columns and column formats, row
spacing, line width, display of omitted
variables and base and empty cells, and
factor-variable labeling

Maximization
*maximize_options* control the maximization process; seldom
used

__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
* **compete(***crvar*[**==***numlist*]**)** is required.
You must **stset** your data before using **stcrreg**; see **[ST] stset**.
*varlist* and *tvarlist* may contain factor variables; see fvvarlist.
**bootstrap**, **by**, **fp**, **jackknife**, **mfp**, **mi estimate**, **nestreg**, **statsby**, and
**stepwise** are allowed; see prefix.
**vce(bootstrap)** and **vce(jackknife)** are not allowed with the **mi estimate**
prefix.
Weights are not allowed with the **bootstrap** prefix.
**fweight**s, **iweight**s, and **pweight**s may be specified using **stset**; see **[ST]**
**stset**. In multiple-record data, weights are applied to subjects as a
whole, not to individual observations. **iweight**s are treated as
**fweight**s that can be noninteger, but not negative.
**coeflegend** does not appear in the dialog box.
See **[ST] stcrreg postestimation** for features available after estimation.

__Menu__

**Statistics > Survival analysis > Regression models >** **Competing-risks**
**regression**

__Description__

**stcrreg** fits, via maximum likelihood, competing-risks regression models
on st data, according to the method of Fine and Gray (1999).
Competing-risks regression posits a model for the subhazard function of a
failure event of primary interest. In the presence of competing failure
events that impede the event of interest, a standard analysis using Cox
regression (see **stcox**) is able to produce incidence-rate curves that
either 1) are appropriate only for a hypothetical universe where
competing events do not occur or 2) are appropriate for the data at hand,
yet the effects of covariates on these curves are not easily quantified.
Competing-risks regression, as performed using **stcrreg**, provides an
alternative model that can produce incidence curves that represent the
observed data and for which describing covariate effects is
straightforward.

**stcrreg** can be used with single- or multiple-record data. **stcrreg** cannot
be used when you have multiple failures per subject.

__Options__

+-------+
----+ Model +------------------------------------------------------------

**compete(***crvar*[**==***numlist***])** is required and specifies the events that are
associated with failure due to competing risks.

If **compete(***crvar***)** is specified, *crvar* is interpreted as an indicator
variable; any nonzero, nonmissing values are interpreted as
representing competing events.

If **compete(***crvar***==***numlist***)** is specified, records with *crvar* taking on
any of the values in *numlist* are assumed to be competing events.

The syntax for **compete()** is the same as that for **stset**'s **failure()**
option. Use **stset, failure()** to specify the failure event of
interest, that is, the failure event you wish to model using **stcox**,
**streg**, **stcrreg**, or whatever. Use **stcrreg, compete()** to specify the
event or events that compete with the failure event of interest.
Competing events, because they are not the failure event of primary
interest, must be **stset** as censored.

If you have multiple records per subject, only the value of *crvar* for
the last chronological record for each subject is used to determine
the event type for that subject.

**tvc(***tvarlist***)** specifies those variables that vary continuously with
respect to time, that is, time-varying covariates. These variables
are multiplied by the function of time specified in **texp()**.

**texp(***exp***)** is used in conjunction with **tvc(***tvarlist***)** to specify the
function of analysis time that should be multiplied by the
time-varying covariates. For example, specifying **texp(ln(_t))** would
cause the time-varying covariates to be multiplied by the logarithm
of analysis time. If **tvc(***tvarlist***)** is used without **texp(***exp***)**, Stata
understands that you mean **texp(_t)**, and thus multiplies the
time-varying covariates by the analysis time.

Both **tvc(***tvarlist***)** and **texp(***exp***)** are explained more in *Option tvc()*
*and testing the proportional-subhazards assumption* in **[ST] stcrreg**.

**offset(***varname***)**, **constraints(***constraints***)**, **collinear**; see **[R] estimation**
**options**.

+------------+
----+ SE/Robust +-------------------------------------------------------

**vce(***vcetype***)** specifies the type of standard error reported, which
includes types that are robust to some kinds of misspecification
(**robust**), that allow for intragroup correlation (**cluster** *clustvar*),
and that use bootstrap or jackknife methods (**bootstrap**, **jackknife**);
see **[R] ***vce_option*. **vce(robust)** is the default in
single-record-per-subject st data. For multiple-record st data,
**vce(cluster ***idvar***)** is the default, where *idvar* is the ID variable
previously **stset**.

Standard Hessian-based standard errors -- *vcetype* **oim** -- are not
statistically appropriate for this model and thus are not allowed.

**noadjust** is for use with **vce(robust)** or **vce(cluster** *clustvar***)**. **noadjust**
prevents the estimated variance matrix from being multiplied by
N/(N-1) or g/(g-1), where g is the number of clusters. The default
adjustment is somewhat arbitrary because it is not always clear how
to count observations or clusters. In such cases, however, the
adjustment is likely to be biased toward 1, so we would still
recommend making it.

+------------+
----+ Reporting +-------------------------------------------------------

**level(***#***)**; see **[R] estimation options**.

**noshr** specifies that coefficients be displayed rather than exponentiated
coefficients or subhazard ratios. This option affects only how
results are displayed and not how they are estimated. **noshr** may be
specified at estimation time or when redisplaying previously
estimated results (which you do by typing **stcrreg** without a variable
list).

**noshow** prevents **stcrreg** from showing the key st variables. This option
is seldom used because most people type **stset, show** or **stset, noshow**
to set whether they want to see these variables mentioned at the top
of the output of every st command; see **[ST] stset**.

**noheader** suppresses the header information from the output. The
coefficient table is still displayed. **noheader** may be specified at
estimation time or when redisplaying previously estimated results.

**notable** suppresses the table of coefficients from the output. The header
information is still displayed. **notable** may be specified at
estimation time or when redisplaying previously estimated results.

**nodisplay** suppresses the output. The iteration log is still displayed.

**nocnsreport**; see **[R] estimation options**.

*display_options*: **noci**, __nopv__**alues**, __noomit__**ted**, **vsquish**, __noempty__**cells**,
__base__**levels**, __allbase__**levels**, __nofvlab__**el**, **fvwrap(***#***)**, **fvwrapon(***style***)**,
**cformat(***%fmt***)**, **pformat(%***fmt***)**, **sformat(%***fmt***)**, and **nolstretch**; see **[R]**
**estimation options**.

+--------------+
----+ Maximization +-----------------------------------------------------
*maximize_options*: __dif__**ficult**, __tech__**nique(***algorithm_spec***)**, __iter__**ate(***#***)**,
[__no__]__lo__**g**, __tr__**ace**, __grad__**ient**, **showstep**, __hess__**ian**, __showtol__**erance**,
__tol__**erance(***#***)**, __ltol__**erance(***#***)**, __nrtol__**erance(***#***)**, __nonrtol__**erance**, and
**from(***init_specs***)**; see **[R] maximize**. These options are seldom used.

The following option is available with **stcrreg** but is not shown in the
dialog box:

**coeflegend**; see **[R] estimation options**.

__Examples__
Setup
**. webuse hypoxia**

Declare data to be survival-time data and declare the failure event of
interest, that is, the event to be modeled
**. stset dftime, failure(failtype==1)**

Fit competing-risks model with **failtype==2** as the competing event
**. stcrreg ifp tumsize pelnode, compete(failtype==2)**

Replay results, but show coefficients rather than subhazard ratios
**. stcrreg, noshr**

__Stored results__

**stcrreg** stores the following in **e()**:

Scalars
**e(N)** number of observations
**e(N_sub)** number of subjects
**e(N_fail)** number of failures
**e(N_compete)** number of competing events
**e(N_censor)** number of censored subjects
**e(k)** number of parameters
**e(k_eq)** number of equations in **e(b)**
**e(k_eq_model)** number of equations in overall model test
**e(k_dv)** number of dependent variables
**e(df_m)** model degrees of freedom
**e(ll)** log pseudolikelihood
**e(N_clust)** number of clusters
**e(chi2)** chi-squared
**e(p)** p-value for model test
**e(rank)** rank of **e(V)**
**e(fmult)** **1** if > 1 failure events, **0** otherwise
**e(crmult)** **1** if > 1 competing events, **0** otherwise
**e(fnz)** **1** if nonzero indicates failure, **0** otherwise
**e(crnz)** **1** if nonzero indicates competing, **0** otherwise
**e(ic)** number of iterations
**e(rc)** return code
**e(converged)** **1** if converged, **0** otherwise

Macros
**e(cmd)** **stcrreg**
**e(cmdline)** command as typed
**e(depvar)** name of dependent variable
**e(mainvars)** variables in main equation
**e(tvc)** time-varying covariates
**e(texp)** function used for time-varying covariates
**e(fevent)** failure event(s) in estimation output
**e(crevent)** competing event(s) in estimation output
**e(compete)** competing event(s) as typed
**e(wtype)** weight type
**e(wexp)** weight expression
**e(title)** title in estimation output
**e(clustvar)** name of cluster variable
**e(offset1)** offset
**e(chi2type)** **Wald**; type of model chi-squared test
**e(vce)** *vcetype* specified in **vce()**
**e(vcetype)** title used to label Std. Err.
**e(opt)** type of optimization
**e(which)** **max** or **min**; whether optimizer is to perform
maximization or minimization
**e(ml_method)** type of **ml** method
**e(user)** name of likelihood-evaluator program
**e(technique)** maximization technique
**e(properties)** **b V**
**e(predict)** program used to implement **predict**
**e(marginsnotok)** predictions disallowed by **margins**
**e(asbalanced)** factor variables **fvset** as **asbalanced**
**e(asobserved)** factor variables **fvset** as **asobserved**

Matrices
**e(b)** coefficient vector
**e(Cns)** constraints matrix
**e(ilog)** iteration log
**e(gradient)** gradient vector
**e(V)** variance-covariance matrix of the estimators
**e(V_modelbased)** model-based variance

Functions
**e(sample)** marks estimation sample

__Reference__

Fine, J. P., and R. J. Gray. 1999. A proportional hazards model for the
subdistribution of a competing risk. *Journal of the American*
*Statistical Association* 94: 496-509.