```help igencox                                  also see:  igencox postestimation
stcox
streg
-------------------------------------------------------------------------------

Title

igencox -- Generalized Cox model

Syntax

igencox [varlist] [if] [in] [, options]

options                              Description
-------------------------------------------------------------------------
Model
transform(trans [#])               transformation function; default is
transform(boxcox 1)
baseq(newvarname)                  save jump sizes of the Lambda
function in newvarname
savesigma(filename [, replace])    save Sigma matrix to filename

SE/Robust
vce(bootstrap, bootstrap_options)   use a bootstrap to estimate the
variance-covariance matrix

Reporting
level(#)                           set confidence level; default is
level(95)
noshow                             do not show st setting information
display_options                    control INCLUDE help
shortdes-displayoptall INCLUDE
help shortdes-coeflegend

EM
iterate(#)                         perform maximum # of iterations;
defalut is iterate(1000)
tolerance(#)                       specify tolerance for the
coefficient vector; default is
tolerance(1e-6)
nolog                              supress the iteration log
from(init_specs)                   specify initial values for the
coefficients

savespace                          conserve memory during estimation
-------------------------------------------------------------------------
You must stset your data before using stcox; see [ST] stset.
varlist may contain factor variables; see fvvarlist.

Description

igencox fits, via the EM algorithm, transformation models for failure
time data (Zeng and Lin 2006, 2007).  The transformation models
considered are

Lambda(t|Z) = G{Lambda(t)*e^(beta'*Z)}

where G() is a known transformation function and Lambda(t) is an unknown
increasing function with Lambda(0)=0.  The available transformations
include the class of Box-Cox transformations, BoxCox(rho):

G(x) = {(1+x)^rho - 1}/rho, rho>=0

and the class of logarithmic transformations, Logarithmic(r):

G(x) = {log(1+r*x)}/r, r>=0

Special cases of these transformation models correspond to proportional
hazards models (Cox 1972) and proportional odds models (Bennett 1983).
Specifically, BoxCox(1) and Logarithmic(0) reduce to the proportional
hazards model, and BoxCox(0) and Logarithmic(1) reduce to the
proportional odds model.

The igencox command allows you to fit more flexible survival models with
non-proportional hazards.  Logarithmic transformation models assume that
covariate effects always decrease over time for any r whereas Box-Cox
models allow covariate effects to increase over time when rho>1.

Options

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

transform(trans [#]) specifies the transformation function G() of the
cumulative hazard function Lambda(t|Z).  trans can be boxcox
(default) or logarithmic.  The optional # specifies the value of the
transformation parameter rho for the Box-Cox transformation and r for
the logarithmic transformation.  By default, # is set to 1.

transform(boxcox 1) or transform(logarithmic 0) corresponds to a
proportional hazards model.  transform(boxcox 0) or
transform(logarithmic 1) corresponds to a proportional odds model.

baseq(newvarname) saves the jump sizes of the Lambda(t) function in the
new variable newvarname.  This option is required for later
prediction of the survivor or cumulative hazard functions using
predict.

savesigma(filename [, replace]) saves the (N_f+q)x(N_f+q) matrix Sigma to
filename in the current directory, where N_f is the number of failed
observations and q is the number of coefficients.  This matrix is
required by predict for calculating the standard errors of the
survivor function.  replace specifies that the file may be replaced
if it already exists.

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

vce(bootstrap, bootstrap_options) uses a bootstrap to compute the
variance-covariance matrix.  bootstrap_options allow you to control
the bootstrap process.  The most commonly used bootstrap_options is
reps(#), which controls the number of replications performed.  The
default is reps(50).

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

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

noshow prevents igencox 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.

display_options:  noomitted, vsquish, noemptycells, baselevels,
allbaselevels, cformat(%fmt), pformat(%fmt), sformat(%fmt), and
nolstretch; see [R] estimation options.

coeflegend; see [R] estimation options.

+----+
----+ EM +---------------------------------------------------------------

iterate(#) specifies the maximum number of iterations.  The default is
iterate(1000).

tolerance(#) specifies the tolerance for the coefficient vector.  The
delault is tolerance(1e-6).

nolog supresses the iteration log.

from(matname) specifies initial values for the coefficients.  from(b0)
causes igencox to begin the optimization algorithm with the values in
b0.  b0 must be a row vector, and the number of columns must be equal
to the number of parameters in the model.

+----------+

savespace conserves memory during estimation and turns off the calculaton
of the covariance matrix.  If the covariance matrix is desired, it
should be obtained by specifying vce(bootstrap).

Examples

Example of a proportional hazards model

Setup
. use va, clear

Show st settings
. stset

Fit Cox proportional hazards model
. igencox status type1 type2 type3

or, equivalently,

. igencox status type1 type2 type3, transform(boxcox 1)

Replay results with 90% confidence intervals
. igencox, level(90)

Example of a proportional odds model

Setup
. sysuse cancer, clear

Map values for drug into 0 for placebo and 1 for nonplacebo
. replace drug = drug == 2 | drug == 3

Declare data to be survival-time data
. stset studytime, failure(died)

Fit a proportional odds model
. igencox drug age, transform(log)

or, equivalently,

. igencox drug age, transform(logarithmic 1)

Saving the jump sizes of Lambda and the Sigma matrix

Setup
. use va, clear

Fit Cox proportional hazards model and save jump sizes and Sigma
. igencox status type1 type2 type3, baseq(bq) savesigma(sigma)

Compute estimates of the survivor function and its standard errors

Saved results

igencox saves the following in e():

Scalars
e(N)                  number of observations
e(N_sub)              number of subjects
e(N_fail)             number of failures
e(risk)               total time at risk
e(ties)               1 if there are ties in sample, 0 otherwise
e(k_eq_model)         number of equations in model Wald test
e(d_fm)               model degrees of freedom
e(ll)                 log likelihood
e(chi2)               chi-squared statistic
e(p)                  significance
e(rank)               rank of e(V)
e(rho)                transformation parameter
e(iter)               number of iterations
e(crit)               convergence criterion
e(tol)                tolerance for the coefficient vector
e(converged)          1 if converged, 0 otherwise

Macros
e(cmdline)            command as typed
e(cmd)                igencox
e(depvar)             _t
e(covariates)         list of covariates
e(t0)                 _t0
e(transformation)     transformation used
e(chi2type)           type of model chi-squared test
e(predict)            program used to implement predict
e(baseq)              name of variable specified in baseq()
e(sigma)              filename specified in savesigma()
e(properties)         b V

Matrices
e(b)                  coefficient vector
e(V)                  variance-covariance matrix of the coefficient
estimates

Functions
e(sample)             marks estimation sample

Acknowledgments

This work was supported by the NIH Phase I SBIR contract “Software for
Modern Extensions of the Cox Model” (HHSN261201000090C) to StataCorp
LP.

References

Bennett, S. 1983. Analysis of survival data by the proportional odds
model.  Statist. Med., 2, 273-277.

Cox, D. R. 1972. Regression models and life-tables (with discussion).  J.
R. Statist. Soc. B, 34, 187-220.

Zeng, D. and Lin, D. Y. 2006. Efficient estimation of semiparametric
transformation models for counting processes.  Biometrika, 93,
627-640.

Zeng, D. and Lin, D. Y. 2007. Maximum likelihood estimation in
semiparametric regression models with censored data (with
discussion).  J. R. Statist. Soc. B, 69, 507-564.

Authors

Rafal Raciborski, StataCorp, College Station, TX.  rraciborski@stata.com.

Yulia Marchenko, StataCorp, College Station, TX.  ymarchenko@stata.com.

```