Title
igencox -- Generalized Cox model
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
Advanced savespace conserve memory during estimation ------------------------------------------------------------------------- You must stset your data before using stcox; see [ST] stset. varlist may contain factor variables; see fvvarlist.
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.
+-------+ ----+ 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.
+----------+ ----+ Advanced +---------------------------------------------------------
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).
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
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.