Stata 15 help for stcox_postestimation

[ST] stcox postestimation -- Postestimation tools for stcox

Postestimation commands

The following postestimation commands are of special interest after stcox:

Command Description ------------------------------------------------------------------------- estat concordance compute the concordance probability estat phtest test the proportional-hazards assumption stcoxkm plot Kaplan-Meier observed survival and Cox predicted curves stcurve plot the survivor, hazard, and cumulative hazard functions stphplot plot -ln{-ln(survival)} curves ------------------------------------------------------------------------- estat concordance is not appropriate after estimation with svy.

The following standard postestimation commands are also available:

Command Description ------------------------------------------------------------------------- contrast contrasts and ANOVA-style joint tests of estimates estat ic Akaike's and Schwarz's Bayesian information criteria (AIC and BIC) estat summarize summary statistics for the estimation sample estat vce variance-covariance matrix of the estimators (VCE) estat (svy) postestimation statistics for survey data estimates cataloging estimation results * hausman Hausman's specification test lincom point estimates, standard errors, testing, and inference for linear combinations of coefficients linktest link test for model specification * lrtest likelihood-ratio test margins marginal means, predictive margins, marginal effects, and average marginal effects marginsplot graph the results from margins (profile plots, interaction plots, etc.) nlcom point estimates, standard errors, testing, and inference for nonlinear combinations of coefficients predict predictions, residuals, influence statistics, and other diagnostic measures predictnl point estimates, standard errors, testing, and inference for generalized predictions pwcompare pairwise comparisons of estimates test Wald tests of simple and composite linear hypotheses testnl Wald tests of nonlinear hypotheses ------------------------------------------------------------------------- * hausman and lrtest are not appropriate with svy estimation results.

Syntax for predict

predict [type] newvar [if] [in] [, sv_statistic nooffset partial]

predict [type] {stub*|newvarlist} [if] [in] , mv_statistic [partial]

sv_statistic Description ------------------------------------------------------------------------- Main hr predicted hazard ratio, also known as the relative hazard; the default xb linear prediction xb stdp standard error of the linear prediction; SE(xb) * basesurv baseline survivor function * basechazard baseline cumulative hazard function * basehc baseline hazard contributions * mgale martingale residuals * csnell Cox-Snell residuals * deviance deviance residuals * ldisplace likelihood displacement values * lmax LMAX measures of influence * effects log frailties -------------------------------------------------------------------------

mv_statistic Description ------------------------------------------------------------------------- Main * scores efficient score residuals * esr synonym for scores * dfbeta DFBETA measures of influence * schoenfeld Schoenfeld residuals * scaledsch scaled Schoenfeld residuals ------------------------------------------------------------------------- Unstarred statistics are available both in and out of sample; type predict ... if e(sample) ... if wanted only for the estimation sample. Starred statistics are calculated only for the estimation sample, even when e(sample) is not specified. nooffset is allowed only with unstarred statistics. mgale, csnell, deviance, ldisplace, lmax, dfbeta, schoenfeld, and scaledsch are not allowed with svy estimation results.

Menu for predict

Statistics > Postestimation

Description for predict

predict creates a new variable containing predictions such as hazard ratios; linear predictions; standard errors; baseline survivor, cumulative hazard, and hazard functions; martingale, Cox-Snell, deviance, efficient score, Schoenfeld, and scaled Schoenfeld residuals; likelihood displacement values; LMAX measures of influence; log frailties; and DFBETA measures of influence.

Options for predict

+------+ ----+ Main +-------------------------------------------------------------

hr, the default, calculates the relative hazard (hazard ratio), that is, the exponentiated linear prediction.

xb calculates the linear prediction from the fitted model. That is, you fit the model by estimating a set of parameters b0, b1, b2, ..., bk, and the linear prediction is xb.

The x used in the calculation is obtained from the data currently in memory and need not correspond to the data on the independent variables used in estimating b.

stdp calculates the standard error of the prediction, that is, the standard error of xb.

basesurv calculates the baseline survivor function. In the null model, this is equivalent to the Kaplan-Meier product-limit estimate. If stcox's strata() option was specified, baseline survivor functions for each stratum are provided.

basechazard calculates the cumulative baseline hazard. If stcox's strata() option was specified, cumulative baseline hazards for each stratum are provided.

basehc calculates the baseline hazard contributions. These are used to construct the product-limit type estimator for the baseline survivor function generated by basesurv. If stcox's strata() option was specified, baseline hazard contributions for each stratum are provided.

mgale calculates the martingale residuals. For multiple-record-per-subject data, by default only one value per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial martingale residuals, one for each record within subject; see partial below. Partial martingale residuals are the additive contributions to a subject's overall martingale residual. In single-record-per-subject data, the partial martingale residuals are the martingale residuals.

csnell calculates the Cox-Snell generalized residuals. For multiple-record data, by default only one value per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial Cox-Snell residuals, one for each record within subject; see partial below. Partial Cox-Snell residuals are the additive contributions to a subject's overall Cox-Snell residual. In single-record data, the partial Cox-Snell residuals are the Cox-Snell residuals.

deviance calculates the deviance residuals. Deviance residuals are martingale residuals that have been transformed to be more symmetric about zero. For multiple-record data, by default only one value per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial deviance residuals, one for each record within subject; see partial below. Partial deviance residuals are transformed partial martingale residuals. In single-record data, the partial deviance residuals are the deviance residuals.

ldisplace calculates the likelihood displacement values. A likelihood displacement value is an influence measure of the effect of deleting a subject on the overall coefficient vector. For multiple-record data, by default only one value per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial likelihood displacement values, one for each record within subject; see partial below. Partial displacement values are interpreted as effects due to deletion of individual records rather than deletion of individual subjects. In single-record data, the partial likelihood displacement values are the likelihood displacement values.

lmax calculates the LMAX measures of influence. LMAX values are related to likelihood displacement values because they also measure the effect of deleting a subject on the overall coefficient vector. For multiple-record data, by default only one LMAX value per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial LMAX values, one for each record within subject; see partial below. Partial LMAX values are interpreted as effects due to deletion of individual records rather than deletion of individual subjects. In single-record data, the partial LMAX values are the LMAX values.

effects is for use after stcox, shared() and provides estimates of the log frailty for each group. The log frailties are random group-specific offsets to the linear predictor that measure the group effect on the log relative-hazard.

scores calculates the efficient score residuals for each regressor in the model. For multiple-record data, by default only one score per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial efficient score residuals, one for each record within subject; see partial below. Partial efficient score residuals are the additive contributions to a subject's overall efficient score residual. In single-record data, the partial efficient score residuals are the efficient score residuals.

One efficient score residual variable is created for each regressor in the model; the first new variable corresponds to the first regressor, the second to the second, and so on.

esr is a synonym for scores.

dfbeta calculates the DFBETA measures of influence for each regressor in the model. The DFBETA value for a subject estimates the change in the regressor's coefficient due to deletion of that subject. For multiple-record data, by default only one value per subject is calculated, and it is placed on the last record for the subject.

Adding the partial option will produce partial DFBETAs, one for each record within subject; see partial below. Partial DFBETAs are interpreted as effects due to deletion of individual records rather than deletion of individual subjects. In single-record data, the partial DFBETAs are the DFBETAs.

One DFBETA variable is created for each regressor in the model; the first new variable corresponds to the first regressor, the second to the second, and so on.

schoenfeld calculates the Schoenfeld residuals. This option may not be used after stcox with the exactm or exactp option. Schoenfeld residuals are calculated and reported only at failure times.

One Schoenfeld residual variable is created for each regressor in the model; the first new variable corresponds to the first regressor, the second to the second, and so on.

scaledsch calculates the scaled Schoenfeld residuals. This option may not be used after stcox with the exactm or exactp option. Scaled Schoenfeld residuals are calculated and reported only at failure times.

One scaled Schoenfeld residual variable is created for each regressor in the model; the first new variable corresponds to the first regressor, the second to the second, and so on.

Note: The easiest way to use the preceding four options is, for example,

. predict double stub*, scores

where stub is a short name of your choosing. Stata then creates variables stub1, stub2, etc. You may also specify each variable name explicitly, in which case there must be as many (and no more) variables specified as there are regressors in the model.

nooffset is allowed only with hr, xb, and stdp, and is relevant only if you specified offset(varname) for stcox. It modifies the calculations made by predict so that they ignore the offset variable; the linear prediction is treated as xb rather than xb + offset.

partial is relevant only for multiple-record data and is valid with mgale, csnell, deviance, ldisplace, lmax, scores, esr, and dfbeta. Specifying partial will produce "partial" versions of these statistics, where one value is calculated for each record instead of one for each subject. The subjects are determined by the id() option to stset.

Specify partial if you wish to perform diagnostics on individual records rather than on individual subjects. For example, a partial DFBETA would be interpreted as the effect on a coefficient due to deletion of one record, rather than the effect due to deletion of all records for a given subject.

Predictions after stcox with the tvc() option

The only predict options supported after stcox with the tvc() option are the hr, xb, and stdp options. The other predictions require that you stsplit your data to draw out the time-varying covariates inferred by tvc(); see tvc note.

Predictions after stcox with the shared() option

All predict options described above are supported for shared-frailty models fit using stcox with the shared() option. Predictions are conditional on the estimated frailty variance, theta, and the definition of baseline is extended to represent covariates equal to 0 and a frailty value of 1 (log frailty of 0).

Syntax for margins

margins [marginlist] [, options]

margins [marginlist] , predict(statistic ...) [predict(statistic ...) ...] [options]

statistic Description ------------------------------------------------------------------------- hr predicted hazard ratio, also known as the relative hazard; the default xb linear prediction xb stdp not allowed with margins basesurv not allowed with margins basechazard not allowed with margins basehc not allowed with margins mgale not allowed with margins csnell not allowed with margins deviance not allowed with margins ldisplace not allowed with margins lmax not allowed with margins effects not allowed with margins scores not allowed with margins esr not allowed with margins dfbeta not allowed with margins schoenfeld not allowed with margins scaledsch not allowed with margins -------------------------------------------------------------------------

Statistics not allowed with margins are functions of stochastic quantities other than e(b).

For the full syntax, see [R] margins.

Menu for margins

Statistics > Postestimation

Description for margins

margins estimates margins of response for hazard ratios and linear predictions.

Syntax for estat concordance

estat concordance [if] [in] [, concordance_options]

concordance_options Description ------------------------------------------------------------------------- Main harrell compute Harrell's C coefficient; the default gheller compute Gönen and Heller's concordance coefficient se compute asymptotic standard error of Gönen and Heller's coefficient all compute statistic for all observations in the data noshow do not show st setting information -------------------------------------------------------------------------

Menu for estat

Statistics > Postestimation

Description for estat

estat concordance calculates the concordance probability, which is defined as the probability that predictions and outcomes are concordant. estat concordance provides two measures of the concordance probability: Harrell's C and Gönen and Heller's K concordance coefficients. estat concordance also reports the Somers's D rank correlation, which is obtained by calculating 2C-1 or 2K-1.

Options for estat concordance

+-------+ ----+ Main +------------------------------------------------------------

harrell, the default, calculates Harrell's C coefficient, which is defined as the proportion of all usable subject pairs in which the predictions and outcomes are concordant.

gheller calculates Gönen and Heller's K concordance coefficient instead of Harrell's C coefficient. The harrell and gheller options may be specified together to obtain both concordance measures.

se calculates the smoothed version of Gönen and Heller's K concordance coefficient and its asymptotic standard error. The se option requires the gheller option.

all requests that the statistic be computed for all observations in the data. By default, estat concordance computes over the estimation subsample.

noshow prevents estat concordance from displaying the identities of the key st variables above its output.

Examples

Setup . webuse drugtr

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

Fit Cox model . stcox drug age

Obtain martingale residuals . predict double mg, mgale

Obtain Cox-Snell residuals . predict double cs, csnell

Obtain deviance residuals . predict double dev, deviance

Calculate Harrell's C . estat concordance

Calculate Gönen and Heller's concordance coefficient . estat concordance, gheller

Stored results

estat concordance stores the following in r():

Scalars r(N) number of observations r(n_P) number of comparison pairs r(n_E) number of orderings as expected r(n_T) number of tied predictions r(C) Harrell's C coefficient r(K) Gönen and Heller's K coefficient r(K_s) smoothed Gönen and Heller's K coefficient r(K_s_se) standard error of the smoothed K coefficient r(D) Somers's D coefficient for Harrell's C r(D_K) Somers's D coefficient for Gönen and Heller's K

r(n_P), r(n_E), and r(n_T) are returned only when strata are not specified.


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