------------------------------------------------------------------------------- help forstcompet-------------------------------------------------------------------------------

Generate Cumulative Incidence in presence of Competing Events

stcompetnewvar={ci|se|hi|lo[[newvar=...] [...] ] [ifexp] [inrange],compet1(numlist)[compet2(numlist)compet3(numlist)compet4(numlist)compet5(numlist)compet6(numlist)by(varname)level(#)]

stcompetis for use with survival-time data; see help st. You must havestsetyour data before using this command; see help stset. In previousstsetyou must specifyfailure(varname==numlist)wherenumlistrefers to the event of interest.

Examples:

Generate variables containing Cumulative Incidence and Standard Error . stset survtime, f(event==1) . stcompet CumInc = ci SError = se, compet1(2) compet2(4)

Generate variables containing Cumulative Incidence Confidence Bounds . stcompet High = hi Low = lo, compet1(2) compet2(4)

Note that each created variable contains functions for all competing events : i.e. event of interest and events in compet# options. So if you want graph functions relating to each event you need to type: . gen CumInc1 = CumInc if event==1 . gen CumInc2 = CumInc if event==2

DescriptionIn survival or cohort studies the failure of an individual may be one of several distinct failure types. In such a situation we observe an event of interest and one or more competing events whose occurrence precludes or alters the probability of occurence of the first one.

stcompetcreates variables containing Cumulative Incidence, a function that in this case appropriately estimates the probability of occurrence of each endpoint, corresponding Standard Error and Confidence Bounds. The values innumlistof the previousstsetare assumed as occurrence of event of interest. Incompet#()options you can specifynumlistrelating to the occurrence of up to six competing events.

Options

compet1(numlist)is not an option because at least one event must to compete with the event of interest. A failure of a competing event occurs wheneverfailvarspecified in previousstsettakes on any of the values of thisnumlist.

compet2(numlist)...compet6(numlist)are optional. Eachnumlistrefers to a failure for other competing events.

by(varname)produces separate functions by making separate calculations for each group identified by equal values of theby()variable taking on integer or string values.

level(#)specifies the confidence level, in percent, for the pointwise confidence interval around the cumulative incidence functions; see help level.

RemarksCumulative Incidence is estimated by summing up to

tS(t-1)* h'(t), where S(t-1)is the KME of the overall survival function and h'(t)is the cause-specific hazard at the timetStandard errors are computed according to the formula in Marubini & Valsecchi (1995) p. 341. They derive the estimator using delta method. Applying delta method Choudhury obtains an other formula presented as Dinse and Larson's variance estimator of the Cumulative Incidence. He provides also Splus codes to compute it. In my checks, using these codes in Splus, standard errors are exactly the same as computed using Marubini & Valsecchi's formula in Stata.

Choudhury proposed and showed that log(-log) trasformation improve coverage accuracy of the confidence intervals. So they are estimated using formula 4 of his article.

Also seeManual:

[R] st sts,[R] st sts generate,[R] st sts graphOn-line: help for sts, stset

References1 - Marubini E., Valsecchi M.G. Analysing Survival Data from Clinical Trials and Observational Studies. Wiley: Chichester, 1995.

2 - Choudhury J.B. Non-parametric confidence interval estimation for competing risks analysis: application to contraceptive data. Statistics in Medicine 2002; 21: 1129-1144.

3 - Gooley T.A., Leisenring W. Crowley J. Storer B.E. Estimation of failure probabilities in the presence of competing risks: new representations of old estimators. Statistics in Medicine 1999; 18: 695-706.

AuthorEnzo Coviello, Azienda U.S.L. BA/1, Italy coviello@mythnet.it