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stpepemori -- Test equality of cumulative incidence or conditional probability in presence of competing risks


stpepemori varname [if] [in] , compet(numlist) [ conditional ]

stpepemori is for use with survival-time data; see help st. In previous stset you must specify failure(varname==numlist) where numlist refers to the event of interest.

stpepemori can be used just with single-record st data.


stpepemori tests the equality of cumulative incidences or conditional probabilities across two groups. So varname specifying the groups to be compared can take just two values. The values in numlist of the previous stset are assumed as occurrence of event of interest. In compet() you must specify numlist corresponding to the occurrence of the competing event. Then, stpepemori computes the test proposed by Pepe and Mori for the main and competing event.


compet(numlist) is not an option. A failure of a competing event occurs whenever failvar specified in the previous stset takes on any of the values of this numlist.

conditional specifies that conditional probability difference must be tested.


Setup . use follic

Create the indicator variable for the event of interest and competing risk . gen byte evcens = (resp=="NR" | relsite!="") + 2*(resp=="CR" & relsite=="" & stat==1)

Declare data to be survival-time data . stset dftime, fail(evcens==1)

Two groups are defined based on age, dichomotized at 65 . gen byte age65 = age>65

Pepe and Mori test comparing the cumulative incidence for the main event and competing risk between two age groups . stpepemori age65, compet(2)

Pepe and Mori test comparing the conditional probability for the main event and competing risk between two age groups . stpepemori age65, compet(2) conditional

Downloading ancillary files in one of your `"`c(adopath)'"' directory you can run this example.

(click to run)


When competing risks are present Kalbfleish and Prentice (1980) suggest the use of the cumulative incidence to estimate the probability of an event. Pepe and Mori(1993) give a method for comparing this function estimated in two groups. This statistic is based on cumulative weighted differences between these functions where the weights decrease as the time progresses. At later time points, in fact, the number of observations still at risk is small so it seems reasonable to down-weights differences at these time points.

Pepe and Mori (1993) proposed the conditional probability as a function incorporating the cumulative incidence of the event of interest and the cumulative incidence of the competing risk. Note that an estimate of the conditional probability can be easily obtained by the cumulative incidence. For example the conditional probability for the event of interest is: CI_main/(1-CI_competing) as shown by running the example. The same test comparing two cumulative incidences can be applied to the conditional probabilities.

Saved results

stpepemori saves the following in r():

Scalars r(1) chi-squared statistic for event of interest r(2) chi-squared statistic for competing risk r(p1) p-value for event of interest r(p2) p-value for competing risk

Also see


[ST] sts test


M.S. Pepe and M. Mori. Kaplan-Meier, marginal or conditional probability curves in summarizing competing risks failure time data. Stat in Med (1993), 12, 737 - 751.

M. Pintilie. Competing risks: A practical perspective. Wiley, Chichester, 2006, p. 71 - 86 and 127 - 137.


Enzo Coviello (


I am grateful to prof. Melania Pintilie for making available R codes computing the above tests and for his book.