```help for  help stpepemori
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Title

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

Syntax

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.

Description

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.

Options

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.

Example

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

run this example.

(click to run)

Remarks

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

stcompet

[ST] sts test

References

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.

Authors

Enzo Coviello (enzo.coviello@alice.it)

Aknowledgments

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