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st: Competing risk life table. Cumulative failures do not add up for different causes of failure...


From   Anna Reimondos <areimondos@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Competing risk life table. Cumulative failures do not add up for different causes of failure...
Date   Sat, 13 Jun 2009 17:35:23 +1000

Hello,
I have survey data on timing to first birth for a group of women which
I think should be modelled within a competing risk framework. I know
if women have had a first birth, and if this birth occurred within a
marriage or outside of marriage. For now  I am only interested in
doing a very basic descriptive analysis using a life table, rather
than multivariate analysis (I am aware of the add ons such as
stcompet).

I would like to see the distribution of failure (failure event=birth)
in total for all first births, and also separately for marital and
non-marital births.
The "age_ch1" variable is the age at which the first birth occurred.
The "birth" variable indicates if the woman had a birth or not by the
time of the survey. If she did not then her age_ch1 is given as her
age at the time of the survey ("age").
So the first thing I did was just:

ltable age_ch1 birth, failure

Then I wanted to see the failure rate for marital and non-marital
births. So I defined two new variables ("birth_s" and "birth_m"). The
first is equal to 1 if the woman had a non-marital birth, and 0
otherwise and the second is equal to 1 if the woman had a marital
birth and 0 otherwise. I believe this is how a competing risk life
table should be set up??
The two life tables are then

ltable age_ch1 birth_s, failure
ltable age_ch1 birth_m, failure


. list id age_ch1 birth birthstatus birth_s birth_m age in 1/20
      +------------------------------------------------------------------------------+
      |  id   age_ch1   birth   births~s   birth_s   birth_m   age |
      |--------------------------------------------------------------------------------|
 40. |  94        47       0   Censored         0         0          47 |
 41. |  96        35       0   Censored         0         0          35 |
 42. |  97        17       1   Other               1         0          42 |
 43. |  98        20       1    Married           0         1          41 |
 44. |  99        28       1    Married           0         1          41 |
     |---------------------------------------------------------------------------------|
 45. | 100        22       1    Married         0         1            55 |
 46. | 101        23       1    Married         0         1           46 |
 47. | 103        22       1    Married         0         1           45 |
 48. | 105        27       0   Censored       0         0            27 |
 49. | 106        27       1      Other         1          0            57 |
       |------------------------------------------------------------------------------|


When I examine the cumulative failure rates they all look very
reasonable on their own. However, if I add up the two cumulative
probabilities for the marital and non-marital births, by age they do
not add up to the total cumulative probability of having a birth.
Should the cumulative probabilities of failure from the different
causes add up to the total cumulative failure? I can't understand what
I am doing wrong....
I hope this question makes sense

Any help would be greatly appreciated.

Cheers
Anna

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