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

 From sjsamuels@gmail.com To statalist@hsphsun2.harvard.edu Subject Re: st: Competing risk life table. Cumulative failures do not add up for different causes of failure... Date Sun, 14 Jun 2009 19:38:38 -0400

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With continuous age, I don't think that you can compute the
cause-specific rates  with -ltable- .  You are assuming that if you
treat excluded outcomes as additional censoring events, then you can
use the Kaplan-Meier curve (==  life-table with no grouping).  This is
incorrect.  For the correct non-parametric estimate of type-specific
cumulative failure rate,  see Kalbfleisch & Prentice, 2002, page 255,
equation 8.11.

Install -stcompet- and compute the cause-specific estimates as shown
in the help. I haven't read the -stcompet- references, but I assume
that they implement the same formula as K & P.

Another potential issue for your analyses:  A single time-dependent
factor, marital status at time t, determines who is at risk for each
type of birth. Conditional on marital status at t, the two types of
birth no longer "compete".

Reference; Kalbfleisch, J. D., & Prentice, R. L. (2002). The
statistical analysis of failure time data (2nd ed) Hoboken, N.J: J.
Wiley.

Good luck.

-Steve

On Sat, Jun 13, 2009 at 3:35 AM, Anna Reimondos<areimondos@gmail.com> wrote:
> 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
>

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