# st: R: Choice of analysis time in survival analysis where the hazard is associated with age

 From "Carlo Lazzaro" To Subject st: R: Choice of analysis time in survival analysis where the hazard is associated with age Date Mon, 14 Dec 2009 15:32:27 +0100

```Roland wrote:
<Knowing that the hazard is age-dependent I think this may give biased
results>.

Roland might be interested in exploring the relationship between age and
relative hazard of appendicitis by plugging a quadratic term (ie, age^2)
into the RHS of Cox regression and then invoke -stcox-.

Given:
a=coefficient for age;
b=coefficient for age^2;
x=age

the quadratic function: y=ax^2+bx shows a maximum (or minimum) at y'=0 (ie,
-b/2a).

Provided that the maximum (or minimum) lies within the range of age data,
Roland can find out a turning point at which the function changes direction.

Depending upon being a maximum or a minimum, up until the turning point the
relative hazard increases and then decreases or the other way round.

A well detailed example of this topic is reported in: Cleves MA, Gould WW,
Gutierrez RG. AnIntroduction to Survival Analysis usung Stata. Revised
edition. College Station: Stata Press, 2004: 160-62.

HTH and Kind Regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di roland andersson
Inviato: lunedì 14 dicembre 2009 13.39
A: statalist@hsphsun2.harvard.edu
Cc: Terlinder John
Oggetto: st: Choice of analysis time in survival analysis where the hazard
is associated with age

I have a large national dataset and plan to analyse socioeconomic
differences in risk of having appendicitis. Persons born after 1949 to
end of 1990 and alive at 1/1/1991 (n=4.500.000) are included in the
dataset. The dataset contains the date when a person was operated for
appendicitis between 1/11/1990 and 31/12/2003 and date of death.

The hazard of having appendicitis is agedependent and is increasing
till age 13 and then decreasing. Previous collaborators have made
Coxregression with time from 1/11/1990 to the appendicitisdiagnosis or
censoring as analysistime, and have entered age at operation as
covariates to control for the age-dependent differencies in hazard.

Knowing that the hazard is age-dependent I think this may give biased
results. I therefore wonder if it would be better to use age as
analysis time (with late entries) instead of time from start of follow
up with adjustment for age. Am I right to think that this will be a
better way of controling for the age-dependent differences in hazard?
If that is the case may I also include age as a covariate in the
analysis or would that complicate things?

I have also considered to use a stratified analysis with ageintervals
as stratification variable. Can you give some advice on how these
ageintervals should be chosen in view of the agedependent increasing
and decreasing hazard?

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```