How do I estimate the risk of mortality after hospital disharge for specific time intervals when intervals are not of the same length?

[Linn Gjersing]

I want to estimate the risk of mortality after hospital disharge for specific time intervals. Is it a higher risk of mortality in the first two days after discharge compared to the other time intervals.
However, these intervals are not of the same length:
0-2 days
3-7 days
8-30 days
31-90 days
91-183 days
184-365 days
>365 days.

I stset the dataset.
stset vartid, failure(dead) id(id)

stptime, at(2 7 30 90 183 365)
gives me the mortality rate for each time period. This shows that the mortality rate is much higher 5 failures/ 1777 person-time compared to the other periods.

I want to add the time intervals as an indendent variable into a cox regression, but this is not possibe given it is discreet time. I therefore intend to use cloglog instead.

If I split the data set intotime intervals of even lengths such as 183 or 365, I find that there is a higher risk of death in the first six months or the first year compared to the other six months periods or years (max 5 years).

However, if I stsplit the data set at(2 7 30 90 183 365), and add the time intervals as independent variables into the cloglog I find a higher risk in the time intervals with the most days, as it does not take into account person-time.

I want to include the time-intervals into the regression, but how to do this and take the person-time into account at the same time?

Anyone who can help me with this problem?

[Paul Dickman]

cloglog regression models (a transformation of) the proportion of deaths in each individual. There's no concept of person-time.

If you want to models rates, then use Poisson regression; either the -poisson- or -glm- commands. If you fit a model with just the time intervals you will find that the predicted rates are identical to those you got from stptime. You can then build the model from there. Poisson regression model is conceptually identical to Cox regression; the big difference is that with Poisson regression the baseline is a step function. Both assume proportional hazards and that assumtption can be tested and relaxed in both models (in Poisson regression that's domne by fitting time by covariate interactions).

[Linn Gjersing]

Thank you!