When considering time dependent data in survival analysis, you have multiple start-stop times for an individual subject with measurements for the covariates. If each season has a different size (for example: repr=90 days,post_r=5,winter=23), the probability of an individual dying in repr it's largest.
How does the Cox model deal with different sizes of time intervals?
I'm using coxph() in R. Here's an example:
subject | start | stop | event | season |
--------+---------+--------+--------+-----------+
1 | 1 | 90 | 0 | repr |
1 | 90 | 95 | 0 | post-r |
1 | 95 | 118 | 1 | winter |
2 | 1 | 23 | 0 | winter |
2 | 23 | 113 | 0 | repr |
2 | 113 | 118 | 0 | post-r |
2 | 118 | 141 | 1 | winter |
Best Answer
Within categories of the covariates there will be a calculation of the cumulative hazard as a function of the time from beginning of the observations, summing intervals until either an event or a final censoring. As an example with your data, the "winter" intervals had two entrants with three intervals and 2 events, first of which was at 118-95 time units for subject 1 and the second of which was at (21-1)+(141-118) units for subject 2. So the cumulative hazard function would be a step function within that covariate would rise to 50% at t=23 and 100% at t=43.