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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    |  
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  • $\begingroup$ This is a broad question. The cox model evaluates the covariable values at all time points at which events occur. Longer intervals should have, all other things equal, a higher chance of containing more time points at which events occur, and therefore the covariable values associated with them a higher influence on the estimated hazard ratio. $\endgroup$ – miura Jan 14 '14 at 12:19
  • $\begingroup$ Basically, the results will always be biased? $\endgroup$ – JMarcelino Jan 28 '14 at 16:41
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    $\begingroup$ Quite the opposite. Using only the baseline values can introduce bias if your predictor changes over time. $\endgroup$ – miura Jan 28 '14 at 20:15
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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.

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