# How does Cox proportional hazards model deal with time-dependent variables?

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    |

• 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. – miura Jan 14 '14 at 12:19
• Basically, the results will always be biased? – JMarcelino Jan 28 '14 at 16:41
• Quite the opposite. Using only the baseline values can introduce bias if your predictor changes over time. – miura Jan 28 '14 at 20:15