Timeline for Residuals pattern in Cox proportional hazards model
Current License: CC BY-SA 4.0
9 events
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| Mar 21, 2023 at 16:25 | history | edited | EdM | CC BY-SA 4.0 |
added 144 characters in body
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| Mar 20, 2023 at 20:28 | history | edited | EdM | CC BY-SA 4.0 |
added 6 characters in body
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| Mar 20, 2023 at 20:08 | comment | added | EdM | @Requin I've added the formal definition of the expected number of events to the answer. It increases at each event time in the data set while an individual is at risk, and can exceed 1 if there's a high estimated hazard ratio and the data set has enough events. | |
| Mar 20, 2023 at 20:01 | history | edited | EdM | CC BY-SA 4.0 |
Expanded on expected number of events
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| Mar 20, 2023 at 19:15 | comment | added | Requin | Thanks! I guess I didn't understand the notion "expected number of events" for an individual. Intuitively, I'd say this is something like "1 minus the survival curve of an individual", but with this, E^i>0 is not possible. So, where do I get the "expected number of events" for an individual from? | |
| Mar 20, 2023 at 13:34 | comment | added | EdM | @Requin Therneau and Grambsch say in Section 4.3 about the deviance residual: "In practice it has not been as useful as anticipated" even in plots. For plots against predictor values, martingale residuals have a stronger theoretical basis. In the approximation shown, $\hat E_i$ is the expected number of events for individual $i$ at the individual's event/censoring time. For a given set of covariate values, an early event ($N_i=1$) might have $\hat E_i=0.1$ and a late event time have $\hat E_i=0.9$. Corresponding approximate $d_i$ are 2.8 and 0.1, respectively. | |
| Mar 20, 2023 at 9:31 | comment | added | Requin | Thank you so much for your very helpful explanations! I understand that the "lines" I see in my deviance residuals plot come from different parameter combinations. 1. Can you explain once more why the residuals are necessarily higher for smaller event times? 2. The plot deviance residuals vs event time is then only useful to detect outliers? I understood that it might also make sense to plot deviance residuals against the predictors to see how those predictors might be related to the target variable. I'm going to try this now. | |
| Mar 20, 2023 at 8:48 | vote | accept | Requin | ||
| Mar 18, 2023 at 15:24 | history | answered | EdM | CC BY-SA 4.0 |