We have learned the calculation formula of Harrell C-index, let's learn further through practical examples
Let's look at an example where we have a group of patients and try to calculate the Harrell C-index for this particular risk model.
Now that we have a risk model that outputs a risk score for each patient, let's see how we can evaluate the model on this data.
may have to allow pairing
Ok, our first step is to look at the allowable pairs in this dataset, so let's first try to figure out which pairs are allowed.
Now let's look at both A and B, A is censored before the event time, we can't compare the results, so this is not an admissible pair.
We now look at A, C, A is censored after C, so this will be an admissible pair.
Then we can look at A, D, both times are censored so we can't compare. A and E are also a compliant allowed pair.
Now let's look at B and C. Both of these have events, so we can definitely compare
B and D can see that the censoring occurred before the event, so this would not be an admissible pair.
Both B and E are events, so this must be an allowed pair.
Now let's see C and D being the first. Note here that C and D are a case where we have an event but we know one of them was truncated at the time. Now, when we know that one of them was truncated at that time, we know that they did not experience the event at or before that time, so we know that the worst outcome is C, so this is an admissible pair.
Please note : I've only looked at the T column so far. I didn't look at the Risk column at all because we don't need a risk column when determining whether a pair is admissible.
Let's look at C and E, and note that this is also a compliant allowed pair, since both are events. Finally, let's look at D and E, and realize that for D, the censoring occurs before the event time, so we can't compare the two, so there are six allowable pairs.
consistent pairing
Now let's look at our consistent pairing. Note that when we look at consistent pairings, we only need to look at allowed pairings, since only allowed pairings are comparable.
Remember, agreement means: did the patient with the worst outcome have a higher risk score?
For A, C, our risk is 0.65 and 0.7, the worst outcome is patient C with the highest score, so A, C are consistent. For the pair of A and E, we can see that the worst result is E, and E has a higher risk score, so A and E are also a consistent pair.
Now let's look at B and C. For B, C, we both have events and a higher risk assigned to B, but B has a longer survival time, so this is not a consistent pair. Finally, let's look at B, E. In B,E, we assign high risk to B, but this is a longer survival time, so this is not a consistent pair either.
Let's look at C and D. For C, D, we find that the worst outcome is C, and C has a higher risk, so this is a consistent pair. In the end, we have C, E, where the worst outcome is C, but the higher risk is E, so this is not a consistent pair.
Let's see if there are any risk ties. We don't have any draws because we've gone through all the pairings. So here we just write None. Bring it into the formula calculation: our C-Index is 3/6, which is equivalent to 0.5.
big big summary
Congratulations on completing the final week of this course. This week, you learned how to build and evaluate a personalized survival prediction model based on patient profiles. You learned about survival models such as Cox proportional hazards models and survival trees, which can use patient variables to capture patient-specific risks. You also learned how to use Harrell's C-index to evaluate survival models on survival data. In your final assignment, you will have the opportunity to apply all of these concepts to real data, building a survival model that predicts mortality in hospitalized patients.
It is also the first time I am exposed to prognostic models, and many concepts are new to me. This part is just one of my study notes. When you forget it, you can look it up and recall it quickly. Of course, I also hope it is useful to you.
The next step is to divide the content into the big homework, the actual combat link~~~
Stay tuned! ! !
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I'm Tina, see you in the next blog~
Working during the day and writing at night, working hard
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