How do we compare the risk of two patients?
Let's talk about how to compare the risks of two patients. Suppose we have two patients, one is 50 years old with a blood pressure of 162 and the other is 61 years old with a blood pressure of 140.
We can use survival trees to first find out which group they belong to. So we see that the first patient's age is less than 60 and their blood pressure is greater than 160, so they belong to group a. The second patient is older than 60, so we see that they belong to group C.
Therefore, for the first patient, we will use the cumulative risk of group A to estimate the cumulative risk for these patients. The cumulative risk for the second patient will be estimated using the cumulative risk for group C. The cumulative risk for the patients
can be plotted using the blue and orange curves. Therefore, we can see that the cumulative risk of blue patients is higher than that of orange patients at all time points. This is good, because we can say that blue patients have a higher cumulative risk across all time points.
But what do we do when we have cumulative hazard crossings? As shown in the figure, at time points below a certain time point T, blue patients have a higher cumulative risk, while orange patients have higher cumulative risk above that time point.
In order to be able to judge which of them is more risky, we must know, what we care about is: when to compare the cumulative risk of the two.
The key idea we'll use is this: we observe the cumulative risk when a population dies. Suppose we have a group consisting of many patients, and then we want to compare the risk of these two patients in the group, as shown in the figure below. Here, we
see that many events occur between 20 and 33. In this area we care about, compare the risk of two patients, that is to say, the black line area in the figure. In this area, the orange patient has a higher risk.
Let's try to formalize this. Let's say we have a crowd, now five people for simplicity. Note that we didn't use the 25+ person because we didn't observe any events happening with him. Therefore, we calculate the cumulative risk in groups, assuming that these 4 people are all in group A, get their cumulative risk, and similarly, get their cumulative risk in group B.
Now that we have these eight values, what we can do is add each column and we get the risk of death score, which is a single value that allows us to compare the risk of two patients. For patient A, the cumulative risk was higher than for patients belonging to group C, so we were able to compare the risks of the two patients.
So far we have learned to use survival numbers to compare the survival risks of different patients, so? How do we evaluate whether the constructed survival number model is excellent?
The next section will evaluate the performance of the survival model~~
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I'm Tina, see you in the next blog~
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