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Ct4 Q5.15

A

Actuary

Member
Probably not too important but it's been bugging me!

I did this question (5.15) and came up with the wrong answer. When calculating the total waiting time in the sick state I took off 128*14.5days to account for those people who are still in the hospital. This wasn't done in the model solution, although 128 was taken off for movements from sick to healthy (clearly, as it cannot be said that they have recovered). On reflection I can maybe see why the 128*14.5days are included, but it doesn't feel right!

Can anyone clear this up for me? Thanks

On a side note, ch5pg20, I found the RHS of the equation at the top of the page (which acted add 'follows by applying eqn 5.7 to pkj(h)') quite hard to deduce. Seems obvious now I have but just thought for future this could be made more explicit. If not here then in the answer to question 5.10 where this step is glossed over again.
 
I see what you mean.

If the information had been "average duration of any hospital stay", then I think I would have taken off half of the average hospital stay for each of the 128 still sick at the end - ie 0.5x128x14.25/365. (note that's different slightly from yours - you don't multiply by 0.5 - I don't think that can be right).

But the question says that the group are followed from their 16th to 17th birthdays. And, during this time, the average stay in hospital was 14.25 days. So this means, I think, that the 14.25 number is calculated by taking the total observed time spent in hospital while between ages 16 and 17, and dividing this by the number of separate stays in hospital. The 128 number is the number of people who were still sick when they reached their 17th birthays . So the time spent by the sickies after age 17 is already excluded from the data count. At least, that's the only way that the solution works, to me. But I do think the question could be clearer - thanks for bringing it up, I'll pass it on to the course writer.

And thanks for your other comment too - I agree with your feelings on this and I'll see if we can get a bit more detail shown here in future.

Good luck!
 
Since Actuary had started this, I might as well post my questions here.

1) When I saw that given "Average stay in hospital" and the question asks to calculate the transitions, I immediately thought of 1/14.25, which doesnt seem to be a solution for any of the estimators. Is it because that from the Sick state, you can either move to Dead or Healthy, and this is why my 1/14.25 does not mean anything?

2) In the end of the solution, there is a comment comparing the average hospital stay of 14.25 days and 0.05; what does this means?

3) I am using the 2008 course notes; is there a way I could obtain a copy of the set of corrections for this?

Thanks.
 
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