Dear List,
Thank you very much for your replies to my question about Diagnostic tests
and CIs. I have read the replies, which were very helpful, and thought I
would take it on a little further.
I am afraid I haven’t yet been able to get hold of the paper in MD
computing, but I will try.
Both Andrew Jull & Steve Simon suggest (roughly) similar approaches (I
think) – calculating the new limits on a (post-test) probability by
looking at bounds on the pre-test prob and LRs. I had considered this, but
there seems to be a slight problem with it. Given the fact that the pre-
test and LR limits are 95% CIs, I can generate some limits this way, and I
think they are the 99.98% limits (2.5% in each tail, so 1-(0.025 x 0.025
x2)). This works for the very extreme limits, but a when I tried to go
further using a ‘combinatorial’ approach, I ran into problems. Although
you can generate the most extreme limits by multiplying the 95% limits, if
you multiply the lower pretest prob limit with the upper LR, you obviously
get a number nearer the middle of the distribution. You can follow this
argument on further, but I don’t see how to work out where all the
different pre-test probabilities are mapped to in the post-test prob.
For this reason, I ended up doing a basic Monte Carlo, and directly
simulating the pre-test prob and the LR distributions. I did this by
generating ‘n’ normally distributed pre-test probs (then converting them
to odds) and ‘n’ log-normal distributed LRs and multiplying them together,
to get ‘n’ post-test probs, and then examining their distribution. This
simulates the fact that when we assume a pre-test prob of, say, 25%, some
of the people with have a probability higher than this, and some lower.
Similarly, when we say the test has an LR of 2, there is some distribution
in this figure as well.
The results are fairly interesting, and even more so when you examine the
effect of running two different tests in series. This was why I wanted to
check the methodology with people before I took it any further.
Can anyone see a problem with what I’ve done?
Thanks (and apologies for length),
Matt Williams
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