Adrian,
We are not seeing eye to eye on this as I am thinking about the probabilities for an indivdual patient and I wonder if you are thinking about probabilities in population terms.

The negative likelihood ratio of 0.02 is a property of the test and is the same for all individuals (and is independent of the prevelance of the disease in the population).

The pre-test probability is what you use clinical skill to attach to an individual patient. An individual patient will not have the 'population average' pre-test probability - you will probably find more or less worrying features in their history. This could be from nearly 0% (here is some paracetamol bye bye) to nearly 100%(you have a SAH).

The population prevelance (the 0.05 Sally Clarke figure) is not relevant here (in calculating the likelihood ratio the prevelance in the population is present on both sides of the equation and therefore cancels out).

I don't really agree with your definition of Likelihood ratio as "the probability of an individual with the condition having a negative test".
LR-ve = (1-sens)/spec. I am not sure that I can put this into words - it is a mathematical number which cannot really be equated to the sort of terms that you are using.

Tim.



-----Original Message-----
From: Accident and Emergency Academic List
[mailto:[log in to unmask]]On Behalf Of Adrian Fogarty
Sent: 28 February 2006 10:38
To: [log in to unmask]
Subject: Re: SAH


But I still think you're overegging it, doing a "Sally Clark" as it were. 
First of all, your whole premise of the pretest probability of 5% is based 
on CT results. Nevertheless, let's accept for a moment that of a LASH 
population (see, you've got me doing it now!), 5% will end up having the 
target disease, so 5% is your pretest probability. But then you're stating 
that the negative likelihood ratio for CT is 0.02. The very definition of 
negative likelihood ratio is tantamount to "the probability of an individual 
with the condition having a negative test" so there's no need to factor the 
0.02 by 0.05, if the figure of 0.02 has already been established as it were.

Yes, by all means factor in the negative likelihood ratio of LP and factor 
that by 0.02, but that will give you those patients who have SAH but are 
negative for both CT and LP. And yes they will indeed be rare, but that's 
not who we're interested in here; we're interested in the vastly greater 
number who will be LP positive after CT negative.

Maybe I'm wrong but if Tim's saying that only 1 in a 1000 negative CTs end 
up having SAH then maybe PB's right, we shouldn't be doing LPs at all. But 
from my understanding, the figures are much higher than 1 in 1000. Am I 
suffering from mental entrenchment syndrome?

AF

----- Original Message ----- 
From: "Andrew Webster" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, February 28, 2006 8:02 AM
Subject: Re: SAH


> >
>> And Tim, you're a better statistician (and neurosurgeon) than me, I've no
>> doubt, but I don't quite follow your maths approach here. If the negative
>> likelihood ratio of CT for SAH is 0.02, that basically means that of all 
>> the
>> negative CTs we get (for LASH!), 1 in 50 of those patients will still 
>> have
>> an SAH, doesn't it? (correct me if I'm wrong here...) It seems to me that
>> you're citing a pretest probability of 5% to the scan-clear patients 
>> (which
>> is fair enough), but you're then factoring in the negative likelihood 
>> ratio
>> of CT testing itself, giving an incredible 1-in-1000 result. That's not
>> rational to my mind. You're citing a pretest probability based on the
>> results of the same test, a circular argument if you like. Surely it 
>> would
>> be more appropriate to take that pre-test probability and then factor in 
>> the
>> positive likelihood ratio of LP wouldn't it? What I'm saying is, for 
>> every
>> 50 patients you get coming out of the CT with a clear scan, you're going 
>> to
>> have one who actually has SAH and that one is very likely to be picked up 
>> by
>> the subsequent LP (assuming LP is fairly sensitive when done at the 
>> correct
>> time etc). So it can't be 1 in a 1000, it's got to be closer to 1 in 50,
>> doesn't it? (which might explain why PB's had two of them in the last few
>> years...)
> No Tim is saying before we do any tests ourselves the pretest probability 
> of the patient having a SAH is 5%. With a negative CT the likelihood ratio 
> of 0.02 the post test probability is 0.1% or 1 in a 1000. Which is why you 
> need to do 1 in 1000 lp's to find a positive LP
>
> Andy Webster 

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