Re: Risk ratio , likelihood and EIF, Nyberg and Huggon definitions
From: art fougner, md (evsono@pipeline.com)
Sun Mar 25 15:40:25 2001
whew! sure wish more efficient enrichment techniques were available for
analyzing fetal cells in maternal circulation. all these odds are
making my head spin.
art
At Sun, 25 Mar 2001, David Hutchon wrote:
>
>I agree it is quite confusing. The truth!!!?
>
>The use of the term likelihood ratio (LR) is well established in the
>medical literature as the probability of an individual with the
>condition achieving a positive test result divided by the probability of
>an individual without the condition achieving a positive test result.
>The LR is multiplied by the prior odds to give the new odds (the
>posterior odds) Note that this relationship with the LR applies to odd
>rather than probabilities so conversion form probability to odd and then
>back form odds to probability (risk) is necessary. This is layed out
>well in Sacket DL, Hayes RB, Guyatt GH and Tugwell P. in Clinical
>epidemiology: a basic science for clinical medicine, 2nd edition. Little
>Brown and Co, Boston 1991 ch 4.
>
>Relative risk (RR) is also called risk ratio and is generally used to
>describe the risk of a complication or side effect of an exposed or
>treated group against an unexposed or untreated group. It is however a
>similar concept to the likelihood ratio.
>
>Huggon et al (UOG 2001;17:11-16) try to provide the complete data
>however I am finding it very difficult to tease out all the figures. For
>example in the third sentence of results they provide us with the number
>of exclusions, n=5 for known trisomy 21, n&6 for known echogenic focus
>but do not give a number for known structural heart defect.
>
>This is one reason why I would like to see the raw data published so
>that the results can be fully analysed.
>
>--
>David Hutchon
>
>At Mon, 19 Mar 2001, Ph Coquel wrote:
>>
>>C'est un message de format MIME en plusieurs parties.
>>
>>You have read in jan 01 UOG issue, a good paper of I Huggon about EIF
>>
>>But I think there is a problem of definition with the terms of relative risk and likelihood ratio
>>
>>I don't agree with I Huggon with the definitions used in the paper and I think this is a source of confusion
>>
>>You can read below the answers of the authors
>>
>> What do you think of these definitions? Where is the truth?
>>
>>--
>>Ph Coquel,MD
>>Annecy, France
>>
>>Question to I Huggon
>>I have read with a lot of interest your paper in UOG about the isolated echogenic foci in Down's Syndrome
>>I agree with your conclusions but I think there is a problem in statistics
>>I don't understand your definition of relative risk.
>> For me, the likelihood ratio is the probability of a positive test in the group with disease divised by the probability of a positive test results in the control group
>>The relative risk is the probability of disease in a group with a positive test result divised by the probability of disease in a group with negative test result.
>>The likelihood is independent of the prevalence and the relative risk depends heavily on the disease prevalence
>>Your definition of the relative risk seems to me to be the likelihood ratio
>>Only odds ratio can be multiplied by prevalence to modify the pre test risk
>>Could you give in formations about your interpretation. Thank you
>> In the references, you don't cite the paper of Th Winter and Nyberg published in Radiology in august 2000.
>> In this paper, the RR and the LR are two different things
>>
>>Answers of the authors
>>Thank you for your interest in our article. As you imply, the problem with statistics is essentially one of definition of the terms used. In fact, in a previous draft of the manuscript, the term likelihood ratio had been used in place of relative risk. Nigel Smeeton who joined the authorship of the paper to give some further statistical assistance had particular objections to use of the term likelihood ratio because of a different and specific meaning in a different statistical context. In papers in a similar vein, likelihood ratio is used with exactly the definition you describe, whereas relative risk seems to be used rather more variably. We did make a point of defining what we meant by the terms used in the paper and you are exactly right that what we refer to as relative risk is the same entity as many papers call likelihood ratio. I think Nigel would argue that these papers are actually using incorrect terminology, though through common usage, most people working in the field have come to understand likelihood to mean exactly as you define it. In retrospect it might have been better to stick with the term likelihood ratio since the paper is unlikely to be read by mathematical statisticians who would be aware of its alternative implications! I hope that this confusion has not detracted too much from your obvious interest in the paper.
>>
>>Yours sincerely
>>
>>Ian Huggon
>>Consultant fetal and neonatal cardiologist
>>
>>Dear Dr Coquel,
>>
>>Thank you for your query. I believe that Dr Huggon has sent a reply but
>>perhaps I could add a few comments on the issue of "likelihood ratio".
>>This has a specific technical meaning in mathematical statistics and in my
>>view the use of this term in medical articles could be misleading.
>>
>>I attach a simple example of the concept as used in maths. stats. A
>>suitable reference book would be S.D. Silvey (1978) "Statistical
>>Inference". Chapman and Hall, London. [see p. 109]
>>
>>Yours sincerely,
>>
>>Nigel Smeeton
>>Lecturer in Medical Statistics
>>
>>Likelihood Ratio in Mathematical Statistics - Example
>>
>> The simplest situation is where only two events can occur.
>>
>> Suppose that a coin is tossed n times and the outcomes for the n tosses are independent - usually the case. If the probability of a "head" is a (most people think in terms of a = ½) so that the probability of a tail is (1-a), the likelihood of r heads and n-r tails is:
>>
>> ar (1-a)n-r
>>
>> However, if the probability of a head is b, in the same situation the likelihood will be
>>
>> br (1-b)n-r
>>
>> The likelihood ratio for the two situations is obtained by dividing the first likelihood by the other, i.e. here it is:
>>
>> ar (1-a)n-r
>>
>>br (1-b)n-r
>>
--
art fougner, md
A series of 1000 cases begins with but a single anecdote.
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