LOD score intrepretation

Dave Curtis dcurtis at hgmp.mrc.ac.uk
Sun Jul 13 16:17:35 EST 1997

On Fri, 11 Jul 1997 14:48:29 GMT, mcclean at plains.nodak.edu (Phil
McClean) wrote:

> I have a question about LOD score calculations.  I have been teaching
>the LOD score method in my intermediate genetics class.  We calculate
>our first z value based on the number of recombinants in the
>population.  So if we have 1/10 recombinants, the theta value is 0.1
>and the probability of a recombinant birth is theta/2 =  0.1/2 = 0.05
>and the probability of parental birth is (1 - theta)/2 = 
>(1 - 0.1)/2 = 0.45.  I next have my students pick one theta value that
>is create than the observed recombination frequency and on that is
>less.  What we have always seen is that the theta associated with the
>actual observed recombination gives the highest LOD score, and is
>therefore the best estimate of the linkage distance.  I know it is
>best to have a LOD > 3.0.  I tell the class this what is looked for in
>clinical situations, but for our in class examples, I always have them
>choose the theta that give the largest LOD score as the best estimate
>of lnkage distance.  In the real world of human linkage estimates,
>does the theta value that represents the observed frequency of
>recombinants always give the highest LOD score.
> You can see what I teach at the following URL:

Here's a few points:

ABO is not such a good example because the alleles are not codominant
- they yield phenotypes A, B AB or O (though the undelrying alleles
are doubtless knowable).

You have "to" instead of "two" at one point.

What you call probabilities are termed likelihoods in this context.

Your reason for multiplying by 0.5 is unclear. Firstly, you should
make it clear that you are only considering alleles transmitted from
the father. You should point out that phase/haplotypes are known in
the father. Then, it would be better to begin by saying that if
theta=0.125 there is a probability of 0.5 for a child to inherit the A
allele, and then a probability of 0.125 for them to get the disease
allele (given they have inherited the A allele). This makes more sense
then talking about inheriting a parental genotype (you mean haplotype)
and then multiplying by 0.5.

Centimorgans are not directly proportional to recombination, and 12.5
cM is only approximately equivalent to theta=0.125

And finally to answer your question. Yes, the maximum likelihood
estimate of the recombination fraction is always the same as the
observed proportion of recombinants, and so is the value of theta
giving the highest lod score. Of course chance factors can mean that
fewer or more recombinants occur in a given dataset in practice.

Don't worry, explaining lod scores is always a very tricky subject,
especially if one tries to do it briefly. Yours is one of the better
attempts I have seen.
Dave Curtis                     Tel   : +44-171-377-7729
Dept Adult Psychiatry           Fax   : +44-171-377-7316
3rd Floor Outpatient Building   Email : dcurtis at hgmp.mrc.ac.uk
Royal London Hospital           WWW   : http://www.gene.ucl.ac.uk/~dcurtis/
Whitechapel, London E1 1BB, UK

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