Page 90 - Genetics_From_Genes_to_Genomes_6th_FULL_Part3

384 Chapter 11 Analyzing Genomic Variation

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The Lod Score Statistic
The Lod score is a mathematical answer to the question: How 1/8. The probability of seven parentals and one recombi-
much more likely is it that the allele transmission pattern seen in nant in the particular birth order PPPPPPPR is:
a pedigree will occur if the loci are linked at a given recombina- 7 7 1 1 1

tion frequency (RF) less than 50%, than if they are not linked? P(RF 12.5% ) = ( 8 ) ( 8 ) ≈ 20
The Lod score, as its name implies (log of the odds) is the loga- A generalized formula for calculating the Lod score
rithm of the ratio between these two probabilities:
numerator is:
#P
P(obtaining observed results if loci are linked at a given RF) (1 − RF obs ) × (RF obs ) #R
Lod = log
[ P(obtaining observed results if loci are unlinked) ]
where RF obs is the RF indicated by the data, #P is the num-
Here, we illustrate the Lod score calculation for the pedi- ber of parentals, and #R is the number of recombinants.
gree in Fig. 11.20a. The pedigree suggests that the NF gene is 4. Calculate the likelihood ratio. This is simply the ratio of
linked to a particular SNP on chromosome 17. The calculation the values you found in steps 2 and 3. For this example,
will allow us to determine our degree of confidence in this pre- 1 1
liminary conclusion. P(RF 12.5% ) P(RF 50% ) = ∕ = 12.8
( 20 ) ( 256 )
1. Tabulate which progeny are parental and which are
recombinant. In Fig. 11.20a, you can see that the first This likelihood ratio means that it is 12.8 times more likely
seven children in generation III have the parental (P) con- that the NF gene and the SNP are linked with RF = 12.5%
figuration of alleles and that only child III-8 has the recom- than that they are not linked (RF = 50%).
binant (R) configuration. We’ll abbreviate these data as 5. Calculate the Lod score. The Lod score is simply the
PPPPPPPR. base 10 logarithm of the likelihood ratio. For the example
2. Calculate the Lod score denominator. If two loci are un- in Fig. 11.20a:
linked, it is equally likely that any one child will be P or R Lod score = log(12.8) = 1.1
(that is, the RF = 50%). The probability of P is thus ½, and 6. Interpret the Lod score. The convention among human
the probability of R is also ½. The probability of obtaining geneticists is that a Lod score ≥3 (that is, a likelihood ratio
children in the particular birth order PPPPPPPR if the NF ≥1000) is required to be confident of linkage. The Lod
gene and the SNP locus are unlinked is: score of 1.1 indicates that the data in Fig. 11.20a are
insufficient to conclude that NF and SNP1 are linked.
1 8 1
P(RF 50% ) = =
( 2 ) 256 Important points about Lod scores:
• The Lod score determined by assuming the precise RF
You can see that a generalized formula for this part of the
calculation is simply: implied by the data will always be the maximum Lod score
obtainable for the data set.
n
(½) , where n is the total number of tabulated individuals. • For a single pedigree, Lod scores can be calculated for
any RF value less than 50%. A Lod score ≥3 indicates that
3. Calculate the Lod score numerator. Loci could be linked the data obtained are compatible statistically with the
if the RF is any value less than 50%, but the calculation particular distance (less than 50 m.u.) being tested.
requires us to assume an RF value. The pedigree in • Likelihood ratios are converted into Lod scores because
Fig. 11.20a indicates an RF of 1/8 = 12.5%, so we will Lod scores calculated for the same RF value in different
use this as our best current estimate. With RF = 1/8, the pedigrees may simply be added to see whether a Lod of
expected frequency of P progeny is 7/8, and R progeny is 3 can be obtained.

DNA marker are genetically linked. The Lod score is used convention adopted by human geneticists is that a Lod
2
in human genetics instead of the χ statistic because the score greater than or equal to 3 indicates two loci are linked.
Lod score better handles a small number of data points A Lod score of 3 means that it is 1000 times more likely
while allowing the data obtained from many different ped- that the two loci are linked than that they are not (because
igrees to be combined. 3 = log1000). The beauty of the Lod score statistic is that
The Lod score statistic is calculated from the ratio of because it is a log function, the Lod scores from different
two probabilities: the probability of obtaining a particular pedigrees may simply be added, so researchers will know
set of results in a pedigree if two loci are linked (assuming when they have enough data to conclude that a disease
a particular RF value), and the chance of observing the allele is linked to a specific marker.
same results if the loci are unlinked. The Lod score statistic The Tools of Genetics Box entitled The Lod Score
is the base 10 logarithm (log) of this likelihood ratio. The Statistic illustrates how to calculate a Lod score, using as