Editing Genetic linkage (section)

===Parametric linkage analysis===
The '''LOD score''' (logarithm (base 10) of odds), developed by [[Newton Morton]],<ref>{{Cite journal |last=Morton NE |date=1955 |title=Sequential tests for the detection of linkage |journal=American Journal of Human Genetics |volume=7 |issue=3 |pages=277–318 |pmc=1716611 |pmid=13258560}}</ref> is a statistical test often used for linkage analysis in human, animal, and plant populations. The LOD score compares the likelihood of obtaining the test data if the two loci are indeed linked, to the likelihood of observing the same data purely by chance. Positive LOD scores favour the presence of linkage, whereas negative LOD scores indicate that linkage is less likely. Computerised LOD score analysis is a simple way to analyse complex family pedigrees in order to determine the linkage between [[Mendelian inheritance|Mendelian]] traits (or between a trait and a marker, or two markers).{{cn|date=December 2024}}

The method is described in greater detail by Strachan and Read.[https://www.ncbi.nlm.nih.gov/nlmcatalog/101523906] Briefly, it works as follows:{{cn|date=December 2024}}
# Establish a [[Pedigree chart|pedigree]]
# Make a number of estimates of recombination frequency
# Calculate a LOD score for each estimate
# The estimate with the highest LOD score will be considered the best estimate

The LOD score is calculated as follows:

: <math>
\text{LOD} = Z = \log_{10} \frac{
\text{probability of birth sequence with a given linkage value}
}{
\text{probability of birth sequence with no linkage}
} = \log_{10} \frac{(1-\theta)^{NR} \times \theta^R}{ 0.5^{NR + R} }
</math>

NR denotes the number of non-recombinant offspring, and R denotes the number of recombinant offspring. The reason 0.5 is used in the denominator is that any alleles that are completely unlinked (e.g. alleles on separate chromosomes) have a 50% chance of recombination, due to independent assortment. ''θ''&nbsp;is the recombinant fraction, i.e. the fraction of births in which recombination has happened between the studied genetic marker and the putative gene associated with the disease. Thus, it is equal to {{nowrap|''R'' / (''NR'' + ''R'')}}.{{cn|date=December 2024}}

By convention, a LOD score greater than 3.0 is considered evidence for linkage, as it indicates 1000 to 1 odds that the linkage being observed did not occur by chance. On the other hand, a LOD score less than −2.0 is considered evidence to exclude linkage. Although it is very unlikely that a LOD score of 3 would be obtained from a single pedigree, the mathematical properties of the test allow data from a number of pedigrees to be combined by summing their LOD scores. A LOD score of 3 translates to a [[p-value|''p''-value]] of approximately 0.05,<ref>{{Cite journal |last=Nyholt |first=Dale R |date=August 2000 |title=All LODs Are Not Created Equal |journal=[[American Journal of Human Genetics]] |volume=67 |issue=2 |pages=282–288 |doi=10.1086/303029 |pmc=1287176 |pmid=10884360}}</ref> and no [[multiple testing correction]] (e.g. [[Bonferroni correction]]) is required.<ref>{{Cite journal |last=Risch |first=Neil |date=June 1991 |title=A Note on Multiple Testing Procedures in Linkage Analysis |journal=[[American Journal of Human Genetics]] |volume=48 |issue=6 |pages=1058–1064 |pmc=1683115 |pmid=2035526}}</ref>