Lod Score Method of Estimating Linkage Distances
We will now introduce a new method to calculate linkage distances called the Lod Score Method. The method developed by Newton E. Morton is an iterative approach were a series of lod scores are calculated from a number of proposed linkage distance. Here is how the method works. A linkage distance is estimated, and given that estimate, the probablity of a given birth sequence is calculated. That value is then divided by the probability of a given birth sequence assuming that the genes are unlinked. The log of this value is calculated, and that value is the lod score for this linkage distance estimate. The same process is repeated with another linkage distance estimate. A series of these lod scores are obtained using different linkage distances, and the linkage distance giving the highest Lod score is considered the estimate of the linkage distance. The following is the formula for the lod score:
The above example will be used to demonstrate the principle. We will first use 0.125 as our estimate of the recombination fraction. In this first birth sequence, we have an individual with a parental genotype.The probablity of this event is (1 - 0.125). Because there are two parental types, this value is divided by two to give a value of 0.4375. In this pedigree we have a total of seven parental types. We also have one recombinant type. The probability of this event is 0.125 which is divided by two because two recombinant types exist.
What would the sequence of births be if these genes were unlinked? When two genes are unlinked the recombination frequency is 0.5. Therefore, the probability of any given genotype would be 0.25.
Now let's put the whole method together. The probability of a given birth sequence is the product of each of the independent events.So the probability of the birth sequence based on our estimate of 0.125 as the recombination frequence would be equal to (0.4375)7(0.0625)1 = 0.0001917. The probability of the birth sequence based on no linkage would be (0.25)8 = 0.0000153. Now divide the linkage probability by the non-linkage probability and you get a value of 12.566. Next take the log of this value, and you obtain a value of 1.099. This value is the lod score.
As was mentioned, this is repeated for a series of recombination frequency estimates. The table below gives the lod score for six different linkage estimates.
Recombination
Frequency Lod Score
0.050 0.951
0.100 1.088
0.125 1.099
0.150 1.090
0.200 1.031
0.250 0.932
As the table shows, the largest lod score corresponds to a linkage estimate of 0.125. In practice, we would like to see a lod score greater that 3.0. What this means is that the likelihood of linkage occurring at this distance is 1000 times greater that no linkage.
The lod score is a widely used technique not only in human research but in plant and animal linkage analyzes as well. An important software package, MAPMAKER, that is widely used in plant mapping research is based in part on the lod score method.
Modifications introduced into Version 1.4
• Maximum-Likelihood Haplotyping analysis, for finding the most likely haplotypes that generated the input.
• An analysis that moves the disease locus over the whole map, or a specified part of it, and finds the position which produces the maximum likelihood, using golden section search.
• MMLS-C analysis (can be used when the inheritance model of the disease isn't known). This analysis finds the position of the disease locus which produced the maximum LOD score, once assuming dominant inheritance with 50% penetrance, and once assuming recesseive inheritance with 50% penetrance. It then commits to the model which produced the higher maximum LOD score and subtracts 0.3 from this score to correct for multiple tests.
• MBLOD analysis (can be used when the inheritance model of the disease isn't known). This analysis finds the position of the disease locus which produced the maximum LOD score, once assuming dominant inheritance, and once assuming recesseive inheritance. The likelihood at a specific position of the disease locus is computed by averaging the likelihood given the specific inheritance model (dominant or recessive) over all penetrance values. The inheritance model which produced the higher maximum LOD score is commited to and and 0.3 is subtracted from the maximum LOD score to correct for multiple tests.
• An option to generate a Postscript graph of the Lod-Score as a function of the position of a disease locus (only possible for the case where one disease locus is iterated).
• An improved faster implementation (more noticeable in case of medium-->large files).
• Correction of some bugs in Version 1.3.
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