Executables required: qdb, pedraw (optional), quiklink, makeped, unknown, mlink, linkmap, vitesse (optional), table (optional), gnuplot (optional), easigraf (optional), ACE/gr (optional), Excel (optional).
In this exercise we see examples of a number of features which need to be taken account of when applying genetic linkage analysis to traits with a complex (non-Mendelian) mode of inheritance. The example trait we will use is Alzheimer's disease. This form of dementia is common in old age, when it occurs sporadically with only relatively minor genetic effects on risk. However rare forms of the disease segregate in an autosomal dominant fashion with very high penetrance, and these highly familial cases have onset in middle age. Mutations at any one of three different loci can cause the presenile disease, so families segregating the disease can show linkage to any one of these loci.
An example set of 10 pedigrees has been set up in qdb database files alz.hdc and alz.dbf. The disease locus has been given the name ALZ. The pedigrees have been typed for the three markers used in the previous exercises and a qdb report file called alz2link.rep has been written which exports the data for these loci into the format required by LINKAGE programs. A report file called alztopd.rep has also been set up to export the data into the format required by pedraw, so that the pedigree diagrams can be displayed. You should run qdb and load alz.hdc. You may get a message saying "Could not open index file alz.idc" and if so just click on OK and select File, Reindex. Next select Records, Modify records and choose a record to inspect. You will see that the information is similar to that which was contained in the autdom database, except that the entry for the age of each subject has been filled in. This will be used subsequently to assign subjects to different liability classes.
The ten pedigree diagrams produced by pedraw from the output of alztopd.rep are displayed on a separate page. The first line under the subject ID is the age in years at assessment or death. If you wish you can examine alztopd.rep with a text editor so that you can see how the age is output, and you can use this report file to produce a data file for pedraw by selecting Reports, All records, choosing alztopd.rep as the report file and entering alzpd.dat as the output file. You can then run pedraw, load alzpd.dat and display the diagrams for yourself.
To set up some analyses with the data, it is first necessary to export the data in the format of a pedigree file which can be input into the LINKAGE programs. In qdb select Reports, All records, choose alz2link.rep as the report file and enter alzall.ped as the output file.
Before alzall.ped can be used by the LINKAGE programs one must run makeped on it to produce a file with pointers added, so at the operating system prompt enter:
makeped alzall.ped alzall.ppd n
This produces a new pedigree file called alzall.ppd.
A LINKAGE locus data file called alzall.par has already been set up which matches the information in the pedigree file alzall.ppd. The information consists of a disease locus, ALZ, and the same three marker loci as we used previously, named MAR1, MAR2 and MAR3. You can examine alzall.par with a text editor and you will see that it contains the following lines to describe the ALZ locus:
1 2 # ALZ 0.9999 0.0001 << gene freqs 1 << number of liability classes 0.0 1.0 1.0
These specify that ALZ is an affection locus with an abnormal allele which is very rare, as is the case with presenile Alzheimer's disease. One liability class is defined and the penetrance values for this are given. The first value is the probability for a subject to be affected if they have two copies of the normal allele (genotype AA), the second value is the probability of affection for heterozygous subjects (Aa) and the third value is the probability of affection for subjects who are homozygous for the abnormal allele (aa). We are treating Alzheimer's disease as an autosomal dominant trait, so providing penetrance values of 0 1 1 means that genotypically normal subjects have zero probability of being affected, but subjects with one or two copies of the abnormal allele will certainly be affected.
In order to facilitate setting up the linkage analyses for ALZ a quiklink command file has been provided called allalz.inp. You should examine this file with a text editor. It appears as follows:
adm1 alz mar1 adm2 alz mar2 adm3 alz mar3 adm1m3m2 alz mar1 mar3 mar2 0.04 0.06
The file is similar to the one used for the DIS1 locus, except that analyses are set up for ALZ instead. Two-point analyses are set up of ALZ against each marker locus, and a four-point analysis against all three markers is also specified.
In order to set up all the desired tests automatically, at the system prompt enter:
quiklink alzall.ppd alzall.par <allalz.inp
You should see that all the files for the desired analyses are written to disk.
Having set up the necessary file for the analyses, we will begin by trying to run the two-point analysis of Alzheimer's disease against the first marker, labelled MAR1. The files for this analysis have names beginning adm1, and the command file is called adm1.bat under MSDOS or adm1.sh under Unix. When you run this command file try to watch the output which mlink sends to the screen. At the MSDOS prompt enter:
adm1.bat (or just adm1)
or at the Unix prompt enter:
sh adm1.sh (or just adm1.sh)
What happens next will depend on which version of the LINKAGE package you have. If you are running a relatively early version then unknown and mlink will run OK, although you may notice that when mlink runs it produces a number of log likelihoods of negative infinity (in previous exercises it only produced log likelihoods of negative infinity at theta=zero). If you have a later version of LINKAGE then unknown will stop running with the error message: Incompatibility detected in this family for locus 1.
The problem is that we have specified that the ALZ locus behaves as a Mendelian autosomal dominant locus, whereas in fact this is not an accurate description of the mode of transmission and some of the pedigrees are inconsistent with this transmission model. Consider pedigrees 2 and 3:
In each case a subject has died young, before having time to develop the disease. It is inconsistent with a Mendelian dominant mode of transmission that an affected subject should have two unaffected parents, so the LINKAGE programs will either report that these pedigrees have zero likelihood or will stop with an error message.
Since Alzheimer's disease does not in fact behave as a Mendelian trait we should change the parameters of the transmission model to more accurately reflect the true mode of transmission.
One way to get the LINKAGE programs to deal with the Alzheimer's disease locus would be to specify it not as a Mendelian trait, but as a close approximation to one. This could be done by supplying penetrance values not of 0 1 1 but of 0.0001 0.9999 0.9999. If this were done the LINKAGE programs would run OK, but this would not really model what we know about the transmission pattern of Alzheimer's disease.
We have said that the presenile, genetically determined, form of Alzheimer's disease has an onset in middle age. Thus if we sample adult subjects who inherit the mutation we can say that approximately half may have developed the disease by the time we assess them, while the rest may be too young to show signs of the illness. In this case we should say that the probability of appearing affected conditional on having a copy of the disease allele is approximately 0.5. We have also said that Alzheimer's disease is common in old age, but in this case genetic factors have only a minor effect on risk (and the loci involved are different to those responsible for the presenile form) and the disease appears sporadic. The senile form of Alzheimer's disease is phenotypically indistinguishable from the presenile form. When we are studying the effect of a genetic locus having a major effect on risk then phenotypically indistinguishable cases which are sporadic or due to effects of other loci are termed phenocopies. If we take a sample of adult subjects then a proportion of them will be elderly and a proportion of elderly subjects will suffer from the quasi-sporadic form of Alzheimer's disease despite lacking the disease allele. Perhaps we could say that of adult subjects who are genetically normal with respect to the locus responsible for presenile disease, around 1% will have Alzheimer's disease.
Taking this view, the probability that a subject who has a copy of the disease allele will be classed as affected is 0.5, while the probability that a subject who is homozygous for the normal allele will be affected is 0.01. These are the penetrance values which we should enter for our transmission model.
Bearing this argument in mind, use a text editor to edit alzall.par and change the entry for the ALZ locus to read:
1 2 # ALZ 0.9999 0.0001 << gene freqs 1 << number of liability classes 0.01 0.5 0.5
Then save alzall.par to disk. Then, at the system prompt enter:
quiklink alzall.ppd alzall.par <allalz.inp
Now the linkage analyses will be set up with ALZ as an autosomal dominant locus with a penetrance of 0.5 and phenocopy risk of 0.01.
The quiklink input file allalz.inp sets up four analyses between the disease and markers, with filenames adm1.*, adm2.*, adm3.*, and adm1m3m2.* . Run all of these analyses, for example by entering at the MSDOS prompt:
adm1.bat (or just adm1)
or at the Unix prompt:
sh adm1.sh (or just adm1.sh)
To examine the lod scores obtained from each analysis, run table on the output file, which has extension .res. For example enter:
table adm1.res
Doing this for each .res file will produce tables of lod scores with the same filenames but having extension .tab. Examine these table files with a text editor and consider the following questions:
If you have gnuplot, easigraf or ACE/gr available, then run table on the output of the multipoint analysis to produce files for the graphing program:
table adm1m3m2.res -p (for gnuplot - makes adm1m3m2.plt and adm1m3m2.gda)
table adm1m3m2.res -g (for easigraf - makes adm1m3m2.plt)
table adm1m3m2.res -x (for ACE/gr - makes adm1m3m2.xgr)
Then run the graphing program and specify the appropriate graph file to display graphs of the multipoint lod score for each pedigree. With gnuplot, run gnuplot and Open the file called adm1m3m2.plt. With easigraf, toggle the display to full screen by pressing Alt-Enter and enter: easigraf adm1m3m2.grp. With ACE/gr, run ACE/gr and Load the file called adm1m3m2.xgr.
If you have Excel then you can view a graph directly from the .tab file by following the relevant instructions.
The total multipoint lod score provides a visual representation of how the evidence in favour of a particular position varies over the map.
Here is an excerpt from the graph of the multipoint lod scores. MAR1 is at 0 centimorgans, MAR3 at 4 and MAR2 at 10. The top dashed line shows the total lod score, while the lines below are the lod scores for individual pedigrees. The multipoint lod score reaches a peak of over 4 at the position of MAR3, while on the other side of MAR1 it peaks at around 2.5 and on the other side of MAR2 at just over 3:
Although our new transmission model incorporating reduced penetrance and allowing for phenocopies provides a better approximation to the true mode of transmission than a Mendelian model, it still does not incorporate all the available information. We have said that the risk of Alzheimer's disease varies markedly with age. Subjects possessing the disease allele have a high risk of developing the disease in middle age, while subjects without it are very unlikely to have the disease before old age. We can use this knowledge to assign subjects to liability classes based on their age. For subjects within the same liability class each genotype at the disease locus will yield a certain probability of being affected, but these sets of probabilities will be different for different liability classes. Thus for subjects aged less than 45 we might say that the probability of being affected if they possess the disease allele is, fairly low, perhaps 0.1, but if they are homozygous for the normal allele they are extremely unlikely to be diagnosed as having Alzheimer's disease, perhaps with probability 0.0001 (these cases would be likely to be misdiagnoses). For subjects aged 45-64 with the disease allele the probability of having become affected might be 0.8, while for those without the probability might be 0.001. Note that we are talking about the probability that a subject of this age might have become affected at any time in their life, so that if they are currently aged between 45 and 64 then they might have become affected below the age of 45 but this possibility would still contribute to the overall risk of affection for their present age group. The age to be used to define the liability class will be the age at which some direct or indirect clinical assessment was possible, or else the age at death, whichever is the earlier. (An alternative scheme is to assign liability classes according to age at onset, but the justification for doing this and the method of application are somewhat more complex.) Finally, for subjects aged 65 or over those with the disease allele might be almost certain to be affected, with probability 0.99, while those without might still have a significant risk of developing the more sporadic form of Alzheimer's disease, perhaps overall with probability 0.1. (Note: These penetrance values are intended only for the purposes of illustrating general principles, and are not intended to be entirely accurate.) The linkage programs allow us to state which liability class each subject belongs to, and to provide a different set of penetrance values for each liability class.
The report file used to produce the LINKAGE pedigree file from the database can be modified so that information regarding the liability class for each subject is exported along with their affection status. The locus data file, alzall.par, will then also be modified to incorporate this new information.
We will specify a new affection locus, called ALZL, which will consist of the combined information regarding the affection status and liability class to which a subject belongs. The format for this information to appear in a LINKAGE pedigree file is that there would be a number specifying affection status, consisting of 1, 2 or 0 for unaffected, affected or unknown, followed by a space and then a number giving the liability class to which the subject belongs.
A file is provided called alz2liab.rep. You can view it with a text editor. We wish to assign liability classes according to the age of the subject, and we will assume that the first class is for subjects aged less than 45, the second for subjects aged 45-64, and the third for subjects 65 or older. The lines which output the affection status appear as follows:
.if (phe0!=" ") " " [phe0,1,1] .else " 0" .endif " "This means that if the field Phe0 is blank a 0 (zero) is output, otherwise the contents of Phe0 are output.
We wish to include an additional locus which we will name ALZL. For this locus, the first character output should consist of a digit specifying the affection status, just as we have done for ALZ, and the second character a digit specifying the age-related liability class. To output the affection status we repeat just the same six lines as used for ALZ to export the information from the Phe0 field, and then in order to output the liability class we have inserted after them the following lines, which are hopefully fairly self-explanatory:
.if (age<45) " 1 " .endif .if (age>=45 & age<65) " 2 " .endif .if (age>=65) " 3 " .endif " "
The statements for the second class read "if the age is greater than or equal to 45 and the age is less than 65 then output 2". (Note the spaces between each number and the double quotes.) Thus subjects will be assigned a liability class of 1, 2 or 3 according to their age.
The whole file appears as follows:
:DETAIL
[id,1,3] fformat "%03.0f "
[id,4,3] fformat "%3.0f "
.if (father=" ")
" 0 "
.else
[father,4,3] fformat "%3.0f "
.endif
.if (mother=" ")
" 0 "
.else
[mother,4,3] fformat "%3.0f "
.endif
.if (sex="M")
"1 "
.else
"2 "
.endif
.if (phe0!=" ")
" "
[phe0,1,1]
.else
" 0"
.endif
" "
.if (phe0!=" ")
" "
[phe0,1,1]
.else
" 0"
.endif
.if (age<45)
" 1 "
.endif
.if (age>=45 & age<65)
" 2 "
.endif
.if (age>=65)
" 3 "
.endif
" "
("123456789abcdefghijklmnopq" strstr [phe1,1,1]) fformat "%2.0f "
("123456789abcdefghijklmnopq" strstr [phe1,2,1]) fformat "%-2.0f "
("123456789abcdefghijklmnopq" strstr [phe2,1,1]) fformat "%2.0f "
("123456789abcdefghijklmnopq" strstr [phe2,2,1]) fformat "%-2.0f "
("123456789abcdefghijklmnopq" strstr [phe3,1,1]) fformat "%2.0f "
("123456789abcdefghijklmnopq" strstr [phe3,2,1]) fformat "%-2.0f "
/1
Do note that the 6 lines beginning .if (phe0!=" ") are repeated. The first set of lines outputs the affection status for the affection locus without liability classes, then the lines are repeated to output the affection status for the affection locus with liability classes
This report file is called alz2liab.rep. With qdb running and alz.hdc loaded select Reports, All records and choose alz2liab.rep, and then enter alzlall.ped as the output file (note the extra "l" to indicate that this file contains the locus with liability classes). The new LINKAGE pedigree file incorporating the ALZL locus with liability classes should be written to disk. You should examine it with a text editor.
The first four lines appear as follows:
001 1 0 0 1 2 2 3 2 2 2 2 2 2 001 2 0 0 2 1 1 3 1 1 3 3 1 1 001 3 1 2 1 2 2 2 1 2 2 3 1 2 001 4 0 0 2 1 1 2 2 3 2 2 1 3The fifth column, consisting of 1's and 2's, contains the gender code for each subject. The next column consists of the affection code, with 1 meaning unaffected and 2 affected. Then there is a pair of numbers representing the affection status with liability class. Thus, the first subject has entry 2 3 meaning that they are affected and belong to liability class 3 (the oldest age group). Likewise, the second subject is unaffected but also belongs to liability class 3. The affection data is followed by the genotypes for the three markers.
Once again, one must run makeped on the new pedigree file, so at the operating system prompt enter:
makeped alzlall.ped alzlall.ppd n
Having produced a modified pedigree file which contains information for an affection locus with liability classes in addition to the original ALZ locus, it is necessary to use modified version of the locus data file containing information about this locus and the transmission model it implements. This is provided as a file called alzall.par. It appears as follows:
5 0 0 5 << no loci, risk locus, sexlinked(if 1) 0 0.0 0.0 0 << mut locus, mut rate, haplotype freq(if 1) 1 2 3 4 5 << order of loci 1 2 # ALZ 0.9999 0.0001 << gene freqs 1 << number of liability classes 0.01 0.5 0.5 1 2 # ALZL 0.9999 0.0001 << gene freqs 3 << number of liability classes 0.0001 0.1 0.1 0.001 0.8 0.8 0.1 0.99 0.99 3 4 # MAR1 0.14 0.32 0.21 0.33 << gene freqs 3 3 # MAR2 0.4 0.4 0.2 3 3 # MAR3 0.3 0.4 0.3 0 0 0.0 0.1 0.1 0.1 1 0.05 0.4
The following modifications have been made:
1 2 # ALZL 0.9999 0.0001 << gene freqs 3 << number of liability classes 0.0001 0.1 0.1 0.001 0.8 0.8 0.1 0.99 0.99
This entry provides penetrance values for a dominant affection locus with three different liability classes, with phenocopy probability of 0.0001 and penetrance of 0.1 for the first class, 0.001 and 0.8 for the second, and 0.1 and 0.99 for the third.
The sensible way to set up analyses using the new locus with liability classes is to modify the quiklink input file to deal with this locus in the same way as ALZ. Use a text editor to load allalz.inp, which appears as follows:
adm1 alz mar1 adm2 alz mar2 adm3 alz mar3 adm1m3m2 alz mar1 mar3 mar2 0.04 0.06
Add lines to set up exactly the same analyses, but use ALZL as the locus name instead of ALZ, and have each of the filenames for these analyses begin al instead of ad. The easiest way to accomplish this is to use your editor's copy function to copy all the lines specifying the ALZ analyses and to paste the copied block underneath the original. Then, within the copied block, use your editor's Search and replace function to alter all occurrences of alz to alzl, and all occurrences of ad to al. However you accomplish it, the modified version of the input file should appear as follows:
adm1 alz mar1 adm2 alz mar2 adm3 alz mar3 adm1m3m2 alz mar1 mar3 mar2 0.04 0.06 alm1 alzl mar1 alm2 alzl mar2 alm3 alzl mar3 alm1m3m2 alzl mar1 mar3 mar2 0.04 0.06
Save the new version of allalz.inp to disk. Then, at the system prompt enter:
quiklink alzlall.ppd alzlall.par <allalz.inp
Run each of the new analyses which quiklink has set up (there is no need to rerun the earlier analyses), for example at the MSDOS prompt enter:
alm1.bat (or just alm1)
or at the Unix prompt enter:
sh alm1.sh (or just alm1.sh)
Then run table on each of the .res files produced by the analyses, for example:
table alm1.res
If you have gnuplot, easigraf or ACE/gr available, then run table on the output of the multipoint analysis:
table alm1m3m2.res -p (for gnuplot - makes alm1m3m2.plt and alm1m3m2.gda)
table alm1m3m2.res -g (for easigraf - makes alm1m3m2.plt)
table alm1m3m2.res -x (for ACE/gr - makes alm1m3m2.xgr)
Then run the graphing program and specify the appropriate graph file to display graphs of the multipoint lod score for each pedigree. With gnuplot, run gnuplot and Open the file called alm1m3m2.plt. With easigraf, toggle the display to full screen by pressing Alt-Enter and enter: easigraf alm1m3m2.grp. With ACE/gr, run ACE/gr and Load the file called alm1m3m2.xgr.
If you have Excel then you can view a graph directly from the alm1m3m2.tab file by following the relevant instructions.
Use your text editor to examine each of the .tab files containing tables of lod scores and consider the same questions as you did for the ALZ locus with no age-related liability classes. What is your interpretation of the results of the two point and multipoint analyses, and how do the results compare with those you obtained with the ALZ locus?
Here is a graph of the multipoint lod scores produced by ALZL obtained for each pedigree, with the total multipoint lod score displayed as a dashed line which is above the lines for each pedigree over most of the region. The three markers are at positions 0, 4 and 10 centimorgans, and the maximum for the total lod score is about 4, which occurs at a position of about -10 centimorgans, or a recombination fraction of 10% with MAR1.
You may recall that for the analysis of the ALZ locus the maximum total lod score occurred in the middle of the marker map, at the position of MAR3. You can also see that most of the pedigrees also produce a maximum in about this position. However one pedigree (graphed as a dotted line) is strongly negative over the whole interval between the markers. This pulls the total lod score right down over this region and means that the maximum for the total lod occurs some distance away.
Till now, we have simply added together the lod scores from different pedigrees in order to obtain an overall lod score at each point on the map. However totalling lods in this way is only valid if the trait under consideration is influenced by the same genetic locus in all pedigrees. Regarding the actual genetics of Alzheimer's disease we have stated above that mutations at any one of three different loci can produce the disease. Therefore a plausible explanation for the observations is that in at least one of the pedigrees the disease is occurring through the action of a locus elsewhere.
Smith described a way to combine lods from different pedigrees under the assumption that only a proportion might show linkage. The proportion of linked pedigrees is conventionally denoted alpha, and, if we denote the likelihood for a pedigree assuming that the disease locus is at position theta as L(theta), then the likelihood for each pedigree is alpha.L(theta)+(1-alpha).L(0.5). Here L(0.5) is the likelihood assuming that the disease locus is unlinked to the marker or, in the case of multipoint analysis, all the markers. The log of the likelihood ratio in favour of linkage is log[alpha.L(theta)/L(0.5)+1-alpha] for each pedigree. It is these values which need to be added together to get an overall estimate of the evidence in favour of linkage at each point on the map. The overall lod score obtained by by totalling these values may be called an admixture lod score or heterogeneity lod. At each point on the map a certain value of alpha will maximise the admixture lod. The maximised lod is sometimes referred to as lod2 or hlod. This kind of admixture analysis is based on Smith's test called the A-test and the program typically used to perform the analysis is called homog. However the table program can carry out a similar analysis by specifying the -a (for admixture) switch. For example, at the operating system prompt enter:
table alm3.res -a
Then with a text editor examine the alm3.tab file produced. It appears as follows:
MLINK : ALZL MAR3
theta 0.000 0.010 0.050 0.100 0.200 0.300 0.400
cM 0.000 1.000 5.017 10.137 21.182 34.657 54.931
1 0.946 0.932 0.875 0.800 0.638 0.455 0.246
2 0.941 0.927 0.870 0.795 0.633 0.451 0.242
3 0.634 0.621 0.564 0.490 0.336 0.180 0.052
4 0.321 0.312 0.276 0.231 0.144 0.070 0.019
5 1.666 1.637 1.519 1.366 1.042 0.700 0.350
6 -4.456 -2.695 -1.407 -0.863 -0.372 -0.142 -0.031
7 0.297 0.293 0.275 0.252 0.202 0.145 0.079
8 0.297 0.293 0.275 0.252 0.202 0.145 0.079
9 0.866 0.852 0.797 0.725 0.571 0.400 0.211
10 0.536 0.528 0.494 0.450 0.356 0.252 0.135
total 2.048 3.699 4.538 4.499 3.752 2.657 1.381
lod2 5.223 5.121 4.789 4.499 3.752 2.657 1.381
alpha 0.850 0.850 0.850 0.900 1.000 1.000 1.000 1.000
The total lod score is shown as previously, but also the admixture lod score together with the value of alpha which maximises it. Note the difference in the magnitude and position of the maximum lod scores under the assumptions of homogeneity and heterogeneity.
The same procedure can be applied to the multipoint lod score, and if you have a graph-drawing program available then you can add the relevant switch to produce a graph file containing the admixture lod scores.
(If you have been using Excel to view the graph of alm1m3m2.tab you will need to exit this sheet in Excel before you can run table to produce a new version of alm1m3m2.tab. Once the new file has been produced you can then import it into Excel.)
table alm1m3m2.res -a -p (for gnuplot - makes alm1m3m2.plt and alm1m3m2.gda)
table alm1m3m2.res -a -g (for easigraf - makes alm1m3m2.plt)
table alm1m3m2.res -a -x (for ACE/gr - makes alm1m3m2.xgr)
table alm1m3m2.res -a (for Excel - just makes alm1m3m2.tab)
You can then run the graph-drawing program to display the admixture lod scores. If you do not have such a program available, then just enter table alm1m3m2.res -a to create alm1m3m2.tab examine this file with a text editor to see how the admixture lod score varies across the map.
Here is the graph of multipoint lod scores, now with the admixture lod score displayed:
While the total lod score, drawn with the long dashed line, dips between the markers, the admixture lod score, drawn with the short dashed line, reaches a maximum of over 5 at the position of MAR3.
It is interesting to see the effects of allowing for admixture on the results obtained with the ALZ analysis which did not include liability classes. This can be done for the multipoint analysis by entering:
table adm1m3m2.res -a -p (for gnuplot - makes adm1m3m2.plt and adm1m3m2.gda)
table adm1m3m2.res -a -g (for easigraf - makes adm1m3m2.plt)
table adm1m3m2.res -a -x (for ACE/gr - makes adm1m3m2.xgr)
table adm1m3m2.res -a (for Excel - just makes adm1m3m2.tab)
The graph obtained appears as follows:
The maximum lod increases by about 1 unit when heterogeneity is allowed for, but the estimate of the position of the disease locus remains unchanged.
Here is the pedigree which produces the negative lod scores:
Given that Alzheimer's disease is extremely rare below the age of 45, it is clear that this pedigree certainly does not demonstrate linkage to these markers. It is worth noting that the very strongly negative lod scores were only obtained with this pedigree when we incorporated age-related liability classes in the analysis, and that otherwise we might not have realised it was unlinked. It is also worth noting that the analysis incorporating liability classes gave a completely erroneous estimate of the position of the disease locus until we allowed for genetic heterogeneity in the analysis.
This section demonstrates many of the factors which may need to be incorporated in the analysis of diseases with complex inheritance, including incomplete penetrance, phenocopies, use of liability classes and locus heterogeneity.
Exercises in genetic linkage analysis
All material copyright (C) Dave Curtis 1996-2004
david.curtis@qmul.ac.uk