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May 1998 - Authors: Martin Farrall and Heather Cordell
A SOFTWARE PACKAGE FOR ANALYSING TWO-LOCUS SUSCEPTIBILITY GENE MODELS
IN AFFECTED SIB-PAIR DATA
VERSION 2 INCLUDES RISCH MULTIPLICATIVE MODELS AS IMPLEMENTED IN THE
GENERAL VARIANCE COMPONENTS MODEL BY HEATHER CORDELL
INTRODUCTION
In this sub-directory (pub/genetics/twoloc) you will find a series of
utility programs, analysis programs and an example dataset that
accompany a paper that appeared in Genetic Epidemiology in 1997
entitled "Affected Sibpair Linkage Tests for Multiple Linked
Susceptibility Genes" by Martin Farrall (volume 14, number 2, pages 103
- 115). The abstract for this paper follows:
Genome-wide searches for susceptibility genes using pairs of affected
siblings are being undertaken to dissect out individual polygenes that
contribute to human multifactorial diseases. Efficient
identity-by-descent (IBD) based sibpair linkage tests are available
that test individual markers or maps of linked markers for linkage to a
single putative susceptibility gene. In order to assess the support
for linkage to a second putative susceptibility gene that happens to
map close to an established susceptibility gene, it is necessary to use
a method that correctly allows for the IBD distortion that directly
results from the linkage between the two genes. A maximum likelihood
based, multilocus linkage test is proposed which accounts for this
interdependency and evaluates the support for an interaction between
constituent susceptibility genes. The size and power of a test for a
second linked susceptibility gene is investigated by simulation
studies.
Please note that these programs are intended to be used by linkage
analysis wizards who have a sound knowledge of the LINKAGE programs and
experience with compiling, linking and running pascal, fortran and C
programs on a UNIX based computer. In due course, I hope to polish up
this software into a much more user friendly package (a
"ready-to-microwave" TV dinner) but for the time being you will have to
make do with a variety of prepared ingredients that you will have to
combine and cook to make your meal! You will need to have the linkage
analysis program VITESSE (and ideally the fortran numerical analysis
library from NAG {Numerical Algorithm Group}) up and running on your
computer before you will be able to use the software to its full extent
as well as a fortran 77 and pascal compiler. I have included
executable binary versions of the fortran and pascal programs for three
Unix platforms, Solaris 2.5, IRIX 6.2 and DEC OSF/1 v3.0.
FILES INCLUDED IN THIS RELEASE
README.FIRST (this file)
TWOLOC.TAR.Z (compressed tarfile containing the following files)
alpha.dat (output from "calc_alpha 0.2 0.3")
awk (subdirectory containing three awk programs)
bin (subdirectory with executables for various UNIX platforms)
calc_alpha (Csh program to calculate alphas)
calc_ibd (Csh program to calculate taus)
datafile.dat (output of "mkp", input for "calc_ibd")
joint_prob.dat (output from "calc_ibd", input for "twoloc")
pedcount.dat (output from "mkp", input for "calc_ibd")
pedfile.dat (output from "mkp", input for "calc_ibd")
pedin.dat (input for "mkp")
src (subdirectory with sources for "mkp" and "twoloc")
Use ftp to retrieve TWOLOC.TAR.Z and uncompress it and "untar" it as
follows:
either
uncompress TWOLOC.TAR.Z; tar xvf TWOLOC.TAR
or
zcat TWOLOC.TAR.Z | tar xvf -
TWOLOC
The main analysis program, twoloc, is written in fortran (f77) (the
source code is called twoloc.f), and this program computes MLS
statistics for various user defined two-locus models. The user is
interactively interrogated to specify the male and female
recombination fractions separating the two susceptibility genes and to
choose from various optional constraints (e.g. two locus additive
model, single locus model, no dominance variance at one or both loci
etc.). The sibpair data is read in from a single text file
(joint_prob.dat) which contains the number of sibpairs to be read in
and a list of probabilities (referred to as taus in the Genetic
Epidemiology paper) for each affected sibling pair (the probability
that a sibpair shares i and j genes IBD for two susceptibility genes at
the two locations). The program also reads in a list of 16
sex-specific joint IBD prior probabilities (referred to as alphas in
the Genetic Epidemiology paper) from a textfile called alpha.dat.
The first line in joint_prob.dat is the number of families to be
analysed. Each subsequent line contains 16 joint IBD probabilities
(taus) (that obviously have to sum to 1!), each sibpair has it's own
list of 16 taus . The list order for the taus is shown below where
each joint IBD probability is listed as IBD(i,j) where i and j can be 1
(IBD=0), 2 (IBD = 1 inherited from father), 3 (IBD = 1 inherited from
mother) or 4 (IBD = 2).
IBD(1,1), IBD(1,2), IBD(1,3), IBD(1,4), IBD(2,1), IBD(2,2), IBD(2,3),
IBD(2,4), IBD(3,1), IBD(3,2), IBD(3,3), IBD(3,4), IBD(4,1), IBD(4,2),
IBD(4,3), IBD(4,4).
So for example, a family in which the joint IBD at two locations is
exactly 2 and 2 will be entered as follows:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
As another example, consider a family which shares exactly 1 gene IBD
(inherited from the father) at the first susceptibility gene and 1 gene
IBD (inherited from the mother) at the second susceptibility gene, this
data will be entered as follows:
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
The file alpha.dat, contains 16 sex-specific prior IBD probabilities
(alphas), these can be calculated using the script calc_alpha (see
below) and are listed in a similar order to that shown for the observed
joint IBD probabilities (taus).
twoloc, calls the quasi-Newtonian minimization subroutine E04JAF from
the Numerical Algorithms Group Ltd. (NAG) to maximize the likelihood
(and MLS). It should be fairly straightforward to replace this function
with your own favourite minimization function and I will try to assist
you with this if you are unable to unfathom the twoloc source code. NAG
fortran libraries are readily available and I suggest that for details
you try contacting your local computing experts (as site licences are
often held by universities). NAG's home page is http://www.nag.co.uk/
where online documentation for E04JAF as well as distributor
information can be found.
Compiling twoloc with a suitably installed fortran compiler and NAG
library can be achieved by:
f77 -O -extend_source -o twoloc twoloc.f -lnag
The "-extend_source" switch (some compilers use "-e") is necessary as
some of the source code lines are longer than 72 characters. The -lnag
switch for the linker is necessary for the NAG subroutines, you may
need an additional -L flag if the libraries are not installed in your
default search path.
An example dataset (joint_prob.dat) is included to try out some
illustrative analyses. The two susceptibility genes are assumed to be
linked (theta = 0.2 in males and 0.3 in females). Results from fitting
several models are listed below:
Option Model MLS
---------------------------------------------------------------------
1 general model - all 8 variance components iterated 5.942
5 additive model (includes dominance components) 5.726
9 Locus 1 on its own with dominance variance 4.777
11 Locus 2 on its own with dominance variance 2.611
---------------------------------------------------------------------
The additional support for locus 2 assuming that locus 1 is linked is
calculated by comparing model 5 with model 9 (5.726 - 4.777 = 0.95).
The additional support for locus 1 assuming that locus 2 is linked is
calculated by comparing model 5 with model 11 (5.726 - 2.611 = 3.12).
Assuming that both loci are linked, then there is no support for an
epistatic interaction (i.e. compare model 1 with model 5, 5.942 - 5.726
= 0.22). I would conclude from this analysis that there is only
support for locus 1 being linked and the "pairwise" MLS at locus 2 is
due to its linkage to a major susceptibility gene (locus 1).
The final output of twoloc is written to the file mls.out (an example
follows):
========================================================================
TWO-LOCUS SIBPAIR LINKAGE ANALYSIS RESULTS
IFAIL = 7
Total number of sibpairs in analysis = 312
Number of function evaluations = 347
2:1:1:0 joint IBD sharing matrix
0 1 (male) 1 (female) 2
0 0.063518 0.036150 0.055627 0.037694
1 (male) 0.032837 0.088857 0.030280 0.093000
1 (female) 0.050529 0.030280 0.088857 0.060437
2 0.025912 0.079839 0.051884 0.174300
Note: locus 1 in columns, locus 2 in rows
MLS = 5.942
option = 1 - general model - all 8 variance components iterated
========================================================================
IFAIL is a diagnostic code generated by the NAG subroutine E04JAF The
program will most often generate a code of 5, 6, 7, 8 indicating that
convergence has been acheived (to varying degrees of confidence). For
more details see the NAG documentation on the WWW pages mentioned
above.
The joint IBD sharing matrix contains maximum likelihood estimates.
CALC_ALPHA
calc_alpha is a (hopefully) useful little script that works in
conjunction with vitesse (as a likelihood computation engine) in order
to compute 16 sex-specific prior IBD sharing probabilities (alphas) for
an affected sibpair. The script expects just two arguments, the male
and female recombination fractions separating the two susceptibility
genes. It then writes out 16 nuclear families, one for each of the 16
sex-specific joint IBD configurations (pedfile.dat), and writes a
datafile.dat file with the pertinent parameters to calculate the
relevant likelihoods (in the format required for a LINKMAP run).
vitesse is then called to calculate the relevant likelihoods. I have
added an awk "program" to read in the voutfile.dat file generated by a
successful vitesse run and to write out the 16 joint IBD probabilities
to a file alpha.dat (which is in a suitable format to be directly read
in by twoloc). The order of listing the alphas is the same as
discussed in the context of the "twoloc" taus.
MKP
mkp is a utility program (written in pascal) that reads in a LINKAGE
formatted pedigree file (which must be called pedin.dat and must have
been been processed through makeped so that it contains the first
offspring and next sibling pointers and so on). The pedigree file must
contain the affection status of each individual (0, 1 or 2) as the
first phenotype (and no liability code please!) and a list of genotypes
for each marker in the analysis (in LINKAGE terms, locus type 3 for
codominant markers). The program will write out 16 new pedigrees for
each original sibpair, with two new loci (dummy markers) that specify
exactly each of the 16 possible sex-specific joint IBD configurations.
If there are more than 2 affected sibs in a particular family, then the
program will write out 16 pedigrees for each pair of sibs that can be
constructed.
For example, here is a LINKAGE formatted pedigree file for two affected
siblings and a third sib whose phenotype status is unknown:
disease marker marker
status one two
7 1 0 0 3 0 0 1 1 0 1 2 0 0 Ped: 7 Per: 1
7 2 0 0 3 0 0 2 0 0 0 0 3 4 Ped: 7 Per: 2
7 3 1 2 0 4 4 1 0 2 1 3 1 3 Ped: 7 Per: 3
7 4 1 2 0 5 5 1 0 2 2 4 2 4 Ped: 7 Per: 4
7 5 1 2 0 0 0 2 0 0 1 4 1 3 Ped: 7 Per: 5
mkp has generated 16 families (one for each sex-specific joint IBD
configuration) as follows:
marker
four ******************************************************
three *********************************************** ****
two **************************************** **** ****
one ********************************* **** **** ****
**** **** **** ****
**** **** **** ****
1 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
1 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
1 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
1 4 1 2 0 5 5 1 0 2 4 2 4 2 4 2 4 Original ped no. 7
1 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
2 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
2 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
2 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
2 4 1 2 0 5 5 1 0 2 4 2 4 2 4 1 4 Original ped no. 7
2 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
3 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
3 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
3 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
3 4 1 2 0 5 5 1 0 2 4 2 4 2 4 2 3 Original ped no. 7
3 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
4 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
4 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
4 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
4 4 1 2 0 5 5 1 0 2 4 2 4 2 4 1 3 Original ped no. 7
4 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
5 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
5 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
5 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
5 4 1 2 0 5 5 1 0 2 4 2 4 1 4 2 4 Original ped no. 7
5 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
6 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
6 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
6 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
6 4 1 2 0 5 5 1 0 2 4 2 4 1 4 1 4 Original ped no. 7
6 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
7 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
7 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
7 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
7 4 1 2 0 5 5 1 0 2 4 2 4 1 4 2 3 Original ped no. 7
7 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
8 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
8 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
8 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
8 4 1 2 0 5 5 1 0 2 4 2 4 1 4 1 3 Original ped no. 7
8 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
9 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
9 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
9 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
9 4 1 2 0 5 5 1 0 2 4 2 4 2 3 2 4 Original ped no. 7
9 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
10 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
10 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
10 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
10 4 1 2 0 5 5 1 0 2 4 2 4 2 3 1 4 Original ped no. 7
10 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
11 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
11 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
11 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
11 4 1 2 0 5 5 1 0 2 4 2 4 2 3 2 3 Original ped no. 7
11 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
12 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
12 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
12 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
12 4 1 2 0 5 5 1 0 2 4 2 4 2 3 1 3 Original ped no. 7
12 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
13 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
13 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
13 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
13 4 1 2 0 5 5 1 0 2 4 2 4 1 3 2 4 Original ped no. 7
13 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
14 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
14 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
14 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
14 4 1 2 0 5 5 1 0 2 4 2 4 1 3 1 4 Original ped no. 7
14 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
15 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
15 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
15 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
15 4 1 2 0 5 5 1 0 2 4 2 4 1 3 2 3 Original ped no. 7
15 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
16 1 0 0 3 0 0 1 1 1 2 0 0 1 2 1 2 Original ped no. 7
16 2 0 0 3 0 0 2 0 0 0 3 4 3 4 3 4 Original ped no. 7
16 3 1 2 0 4 4 1 0 1 3 1 3 1 3 1 3 Original ped no. 7
16 4 1 2 0 5 5 1 0 2 4 2 4 1 3 1 3 Original ped no. 7
16 5 1 2 0 0 0 2 0 1 4 1 3 0 0 0 0 Original ped no. 7
Markers one and two are as before, markers three and four are new dummy
markers, one for each susceptibility gene.
mkp also writes out a suitable datafile (in LINKMAP format) to
accompany the pedigree file. In order to set up a LINKMAP run to
calculate likelihoods for susceptibility genes being separated by theta
= 0.2 (males) and theta = 0.3 (females) tightly linked to markers one
and two, then specify the order of loci as 1 3 2 4 and the male and
female recombination fractions between the loci as:
4 0 0 4
0 0.0 0.0 0
1 3 2 4
3 4 # marker no: 1
0.25000 0.25000 0.25000 0.25000
3 4 # marker no: 2
0.25000 0.25000 0.25000 0.25000
3 4 # first susceptibility gene
0.25 0.25 0.25 0.25
3 4 # second susceptibility gene
0.25 0.25 0.25 0.25
2 0
0.00000 0.20000 0.00000
0.00000 0.30000 0.00000
1 0.00000 1
I have not tested this part of the program extensively and I would not
be surprised if problems with the datafile.dat file were not
encountered on occasion (especially with the last line). The idea is
to compute a single likelihood for each family (with separate male and
female recombination fractions) for the recombination fractions
selected when running mkp. The last line may require editing by the
user I'm afraid.
mkp also writes out the total number of families in pedfile.dat to a
new file pedcount.dat
mkp is a very simple program that was designed to work with nuclear
families (i.e. parental and sibling generations ONLY). It assumes that
parents can be identified as they have no specified ancestors (i.e.
their parents are missing) and everyone else in a family is assumed to
belong to the sibling generation. An example pedin.dat file is
included for you to try out, I have also included the output of mkp
(pedcount.dat, datafile.dat and pedfile.dat) in case you wish to try
out calc_ibd in the first instance. I have compiled and run the
program under Solaris 2.5 and IRIX 6.2. Curiously, under OSF/1 v3.2,
the program crashes with a segmentation violation which I have been
unable to resolve to date. Also, mkp writes out equal frequencies in
the datafile.dat file for your markers, you should edit the
datafile.dat file using a text editor to change them if necessary.
CALC_IBD
calc_ibd is a script that uses vitesse as a likelihood computation
engine to calculate sex-specific joint IBD probabilities (taus). An
"awk" program is included to read in the resulting voutfile.dat and
apply Bayes's theorem and write out the joint IBD matrix to the file
joint_prob.dat.
VITESSE
Authors: Jeff O'Connell and Dan Weeks.
For more details:
"The VITESSE algorithm for rapid exact multilocus linkage analysis
via genotype set-recoding and fuzzy inheritance," O'Connell JR, Weeks
DE, Nature Genetics 11:402-408, December 1995
This program can be obtained from ftp://watson.hgen.pitt.edu/pub (USA)
or ftp://ftp.ebi.ac.uk/pub/software/linkage_and_mapping/hgen_pitt
(EUROPE).
PLEASE ENSURE THAT IF YOU USE VITESSE THAT YOU CITE O'CONNELL AND WEEKS
A brief outline to two-locus sibpair analysis.
1) Run calc_alpha to create a file alpha.dat that contains 16
sex-specific, joint IBD probabilities (alphas). vitesse must have been
installed on your system as this is called to calculate the relevant
likelihoods.
INPUT FILES: awk/awk.alpha.0, awk/awk.alpha.1
OUTPUT FILE: alpha.dat
2) Create a pedigree file (pedin.dat) in LINKAGE format containing the
affection status (no more than 1 liability class please!), followed by
at least two markers.
3) Process pedigree file with the program mkp to split up multiplex
families into affected sibpairs and add dummy markers to specify all 16
possible, sex-specific, joint IBD configurations; edit the resultant
datafile.dat file to check that the marker allele frequencies are
correct:
INPUT FILES: pedin.dat
OUTPUT FILES: pedfile.dat, datafile.dat, pedcount.dat
3) Run calc_ibd to create a file (joint_prob.dat) containing the
sex-specific, joint IBD probabilities (taus). vitesse must have been
installed on your system as this is called to calculate the relevant
likelihoods.
INPUT FILES: pedfile.dat, datafile.dat, pedcount.dat, awk/awk.ibd
OUTPUT FILES: joint_prob.dat
4) Finally run twoloc to fit various two-locus models to your sibpair
data.
INPUT FILES: joint_prob.dat (see step 3), alpha.dat (see step 1)
OUTPUT FILE: mls.out
Conditions of use:
This software is provided as a "gift" to a non-profit making research
organization, no attempts should be made to sell or patent this program
or incorporate it into another program. The software is provided "as
is", no warranty as to the accuracy or reliability of the results can
be provided or the fitness of the program for any particular
application. Please feel free to modify or adapt the code as you
wish.
For further enquiries, bug-reports and general advice on sib-pair
linkage analysis, feel free to contact (preferably by e-mail):
Martin Farrall is ........
Dept. Cardiovascular Medicine
The Wellcome Trust Centre for Human Genetics
Roosevelt Drive
Oxford
OX3 7BN
UK
phone: +44 (0)1865 740 012 (direct line)
phone: +44 (0)1865 742 441 (general enquiries)
FAX: +44 (0)1865 742 196
e-mail: mfarrall@well.ox.ac.uk
Dr. Heather Cordell may be contacted by e-mail at
cordell@darwin.cwru.edu
If you send me your e-mail message, I will send you notice of updates,
bugs etc. that will no doubt arise. Curiously no one has bother to
register so far although from our anonymous FTP log, a fair number of
people have downloaded the software.