section 3.2 ILINK

linkage user's guide (version 5.2)

3.2 ILINK

Purpose

ILINK is a program for maximum likelihood estimation of recombination fractions for an arbitrary number of marker and disease loci. For two loci, the program determines the maximum lod score in addition to the recombination estimate. Sex-specific differences in the recombination rates can be incorporated as described in Chapter 2. ILINK can also estimate penetrance, gene frequencies and other parameters.

Using the Program

ILINK is used with the accompanying program UNKNOWN. The calling order is:

     UNKNOWN
     ILINK

The input files for this suite of programs are:

     PEDFILE 
     DATAFILE

The output files are:

     FINAL
     OUTFILE
     STREAM

UNKNOWN produces temporary files called IPEDFILE and SPEEDFILE; along with DATAFILE, these serve as input for ILINK.

Program Constants Specific to ILINK

The following constants can be modified for various purposes:


fitmodel = false;   {TRUE IF ESTIMATING PARAMETERS OTHER THAN RECOMBINATION}
dostream = true;    {STREAM FILE OUTPUT}
byfamily = false;   {GIVE LOD SCORES BY FAMILY IN FINAL}

     { GRADIENT APPROXIMATIONS }

approximate = true;
epsilon = 1.0E-3;

     { GEMINI }
maxn = 20;          {MAXIMUM NUMBER OF ITERATED PARAMETERS}

Datafile Structure

The program-specific parts of DATAFILE consist of two lines. The first contains a number that indicates a locus (iterated locus) for which parameters, such as gene frequency or penetrance, can be estimated. The locus number is given in phenotype order.

The second line consists of a list of zeros and ones (binary list) to indicate parameters that are to be estimated or fixed. If a 1 is entered in a given location, the parameter corresponding to that location is estimated (iterated parameter); if the entry is zero, the corresponding parameter is fixed at the initial value specified in the DATAFILE (non-iterated parameter).

Specifications for Estimating Recombination Rates

For n loci, the first n-1 locations in the list correspond to the recombination rates between adjacent loci. In most applications, estimates of these recombination rates will be made with other parameters held fixed. In this case, any of the locus numbers can be used for the iterated locus (the value must be between 0 and n, where 0 indicates that none of the loci can have iterated parameters). For example, if 1 is chosen for the iterated locus and n is 3, the two lines to add to the DATAFILE are:

     1         << iterated locus
     1 1

The last line must end directly after the specification of the last iterated or non-iterated parameter, without trailing blanks. This end-of-line deliminator tells the program that only recombination fractions will be estimated.

Sometimes it is useful to fix the value of one of the recombination rates; for example, if the first two loci are known to be completely linked we might wish to fix the first recombination rate to 0.0 while estimating the second rate. In this case, the last two lines are:

     1         << iterated locus
     0 1

With sex-specific recombination rates, the number of parameters is increased by 1 (to n) when assuming a constant ratio of female/male genetic distances, or by n-1 (to 2n-2) when estimating different male and female recombination fractions in each interval. For the former, the last two lines are:

     1         << iterated locus
     1 1 1

and for the latter, they are:

     1         << iterated locus
     1 1 1 1

With three loci, ILINK supports interference. When a mapping function is used, two iterated parameters are specified for each sex. Without a mapping function, three recombination rates can be estimated for each sex, and the number of iterated parameters should be adjusted accordingly.

Specifications for Estimating Other Parameters

All locus types support the estimation of gene frequencies; these add an additional nallele-1 parameters to the list of iterated or non-iterated values. If the iterated locus is of the affection status or quantitative type, other parameters can also be estimated.

The list of iterated parameters has the following orders for the four types of loci:

Numbered alleles or binary factors: The order is recombination fractions (and female/male genetic distance under the sex-difference option 1) followed by nallele-1 gene frequencies.
Affection status: The order is recombination fractions (and female/male genetic distance under the sex-difference option 1); nallele-1 gene frequencies; penetrance for each genotype in each of liability class [nliability x nallele x (nallele + 1)/2]; an additional penetrance for each allele for sex-linked loci.
Quantitative variables: The order is recombination fractions (and female/male genetic distance under the sex-difference option 1); nallele-1 gene frequencies, means for each of ntrait quantitative traits (ntrait x nallele); and the upper-triangle of the variance covariance matrix [ntrait x (ntrait-1)/2]. Within the program, quantitative variables are restricted to two alleles at a locus. The genotype means are transformed to the mean of first homozygote, displacement between the first and the second homozygote mean, and the dominance (ratio of the difference between heterozygotes and first homozygotes means to the displacement).

Gradient Approximation

Approximations to the gradient are controlled by the boolean constant APPROXIMATE and the value of the constant EPSILON. The approximation applies only to the calculation of the gradient prior to a line search in the numerical estimation procedure. In a variety of examples, EPSILON = 0.00001 has been found satisfactory. To assure a maximum gain in efficiency a pedigree with little genotypic information should be selected for the proband.
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