Computational Intelligence - November 2015 - 57

individual effects but the combined
effect of SNPs is large. This usually
implements the AND model of combination [23], individuals will have one
genotype (e.g. RH) AND another genotype (e.g. H) if they are to be included
in the positive group. However, when
considering the details of the combination at the genotype level a number of
different possibilities present themselves.
In this work, the algorithm can explore
a number of combination types providing it with greater expressive power. Initially all logical boolean operations
between two genotypes were considered
by the algorithm, but analysis revealed
that this can be reduced down to the
following four combinations that
encompass all real-world possibilities.
In the approach described here, the
following logical interactions between
two SNPs are considered:
❏ An individual is positive if and only
if the first SNP takes a specific value
and the second SNP takes a specific
value. (AND)
❏ An individual is positive if and only
if the first SNP or the second SNP
takes their specific values. (OR)
❏ An individual is positive if and only
if the first SNP takes a specific value
and the second SNP does not take a
specific value. (AND NOT)
❏ An individual is positive if and only
if exactly one of the two SNPs takes
a specific value and the other SNP
does not take a specific value. (XOR)
From the above list it can be seen
that this extension allows the algorithm
to search for more sophisticated interactions between genotypes than the standard AND relationship. During the
search process, when two SNPs are
selected by the ACO approach, their
genotypes are investigated using all of
these four logical combinations, from
which the best is selected to be used as
the fitness of the combination.
3) Fitness Function: The fitness function must represent the discriminatory
ability of a combination between control individuals and cases. SNPs in combination with high fitness values will
receive more pheromone and are therefore more likely to be selected for new

combinations. Thus this function leads
the search process of the algorithm and
is therefore a key aspect of the algorithm. The fitness function is based on
standard statistical measures that are
implemented on a binary classification
of controls and cases in genome wide
association studies [16], [23] and are
described below.
The efficacy of two SNPs snp1 and
snp2 in discriminating between the two
classes is evaluated by the numbers of
positive (p) and negative (n) individuals
among the cases (D p and D n) and controls (C p and C n), where the determination of positive and negative individuals is
achieved through the use of the logical
combination rules described previously,
and according to the following process.
1: Initialise two 4 by 4 tables TControls
and TCases;
2: for all controls do
3: Increment TControls [Value_of_snp1]
[Value_of_snp2] by 1;
4: end for
5: for all cases do
6: Increment TCases [Value_of_snp1]
[Value_of_snp2] by 1;
7: end for
8: C p (C n) ! sum of cells of TControls for
which the combination is true (false);
9: D p (D n) ! sum of cells of TCases for
which the combination is true (false);
The complexity of this calculation is
O (n) where n is the total number of
individuals (controls and cases). This is
important because an ACO run may
require over a million fitness evaluations,
the main computational load of the
algorithm is devoted to the evaluation of
the fitness function and therefore this
must be as efficient as possible.
To calculate fitness, Pearson's chisquared test on a binary classification of
controls and cases is used. The four values
C p, C n, D p and D n are used to calculate
the expected values E.C p, E.C n, E.D p
and E.D n The chi-squared statistic
2
X snp
1, snp2 (v1, v2) is given by the formula:
2
X snp
1, snp2 (v1, v2) =
(E.D p - D p) 2 (E.D n - D n) 2
+
E.D p
E.D n
(E.C p - C p) 2 (E.C n - C n) 2
(1)
+
+
E.C p
E.C n

As described previously, there are three
possible values CH, H and RH for v1 and
again three possible values for v2. Therefore there are 9 (3 # 3) different chisquared values for snp1 and snp2 and the
largest of these is selected as the fitness
function value f (snp1, snp2) of the combination of the two SNPs snp1 and snp2.
f (snp1, snp2) =
max {X 2snp1, snp2 (v1, v2)}
such that (v1, v2) ! {CH, H, RH} 2
(2)
From the Pearson's chi-squared the
p-value (probability of achieving this
result through chance) of the association
can be calculated.
4) Updating pheromone: At each generation of the algorithm, each of the nbant
ants selects two SNPs to test their combination. The amount of pheromone of
the two SNPs contained in the combination with the highest fitness are
updated. For the two pheromone levels
the following is applied:
P (snp1) ! P (snp1) + f (snp1, snp2) (3)
P (snp2) ! P (snp2) + f (snp1, snp2) (4)
B. Memory Management

The database used is composed of samples of the genome of approximately
2,000 individuals (Cases) with the disease (1,999 for T2D, 2,000 for T1D,
2,005 for IBD and 1,999 for RA) and
3,004 control samples. Each sample is
composed of 490,294 SNPs and due to
the diploid nature of the human
genome each SNP consists of two alleles
(two among Adenine (A), Cytosine (C),
Guanine (G) and Thymine (T)) leading
to three possible genotypes described
above. Additionally, due to the sequencing of the genome, a genotype can be
unknown and therefore a fourth possible value of 'unknown' exists for a SNP.
The data for approximately 5,000
individuals were stored in 'oxstat' and
'plink' formats [33] on a normal hard
drive and required more than an hour to
open and to read these files for each disease with an Intel ® Core™ i7-2600
CPU @3.40GHz processor.

November 2015 | Ieee ComputatIoNal INtellIgeNCe magazINe

57



Table of Contents for the Digital Edition of Computational Intelligence - November 2015

Computational Intelligence - November 2015 - Cover1
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Computational Intelligence - November 2015 - 1
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