Biomedical Engineering Reference
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Fig. 4.
−log
10
(p-value) values for the different layers of the FLTM, resulting from association
tests of the phenotype with the causal SNP ancestor nodes (As) and with the other latent nodes
(Os) - simulated data. (a) Boxplots. (b) Median values. Layer
0
shows the results of the associa-
tion tests between the phenotype and the causal SNP (over all simulated scenarii). See Figure 3
for details about the scenarii, see Subsection 6.3 for the definition of error rate
α
Figure 4(b) emphasizes the general trend of
−
log
10
(p-value) observed for A and O
nodes, and compares the median
log
10
(p-value) value obtained for each layer to the
value corresponding to the significance threshold
α
specific to this layer (see Subsec-
tion 6.3, second paragraph). The remarkable conclusion drawn from this figure is the
following: up to the second layer,
significant
associations are identified for A nodes; in
contrast, regarding O nodes, for all layers, median
−
−
log
10
(p-value) values are smaller
log
10
(
α
) values. Focusing on the O distribution, we observe
that the percentage of p-values lower than
α
(false positives) is
4
.
7%
.
In the following, we refer to the terminology defined in Figure 2. The causal tree is
the tree containing the causal SNP. The O nodes divide between nodes located in the
causal (OTs) tree and nodes outside the causal tree (OOs) (Os = OTs (21%) + OOs
(79%)). The true positives are all A nodes. The distribution for O nodes shows
4
.
7%
of
false positives (FPs) on average. But examining separately the OT distribution and the
OO distribution reveals respective FP percentages of
16%
and
1
.
6%
. Turning it the other
way, focusing on FPs shows the following allotment: FPs = FP Os = FP OTs (73%) +
FP OOs (27%). Thus 73% of FPs are in the causal tree, representing less than 21% of
O nodes. In conclusion, the false positives are mainly confined in the causal tree; in this
case, the false discovery is explained by the presence of indirect dependences between
the causal SNP and the OTs.
than the corresponding
−
Behaviour under Thirty-Six Genetic Scenarii.
The distributions relative to A and
O nodes are now compared for each scenario described in Subsection 6.1 (see Figure
5). Globally, similar tendencies are observed over all scenarii: the association strength
drops continuously from bottom to top layer; in the case of O nodes, an overwhelming
majority of results points out the absence of association, whichever the FLTM's layer
concerned.
When considering the easiest case (MAF range
=
0.3-0.4, GRR
=1
.
8
and multi-
plicative
model),
over
all
layers,
the
A
nodes
present
strong
associations
(
log
10
(p-value)
>
7
). Regarding a less ideal but more plausible configuration (MAF
range
=
0.2-0.3, GRR
=1
.
6
and additive model), the median
−
log
10
(p-value) value
computed for A nodes decreases from
8
.
3
at layer
0
, to reach
4
.
6
,
3
.
2
and
2
.
2
at layers
1
,
2
and
3
, respectively. On the contrary, when the model is recessive, the association
with the causal SNP is low and the A nodes cannot capture anything (similar results are
−
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