Biomedical Engineering Reference
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(wake.Q3 >= 44) => cluster=cluster2 (12.0/1.0)
(wake.Q2 >= 6) and (SWS.Q1 <= 5) => cluster=cluster2 (5.0/1.0)
(NREM1.Q2 >= 3) and (NREM2.Q2 <= 9) => cluster=cluster2 (5.0/1.0)
(SWS.Q1 >= 30) => cluster=cluster3 (41.0/2.0)
(NREM1.Q3 >= 4) => cluster=cluster3 (22.0/1.0)
(SWS.Q3 >= 79) => cluster=cluster3 (15.0/3.0)
(SWS.Q2 >= 49) => cluster=cluster3 (5.0/2.0)
=> cluster=cluster1 (139.0/0.0)
Fig. 8.
JRIP conjunctive rule model of the clusters for
k
=3
1
. In other words, cluster
3
for
k
=3
consists mainly of those
k
=2
cluster
1
instances
with higher SWS bout duration quartiles. This high SWS bout duration description of
cluster
3
persists for
k
=4
. However, the observed SWS quartile bout durations for
cluster
3
, though highest among all clusters, are not significantly higher than those of
clusters
2
and
4
, again due likely to the small sizes of the latter clusters.
Cluster
4
.
Cluster
4
is characterized by significantly higher REM bout quartile dura-
tions than any other cluster (Wilcoxon
p<
10
−
3
).
Clustering Description via Classification Rules.
One can compare the characterizations
of the clusters described in the preceding paragraphs with the model constructed by the
JRIP conjunctive rule classifier in the case
k
=3
. The model is as shown in Fig. 8, and
achieves a classification accuracy of
0
.
86
and mean ROC area of
0
.
88
. The rules of this
model closely agree with the descriptions provided above.
3.4
Health-Related Cluster Differences
Comparisons of Sleep-Related and Health-Related Variables.
The bout duration
clusters identified by the EM procedure were examined to determine differences among
them in the values of sleep-related and health-related variables not used in the cluster-
ing procedure itself. Group comparisons of means and medians were performed using
ANOVA and Kruskal-Wallis tests, respectively. Pairwise comparisons of means and
medians used a
t
-test and Wilcoxon rank sum test.
Sleep Latency.
For all values of
k
=2
,
3
,
4
, Kruskal-Wallis and ANOVA determined
that mean sleep latency (time elapsed from getting in bed until first non-wake epoch)
differs significantly among bout duration clusters (
p<
0
.
05
). The highest mean value
of sleep latency occurs in cluster
2
. The pairwise difference in mean and median sleep
latency between cluster
2
and all other clusters is also significant
(
p<
0
.
05)
. As ob-
served in Table 4 and discussed in section 3.3, cluster
2
has the highest mean wake bout
duration quartiles of all of the clusters. It is entirely possible that the high sleep latency
contributes to the increased wake bout durations in cluster
2
.
Sleep Questionnaire Variables.
Certain variables that correspond to items in the Ep-
worth Daytime Sleepiness questionnaire are significantly different among clusters, and
are significantly different in pairwise comparisons between cluster
2
and the others:
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