Norma OHSAS 18001: 2007 sistema de gestión de la seguridad

As mentioned in the previous chapter, sleep characteristics which are not encoded in features are defined asinf luencial f actors. Theinf luencial f actors in the regression analysis are: age, fragmentation index, lengths, number of epochs and cycle index. In order to have sufficient data for the regression analysis, whole-night recordings of 45 subjects are segmented into sleep cycles. Instead of having 45 groups of variables, there are 135 groups of variables for the analysis after cycle segmentation. The cycle segmentation procedure is the same as those explained in Chapter3.

• Age

Age has an impact on sleep. The sleep process changes with age. As we age, the duration of sleep declines. And elderly people are more vulnerable to sleep

0 0.5 1 1.5 N3 N2 N1 REM Wake Hours Four deep sleep intervals.

Figure 4.1: An example of one sleep cycle.

problems, such as insomnia and disrupted sleep. Even healthy elderly people who does not suffer from sleep problems, their deep sleep (slow-wave sleep) are reduced [17]. The cardiac and respiratory dynamics in healthy subjects across sleep stages are also affect by age [18]. Therefore, it can be expected that the classification performance for older subjects is worse than that of younger subjects.

Cycles within one subject receive the same value for theagevariable. The values of variableageare normalized to 0-1 range. The normalized value ofage_iis calculated as:

N ormalized(age_i) = agei−Agemin

Age_max−Age_min, (4.1)

whereAge_min is the youngest age among the 45 subjects andAge_max is the eldest age among the 45 subjects.

• Fragmentation index and Lengths

The criteria evaluating the classification performance is the area under the precision- recall curve (AUCPR). Discontinuities in the deep sleep intervals can be charac- terized by a fragmentation index (F index). Within a sleep cycle, a deep sleep interval is defined if the interval is not disrupted by non-deep sleep stages or the interval is disrupted but each disruption is no longer than 5 minutes (10 epochs). Therefore, there are four deep sleep intervals in Fig.4.1. Each deep sleep interval is assigned anf value. f valueis called fragmentation value and is used to quantify the continuity of one deep sleep interval. The sleep cycle in Fig.4.1 therefore has

0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 25 30 35 40 Findex Count

Figure 4.2: Distribution ofF index.

fourf values. f value_i is calculated as:

f value_i= #disruptions

lengths of the ith_{deep sleep interval in the sleep cycle(in epochs)}.

(4.2) The fragmentation index F index is then the weighted average of the f values.

F indexis computed as:

F index=

n

X

i=1

wif valuei, (4.3)

where n is the number of deep sleep intervals within one sleep cycle, wi is the

weight of the f value_i and it is calculated as:

wi =

lengths of the ith _{deep sleep interval}

total lengths of deep sleep intervals in current cycle. (4.4)

The calculation ofF indexcaptures the frequency of disruptions by non-deep sleep stages in the deep sleep interval. The value of F index can be interpreted as the probability of one deep-sleep epoch being followed by a non deep-sleep epoch. Fig.4.2shows the distribution ofF indexin the 135 cycles.

Each cycle has variableLengths. Lengthsvariable is the weighted average lengths of deep sleep intervals within one sleep cycle. The calculation ofLengths is :

Lengths=

n

X

i=1

wilengthsi, (4.5)

where n is the number of deep sleep intervals within one sleep cycle, wi is the

weight of the lengths_i and it is calculated using equation (4.4). Then the values of Lengths are normalized to 0-1 range. The distribution of Lengths in the 135 cycles is shown in Fig.4.3.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 Lengths Count

Figure 4.3: Distribution ofLengths.

We have already had the impression that there is a link between classification per- formance, continuity and lengths of the deep sleep intervals from Fig.2.8. We can roughly draw the conclusion that the difference between deep sleep and non-deep sleep described in the features are larger when a deep sleep interval is continuous and longer. If a deep sleep interval is frequently interrupted by other stages, then we can hardly tell the difference between deep sleep and non-deep sleep from the feature expression. We attach another figure (Fig.4.4) here, further demonstrating the relationship between classification performance, lengths and continuity of deep sleep intervals.

Fig.4.4clearly demonstrates the impact ofF indexand Lengthson AUCPR. Ma- jority of cycles which have worse classification performance are those cycles whose

F index are below 0.1 and/or Lengths are below 0.2. This observation is in ac- cordance with the conclusion drawn from Fig.2.8. This is not unexpected. From the physiological point of view, it is too late to reflect the characteristics featuring deep sleep on the cardiorespiratory signals if the duration of deep sleep is too short or the transitions between deep sleep and non-deep sleep are constant.

• Number of epochs

Number of epochs (N r epochs) computes the total number of deep sleep epochs within one sleep cycle. N r epochsis normalized to 0-1 range. ThoughN r epochs

seems a repetition to Lengths, N r epochs commits to describe the proportion of deep sleep within one sleep cycle. Two cycles can have the same value for

F index, but the one with bigger value ofN r epochsmay have better classification performance compared to the other with smallerN r epochs.

0 0.01 0.02 0.03 0.04 0.05 0 0.2 0.4 0.6 0.8 1 Findex Lengths AUCPR >= 0.7 0.4 <= AUCPR < 0.7 AUCPR < 0.4 (a) 0.050 0.1 0.15 0.2 0.25 0.3 0.2 0.4 0.6 0.8 1 Findex Lengths AUCPR >= 0.7 0.4 <= AUCPR < 0.7 AUCPR < 0.4 (b)

Figure 4.4: Relationships betweenF index,LengthsandAUCPR. (a) and (b) differ-

entiate in the range of theF index. F indexgoes from 0 to 0.05 in (a) while it runs from 0.05 to 0.3 in (b). It can be seen from (a) that the longer and/or the more continuous the deep sleep interval, the better the classification performance. From (b), it can be seen that most misclassifications happen in the interrupted and/or short deep sleep

1 2 3 4 5 -0.05 0 0.05 0.1 0.15 0.2 Cycle Findex 1 2 3 4 5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Cycle Lengths

Figure 4.5: F indexandLengthschanging with time.

As mentioned in the sleep physiology, both the duration and intensity of deep sleep decrease as sleep progresses. Thus we can expect the first sleep cycle has a small F index and big Lengths compared to the last sleep cycle within one night. Fig.4.5 depicts how F index and Lengths evolve throughout the night. Therefore, we consider cycle index (Cindex) as one of theinf luential f actorsto the classification performance. Cindexis a categorical variable, with 1 indicating the first sleep cycle, 2 indicating the second sleep cycle and so on.