Twenty-seven conditions with a prevalence range of 33.1–1.5% for ‘eye, ear diseases’ were selected (Table 1), where lower rank indicates higher prevalence.
Table 1
Prevalence of the conditions listed anywhere on the death certificates for women in Australia aged 85 years or more who had more than one cause of death mentioned (N = 283,195)
Rank
|
Condition
|
Prevalence (%)
|
1
|
Dementia, Alzheimer's disease
|
33.4
|
2
|
Ischemic Heart Disease
|
32.2
|
3
|
Hypertensive disease
|
26.7
|
4
|
Cerebrovascular disease
|
20.6
|
5
|
Other circulatory diseases
|
17.1
|
6
|
Heart failure
|
16.4
|
7
|
Cardiac arrhythmia
|
15.1
|
8
|
Kidney disease
|
14.5
|
9
|
Diabetes
|
12.5
|
10
|
Symptoms, signs, ill-defined conditions
|
11.1
|
11
|
Chronic lower respiratory disease
|
11.0
|
12
|
Musculoskeletal disease
|
10.4
|
13
|
Other digestive diseases
|
7.9
|
14
|
Infectious, parasitic diseases
|
6.7
|
15
|
Other malignant neoplasms
|
5.9
|
16
|
Other respiratory diseases
|
5.1
|
17
|
Psychiatric and other mental disorders
|
4.6
|
18
|
Influenza, pneumonia
|
4.4
|
19
|
Breast cancer
|
3.3
|
20
|
Colorectal cancer
|
3.1
|
21
|
Lymph, blood cancer
|
3.0
|
22
|
Other endocrine diseases
|
3.0
|
23
|
Other neurological conditions
|
2.2
|
24
|
Parkinson's disease
|
2.2
|
25
|
Skin disease
|
2.0
|
26
|
Lung, tracheal cancer
|
1.5
|
27
|
Eye, ear disease
|
1.5
|
Weights derived from OR, lift, and NF were approximately linearly associated (Figs. 1a, 1d, and 1g). The associations between the other statistics were more complicated (Figs. 1b, 1c, 1e, 1f, 1h, 1i, and 1j).
Figure 1: Scatterplot of different weights (for all 351 possible pairs)
OR: Odds ratio, SCI: Salton cosine index, NF: normalised joint frequency
The total number of unique pairs selected as being strongly associated (‘top pairs’) by any measure was 56, with 13 pairs being selected by all five measures of association (Table 2). Ten pairs were selected only by one statistic (6 only by SCI and 4 only by NF).
The number of times three conditions with the lowest prevalence (i.e., rank 25, 26, and 27 in Table 1) contributed to form ‘top pairs’ by each measure of association was 13 by OR, 13 by lift, 9 by phi, 3 by SCI, and 9 by NF. Corresponding numbers for three conditions with the highest prevalence (i.e., those ranked 1, 2, and 3 in Table 1) was 4 in OR, 3 in lift, 7 in phi, 10 in SCI, and 2 in NF.
Most of the pairs selected by OR and lift statistics were the same (33 out of 35), giving a Kappa for agreement of 0.85. The Kappa values for agreement between SCI and all other measures, except Phi, were negative suggesting they measure different constructs.
Table 2
Pairs of conditions selected as being strongly associated by each of five measures of association
Pair
|
OR
|
Lift
|
Phi
|
SCI
|
NF
|
1 + 4
|
0
|
0
|
0
|
1
|
1
|
2 + 3
|
0
|
0
|
0
|
1
|
0
|
3 + 4
|
1
|
1
|
1
|
1
|
1
|
3 + 7
|
0
|
0
|
1
|
1
|
0
|
3 + 9
|
0
|
0
|
1
|
1
|
0
|
4 + 5
|
0
|
0
|
0
|
1
|
1
|
4 + 7
|
0
|
0
|
0
|
1
|
1
|
5 + 7
|
0
|
0
|
1
|
1
|
0
|
6 + 7
|
1
|
1
|
1
|
1
|
1
|
6 + 8
|
1
|
1
|
1
|
1
|
1
|
8 + 9
|
0
|
0
|
1
|
1
|
1
|
1 + 17
|
0
|
0
|
1
|
1
|
0
|
3 + 12
|
1
|
0
|
1
|
1
|
0
|
3 + 17
|
0
|
0
|
0
|
1
|
0
|
6 + 11
|
1
|
1
|
1
|
1
|
1
|
6 + 16
|
1
|
0
|
1
|
1
|
1
|
8 + 14
|
0
|
0
|
1
|
1
|
1
|
8 + 18
|
0
|
0
|
0
|
0
|
1
|
3 + 22
|
1
|
1
|
1
|
1
|
0
|
3 + 27
|
1
|
1
|
1
|
1
|
0
|
4 + 23
|
1
|
1
|
1
|
1
|
1
|
4 + 24
|
0
|
0
|
0
|
0
|
1
|
10 + 12
|
0
|
0
|
0
|
1
|
0
|
10 + 13
|
0
|
0
|
0
|
1
|
0
|
10 + 14
|
1
|
1
|
1
|
1
|
1
|
10 + 16
|
0
|
1
|
1
|
1
|
1
|
10 + 17
|
0
|
0
|
0
|
1
|
0
|
10 + 18
|
1
|
1
|
1
|
1
|
1
|
11 + 12
|
0
|
0
|
0
|
1
|
0
|
11 + 17
|
1
|
1
|
1
|
1
|
0
|
12 + 13
|
1
|
1
|
1
|
1
|
0
|
12 + 17
|
1
|
1
|
1
|
1
|
1
|
14 + 18
|
0
|
0
|
0
|
0
|
1
|
16 + 18
|
1
|
1
|
1
|
0
|
1
|
10 + 27
|
1
|
1
|
0
|
0
|
0
|
11 + 26
|
1
|
1
|
1
|
1
|
1
|
12 + 22
|
1
|
1
|
1
|
1
|
1
|
12 + 23
|
1
|
1
|
0
|
0
|
0
|
12 + 25
|
1
|
1
|
0
|
0
|
0
|
12 + 27
|
1
|
1
|
1
|
1
|
1
|
13 + 27
|
1
|
1
|
1
|
0
|
1
|
14 + 25
|
1
|
1
|
1
|
0
|
1
|
15 + 19
|
1
|
1
|
1
|
1
|
1
|
15 + 20
|
1
|
1
|
1
|
1
|
1
|
15 + 26
|
1
|
1
|
1
|
0
|
1
|
16 + 26
|
0
|
1
|
0
|
0
|
1
|
17 + 22
|
1
|
1
|
1
|
0
|
0
|
17 + 23
|
1
|
1
|
0
|
0
|
0
|
17 + 24
|
1
|
1
|
0
|
0
|
1
|
17 + 26
|
1
|
1
|
1
|
0
|
1
|
17 + 27
|
1
|
1
|
1
|
0
|
1
|
19 + 20
|
1
|
1
|
0
|
0
|
1
|
19 + 21
|
0
|
0
|
0
|
0
|
1
|
22 + 27
|
1
|
1
|
1
|
0
|
1
|
23 + 24
|
1
|
1
|
1
|
0
|
1
|
23 + 27
|
1
|
1
|
0
|
0
|
0
|
1: the pair selected as top; 0: the pair did not select as top |
Figure 2 shows the networks and communities obtained using each of the five measures of association. The total number of communities found in each of the five networks were 3 for OR, 4 for lift, 5 for Phi, 5 for SCI, and 4 for NF. In the networks based on OR and lift, four conditions ranked below nine in Table 2 did not join other communities. All three conditions that did not join other communities in the SCI network all had ranks above 21 in Table 2. On the other hand, in the network based on NF the condition ranked two on prevalence list in Table 2 was not in any community.
Figure 2: Communities identified in networks based on different weights: OR (top left), lift (top middle), Phi (top right), SCI (bottom left), and NF (bottom middle)
There were differences between the measures of association in terms of which conditions had the highest degree, closeness and betweenness. The top three conditions with the highest value for each measure are shown in Table 3. For example, condition 27 had high degree in networks of OR, lift, and Phi but not in networks of SCI and NF, suggesting that the association between this condition and other conditions was more likely to be captured by OR, lift, and Phi measures of association.
Table 3
The three conditions (as ranked in Table 1) with the highest values for degree, closeness and betweenness based on each of the five measures of association
Rank of condition in Table 1
|
Degree
|
Closeness
|
Betweenness
|
OR
|
Lift
|
Phi
|
SCI
|
NF
|
OR
|
Lift
|
Phi
|
SCI
|
NF
|
OR
|
Lift
|
Phi
|
SCI
|
NF
|
3
|
|
|
✓
|
✓
|
|
|
|
✓
|
✓
|
|
|
|
✓
|
✓
|
|
4
|
|
|
|
✓
|
✓
|
|
|
|
|
|
|
|
|
|
✓
|
6
|
|
|
|
|
|
|
|
✓
|
|
|
|
|
✓
|
|
|
10
|
|
|
|
|
|
|
|
|
|
|
|
|
|
✓
|
|
11
|
|
|
|
|
|
✓
|
|
|
|
|
✓
|
✓
|
|
|
|
12
|
✓
|
✓
|
✓
|
✓
|
|
|
|
|
|
|
|
|
|
✓
|
|
15
|
|
|
|
|
✓
|
|
|
|
|
|
|
|
|
|
|
16
|
|
|
|
|
|
|
|
|
|
✓
|
|
|
|
|
|
17
|
✓
|
✓
|
|
|
|
|
✓
|
✓
|
|
✓
|
✓
|
✓
|
✓
|
|
✓
|
19
|
|
|
|
|
|
|
|
|
✓
|
|
|
|
|
|
|
20
|
|
|
|
|
|
|
|
|
✓
|
|
|
|
|
|
|
26
|
|
|
|
|
✓
|
✓
|
✓
|
|
|
✓
|
✓
|
✓
|
|
|
✓
|
27
|
✓
|
✓
|
✓
|
|
|
✓
|
✓
|
|
|
|
|
|
|
|
|