Background
Methods
Study 1 Methods. Making predictions with support vector machines
Background
Data
Covariates and Description | Original Value | Recoded Value | % = 1 | Chi-square | Corr | |
---|---|---|---|---|---|---|
h2a | Mobility in bed (moving to/from lying in bed) | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 9.5 | 42.67 | -0.04 |
h2b | Transferring (moving to/from bed or chair) | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 18.0 | 29.32 | -0.03 |
h2c | Locomotion in home | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 14.8 | 38.56 | -0.04 |
h2d | Locomotion outside of home | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 38.2 | 40.98 | -0.04 |
h2e | Dressing upper body | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 32.0 | 138.18 | -0.07 |
h2f | Dressing lower body | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 37.8 | 76.20 | -0.06 |
h2g | Eating | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 10.4 | 87.05 | -0.06 |
h2h | Toilet use | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 19.8 | 125.64 | -0.07 |
h2i | Personal hygiene (grooming) | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 25.6 | 164.36 | -0.08 |
h2j | Bathing | 0, 1, 2, 3, 4, 5, 6, 8 | 0, 1 → 0; else 1 | 77.9 | 1488.07 | -0.25 |
c3 | Ability to understand others | 0, 1, 2, 3, 4 | 0, 1, 2 → 0; else 1 | 4.7 | 74.93 | -0.06 |
p6 | Overall change in care need (deterioration) | 0, 1, 2 | 0, 1 → 0; else 1 | 34.8 | 364.56 | 0.12 |
h3 | ADL decline (past 90 days) | 0, 1 | 0, 1 | 39.8 | 326.49 | 0.12 |
k8b | Conditions or diseases causing instability | 0, 1 | 0, 1 | 29.1 | 53.34 | -0.05 |
k8c | Flare-up of recurrent/chronic problem | 0, 1 | 0, 1 | 7.8 | 6.23 | 0.02 |
k8d | Treatment changed in last 30 days | 0, 1 | 0, 1 | 16.6 | 390.95 | 0.13 |
h7a | Client optimistic about functional improvement | 0, 1 | 0, 1 | 22.6 | 1231.44 | 0.22 |
h7b | Caregivers optimistic about functional improvement | 0, 1 | 0, 1 | 11.4 | 726.04 | 0.17 |
h7c | Good prospect of recovery from current conditions | 0, 1 | 0, 1 | 10.7 | 1261.85 | 0.23 |
The Support Vector Machine
Performance Evaluation
Study 2 Methods. Relaxation of covariates
Background
Data
Data Analysis
Results
Study 1 Results. Making predictions with support vector machines
Overall Error | False + | False - | DLR + | DLR - | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Region | CAP | KNN | SVM | CAP | KNN | SVM | CAP | KNN | SVM | CAP | KNN | SVM | CAP | KNN | SVM |
1
| 0.37 | 0.34 | 0.35 | 0.30 | 0.34 | 0.35 | 0.65 | 0.36 | 0.35 | 1.18 | 1.88 | 1.86 | 0.92 | 0.55 | 0.54 |
2
| 0.37 | 0.32 | 0.29 | 0.31 | 0.31 | 0.25 | 0.62 | 0.38 | 0.43 | 1.24 | 2.01 | 2.22 | 0.89 | 0.55 | 0.58 |
3
| 0.38 | 0.31 | 0.32 | 0.32 | 0.27 | 0.29 | 0.63 | 0.50 | 0.46 | 1.14 | 1.84 | 1.88 | 0.93 | 0.68 | 0.64 |
4
| 0.46 | 0.32 | 0.31 | 0.36 | 0.30 | 0.28 | 0.65 | 0.35 | 0.36 | 0.99 | 2.15 | 2.25 | 1.00 | 0.50 | 0.51 |
5
| 0.31 | 0.23 | 0.24 | 0.27 | 0.18 | 0.22 | 0.67 | 0.53 | 0.44 | 1.25 | 2.57 | 2.58 | 0.91 | 0.65 | 0.56 |
6
| 0.43 | 0.28 | 0.29 | 0.38 | 0.24 | 0.27 | 0.62 | 0.41 | 0.38 | 1.01 | 2.40 | 2.33 | 1.00 | 0.55 | 0.52 |
7
| 0.48 | 0.30 | 0.32 | 0.43 | 0.28 | 0.31 | 0.59 | 0.37 | 0.34 | 0.95 | 2.29 | 2.14 | 1.04 | 0.51 | 0.50 |
8
| 0.42 | 0.31 | 0.33 | 0.37 | 0.28 | 0.32 | 0.62 | 0.42 | 0.37 | 1.03 | 2.08 | 1.96 | 0.98 | 0.58 | 0.54 |
Mean
|
0.40
|
0.30
|
0.31
|
0.34
|
0.28
|
0.29
|
0.63
|
0.42
|
0.39
|
1.10
|
2.15
|
2.15
|
0.96
|
0.57
|
0.55
|
Clearly Have | Clearly No | Absolute | |
---|---|---|---|
Covariates | Potential | Potential | Difference |
h2a = 1 | 0.01 | 0.10 | 0.09 |
h2b = 1 | 0.08 | 0.16 | 0.08 |
h2c = 1 | 0.04 | 0.15 | 0.11 |
h2d = 1 | 0.22 | 0.37 | 0.15 |
h2e = 1 | 0.11 | 0.32 | 0.21 |
h2f = 1 | 0.17 | 0.37 | 0.20 |
h2g = 1 | 0.01 | 0.12 | 0.12 |
h2h = 1 | 0.03 | 0.24 | 0.20 |
h2i = 1 | 0.07 | 0.27 | 0.20 |
h2j = 1 | 0.29 | 1.00 |
0.71
|
c3 = 1 | 1.00 | 0.94 | 0.06 |
p6 = 1 | 0.49 | 0.11 | 0.37 |
h3 = 1 | 0.49 | 0.12 | 0.37 |
k8b = 1 | 0.17 | 0.29 | 0.12 |
k8c = 1 | 0.05 | 0.05 | 0.00 |
k8d = 1 | 0.32 | 0.02 | 0.30 |
h7a = 1 | 0.65 | 0.00 |
0.65
|
h7b = 1 | 0.35 | 0.00 | 0.35 |
h7c = 1 | 0.46 | 0.00 |
0.46
|
Summary
Study 2 Results. Relaxation of Covariates
Overall Error | False + | False - | DLR + | DLR - | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Region | Old | New | Old | New | Old | New | Old | New | Old | New |
1
| 0.34 | 0.36 | 0.34 | 0.35 | 0.36 | 0.41 | 1.88 | 1.69 | 0.55 | 0.63 |
2
| 0.32 | 0.33 | 0.31 | 0.29 | 0.38 | 0.46 | 2.01 | 1.85 | 0.55 | 0.65 |
3
| 0.31 | 0.34 | 0.27 | 0.30 | 0.50 | 0.48 | 1.84 | 1.70 | 0.68 | 0.70 |
4
| 0.32 | 0.32 | 0.30 | 0.24 | 0.35 | 0.47 | 2.15 | 2.21 | 0.50 | 0.62 |
5
| 0.23 | 0.32 | 0.18 | 0.30 | 0.53 | 0.45 | 2.57 | 1.84 | 0.65 | 0.64 |
6
| 0.28 | 0.31 | 0.24 | 0.27 | 0.41 | 0.42 | 2.40 | 2.11 | 0.55 | 0.58 |
7
| 0.30 | 0.32 | 0.28 | 0.26 | 0.37 | 0.46 | 2.29 | 2.12 | 0.51 | 0.61 |
8
| 0.31 | 0.35 | 0.28 | 0.33 | 0.42 | 0.42 | 2.08 | 1.75 | 0.58 | 0.63 |
Mean
|
0.30
|
0.33
|
0.28
|
0.29
|
0.42
|
0.45
|
2.15
|
1.91
|
0.57
|
0.63
|
Overall Error | False + | False - | DLR + | DLR - | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Region | Old | New | Old | New | Old | New | Old | New | Old | New |
1
| 0.35 | 0.34 | 0.35 | 0.34 | 0.35 | 0.33 | 1.86 | 1.97 | 0.54 | 0.50 |
2
| 0.29 | 0.30 | 0.25 | 0.26 | 0.43 | 0.42 | 2.22 | 2.20 | 0.58 | 0.57 |
3
| 0.32 | 0.34 | 0.29 | 0.33 | 0.46 | 0.42 | 1.88 | 1.77 | 0.64 | 0.63 |
4
| 0.31 | 0.31 | 0.28 | 0.28 | 0.36 | 0.37 | 2.25 | 2.24 | 0.51 | 0.51 |
5
| 0.24 | 0.23 | 0.22 | 0.20 | 0.44 | 0.45 | 2.58 | 2.69 | 0.56 | 0.57 |
6
| 0.29 | 0.29 | 0.27 | 0.26 | 0.38 | 0.40 | 2.33 | 2.36 | 0.52 | 0.53 |
7
| 0.32 | 0.31 | 0.31 | 0.29 | 0.34 | 0.35 | 2.14 | 2.23 | 0.50 | 0.49 |
8
| 0.33 | 0.32 | 0.32 | 0.30 | 0.37 | 0.38 | 1.96 | 2.04 | 0.54 | 0.55 |
Mean
|
0.31
|
0.30
|
0.29
|
0.28
|
0.39
|
0.39
|
2.15
|
2.19
|
0.55
|
0.54
|
Summary and new method of defining ADLCAP
initialize score = 0; threshold = 15.8 | |
---|---|
if (c3 = 0) |
then score = score + 1.5; |
if (h2a = 0) |
then score = score + 1.1; |
if (h2b = 0) |
then score = score + 1.1; |
if (h2c = 0) |
then score = score + 1.1; |
if (h2d = 0) |
then score = score + 1.2; |
if (h2e = 0) |
then score = score + 1.3; |
if (h2f = 0) |
then score = score + 1.3; |
if (h2g = 0) |
then score = score + 1.3; |
if (h2h = 0) |
then score = score + 1.3; |
if (h2i = 0) |
then score = score + 1.4; |
if (h2j = 0) |
then score = score + 3.1; |
if (h3 = 1) |
then score = score + 1.7; |
if (h7a = 1) |
then score = score + 3.0; |
if (h7b = 1) |
then score = score + 2.9; |
if (h7c = 1) |
then score = score + 4.1; |
if (k8b = 0) |
then score = score + 1.3; |
if (k8c = 1) |
then score = score + 1.1; |
if (k8d = 1) |
then score = score + 2.0; |
if (p6 = 1 or 2) |
then score = score + 1.9; |
Overall Error | False + | False - | DLR + | DLR - | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Region | OLD | SVM | NEW | OLD | SVM | NEW | OLD | SVM | NEW | OLD | SVM | NEW | OLD | SVM | NEW |
1
| 0.37 | 0.34 | 0.36 | 0.30 | 0.34 | 0.36 | 0.65 | 0.33 | 0.37 | 1.18 | 1.97 | 1.75 | 0.92 | 0.50 | 0.58 |
2
| 0.37 | 0.30 | 0.30 | 0.31 | 0.26 | 0.25 | 0.62 | 0.42 | 0.48 | 1.24 | 2.20 | 2.10 | 0.89 | 0.57 | 0.64 |
3
| 0.38 | 0.34 | 0.32 | 0.32 | 0.33 | 0.28 | 0.63 | 0.42 | 0.50 | 1.14 | 1.77 | 1.79 | 0.93 | 0.63 | 0.69 |
4
| 0.46 | 0.31 | 0.34 | 0.36 | 0.28 | 0.31 | 0.65 | 0.37 | 0.39 | 0.99 | 2.24 | 1.99 | 1.00 | 0.51 | 0.56 |
5
| 0.31 | 0.23 | 0.20 | 0.27 | 0.20 | 0.16 | 0.67 | 0.45 | 0.52 | 1.25 | 2.69 | 3.05 | 0.91 | 0.57 | 0.62 |
6
| 0.43 | 0.29 | 0.27 | 0.38 | 0.26 | 0.22 | 0.62 | 0.40 | 0.45 | 1.01 | 2.36 | 2.53 | 1.00 | 0.53 | 0.58 |
7
| 0.48 | 0.31 | 0.32 | 0.43 | 0.29 | 0.29 | 0.59 | 0.35 | 0.38 | 0.95 | 2.23 | 2.17 | 1.04 | 0.49 | 0.53 |
8
| 0.42 | 0.32 | 0.29 | 0.37 | 0.30 | 0.23 | 0.62 | 0.38 | 0.49 | 1.03 | 2.04 | 2.16 | 0.98 | 0.55 | 0.64 |
Mean
|
0.40
|
0.30
|
0.30
|
0.34
|
0.28
|
0.26
|
0.63
|
0.39
|
0.45
|
1.10
|
2.19
|
2.19
|
0.96
|
0.54
|
0.61
|
Discussion
Conclusion
Appendix: Simulation experiments
j
| Pr(x
1|y = 1) | Pr(x
1|y = 0) | Pr(x
2|y = 1) | Pr(x
2|y = 0) | ||
---|---|---|---|---|---|---|
0 | 0.40 | 0.10 |
4.00
| 0.20 | 0.10 |
2.00
|
1 | 0.40 | 0.10 |
4.00
| 0.10 | 0.15 | 0.67 |
2 | 0.04 | 0.16 | 0.25 | 0.09 | 0.15 | 0.60 |
3 | 0.03 | 0.16 | 0.19 | 0.10 | 0.15 | 0.67 |
4 | 0.05 | 0.16 | 0.31 | 0.11 | 0.15 | 0.73 |
5 | 0.05 | 0.16 | 0.31 | 0.10 | 0.15 | 0.67 |
6 | 0.03 | 0.16 | 0.19 | 0.10 | 0.15 | 0.67 |