Introduction
Methods
Design and participants
HRQoL measures
Statistical analysis
External validation of previously published mapping algorithms
Developing new mapping algorithms
Goodness of fit measures
Ethical considerations
Results
Sample and descriptive data
Full sample (N = 1225) | Dimension scores sample (N = 1198) | Item scores sample (N = 842) | Estimation sample (N = 674) | Validation sample (N = 168) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Age categories, n (%) | ||||||||||
0–12 months | 9 | 0.73% | – | – | – | – | – | – | – | |
13–24 months | 18 | 1.47% | – | – | – | – | – | – | – | |
2–4 years | 333 | 27.18% | 333 | 27.80% | – | – | – | – | – | |
5–7 years | 252 | 20.57% | 252 | 21.04% | 245 | 29.10% | 204 | 30.27% | 41 | 24.40% |
8–12 years | 413 | 33.71% | 413 | 34.47% | 404 | 47.98% | 320 | 47.48% | 84 | 50.00% |
13–17 years | 200 | 16.33% | 200 | 16.69% | 193 | 22.92% | 150 | 22.26% | 43 | 25.60% |
Sex, n (%) | ||||||||||
Female | 578 | 47.18% | 569 | 47.50% | 402 | 47.74% | 320 | 47.48% | 82 | 48.81% |
Male | 647 | 52.82% | 629 | 52.50% | 440 | 52.26% | 354 | 52.52% | 86 | 51.19% |
Tracer condition, n (%) | ||||||||||
Asthma only | 323 | 26.37% | 322 | 26.88% | 275 | 32.66% | 217 | 32.20% | 58 | 34.52% |
Constipation only | 194 | 15.84% | 188 | 15.69% | 95 | 11.28% | 78 | 11.57% | 17 | 10.12% |
Eczema only | 433 | 35.35% | 415 | 34.64% | 249 | 29.57% | 207 | 30.71% | 42 | 25% |
Multimorbidity | 275 | 22.45% | 273 | 22.79% | 223 | 26.48% | 172 | 25.52% | 51 | 30.36% |
IMD (2019), n (%) | ||||||||||
1—Most deprived | 23 | 1.88% | 22 | 1.84% | 13 | 1.54% | 10 | 1.48% | 3 | 1.79% |
2 | 282 | 23.02% | 276 | 23.04% | 198 | 23.52% | 162 | 24.04% | 36 | 21.43% |
3 | 361 | 29.47% | 352 | 29.38% | 244 | 28.98% | 198 | 29.38% | 46 | 27.38% |
4 | 204 | 16.65% | 200 | 16.69% | 151 | 17.93% | 122 | 18.10% | 29 | 17.26% |
5 | 131 | 10.69% | 127 | 10.60% | 87 | 10.33% | 66 | 9.79% | 21 | 12.50% |
6 | 134 | 10.94% | 132 | 11.02% | 84 | 9.98% | 70 | 10.39% | 14 | 8.33% |
7 | 45 | 3.67% | 44 | 3.67% | 33 | 3.92% | 25 | 3.71% | 8 | 4.76% |
8 | 35 | 2.86% | 35 | 2.92% | 27 | 3.21% | 18 | 2.67% | 9 | 5.36% |
9 | 10 | 0.82% | 10 | 0.83% | 5 | 0.59% | 3 | 0.45% | 2 | 1.19% |
10—Least deprived | 0 | 0.00% | 0 | 0.00% | 0 | 0.00% | 0 | 0 | 0 | 0.00% |
IDACI (2019), n (%) | ||||||||||
1—Most deprived | 189 | 15.43% | 184 | 15.36% | 136 | 16.15% | 111 | 16.47% | 25 | 14.88% |
2 | 380 | 31.02% | 373 | 31.14% | 273 | 32.42% | 213 | 31.60% | 60 | 35.71% |
3 | 240 | 19.59% | 234 | 19.53% | 162 | 19.24% | 132 | 19.58% | 30 | 17.86% |
4 | 129 | 10.53% | 125 | 10.43% | 84 | 9.98% | 72 | 10.68% | 12 | 7.14% |
5 | 84 | 6.86% | 81 | 6.76% | 47 | 5.58% | 35 | 5.19% | 12 | 7.14% |
6 | 70 | 5.71% | 69 | 5.76% | 47 | 5.58% | 41 | 6.08% | 6 | 3.57% |
7 | 69 | 5.63% | 68 | 5.68% | 49 | 5.82% | 40 | 5.93% | 9 | 5.36% |
8 | 40 | 3.27% | 40 | 3.34% | 27 | 3.21% | 19 | 2.82% | 8 | 4.76% |
9 | 16 | 1.31% | 16 | 1.34% | 10 | 1.19% | 7 | 1.04% | 3 | 1.79% |
10—Least deprived | 8 | 0.65% | 8 | 0.67% | 7 | 0.83% | 4 | 0.59% | 3 | 1.79% |
Ethnicity, n (%) | ||||||||||
White | 445 | 36.33% | 437 | 36.48% | 287 | 34.09% | 228 | 33.83% | 59 | 35.12% |
Black | 381 | 31.10% | 372 | 31.05% | 288 | 34.20% | 235 | 34.87% | 53 | 31.55% |
Mixed | 218 | 17.80% | 215 | 17.95% | 146 | 17.34% | 108 | 16.02% | 38 | 22.62% |
Asian | 69 | 5.63% | 65 | 5.43% | 44 | 5.23% | 39 | 5.79% | 5 | 2.98% |
Other ethnic groups | 48 | 3.92% | 48 | 4.01% | 33 | 3.92% | 30 | 4.45% | 3 | 1.79% |
Prefer not to say | 41 | 3.35% | 41 | 3.42% | 30 | 3.56% | 23 | 3.41% | 7 | 4.17% |
Missing | 23 | 1.88% | 20 | 1.67% | 14 | 1.66% | 11 | 1.63% | 3 | 1.79% |
External validation of published mapping algorithms
Group | N | Mean | Min. Max | Correlation coefficient | R2 | MAE | MSE | RMSE | Absolute errors < 0.05 (%) | Average error | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Observed | Predicted | Observed | Predicted | |||||||||||
Panel A—Total score mapping | ||||||||||||||
Total | 1225 | 0.888 | 0.823 | 0.384 | 1 | 0.331 | 0.992 | 0.625 | 0.391 | 0.092 | 0.016 | 0.107 | 40.49 | 0.065 |
0–12 months | 9 | 0.902 | 0.881 | 0.857 | 1 | 0.783 | 0.976 | 0.140 | 0.020 | 0.069 | 0.006 | 0.082 | 33.33 | 0.021 |
13–24 months | 18 | 0.922 | 0.861 | 0.710 | 1 | 0.658 | 0.975 | 0.783 | 0.613 | 0.064 | 0.008 | 0.067 | 61.11 | 0.061 |
2–4 years | 333 | 0.912 | 0.878 | 0.581 | 1 | 0.393 | 0.992 | 0.593 | 0.352 | 0.069 | 0.009 | 0.088 | 49.55 | 0.034 |
5–7 years | 252 | 0.892 | 0.811 | 0.507 | 1 | 0.429 | 0.992 | 0.337 | 0.581 | 0.102 | 0.019 | 0.111 | 36.51 | 0.081 |
8–12 years | 413 | 0.878 | 0.796 | 0.384 | 1 | 0.380 | 0.992 | 0.618 | 0.382 | 0.105 | 0.020 | 0.114 | 35.59 | 0.082 |
13–17 years | 200 | 0.861 | 0.798 | 0.481 | 1 | 0.331 | 0.992 | 0.661 | 0.437 | 0.095 | 0.016 | 0.109 | 39.00 | 0.063 |
Asthma only | 323 | 0.880 | 0.827 | 0.464 | 1 | 0.396 | 0.992 | 0.605 | 0.366 | 0.085 | 0.014 | 0.105 | 42.11 | 0.052 |
Constipation only | 194 | 0.873 | 0.810 | 0.504 | 1 | 0.380 | 0.992 | 0.701 | 0.492 | 0.093 | 0.015 | 0.105 | 37.63 | 0.063 |
Eczema only | 433 | 0.911 | 0.852 | 0.467 | 1 | 0.393 | 0.992 | 0.564 | 0.318 | 0.086 | 0.014 | 0.105 | 45.27 | 0.059 |
Multimorbidity | 275 | 0.872 | 0.783 | 0.384 | 1 | 0.331 | 0.992 | 0.627 | 0.394 | 0.111 | 0.021 | 0.112 | 33.09 | 0.090 |
Panel B—Dimension score mapping | ||||||||||||||
Total | 1198 | 0.887 | 0.873 | 0.384 | 1 | 0.249 | 0.988 | 0.634 | 0.402 | 0.071 | 0.010 | 0.098 | 51.59 | 0.014 |
2–4 years | 333 | 0.912 | 0.953 | 0.581 | 1 | 0.748 | 0.988 | 0.532 | 0.283 | 0.059 | 0.007 | 0.072 | 58.86 | − 0.042 |
5–7 years | 252 | 0.892 | 0.899 | 0.507 | 1 | 0.656 | 0.982 | 0.663 | 0.439 | 0.056 | 0.006 | 0.079 | 61.11 | − 0.007 |
8–12 years | 413 | 0.878 | 0.841 | 0.384 | 1 | 0.339 | 0.975 | 0.693 | 0.480 | 0.073 | 0.010 | 0.092 | 48.91 | 0.037 |
13–17 years | 200 | 0.861 | 0.774 | 0.481 | 1 | 0.249 | 0.956 | 0.721 | 0.520 | 0.106 | 0.019 | 0.107 | 33.00 | 0.086 |
Asthma only | 322 | 0.879 | 0.861 | 0.464 | 1 | 0.339 | 0.988 | 0.687 | 0.472 | 0.067 | 0.008 | 0.089 | 51.55 | 0.018 |
Constipation only | 188 | 0.871 | 0.881 | 0.504 | 1 | 0.249 | 0.988 | 0.671 | 0.450 | 0.070 | 0.010 | 0.099 | 52.66 | − 0.010 |
Eczema only | 415 | 0.911 | 0.905 | 0.467 | 1 | 0.433 | 0.988 | 0.535 | 0.286 | 0.065 | 0.008 | 0.092 | 57.59 | 0.007 |
Multimorbidity | 273 | 0.872 | 0.835 | 0.384 | 1 | 0.339 | 0.987 | 0.626 | 0.392 | 0.085 | 0.013 | 0.110 | 41.76 | 0.037 |
Panel C—Item-level mapping | ||||||||||||||
Total | 842 | 0.877 | 0.809 | 0.384 | 1 | 0.372 | 1 | 0.616 | 0.379 | 0.098 | 0.017 | 0.112 | 37.05 | 0.069 |
5–7 years | 245 | 0.891 | 0.813 | 0.507 | 1 | 0.410 | 1 | 0.535 | 0.286 | 0.104 | 0.020 | 0.119 | 37.96 | 0.078 |
8–12 years | 404 | 0.878 | 0.807 | 0.384 | 1 | 0.434 | 1 | 0.642 | 0.412 | 0.098 | 0.017 | 0.110 | 35.64 | 0.071 |
13–17 years | 193 | 0.860 | 0.807 | 0.481 | 1 | 0.372 | 1 | 0.660 | 0.436 | 0.089 | 0.014 | 0.107 | 38.86 | 0.052 |
Asthma only | 275 | 0.874 | 0.832 | 0.464 | 1 | 0.464 | 1 | 0.590 | 0.348 | 0.084 | 0.013 | 0.108 | 42.55 | 0.043 |
Constipation only | 95 | 0.844 | 0.777 | 0.504 | 1 | 0.380 | 1 | 0.731 | 0.535 | 0.097 | 0.015 | 0.103 | 31.58 | 0.066 |
Eczema only | 249 | 0.907 | 0.827 | 0.467 | 1 | 0.481 | 1 | 0.533 | 0.284 | 0.101 | 0.020 | 0.116 | 38.96 | 0.080 |
Multimorbidity | 223 | 0.863 | 0.774 | 0.384 | 1 | 0.372 | 1 | 0.652 | 0.425 | 0.111 | 0.021 | 0.113 | 30.49 | 0.089 |
Developing new mapping algorithms
Variable | Total score model | Dimension score model | Item model | ||||||
---|---|---|---|---|---|---|---|---|---|
Parameter | SE | p | Parameter | SE | p | Parameter | SE | p | |
Constant | 0.58679 | 0.04551 | < .0001 | 0.58625 | 0.04064 | < .0001 | 0.50166 | 0.03533 | < .0001 |
Age | − 0.00272 | 0.00115 | 0.0178 | − 0.00232 | 0.00105 | 0.0281 | − 0.00160 | 0.00111 | 0.1516 |
PedsQL total | 0.00484 | 0.00130 | 0.0002 | ||||||
PedsQL total2 | − 0.00001 | 0.00001 | 0.4056 | ||||||
Physical dimension | − 0.00150 | 0.00106 | 0.1589 | ||||||
Emotional dimension | 0.00570 | 0.00073 | < .0001 | ||||||
School dimension | 0.00106 | 0.00022 | < .0001 | ||||||
Social dimension | 0.00012 | 0.00104 | 0.9115 | ||||||
Physical dimension2 | 0.00002 | 0.00001 | 0.0404 | ||||||
Emotional dimension2 | − 0.00002 | 0.00001 | < .0001 | ||||||
Social dimension2 | 0.00000 | 0.00001 | 0.0281 | ||||||
Item 3 | − 0.00028 | 0.00048 | 0.5635 | ||||||
Item 4 | − 0.00023 | 0.00015 | 0.1355 | ||||||
Item 5 | − 0.00021 | 0.00013 | 0.1009 | ||||||
Item 6 | − 0.00008 | 0.00046 | 0.8585 | ||||||
Item 7 | 0.00163 | 0.00050 | 0.0012 | ||||||
Item 8 | 0.00067 | 0.00016 | < .0001 | ||||||
Item 9 | 0.00213 | 0.00064 | 0.0009 | ||||||
Item 10 | − 0.00027 | 0.00078 | 0.7265 | ||||||
Item 11 | 0.00157 | 0.00054 | 0.0037 | ||||||
Item 12 | 0.00111 | 0.00052 | 0.0329 | ||||||
Item 13 | − 0.00087 | 0.00060 | 0.1452 | ||||||
Item 14 | − 0.00088 | 0.00051 | 0.0822 | ||||||
Item 15 | 0.00149 | 0.00074 | 0.0456 | ||||||
Item 17 | − 0.00084 | 0.00061 | 0.1662 | ||||||
Item 19 | − 0.00090 | 0.00047 | 0.0546 | ||||||
Item 20 | 0.00165 | 0.00056 | 0.0031 | ||||||
Item 21 | − 0.00015 | 0.00048 | 0.7557 | ||||||
Item 23 | 0.00186 | 0.00067 | 0.0061 | ||||||
Item 32 | 0.000003 | 0.00000 | 0.3660 | ||||||
Item 62 | 0.000003 | 0.00000 | 0.3876 | ||||||
Item 72 | − 0.00001 | 0.00000 | 0.0047 | ||||||
Item 92 | − 0.00001 | 0.00000 | 0.0057 | ||||||
Item 102 | 0.000004 | 0.00001 | 0.4870 | ||||||
Item 112 | − 0.00001 | 0.00000 | 0.0460 | ||||||
Item 122 | − 0.000005 | 0.00000 | 0.2321 | ||||||
Item 132 | 0.00001 | 0.00000 | 0.0788 | ||||||
Item 142 | 0.00001 | 0.00000 | 0.2117 | ||||||
Item 152 | − 0.00001 | 0.00001 | 0.0782 | ||||||
Item 172 | 0.00001 | 0.00000 | 0.1240 | ||||||
Item 192 | 0.00001 | 0.00000 | 0.0518 | ||||||
Item 202 | − 0.00001 | 0.00000 | 0.0109 | ||||||
Item 212 | 0.000004 | 0.00000 | 0.2700 | ||||||
Item 232 | − 0.00001 | 0.00000 | 0.0485 |
Group | N | Mean | Min | Max | Correlation coefficient | R2 | MAE | MSE | RMSE | Absolute errors < 0.05 (%) | Average error |
---|---|---|---|---|---|---|---|---|---|---|---|
Panel A—Total score mapping | |||||||||||
Observed CHU9D | 674 | 0.879 | 0.384 | 1 | – | – | – | – | – | – | – |
OLS | 674 | 0.879 | 0.607 | 0.980 | 0.624 | 0.390 | 0.066 | 0.008 | 0.089 | 51.63 | 0 |
GLM | 674 | 0.879 | 0.616 | 0.981 | 0.623 | 0.388 | 0.066 | 0.008 | 0.089 | 51.63 | 0 |
BETA | 674 | 0.886 | 0.746 | 0.975 | 0.580 | 0.336 | 0.068 | 0.009 | 0.092 | 52.23 | − 0.007 |
CLAD | 674 | 0.890 | 0.573 | 0.997 | 0.624 | 0.389 | 0.064 | 0.008 | 0.089 | 53.12 | − 0.012 |
Panel B—Dimension score mapping | |||||||||||
Observed CHU9D | 674 | 0.879 | 0.384 | 1 | – | – | – | – | – | – | – |
OLS | 674 | 0.879 | 0.537 | 0.990 | 0.712 | 0.506 | 0.059 | 0.006 | 0.080 | 54.45 | 0 |
GLM | 674 | 0.879 | 0.577 | 0.991 | 0.708 | 0.502 | 0.059 | 0.006 | 0.080 | 53.41 | 0 |
BETA | 674 | 0.886 | 0.480 | 0.980 | 0.676 | 0.458 | 0.062 | 0.007 | 0.084 | 55.93 | − 0.007 |
CLAD | 674 | 0.889 | 0.515 | 1 | 0.711 | 0.505 | 0.058 | 0.007 | 0.080 | 56.38 | − 0.010 |
Panel C—Item-level mapping | |||||||||||
Observed CHU9D | 648 | 0.878 | 0.384 | 1 | – | – | – | – | – | – | – |
OLS | 648 | 0.878 | 0.442 | 1 | 0.761 | 0.579 | 0.055 | 0.005 | 0.074 | 59.79 | 0 |
GLM | 648 | 0.878 | 0.489 | 1* | 0.760 | 0.578 | 0.055 | 0.005 | 0.074 | 59.2 | 0 |
BETA | 648 | 0.884 | 0.418 | 0.986 | 0.715 | 0.511 | 0.059 | 0.007 | 0.081 | 60.24 | − 0.007 |
CLAD | 648 | 0.889 | 0.453 | 1 | 0.749 | 0.561 | 0.053 | 0.006 | 0.075 | 62.91 | − 0.011 |
Group | N | Mean | Min | Max | Correlation coefficient | R2 | MAE | MSE | RMSE | Absolute errors < 0.05 (%) | Average error |
---|---|---|---|---|---|---|---|---|---|---|---|
Panel A—Total score mapping | |||||||||||
Observed CHU9D | 168 | 0.872 | 0.464 | 1 | – | – | – | – | – | – | – |
OLS | 168 | 0.881 | 0.648 | 0.972 | 0.664 | 0.440 | 0.066 | 0.008 | 0.088 | 47.62 | − 0.009 |
GLM | 168 | 0.881 | 0.651 | 0.972 | 0.664 | 0.441 | 0.066 | 0.008 | 0.088 | 47.62 | − 0.009 |
BETA | 168 | 0.887 | 0.749 | 0.971 | 0.625 | 0.390 | 0.067 | 0.009 | 0.092 | 48.81 | − 0.015 |
CLAD | 168 | 0.893 | 0.619 | 0.990 | 0.661 | 0.437 | 0.065 | 0.008 | 0.087 | 54.17 | − 0.021 |
Sweeney | 168 | 0.8061 | 0.379 | 0.991 | 0.651 | 0.424 | 0.066 | 0.015 | 0.106 | 37.5 | 0.066 |
Panel B—Dimension score mapping | |||||||||||
Observed CHU9D | 168 | 0.872 | 0.464 | 1 | – | – | – | – | – | – | – |
OLS | 168 | 0.880 | 0.683 | 0.982 | 0.684 | 0.469 | 0.064 | 0.007 | 0.085 | 51.19 | − 0.009 |
GLM | 168 | 0.880 | 0.678 | 0.982 | 0.684 | 0.468 | 0.064 | 0.007 | 0.085 | 51.79 | − 0.008 |
BETA | 168 | 0.885 | 0.657 | 0.977 | 0.643 | 0.414 | 0.064 | 0.008 | 0.089 | 56.55 | − 0.013 |
CLAD | 168 | 0.890 | 0.669 | 0.999 | 0.681 | 0.464 | 0.064 | 0.008 | 0.085 | 55.36 | − 0.018 |
Sweeney | 168 | 0.841 | 0.420 | 0.978 | 0.652 | 0.426 | 0.072 | 0.010 | 0.098 | 50 | 0.031 |
Panel C—Item-level mapping | |||||||||||
Observed CHU9D | 161 | 0.873 | 0.464 | 1 | – | – | – | – | – | – | – |
OLS | 161 | 0.882 | 0.633 | 0.984 | 0.697 | 0.486 | 0.062 | 0.007 | 0.084 | 55.95 | − 0.009 |
GLM | 161 | 0.882 | 0.639 | 0.993 | 0.688 | 0.474 | 0.063 | 0.007 | 0.085 | 57.14 | − 0.009 |
BETA | 161 | 0.889 | 0.588 | 0.979 | 0.689 | 0.474 | 0.063 | 0.007 | 0.085 | 58.93 | − 0.016 |
CLAD | 161 | 0.894 | 0.554 | 1 | 0.718 | 0.515 | 0.060 | 0.007 | 0.082 | 61.9 | − 0.020 |
Sweeney | 161 | 0.812 | 0.410 | 1 | 0.638 | 0.407 | 0.060 | 0.016 | 0.110 | 34.52 | 0.060 |