Table 2.
Apparent and external validity of six candidate Bayesian Poisson regression models
| Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | |
|---|---|---|---|---|---|---|
| Covariates | Age, gender, age×gender, ethnicity | Model 1 plus deprivation, social fragmentation | Model 1 plus deprivation, population density | Model 2 plus cannabis use | Model 4 plus population density | Model 2 plus population density |
| Apparent validity | ||||||
| Model DIC | 11 614.04 | 11 533.86 | 11 539.75 | 11 533.72 | 11 531.93 | 11 531.88 |
| External validity | ||||||
| National level | ||||||
| Observed cases,a n | 8038 | 8038 | 8038 | 8038 | 8038 | 8038 |
| Predicted cases, n (95% CI)b | 8984 (8497 to 9460) | 8137 (7642 to 8637) | 8362 (7907 to 8851) | 8112 (7623 to 8597) | 8187 (7722 to 8707) | 8205 (7716 to 8763) |
| Difference, n (%) | 946 (11.77) | 99 (1.24) | 324 (4.04) | 74 (0.92) | 149 (1.85) | 167 (2.08) |
| CCG level (n = 205)c | ||||||
| RMSE | 23.56 | 20.95 | 21.55 | 20.94 | 21.29 | 21.32 |
| R2 | 0.49 | 0.54 | 0.54 | 0.54 | 0.53 | 0.53 |
| Correlation coefficient, R | 0.70 | 0.74 | 0.74 | 0.74 | 0.73 | 0.73 |
| Calibration slope, β (s.e.) | 0.66 (0.05) | 0.64 (0.04) | 0.69 (0.04) | 0.64 (0.04) | 0.64 (0.04) | 0.64 (0.04) |
| Calibration intercept | 18.08 | 14.90 | 14.21 | 14.84 | 15.00 | 15.03 |
| Rate difference per 100 000 person-years between predicted and observed, n (%)d | ||||||
| <−20 | 13 (6.34) | 15 (7.32) | 14 (6.83) | 15 (7.32) | 15 (7.32) | 15 (7.32) |
| −20 to −11 | 24 (11.71) | 21 (10.24) | 22 (10.73) | 22 (10.73) | 23 (11.22) | 23 (11.22) |
| −10 to 10 | 109 (53.17) | 123 (60.00) | 122 (59.51) | 123 (60.00) | 121 (59.02) | 121 (59.02) |
| 11 to 20 | 35 (17.07) | 35 (17.07) | 35 (17.07) | 34 (16.59) | 35 (17.07) | 35 (17.07) |
| >20 | 24 (11.71) | 11 (5.37) | 12 (5.85) | 11 (5.37) | 11 (5.37) | 11 (5.37) |
DIC, deviance information criterion; RMSE, root-mean-square error; MHSDS, Mental Health Services Dataset; CCG, Clinical Commissioning Group.
Observed data from NHS Digital MHSDS for the financial year April 2016 – March 2017.
Predicted data were age-matched to observed MHSDS data, according to the corresponding age range served by each CCG as reported in the Early Intervention in Psychosis Network national audit for the same period (see Supplementary Section 7 for further details). Not all CCGs served the entire population aged 16–64 years, so the figures in this table should not be interpreted as total predicted cases in England for a given stratum. For total predicted case-load sizes in England, for 2019–2025, see Supplementary Table 10.
Out of 207 CCGs, 205 were included in validation statistics; two CCGs were excluded because of reliability concerns over the observed MHSDS data.
Number and percentage of CCGs where difference between the observed and predicted incidence rate (per 100 000 person-years) fell within the category range shown.