Table 1.
Comparison of hierarchical models with different temporal structures, adjustment factors and covariates.
| Model/predictor (definition) | WAIC | Univariable SIR percentile | Multivariable SIR percentile | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2.5th | 25th | 50th | 75th | 97.5th | 2.5th | 25th | 50th | 75th | 97.5th | ||
| Base model | 23,134.0 | ||||||||||
| Linear time | 23,210.8 | ||||||||||
| Linear time + random walk | 23,166.9 | ||||||||||
| Linear time + random walk + seasonality | 23,134.0 | ||||||||||
| Adjusted base model | 23,128.0 | ||||||||||
| Percentage population 0–4 years old per region | 23,133.1 | 1.008 | 1.046 | 1.068 | 1.089 | 1.131 | 1.007 | 1.042 | 1.061 | 1.080 | 1.117 |
| Percentage population self-identifying as East Asian per region | 23,127.0 | 1.119 | 1.161 | 1.184 | 1.207 | 1.252 | 1.089 | 1.131 | 1.153 | 1.176 | 1.221 |
| Main regression model | 23,059.7 | ||||||||||
| Exposures at the FSA level | |||||||||||
| Median household income in FSA† | 23,125.5 | 0.882 | 0.912 | 0.929 | 0.946 | 0.978 | 0.900 | 0.931 | 0.947 | 0.964 | 0.997 |
| Proportion of rural postal codes in FSA | 23,127.5 | 0.864 | 0.894 | 0.910 | 0.926 | 0.957 | 0.898 | 0.930 | 0.947 | 0.964 | 0.998 |
| Population density in FSA | 23,128.3 | 1.001 | 1.049 | 1.075 | 1.102 | 1.154 | |||||
| Weather | |||||||||||
| Evaporation (m)† | 23,124.7 | 1.021 | 1.068 | 1.093 | 1.119 | 1.170 | |||||
| Soil temperature at 0–7 cm depth (layer 1, K)† | 23,125.2 | 0.812 | 0.861 | 0.888 | 0.916 | 0.972 | |||||
| Planetary boundary layer height, lowest part of the atmosphere (m)† | 23,125.6 | 1.000 | 1.024 | 1.037 | 1.050 | 1.075 | |||||
| Instantaneous eastward turbulent surface stress (N m-2)† | 23,126.8 | 0.994 | 1.016 | 1.027 | 1.039 | 1.062 | |||||
| Surface pressure (Pa) | 23,127.3 | 0.977 | 1.035 | 1.067 | 1.100 | 1.164 | |||||
| 10 m U (zonal, eastward) wind component at 10 m (m s−1) | 23,127.9 | 0.982 | 1.014 | 1.032 | 1.050 | 1.085 | |||||
| 2 m temperature (K) | 23,128.1 | 0.846 | 0.897 | 0.925 | 0.954 | 1.011 | |||||
| Total cloud cover (0–1) | 23,128.1 | 0.929 | 0.958 | 0.973 | 0.989 | 1.018 | |||||
| Total precipitation (m) | 23,128.3 | 0.950 | 0.971 | 0.982 | 0.994 | 1.015 | |||||
| 10 m V (meridional, northward) wind component at 10 m (m s−1) | 23,128.4 | 0.989 | 1.009 | 1.019 | 1.030 | 1.051 | |||||
| Low vegetation cover (0–1) | 23,128.7 | 0.893 | 0.950 | 0.981 | 1.013 | 1.077 | |||||
| High vegetation cover (0–1) | 23,129.0 | 0.936 | 0.978 | 1.001 | 1.024 | 1.071 | |||||
| Photosynthetically active radiation (J m−2) | 23,129.0 | 0.811 | 0.896 | 0.944 | 0.995 | 1.098 | |||||
| Instantaneous northward turbulent surface stress (N m−2) | 23,129.0 | 0.980 | 1.002 | 1.014 | 1.027 | 1.050 | |||||
| Volumetric soil water layer at 0–7 cm depth (layer 1, m3 m−3) | 23,129.2 | 0.953 | 0.981 | 0.997 | 1.012 | 1.043 | |||||
| UV-radiation (J m) | 23,129.2 | 0.828 | 0.908 | 0.953 | 1.001 | 1.097 | |||||
| 10 m wind speed at 10 m (m s−1) | 23,129.6 | 0.963 | 0.993 | 1.010 | 1.027 | 1.059 | |||||
| Pollution (total column) | |||||||||||
| Sulphur dioxide and nitrogen oxide (SO2 + NO2) (kg m−2)† | 23,124.2 | 1.014 | 1.055 | 1.077 | 1.099 | 1.143 | 1.055 | 1.102 | 1.127 | 1.153 | 1.204 |
| Ozone (kg m−2) | 23,128.9 | 0.969 | 1.011 | 1.034 | 1.057 | 1.103 | |||||
| Carbon monoxide (CO) (kg m−2) | 23,129.5 | 0.949 | 0.993 | 1.017 | 1.041 | 1.088 | |||||
| Fine particulate matter < 2.5 ug (kg m−2) | 23,131.1 | 0.958 | 0.984 | 0.997 | 1.010 | 1.034 | |||||
| Spores | |||||||||||
| Algae†,‡ | 23,121.3 | 1.017 | 1.040 | 1.052 | 1.063 | 1.085 | 1.018 | 1.042 | 1.054 | 1.066 | 1.088 |
| Deuteromycetes (fungi imperfecti)† | 23,125.7 | 0.994 | 1.030 | 1.049 | 1.068 | 1.105 | 1.019 | 1.058 | 1.078 | 1.099 | 1.139 |
| Myxomycetes† | 23,126.5 | 0.993 | 1.018 | 1.030 | 1.043 | 1.065 | 0.989 | 1.014 | 1.027 | 1.040 | 1.063 |
| Dothideomycetes† | 23,126.8 | 0.905 | 0.937 | 0.954 | 0.971 | 1.004 | 0.892 | 0.925 | 0.943 | 0.961 | 0.996 |
| Ascomycetes (other than dothideomycetes) | 23,128.1 | 0.998 | 1.021 | 1.032 | 1.044 | 1.065 | |||||
| Basidiomycetes | 23,130.0 | 0.939 | 0.975 | 0.995 | 1.015 | 1.053 | |||||
| Zygomycetes | 23,130.0 | 0.968 | 0.993 | 1.004 | 1.015 | 1.032 | |||||
| Pollens | |||||||||||
| Malvids (Acer, Tilia, Aesculus, Cruciferae)† | 23,126.8 | 0.933 | 0.956 | 0.968 | 0.980 | 1.003 | |||||
| Lamiidis (Fraxinus, Oleaceae, Plantago)† | 23,126.8 | 0.934 | 0.957 | 0.968 | 0.980 | 1.002 | |||||
| Rosales (Ulmus, Morus, Prunus, Urticaceae, Crataegus) | 23,128.1 | 0.944 | 0.966 | 0.977 | 0.989 | 1.010 | |||||
| Grasses (Cyperaceae, Gramineae) | 23,128.6 | 0.978 | 1.010 | 1.026 | 1.042 | 1.071 | |||||
| Poales (Typhacaea) | 23,128.9 | 0.932 | 0.960 | 0.975 | 0.989 | 1.015 | |||||
| Proteales (Platanus) | 23,128.9 | 0.944 | 0.971 | 0.984 | 0.996 | 1.016 | |||||
| Malpighiales (Salix, Populus) | 23,129.0 | 0.981 | 1.004 | 1.016 | 1.028 | 1.050 | |||||
| Caryophyllales (Chenopodiaceae, Rumex, Salsola pestifer) | 23,129.1 | 0.974 | 1.003 | 1.018 | 1.032 | 1.059 | |||||
| Conifers (Cupressaceae, Larix, Pinaceae, Tsuga) | 23,129.4 | 0.982 | 1.002 | 1.012 | 1.022 | 1.041 | |||||
| Fagales (Betula, Alnus, Corylus, Quercus, Fagus, Castanea) | 23,129.5 | 0.978 | 0.998 | 1.009 | 1.020 | 1.040 | |||||
| Juglandaceae (Juglans, Carya) | 23,130.0 | 0.962 | 0.985 | 0.996 | 1.007 | 1.028 | |||||
| Campanulids (Sambucus, Ambrosia, Solidago, Artemisia) | 23,130.1 | 0.955 | 0.986 | 1.003 | 1.020 | 1.028 | |||||
| Incidence of healthcare encounters for atopy (ICD codes) | |||||||||||
| Atopic dermatitis (L20)† | 23,121.1 | 1.006 | 1.026 | 1.036 | 1.047 | 1.067 | 1.007 | 1.028 | 1.040 | 1.040 | 1.072 |
| Asthma (J45) | 23,127.7 | 0.951 | 0.982 | 0.998 | 1.015 | 1.047 | |||||
| Rhinitis (J30) | 23,128.5 | 0.934 | 0.959 | 0.972 | 0.986 | 1.011 | |||||
| Urticaria (L50) | 23,132.1 | 0.971 | 0.994 | 1.007 | 1.019 | 1.043 | |||||
| Incidence of healthcare encounters by infectious categories (ICD codes) | |||||||||||
| Viral intestinal infections (A08)† | 23,120.0 | 1.017 | 1.041 | 1.054 | 1.066 | 1.091 | 1.028 | 1.054 | 1.068 | 1.082 | 1.108 |
| Bacterial skin infections (A69.2, K05.0, L00–L03, L08)† | 23,126.7 | 0.883 | 0.914 | 0.930 | 0.947 | 0.979 | 0.870 | 0.906 | 0.925 | 0.945 | 0.983 |
| Viral LRTI (J09, J10, J11, J12, J17.1, J20.3/.4/.5/.6/.7/.8^, J21.0/.1/.8^) | 23,127.5 | 0.955 | 0.976 | 0.987 | 0.997 | 1.017 | |||||
| Viral URTI (B27, J00, J02.8^, J03.8^, J04^, J05.0^) | 23,127.6 | 0.953 | 0.976 | 0.988 | 1.000 | 1.024 | |||||
| Intestinal infections no organism identified (A06, A07, A09) | 23,127.8 | 0.933 | 0.960 | 0.975 | 0.990 | 1.019 | |||||
| Bacterial LRTI (A15, A16, J13, J14, J15, J16.0, J17.0, J20.0/.1/.2/.8^, J21.8^) | 23,127.9 | 0.961 | 0.981 | 0.992 | 1.003 | 1.022 | |||||
| Bacterial intestinal infections (A01–A05) | 23,128.4 | 0.951 | 0.975 | 0.987 | 1.000 | 1.025 | |||||
| Bacterial URTI (J02.0/.8^, J03.0/.8^, J04^, J05^, J36.0^) | 23,129.4 | 0.888 | 0.918 | 0.933 | 0.949 | 0.980 | |||||
| URTI no organism identified (J01, J02.8/.9, J03.8/.9, J04, J05.0, J06, J36, J39) | 23,129.7 | 0.929 | 0.958 | 0.974 | 0.990 | 1.020 | |||||
| Fungal infections (B37, J17.2) | 23,129.9 | 0.900 | 0.930 | 0.946 | 0.962 | 0.993 | |||||
| Viral skin infections (B00–B02, B05–B09) | 23,129.9 | 0.909 | 0.940 | 0.957 | 0.974 | 1.007 | |||||
| LRTI no organism identified (J16.8, J17.3/.8, J18, J20.8/.9, J21.8/.9, J22) | 23,130.1 | 0.921 | 0.950 | 0.966 | 0.982 | 1.013 | |||||
| Incidence of healthcare encounters for specific pathogens (N of admissions) | |||||||||||
| Mycoplasma (8296)† | 23,117.2 | 1.021 | 1.038 | 1.047 | 1.056 | 1.073 | 1.024 | 1.041 | 1.050 | 1.059 | 1.076 |
| Candida (283,837)† | 23,123.6 | 0.869 | 0.900 | 0.917 | 0.934 | 0.966 | 0.848 | 0.884 | 0.903 | 0.923 | 0.962 |
| Campylobacter (8368)† | 23,123.6 | 0.996 | 1.015 | 1.025 | 1.036 | 1.055 | 1.005 | 1.025 | 1.036 | 1.047 | 1.067 |
| Coronavirus (1658)† | 23,124.2 | 1.000 | 1.014 | 1.020 | 1.027 | 1.040 | 0.998 | 1.011 | 1.018 | 1.025 | 1.038 |
| Measles (2262)† | 23,124.4 | 0.998 | 1.012 | 1.019 | 1.027 | 1.040 | 1.000 | 1.015 | 1.022 | 1.029 | 1.042 |
| Klebsiella (120,905)† | 23,124.8 | 0.983 | 1.011 | 1.027 | 1.042 | 1.073 | 1.003 | 1.036 | 1.053 | 1.071 | 1.105 |
| Haemophilus influenzae (19,927)† | 23,125.9 | 0.988 | 1.007 | 1.017 | 1.027 | 1.047 | |||||
| Salmonella (16,585)† | 23,126.0 | 0.991 | 1.009 | 1.019 | 1.029 | 1.048 | 0.990 | 1.009 | 1.019 | 1.029 | 1.048 |
| Clostridium (214,593)† | 23,126.1 | 0.920 | 0.947 | 0.962 | 0.976 | 1.005 | |||||
| Herpes simplex (103,857)† | 23,126.2 | 0.918 | 0.945 | 0.959 | 0.974 | 1.002 | |||||
| Borrelia (6955)† | 23,126.3 | 0.936 | 0.960 | 0.972 | 0.984 | 1.006 | |||||
| Adenovirus (10,012)† | 23,126.3 | 0.988 | 1.005 | 1.015 | 1.024 | 1.041 | |||||
| Metapneumovirus (2655)† | 23,126.6 | 0.957 | 0.975 | 0.983 | 0.992 | 1.008 | 0.952 | 0.970 | 0.979 | 0.987 | 1.004 |
| Cytomegalovirus (8749)† | 23,126.8 | 0.989 | 1.006 | 1.015 | 1.024 | 1.041 | |||||
| Pseudomonas (103,288)† | 23,127.0 | 0.930 | 0.957 | 0.971 | 0.986 | 1.014 | |||||
| Mycobacterium (23,866) | 23,127.0 | 0.959 | 0.979 | 0.990 | 1.001 | 1.021 | |||||
| Molluscum contagiosum (10,336) | 23,127.0 | 0.942 | 0.963 | 0.974 | 0.985 | 1.006 | |||||
| Meningococcus (1839) | 23,127.0 | 0.961 | 0.977 | 0.986 | 0.995 | 1.011 | |||||
| Varicella (53,077) | 23,127.0 | 0.972 | 0.995 | 1.007 | 1.019 | 1.042 | |||||
| Papillomavirus (77,856) | 23,127.3 | 0.922 | 0.951 | 0.966 | 0.981 | 1.008 | |||||
| Mumps (10,498) | 23,127.3 | 0.981 | 1.000 | 1.009 | 1.019 | 1.037 | |||||
| Bordetella (13,630) | 23,127.5 | 0.953 | 0.973 | 0.983 | 0.993 | 1.012 | |||||
| Influenza (410,237) | 23,127.6 | 0.957 | 0.976 | 0.986 | 0.996 | 1.014 | |||||
| Epstein Barr Virus (6007) | 23,127.7 | 0.974 | 0.990 | 0.999 | 1.007 | 1.024 | |||||
| Herpes virus (5167) | 23,127.7 | 0.977 | 0.994 | 1.003 | 1.012 | 1.029 | |||||
| Parainfluenza (2490) | 23,127.8 | 0.967 | 0.983 | 0.992 | 1.000 | 1.016 | |||||
| Zoster (248,482) | 23,127.8 | 0.891 | 0.921 | 0.937 | 0.953 | 0.985 | |||||
| Hepatitis (2826) | 23,127.8 | 0.981 | 0.997 | 1.005 | 1.013 | 1.028 | |||||
| Shigella (1274) | 23,127.8 | 0.984 | 0.998 | 1.006 | 1.014 | 1.028 | |||||
| Norovirus (7507) | 23,127.8 | 0.974 | 0.992 | 1.001 | 1.009 | 1.026 | |||||
| Respiratory Syncytial Virus (86,764) | 23,128.0 | 0.970 | 0.989 | 0.999 | 1.009 | 1.028 | |||||
| Model/predictor (definition) | WAIC | Univariable SIR percentile | Multivariable SIR percentile | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2.5th | 25th | 50th | 75th | 97.5th | 2.5th | 25th | 50th | 75th | 97.5th | ||
| Bacillus (3224) | 23,128.0 | 0.969 | 0.987 | 0.997 | 1.006 | 1.024 | |||||
| Proteus (42,125) | 23,128.0 | 0.958 | 0.981 | 0.993 | 1.005 | 1.028 | |||||
| Staphylococcus (348,123) | 23,128.0 | 0.941 | 0.973 | 0.991 | 1.008 | 1.043 | |||||
| Rotavirus (11,846) | 23,128.1 | 0.978 | 0.997 | 1.006 | 1.016 | 1.033 | |||||
| Enterovirus (73,642) | 23,128.2 | 0.955 | 0.977 | 0.989 | 1.001 | 1.024 | |||||
| Escherichia coli (588,333) | 23,128.4 | 0.915 | 0.947 | 0.965 | 0.983 | 1.017 | |||||
| Streptococcus (348,123) | 23,128.4 | 0.888 | 0.919 | 0.936 | 0.953 | 0.985 | |||||
| Parvovirus (14,450) | 23,128.6 | 0.952 | 0.973 | 0.984 | 0.995 | 1.016 | |||||
In the Bayesian model framework, a decrease in the Watanabe-Akaike information criterion (WAIC) is an indication of improved predictive accuracy. The simplest model in the table is the linear time model which consists of the spatially structured and unstructured term (Besag-York-Mollie model) and a linear time trend. A random walk of order 1 (temporally structured effect) and a seasonal cycle with length 12 months are sequentially added. The latter model shows the lowest WAIC and is therefore used as the base model. The WAICs for the adjustment factors (percentage of population age 0–4 and East Asians) were only listed for completeness, but not used as a selection criterion. In all models listed under ‘Main regression model’, candidate variables were added to the adjusted base model one-by-one and listed by ascending WAIC within the variable category. Variables which, when added to the adjusted base model, resulted in a model with a lower WAIC (> 1 change), were included in a preliminary multivariable model. These variables were further subject to selection through backward elimination based on them increasing the multivariable WAIC. The percentile landmarks of the posterior coefficients of the fixed effects for all univariable models (‘Screening’) and that were included in the multivariable model are presented with standardized incidence rate associated with a 1 standard deviation change in the predictor. The original units for each variable are indicated for general information.
FSA forward sortation area, ICD international classification of disease, SIR standardized incidence rate, WAIC Watanabe-Akaike Information Criterion.
† Improved (i.e. lowered) WAIC by >1 over the adjusted based model.
^ICD code associated with a known organism indicate by ICD codes B95–B98.