Table 1 Comparison of hierarchical models with different temporal structures, adjustment factors and covariates.

From: Associations between the spatiotemporal distribution of Kawasaki disease and environmental factors: evidence supporting a multifactorial etiologic model

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

     
  1. 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.
  2. FSA forward sortation area, ICD international classification of disease, SIR standardized incidence rate, WAIC Watanabe-Akaike Information Criterion.
  3. † Improved (i.e. lowered) WAIC by >1 over the adjusted based model.
  4. ^ICD code associated with a known organism indicate by ICD codes B95–B98.
Back to article page