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Table 2 Estimated average incidence rate \(\left (\overline {IR}\right)\) in number of episodes per child year and estimated hazard ratios for the different covariates from model 1 i.e. \(\widehat {HR}=\text {exp} \left ({\widehat {\beta }}_{1}\right)\), and for model 2 the estimated average incidence rate, \(\left (\widehat {\overline {HR(t)}}\right)={\text {exp} {\widehat {\beta }}_{1}\ }\), as well as the estimated degrees of freedom (EDF) for the time-varying smooth function in the hazard ratio, \({\hat {f}}_{1}(t)\)

From: Flexible modelling of risk factors on the incidence of pneumonia in young children in South Africa using piece-wise exponential additive mixed modelling

  Model 1   Model 2   
  \(\overline {IR}\) (95% CI) \(\widehat {HR}\ \) (95% CI; p-value) \(\overline {IR}\) (95% CI) \(\widehat {\overline {HR(t)}}\) (95% CI; p-value) EDF (p-value)
HU 0.29 (0.26, 0.32)   0.29 (0.26, 0.33)   
HEU 0.42 (0.35, 0.51) 1.49 (1.21, 1.83; p<0.001) 0.40 (0.33, 0.48) 1.37 (1.10, 1.71; p=0.004) 1.00 (p=0.036)
Girls 0.25 (0.22, 0.29)   0.25 (0.22, 0.29)   
Boys 0.38 (0.34, 0.43) 1.53 (1.28, 1.84; p<0.001) 0.37 (0.33, 0.43) 1.48 (1.22, 1.79; p<0.001) 1.00 (p=0.261)
Not low WfL 0.30 (0.26, 0.33)   0.29 (0.25, 0.33)   
Low WfL 0.29 (0.25, 0.35) 0.99 (0.81, 1.22; p=0.926) 0.31 (0.26, 0.37) 1.07 (0.87, 1.33; p=0.522) 1.00 (p=0.023)
Mbekweni 0.34 (0.30, 0.38)   0.33 (0.29, 0.38)   
TC Newman 0.29 (0.25, 0.33) 0.85 (0.71, 1.02; p=0.074) 0.29 (0.25, 0.34) 0.89 (0.73, 1.07; p=0.212) 1.00 (p=0.162)
Not preterm birth 0.30 (0.27, 0.33)   0.29 (0.26, 0.33)   
Preterm birth 0.42 (0.34, 0.51) 1.41 (1.12, 1.77; p=0.003) 0.42 (0.34, 0.52) 1.43 (1.12, 1.81; p=0.003) 1.00 (p=0.752)
Not low birthweight 0.29 (0.26, 0.32)   0.29 (0.26, 0.32)   
Low birthweight 0.46 (0.37, 0.56) 1.56 (1.23, 1.97; p<0.001) 0.47 (0.37, 0.58) 1.61 (1.26, 2.05; p<0.001) 2.11 (p=0.168)
Lower SES 0.37 (0.32, 0.41)   0.37 (0.33, 0.42)   
Higher SES 0.26 (0.23, 0.30) 0.72 (0.60, 0.87; p<0.001) 0.26 (0.22, 0.30) 0.69 (0.57, 0.83; p<0.001) 1.00 (p=0.127)
Uncrowded 0.30 (0.27, 0.34)   0.30 (0.27, 0.34)   
Crowded 0.34 (0.29, 0.41) 1.14 (0.94, 1.39; p=0.177) 0.35 (0.29, 0.41) 1.16 (0.95, 1.43; p=0.152) 1.01 (p=0.635)
No maternal smoking 0.28 (0.25, 0.32)   0.28 (0.25, 0.32)   
Maternal smoking 0.38 (0.33, 0.45) 1.35 (1.12, 1.64; p=0.002) 0.39 (0.33, 0.45) 1.38 (1.13, 1.68; p=0.001) 1.00 (p=0.537)
Indoor air pollution unexposed 0.32 (0.28, 0.36)   0.32 (0.28, 0.36)   
Indoor air pollution exposed 0.27 (0.21, 0.36) 0.85 (0.63, 1.15; p=0.279) 0.26 (0.20, 0.35) 0.83 (0.61, 1.12; p=0.224) 2.00 (p=0.337)
High maternal education 0.27 (0.23, 0.32)   0.28 (0.24, 0.33)   
Low maternal education 0.34 (0.30, 0.38) 1.24 (1.03, 1.50; p=0.022) 0.33 (0.30, 0.38) 1.18 (0.97, 1.44; p=0.093) 1.47 (p=0.218)