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Table 6 Sensitivity analysis results for linear term models using Mixture median and Mixture mean with interactions and quadratic terms

From: Associations between ambient air pollutant mixtures and pediatric asthma emergency department visits in three cities: a classification and regression tree approach

   Comparison models with continuous terms
C&RT-identified mixtures (modeled with indicators) Linear terms (mixture median) Linear terms + all two- and three-way interaction terms (mixture mean) Linear terms + quadratic effects (mixture mean)
Label RR 95 % CI RRa 95 % CI RRb 95 % CI RRb 95 % CI
Mixture 1 0.99 (0.97, 1.02) 1.01 (1.00, 1.02) 1.02 (0.96, 1.08) 1.01 (1.00, 1.03)
Mixture 2 1.04 (0.99, 1.09) 1.02 (1.00, 1.03) 1.03 (0.97, 1.11) 1.02 (1.00, 1.04)
Mixture 3 1.01 (0.98, 1.04) 1.01 (1.00, 1.02) 1.01 (0.97, 1.06) 1.01 (1.00, 1.03)
Mixture 4 1.03 (1.01, 1.06) 1.02 (1.00, 1.03) 1.02 (0.97, 1.07) 1.02 (1.01, 1.04)
Mixture 5 1.04 (1.01, 1.07) 1.03 (1.01, 1.05) 1.04 (0.98, 1.10) 1.04 (1.02, 1.06)
Mixture 6 1.03 (0.99, 1.08) 1.03 (1.02, 1.04) 1.04 (0.97, 1.12) 1.04 (1.02, 1.06)
Mixture 7 1.02 (0.99, 1.06) 1.04 (1.02, 1.05) 1.05 (0.98, 1.13) 1.05 (1.02, 1.07)
Mixture 8 1.04 (1.01, 1.08) 1.04 (1.02, 1.06) 1.05 (0.96, 1.14) 1.04 (1.02, 1.07)
Mixture 9 1.00 (0.97, 1.03) 1.04 (1.02, 1.06) 1.05 (0.96, 1.15) 1.04 (1.02, 1.07)
Mixture 10 1.07 (1.03, 1.12) 1.04 (1.02, 1.07) 1.06 (0.97, 1.15) 1.05 (1.02, 1.08)
Mixture 11 1.04 (0.99, 1.08) 1.05 (1.03, 1.07) 1.06 (0.97, 1.15) 1.05 (1.03, 1.08)
Mixture 12 1.04 (0.99, 1.08) 1.06 (1.03, 1.08) 1.08 (0.99, 1.18) 1.06 (1.03, 1.09)
Mixture 13 1.06 (1.02, 1.09) 1.06 (1.04, 1.08) 1.08 (0.99, 1.17) 1.07 (1.04, 1.10)
Mixture 14 1.01 (0.97, 1.05) 1.06 (1.02, 1.08) 1.07 (0.96, 1.19) 1.06 (1.03, 1.10)
Mixture 15 1.03 (0.98, 1.08) 1.07 (1.03, 1.10) 1.08 (0.97, 1.21) 1.08 (1.04, 1.11)
Mixture 16 1.05 (1.01, 1.09) 1.08 (1.04, 1.11) 1.09 (0.98, 1.22) 1.09 (1.05, 1.13)
Mixture 17 1.05 (1.01, 1.09) 1.09 (1.05, 1.13) 1.10 (0.98, 1.24) 1.10 (1.06, 1.15)
Wald Testc χ 2df = 18 =36.6, p = 0.006 χ 2df = 3 =27.06, p < 0.001 χ 2df = 7 =40.69, p < 0.001 χ 2df = 6 =28.77, p < 0.001
Wald Testd NA NA χ 2df = 4 =13.55, p = 0.009 χ 2df = 3 =1.72, p = 0.633
  1. C&RT classification and regression tree, CI confidence interval, DF degrees of freedom, RR rate ratio
  2. aRate ratios for the comparison model are calculated for the effect of an increase equal to the mixture median minus the referent median for all three pollutants
  3. bRate ratios for the comparison model are calculated for the effect of an increase equal to the mixture mean minus the referent mean for all three pollutants
  4. cSimultaneous Wald test for all exposure parameters in the model
  5. dSimultaneous Wald test for additional exposure parameters beyond the linear effects