Supplemental GEE Tables

Total WWTFs in compiled dataset: 24. Analyte-specific sample sizes differ because reporting availability and complete predictor information vary among facilities.

Table S1. Sample sizes and selected GEE working correlation structures.
Analyte Response Scale n_observations n_facilities Selected_working_correlation
Nitrogen Nitrogen Original 79 20 independence
Phosphorus Phosphorus Original 79 20 independence
Fecal indicator bacteria logFIB log10 71 22 exchangeable
Sulfate logSulfate log10 65 17 ar1
Chloride logChloride log10 73 19 ar1
pH pH Original 83 21 exchangeable


Table S2. QIC comparison of GEE working correlation structures.
Analyte Response Scale Working_correlation n_observations n_facilities QIC QICu Selected
Nitrogen Nitrogen Original independence 79 20 1447.70 1462.80 Yes
Nitrogen Nitrogen Original exchangeable 79 20 1447.79 1462.81 No
Nitrogen Nitrogen Original ar1 79 20 1450.86 1465.55 No
Phosphorus Phosphorus Original independence 79 20 155.35 149.68 Yes
Phosphorus Phosphorus Original exchangeable 79 20 159.35 150.31 No
Phosphorus Phosphorus Original ar1 79 20 161.26 151.43 No
Fecal indicator bacteria logFIB log10 independence 71 22 40.34 40.21 No
Fecal indicator bacteria logFIB log10 exchangeable 71 22 40.17 40.21 Yes
Fecal indicator bacteria logFIB log10 ar1 71 22 41.67 40.23 No
Sulfate logSulfate log10 independence 65 17 31.41 31.68 No
Sulfate logSulfate log10 exchangeable 65 17 31.07 31.68 No
Sulfate logSulfate log10 ar1 65 17 29.17 31.69 Yes
Chloride logChloride log10 independence 73 19 62.01 37.63 No
Chloride logChloride log10 exchangeable 73 19 61.71 37.65 No
Chloride logChloride log10 ar1 73 19 57.20 37.89 Yes
pH pH Original independence 83 21 62.41 52.23 No
pH pH Original exchangeable 83 21 62.21 52.23 Yes
pH pH Original ar1 83 21 63.47 52.64 No


Table S3. Coefficient summaries from selected GEE models.
Analyte Scale Working_correlation Term Estimate Robust_SE Wald p_value
Nitrogen Original independence (Intercept) 11.16 1.70 43.00 <0.001
Nitrogen Original independence Treatment5BNR 5.40 1.07 25.31 <0.001
Nitrogen Original independence TreatmentA2 -5.91 1.27 21.76 <0.001
Nitrogen Original independence TreatmentAS 4.63 2.82 2.68 0.101
Nitrogen Original independence TreatmentAS + UV -3.37 2.71 1.54 0.214
Nitrogen Original independence TreatmentEA -3.28 2.45 1.80 0.180
Nitrogen Original independence TreatmentEA + OD -2.11 1.26 2.81 0.093
Nitrogen Original independence TreatmentMBR + UV -3.89 2.75 2.00 0.158
Nitrogen Original independence TreatmentOD -3.69 1.02 13.12 <0.001
Nitrogen Original independence TreatmentTF 22.01 0.26 7047.22 <0.001
Nitrogen Original independence Year2020 0.34 0.80 0.18 0.671
Nitrogen Original independence Quarter3 -0.15 1.31 0.01 0.907
Nitrogen Original independence RegionC -1.40 2.75 0.26 0.610
Nitrogen Original independence RegionS 3.56 0.90 15.63 <0.001
Nitrogen Original independence Location_typeU -2.94 2.34 1.58 0.209
Nitrogen Original independence Capacity_r -2.29 0.32 50.62 <0.001
Phosphorus Original independence (Intercept) -2.01 0.81 6.11 0.013
Phosphorus Original independence Treatment5BNR 2.31 0.66 12.37 <0.001
Phosphorus Original independence TreatmentA2 5.19 0.77 45.55 <0.001
Phosphorus Original independence TreatmentAS 4.13 1.42 8.47 0.004
Phosphorus Original independence TreatmentAS + UV 3.07 1.33 5.32 0.021
Phosphorus Original independence TreatmentEA 4.32 1.26 11.77 <0.001
Phosphorus Original independence TreatmentEA + OD 4.88 0.77 40.55 <0.001
Phosphorus Original independence TreatmentMBR + UV 3.05 1.43 4.57 0.033
Phosphorus Original independence TreatmentOD 3.43 0.62 30.11 <0.001
Phosphorus Original independence TreatmentTF -0.70 0.13 30.84 <0.001
Phosphorus Original independence Year2020 0.50 0.19 6.98 0.008
Phosphorus Original independence Quarter3 0.44 0.24 3.43 0.064
Phosphorus Original independence RegionC 3.60 1.41 6.52 0.011
Phosphorus Original independence RegionS 0.69 0.60 1.34 0.246
Phosphorus Original independence Location_typeU -1.05 1.13 0.87 0.351
Phosphorus Original independence Capacity_r -0.19 0.15 1.51 0.220
Fecal indicator bacteria log10 exchangeable (Intercept) -0.31 0.23 1.71 0.191
Fecal indicator bacteria log10 exchangeable Treatment5BNR 0.10 0.46 0.05 0.828
Fecal indicator bacteria log10 exchangeable TreatmentA2 0.33 0.22 2.22 0.136
Fecal indicator bacteria log10 exchangeable TreatmentAS 0.41 0.26 2.57 0.109
Fecal indicator bacteria log10 exchangeable TreatmentAS + UV 0.15 0.29 0.27 0.601
Fecal indicator bacteria log10 exchangeable TreatmentEA 0.41 0.22 3.44 0.064
Fecal indicator bacteria log10 exchangeable TreatmentEA + OD 0.34 0.22 2.36 0.124
Fecal indicator bacteria log10 exchangeable TreatmentMBR + UV 0.28 0.23 1.47 0.225
Fecal indicator bacteria log10 exchangeable TreatmentOD 0.36 0.21 2.99 0.084
Fecal indicator bacteria log10 exchangeable TreatmentTF 0.42 0.06 52.54 <0.001
Fecal indicator bacteria log10 exchangeable Year2020 0.06 0.09 0.42 0.518
Fecal indicator bacteria log10 exchangeable Quarter3 -0.02 0.08 0.04 0.843
Fecal indicator bacteria log10 exchangeable RegionC 0.34 0.23 2.34 0.126
Fecal indicator bacteria log10 exchangeable RegionS 0.79 0.40 3.87 0.049
Fecal indicator bacteria log10 exchangeable Location_typeU 0.11 0.14 0.63 0.426
Fecal indicator bacteria log10 exchangeable Capacity_r -0.09 0.07 1.85 0.173
Sulfate log10 ar1 (Intercept) 1.32 0.07 340.18 <0.001
Sulfate log10 ar1 TreatmentA2 -0.96 0.06 245.07 <0.001
Sulfate log10 ar1 TreatmentAS 0.00 0.12 0.00 0.995
Sulfate log10 ar1 TreatmentAS + UV -1.37 0.08 283.57 <0.001
Sulfate log10 ar1 TreatmentEA -0.46 0.09 29.05 <0.001
Sulfate log10 ar1 TreatmentEA + OD -0.90 0.06 212.20 <0.001
Sulfate log10 ar1 TreatmentMBR + UV 1.21 0.09 178.50 <0.001
Sulfate log10 ar1 TreatmentOD -1.11 0.08 170.51 <0.001
Sulfate log10 ar1 TreatmentTF -0.35 0.12 7.66 0.006
Sulfate log10 ar1 Year2020 0.09 0.04 3.96 0.046
Sulfate log10 ar1 Quarter3 0.03 0.02 1.40 0.237
Sulfate log10 ar1 RegionC 1.37 0.16 77.41 <0.001
Sulfate log10 ar1 RegionS 1.62 0.06 721.33 <0.001
Sulfate log10 ar1 Location_typeU -0.79 0.06 169.46 <0.001
Sulfate log10 ar1 Capacity_r 0.30 0.03 104.11 <0.001
Chloride log10 ar1 (Intercept) 2.20 0.23 93.20 <0.001
Chloride log10 ar1 Treatment5BNR -0.97 0.29 11.58 <0.001
Chloride log10 ar1 TreatmentA2 -1.36 0.23 34.20 <0.001
Chloride log10 ar1 TreatmentAS 0.28 0.34 0.68 0.408
Chloride log10 ar1 TreatmentAS + UV -1.82 0.20 87.35 <0.001
Chloride log10 ar1 TreatmentEA -0.97 0.16 37.30 <0.001
Chloride log10 ar1 TreatmentEA + OD -1.44 0.23 39.27 <0.001
Chloride log10 ar1 TreatmentMBR + UV 0.96 0.34 7.95 0.005
Chloride log10 ar1 TreatmentOD -1.31 0.23 33.71 <0.001
Chloride log10 ar1 TreatmentTF -0.44 0.02 378.83 <0.001
Chloride log10 ar1 Year2020 0.03 0.03 1.15 0.283
Chloride log10 ar1 Quarter3 0.00 0.04 0.00 0.988
Chloride log10 ar1 RegionC 1.46 0.34 18.54 <0.001
Chloride log10 ar1 RegionS 2.35 0.30 61.94 <0.001
Chloride log10 ar1 Location_typeU -1.26 0.31 16.85 <0.001
Chloride log10 ar1 Capacity_r 0.21 0.03 55.99 <0.001
pH Original exchangeable (Intercept) 6.57 0.47 194.14 <0.001
pH Original exchangeable Treatment5BNR -0.58 0.20 8.58 0.003
pH Original exchangeable TreatmentA2 0.20 0.47 0.17 0.676
pH Original exchangeable TreatmentAS -1.77 0.26 44.96 <0.001
pH Original exchangeable TreatmentAS + UV -0.65 0.24 7.52 0.006
pH Original exchangeable TreatmentEA -0.64 0.19 10.91 <0.001
pH Original exchangeable TreatmentEA + OD -2.72 0.48 32.68 <0.001
pH Original exchangeable TreatmentMBR + UV -0.24 0.22 1.28 0.257
pH Original exchangeable TreatmentOD 0.37 0.29 1.66 0.198
pH Original exchangeable TreatmentTF -0.18 0.04 25.06 <0.001
pH Original exchangeable Year2020 0.02 0.07 0.10 0.752
pH Original exchangeable Quarter3 -0.08 0.08 1.15 0.284
pH Original exchangeable RegionC 0.33 0.23 1.97 0.161
pH Original exchangeable RegionS 0.89 0.24 13.37 <0.001
pH Original exchangeable Location_typeU -0.33 0.45 0.54 0.461
pH Original exchangeable Capacity_r 0.53 0.04 148.07 <0.001


Table S4. Estimated marginal means from selected GEE models.
Analyte Scale Working_correlation Predictor Level Estimate SE Lower_CL Upper_CL
Nitrogen Original independence Treatment 2SND 8.11 0.87 6.37 9.85
Nitrogen Original independence Treatment 5BNR 13.51 0.96 11.59 15.43
Nitrogen Original independence Treatment A2 2.19 0.63 0.93 3.46
Nitrogen Original independence Treatment AS 12.73 2.31 8.11 17.35
Nitrogen Original independence Treatment AS + UV 4.74 2.17 0.41 9.06
Nitrogen Original independence Treatment EA 4.82 1.83 1.16 8.49
Nitrogen Original independence Treatment EA + OD 5.99 0.63 4.74 7.25
Nitrogen Original independence Treatment MBR + UV 4.21 2.17 -0.12 8.55
Nitrogen Original independence Treatment OD 4.42 0.89 2.64 6.19
Nitrogen Original independence Treatment TF 30.12 0.83 28.46 31.78
Nitrogen Original independence Year 2019 8.91 0.65 7.62 10.21
Nitrogen Original independence Year 2020 9.26 0.82 7.61 10.90
Nitrogen Original independence Quarter 1 9.16 0.82 7.51 10.81
Nitrogen Original independence Quarter 3 9.01 0.97 7.06 10.96
Nitrogen Original independence Region N 8.37 0.58 7.21 9.53
Nitrogen Original independence Region C 6.96 2.28 2.41 11.52
Nitrogen Original independence Region S 11.92 0.68 10.56 13.29
Nitrogen Original independence Location_type R 10.55 1.76 7.03 14.08
Nitrogen Original independence Location_type U 7.62 0.63 6.36 8.88
Phosphorus Original independence Treatment 2SND -0.83 0.52 -1.87 0.22
Phosphorus Original independence Treatment 5BNR 1.48 0.57 0.34 2.62
Phosphorus Original independence Treatment A2 4.36 0.38 3.59 5.12
Phosphorus Original independence Treatment AS 3.30 1.09 1.12 5.49
Phosphorus Original independence Treatment AS + UV 2.25 0.96 0.32 4.17
Phosphorus Original independence Treatment EA 3.49 0.88 1.73 5.25
Phosphorus Original independence Treatment EA + OD 4.05 0.38 3.28 4.81
Phosphorus Original independence Treatment MBR + UV 2.22 1.07 0.08 4.35
Phosphorus Original independence Treatment OD 2.60 0.54 1.51 3.69
Phosphorus Original independence Treatment TF -1.52 0.50 -2.52 -0.53
Phosphorus Original independence Year 2019 1.89 0.28 1.33 2.45
Phosphorus Original independence Year 2020 2.39 0.35 1.69 3.09
Phosphorus Original independence Quarter 1 1.92 0.30 1.31 2.52
Phosphorus Original independence Quarter 3 2.36 0.35 1.66 3.06
Phosphorus Original independence Region N 0.71 0.33 0.04 1.37
Phosphorus Original independence Region C 4.31 1.13 2.04 6.57
Phosphorus Original independence Region S 1.40 0.48 0.43 2.37
Phosphorus Original independence Location_type R 2.66 0.84 0.99 4.34
Phosphorus Original independence Location_type U 1.61 0.35 0.92 2.30
Fecal indicator bacteria log10 exchangeable Treatment 2SND 0.06 0.20 -0.33 0.45
Fecal indicator bacteria log10 exchangeable Treatment 5BNR 0.16 0.29 -0.42 0.73
Fecal indicator bacteria log10 exchangeable Treatment A2 0.39 0.16 0.07 0.70
Fecal indicator bacteria log10 exchangeable Treatment AS 0.47 0.25 -0.03 0.97
Fecal indicator bacteria log10 exchangeable Treatment AS + UV 0.21 0.24 -0.28 0.70
Fecal indicator bacteria log10 exchangeable Treatment EA 0.47 0.16 0.16 0.78
Fecal indicator bacteria log10 exchangeable Treatment EA + OD 0.40 0.16 0.08 0.71
Fecal indicator bacteria log10 exchangeable Treatment MBR + UV 0.34 0.19 -0.03 0.71
Fecal indicator bacteria log10 exchangeable Treatment OD 0.42 0.24 -0.07 0.90
Fecal indicator bacteria log10 exchangeable Treatment TF 0.47 0.18 0.11 0.84
Fecal indicator bacteria log10 exchangeable Year 2019 0.31 0.12 0.08 0.54
Fecal indicator bacteria log10 exchangeable Year 2020 0.37 0.11 0.16 0.58
Fecal indicator bacteria log10 exchangeable Quarter 1 0.35 0.11 0.13 0.56
Fecal indicator bacteria log10 exchangeable Quarter 3 0.33 0.11 0.11 0.55
Fecal indicator bacteria log10 exchangeable Region N -0.04 0.07 -0.19 0.11
Fecal indicator bacteria log10 exchangeable Region C 0.30 0.18 -0.05 0.66
Fecal indicator bacteria log10 exchangeable Region S 0.75 0.36 0.03 1.48
Fecal indicator bacteria log10 exchangeable Location_type R 0.28 0.14 0.01 0.55
Fecal indicator bacteria log10 exchangeable Location_type U 0.39 0.11 0.17 0.62
Sulfate log10 ar1 Treatment 5BNR 2.26 0.04 2.17 2.35
Sulfate log10 ar1 Treatment A2 1.30 0.08 1.14 1.46
Sulfate log10 ar1 Treatment AS 2.26 0.10 2.06 2.46
Sulfate log10 ar1 Treatment AS + UV 0.89 0.05 0.79 0.99
Sulfate log10 ar1 Treatment EA 1.80 0.08 1.64 1.96
Sulfate log10 ar1 Treatment EA + OD 1.37 0.08 1.21 1.52
Sulfate log10 ar1 Treatment MBR + UV 3.48 0.08 3.32 3.63
Sulfate log10 ar1 Treatment OD 1.15 0.05 1.05 1.26
Sulfate log10 ar1 Treatment TF 1.92 0.09 1.73 2.10
Sulfate log10 ar1 Year 2019 1.78 0.04 1.71 1.86
Sulfate log10 ar1 Year 2020 1.87 0.04 1.79 1.95
Sulfate log10 ar1 Quarter 1 1.81 0.03 1.74 1.88
Sulfate log10 ar1 Quarter 3 1.84 0.03 1.77 1.91
Sulfate log10 ar1 Region N 0.83 0.04 0.74 0.91
Sulfate log10 ar1 Region C 2.20 0.12 1.97 2.44
Sulfate log10 ar1 Region S 2.44 0.03 2.39 2.50
Sulfate log10 ar1 Location_type R 2.22 0.05 2.12 2.32
Sulfate log10 ar1 Location_type U 1.43 0.04 1.35 1.50
Chloride log10 ar1 Treatment 2SND 3.07 0.13 2.80 3.33
Chloride log10 ar1 Treatment 5BNR 2.09 0.25 1.59 2.60
Chloride log10 ar1 Treatment A2 1.71 0.13 1.44 1.97
Chloride log10 ar1 Treatment AS 3.35 0.34 2.67 4.02
Chloride log10 ar1 Treatment AS + UV 1.25 0.15 0.95 1.54
Chloride log10 ar1 Treatment EA 2.10 0.12 1.86 2.34
Chloride log10 ar1 Treatment EA + OD 1.62 0.13 1.36 1.89
Chloride log10 ar1 Treatment MBR + UV 4.03 0.33 3.36 4.70
Chloride log10 ar1 Treatment OD 1.76 0.22 1.32 2.20
Chloride log10 ar1 Treatment TF 2.62 0.13 2.37 2.88
Chloride log10 ar1 Year 2019 2.34 0.10 2.15 2.54
Chloride log10 ar1 Year 2020 2.38 0.10 2.18 2.58
Chloride log10 ar1 Quarter 1 2.36 0.10 2.16 2.56
Chloride log10 ar1 Quarter 3 2.36 0.10 2.16 2.56
Chloride log10 ar1 Region N 1.09 0.13 0.82 1.36
Chloride log10 ar1 Region C 2.55 0.23 2.09 3.01
Chloride log10 ar1 Region S 3.44 0.20 3.05 3.83
Chloride log10 ar1 Location_type R 2.99 0.25 2.50 3.48
Chloride log10 ar1 Location_type U 1.73 0.07 1.58 1.88
pH Original exchangeable Treatment 2SND 7.30 0.21 6.88 7.72
pH Original exchangeable Treatment 5BNR 6.72 0.10 6.52 6.92
pH Original exchangeable Treatment A2 7.50 0.29 6.93 8.07
pH Original exchangeable Treatment AS 5.54 0.26 5.01 6.06
pH Original exchangeable Treatment AS + UV 6.65 0.28 6.09 7.21
pH Original exchangeable Treatment EA 6.66 0.27 6.13 7.19
pH Original exchangeable Treatment EA + OD 4.58 0.29 4.01 5.16
pH Original exchangeable Treatment MBR + UV 7.06 0.22 6.61 7.50
pH Original exchangeable Treatment OD 7.67 0.36 6.96 8.39
pH Original exchangeable Treatment TF 7.12 0.22 6.69 7.56
pH Original exchangeable Year 2019 6.67 0.11 6.45 6.89
pH Original exchangeable Year 2020 6.69 0.11 6.47 6.91
pH Original exchangeable Quarter 1 6.72 0.11 6.50 6.94
pH Original exchangeable Quarter 3 6.64 0.12 6.41 6.87
pH Original exchangeable Region N 6.27 0.16 5.96 6.59
pH Original exchangeable Region C 6.60 0.22 6.16 7.04
pH Original exchangeable Region S 7.17 0.17 6.83 7.50
pH Original exchangeable Location_type R 6.85 0.32 6.21 7.49
pH Original exchangeable Location_type U 6.51 0.15 6.22 6.80