Supplemental Digital Content 2
MIXED-EFFECTS REGRESSION MODELS
The main multiple mixed-effects regression models can be summarized as follows:
Multi-level models vs. Composite models Eq.
1.1-1.4 Yij
0i
1iTimeij
iji l
k
ik ij k
a a
i X Z 0
1 0 0
00
0
i n
m
im ij m
a a
i
X Z
11 1 1
10
1
) (
0 11 1
1 10
1 0 0
00
ij ij i i
ij n
m m im
ij ij a a ij
l k
ik k aij
a ij
Time Time Z
Time X Time
Z X
Y
Where Yij is the outcome (eGFR) for each individual “i” and visit “j”;
0iis the level-1 intercept forindividual i;
1iis the level-1 slope for individual i;
00is the level-2 intercept of the random intercepti
0 ;
10is the level-2 intercept of the slope
1i;Z
ikis a vector of fixed covariates for each individual i that are used to predict level-1 intercepts and slopes and included baseline age (Agebase) among othercovariates. Xija, represents the main predictor variables (PGD and PRD);
0i and
1iare level-2disturbances;
ijis the within-person level-1 disturbance. Of primary interest are the main effects of each exposure Xa (γ0a) and their interaction with TIME (γ1a), as described in a previous methodological paper.
(55)
Table S1. Crude association of baseline, follow-up and annual rate of change in eGFR with continuous summation scores on EOD, PRD and PGD, stratifying by sex and race; HANDLS 2004-2013
Baseline eGFR Follow-up eGFR Annual rate of change in eGFR
r P-
value r P-value r P-value
EOD summation score
Overall +0.062* 0.013 +0.066* 0.008 +0.011 0.65
White women -0.012 0.80 -0.010 0.85 +0.004 0.94
White men +0.223* <0.001 +0.205* <0.001 +0.005 0.94
AA women +0.089* 0.034 +0.072 0.088 -0.012 0.78
AA men +0.049 0.34 +0.091 0.071 +0.053 0.29
PRD summation score
Overall +0.013 0.60 +0.010 0.69 -0.004 0.87
White women +0.001 0.99 +0.067 0.20 +0.086 0.092
White men +0.048 0.44 +0.087 0.15 +0.076 0.21
AA women -0.083* 0.048 -0.151* <0.001 -0.090* 0.032
AA men -0.084 0.097 -0.029 0.56 +0.060 0.24
PGD summation score
Overall -0.028 0.25 -0.015 0.55 +0.015 0.54
White women -0.075 0.15 +0.013 0.80 +0.11* 0.031
White men -0.038 0.53 -0.004 0.94 +0.046 0.45
AA women -0.089* 0.034 -0.148* <0.001 -0.078 0.064
AA men -0.069 0.17 +0.005 0.93 +0.085 0.095
Abbreviations: AA=African-American; eGFR=Estimated Glomerular Filtration Rate;
EOD=EveryDay experience of Discrimination scale; PGD=Perceived gender discrimination scale PRD=Perceived racial discrimination scale; r=Pearson’s correlation coefficient.
*P<0.05 for null hypothesis that r=0.
Table S2. Follow-up eGFR by perceived racial/gender discrimination (PRD, PGD), overall and by sex×race: Ordinary Least Square regression models.
Models N
Model 1
Model 2
Model 3
Model 4
β(SE) P β(SE) P β(SE) P β(SE) P
Overall 1,616
Model A: PRD
PRD (Medium vs. low) -1.48(1.07) 0.17 -1.52(1.07) 0.16 -1.49(1.08) 0.17 -1.46(1.08) 0.18
PRD (High vs. low) -2.07(1.39) 0.14 -2.13(1.41) 0.13 -2.17(1.42) 0.13 -2.23(1.42) 0.11
Model B: PGD
PGD (Medium vs. low) -0.88(0.98) 0.37 -0.91(0.99) 0.36 -0.90(0.99) 0.36 -1.00(0.99) 0.31
PGD (High vs. low) -2.81(1.42) 0.045 -2.86(1.43) 0.046 -2.93(1.45) 0.043 -3.03(1.45) 0.036
White women 381
Model A: PRD
PRD (Medium vs. low) -0.36(2.38) 0.88 -0.51(2.40) 0.83 -0.24(2.40) 0.92 -0.58(2.40) 0.81
PRD (High vs. low) +1.84(5.26) 0.73 +1.90(5.31) 0.72 +1.63(5.35) 0.76 +1.59(5.33) 0.77
Model B: PGD
PGD (Medium vs. low) +0.28(1.89) 0.87 +0.07(1.92) 0.97 +0.17(1.93) 0.93 -0.28(1.94) 0.88
PGD (High vs. low) -0.23(2.78) 0.93 -0.49(2.80) 0.86 -0.30(2.83) 0.92 -0.71(2.83) 0.80
White men 278
Model A: PRD
PRD (Medium vs. low) +4.02(2.05) 0.051 +4.13(2.04) 0.045 +4.33(2.07) 0.037 +4.09(2.08) 0.050
PRD (High vs. low) -1.87(4.56) 0.68 -1.95(4.59) 0.67 -1.00(4.60) 0.83 -1.44(4.62) 0.76
Model B: PGD
PGD (Medium vs. low) -0.29(1.95) 0.88 -0.01(1.95) 0.99 -0.73(1.94) 0.71 -0.62(1.95) 0.75
PGD (High vs. low) -5.01(5.40) 0.35 -5.61(5.38) 0.30 -5.19(5.47) 0.34 -5.31(5.48) 0.33
AA women 565
Model A: PRD
PRD (Medium vs. low) -4.02(1.82) 0.027 -4.27(1.81) 0.021 -4.03(1.87) 0.032 -3.91(1.87) 0.037
PRD (High vs. low) -3.92(2.28) 0.086 -3.98(2.34) 0.090 -3.65(2.39) 0.13 -3.46(2.40) 0.15 Model B: PGD
PGD (Medium vs. low) -3.66(1.80) 0.042 -3.82(1.82) 0.036 -3.58(1.84) 0.051 -3.61(1.84) 0.050 PGD (High vs. low) -4.66(2.51) 0.063 -4.79(2.55) 0.061 -4.45(2.60) 0.087 -4.38(2.60) 0.093
AA men 392
Model A: PRD
PRD (Medium vs. low) +0.83(2.29) 0.72 +0.83(2.29) 0.72 +0.86(2.29) 0.71 +0.85(2.30) 0.71
PRD (High vs. low) +0.62(2.49) 0.80 +0.62(2.49) 0.80 -0.22(2.49) 0.93 -0.19(2.49) 0.94
Model B: PGD
PGD (Medium vs. low) +3.50(2.09) 0.095 +3.35(2.11) 0.11 +3.15(2.10) 0.14 +3.20(2.10) 0.13
PGD (High vs. low) +0.22(2.77) 0.94 -0.01(2.76) 0.99 -0.93(2.77) 0.74 -1.02(2.76) 0.71
Note: Selected participants with preserved kidney function. PRD and PGD are coded as 2=High, 1=Medium, 0=Low were entered separately in models A or B. For instance PGD10 refers to Medium PGD contrasted with Low PGD. Model 1: adjusted for inverse mills ratio, age, sex and race; Model 2: further adjusted for poverty status, marital status and educational level; Model 3: further adjusted for current smoking status and illicit drug use, BMI, self-rated health and elevated depressive symptoms; Model 4: further adjusted for diabetes and hypertension.
a In a separate model with sex×race (0=White women vs. each of the other categories), sex×race, sex×race×PRDk0 (or sex×race×PGDk0), in addition to the other covariates in each model, p<0.05 for the null hypothesis that the term sex×race×PRDk0=0 , where k=1 for Medium and k=2 for High contrasted with 0=Low.
Table S3. Follow-up eGFR by perceived everyday discrimination (EOD), overall and by sex×race: Ordinary Least Square regression models.
55 N Model 1 Model 2 Model 3 Model 4
β(SE) P β(SE) P β(SE) P β(SE) P
Overall 1,616
EOD (Medium vs. low) +0.34(1.02) 0.74 +0.33(1.02) 0.75 +0.33(1.03) 0.75 +0.34(1.03) 0.74
EOD (High vs. low) -0.16(1.27) 0.90 -0.13(1.27) 0.92 -0.15(1.29) 0.91 -0.16(1.29) 0.90
White women 381
EOD (Medium vs. low) -0.07(1.93) 0.97 -0.17(1.95) 0.93 +0.40(2.03) 0.85 +0.38(2.02) 0.85
EOD (High vs. low) -3.62(2.64) 0.17 -3.86(2.66) 0.15 -2.63(2.77) 0.34 -3.23(2.76) 0.25
White men 278
EOD (Medium vs. low) +0.01(1.67) 1.00 -0.14(1.68) 0.93 -0.83(1.73) 0.63 -0.97(1.73) 0.58
EOD (High vs. low) +1.94(2.23) 0.39 +1.05(2.25) 0.64 +0.65(2.30) 0.78 +0.37(2.33) 0.87
AA women 565
EOD (Medium vs. low) +0.27(1.89) 0.89 +0.51(1.91) 0.79 +0.83(1.93) 0.67 +0.76(1.93) 0.69
EOD (High vs. low) +0.79(2.46) 0.75 +1.20(2.48) 0.63 +1.78(2.53) 0.48 +1.77(2.53) 0.48
AA men 392
EOD (Medium vs. low) +1.58(2.29) 0.49 +1.42(2.29) 0.54 +0.68(2.33) 0.77 +0.76(2.33) 0.75
EOD (High vs. low) +1.28(2.45) 0.60 +1.58(2.45) 0.52 +0.94(2.45) 0.70 +0.88(2.45) 0.72
Note: Selected participants with preserved kidney function. EOD is coded as 2=High, 1=Medium, 0=Low. For instance, EOD10 refers to Medium EOD contrasted with Low PGD. Model 1: adjusted for inverse mills ratio, age, sex and race; Model 2: further adjusted for poverty status, marital status and educational level; Model 3: further adjusted for current smoking status and illicit drug use, BMI, self-rated health and elevated depressive symptoms; Model 4: further adjusted for diabetes and hypertension.
a In a separate model with sex×race (0=White women vs. each of the other categories), sex×race, sex×race×EODk0, (in addition to the other covariates in each model), p<0.05 for the null hypothesis that the term sex×race× EODk0=0, where k=1 for Medium and k=2 for High contrasted with 0=Low.
SENSITIVITY ANALYSIS
A sensitivity analysis was conducted whereby albumin-to-creatinine ratio was added to the models as an additional covariate and results were compared to the main models (Model 5). In addition, the sensitivity analysis restricted the analytic sample to the participants with complete data on ACR (N=1,158) even in models where ACR was not included as covariate (i.e. Models 1-4). The results of the mixed-effects regression models are presented in Tables S4 and S6 and those of the OLS regression model with follow-up eGFR as the outcome variable are presented in Tables S5 and S7.
Based on Table S4 findings, overall, the new analysis revealed that “Medium vs. High” PRD was inversely related to baseline eGFR (Models 1-5), a finding that was not detected in the initial models. In contrast, among AA women, the inverse relationship between “High vs. Low”
PGD and rate of change in eGFR was no longer detected in Model 1. “High vs. Low” PGD was found to be inversely related to baseline eGFR among AA men in Model 3, unlike in the main analyses which found no effect.
Another key difference between the main analyses and those of the sensitivity analyses (Table S5), is that in the latter there was no significant association between PRD (“Medium vs.
Low”) and follow eGFR among White men in all models, though the direction of the relationship was the same. This indicates a lower statistical power to detect such an association, given the small sample size among White men (N=213). Similarly, the previously detected inverse relationship between PGD and follow-up eGFR among AA men became non-significant in the smaller sample. There was no indication for a mediating effect by ACR.
While no changes were found in the relationships observed between EOD and follow-up eGFR (Table S7), the results of the mixed-effect regression models with EOD as the main predictor showed a few differences with the initial findings, given the reduced sample size. Notably, the inverse relationship between “High vs. Low” EOD and baseline eGFR found among White women was non-significant or marginally significant in models Models 2-5, with no indication for a mediating effect by ACR. Moreover, the positive association between “High vs. Low” EOD and baseline eGFR found among White men in the initial analyses became null in the sensitivity analyses.
Table S4. Sensitivity analyses for mixed-effects regression models with PRD (Models A) or PGD (Models B): overall, and stratified by sex×race
Model 1 Model 2 Model 3 Model 4 Model 5a
Overall (N=1,158) Sig Null Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
PRD -2.71(1.15)p=0.019 -2.58(1.15)
p=0.025 -2.58(1.15) p=0.025 -2.68(1.15)
p=0.020 -2.66(1.15)p=0.021
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
White women (N=289) Sig Null Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
White men (N=213) Sig Null Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PGD -- -- -- -- --
PRD×time -- -- -- -- --
PGD×time -- -- -- -- --
AA women (N=383) Sig Null Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -0.45(0.36)p=0.21 -- -- -- --
Null Sig.
Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
AA men (N=273) Sig Null Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -- -- --
PGD×time -- -- -- -- --
High vs. Low
PRD -- -- -- -- --
PRD×time -- -- -- -- --
PGD -- -- -5.92(3.01)p=0.048 -- --
PGD×time -- -- -- -- --
-- no change in significance was noted between the main analysis and the sensitivity analysis.
a Model 5 included ACR as an additional variable to Model 4. All models had a total sample size of N=1,158 and thus included only participants with complete data on ACR.
Table S5. Sensitivity analysis for OLS regression models with PRD (Models A) or PGD (Models B): overall, and stratified by sex×race
Model 1 Model 2 Model 3 Model 4 Model 5
Overall (N=1,158) Medium vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
High vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
White women (N=289) Medium vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
High vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
White men (N=213) Medium vs. Low Sig Null
PRD +3.82(2.41)p=0.
11 +3.98(2.40)p=0.
10 +3.60(2.46)p=0.
14 +3.05(2.49)p=0.2
2 +2.82(2.47)p=0.26
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
High vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
AA women (N=383) Medium vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
High vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
AA men (N=273) Medium vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- 4.10(2.10)p=0.52 3.94(2.11)p=0.062 -3.83(2.10)p=0.069
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
High vs. Low Sig Null
PRD -- -- -- -- --
PGD -- -- -- -- --
Null Sig.
PRD -- -- -- -- --
PGD -- -- -- -- --
-- no change in significance was noted between the main analysis and the sensitivity analysis.
a Model 5 included ACR as an additional variable to Model 4. All models had a total sample size of N=1,158 and thus included only participants with complete data on ACR.
Table S6. Sensitivity analyses for mixed-effects regression models with EOD: overall, and stratified by sex×race
Model 1 Model 2 Model 3 Model 4 Model 5a
Overall (N=1,158) Sig Null Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
White women (N=289) Sig Null Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -4.21(2.73)p=0.12 -4.89(2.81)p=0.082 -4.92(2.82)p=0.081 -4.85(2.83)p=0.086
EOD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
White men (N=213) Sig Null Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD +2.42(2.36)p=0.31 -- -- -- --
EOD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
AA women (N=383) Sig Null Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
AA men (N=273) Sig Null Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
EOD×time -- -- -- -- --
-- no change in significance was noted between the main analysis and the sensitivity analysis.
a Model 5 included ACR as an additional variable to Model 4. All models had a total sample size of N=1,158 and thus included only participants with complete data on ACR.
Table S7. Sensitivity analysis for OLS regression models with EOD: overall, and stratified by sex×race
.
Model 1 Model 2 Model 3 Model 4 Model 5a
Overall (N=1,158) Sig Null Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
White women (N=289) Sig Null Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
White men (N=213) Sig Null Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
AA women (N=383)
Sig Null Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
AA men (N=273) Sig Null Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
Null Sig.
Medium vs.
Low
EOD -- -- -- -- --
High vs. Low
EOD -- -- -- -- --
-- no change in significance was noted between the main analysis and the sensitivity analysis.
a Model 5 included ACR as an additional variable to Model 4. All models had a total sample size of N=1,158 and thus included only participants with complete data on ACR.