Load Packages
Import Data
Create eGFR Difference Groups
Descriptive Statistics
Frequency of eGFR Difference Groups
Summary Table by Group
Paired t-test: ScreGFR vs CysCeGFR
ANOVA: eGFR Difference by Group
Compare BMI by eGFR Group
Compare Age by eGFR Group
Chi-square Test: Gender by eGFR Group
Chi-square Test: Smoking by eGFR Group
Linear Regression Model
Multinomial Logistic Regression
Scatterplot: ScreGFR vs CysCeGFR
Boxplot: BMI by eGFR Group
Boxplot: Age by eGFR Group
Histogram of eGFR Difference

Load Packages

Import Data

##  [1] "patientname"             "lastfour"               
##  [3] "patientsid"              "gender"                 
##  [5] "CysCLabDate"             "correctedage...6"       
##  [7] "LabChemResultValue...7"  "CysCeGFR"               
##  [9] "ScrLabDate"              "correctedage...10"      
## [11] "LabChemResultValue...11" "ScreGFR"                
## [13] "eGFRDifference"          "Smoking"                
## [15] "BMI"

Create eGFR Difference Groups

eGFRDifference = ScreGFR - CysCeGFR

Descriptive Statistics

##  correctedage...6      BMI           CysCeGFR          ScreGFR       
##  Min.   : 20.00   Min.   :14.14   Min.   :  7.796   Min.   :  4.627  
##  1st Qu.: 62.00   1st Qu.:27.54   1st Qu.: 23.818   1st Qu.: 38.629  
##  Median : 73.00   Median :33.51   Median : 37.938   Median : 57.287  
##  Mean   : 69.13   Mean   :34.34   Mean   : 42.954   Mean   : 62.468  
##  3rd Qu.: 78.00   3rd Qu.:40.83   3rd Qu.: 57.010   3rd Qu.: 85.361  
##  Max.   :101.00   Max.   :97.60   Max.   :121.296   Max.   :154.002  
##  eGFRDifference  
##  Min.   :-36.12  
##  1st Qu.: 10.45  
##  Median : 17.28  
##  Mean   : 19.51  
##  3rd Qu.: 28.26  
##  Max.   :101.82

Frequency of eGFR Difference Groups

## 
##   Group 1: <10 Group 2: 10-30   Group 3: >30 
##            349            950            371

## 
##   Group 1: <10 Group 2: 10-30   Group 3: >30 
##      0.2089820      0.5688623      0.2221557

Summary Table by Group

Body Mass Index (BMI) is categorized as: Underweight (< 18.5), Normal weight (18.5–24.9), Overweight (25.0–29.9), and Obese (30.0 or higher)

Characteristic	Group 1: <10 N = 349¹	Group 2: 10-30 N = 950¹	Group 3: >30 N = 371¹	p-value²
gender				<0.001
F	21 (6.0%)	107 (11%)	65 (18%)
M	328 (94%)	843 (89%)	306 (82%)
Smoking				0.3
CURRENT	35 (10%)	134 (14%)	54 (15%)
FORMER	166 (48%)	446 (47%)	178 (48%)
NEVER	148 (42%)	370 (39%)	139 (37%)
bmi_group
Normal	22 (14%)	54 (13%)	14 (8.3%)
Obese	87 (57%)	261 (61%)	134 (79%)
Overweight	42 (27%)	108 (25%)	20 (12%)
Underweight	2 (1.3%)	2 (0.5%)	1 (0.6%)
¹ n (%)
² Pearson’s Chi-squared test; NA

Paired t-test: ScreGFR vs CysCeGFR

Results: There is significance in mean difference between SCreGFR and CysCeGFR.

## 
##  Paired t-test
## 
## data:  paired_data$ScreGFR and paired_data$CysCeGFR
## t = 53.609, df = 1669, p-value < 2.2e-16
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  18.90153 20.33714
## sample estimates:
## mean difference 
##        19.61933

ANOVA: eGFR Difference by Group

Reults: At least one mean is different. In the multiple comparsions of means, all pairs of means are significantly different.

##               Df Sum Sq Mean Sq F value Pr(>F)    
## eGFRGroup      2 212917  106459    1107 <2e-16 ***
## Residuals   1667 160384      96                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = eGFRDifference ~ eGFRGroup, data = anova_data)
## 
## $eGFRGroup
##                                 diff      lwr      upr p adj
## Group 2: 10-30-Group 1: <10 12.06474 10.62450 13.50497     0
## Group 3: >30-Group 1: <10   33.50267 31.78686 35.21849     0
## Group 3: >30-Group 2: 10-30 21.43794 20.02928 22.84660     0

Compare BMI by eGFR Group

This tests if the mean BMI’s are different for 3 eGFR groups. Results: At least one mean BMI is different.

##              Df Sum Sq Mean Sq F value   Pr(>F)    
## eGFRGroup     2   2766    1383   19.76 4.36e-09 ***
## Residuals   744  52074      70                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 923 observations deleted due to missingness

Compare Age by eGFR Group

This tests if the mean ages are different for 3 eGFR groups. Results: At least one mean age is different.

##               Df Sum Sq Mean Sq F value   Pr(>F)    
## eGFRGroup      2   8689    4345   20.08 2.42e-09 ***
## Residuals   1667 360704     216                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Chi-square Test: Gender by eGFR Group

This tests to see if the gender and the eGFR group are associated or not. Results: Gender and eGFR group are significantly associated.

##    
##     Group 1: <10 Group 2: 10-30 Group 3: >30
##   F           21            107           65
##   M          328            843          306

## 
##  Pearson's Chi-squared test
## 
## data:  gender_table
## X-squared = 23.466, df = 2, p-value = 8.024e-06

Chi-square Test: Smoking by eGFR Group

This tests to see if the smoking and the eGFR group are associated or not. Results: Smoking and eGFR group are not significantly associated using a significance level of 5%.

##          
##           Group 1: <10 Group 2: 10-30 Group 3: >30
##   CURRENT           35            134           54
##   FORMER           166            446          178
##   NEVER            148            370          139

## 
##  Pearson's Chi-squared test
## 
## data:  smoking_table
## X-squared = 4.9614, df = 4, p-value = 0.2913

Linear Regression Model

We fit the model with outcome variable eGFRDifference against the variables: age, gender, BMI, smoking. Results: All variables are highly significant. However, we cannot rely on this model since the model fit is poor.

## 
## Call:
## lm(formula = eGFRDifference ~ correctedage...6 + gender + BMI + 
##     Smoking, data = reg_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -53.783  -8.359  -1.788   7.710  87.023 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       4.35051    4.42195   0.984 0.325513    
## correctedage...6  0.11357    0.04272   2.658 0.008025 ** 
## genderM          -6.24007    1.86541  -3.345 0.000864 ***
## BMI               0.49240    0.06717   7.331    6e-13 ***
## SmokingFORMER    -4.05322    1.64302  -2.467 0.013853 *  
## SmokingNEVER     -5.19722    1.68242  -3.089 0.002082 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.13 on 741 degrees of freedom
##   (923 observations deleted due to missingness)
## Multiple R-squared:  0.08589,    Adjusted R-squared:  0.07972 
## F-statistic: 13.92 on 5 and 741 DF,  p-value: 5.024e-13

term	estimate	std.error	statistic	p.value	conf.low	conf.high
(Intercept)	4.351	4.422	0.984	0.326	-4.331	13.032
correctedage…6	0.114	0.043	2.658	0.008	0.030	0.197
genderM	-6.240	1.865	-3.345	0.001	-9.902	-2.578
BMI	0.492	0.067	7.331	0.000	0.361	0.624
SmokingFORMER	-4.053	1.643	-2.467	0.014	-7.279	-0.828
SmokingNEVER	-5.197	1.682	-3.089	0.002	-8.500	-1.894

Multinomial Logistic Regression

In this model, the outcome variable is eGFRGroup: Group 1:<10, Group 2: 11-30, Group 3:>30.
This is different model than Linear Regression. Results: all variables are significant. The baseline model is Group 1.
We can examine the odd ratios. For instance, for every 1-unit increase in BMI, the odds of being in Group 2 rather than Group 1 are estimated to increase by a factor of exp(1.035) = 2.815, holding all other variables fixed.

## # weights:  21 (12 variable)
## initial  value 820.663380 
## iter  10 value 708.910142
## final  value 707.280693 
## converged

## Call:
## multinom(formula = eGFRGroup ~ correctedage...6 + gender + BMI + 
##     Smoking, data = multi_data)
## 
## Coefficients:
##                (Intercept) correctedage...6    genderM        BMI SmokingFORMER
## Group 2: 10-30 -0.05562948      0.013359042 -0.4626742 0.03450049    -0.6398211
## Group 3: >30   -1.59626203      0.005026133 -1.0057590 0.08139553    -0.5344605
##                SmokingNEVER
## Group 2: 10-30   -0.6461488
## Group 3: >30     -0.8028115
## 
## Std. Errors:
##                (Intercept) correctedage...6   genderM        BMI SmokingFORMER
## Group 2: 10-30   0.8723055      0.007873574 0.4035706 0.01370456     0.3323751
## Group 3: >30     1.0051243      0.009272391 0.4322174 0.01591294     0.3904649
##                SmokingNEVER
## Group 2: 10-30    0.3392302
## Group 3: >30      0.3999041
## 
## Residual Deviance: 1414.561 
## AIC: 1438.561

y.level	term	estimate	std.error	statistic	p.value	conf.low	conf.high
Group 2: 10-30	(Intercept)	0.946	0.872	-0.064	0.949	0.171	5.228
Group 2: 10-30	correctedage…6	1.013	0.008	1.697	0.090	0.998	1.029
Group 2: 10-30	genderM	0.630	0.404	-1.146	0.252	0.285	1.389
Group 2: 10-30	BMI	1.035	0.014	2.517	0.012	1.008	1.063
Group 2: 10-30	SmokingFORMER	0.527	0.332	-1.925	0.054	0.275	1.012
Group 2: 10-30	SmokingNEVER	0.524	0.339	-1.905	0.057	0.270	1.019
Group 3: >30	(Intercept)	0.203	1.005	-1.588	0.112	0.028	1.453
Group 3: >30	correctedage…6	1.005	0.009	0.542	0.588	0.987	1.023
Group 3: >30	genderM	0.366	0.432	-2.327	0.020	0.157	0.853
Group 3: >30	BMI	1.085	0.016	5.115	0.000	1.051	1.119
Group 3: >30	SmokingFORMER	0.586	0.390	-1.369	0.171	0.273	1.260
Group 3: >30	SmokingNEVER	0.448	0.400	-2.008	0.045	0.205	0.981

Scatterplot: ScreGFR vs CysCeGFR

Boxplot: BMI by eGFR Group

Boxplot: Age by eGFR Group

Histogram of eGFR Difference

ScreGFR and CysCeGFR Analysis

Steve Chung, Ph.D

2026-06-14