Load Packages
Import Data
Create eGFR Difference Groups
Descriptive Statistics
Frequency of eGFR Difference Groups
Summary Table by Group
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 = CysCeGFR - ScreGFR

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.   :-101.82  
##  1st Qu.: -28.26  
##  Median : -17.28  
##  Mean   : -19.51  
##  3rd Qu.: -10.45  
##  Max.   :  36.12

Frequency of eGFR Difference Groups

## 
## Group 1A Group 1B Group 2A Group 2B 
##     1578       73        0       19

## 
##   Group 1A   Group 1B   Group 2A   Group 2B 
## 0.94491018 0.04371257 0.00000000 0.01137725

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 1A N = 1,578¹	Group 1B N = 73¹	Group 2A N = 0¹	Group 2B N = 19¹	p-value²
gender					0.3
F	185 (12%)	8 (11%)	0 (NA%)	0 (0%)
M	1,393 (88%)	65 (89%)	0 (NA%)	19 (100%)
Smoking					0.2
CURRENT	213 (13%)	8 (11%)	0 (NA%)	2 (11%)
FORMER	755 (48%)	29 (40%)	0 (NA%)	6 (32%)
NEVER	610 (39%)	36 (49%)	0 (NA%)	11 (58%)
bmi_group					0.2
Normal	82 (12%)	8 (23%)	0 (NA%)	0 (0%)
Obese	456 (65%)	21 (60%)	0 (NA%)	5 (83%)
Overweight	164 (23%)	5 (14%)	0 (NA%)	1 (17%)
Underweight	4 (0.6%)	1 (2.9%)	0 (NA%)	0 (0%)
¹ n (%)
² Fisher’s exact test

ANOVA: eGFR Difference by Group

Reults: At least one mean is different. In the multiple comparison of means, all pairs of means are significantly different. In this case, since Group 2A has 0 observations, this test for means of eGFR differences among Group 1A, Group 1B, and Group 2B.

##               Df Sum Sq Mean Sq F value Pr(>F)    
## eGFRGroup      2 111083   55541   353.1 <2e-16 ***
## Residuals   1667 262218     157                   
## ---
## 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 1B-Group 1A 30.80464 27.28244 34.32683     0
## Group 2B-Group 1A 50.23909 43.44899 57.02920     0
## Group 2B-Group 1B 19.43446 11.85723 27.01168     0

Compare BMI by eGFR Group

This tests if the mean BMI’s are different for 3 eGFR groups. Results: No significant differences in mean BMI among different groups.

##              Df Sum Sq Mean Sq F value Pr(>F)
## eGFRGroup     2    210  105.18   1.432  0.239
## Residuals   744  54629   73.43               
## 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 among the groups.

##               Df Sum Sq Mean Sq F value Pr(>F)    
## eGFRGroup      2  17147    8573   40.57 <2e-16 ***
## Residuals   1667 352247     211                   
## ---
## 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. This can’t be tested since there are 0’s in the categories.

##    
##     Group 1A Group 1B Group 2A Group 2B
##   F      185        8        0        0
##   M     1393       65        0       19

## 
##  Pearson's Chi-squared test
## 
## data:  gender_table
## X-squared = NaN, df = 3, p-value = NA

Chi-square Test: Smoking by eGFR Group

This tests to see if the smoking and the eGFR group are associated or not. Cannot be tested because of 0’s.

##          
##           Group 1A Group 1B Group 2A Group 2B
##   CURRENT      213        8        0        2
##   FORMER       755       29        0        6
##   NEVER        610       36        0       11

## 
##  Pearson's Chi-squared test
## 
## data:  smoking_table
## X-squared = NaN, df = 6, p-value = NA

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 
## -87.023  -7.710   1.788   8.359  53.783 
## 
## 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	-13.032	4.331
correctedage…6	-0.114	0.043	-2.658	0.008	-0.197	-0.030
genderM	6.240	1.865	3.345	0.001	2.578	9.902
BMI	-0.492	0.067	-7.331	0.000	-0.624	-0.361
SmokingFORMER	4.053	1.643	2.467	0.014	0.828	7.279
SmokingNEVER	5.197	1.682	3.089	0.002	1.894	8.500

Multinomial Logistic Regression

In this model, the outcome variable is eGFRGroup: Group 1A, Group 1B, Group 2B.
This is different model than Linear Regression. Results: all variables are significant. The baseline model is Group 1A.
We can examine the odd ratios. For instance, for every 1-unit increase in BMI, the odds of being in Group 1B rather than Group 1A are estimated to increase by a factor of exp(0.906) = 2.474, holding all other variables fixed.

## # weights:  21 (12 variable)
## initial  value 820.663380 
## iter  10 value 268.194624
## iter  20 value 183.106181
## iter  30 value 152.974601
## final  value 152.858401 
## converged

## Call:
## multinom(formula = eGFRGroup ~ correctedage...6 + gender + BMI + 
##     Smoking, data = multi_data)
## 
## Coefficients:
##          (Intercept) correctedage...6   genderM         BMI SmokingFORMER
## Group 1B    2.909255      -0.06692533 0.8842306 -0.09870523      0.790111
## Group 2B  -12.300964      -0.07205580 7.6232867 -0.06884902      7.454417
##          SmokingNEVER
## Group 1B     1.301076
## Group 2B     6.958546
## 
## Std. Errors:
##          (Intercept) correctedage...6   genderM        BMI SmokingFORMER
## Group 1B    1.468054       0.01200439 0.6532557 0.02659680     0.6696008
## Group 2B    1.019340       0.02285097 1.0209226 0.05467945     0.6330254
##          SmokingNEVER
## Group 1B    0.6572652
## Group 2B    0.7275093
## 
## Residual Deviance: 305.7168 
## AIC: 329.7168

y.level	term	estimate	std.error	statistic	p.value	conf.low	conf.high
Group 1B	(Intercept)	18.343	1.468	1.982	0.048	1.032	325.899
Group 1B	correctedage…6	0.935	0.012	-5.575	0.000	0.914	0.958
Group 1B	genderM	2.421	0.653	1.354	0.176	0.673	8.711
Group 1B	BMI	0.906	0.027	-3.711	0.000	0.860	0.954
Group 1B	SmokingFORMER	2.204	0.670	1.180	0.238	0.593	8.187
Group 1B	SmokingNEVER	3.673	0.657	1.980	0.048	1.013	13.320
Group 2B	(Intercept)	0.000	1.019	-12.068	0.000	0.000	0.000
Group 2B	correctedage…6	0.930	0.023	-3.153	0.002	0.890	0.973
Group 2B	genderM	2045.273	1.021	7.467	0.000	276.529	15127.330
Group 2B	BMI	0.933	0.055	-1.259	0.208	0.839	1.039
Group 2B	SmokingFORMER	1727.476	0.633	11.776	0.000	499.551	5973.711
Group 2B	SmokingNEVER	1052.102	0.728	9.565	0.000	252.814	4378.395

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