Table 1 Supplementary Appendix 1. Microsoft Excel

Table 1 Supplementary Appendix 1. Microsoft Excel spreadsheet used to derive an eGFR and its standard uncertainty by Monte Carlo simulation.

A

B

D

E

F

G

H

Input quantities: eGFR for female with SCr > 62 μmol/L

1 2

C

Generic terms

3

I

J

K

eGFR calculation with uncertainty

A

B

K

C

D

J

T

Constant 144

SCr μmol/L

SCr units

Constant 0.7

Constant − 1.209

Constant 0.993

Age year

eGFR

GUM u(eGFR)

51.0584

1.4115

eGFR with 1,000,000 MCS trials

MCS eGFR

MCS u(eGFR)

EXCEL macro, refer to footnote

51.0907

1.4141

Calculation equation eGFR=144(SCr×0.011312/0.7)

−1.209

×0.993

age

4

Value

144

100

0.011312

0.700

−1.209

0.993

65.00

5

SD (u)

0.141112

2.00

footnote

0.00000

0.00561

0.00020

0.000791

6

PDF

Normal

Normal

footnote

Normal

Normal

Normal

footnote

7

Trial #

8

1

143.8667

100.1592

0.011312

0.7000

-1.2109

0.9931

64.9989

51.273

9

2

144.1515

100.0235

0.011312

0.7000

-1.2125

0.9935

65.0008

52.772

MCS Maximum

MCS Minimum

10

3

143.9687

96.5883

0.011312

0.7000

-1.2077

0.9929

65.0004

53.045

58.4990

44.9870

11

4

143.9917

101.4594

0.011312

0.7000

-1.2120

0.9932

65.0014

50.679

12

5

144.0467

101.7998

0.011312

0.7000

-1.2120

0.9926

64.9995

48.587

13

6

144.1372

99.7512

0.011312

0.7000

-1.2178

0.9928

64.9993

50.502

14

7

144.1032

98.6442

0.011312

0.7000

-1.2050

0.9930

64.9999

52.104

15

8

143.8384

100.6926

0.011312

0.7000

-1.2083

0.9930

64.9996

50.626

16

9

144.1250

103.3691

0.011312

0.7000

-1.2142

0.9929

65.0004

48.489

17

10

144.3197

101.0362

0.011312

0.7000

-1.2075

0.9929

64.9994

50.260

↓

↓

↓

↓

↓

↓

↓

↓

↓

1000000

143.9099

99.1609

0.011312

0.7000

-1.2027

0.9928

64.9997

51.016

Row 2: column headings which show the generic terms which have been used to describe the various CKD-EPI eGFR equations. Row 3: column headings which show the input variables to the particular eGFR equation. Row 4: the actual numeric values for the stated input variables. Row 5: the standard uncertainty values (as a standard deviation) for the chosen numeric values in row 4. The uncertainty for serum creatinine is obtained from IQC and the values for the creatinine units conversion factor and age are as described in the main text. Using IUPAC atomic mass values with their associated uncertainties, a creatinine conversion factor of 0.01131181 with a standard uncertainty of 0.00000013 is obtained. When age is entered as an ordinal date, with the months and days being converted to a decimal fraction of 365, the uncertainty in the age is ± 0.5 days or 0.5 / 365 = 0.0014 years with a standard uncertainty of 0.000791. Row 6: the probability density function (PDF) which has been used to generate the simulated values in that particular column. A normal (Gaussian) PDF has been chosen for simulations in columns B, C, E, F and G, with a rectangular probability distribution for columns D and H. Rows 8 to 1,000,007, columns B to H: the simulations which represent the distribution of possible values. Column B, rows 8 to 1,000,007: =IF($B$5=0,$B$4,(NORMINV(RAND(),$B$4,$B$5))), Column C, rows 8 to 1,000,007: =IF($C$5=0,$C$4,(NORMINV(RAND(),$C$4,$C$5))),

Column D, rows 8 to 1,000,007: =($D$4−($D$5*SQRT(3)))+(2*($D$5*SQRT(3))*RAND()), Column E, rows 8 to 1,000,007: =IF($E$5=0,$E$4,(NORMINV(RAND(),$E$4,$E$5))), Column F, rows 8 to 1,000,007: =IF($F$4=0,$F$3,(NORMINV(RAND(),$F$3,$F$4))), Column G, rows 8 to 1,000,007: =IF($G$5=0,$G$4,(NORMINV(RAND(),$G$4,$G$5))), Column H, rows 8 to 1,000,007: =($H$4−($H$5*SQRT(3)))+(2*($H$5*SQRT(3))*RAND()), Column I, rows 8 to 1,000,007: the eGFR calculated from the simulated values in that row. The mean and standard deviation of the simulations in column I, rows 8 to 1,000,007, are the estimated eGFR and its standard uncertainty respectively. The arrow (↓) plays no part in the calculations, they has been added to the Table for illustrative purposes only.