Statistical
Historical MELD-Na arithmetic: logarithms, bounds and rounding
Explore a simplified historical non-dialysis MELD-Na example with fictional laboratory inputs. This is not the current transplant-allocation calculator.
Identify the historical model before calculating
This is a simplified historical MELD-Na arithmetic exercise using fictional inputs and no dialysis. It is not current US allocation software, a transplant-priority assessment or an individual mortality prediction. Dialysis adjustments, exceptions, eligibility and allocation policy are outside this exercise.
Current OPTN MELD calculations differ, including albumin and additional factors. Use the official HRSA calculator and applicable policy for current clinical work. Do not infer transplant eligibility from this example.
The older sodium adjustment uses coefficients 1.32 and 0.033 and a sodium interval of 125–137 mEq/L. Here the rounded base score is bounded to 6–40 before adjustment, and the final result is also rounded and bounded. These choices are explicit teaching conventions, not a claim of complete allocation-policy implementation.
Calculate the bounded historical base score
B2 and B3 use mg/dL for creatinine and bilirubin; B4 is dimensionless INR. Missing, nonnumeric or nonpositive inputs are rejected before model floors are applied. Positive inputs below 1 are floored to 1, and creatinine is capped at 4. LN of a positive value below 1 is mathematically valid; the floor comes from the model, not the logarithm domain.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(MIN(B2:B4)<=0,"Invalid inputs",MAX(6,MIN(40,ROUND(9.57*LN(MAX(1,MIN(4,B2)))+3.78*LN(MAX(1,B3))+11.2*LN(MAX(1,B4))+6.43,0)))))Apply sodium adjustment above a base score of 11
B6 contains the preceding formula. B5 must be positive numeric sodium in mEq/L, then is bounded to 125–137 for this calculation. The initial example yields 24, followed by 29 after adjustment. A floor score is not evidence that a person is healthy.
=IF(COUNT(B5:B6)<>2,"Invalid inputs",IF(OR(B5<=0,B6<6,B6>40,B6<>INT(B6)),"Invalid inputs",MAX(6,MIN(40,IF(B6<=11,B6,ROUND(B6+1.32*(137-MIN(137,MAX(125,B5)))-0.033*B6*(137-MIN(137,MAX(125,B5))),0))))))Try the example
Use the original values or change them to test your understanding.