Can Every Calculated BAC Use the Same Percentage Uncertainty?

No. A percentage uncertainty calculated for one drinking scenario cannot automatically be applied to every calculated BAC. Searle’s 2015 technical analysis showed that uncertainty depends on the inputs and on how much estimated elimination is subtracted from the initial concentration. A precise-looking calculation can have substantially different uncertainty at different times.

This concerns uncertainty in an estimate derived from a drinking history, not simply the analytical uncertainty of a laboratory blood test. The two should remain separate in DUI evidence.

What the original analysis examined

The paper derived error-propagation expressions for two uses of a Widmark-style dilution model: estimating concentration from drinking history and estimating drink volume from a measured concentration. It reworked published numerical examples and examined inconsistencies in commonly cited distribution-factor tables.

This was original mathematical analysis, not a new alcohol-dosing or driving trial. Its conclusions are conditional on the model, input distributions and relationships assumed.

Why the percentage can increase as calculated BAC falls

A simple dose-based model first estimates the concentration that would exist without elimination, then subtracts the amount assumed eliminated over time. When those two large quantities nearly cancel, the remaining concentration can be small while substantial uncertainty remains in the quantities used to calculate it.

Relative uncertainty divides uncertainty by the estimated result. It can therefore become very large near zero. That behavior is not proof that a negative alcohol concentration is biologically possible or that extending a straight line through zero is valid.

Searle reproduced an example yielding a calculated 114 mg/100 mL and a coefficient of variation of approximately 21%. The point was that this percentage belonged to that example. It was not a universal allowance applicable after a different elapsed time or to a different drinking history.

Which uncertain inputs matter?

Potential inputs include beverage volume and strength, the proportion absorbed, the distribution factor, elimination rate and elapsed time. A controlled laboratory dose may have accurately known volume and timing; a reconstructed social-drinking history may not.

The analysis also included an assumed relationship between distribution factor and elimination rate. Dependencies between inputs matter: treating all uncertainties as independent can change the calculated uncertainty. The paper’s illustrative values are assumptions to evaluate, not biological constants known for a defendant.

Body mass and ethanol density were treated as sufficiently precise to omit their contributions in the examples. That simplification should not be copied where the available body measurement or other inputs are uncertain.

A coefficient of variation is not a guaranteed interval

A coefficient of variation expresses standard deviation relative to a mean. Doubling it does not automatically produce a valid confidence statement under every model or circumstance. Distribution assumptions, nonlinearity, boundaries and the quality of the input evidence remain relevant.

Error propagation also cannot fix a structurally wrong model. If absorption is incomplete, the drink history is mistaken or elimination stopped after concentration reached zero, attaching a percentage margin does not establish that the reconstructed BAC is reliable.

Concentration and drink-count calculations differ

Calculating a drink volume from a later alcohol result reverses the model and changes how the inputs contribute. An uncertainty percentage from a forward BAC calculation cannot simply be transferred to the estimated number of drinks.

The starting specimen must also be clear. Whole-blood BAC, serum/plasma alcohol, breath, urine and biomarkers are not interchangeable inputs. Conversion assumptions, when applicable, introduce additional questions that this mathematical framework does not remove.

What to request in a DUI report

Ask for the equation, source and units of each input, which values were measured, which were assumed, and how the uncertainty was obtained. Determine whether the stated percentage is specific to the actual scenario or borrowed from an unrelated example.

This is more specific than the general question of whether BAC extrapolation assumptions are justified. Here the issue is whether a numerical uncertainty claim follows from the calculation itself. Neither a fixed margin nor a case-specific interval turns an estimate into an earlier measurement or establishes person-specific impairment.

Primary technical source

Searle J. Alcohol calculations and their uncertainty. Medicine, Science and the Law. 2015;55(1):58–64. https://doi.org/10.1177/0025802414524385.