Accepted answer
The quantity you have reinvented is the reference change value, and for ALT it is roughly 70%. Your 71% rise is therefore sitting exactly on the boundary of significance — which is an unsatisfying answer, but it is the correct one, and the machinery for getting it generalises to everything else you are tracking.
The formula
Two sources of variation stand between you and the truth. Analytical imprecision, CVa, is how much the same sample varies on repeat measurement. Within-subject biological variation, CVi, is how much your true value oscillates around your own set point from day to day. They combine in quadrature, and because you are comparing two measurements rather than one against a fixed point, the combined uncertainty gets multiplied by the square root of two:
RCV = 2^(1/2) × Z × sqrt(CVa² + CVi²)
For a two-sided 95% criterion, Z = 1.96, and 1.414 × 1.96 = 2.77. So:
RCV(95%) = 2.77 × sqrt(CVa² + CVi²)
Worked for ALT
- Analytical CV for a modern ALT assay: about 5%.
- Within-subject biological CV for ALT: about 25%. It is one of the most variable common analytes.
- CVa² + CVi² = 25 + 625 = 650.
- sqrt(650) = 25.5.
- RCV = 2.77 × 25.5 = 70.6%.
So a change of about 71% is the threshold at which you can say, at the 95% level, that something other than noise has happened. Your 24 to 41 is a 70.8% increase. It has landed on the line. The honest interpretation is: probably real, not certainly real, and the way to resolve it is a third draw rather than an argument.
The same arithmetic for the rest of your panel
| Analyte | CVa (typical) | CVi (typical) | RCV 95% | Example: change that just clears it |
| HbA1c | 2% | 1.7% | ~7% | 7.0% → 6.5% (a 7.1% relative fall) |
| Creatinine | 3% | 5% | ~16% | 85 → 99 µmol/L |
| Total cholesterol | 2.5% | 6% | ~18% | 5.5 → 4.5 mmol/L |
| Triglycerides | 4% | 21% | ~59% | 2.4 → 1.0 mmol/L |
| ALT | 5% | 25% | ~71% | 24 → 41 U/L |
| TSH | 5% | 19% | ~54% | 2.0 → 3.1 mIU/L |
| Urine albumin:creatinine | 5% | 30–40% | ~85–110% | Requires roughly a halving or a doubling |
The CV figures above are representative values from published biological-variation databases rather than your lab's actual performance; ask your lab for its own imprecision figures if you want to tighten the analytical term. It will not change much, because for almost every analyte in the table the biological term dominates.
Two things this table immediately explains
First, why triglycerides look like they are on a random walk. With an RCV near 60%, a fall from 2.4 to 1.6 mmol/L — which looks dramatic — is inside the noise for a single pair of draws. This is the single most misread line on a lipid panel.
Second, why HbA1c is the workhorse of this whole area. An RCV of about 7% on a value of 7.0% means a change of half a point is detectable from two measurements. That is an unusually favourable ratio, and it is why the trials use it.
Why three points beat two
Your intuition is right, and the reason is that you stop asking a different question. With two points you are testing a difference, and the uncertainty on a difference carries that factor of the square root of two. With three or more points you can fit a slope, and the uncertainty on a slope falls with the number of observations and with the spread of the time axis, roughly as one over the square root of n for the noise term and inversely with the time span. Practically:
- Two points establish that a change may have occurred. They cannot establish direction of travel, because a single high value could be an excursion.
- Three points spaced over enough time distinguish a step from a trend. If draws 1 and 3 agree and draw 2 is the outlier, you have learned something a two-point comparison would have got backwards.
- Four or more, plotted against time, let you see whether the slope changed when the dose changed — which is usually the question you actually care about.
So for your ALT: draw a third, under standardised conditions, at least six weeks out, no hard training for 48 hours beforehand, and no alcohol for a week. If it comes back near 40 you have a real elevation of modest size to discuss with a clinician. If it comes back at 26 you have learned that draw two was an excursion, which was always the more likely single explanation of a value that is still inside the reference interval.
edited 20 Jul 2025 by bea_castellanos — added the placebo-arm figures
7The RCV table is worth more than every "is this normal" thread combined. – halvard_ness 5 months ago 6Worth adding that ALT reference intervals are themselves contested and 50 U/L is generous by current thinking. – mira_sundqvist 3 months ago 5For triglycerides the CVi is often quoted even higher than 21% in unfasted populations. – forty_two_c 8 months ago add a comment