Reference change value: is the difference between two results real?

What the reference change value answers

A population reference interval asks whether one result is unusual for people in general. A serial result asks something narrower: is this person different from how they were? For many measurands each person runs in a band much narrower than the population interval, so a result can move a long way and stay inside the reference interval. The reference change value (RCV) is the tool for that second question. It gives an objective test of whether serial results from one individual differ by more than chance [Fraser, 2011], and for measurands with marked individuality it is the better guide to serial results than the population interval [Díaz-Garzón Marco et al., 2020].

The formula, term by term

In its classic form [Fraser, 2011]:

RCV = √2 × Z × √(CVA² + CVI²)

• CVA, analytical imprecision. The coefficient of variation of the method in your own laboratory, usually taken from internal quality control [Díaz-Garzón Marco et al., 2020]. Use a period long enough to include routine recalibrations and reagent lot changes; a short within-run figure makes the RCV too narrow.
• CVI, within-subject biological variation. How much the measurand varies around a person’s own set point from day to day. Estimates for many measurands are collected and appraised in the [EFLM Biological Variation Database]. CVI is generally constant over time, geography, method, and in health and stable chronic disease [Fraser, 2011], which is why a published value can be used locally.
• √2. Both results carry the same two sources of variation, so the variance of their difference is twice that of one result.
• Z. The number of standard deviations that sets how sure you want to be. The next section covers it.

The result is a percentage of the first value. A difference larger than the RCV is called significant at the chosen probability; a smaller one is consistent with no change in the patient.

Choosing Z

Two values are in common use: 1.96 when any change in either direction matters, and 1.65 when only one direction does [Díaz-Garzón Marco et al., 2020]. The second is not a looser test: it spends all of the same error rate on one side. Use it when the clinical question is already directional, such as a rise in creatinine after a nephrotoxic drug, or a fall in a tumour marker after treatment. Getting the wording of that clinical question right is what decides Z [Fraser, 2011]. Fix it before looking at the second result, not after.

Why a rise and a fall are not the same size

The classic formula gives one number for both directions, which assumes results are normally distributed. Many measurands are closer to log-normal: a doubling and a halving are equally likely, so the limit for a rise is wider than the limit for a fall. The currently recommended calculation works on the log scale and gives an asymmetric pair of limits [Díaz-Garzón Marco et al., 2020]:

σ = √ln(CVT² + 1), with CVT² = CVA² + CVI² (as fractions)

rise limit = exp(+Z × √2 × σ) − 1; fall limit = exp(−Z × √2 × σ) − 1

In simulation, this log-normal RCV performed best when data were log-normal or when CVI was below about 12%, and the authors advise against the standard calculation when working with coefficients of variation [Røraas et al., 2016]. For small CVs the two forms are close; the gap grows with CV.

A worked example

Take serum creatinine with the CVI the calculator uses, 5.0% [Thöni et al., 2022], and an analytical CV of 3%, assumed here for illustration (use your own quality-control figure). Combined, CVT is 5.83%.

• Two-sided, Z = 1.96: the classic RCV is ±16.2%. The log-normal limits are +17.5% for a rise and −14.9% for a fall.
• One-sided, Z = 1.65: +14.6% for a rise and −12.7% for a fall.

A patient goes from 80 to 92 µmol/L, a change of +15.0%. Asked as “has it changed in either direction?”, that is inside the limit: not a significant change. Asked as “has it risen?”, decided before the second result was seen, it is outside the limit: a significant change. Same numbers, different question, different answer: that is why Z belongs to the question and not to the result.

When the method changed between the two results

The RCV assumes both results came from the same measurement procedure. If the laboratory changed analyser, method or calibration between them, the difference now contains a third component: the systematic difference between the old and new procedures. That bias is not noise. It applies to every patient in the same direction, so it cannot be absorbed by widening the limits; it has to be taken out.

Where the method comparison gives the new procedure’s bias against the old at the relevant concentration, divide the second result by one plus that bias before testing. In the example, if the new analyser reads 5% higher, the +15.0% change becomes +9.5% in the patient. Two-sided, that is inside the limit: not a significant change; asked as a rise, it is inside the limit: not a significant change. Uncorrected, the method change alone was enough to make the rise look significant.

Two cautions. The bias has to be the bias at that patient’s concentration, read off the comparison line, not the average across the range: the guide to method comparison regression covers how to get it. And the bias estimate has its own uncertainty, which a single corrected test does not carry; a result that only just crosses the limit after correction deserves a repeat on the new method before anyone acts on it.

Where the RCV misleads

• One CVI for everyone. The RCV assumes all individuals share the same within-subject variation and needs a robust, representative CVI for the population it is used in [Díaz-Garzón Marco et al., 2020]. Some patient groups vary more than the healthy volunteers most estimates come from.
• Uncontrolled pre-analytical conditions. Biological variation studies standardise collection and handling; routine samples often do not, so the RCV can be too strict and call a change significant when it is not [Díaz-Garzón Marco et al., 2020].
• More than two results. The formula compares two results. A trend over several is a different calculation, and repeating the two-result test across a series inflates false alarms.
• Calculated values. For a derived quantity such as eGFR, the variation of the input moves through the equation. One meta-analysis puts a minimum conservative RCV for eGFR at ±12.5% [Thöni et al., 2022]; the guide to eGFR after a creatinine bias sets a method change against that figure.

The RCV is also distinct from the question of how many results cross a fixed decision limit after a change. That is a count over a population, set against repeat testing; the guide to crossings by chance covers it.

Try it on your own results

The free RCV calculator runs this calculation in your browser: enter two results, your CVA and a CVI (presets are given with their sources), choose any change, a rise or a fall, and optionally a known method bias between the two results. It gives the classic and log-normal limits and whether the change exceeds them.

If the reason you are asking is an analyser change, the bias that the calculator needs comes from your method comparison. The change check reads your paired results in the browser and gives the bias at each of your decision lines and how many results crossed each one, so the correction is grounded in your own data.

Sources

1. Fraser CG (2011). Reference change values. Clinical Chemistry and Laboratory Medicine. doi.org/10.1515/cclm.2011.733
2. Díaz-Garzón Marco J, Fernández-Calle P, Ricós C (2020). Models to estimate biological variation components and interpretation of serial results: strengths and limitations. Advances in Laboratory Medicine. pmc.ncbi.nlm.nih.gov/articles/PMC10270238/
3. Røraas T, Støve B, Petersen PH, Sandberg S (2016). Biological variation: the effect of different distributions on estimated within-person variation and reference change values. Clinical Chemistry. doi.org/10.1373/clinchem.2015.252296
4. European Federation of Clinical Chemistry and Laboratory Medicine. EFLM Biological Variation Database. biologicalvariation.eu. biologicalvariation.eu/
5. Thöni S, Keller F, Denicolò S, et al. (2022). Biological variation and reference change value of the estimated glomerular filtration rate in humans: a systematic review and meta-analysis. Frontiers in Medicine. pmc.ncbi.nlm.nih.gov/articles/PMC9583397/