One trap is the phenomenon of 'regression to the mean'.4 Results within an apparently homogeneous group of patients are likely to lie within the 95% reference range for that measurement. If the same patients are retested at a different time, the pattern of the overall results will look much the same. In a normal distribution, values are bunched around the group mean and progressively 'thin out' further from the mean. However, individual results are likely to have changed, particularly those at the extremes.
The initial results at the extremes are the result of extreme random variability in one direction or the other. The same amount and direction of variability is unlikely to occur on the second measurement in the same individual. Subsequent measurements will therefore move closer to the middle (or 'regress to the mean'). Results from other individuals who initially were closer to the mean may now lie closer to the extremes of the distribution.
This phenomenon can be exploited intentionally or unintentionally in trials that select and treat individuals with high values of a measurement to demonstrate that a treatment is effective. 'Regression to the mean' is one reason why randomised placebo-controlled prospective trials are the gold standard for assessing treatments.
A large difference between two measurements is more likely to be a signal of a true change than the result of the background noise of measurement variability. Similarly, the smaller the total intra-individual variability, the more likely a specific absolute change is a signal. The less likely the observed change is caused by variability, the surer one can be that the change is real.
These three elements are brought together in the concept of the least significant change. To be 80% confident the observed change is real, the change should exceed approximately twice the intra-individual coefficient of variation (CVi) (Box 3). For example:
- A total cholesterol which decreases from 7.0 to 5.6 mmol/L, after starting a statin, is a 20% fall from the initial value. The CVi for total cholesterol is 8% so the least significant change is approximately 16% (2CVi). You can be 80% sure that the 20% change is real rather than apparent.
- A decrease in microalbuminuria from an albumin:creatinine ratio of 5.0 to 2.0 mg/mmol, after starting an ACE inhibitor, is a 60% fall. The total CVi of the albumin:creatinine ratio is 40% so the least significant change is approximately 80% (2CVi). It is likely that this 60% change is apparent rather than real.
Box 1
Normal results in normal people
If the reference range covers 95% of results for a normal population, the chance of a healthy individual having a certain number of normal tests is:
- Two out of two tests 90% (0.95 x 0.95 = 0.90)
- All 20 of 20 tests 36% (0.9520)
Box 2
Coefficient of variation
The coefficient of variation (CV) is calculated as:
CV = standard deviation of the measured value x 100
mean value
Variability is different at different absolute values of the measurement and is usually quoted at a specific clinically relevant value. For example:
CV for plasma sodium 0.8% at 139 mmol/L
CV for plasma bilirubin 6.1% at 10 micromol/L
The coefficient of variation is one way of expressing the variability of biological measurements. Laboratories sometimes also refer to the imprecision of a measurement.
Box 3 Variability and least significant change
a. Least significant change
- The overall variability of the difference between two measurements is greater than the variability of the individual measurements:
- The more confident one wishes to be that the change in a measurement is a signal rather than noise, the greater the change needs to be relative to this:
The z value is used to refer to normally distributed values and describes the distance of a particular value from the mean in numbers of standard deviations (SD). The greater the distance from the mean (the z value) the less likely a result has occurred by chance.
z varies from 1.28 for 80% confidence to 2.6 for 99% confidence.
- Generally 80% confidence is used (z = 1.28):
Least significant change =
This approximates to 2CVi
CVi Intra-individual coefficient of variation
b. Variability of the difference between two measurements
CVi1 = intra-individual coefficient of variation for 1st measurement
CVi2 = intra-individual coefficient of variation for 2nd measurement
Variability of the difference between 2 measurements is
If CVi1 = CVi2 (as measuring the same variable)
then CVi12 + CVi22 = 2CVi12
so the variability of difference
=
=
=