The False Precision of Quantitative Imaging

Modern medical imaging increasingly does more than produce pictures. CT, MRI, PET, ultrasound, and other modalities can generate measurements: lesion dimensions, tissue characteristics, standardized uptake values, apparent diffusion coefficients, volumes, densities, and a growing range of imaging biomarkers.

The appeal is obvious. A visual impression can seem subjective. A number appears concrete.

But a value displayed to three decimal places is not necessarily known to three decimal places. The number on the screen is the end of a chain that may include image acquisition, reconstruction, segmentation, calibration, software processing, and operator decisions. Each stage can affect the result.

That is where quantitative imaging can create a subtle kind of false confidence. The calculation may be mathematically exact while the measurement itself remains uncertain.

The US Food and Drug Administration makes this distinction explicit in its guidance on quantitative imaging. It defines precision in terms of agreement among repeated measurements, accuracy in relation to an accepted reference value, and bias as a systematic difference between a quantitative imaging value and the true value. The same guidance distinguishes repeatability, where measurements are made under the same conditions, from reproducibility, where conditions such as the site, device, or operator may change.

These are not interchangeable properties. A measurement can be highly repeatable and still be consistently wrong.

The decimal point is not an uncertainty estimate

Suppose a software package reports a lesion volume as 12.437 cm³. The display suggests extraordinary specificity. Yet the clinically meaningful question is not whether the software can perform arithmetic to three decimal places. It is whether another measurement of the same lesion, under the same or slightly different conditions, would produce a sufficiently similar result.

A scanner may change. A reconstruction method may change. The boundaries selected during segmentation may shift. Even when the underlying biological state has not meaningfully changed, the reported number may move.

This is why measurement science treats the numerical result and its uncertainty as related but distinct pieces of information. NIST notes that uncertainty depends on factors including instrument repeatability, reproducibility over time, the number of measurements, and sources of both random and systematic error. It also distinguishes uncertainty in a particular result from broader properties of a measurement method, such as precision and bias.

In other words, 12.437 is a result. It is not, by itself, a statement about how much confidence should be placed in that result.

Averages can make unstable measurements look stable

Repeated measurements are often summarized into a single value. That can be useful, but the choice of summary matters.

Consider five hypothetical measurements:

9.8, 10.0, 10.1, 10.2, and 14.9

The arithmetic mean is 11.0. The median is 10.1.

Neither result is mathematically wrong. They answer different questions.

The unusually high fifth value pulls the mean upward, while the median remains near the center of the other observations. In a real imaging dataset, that unusual value could represent genuine biological variation, an acquisition problem, a segmentation difference, an artifact, or something else entirely. Statistics alone cannot decide which.

That is why reducing repeated measurements to one summary number can hide the very pattern that needs investigation. Calculating the mean of a set of observations may be a sensible first step, but it should not automatically end the analysis. Checking the median value of the ordered data can reveal whether the apparent center changes substantially when extreme observations have less influence.

This does not make the median inherently superior to the mean. It makes the disagreement between them informative.

The broader quantitative-imaging literature treats technical performance as something that must be characterized through more than a single summary statistic. Work published in Radiology on metrology standards for quantitative imaging biomarkers emphasizes evaluation of properties such as bias, precision, repeatability, and reproducibility, with uncertainty estimates accompanying performance measures.

A clean average can therefore conceal a messy measurement process.

Agreement is not the same as truth

There is another trap. Suppose repeated measurements are tightly clustered:

20.1, 20.2, 20.1, 20.2, 20.1

The consistency looks reassuring. But imagine that a well-established reference value is 22.0.

The measurement system may be precise in the everyday sense of producing similar results repeatedly, yet systematically displaced from the reference. That is bias.

The FDA defines a reference value as a true or accepted value that may come from scientific principles, experimental work by a national or international organization, or collaborative consensus work. It also defines percent bias as bias divided by the true value and expressed as a percentage.

Where a defensible reference value exists, and the scale supports a meaningful relative comparison, expressing the discrepancy proportionally can be useful. A simple percent error calculator can make the arithmetic straightforward.

But even here, context matters.

Not every imaging quantity should be treated as though a percentage comparison is automatically meaningful. The FDA guidance specifically distinguishes ratio variables, where ratios between values are meaningful, from interval variables such as CT Hounsfield units, where differences can be meaningful, but ratios are not.

That distinction is easy to overlook. Saying that one Hounsfield-unit value is “twice” another does not necessarily carry the same mathematical meaning as saying one physical volume is twice another. A percentage can look sophisticated while being conceptually inappropriate.

False precision is not only about too many decimal places. It can also come from using the wrong statistic.

The number is only as good as the measurement system behind it

Quantitative imaging has enormous value precisely because it can move observation toward measurement. But that transition demands more discipline, not less.

A useful quantitative result should provoke several questions:

Was the quantity measured consistently under the same conditions? Does it remain stable when conditions change? Is there a credible reference against which bias can be assessed? Are unusual observations being hidden by an average? Does the chosen statistic actually make sense for the type of measurement being reported?

These questions become especially important when small numerical differences are interpreted as biological change.

The goal, then, is not to distrust numbers. It is to ask more of them.

A result with fewer decimal places but a well-characterized uncertainty may be more informative than a highly specific number whose repeatability, bias, and reproducibility are unknown. A mean may summarize a dataset efficiently, while the median reveals that the distribution deserves another look. A percentage difference from a reference may be helpful, but only when the reference and measurement scale make that comparison defensible.

Quantitative imaging becomes most powerful when numerical output is treated not as the end of interpretation, but as the beginning of a more rigorous question:

How much does this number actually deserve to be trusted?