Chapter 5 — Quantitative Measurement and Operational Definitions

A number is the output of a measurement system

Chapter 4 ended with a useful limit on what geometry can establish. A viewer can show that a segmentation is grossly on the anatomy, and a geometric check can show that two objects have compatible coordinates, but neither result is yet a quantitative measurement. The image may be correctly located and the mask may be correctly represented while the number extracted from them still answers the wrong question. Chapter 5 begins at that boundary: geometric validity is a condition for measurement validity, not a substitute for it.

Consider a feature reported as a precise decimal. It may have been calculated from one reconstruction rather than another, from one segmentation procedure rather than another, on a particular resampling grid, after a particular intensity transformation, and with one implementation’s interpretation of the feature name. The decimal is the last step of that history. It is not a direct property of the tumour, organ, or patient. A quantitative result is an output of a measurement system whose inputs, transformations, estimator, and intended interpretation must be made explicit.

This distinction does not make image-derived measurement futile. It makes the claim more precise. A measurement can be useful when its target is defined, its inputs are appropriate, its processing is reproducible, and its uncertainty is understood for the use being proposed. Radiomics extends the same idea to a large collection of image-derived values; it does not remove the obligations that apply to a volume, diameter, attenuation statistic, or any other simpler measurement.

The chapter therefore follows one argument rather than a catalogue of features. It first follows the path from an image and a region to a measurement table. It then makes the measurement layer explicit: image, mask, geometry, preprocessing, and implementation jointly determine what has been measured, while modelling and inference can only operate on the resulting object. A feature name is then treated as the beginning of an operational definition, not the end of one. The choice of region is developed as a hypothesis about tissue, before agreement statistics distinguish linear association from agreement with the identity line. Paired uncertainty follows, including the reason the subject pair rather than an isolated value is the resampling unit. The chapter closes with longitudinal change, where a difference between two timepoints is itself a derived measurement with a scale- and estimand-compatible absolute error model selected and justified for the intended decision.

The order is deliberate. The next chapter can discuss feature families and texture matrices without pretending that a feature name floats free of its measurement system. The first step is to make that system visible, from the image to the table.

Sources

• Zwanenburg A, Vallières M, Abdalah MA, et al. The Image Biomarker Standardisation Initiative: standardized quantitative radiomics for high-throughput image-based phenotyping. Radiology. 2020;295(2):328-338. doi:10.1148/radiol.2020191145, PMID 32154773, and published full text at PMC7193906.
• Quantitative Imaging Biomarkers Alliance (QIBA), RSNA — official QIBA information.
• QIBA. CT Tumor Volume Change for Advanced Disease, Clinically Feasible Profile. doi:10.1148/qiba/20220721.
• Ye S, Lim JY, Huang W. Statistical considerations for repeatability and reproducibility of quantitative imaging biomarkers. BJR Open. 2022;4(1):20210083. doi:10.1259/bjro.20210083, PMID 36452056.
• Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;1(8476):307-310. doi:10.1016/S0140-6736(86)90837-8, PMID 2868172.
• de Vet HCW, Terwee CB, Knol DL, Bouter LM. When to use agreement versus reliability measures. Journal of Clinical Epidemiology. 2006;59(10):1033-1039. doi:10.1016/j.jclinepi.2005.10.015, PMID 16980142.