December 2, 2023
December 2, 2023

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Charles Moertel 2. The Imprecision of Measurement

Measurement is central to science and medicine, and therefore any imprecision in this critical function can obscure our analyses and interventions. This issue applies to the extensive data we utilize in clinical medicine, including vital statistics (blood pressure, pulse, temperature, etc.), lab tests, physical exams, and radiologic assessments. In the world of oncology, we are particularly attuned to tumor growth and often refer to tumor doubling time. This measurement obviously depends on what point in time one does the assessment and how one defines the issue. Going from one cell to two cells can take but 15-20 minutes, while going from 100 to 200 cells may take some hours. On the other hand, increasing from 1cm to 2cm may take months.

Old assessments depended on one-dimensional estimates, e.g., a doubling was going from a 1cm to a 2cm tumor, but it is obviously a much greater leap to go from 2cm to 4cm. We must appreciate that a tumor is a 3-dimensional entity, approximating a sphere, and the volume of a sphere varies as the cube of the radius (to be exact, (4/3)(pi)r(cubed)—ask your tenth-grader). So if a 1cm tumor contains 1 billion cells, a 2cm tumor has 8 billion cells (1x1x1=1 versus 0.5×0.5×0.5=0.125 and 1/0.125=8). Doubling a 1cm tumor would be going to a size of 1.26cm in diameter.

Operationally, a medical oncologist is usually confronted with a two-dimensional presentation of a tumor, either as a palpable mass or as a visual image on a radiograph. The third dimension, depth, is typically not available. As a result, the standard practice in assessing a tumor has been to measure a pseudo-representation of area, i.e., taking the two largest dimensions of the tumor and multiplying them by each other (ignoring depth). Thus, if a tumor is 1.6cm x 1.9cm = 3.04, and on a follow-up measurement has grown to 1.8cm x 2.0cm = 3.60, this would be an (3.60/3.04=1.18) 18% increase in the size of the tumor. The general practice has been to measure multiple tumors and take an average. In the 1960s and 1970s, a change of 25% or more in either a positive direction (tumor progression) or in a negative direction (tumor regression) was considered meaningful and would engender a treatment change or a feeling of success.

One evening in 1974, Charles Moertel invited and hosted 16 oncologists to a dinner at an Italian restaurant during the annual meeting of the American Society of Clinical Oncology. During the course of a convivial evening, following the antipasto, pasta, chicken parmigiana, wine and cannolis with coffee, he made clear the true reason for the invitations. His assistant brought to each oncologist a set of twelve solid spheres varying in size from 1.8cm to 14.5cm in size. These were considered the sizes usually encountered in normal clinical practice for subcutaneous, lymph nodes, or abdominal masses. They were arranged in random order on a soft cushion, and each of the six smaller “tumors” was covered with a 0.5 inch layer of foam rubber to simulate skin and soft tissue, while the six larger masses had a 1.5 inch layer.

Each of the oncologists was then invited to measure the various tumors using the technique he (I wish I could say “he/she”) usually used in his practice (ruler, tape, caliper). They were unaware that tumors 5 and 6 had the same diameter, as did tumors 7 and 8. Of course, it was appreciated by Moertel as well as the others that the setting and conditions were idealized relative to true clinical conditions, where tumors are generally less accessible, non-spherical, and the patient is not as immobile or compliant as a cushion. Thus, the results should be viewed as conservative or optimal.

The group, on average, underestimated the size of 11 out of 12 of the spheres; this negative bias varied from 1% to 18%. Individual biases were apparent as well—two of the oncologists consistently measured below the group mean. Another observation, also consistent with measurement studies in other fields, was that rounding conventions were apparent—measurements tended to overmeasure to the nearest centimeter or half-centimeter.

Looking at the reproducibility of tumors 5 and 6, the coefficient of variation was 14% across the 16 oncologists, while for tumors 7 and 8 it was 16%. The estimate of the degree of variation on average for the same tumors between two different investigators was 17%.

Recall that we indicated that clinical decisions were based on two measurements of a tumor, one before treatment and one after treatment. It was estimated that the errors based on two measurements, a before measurement and a repeat measurement several months later, that the use of a progression/regression rate of 25% would lead to an error in 25% of the cases, i.e., one-quarter of the time the treatment would be changed inappropriately. In contrast, if a 50% criterion were utilized instead, the error rate would be only 7%.

This study, published in Cancer in 1976 by Moertel and colleagues, had a profound impact on the approach to tumor assessment from that time going forward, which mandated a 50% change for altering the treatment regimen. More recently, other criteria have been developed so this criterion is not necessarily still used.

Alfred I. Neugut, MD, PhD, is a medical oncologist and cancer epidemiologist at Columbia University Irving Medical Center/New York Presbyterian and Mailman School of Public Health in New York. Email: [email protected].

This article is for educational purposes only and is not intended to be a substitute for professional medical advice, diagnosis, or treatment, and does not constitute medical or other professional advice. Always seek the advice of your qualified health provider with any questions you may have regarding a medical condition or treatment.

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