© 1999 by Oxford University Press
Journal of the National Cancer Institute, Vol. 91, No. 6, 523-528,
March 17, 1999
© 1999 Oxford University Press
ARTICLES |
Measuring Response in Solid Tumors: Unidimensional Versus Bidimensional Measurement
Affiliations of authors: K. James, E. Eisenhauer, A. Muldal, National Cancer Institute of Canada Clinical Trials Group, Queen's University, Kingston, ON, Canada; M. Christian, Cancer Therapy Evaluation Program, National Cancer Institute (NCI), Bethesda, MD; M. Terenziani, Division of Medical Oncology, NCI, Milan, Italy; D. Vena, The Emmes Corporation, Rockville, MD; P. Therasse, European Organization for Research and Treatment of Cancer, Data Center, Brussels, Belgium.
Correspondence to: Keith James, M.A., M.B., F.R.C.R., National Cancer Institute of Canada Clinical Trials Group, Queen's University, 82-84 Barrie St., Kingston, ON K7L 3N6, Canada (e-mail: jamesk{at}ncic.ctg.queensu.ca).
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ABSTRACT |
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BACKGROUND: Tumor shrinkage is a common end point used in screening new cytotoxic agents. The standard World Health Organization criterion for partial response is a 50% or more decrease in the sum of the products of two measurements (the maximum diameter of a tumor and the largest diameter perpendicular to this maximum diameter) of individual tumors. However, theoretically, the simple sum of the maximum diameters of individual tumors is more linearly related to cell kill than is the sum of the bidimensional products. It has been hypothesized that the calculation of bidimensional products is unnecessary, and a 30% decrease in the sum of maximum diameters of individual tumors (assuming spherical shape and equivalence to a 50% reduction in the sum of the bidimensional products) was proposed as a new criterion. We have applied the standard response and the new response criteria to the same data to determine whether the same number of responses in the same patients would result. METHODS: Data from 569 patients included in eight studies of a variety of cancers were reanalyzed. The two response criteria were separately applied, and the results were compared using the
statistic. The importance of confirmatory measurements and the frequency of
nonspherical tumors were also examined. In addition, for a subset of 128 patients, a
unidimensional criterion for disease progression (30% increase in the sum of maximum
diameters) was applied and compared with the standard definition of a 25% increase in the
sum of the bidimensional products. RESULTS: Agreement between the unidimensional and
bidimensional criteria was generally found to be good. The statistic for concordance for
overall response was 0.95. CONCLUSION: We conclude that one dimensional measurement of
tumor maximum diameter may be sufficient to assess change in solid tumors.
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INTRODUCTION |
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Objective tumor shrinkage, or tumor response, has been adopted as a standard end point to select new anticancer agents for further study and has played a role in the development of all drugs approved for use in cancer treatment to date. Newer, noncytotoxic agents that are not anticipated to produce tumor shrinkage may require the development of a different intermediate end point to identify agents of promise for evaluation in large trials. However, since objective tumor response will continue to be of relevance in screening new cytotoxic anticancer agents and in comparing their relative merits, a standardized approach to tumor measurement and response criteria is important.
The criteria for both response and progression are necessarily arbitrary and have traditionally been expressed as percentage changes in tumor measurement from baseline to allow their application to all patients who have measurable disease. Several attempts have been made to harmonize the criteria for tumor response and progression (1-4), and those developed by the World Health Organization (WHO) (3) are the ones most frequently used. Four response categories are defined: complete response, partial response, stable disease, and progressive disease. Complete response is not problematic because regardless of the criteria employed, disappearance of all known disease is required. WHO defines partial response as a 50% or more decrease in "total tumor load of the lesions that have been measured." The definition states that, where possible, lesions should be measured bidimensionally (multiplying the largest diameter by its perpendicular—giving the "product") and, where there are multiple lesions, all the products should be summed. In contrast, progressive disease is defined as an increase of 25% in the size of one or more measurable lesions or the appearance of new lesion(s). In practice, many groups also define disease progression as a 25% increase in the sum of the products, rather than on the basis of change in a solitary lesion.
Because the process of measurement of two dimensions and the calculation of products and their sum is laborious, we were interested in determining whether an approach based on utilizing only one dimension was theoretically valid and practically feasible. In this article, we will discuss the mathematical justification for a unidimensional approach, a proposed partial response criterion based on unidimensional assessment, and finally will apply the new proposed criterion to a large dataset from several phase II and III trials to compare the study outcomes when unidimensional and bidimensional (WHO) criteria are applied to the same datasets.
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THEORETICAL REASON FOR USING ONLY ONE DIMENSION FOR THE MEASUREMENT OF TUMOR RESPONSE |
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A theoretical reason that unidimensional measurement may be preferred to the bidimensional product is as follows: The changes in diameter relate more closely to the fixed proportion of cells killed by a standard dose of chemotherapy than do changes in the bidimensional product. If a fixed dose of cytotoxic agent kills a constant proportion of cancer cells, then the logarithm of cell kill is directly related to arithmetic dose increases. A consequence of this relationship is that the absolute number of cells killed depends on the mass of cells present at the time of drug exposure and thus varies from patient to patient; therefore, a partial response must be defined as a proportionate reduction of this initial mass. Ideally, therefore, the change in tumor size should be directly (linearly) related to the logarithm of the number of cells killed. Assuming tumors are spherical, the theoretical relationship between cell number and bidimensional product, on the one hand, and maximum diameter, on the other, may be examined knowing that a tumor 1 cm in diameter contains 109 cells and the arithmetic formulas are 4/3
r3
(where r is the radius) for the volume, 2r for the
diameter, and (2r)2 for the bidimensional product.
The legend for Fig. 1
demonstrates the calculation.
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Fig. 1
shows this theoretical relationship for both simple diameter
and product over the clinical range of tumor sizes, from 1 cm in diameter (assumed to contain 109 cells) to about 10 cm, assuming the tumors are spherical. Neither relationship is
exactly linear but diameter is much more nearly proportional to the logarithm of cell number than
is product and so changes expressed in units of diameter are approximately independent of the
initial tumor sizes in different patients. Of course, the bidimensional product could be further
mathematically transformed, by taking its square root, so as to have the same relationship to
logarithm of cell number; the point is that simple maximum diameter already possesses this
relation. The direct nature of the relationship of tumor diameter (in this case, the average
diameter) and an exponent of cell number (in this case, the number of tumor cell doublings from
a single cell) was, in fact, noted early in the history of clinical tumor measurement (5). This mathematical consideration would favor the use of diameter rather than product but the strong intuitive feeling that two measurements must be better than one probably influenced the selection of the current response criteria. There is empiric evidence in the literature, however, that indicates that bidimensional measurement adds no further information than that provided by maximum diameter. Gurland and Johnson (6) demonstrated that maximum diameter correlates well with the greatest diameter perpendicular to it (correlation, 0.79-0.99, depending on the observer) and with the surface areas of various-shaped tumors (correlation, 0.85-0.99, depending on the observer) and with tumor perimeter (correlation, 0.98-0.99). Spears (7) has demonstrated that diameter becomes grossly inaccurate as an estimate of tumor size only when the length of the tumor mass is more than twice its width. The use of the bidimensional product is hallowed by many years of use, however, and has been successful in establishing many clinically useful drugs. Therefore, any suggestion for change would have to be accompanied by a demonstration that the new method is able to identify the same degree of response in the same patients as do current criteria.
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PROPOSED CRITERIA FOR PARTIAL RESPONSE AND PROGRESSION USING ONE DIMENSION |
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Assuming spherical tumors, a 50% reduction in the product results in a decrease in volume of 65% in the tumor, as would a 30% reduction in the diameter (Table 1).
Thus,
we propose that the unidimensional criterion for partial response be a
30% decrease in the sum of the diameters.
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In addressing the substitution of a single dimension for the product in developing partial response criteria, we also recognize that the WHO criteria for disease progression utilize changes in the bidimensional product and thus a change to unidimensional measurements in the assessment of progressive disease is also in order. We propose that disease progression be defined as a 30% increase in the sum of diameters. Although the change in volume to achieve this is much greater than the change in volume attributable to a 25% increase in products (Table 1
), the risk of overcalling progression with the WHO
criteria is high because of measurement error considerations. In fact, for small lesions, Lavin and
Flowerdew (8) have shown that the current 25% increase in
product results in a one in four chance of declaring that progression has occurred when, in fact,
the tumor is unchanged. Thus the current WHO criterion which determines that progression is
achieved on the basis of only one (possibly small) lesion increasing in size by 25% (3) is very likely to result in a large number of false progressions. A
further point is that, because such "progressions" are due to measurement error
rather than to a real change in size, the more frequently an observation is made the greater the
chance of a false progression being recorded (8). A 30% increase
in the largest diameter would represent slightly more than a doubling of tumor volume
(120% increase) versus a 40% increase in tumor volume noted when there is a
25% increase in bidimensional product. |
METHODS |
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Having postulated that a 30% decrease in the sum of longest diameters should produce partial response rates similar to a 50% decrease in the sum of the products, we decided to evaluate both criteria on the same dataset by reanalyzing eight studies of cytotoxic anticancer treatment that have shown overall response rates of greater than or equal to 15% (partial plus complete responses) in bidimensionally measurable disease. Included were seven National Cancer Institute of Canada Clinical Trials Group (NCIC CTG) phase II and phase III studies (411 total number of patients; 397 assessable patients) and one Treatment Referral Center trial of the National Cancer Institute (NCI) of the United States (all 172 patients assessable). Each study was evaluated individually because data on different clinical trials were not available centrally on one computerized database. The study details are shown in Table 2.
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Patients in all NCIC CTG studies had at least one bidimensionally measurable lesion greater than or equal to 1 x 1 cm in size, if measured by physical examination or chest x-ray, and greater than or equal to 2 x 2 cm, if measured by computed tomography (CT) scan, magnetic resonance imaging (MRI) scan, or ultrasound. For the NCI trial, the requirement for measurable disease was a lesion that could be measured on either physical examination or on x-ray film with ruler or calipers or be a CT or MRI lesion of at least 1.5 cm. Tumors were measured at baseline (prestudy) and at regular intervals during the trials and lesion measurements recorded on study-specific case report forms. The majority of patients on all trials (and all of the patients on the brain tumor study) had disease documented by radiologic evaluation (CT scan, ultrasound, or MRI). Each patient's tumor measurements, as derived from case report forms, were evaluated for partial response according to two criteria: 1) WHO—a greater than or equal to 50% decrease in the sum of the product of bidimensional measurements (i.e., the maximum diameter multiplied by the largest diameter at right angles to this, for each lesion) maintained for a minimum of 4 weeks; 2) unidimensional—a greater than or equal to 30% decrease in the sum of the largest unidimensional measurements maintained for a minimum of 4 weeks.
The criteria for complete response were the same for both definitions, i.e., disappearance of all known disease maintained for a minimum of 4 weeks.
In the first three NCIC CTG studies and the NCI trial shown in Table 2, partial response and complete response were calculated by both methods. In the
second group of four NCIC CTG trials (128 patients), in addition to complete and partial
response, patients were also categorized as having progressive disease or stable disease according
to the following definitions:
Progressive disease was defined as 1) WHO—a greater than or equal to 25% increase in the sum of the products of bidimensional measurements or the appearance of any new lesion; or 2) unidimensional—a greater than or equal to 30% increase in the sum of the largest unidimensional measurements or the appearance of any new lesion.
Stable disease was defined as 1) WHO—change in the sum of the products insufficient for partial response and for progressive disease maintained for a minimum of 4 weeks from baseline; 2) Unidimensional—change in the sum of diameters insufficient for partial response and progressive disease maintained for a minimum of 4 weeks from baseline.
Patients without repeat measurements were classified as inassessable. At the time of this analysis, some patients remained on treatment and some trials had not completed accrual so the final reported response rate on some of these trials differs from those indicated here.
Analyses performed on the final set of four NCIC CTG trials (128 patients) shown in Table 2 in addition to the progression and stable disease determinations detailed
above included the following: (a) an assessment of the need for confirmation of
response by determining how many additional partial responders would be documented by both
methods if only one set of measurements meeting partial response criteria were required; (b) the documentation of the lesion geometry: How often were lesions spherical or
nonspherical (defined as a ratio of 
1.5 : 1 in perpendicular diameters)?; and (c)
determination of the frequency with which progressive disease was shown on the basis of new
lesions as opposed to an increase in the sum of the products.
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RESULTS |
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Results of the comparison of the standard WHO and new unidimensional criteria are shown in Table 3.
There was, by
definition, complete concordance with regard to complete response.
Results for measuring partial responses also show an excellent
agreement. In the following text, the observed proportions are followed
by parentheses containing two percentage numbers. The first percentage
is the observed proportional percentage and the second percentage
following the ± sign represents the 95% confidence intervals of
that proportion. There were 126 of 569 (22.1% ± 3.4%)
partial responses to the 50% product (WHO) criterion and 126 of 569
(22.1% ± 3.4%) to the 30% diameter criterion. Only five
of 569 (0.88% ± 0.8%) patients were judged partial
responders by the 50% product criterion but not so by the 30%
diameter criterion and only five of 569 (0.88% ± 0.8%)
patients were judged partial responders by the unidimensional criterion
but not by the bidimensional criterion. Thus, there was an agreement in
121 of 126 responses (96% ± 3%). Concordance for overall
response rate judged by the two criteria was tested using the
statistic, the calculation of which is given in the footnote to Table
4. This discounts for any agreement between the two
criteria that might be due to chance alone. The statistic (
= 0.95) demonstrates excellent agreement.
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As noted, we also examined the impact of requiring a confirmation of measurement change for the designation of partial response in a subset of four trials. When the 4-week confirmatory measurement for partial response was eliminated, an additional five responses were identified using WHO criteria (all had been designated as stable disease), giving an overall partial response rate of 21 + 5 = 26 of 128 (20% ± 7%). In the same patients with the use of the unidimensional approach, six additional responses were identified (all had been designated as stable disease) giving an overall partial response rate of 20 + 6 = 26 of 128 (20% ± 7%). Although some of these cases had no subsequent measurement available, when such data were available, it is of interest that three of the bidimensional partial responses and four of the unidimensional partial responses showed an increase in size of measurable disease.
As would be expected from the volume relationship between the WHO criterion for progressive disease (25% sum product increase; 40% volume change) and the unidimensional criterion (30% sum diameter increase; 120% volume change), there were more patients with stable disease using the latter definition than with the WHO definition because some patients with progressive disease measured by WHO criteria had insufficient increase in unidimensional sum to qualify for progressive disease according to the newly proposed criterion. The patients under discussion are those who met the criterion for progression without either having first shown a response or having met the time requirement that would classify them as having had stable disease. In the 128 patients studied for this end point, 18 were found to have disease progression because they developed new lesions. By an increase in measurement of pre-existing lesions, a further 24 were judged to have disease progression by the WHO bidimensional criterion, but only nine by the more stringent proposed unidimensional criterion. Thus, 42 (18 + 24) of the 128 patients (32.8%) had a "best response" of progression according to the WHO criterion, but only 27 (18 + 9) (21%) by the new proposal.
As would be expected in the evaluation of tumor masses assessed from real patient data, not all lesions were spherical in their geometry. In the last four trials, 128 patients had a total of 370 measurable lesions recorded, 351 of which were bidimensionally measurable. Of these bidimensional lesions, 69 (19.7%) were, in fact, nonspherical, as defined by a ratio of perpendicular diameters of greater than or equal to 1.5 : 1.
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DISCUSSION |
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TopAbstractIntroductionTheoretical Reason for Using...Proposed Criteria for Partial...MethodsResultsDiscussionReferences |
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Comparison of sequential tumor measurement data from eight phase II and phase III trials of the NCIC CTG and the U.S. NCI allowed partial response evaluation by both the criterion of a 50% decrease in the sum of the products (WHO criterion) and the criterion of a 30% decrease in the sum of the diameters (new criterion). A high degree of concordance was found between these two methods of evaluation: Regardless of the method used, the same conclusions about the efficacy of the regimen under study were reached. Furthermore, in general, the same patients were considered responders by either method. Of interest, a few additional patients would have been declared responders had there been no requirement for a 4-week confirmatory measurement. Some of these patients did, in fact, have subsequent measurements that failed to confirm that sufficient tumor shrinkage had been obtained to qualify for response. However, the majority of cases in which a measurement change sufficient for partial response was documented had tumor shrinkage confirmed by subsequent measurement.
Thus, it seems that, on the basis of the theoretical considerations presented above in which tumors were assumed to be spherical and our findings in a large set of actual patient data that included a range of both spherical and nonspherical lesions, the bidimensional measurement of solid tumors adds nothing to simple maximum diameter in assessing their response to treatment. This was first suggested by Gurland and Johnson (6) and was reaffirmed, on the basis of measuring experimental tumors in animals, by Watson (9). In addition, there are practical reasons why diameter should be chosen over product. There is a saving in calculation in that products are no longer required. The sum of diameters, because of its approximation to the logarithm of cell number (and thus, unlike the sum of the products, not exaggerating initial decreases in large tumors), is an ongoing indicator of how real tumor load is changing. The simplicity of the measurement also encourages the measurement of more lesions in an individual patient, and the greater the number of lesions measured, the less chance there is of falsely deciding that a partial response has occurred (10).
In terms of progression, the use of the WHO criterion (a 25% increase in product of a single lesion) creates a very high-risk situation for overcalling progression. As noted in our results, in many cases progression is obvious because of the appearance of new lesions, but for measurement-based progression, consideration could be given to ignoring small tumors (the minimum size depending on the number being measured) and to limiting the frequency of observations. A simpler solution, that a doubling of nadir size should be required for progression, was first proposed many years ago (11) and has been revived (10). Measuring only maximum diameter and retaining the current 25% increase criterion would be consistent with this suggestion. We have tested the application of a 30% increase in the sum of diameters and found that, as would have been predicted, fewer patients are considered to have progression as their best response than when WHO criteria were used. In practice, however, the impact of this change is small: Patients who are truly progressing will declare that fact within another few weeks, and patients who truly have unchanging disease (and were incorrectly considered to have progressed) would continue to receive therapy. Since most decisions about the pursuit of new cytotoxic agents are based on the proportion of patients responding to therapy, small shifts in progression rate are unlikely to have an impact. The other advantage of utilizing a criterion of a 30% increase is that it is "symmetrical" with the partial response criterion of a 30% decrease and thus easy to remember.
In summary, we have shown that the simple maximum diameter of a tumor as well as the sum of such diameters is all that is required to determine tumor response, and we feel that this approach should replace response criteria utilizing the sum of the products in clinical cancer research.
Although not the primary intent of this article, it is also useful to raise the more philosophic issue about the "meaning" of partial response. As we have noted, any criterion of what should be called a response is arbitrary. Presumably the change of 50% in the sum of products (or 30% in sum of diameters) was chosen for its arithmetic convenience, but it may also be interesting to examine what happens when the criterion of a 50% reduction of the diameter rather than the product is applied. This criterion would certainly be more stringent: representing a reduction in tumor volume (a surrogate for cell number) of just over 87%. This is close to a one log reduction in cell number. Would this change give a greater biologic meaning to achieving a partial response? It would certainly change the numbers of responders and lower the response rates in many studies. It might also cause us to reject some of the agents as "inactive" that went on to further study following phase II evaluation. To determine if the adoption of a more stringent requirement for response was useful, a similar type of retrospective analysis to the one performed here would be of value. Perhaps it would make us more efficient in discarding agents early on in drug development, but before suggesting this be adopted, it must be certain that regimens shown to have an impact on patient survival or palliation would not have been rejected because of lack of response activity in early phase trials.
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NOTES |
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We thank Kathy Bennett and Wendy Walsh in the National Cancer Institute of Canada Clinical Trials Group (NCIC CTG) office for their help in data review. We also thank the following individuals for their helpful comments on the manuscript: Susan Arbuck (National Cancer Institute [NCI], Bethesda, MD), Jantien Wanders (New Drug Development Office, European Organization for Research and Treatment of Cancer [EORTC], Amsterdam, The Netherlands), Jaap Verweij (Early Clinical Studies Group, EORTC, Rotterdam, The Netherlands), Richard Kaplan (NCI, Bethesda), and Stephen Gwyther (East Surrey Hospital, Redhill, Surrey, U.K.).
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