Modeling minimal residual disease (MRD)-testing

Modeling minimal residual disease (MRD)-testing

Leukemia Research 27 (2003) 293–300 Open forum Modeling minimal residual disease (MRD)-testing Anna Butturini a,b,∗ , John Klein c , Robert Peter Ga...

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Leukemia Research 27 (2003) 293–300

Open forum

Modeling minimal residual disease (MRD)-testing Anna Butturini a,b,∗ , John Klein c , Robert Peter Gale d,e a c

Department of Pediatrics, Division of Hematology Oncology, Childrens’ Hospital Los Angeles, 4650 Sunset Blvd., Los Angeles, CA 90027-6016, USA b Keck Medical School University Southern California, Los Angeles, CA 90027-6016, USA Department of Biostatistics and International Bone Marrow Transplant Registry, Biostatistics Unit, Medical College of Wisconsin, Milwaukee, WI, USA d Center for Advanced Studies in Leukemia, Los Angeles, CA 90027-6016, USA e Imperial College of Science, Technology and Medicine, Hammersmith Hospital, London, UK Received 15 March 2002; accepted 25 June 2002

Abstract There is considerable effort to develop more sensitive methods to detect minimal residual disease (MRD) in bone marrow and blood samples of persons with cancer. Results of MRD-testing are used to predict clinical outcome and determine if more anti-cancer therapy is needed. Mathematical models were developed to assess factors affecting sensitivity and specificity of MRD-testing at diverse cancer cell prevalences. Modeling results and predictions were compared to results of large published studies. Accuracy of MRD-testing depends on cancer cell prevalence and distribution in the blood or bone marrow of the subject, sensitivity and specificity of the MRD-test and sample size. In subjects with low cancer cell prevalences (≤10−4 ) results of MRD testing are likely inaccurate. Increasingly sensitive MRD-tests are only marginally useful; the major obstacle to accuracy is inadequate sampling. Increasing sensitivity of methods to detect MRD is unlikely sufficient to increase accuracy of MRD-testing. In contrast, increased sampling (size and frequency) and assigning a high cut-off value (for example, ≥10−3 ) to declare a MRD-test positive will increase sensitivity and specificity, respectively. © 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction Clinicians want to know whether a person who responds to cancer therapy and is cancer-free as determine by conventional testing is really completely free of cancer cells or whether small numbers of otherwise undetectable cancer cells remain. This information may be used (appropriately or not) to predict outcome and determine whether to begin, continue or stop therapy. Cancer cells detected by these but not conventional techniques are termed minimal residual disease (MRD) [1,2]. Use of MRD-testing under these conditions assumes that detection of rare cancer cells correlates with likelihood of cancer recurrence. It is also widely believed that more sensitive MRD assays are better predictors of cancer recurrence than less sensitive tests and are greatly needed. Several studies correlated results of MRD-testing with cancer recurrence; results are controversial [2–5]. Discordances between studies are ascribed to differences in method of MRD-testing, quality, size, and frequency of samples tested and biology of the cancer studied. Whether improv∗

Corresponding author. Tel.: +1-323-669-5928; fax: +1-323-660-7128. E-mail address: [email protected] (A. Butturini).

ing MRD-testing methods may make this approach more reliable is unproved but highly desired by most. To understand if technical aspects of MRD-testing affects ability to accurately predict clinical outcome is important because these variables can be modified. Analysis of published results is complicated by the interference of cancer prognosis on the interpretation of MRD-testing. For example, MRD assays prone to false-negative results will appear correct in persons with low relapse risk, and vice versa [6,7]. We reviewed the different aspects of MRD-testing and developed mathematical models to assess variables affecting the likelihood of correct predictions of clinical outcome. 1.1. MRD-testing The aim of MRD-testing is to correctly predict clinical outcome. A positive test will correctly identify persons who will relapse (sensitivity) and a negative test, those who are cured (specificity). The probability of correct predictions depends on three discrete aspects of MRD-testing: the assay, the test-sample and the correlation between MRD-test results and clinical outcome.

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A. Butturini et al. / Leukemia Research 27 (2003) 293–300

1.2. The assay A perfect MRD-test identifies all cancer cells (sensitivity) but no normal cells (specificity). Cancer cells can be identified because they have a unique gene recombination (cancer-specific markers) or because they express gene(s) not expressed by normal hematopoietic cells (tissue- or differentiation-specific markers). These markers are usually detected by immune or molecular techniques. No marker(s) correlates perfectly with cancer. Consequently, false-positive results arise if the marker is occasionally present in/on normal cells. This is typical of tissue- and differentiation-specific markers but also possible with “cancer-specific” markers [8–10]. False-negative results also occur if a marker is inconstantly present in/on cancer cells. Gene transcription and translation vary between cells within a cancer. Again, this applies to not only to tissue- and differentiation-specific but also to “cancerspecific” markers [11]. Technical aspects of MRD assays also affect accuracy including: characteristics of nucleic acid sequences or antigens, characteristics of antibodies or molecular primers used for detection and characteristics of the technique used. Combinations of these variables explain the large range of sensitivity (10−2 to 10−7 ) reported in different studies. As a reference, the conventional threshold of routine morphology studies of bone marrow is 5 × 10−2 [12].

or eradicated by subsequent therapy or by immune or biochemical (hormonal) means. Another possible reason why a “true” positive result might not correlate with clinical outcome is incomplete follow-up because of a short observation interval or competing causes of treatment-failure (for example, early death from pneumonia in a person with residual leukemia otherwise fated to relapse). There are also reasons why persons with a “true” negative MRD-test might relapse. Relapse can arise from cancer cells persisting in tissues and/or organs different from those being sampled (for example, a chloroma in a person with leukemia).

2. Design We used mathematical models to assess variables affecting the probability of correct MRD-test results at level of assay and sample. We modeled MRD studies on adult bone marrow but the same formulae apply to detection of MRD in blood samples or in children. In these models, N is total bone marrow cellularity (about 1012 cells). We assume cancer cells to be homogeneously distributed with Y, their prevalence in the bone marrow. We also assume the MRD-test has no technical error rate. Here, n is number of cells tested (sample size).

1.3. The sample

3. Results

A perfect sample is not itself the cause of false-positive or -negative results. False-positive results (imperfect specificity) are typical of PCR-based assays because of technical errors and/or laboratory contamination [13]. False-negative results (imperfect sensitivity) are caused by the non-homogeneous distribution of cancer cells in bone marrow [14], small sample size or both. Sample size is determined by the availability of cells and the MRD-test used. Typical samples contain 103 to 5 × 105 cells; efforts have been recently made to use larger samples (>106 ).

3.1. The assay The effect of using MRD-tests with low sensitivity is clear: false-negative results. The effect of MRD-test specificity is more complex. Here, the probability of false-positive results correlates with cancer cell prevalence (Table 1). For example, an assay with 99.9% specificity has 50% or less probability of a correct MRD-test result in persons when cancer cell prevalence is ≤10−3 . 3.2. The sample

1.4. Correlation with outcome Even when sensitivity and specificity of assay and sample are optimal, the correlation between a MRD-test result and clinical outcome depends on biology of the cancer cells and the clinical observation interval. For example, cells identified as cancer may persist for many years without causing relapse [15,16]. Explanations are diverse. First, the marker chosen to identify cancer cells may correspond to an early event in cancerogenesis [17] necessary but insufficient to cause cancer or to a genetic event in a sub-clone of cancer cells [19,20]. Second, cells identified as cancer may be terminally differentiated, dormant or lack the self-renewal capacity needed to cause relapse [18]. Third, persisting cancer cells may not cause relapse because they are damaged

To avoid false-negative MRD-test results, sample size must be sufficiently large to contain ≥1 cancer cell. This is Table 1 Probability (in %) of false-positive MRD-test using assays with variable specificity in samples with different cancer cells prevalences Cancer cell prevalencea

Assay specificity (%) 99







90 99 99.9 99.99 >99.99

50 90 99 99.9 99.99

10 50 90 99 99.9

1 10 50 90 99

0.1 1 10 50 90

0.01 0.1 1 10 10

10−4 10−5 10−6 10−7 a

Cancer cell prevalence in bone marrow.

A. Butturini et al. / Leukemia Research 27 (2003) 293–300

prevalence in the bone marrow is ≥10−4 . However, there is still about a 40% probability that the prevalence of cancer cells in the bone marrow sample is 1−log lower than cancer cell prevalence in the bone marrow. Probability of detecting ≥1 cancer cell in any sample at different cancer cell prevalences is shown in Table 3.

Table 2 Probability (in %) of false-negative MRD-test because of small sample size in cancer with different cancer cell prevalences Cancer cell prevalencea

Sample sizeb

10−3 10−4 10−5 10−6 10−7

0.005 36.788 90.484 99.99 >99.99


105 <0.001 0.005 36.788 90.484 99.99



<0.001 <0.001 0.005 36.788 90.484


<0.001 <0.001 <0.001 0.005 36.788

3.3. Multiple MRD-tests Every MRD-test may give false-positive or -negative results because of the assay and/or sample. The effect of imperfect assays and imperfect samples is different. For example, by repeating a MRD-test with Z specificity K times on the same sample, the probability that ≥1 MRD-test result is correct is 1 − (1 − Z)K . The probability that all results are correct is ZK . Alternatively, by repeating the same (hypothetically perfect) MRD-test K times on independent samples, the probability that x of these samples contain ≥1 cancer cell is given by the binomial:   K [1 − e−nY ]x [e−nY ]n−x x


Cancer cell prevalance in bone marrow. b N cells in sample.

a function of sample size and prevalence of cancer cells in the bone marrow. The probability a sample of size n contains ≥1 cancer cells is found by using a hypergeometric distribution: Pr[≥1 cancer cell in sample of size n] =   N − NY n (N − NY)!(N − n)!   1− =1− N!(N − n − NY)! N n

The probability ≥1 sample is adequate is: 1−(e−nY )K and the expected number of adequate samples is: K(1 − e−nY ). In both cases, repeated MRD-testing increases the probability of discordant results. Requiring multiple concordant results to define an MRD-test positive increases specificity but decreases sensitivity.

When n/N < 0.01, the Poison approximation can be used: Pr[≥1 cancer cell in sample of size n] = 1−exp{−n×Y }. The probability of false-negative results from inadequate sample size is the complement (Table 2). For example, samples containing 105 cells are adequate only if cancer cell

Table 3 Probability (in %) of detecting ≥1 cancer cell in any sample containing 105 cells at different cancer cell prevalences Sample sizea

Cancer cell prevalenceb

10−3 10−4 10−5 10−6 10−7 10−3 10−4 10−5 10−6 10−7 10−3 10−4 10−5 10−6 10−7 10−3 10−4 10−5 10−6 10−7

104 104 104 104 104 105 105 105 105 105 106 106 106 106 106 107 107 107 107 107 a b

N cells in sample. Cancer cell prevalence in bone marrow.

N samples 1






99.995 63.212 9.516 0.995 0.100 >99.999 99.995 98.168 9.516 0.995 >99.999 >99.999 99.995 63.212 9.516 >99.999 >99.999 >99.999 99.995 63.212

>99.999 86.466 18.127 1.980 0.200 >99.999 >99.999 99.966 18.127 1.980 >99.999 >99.999 >99.999 86.466 18.127 >99.999 >99.999 >99.999 >99.999 86.466

>99.999 95.021 25.918 2.955 0.300 >99.999 >99.999 99.999 25.918 2.955 >99.999 >99.999 >99.999 95.021 25.918 >99.999 >99.999 >99.999 >99.999 95.021

>99.999 98.168 32.968 3.921 0.399 >99.999 >99.999 >99.999 32.968 3.921 >99.999 >99.999 >99.999 98.168 32.968 >99.999 >99.999 >99.999 >99.999 98.168

>99.999 99.326 39.347 4.877 0.499 >99.999 >99.999 >99.999 39.347 4.877 >99.999 >99.999 >99.999 99.326 39.347 >99.999 >99.999 >99.999 >99.999 99.326

>99.999 99.995 63.212 9.516 0.995 >99.999 >99.999 >99.999 63.212 9.516 >99.999 >99.999 >99.999 99.995 63.212 >99.999 >99.999 >99.999 >99.999 99.995


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A. Butturini et al. / Leukemia Research 27 (2003) 293–300



A. Butturini et al. / Leukemia Research 27 (2003) 293–300

4. Conclusions Our model indicates that cancer cell prevalence in a subject’s bone marrow is as or more important than features of MRD-test and test-sample in determining accuracy of MRD-testing. When cancer cell prevalence is low, one must increase sample size and specificity and specificity of the MRD-test; increasing MRD-test sensitivity alone is insufficient to overcome low cancer cell prevalence. However, practical considerations (like how large a sample one can take and how many times a subject can be samples) limit the prevalence of cancer cells we can detect regardless of how sensitive and specific the MRD-test is. For example, the probability of an ≥95% accurate MRD-test result in persons with bone marrow cancer cell prevalence of 10−4 requires testing samples of 105 cells using assays with 10−5 sensitivity and 99.99999% specificity. This is somewhere between impractical and undoable. Results using our model imply that developing increasingly sensitive MRD-tests is unnecessary. To prove this, we reviewed results of studies correlating MRD-testing with clinical outcome [21–48]. Those reporting subject-specific data in >20 subjects are summarized in Table 4. With few exceptions [32,36,40], cohorts with positive MRD-tests had higher relapse risks than the cohorts with negative MRD-tests. However, analysis of correlations between MRD-test results and subject-specific clinical outcomes is less convincing. With a median follow-up of 0.5–8 years, 6–100% of persons with positive MRD-tests relapsed (true-positive tests) while 32–100% of those with negative MRD-tests remained in remission (true-negative tests). This means that in some studies as high as 94% of persons with positive MRD-tests remained in remission (false-positive tests) while up to 68% of subjects with negative MRD-tests relapsed (false-negative tests). Some of these studies use different cut-offs to define a positive MRD-test. Those with the highest cut-off had a higher proportion of true-positive MRD-tests but about the same proportion of true-negative MRD-tests [34,35,37,38,46]. These data are consistent with predictions from our model. Another important implication from our model is the importance of cancer cell prevalence in determining accuracy of MRD-testing. Results of MRD-tests are likely to be correct when cancer cell prevalence is high. (This is obviously where these tests are least needed). Consequently, results of MRD-tests may be more useful when substantial numbers of cancer cells remain, such as during or soon after therapy, but less useful after extensive therapy and/or follow-up (unless recurrence is imminent.) The same concept applies to MRD-testing performed after therapies of different efficacies. This suggests it is inappropriate to use results of MRD-tests to predict clinical outcome in clinical settings different from those where the value of the MRD-test was confirmed. Despite these limitations, might MRD-testing be used to guide therapy? In some cancers, like childhood ALL

[48–50], early response to therapy assessed by routine techniques (morphology) predicts outcome and it is already used to assign treatment. In such situations, it is likely that an MRD-test using a high threshold may as useful as or better role than routine techniques which are inexpensive but imprecise [48]. MRD-testing is expensive and laborious but might give more informative in subjects with a bone marrow cancer cell prevalence ≥10−2 . Whether replacing conventional cancer cell detection techniques with MRD-testing will improve results of cancer treatment is unknown. Our model suggests how these tests are best used and under what circumstances results are most likely to correlate with clinical outcome and optimize therapy.

Acknowledgements We thank Drs. Paul Gaynon, Susan Groshon and Myles Cockburn for comments and critiques. Dr. Butturini planned the study with input from Drs. Gale and Klein. Dr. Klein did the statistical calculations. Dr. Gale wrote the study with input from Drs. Butturini and Klein. References [1] Butturini A, Gale RP. Detecting minimal residual leukemia. Cancer Genet Cytogenet 1991;52:12–26. [2] Pui CH, Campana D. New definition of remission in childhood acute lymphoblastic leukemia. Leukemia 2000;14:783–5. [3] Faderl S, Estrov Z. Detection of residual disease in childhood acute lymphoblastic leukemia. N Engl J Med 1999;340:152. [4] Goldman JM, Kaeda JS, Cross NC, Hochhaus A, Hehlmann R. Clinical decision making in chronic myeloid leukemia based on polymerase chain reaction analysis of minimal residual disease. Blood 1999;94:1484–6. [5] Faderl S, Talpaz M, Kantarjian HM, Estrov Z. Should polymerase chain reaction analysis to detect minimal residual disease in patients with chronic myelogenous leukemia be used in clinical decision making? Blood 1999;93:2755–9. [6] Machida U, Kami M, Hirai H. Detection of residual disease in childhood acute lymphoblastic leukemia. N Engl J Med 1999;340:153. [7] Matsumara T, Kami M, Saito T, Sakamaki H, Hirai H. Prognostic value of minimal residual disease in acute lymphoblastic leukaemia in childhood. Lancet 1998;353:752. [8] Biernaux C, Loos M, Sels A, Huez G, Stryckmans P. Detection of major BCR/ABL gene expression at very low level in blood cells of some healthy individuals. Blood 1995;86:3118–22. [9] Bose S, Deininger M, Gora-Tybor J, Goldman JM, Melo JV. The presence of typical and atypical BCR/ABL fusion genes in leukocytes of normal individuals: biologic significance and implications for the assessment of minimal residual disease. Blood 1998;92:3362–7. [10] Ji W, Qu G, Ye P, Zhang XY, Halebi S, Ehrlich M. Frequent detection of BCL2/JH translocation in human blood and organ samples by a quantitative polymerase chain reaction assay. Cancer Res 1995;55:2876–82. [11] Keating A, Wang XH, Laraya P. Variable transcription of BCR/ABL by Ph+ cells arising from hematopoietic precursors in chronic myelogenous leukemia. Blood 1994;84:1744–9. [12] Gutterman JU, Magvligit G, Burgess MA, et al. Immunodiagnosis of acute leukemia: detection of residual disease. J Natl Cancer Inst 1974;53:389–99.

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