# Predicting the risk of relapse after stopping imatinib in chronic myeloid leukemia

To escape the Montreal cold, I am visiting the Sunshine State this week. I’m in Tampa for Moffitt’s 3rd annual integrated mathematical oncology workshop. The goal of the workshop is to lock clinicians, biologists, and mathematicians in the same room for a week to develop and implement mathematical models focussed on personalizing treatment for a range of different cancers. The event is structured as a competition between four teams of ten to twelve people focused on specific cancer types. I am on Javier Pinilla-Ibarz, Kendra Sweet, and David Basanta‘s team working on chronic myeloid leukemia. We have a nice mix of three clinicians, one theoretical biologist, one machine learning scientist, and five mathematical modelers from different backgrounds. The first day was focused on getting modelers up to speed on the relevant biology and defining a question to tackle over the next three days.

Chronic myeloid leukemia (CML) is a myeloproliferative disease caused by a single reciprocal chromosomal translocation between chromosome 9 and 22 in a hematopoietic stem cell in the bone marrow (Rowly, 1973). This results in a BCR-ABL fusion gene which encodes for active tyrosince kinase and leads to an accelerated cell cycle (Deininger, et al., 2000). The treatment of CML improved greatly in after 2001 with the release of the first generation of tyrosine-kinase inhibitors (TCI; such as imatinib), but the treatment is life-long, expensive — around \$90,000/year in the US — and not side-effect free. Although the patent protecting imatinib is to expire at the start of 2015 and lead to a drastic reduction in price, there is still a strong interest in controlling CML without daily pills.

Since CML is frequently detected before any symptoms are manifest, doctors use a molecular marker to track disease progress. They take PCR readings of mRNA transcripts corresponding to the expression of BCR-ABL in the peripheral blood. For most patients, PCR levels drop quickly to around 0.1% of their starting values in a several months after starting treatment and remain there; these patients cannot be taken off TCIs without relapse. However, a minority of patients’ PCR levels continue to drop until reaching undetectable levels (~0.001% of initial levels). Although the current standard of care for these patients is to continue administering TCIs, in recently clinical studies it has been found that around 25% to 40% of the below threshold-PCR level patients can be taken off TCIs without relapse. Currently, the same decision procedure is used for all patients: if PCR levels remain below detectable levels for two-year of treatment, then the clinical study stops administering TCIs. Our goal is to develop a personalized procedure for predicting which patients are less likely to relapse, and use that to guide when/if patients are taken off TCIs.

Horn et al. (2013) started working on this question by calibrating an established agent-based model of CML progression (Roeder et al., 2002; 2006) with patient data and then using this in silico population to predict which patients will relapse or not and to develop a model-independent approximation for when it is best to take patients off TCIs. They trained their model on a data set of PCR-level measurements of 51 patients from the German cohort of the IRIS trial (Hochhaus et al., 2009), and validated with a data set of 31 patients from the CML IV trial (Hehlmann et al., 2011). In particular, they looked at the log(PRC)-curves and fitted two lines and breakpoint for each patient with an initial steep slope of decline $\alpha$ followed by a gentler post-breakpoint slope of $\beta$. For each patient, these three values determined the transition characteristic from a quiescent environment to a growth environment ($f_\omega$), and aptoptotic degredation rate ($r_\mathrm{def}$). With the virtual cohort generated from the IRIS trial, they were able to ask theoretically: “what would happen if we took patients off first-generation TCIs?”

Taking virtual patients off TCIs after two years at non-detectable levels resulted in similar qualitative rates of remissions as existing clinical data, although no formal comparison was made (Ross et al., 2010; Mahon et al., 2010). In particular, the data showed the same trend of if remission happened then it was in the first ~6 months. In the in silico model, however, a perfect predictor of if relapse would occur was possible in terms of the number of leukemia stem cells (LSCs). In particular, if there was fewer than $10^{2.3} \approx 200$ LSCs left from an initial population of $10^5$ then if treatment was stopped, no replace occurred in the virtual model. Unfortunately, even if reality was exactly like the computer model, we wouldn’t be able to use this information since it is impossible to measure the LSC count directly. However, the authors were able to find a useful model-free predictor in terms of the ratio of $\alpha$ to $\beta$. Specifically, if treatment is withdrawn only if $\frac{\alpha}{\beta} \leq 16$ then the rate of approximately 5% misclassification can be achieved after 2 years at undetectable levels of PCR. Alternatively, the results can be manipulated to give a waiting time of $t \geq \frac{\alpha}{8\beta}$ years at the undetectable level before treatment is withdrawn. Using this rule instead of the 2-year waiting period results in 3 times less relapse in the virtual patients.

Horn et al. (2013) also establish that both $\alpha$ and $\beta$ are needed for accurate prediction in this setting. In fact, $\alpha$ and $\beta$, and the breakpoint and $\beta$ are uncorrelated. This means, that we need to wait until after the rapid decline stops and we are well into the slow decline phase. To reliably calibrate their model, around 7 PCR-measurement points are needed before and after the breakpoint. This means that if we measurement PCR 3 to 4 times a year after the initial rapid decrease (which is usually on the order of a year) then we will need at least three years before we can have confidence in the model. Our primary goal is to see if we can expedite this predictive process by refining the model, adding data such as the components of the Sokal score (Sokal et al, 1984) or other information typically collected about patients. Our secondary goal is to see if the timing of administrating stem cell niche targeting drugs can be optimized to create short-term combination therapies to ensure patients can transition to the non-relapse group. Although not a cure, carefully monitored drug-free control of cancer can be the second best thing.

### References

Deininger, M. W., Goldman, J. M., & Melo, J. V. (2000). The molecular biology of chronic myeloid leukemia. Blood, 96(10): 3343-3356.

Hehlmann, R., Lauseker, M., Jung-Munkwitz, S., Leitner, A., Müller, M. C., Pletsch, N., … & Saufsele, S. (2011). Tolerability-adapted imatinib 800 mg/d versus 400 mg/d versus 400 mg/d plus interferon-α in newly diagnosed chronic myeloid leukemia. Journal of Clinical Oncology, 29(12): 1634-1642.

Hochhaus, A., O’Brien, S. G., Guilhot, F., Druker, B. J., Branford, S., Foroni, L., … & Larson, R. A. (2009). Six-year follow-up of patients receiving imatinib for the first-line treatment of chronic myeloid leukemia. Leukemia, 23(6): 1054-1061.

Horn, M., Glauche, I., Müller, M.C., Hehlmann, R., Hochhaus, A., Loeffler, M., & Roeder, I. (2013). Model-based decision rules reduce the risk of molecular relapse after cessation of tyrosine kinase inhibitor therapy in chronic myeloid leukemia. Blood, 121 (2), 378-84 PMID: 23175686

Mahon, F. X., Réa, D., Guilhot, J., Guilhot, F., Huguet, F., Nicolini, F., … & Rousselot, P. (2010). Discontinuation of imatinib in patients with chronic myeloid leukaemia who have maintained complete molecular remission for at least 2 years: the prospective, multicentre Stop Imatinib (STIM) trial. The lancet oncology, 11(11), 1029-1035.

Roeder, I., & Loeffler, M. (2002). A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Experimental Hematology, 30(8): 853-861.

Roeder, I., Horn, M., Glauche, I., Hochhaus, A., Mueller, M. C., & Loeffler, M. (2006). Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nature Medicine, 12(10): 1181-1184.

Ross, D. M., Branford, S., Seymour, J. F., Schwarer, A. P., Arthur, C., Bartley, P. A., … & Hughes, T. P. (2010). Patients with chronic myeloid leukemia who maintain a complete molecular response after stopping imatinib treatment have evidence of persistent leukemia by DNA PCR. Leukemia, 24(10): 1719-1724.

Rowly, J. D. (1973). A new consistent chromosomal abnormality in chronic myelogenous leukemia identified by quinacrine fluorescence and Giemsa staining. Nature, 243: 290-293. [Also in: Landmarks in Medical Genetics: Classic Papers with Commentaries, 51: 104. (2004)]

Sokal, J. E., Cox, E. B., Baccarani, M., Tura, S., Gomez, G. A., Robertson, J. E., … & Cervantes, F. (1984). Prognostic discrimination in” good-risk” chronic granulocytic leukemia. Blood, 63(4): 789-799.

Advertisements

About Artem Kaznatcheev
From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.