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Editorials
To what extent can mathematical modeling inform the design of clinical trials? The example of safe dose reduction of tyrosine kinase inhibitors in responding patients with chronic myeloid leukemia
Joshua T. Schiffer1,2 and Charles A. Schiffer3
1Vaccine and Infectious Diseases and Clinical Research Divisions, Fred Hutchinson Cancer Research Center, Seattle, WA; 2Department of Medicine, University of Washington, Seattle, WA and 3Department of Oncology Wayne State University School of Medicine, Karmanos Cancer Institute, Detroit, MI, USA
E-mail: schiffer@karmanos.org doi:10.3324/haematol.2018.201897
The development of the tyrosine kinase inhibitors (TKIs) that inhibit the BCR/ABL oncoprotein driving the growth and persistence of chronic myeloid leukemia (CML) is one of the most remarkable advances in anti-cancer treatment in recent decades, and has served as the model, if not the Platonic ideal, for targeted therapies of other cancers. It remains standard practice to administer TKIs indefinitely because of concern about relapse should compliance be erratic or therapy stopped. However, a number of recent trials have demonstrated that approxi- mately 50% of patients whose transcript levels were either extremely low or undetectable for at least 2-3 years using sensitive polymerase chain reaction (PCR) assays, have not relapsed after therapy was stopped with many patients relapse free for more than five years after discontinuation.1,2 Remarkably, almost all relapses occurred within the first 6- 8 months after therapy cessation. The mechanism(s) by which CML remains dormant is not known, although immunological explanations are proposed, and the only predictors of continued remission are longer durations of TKI therapy and PCR negativity.
The benefits of these so-called “treatment-free remis- sions”3 are obvious, and include substantially reduced costs (CML-directed TKIs also served as the prototype for the obscene pricing of “targeted” agents),4 decreases in the potential for serious longer term organ toxicities (fortunate- ly very rare with imatinib5), elimination of the often both- ersome, low-grade chronic side-effects such as fatigue and diarrhea, as well as the ability to plan for pregnancies in younger patients. But, it is estimated that less than 20% of patients who are started on TKI treatment will be able to successfully discontinue therapy. It is likely, however, that some of these same benefits would be achieved if it were possible to reduce the dose of the TKIs without loss of dis- ease control. Indeed, the selection of doses and schedule for many drugs is often based on very small, under-pow- ered trials with relatively few subsequent attempts to deter- mine whether lower doses might result in similar out- comes. In this regard, it was recently shown in a large phase II trial in newly diagnosed patients in chronic phase that a starting dose of 50 mg of dasatinib seems to produce the same response rate as the “standard” dose of 100 mg with perhaps fewer side-effects.6,7
In this issue of the Journal, Fassoni et al. propose what they consider to be a safe strategy of dose reduction of TKIs for CML patients in chronic phase based on mathematical models generated from large recently generated clinical trial data.8 The authors evaluated patients who were in major molecular response (MMR) for at least one year, defined as
a greater than 3 log reduction in transcripts from baseline, and who had received imatinib therapy for more than three years. Their model concludes that, for most patients, halv- ing the dose of the TKI will maintain the current level of response, albeit with a high likelihood of a temporary increase in transcript levels which return to baseline after continued treatment with the reduced dose.
Fassoni et al.’s paper8 highlights the crucial role that math- ematical models can play in providing a mechanistic under- pinning of observed data, and in influencing therapeutic strategies. As a general principle, differential equation- based models are a necessary tool to capture non-linearity in biomedical datasets. CML treatment involves the cou- pling of mechanisms governing tumor cell division, transi- tion rates between progenitor cells and terminally differen- tiated tumor cells, anti-tumor immune responses and the selective pressure of TKIs. The non-linearity inherent in a model which captures the dynamics of this system can yield counterintuitive and useful predictions, such as Fassoni et al.’s calculation that the increase in BCR/ABL lev- els that may occur following TKI dose reduction is transito- ry.8 Fassoni et al. hypothesize that an increase in transcripts is due to a self-limited increase in proliferating leukemia stem cells (LSCs), rather than mutations leading to TKI resistance or changes in the underlying dynamics of quies- cent, non-proliferating LSCs.8
Mathematical modeling as a field would benefit from some demystification. Well-designed models represent nothing more than in silico experiments where models with competing structures and mechanistic assumptions are compared for their ability to fit to observed data. Fassoni et al.’s model recapitulates data from selected patients from the IRIS and CML IV trials in whom the pattern of second phase decrease in transcripts is thought to result from slow depletion of quiescent LSCs. This depletion is predicted to occur independently of TKI dose reduction because the transition from quiescent to proliferating LSC, rather than incomplete efficacy of TKIs, is the rate-limiting step for CML eradication during MMR. The model’s generalizabili- ty to patients with an adequate treatment response is fur- ther supported by the scalability of its key parameters gov- erning transitions between quiescent and proliferating LSCs across all patients. Finally, the model’s main prediction, that TKI dose reduction will not usually lead to loss of MMR, is qualitatively consistent with interim analyses from the DESTINY trial, a study in which 174 participants under- went 50% dose reduction as the initial phase of a “stop- ping” trial.9 It is not known whether the transcript increases seen in some of these patients at the reduced dose would
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