Recent clinical findings in patients with chronic myeloid leukemia (CML) suggest that the risk of molecular recurrence after stopping tyrosine kinase inhibitor (TKI) treatment substantially depends on an individual's leukemia-specific immune response. However, it is still not possible to prospectively identify patients that will remain in treatment-free remission (TFR). Here, we used an ordinary differential equation model for CML, which explicitly includes an antileukemic immunologic effect, and applied it to 21 patients with CML for whom BCR-ABL1/ABL1 time courses had been quantified before and after TKI cessation. Immunologic control was conceptually necessary to explain TFR as observed in about half of the patients. Fitting the model simulations to data, we identified patient-specific parameters and classified patients into three different groups according to their predicted immune system configuration (“immunologic landscapes”). While one class of patients required complete CML eradication to achieve TFR, other patients were able to control residual leukemia levels after treatment cessation. Among them were a third class of patients that maintained TFR only if an optimal balance between leukemia abundance and immunologic activation was achieved before treatment cessation. Model simulations further suggested that changes in the BCR-ABL1 dynamics resulting from TKI dose reduction convey information about the patient-specific immune system and allow prediction of outcome after treatment cessation. This inference of individual immunologic configurations based on treatment alterations can also be applied to other cancer types in which the endogenous immune system supports maintenance therapy, long-term disease control, or even cure.

Significance:

This mathematical modeling approach provides strong evidence that different immunologic configurations in patients with CML determine their response to therapy cessation and that dose reductions can help to prospectively infer different risk groups.

See related commentary by Triche Jr, p. 2083

Chronic myeloid leukemia (CML) is a myeloproliferative disorder, which is characterized by the unregulated proliferation of immature myeloid cells in the bone marrow. CML is caused by a chromosomal translocation between chromosomes 9 and 22. The resulting BCR-ABL1 fusion protein acts as constitutively activated tyrosine kinase triggering a cascade of protein phosphorylation, which deregulate cell cycle, apoptosis regulation, cell adhesion, and genetic stability. Because of their unregulated growth and their distorted differentiation, immature leukemic cells accumulate and impair normal hematopoiesis in the bone marrow, leading to the patient's death if left untreated.

Tyrosine kinase inhibitors (TKI) specifically target the kinase activity of the BCR-ABL1 protein with high efficiency and have been established as the first line treatment for patients with CML (1). Individual treatment responses are monitored by measuring the proportion of BCR-ABL1 transcripts relative to a reference gene, for example, ABL1 or GUS, in blood cell samples by using reverse transcription and quantitative real-time PCR (qRT-PCR; refs. 2–4). Most patients show a typical biexponential treatment response with a rapid, initial decline (α slope), followed by a moderate, second decline (β slope; refs. 5–7). Whereas the initial decline can be attributed to the eradication of proliferating leukemic cells, the second decline has been suggested to result from a slower eradication of quiescent leukemic stem cells (3, 4, 8, 9). Within five years of treatment, about two thirds of the patients achieve a major molecular remission (MMR), that is, a BCR-ABL1 reduction of three logs from the baseline (MR3), while at least one third of these additionally achieve a deep molecular remission (DMR, i.e., MR4 or lower; refs. 4, 7, 10).

TKI discontinuation has been established as an experimental option for well responding patients with DMR for at least one year (11, 12). Different studies independently confirmed that about half of the patients show a molecular recurrence, while the others stay in sustained treatment-free remission (TFR) after TKI stop. Consistently, most patients present with a recurrence within 6 months, while only a few cases are observed thereafter (11–14). The overall good response of those patients after restarting treatment with the previously administered TKI indicates that clonal transformation and resistance occurrence is not a primary problem in CML. As it appears unlikely that even a sustained remission truly indicates a complete eradication of the leukemic cells, other factors have to account for a continuing control of a minimal, potentially undetectable residual leukemic load. Although treatment discontinuation is highly desirable to reduce treatment-related side-effects and lower financial expenditures (15, 16), it is still not possible to prospectively identify those patients that are at risk for a molecular recurrence. Investigations of clinical markers and scores to predict the recurrence behavior of patients after the treatment cessation revealed that both TKI treatment duration and the duration of a DMR were also associated with a higher probability of TFR (11, 13, 17, 18). However, it is still unclear whether the dynamics of the initial TKI treatment response (e.g., the initial slope of decline) correlate with the remission occurrence after treatment discontinuation.

The underlying mechanisms of the recurrence behavior after TKI stop are still controversial. While fewer recurrences for patients with longer treatment suggest that a leukemic stem cell exhaustion is an important determinant, it is not a sufficient criteria to prospectively identify nonrecurring patients (13, 17). Favorable outcomes of treatment discontinuation for patients that were previously treated with immune-modulating drugs, such as IFNα, suggest that immunologic factors might play an additional and important role (11, 18, 19). In this context, it has been demonstrated that specific subpopulations of dendritic cells and natural killer cells, as well as the cytokine secretion rate of natural killer cells are associated with higher probabilities of a treatment-free remission (20, 21). Furthermore, there are several reports about patients with low but detectable BCR-ABL1 levels over longer time periods after therapy discontinuation that do not relapse (14, 22). This is a strong indicator that also other control mechanisms, such as the patient's immune response, are important determinants of a TFR.

Mathematical oncology has been established as a complementary effort to obtain insights into cancer biology and treatment. At the same time, model-based understanding of individual patient records is developing into a key method for devising adaptive therapies in the coming era of personalized medicine (23–26). CML is a show-case example, where several models have propelled the conceptual understanding of CML treatment dynamics (5–7, 9, 27–33) and are considered for the design of new clinical trials (34). Especially the long-term effect of TKI treatment on residual stem cell numbers and the effect of combination therapies were in focus. In a recent publication, we provided evidence that TKI dose reduction is a safe strategy for many patients in sustained remission while preserving the antileukemic effect (9). Complementary efforts also accounted for interactions between leukemic and immune cells (35–39). In a prominent approach, Clapp and colleagues used a CML–immune interaction to explain fluctuations of BCR-ABL1 transcripts in TKI-treated patients with CML (37). However, it remains elusive to which extent an immunologic control is a crucial mediator to distinguish patients that maintain TFR from those that will eventually relapse.

Here, we used BCR-ABL1 time courses of TKI-treated patients with CML that were enrolled in previously published TKI discontinuation studies from different centers in Europe. In particular, we focused on patients for which complete time courses during the initial TKI therapy and after treatment cessation are available. Therefore, potential correlations between response dynamics, remission occurrences, and timings after cessation become accessible. Motivated by the observation that the initial treatment response before TKI cessation does not show obvious correlations with remission occurrences, we aim to explain the resulting dynamics in terms of an ordinary differential equation (ODE) model of TKI-treated CML. Explicitly including a patient-specific, CML-dependent immune component, we are able to demonstrate that three different immunologic configurations can determine the overall outcome after treatment cessation. We further investigate how this patient-specific configuration can be estimated from system perturbations, such as TKI dose reduction scenarios prior to treatment cessation. Our predictions closely resemble recent clinical findings substantiating our conclusion that treatment response during TKI dose reduction is indeed informative to predict a patient's future outcome after stopping therapy (40).

Patient selection

We analyzed time courses of 60 TKI-treated patients with CML, for whom TKI therapy had been stopped as a clinical intervention. Informed written consent was obtained from each subject according to the local regulations of the participating centers. Corresponding clinical trials were conducted in accordance with the Declaration of Helsinki and applicable regulatory requirements. The protocols were approved by the Institutional Review Board or ethics committee of each participating center. Detailed information on the patient cohort is available in the Supplementary Materials. For all 60 patients, serial BCR-ABL1/ABL1 measurements before as well as after cessation are available. For the purpose of this analysis, the date of a molecular recurrence after cessation was defined as the first detected BCR-ABL1/ABL1-ratio above 0.1%, indicating a loss of MR3, or the reinitiation of TKI treatment, whatever was reported first.

Furthermore, we selected patients who received TKI monotherapy before stopping, who were monitored at a sufficient number of time points to estimate the initial and secondary slopes, and who presented with the typical biexponential response dynamic (Fig. 1A, Supplementary Materials). The 21 selected patients, fulfilling those criteria, were compared with the full patient cohort (n = 60) and showed no obvious differences for the initial BCR-ABL1 levels, treatment duration, recurrence behavior, follow-up duration, recurrence times and used TKI, and are, therefore, considered to be representative examples (Supplementary Fig. S1). Moreover, the overall recurrence behavior of the selected patient cohort is comparable with larger clinical studies (11, 14).

Figure 1.

Strategy for patient selection and model sketch of TKI-treated CML. A, Flow diagram indicating the process of data selection. Patients were excluded with less than 5 BCR-ABL1 measurements during TKI treatment, missing or extremely low initial measurements (i.e., first measurement was only available after more than 10 months or below MMR). Furthermore, we only included patients with a biexponential decline in which the initial slope was steeper than the second slope. We also selected patients that were under continuous therapy with one TKI, thereby excluding patients with a pretreatment, TKI change during, combination therapy, and missing therapy/cessation information. B, General scheme of the ODE model setup indicating the relevant cell populations and their mutual interactions (arrows with rate constants) that govern their dynamical responses. Leukemic cells can reversibly switch between the quiescent (⁠X$⁠) and proliferating (⁠Y$⁠) state with corresponding transition rates {p_{XY}}$ and {p_{YX}}$⁠. Proliferating cells divide with rate {p_Y}( {1 - {\frac{Y}{{{K_Y}}}} )$⁠. The TKI treatment has a cytotoxic effect TKI$ on proliferating cells (thunder symbol)$ while quiescent cells are not affected. Immune cells in Z$ have a cytotoxic effect (with rate m$⁠) on proliferating leukemic cells in Y$⁠. The proliferation of immune cells is stimulated in the presence of proliferating leukemic cells by an immune recruitment rate {p_Z}\cdot{\frac{Y}{{{K_Z}^2 + {Y^2}}}}$⁠. This nonlinear term describes an immune window, where the immune response is suppressed for high leukemic cell levels above the constant {K_Z}$⁠. Moreover, immune cells are generated by a constant production {r_Z}$ and undergo apoptosis with rate a$ (see Materials and Methods).

Figure 1.

Strategy for patient selection and model sketch of TKI-treated CML. A, Flow diagram indicating the process of data selection. Patients were excluded with less than 5 BCR-ABL1 measurements during TKI treatment, missing or extremely low initial measurements (i.e., first measurement was only available after more than 10 months or below MMR). Furthermore, we only included patients with a biexponential decline in which the initial slope was steeper than the second slope. We also selected patients that were under continuous therapy with one TKI, thereby excluding patients with a pretreatment, TKI change during, combination therapy, and missing therapy/cessation information. B, General scheme of the ODE model setup indicating the relevant cell populations and their mutual interactions (arrows with rate constants) that govern their dynamical responses. Leukemic cells can reversibly switch between the quiescent (⁠X$⁠) and proliferating (⁠Y$⁠) state with corresponding transition rates {p_{XY}}$ and {p_{YX}}$⁠. Proliferating cells divide with rate {p_Y}( {1 - {\frac{Y}{{{K_Y}}}} )$⁠. The TKI treatment has a cytotoxic effect TKI$ on proliferating cells (thunder symbol)$ while quiescent cells are not affected. Immune cells in Z$ have a cytotoxic effect (with rate m$⁠) on proliferating leukemic cells in Y$⁠. The proliferation of immune cells is stimulated in the presence of proliferating leukemic cells by an immune recruitment rate {p_Z}\cdot{\frac{Y}{{{K_Z}^2 + {Y^2}}}}$⁠. This nonlinear term describes an immune window, where the immune response is suppressed for high leukemic cell levels above the constant {K_Z}$⁠. Moreover, immune cells are generated by a constant production {r_Z}$ and undergo apoptosis with rate a$ (see Materials and Methods).

Close modal

Mathematical model of TKI-treated CML

For our analysis, we apply an ODE model, which we proposed earlier in a methodologic article qualitatively comparing a set of CML models with different functional interaction terms between leukemic cells and immune cells (39).

This model is sketched in Fig. 1B and formally described by:

formula
formula
formula

The model distinguishes between a population of quiescent leukemic cells (⁠X$⁠) and a population of actively cycling leukemic cells (⁠Y$⁠), which proliferate with the rate {p_Y}$⁠, whereas the growth is limited by a carrying capacity {K_Y}$⁠. Leukemic cells can switch reversibly between the active and the quiescent state with transition rates {p_{XY}}$ and {p_{YX}}$⁠. Apoptosis is negligible for the quiescent population X$ and can be efficiently integrated in the proliferation term for the activated cells Y$⁠. TKI treatment is modeled by a kill rate TKI$⁠, which acts on proliferating cells Y,$ but does not affect quiescent cells X$⁠. Furthermore, we do not explicitly include resistance occurrence in the current model as it does not present a major challenge in CML treatment. A complete eradication of leukemic cells is defined as a decrease of leukemic cells in X$ and Y$ below the threshold of one cell. The corresponding BCR-ABL1/ABL1 ratio in the peripheral blood is calculated as the ratio of proliferating leukemic cells to the carrying capacity {K_Y}$ (see Supplementary Materials for details).

Furthermore, the model integrates a population of CML-specific immune effector cells (⁠Z),$ which are generated at a constant, low production rate {r_Z}$ and undergo apoptosis with rate a$⁠. They eliminate proliferating leukemic cells Y$ with the kill rate m$⁠. The leukemia-dependent recruitment of immune cells follows a nonlinear functional response where {p_Z}$ and {K_Z}$ are positive constants. This functional response leads to an optimal immune cell recruitment for intermediate leukemic cell levels. Low numbers of proliferating leukemic cells (Y \lt \, {K_Z}$⁠), the immune cell recruitment increases, and the immune cells Z$ are stimulated to replicate in presence of proliferating leukemic cells Y$⁠, reaching a maximum {p_Z}/( {2{K_Z}} )$ when Y\ = \ {K_Z}$⁠. For higher leukemic cell numbers (⁠Y \gt \, {K_Z}$⁠), the immune cell recruitment decreases with Y$⁠, reflecting the assumption that the proliferation of immune cells is decreased for high levels of proliferating leukemic cells Y$⁠. This assumption follows recent findings, suggesting that a high load of CML cells inhibits the immune effector cells' function and number (41). As a result, we obtain an immune window for which the recruitment exceeds the degradation rate a$ of the immune cells and leads to an optimal immune response (see Supplementary Materials).

For all patients, we use fixed, universal values for the immune-mediated killing rate m$⁠, the proliferation rate {p_Y}$⁠, the carrying capacity {K_Y}$⁠, the immune cells natural influx {r_Z},$ and the immune cells apoptosis rate a$⁠. In contrast, the transition rates {p_{XY}}$ and {p_{YX}}$⁠, the TKI kill rate TKI$⁠, and the immune parameters {K_Z}$ and {p_Z}\ $are considered patient-specific parameters and are estimated with different strategies (see Supplementary Material).

Individual BCR-ABL1 dynamics after TKI stop can be explained by a patient-specific immune component

Comparing the BCR-ABL1 kinetics of the 21 TKI-treated patients with CML before treatment cessation, we detected no obvious differences between the recurring and nonrecurring patient groups, that is, we found no markers in the patient data, which could potentially serve as a predictive measure to prospectively identify patients that show a treatment-free remission after treatment cessation (see Supplementary Materials and Supplementary Figs. S2 and S3). Motivated by these results, we developed an ODE model of CML treatment to investigate which part of a patient's individual therapy response confers the relevant information to reliably distinguish recurrence from nonrecurrence patients. To do so, we investigated which level of model complexity and what type of patient data are necessary as inputs to obtain model fits that sufficiently represent the available BCR-ABL1 data before and after treatment stop and that would allow to anticipate the response dynamics to TKI cessation. The models and input data used in each fitting strategy are presented below, with an increasing level of complexity.

As a reference model, we use a reduced version of the suggested ODE model without an immunologic component, that is, all immunologic parameters values are set to zero (Fig. 1B; see Materials and Methods, {p_Z}$ = {K_Z}\ = \ a\ = \ {r_Z}\ = \ m\ = \ 0$⁠). This model predicts a complete eradication of residual disease levels only for very long treatment times. Thus, treatment cessation at any earlier time point will eventually lead to recurrence. Adapting this model to each available, individual patient time course by estimating the patient-specific model parameters {p_{XY}}$⁠, {p_{YX}},$ and TKI$ from the precessation BCR-ABL1 data, we confirm that relapse is predicted for all patients (Fig. 2A, example time courses in Fig. 2B and C), which is in contrast to the clinical observations. In summary, the reference model without immune system is not suitable to describe the nonrecurrence cases and thereby opposes clinical findings of TFR (11–14).

Figure 2.

Model comparison using different fitting strategies. A, D, E, and F, Kaplan–Meier estimators comparing the cumulative recurrence rates of four different fitting strategies (gray) with the clinical data (black). A, The reduced model without an immune component, and three different configurations of the immune model [D, generic immune system configuration (fitting strategy I); E, individual immune system configuration estimated by fitting pre-cessation data of the BCR-ABL1/ABL1 time courses (fitting strategy II); F, individual immune system configuration estimated by fitting the complete BCR-ABL1/ABL1 time courses (fitting strategy III)]. The insets show the rate of true positive (tp) and true negative (tn) predictions of the model. B and C, Examples of clinical data for a representative recurring (B) and a nonrecurring (C) patient, with corresponding model predictions for the reduced model without an immune component (black) and the full model using an individual immune system configuration estimated by fitting complete BCR-ABL1/ABL1 time courses (fitting strategy III, gray). Black dots, BCR-ABL1/ABL1 measurements. Black triangles indicate the lower quantification limit for undetectable BCR-ABL1 levels (see Supplementary Materials). The gray area indicates the time period after treatment cessation.

Figure 2.

Model comparison using different fitting strategies. A, D, E, and F, Kaplan–Meier estimators comparing the cumulative recurrence rates of four different fitting strategies (gray) with the clinical data (black). A, The reduced model without an immune component, and three different configurations of the immune model [D, generic immune system configuration (fitting strategy I); E, individual immune system configuration estimated by fitting pre-cessation data of the BCR-ABL1/ABL1 time courses (fitting strategy II); F, individual immune system configuration estimated by fitting the complete BCR-ABL1/ABL1 time courses (fitting strategy III)]. The insets show the rate of true positive (tp) and true negative (tn) predictions of the model. B and C, Examples of clinical data for a representative recurring (B) and a nonrecurring (C) patient, with corresponding model predictions for the reduced model without an immune component (black) and the full model using an individual immune system configuration estimated by fitting complete BCR-ABL1/ABL1 time courses (fitting strategy III, gray). Black dots, BCR-ABL1/ABL1 measurements. Black triangles indicate the lower quantification limit for undetectable BCR-ABL1 levels (see Supplementary Materials). The gray area indicates the time period after treatment cessation.

Close modal

Clinical studies suggest that immunologic components can potentially control minimal residual disease levels and, therefore, might prevent (molecular) recurrences after TKI stop (20, 21). Therefore, we use the ODE model (Materials and Methods, Eqs. A–C) that explicitly considers an immune component (39). Because measurements of individual antileukemic immune conditions are not available, we investigate three different approaches (fitting strategy I–III) for estimating the relevant immune parameters {K_Z}$ and {p_Z}$ and compare the corresponding simulation results with the clinical data.

In fitting strategy I, we consider a generic immune system configuration with identical immune parameters {K_Z}$ and {p_Z}$ for all patients. The remaining parameters {p_{XY}}$⁠, {p_{YX}},$ and TKI$ are estimated by individually fitting the model to the precessation BCR-ABL1 time courses. A grid-based search in the ({K_Z}$⁠, {p_Z})$ space of immune parameters only identifies configurations in which the overall rates and timings of recurrence are not sufficiently met (Fig. 2D). Furthermore, the model predictions fail on the individual level, as neither the time courses nor the recurrence behavior could be predicted reliably (Fig. 2D, inset). These findings as well as the recognition of immunologic differences between different patients argues in favor of patient-specific immune parameters.

In fitting strategy II, besides parameters {p_{XY}}$⁠, {p_{YX,}}$ and TKI$⁠, we also estimate patient-specific values for immune parameter {K_Z}$ and {p_Z}$⁠; however, we only apply the fitting routine to the precessation BCR-ABL1 time courses. We observe no statistically significant difference between recurring and nonrecurring patients with respect to the fitted immune parameter values (Supplementary Fig. S4). Furthermore, the optimal fits fail to correctly predict the outcomes for individual patients (Fig. 2E). This indicates that the configuration of the immune response is most likely not imprinted in the patient response under TKI treatment, in which the drug mediated leukemia reduction is the dominating process.

In fitting strategy III, we provide pre- and postcessation data to fit patient specific model parameters {p_{XY}}$⁠, {p_{YX}}$⁠, TKI$⁠, {K_{Z,}}$ and {p_Z}$⁠. We demonstrate that a patient-specific immune configuration is sufficient to consistently explain the clinical data (example time courses in Fig. 2B and C; complete data in Supplementary Fig. S5; Supplementary Table S1), and that it can be obtained from patient's response after TKI stopping. The model correctly describes the behavior on the population level (Fig. 2F), as well as on the individual patients (Fig. 2F, inset).

Having a univariate look at the individually estimated parameters of the immune model using fitting strategy III (Fig. 3AE), we observed only minor differences between the recurring and the nonrecurring patients, that do not allow to clearly distinguish the patient groups. However, a bivariate analysis of the immune parameters {K_Z}$ and {p_Z}$ reveals a distinction between recurrence and nonrecurrence cases (Fig. 3F). In particular, a lower value for the location of the immune window {K_Z}$ together with a higher proliferation of the immune cells {p_Z}$ convey a favorable outcome after therapy stop. This pattern is also confirmed at the level of individual patients in which we studied the predicted outcome for optimal fits with systematically varying immune parameters (Fig. 3G; Supplementary Fig. S6). This analysis reveals distinct parameter regions for which either remission or recurrence is predicted, although the precise location of those regions further depends on all model parameters.

Figure 3.

Comparison of estimated immune model parameters for recurring and nonrecurring patients. AE, Violin plots of the best fit values for model parameters {p_Z}$⁠, {K_Z},\ {p_{XY}}$⁠, {p_{YX}}$⁠, and TKI$ obtained by using fitting strategy III, shown separately for the groups of recurring (dark gray) and nonrecurring (light gray) patients. The individual parameter values are shown as short horizontal black (recurring patients) and white tick marks (nonrecurring patients). The horizontal black lines indicate the median value of each group, while the dashed gray line depicts the mean value of the complete cohort. P values are based on Kolmogorov–Smirnov tests to compare the distribution of the estimated parameters. F, Scatter plot for the best fitting immune parameter {p_Z}$ versus {K_Z}$ obtained for each patient (fitting strategy III) from the recurrence (dark gray) and nonrecurrence group (light gray). G, Predicted recurrence behavior (recurrence, dark gray; nonrecurrence, light gray) for an individual patient depending on the values of the immune parameters (⁠{p_Z}$⁠, {K_Z}$⁠), which are varied within a predefined grid. The remaining free parameters (⁠{p_{XY}}$⁠, {p_{YX}},\ TKI$⁠) were optimized according to fitting strategy III. Only parameter estimations resulting in sufficiently good fits (i.e., with a residual sum of squares less than twice the residual sum of squares of the best fit) are shown. Supplementary Figure S6 provides the corresponding plots for all 21 patients.

Figure 3.

Comparison of estimated immune model parameters for recurring and nonrecurring patients. AE, Violin plots of the best fit values for model parameters {p_Z}$⁠, {K_Z},\ {p_{XY}}$⁠, {p_{YX}}$⁠, and TKI$ obtained by using fitting strategy III, shown separately for the groups of recurring (dark gray) and nonrecurring (light gray) patients. The individual parameter values are shown as short horizontal black (recurring patients) and white tick marks (nonrecurring patients). The horizontal black lines indicate the median value of each group, while the dashed gray line depicts the mean value of the complete cohort. P values are based on Kolmogorov–Smirnov tests to compare the distribution of the estimated parameters. F, Scatter plot for the best fitting immune parameter {p_Z}$ versus {K_Z}$ obtained for each patient (fitting strategy III) from the recurrence (dark gray) and nonrecurrence group (light gray). G, Predicted recurrence behavior (recurrence, dark gray; nonrecurrence, light gray) for an individual patient depending on the values of the immune parameters (⁠{p_Z}$⁠, {K_Z}$⁠), which are varied within a predefined grid. The remaining free parameters (⁠{p_{XY}}$⁠, {p_{YX}},\ TKI$⁠) were optimized according to fitting strategy III. Only parameter estimations resulting in sufficiently good fits (i.e., with a residual sum of squares less than twice the residual sum of squares of the best fit) are shown. Supplementary Figure S6 provides the corresponding plots for all 21 patients.

Close modal

From these results, we conclude that an individual immunologic component (or another TKI-independent antileukemic effect) is necessary to quantitatively explain the individual BCR-ABL1 time courses of CML patients before and after stopping the TKI treatment. Our results also suggest that the correct estimation of the parameters describing such immunologic component for each patient is not possible based on the BCR-ABL1 dynamics under constant TKI treatment alone and cannot be used for the prospective prediction of the molecular recurrence after TKI stop.

Individual recurrence classification based on an “immunologic landscape”

Dynamical models, as the one suggested here for the interaction between leukemic and immunologic cells (Fig. 4A), are characterized by steady states that describe configurations in which the model quantities (in our case, cell populations) have reached an equilibrium. Stable steady states and their basins of attractions are conveniently depicted in a state space representation, which mimics a physical landscape (Fig. 4B; ref. 42). Typical steady states in our model refer to a fully developed leukemia (“disease steady state”, Y \approx {K_Z}$⁠) or an immunologic control of residual leukemic levels (“remission steady state”, Y \ll {K_Z}$⁠), while trajectories represent dynamical changes of the system state along time. The existence and the precise location of the steady states and their basins of attraction depend on the particular leukemic and immunologic model parameters and thereby determines the range of possible steady states that can be achieved after treatment cessation (Fig. 4C). As these parameters, obtained from fitting strategy III, differ between individual patients, they also describe “patient-specific immunologic landscapes.”

Figure 4.

Conceptual approach to obtain immunologic landscapes. A, A set of optimal, patient-specific model parameters is obtained by fitting the ODE model to the pre- and postcessation BCR-ABL1 time courses of each patient (black lines indicating the optimal model fit to the data). B, On the basis of the obtained parameters, a phase portrait of system (Eqs. A–C) can be reconstructed, in which the abundance of leukemic (in terms of BCR-ABL1/ABL1 ratio) and immune cells are shown on the respective axes. For the situation of no TKI treatment (TKI = 0), several stable steady states can be identified to which the system would converge in the long run. Typically, the disease steady state {E_H}$ is characterized by a high number of leukemic cells and few immune cells, while in the remission steady state {E_L}$⁠, an increased number of immune cells exerts control of a residual leukemic disease. Each stable steady state has a basin of attraction, which is the set of all points that approach the stable point as time passes. A complete eradication of leukemic cells constitutes the cure steady state {E_0}$⁠, which is intrinsically unstable and does not have a basin of attraction. At diagnosis, the system state is near the disease steady state and will remain there unless the TKI treatment drives the system away from this basin of attraction (green trajectory, lowering the abundance of leukemic cells). The outcome after treatment cessation depends on whether the trajectory has crossed the separatrix (dashed line separating the different basins of attraction) or not (indicated by the orange or purple star, respectively). The system either returns to the disease steady state, indicating recurrence (red trajectory), or approaches the remission steady state (blue trajectory), indicating sufficient immune activation and sustained disease control. The resulting “immunologic landscape” is patient-specific and the location of the separatrix may differ for different patients. This implies that the minimum level of leukemic cells to guarantee TFR differs between patients. C, Given the particular model parameterization and the resulting immunologic landscape for each patient, it is now possible to simulate different treatment scenarios for that particular patient including different cessation times (indicated by the orange or purple star).

Figure 4.

Conceptual approach to obtain immunologic landscapes. A, A set of optimal, patient-specific model parameters is obtained by fitting the ODE model to the pre- and postcessation BCR-ABL1 time courses of each patient (black lines indicating the optimal model fit to the data). B, On the basis of the obtained parameters, a phase portrait of system (Eqs. A–C) can be reconstructed, in which the abundance of leukemic (in terms of BCR-ABL1/ABL1 ratio) and immune cells are shown on the respective axes. For the situation of no TKI treatment (TKI = 0), several stable steady states can be identified to which the system would converge in the long run. Typically, the disease steady state {E_H}$ is characterized by a high number of leukemic cells and few immune cells, while in the remission steady state {E_L}$⁠, an increased number of immune cells exerts control of a residual leukemic disease. Each stable steady state has a basin of attraction, which is the set of all points that approach the stable point as time passes. A complete eradication of leukemic cells constitutes the cure steady state {E_0}$⁠, which is intrinsically unstable and does not have a basin of attraction. At diagnosis, the system state is near the disease steady state and will remain there unless the TKI treatment drives the system away from this basin of attraction (green trajectory, lowering the abundance of leukemic cells). The outcome after treatment cessation depends on whether the trajectory has crossed the separatrix (dashed line separating the different basins of attraction) or not (indicated by the orange or purple star, respectively). The system either returns to the disease steady state, indicating recurrence (red trajectory), or approaches the remission steady state (blue trajectory), indicating sufficient immune activation and sustained disease control. The resulting “immunologic landscape” is patient-specific and the location of the separatrix may differ for different patients. This implies that the minimum level of leukemic cells to guarantee TFR differs between patients. C, Given the particular model parameterization and the resulting immunologic landscape for each patient, it is now possible to simulate different treatment scenarios for that particular patient including different cessation times (indicated by the orange or purple star).

Close modal

A detailed mathematical analysis suggests that the available patients can be grouped in three general classes that correspond to structurally different underlying landscapes of the ODE model:

  • Class A: For certain parameter configurations, the immunologic landscape has only one stable steady state, namely the recurrence steady state {E_H}$⁠. This means that the patient will always present with recurring disease after treatment cessation in this model due to an insufficient immune response, if CML is not completely eradicated, irrespective of the degree of tumor load reduction. The corresponding immunological landscape is visualized in Fig. 5A and depicts the recurrence behaviour depending on the number of immune cells and leukemic cells at treatment cessation. According to our estimates, 6 of 21 patients fall into class A and ultimately present with recurring disease after treatment cessation (example in Fig. 5B).

  • Class B: For other parameter configurations, the immunologic landscape has two stable steady states: the disease steady state {E_H},$ and the remission steady state {E_L}$⁠. In this case, there is a distinct remission level of BCR-ABL1 abundance, below which a strong immune system can further diminish the leukemia without TKI support. The corresponding immunologic landscape is divided into these two basins of attraction and is visualized in Fig. 5C. We estimate 8 of 21 patients in this class, which all maintain TFR (example in Fig. 5D).

  • Class C: The third class has the same stable steady states as class B, but in this case a small disturbance from the cure steady state {E_0}$ leads to the attraction basin of the recurrence steady state {E_H}$ instead of the remission steady state {E_L}$⁠. Only for a small range of CML abundance and a sufficiently high level of immune cells, the immune system is appropriately activated to keep the leukemia under sustained control. Figure 5E and F illustrates this control region as an isolated attractor basin. In the ideal case, the TKI therapy only reduces the leukemic load to a level that is sufficient to still activate the immune system to achieve this balance. However, if TKI treatment reduces tumor load to a very deep level, the CML cells regrow after therapy cessation as the immune response was also reduced too much. This represents a patient with CML that may potentially achieve TFR but has a weak immune response. We estimate that 7 of 21 patients fall in this class, of which four have a recurrence and three remain in TFR (two examples in Fig. 5G and H).

Figure 5.

Immunologic landscapes for typical clinical scenarios and corresponding time courses. A, C, E, and G, Examples of patient specific landscapes are shown on the left side (compare Fig. 4). The disease and remission state is represented by solid circles (). The y-axis (BCR-ABL1/ABL1) is set to a nonlinear scale via a root transformation. The black solid line describes trajectories under TKI treatment, while the gray line describes the time course after treatment cessation. B, D, F, and H, Corresponding clinical data (dots and triangles; compare Fig. 2B and C) and optimal simulation results (black line, predicted BCR-ABL1/ABL1 ratio; gray line, predicted number of immune cells) are shown on the right side (compare Fig. 2B and C). Horizontal dashed lines indicate the immune window if it exists (see Materials and Methods and Supplementary Material). A and B, For patients in class A (insufficient immune response), only the disease steady state {E_H}$ is available, and all trajectories lead to recurrence after treatment cessation. C and D, Class B patients (strong immune response) present with the disease steady state {E_H}$ and remission steady state {E_L}$⁠. The separatrix between their basins of attraction is represented by a dashed line. After treatment cessation, the patients stays in TFR. EH, Patients of class C (weak immune response) present with an isolated basin of attraction for the remission steady state {E_L}$⁠, which is more difficult to reach. The example in E and G maintains TFR after TKI cessation, while the lower example in F and H presents with recurrence.

Figure 5.

Immunologic landscapes for typical clinical scenarios and corresponding time courses. A, C, E, and G, Examples of patient specific landscapes are shown on the left side (compare Fig. 4). The disease and remission state is represented by solid circles (). The y-axis (BCR-ABL1/ABL1) is set to a nonlinear scale via a root transformation. The black solid line describes trajectories under TKI treatment, while the gray line describes the time course after treatment cessation. B, D, F, and H, Corresponding clinical data (dots and triangles; compare Fig. 2B and C) and optimal simulation results (black line, predicted BCR-ABL1/ABL1 ratio; gray line, predicted number of immune cells) are shown on the right side (compare Fig. 2B and C). Horizontal dashed lines indicate the immune window if it exists (see Materials and Methods and Supplementary Material). A and B, For patients in class A (insufficient immune response), only the disease steady state {E_H}$ is available, and all trajectories lead to recurrence after treatment cessation. C and D, Class B patients (strong immune response) present with the disease steady state {E_H}$ and remission steady state {E_L}$⁠. The separatrix between their basins of attraction is represented by a dashed line. After treatment cessation, the patients stays in TFR. EH, Patients of class C (weak immune response) present with an isolated basin of attraction for the remission steady state {E_L}$⁠, which is more difficult to reach. The example in E and G maintains TFR after TKI cessation, while the lower example in F and H presents with recurrence.

Close modal

For completeness, there is a fourth class, in which only a cure steady state exists. In this case, CML would not develop at all due to a strongly suppressive immune system. Naturally, those individuals do not appear in the patient cohort at all.

Treatment optimization informed by the immunologic configuration

We showed that the immunologic configuration of each patient determines which steady states can be reached using TKI treatment. It should be pointed out that the resulting conclusion does not depend only on the model fits to the data, but also on the particular mechanisms assumed by the model structure. Within those restrictions, it appears that patients in class A can only stop TKI treatment in the case that the disease is completely eradicated. This would require a median treatment time of 29 years in our simulations and was not achieved in any of the considered patients. However, even if treatment cessation is not an option for these patients, our previously published results suggests that TKI dose reduction could be considered as a long-term treatment alternative (9).

From a perspective of treatment optimization, patients in classes B and C are most interesting as they present an immune window, in which a TKI-based reduction of the leukemic cells can sufficiently stimulate the expansion of the immune cell population (Supplementary Fig. S7; Supplementary Materials). Our model suggests that patients in class B are characterized by an immunologic response that is sufficient to control the leukemia once the leukemic load has initially been reduced below a certain threshold. This remission allows for an activation of the immune system to further control the leukemia eradication even in the absence of TKI treatment. It is essential that the initial remission and the immunologic activation surpass a certain threshold, which is indicated by the line separating the different basins of attraction in Figs. 4B and 5C (separatrix). Clinically, this can be achieved by a sufficiently long TKI therapy, although we predict that this necessary time span was already reached much earlier for the respective six patients, in comparison with their actual treatment times (Supplementary Table S2).

In contrast to class B, the model analysis implies that patients in class C can also present with recurrence if a long TKI treatment is applied. Only in a narrow region of CML abundance the immune system is sufficiently stimulated: if leukemic load is too high, the immunologic component is still suppressed, while for too low levels the stimulation is not strong enough. In this respect, TFR can only be achieved if treatment keeps the patient within his individualized immune window for a sufficient time thereby supporting the adequate proliferation of immune cells, such that the patient reaches the basin of attraction of the remission steady state {E_L}$ (Fig. 6A and B). If the treatment intensity is too high or the treatment duration is too long, this might lead to an “overtreatment” where the inherent immunologic defense is not quickly and sufficiently activated to control a recurrence once TKI is stopped (Fig. 6CH). We show with a hypothetical treatment protocol that an adjustment of the necessary balance between leukemia abundance and immunologic activation can be achieved within this model by detailed assessment of both cell populations and a narrowly adapted TKI administration (Supplementary Figs. S8 and S9).

Figure 6.

Predicted recurrence behavior of patients with weak immune response (class C). Typical immunologic landscapes, as they can occur for patients with a weak immune response (class C), are complemented with corresponding simulation time courses for BCR-ABL1/ABL1 ratio and immune cell number for different simulated treatment times (see Fig. 5). A and B, TKI treatment “drives” the system within the isolated basin of the remission steady state {E_L}$⁠, and the simulated patient achieves TFR. C and D, Using the same parameterization as in A and B, but a longer treatment time, makes the trajectory leave the basin of attraction for the remission steady state. This leads to a considerable decrease in the recruitment of immune cells and results in recurrence after TKI cessation. E, F, G, and H, For another parameterization of the ODE model, the treatment trajectory would never reach the basin of the remission steady state, independent of the applied treatment time (35 months in E and F; 70 months in G and H), and ultimately lead to disease recurrence.

Figure 6.

Predicted recurrence behavior of patients with weak immune response (class C). Typical immunologic landscapes, as they can occur for patients with a weak immune response (class C), are complemented with corresponding simulation time courses for BCR-ABL1/ABL1 ratio and immune cell number for different simulated treatment times (see Fig. 5). A and B, TKI treatment “drives” the system within the isolated basin of the remission steady state {E_L}$⁠, and the simulated patient achieves TFR. C and D, Using the same parameterization as in A and B, but a longer treatment time, makes the trajectory leave the basin of attraction for the remission steady state. This leads to a considerable decrease in the recruitment of immune cells and results in recurrence after TKI cessation. E, F, G, and H, For another parameterization of the ODE model, the treatment trajectory would never reach the basin of the remission steady state, independent of the applied treatment time (35 months in E and F; 70 months in G and H), and ultimately lead to disease recurrence.

Close modal

TKI dose alteration informs molecular recurrence after treatment cessation

Detailed information about a patient's response to TKI treatment cessation (according to fitting strategy III) can only be obtained if the complete data (including postcessation measurements) is available. Thus, this approach can obviously not serve as a prediction strategy before therapy stop. However, we show in the following that response to dose reduction, prior to therapy stop, will also provide information to identify the patient specific immunologic landscape and is, therefore, likely to provide important information about the disease dynamics after treatment cessation. Both, clinical and modeling evidence support the strategy to use information from intermediate dose reduction as this appears as a safe treatment option for almost all well-responding patients with CML (9, 43).

Specifically, individual fits for all patients according to the immune model and fitting strategy III allow to mathematically simulate how the patients would have responded if they were treated with a reduced TKI dose instead of stopping TKI completely. We use these model simulations to derive information about the predicted BCR-ABL1 ratio during a 50% dose reduction within a 12-month period. Figure 7A and B illustrates two typical time courses.

Figure 7.

Simulation of individual responses to TKI dose reduction and association with the final remission state. A and B, Representative time courses illustrate simulated patient responses [in terms of BCR-ABL1/ABL1 ratios (black line) and number of immune cells (gray line), compare Fig. 5] under the assumption that the TKI dose is reduced to 50% of the initial dose during a 12-month dose reduction period (gray background). From these simulations, the linear slope of the log(BCR-ABL1/ABL1) ratio during the dose reduction period (dashed white line; the inset shows an enlarged view of the dose reduction period) is obtained using a linear regression model. C, Logistic regression analysis for the remission status of all 21 patients after treatment cessation [either recurring or nonrecurring; class indicated by symbol; class A, circle; class B, square; class C, rhombus; overlapping points are stacked horizontally (*)] versus their simulated log(BCR-ABL1/ABL1) slope during the 12-month dose reduction period. The solid line indicates the estimated chance that a patient presenting with the particular slope during dose reduction will show disease recurrence after finally stopping TKI treatment. The corresponding OR = 1.21 (95% CI: 1.07–1.51) indicates that the chance for disease recurrence after TKI stop increases by 21% for each 0.01 increase in the log10(BCR-ABL1/ABL1) slope during dose reduction.

Figure 7.

Simulation of individual responses to TKI dose reduction and association with the final remission state. A and B, Representative time courses illustrate simulated patient responses [in terms of BCR-ABL1/ABL1 ratios (black line) and number of immune cells (gray line), compare Fig. 5] under the assumption that the TKI dose is reduced to 50% of the initial dose during a 12-month dose reduction period (gray background). From these simulations, the linear slope of the log(BCR-ABL1/ABL1) ratio during the dose reduction period (dashed white line; the inset shows an enlarged view of the dose reduction period) is obtained using a linear regression model. C, Logistic regression analysis for the remission status of all 21 patients after treatment cessation [either recurring or nonrecurring; class indicated by symbol; class A, circle; class B, square; class C, rhombus; overlapping points are stacked horizontally (*)] versus their simulated log(BCR-ABL1/ABL1) slope during the 12-month dose reduction period. The solid line indicates the estimated chance that a patient presenting with the particular slope during dose reduction will show disease recurrence after finally stopping TKI treatment. The corresponding OR = 1.21 (95% CI: 1.07–1.51) indicates that the chance for disease recurrence after TKI stop increases by 21% for each 0.01 increase in the log10(BCR-ABL1/ABL1) slope during dose reduction.

Close modal

Quantitatively, we estimate the linear slopes of the individual BCR-ABL1/ABL1 response during dose reduction and correlate it to the final remission status after treatment cessation (Fig. 7C). A logistic regression analysis reveals that a 0.01 increase in the estimated slope increases the chance of recurrence by 21% (OR: 1.21; 95% CI: 1.07–1.51), thereby indicating that recurring patients are predicted to present with higher (positive) slopes of the BCR-ABL1 ratio during the dose reduction period. Moreover, complementing this plot with the association of each patient with its predicted particular response class A, B, or C, we observe that class A patients have higher positive slopes and always have a recurrence, while most of class B patients show constant BCR-ABL1 levels, therefore, staying in TFR. Class C patients show both, constant or increasing BCR-ABL1 levels. However, higher positive slopes are more often observed in recurring patients. We suggest that patients with pronounced increases in BCR-ABL1 levels after dose reduction should not stop TKI treatment as this increase points toward an insufficient immune control and conveys an increased risk for molecular recurrence.

Our results are in qualitative and quantitative agreement with a recent reanalysis of clinical data from the DESTINY trial (NCT01804985; refs. 43, 44), which differs from other TKI stop studies as in this trial the TKI treatment is reduced to 50% of the standard dose for 12 months prior to cessation. On the basis of a dataset of 171 patients, we could demonstrate that the patient-individual slope of BCR-ABL1/ABL1 ratios monitored during TKI dose reduction strongly correlates with the risk of individual recurrence after TKI stop (OR: 1.28; 95% CI: 1.17–1.42) and can serve as a promising indicator for high-risk patients (40). Although time courses prior to dose reduction are not available from this study and preclude fitting of the complete ODE model, the overall conclusion of both, the presented conceptual approach and a paralleling data analysis, suggest that dose alterations are a valid means to probe the immunologic configuration of leukemic remission.

Here we present an ODE model for CML treatment that explicitly includes an immunologic component and apply it to describe the therapy response and recurrence behavior of a cohort of 21 patients with CML with detailed BCR-ABL1 follow-up over their whole patient history. We demonstrate that an antileukemic immunologic mechanism is necessary to account for a TKI-independent disease control, which prevents molecular recurrence emerging from residual leukemic cell levels after TKI cessation. Without such a mechanism, a long-term TFR can only be achieved if a complete eradication of leukemic cells is assumed. However, the presence of detectable MRD levels in many patients after therapy cessation (14) is not consistent with this assumption, which strongly suggests an additional control instance, which others (20, 21, 45, 46) and we (39) interpret as a set of immunologic factors. Including these aspects into our modeling approach, the available clinical data can be sufficiently described on the level of individual patients.

On the basis of our simulation results we classify patients into three different groups regarding their predicted immune system configuration (“immunologic landscape”): insufficient immune response (class A), strong immune response (class B), and weak immune response (class C). Class A patients are not able to control residual leukemic cells and would always present with CML recurrence as long as the disease is not completely eradicated. Consistent with the results of Horn and colleagues (47), this is only accomplished on very long timescales in our simulations and would, therefore, result in a lifelong therapy for most affected patients. However, as we suggested earlier, those patients might be eligible for substantial TKI dose reductions during long-term maintenance therapy (9). In contrast, class B patients are predicted to have a strong immune response and to control the leukemia once the leukemic load has been reduced below a certain threshold and thus, are predicted to require only a minimal treatment time (less than 5 years for the studied patients, see Supplementary Table S2) to achieve TFR. For class C patients with a weak immune response, our model predicts that TFR achievement depends on an optimal balance between leukemia abundance and immunologic activation before treatment cessation and could be accomplished by a narrowly adapted TKI administration. These results are in line with those from a recent modeling study that suggested the existence a “Goldilocks Window” in which treatment is required to optimize the balance between maximal tumor reduction and preservation of patient immune function (26).

We also show that the information required to classify the patients according to their immune response and to predict their recurrence behavior cannot be obtained from BCR-ABL1 measurements before treatment cessation only. A different fitting strategy (III) assessing also BCR-ABL1 measurements after treatment cessation shows that the BCR-ABL1 changes resulting from this system perturbation (i.e., TKI stop) yields the necessary information. Interestingly, our simulation results demonstrate that also a less drastic system perturbation, that is, a TKI dose reduction, can provide similar information and can be used to predict the individual outcome after treatment cessation. The feasibility of such an approach has been complemented by a recent reanalysis of the DESTINY trial (NCT01804985), which evaluated a beneficial effect of a 12-month dose reduction treatment prior to TKI stop. We could confirm based on the clinical data of 171 patients that the patient's response dynamic during TKI dose reduction is indeed predictive for the individual risk of CML recurrence after TKI stop (40, 43).

Direct measurements of the individual immune compartments and their activation states represent another road to better understand the configuration of the antileukemic immune response in patients with CML. Several studies identified different immunologic markers in patients with CML that correlate with the probability of treatment-free remission after therapy cessation (20, 21). Learning from the behavior of these populations under continuing TKI treatment and with lowered leukemic load could further contribute to identify a patient's “immunologic landscape” and be informative for the prediction of individual outcomes after treatment stopping. However, as it is not clear which immunologic subset provides the suggested observed anti-CML response (48, 49), corresponding measurements are currently not feasible and strongly argue in favor of our indirect modeling approach, suggesting retrieval of similar information from BCR-ABL1 dynamics after TKI dose reduction.

Our analysis is based on a rather small cohort of patients. Although our results do not depend on the study size, we can derive the strongest conclusions with respect to illustrating the conceptual approach of inferring immune responses from treatment alterations and demonstrating its predictive power. Our results are further based on a set of simplifications and assumptions. As such, we do not consider resistance mutations as almost no such events have been reported during TKI cessation studies in CML and almost all patients respond well to reinitiation of TKI treatment with their previous drug (11). This might be different for other disease entities in which tumor evolution imposes serious challenges to long-term disease control. Focusing on a related aspect it has been shown that different immune cell types are associated with recurrence behavior of patients with CML (20, 21). However, for simplicity, we restricted our analysis to a unified antileukemic immune compartment in the model and did not distinguish between different immune cell populations and interactions between them. Furthermore, the model is based on an interaction between leukemic and immune cells, in which the immune cell population is only activated for intermediate levels of leukemic burden, reflecting the assumption that immune cells are not efficiently activated for small numbers of leukemic cells and are additionally suppressed by high tumor load. Similar assumptions have been discussed recently (37) while we also illustrated the suitability of other mechanisms of interaction (39).

In summary, our results support the notion of immunologic mechanisms as an important factor to determine the success of TFR in patients with CML. Importantly, we show that besides the direct measurement of the immune response, also system perturbations, such as a TKI dose reduction, can (indirectly) provide information about the individual disease dynamics and, therefore, allow to predict the risk of CML recurrence for individual patients after TKI stop. Such results demonstrate the potential of mathematical models in providing insights on the mechanisms underlying cancer treatment as well in delineating different treatment strategies. Applications to other cancer entities, in which the endogenous immune system can support the control or even the eradication of residual tumor cells, are a natural continuation of this work and will become even more important with the availability of cancer immunotherapies that allow modulation of individual immune responses (50).

S. Mustjoki reports receiving a commercial research grant from Pfizer, Novartis, and Bristol Myers Squibb and has received speakers bureau honoraria from Bristol Myers Squibb, Incyte, and Novartis. P.J. Jost reports receiving a commercial research grant from Böhringer and Abbvie, has received speakers bureau honoraria from Novartis, BMS/Celgene, Abbvie, Böhringer, Servier, Pfizer, and has done expert testimony for WEHI. F.-X. Mahon reports receiving speakers bureau honoraria from Novartis and is a consultant/advisory board member for Novartis. I. Roeder reports receiving a commercial research grant from Bristol-Myers Squibb and has received speakers bureau honoraria from Bristol-Myers Squibb and Janssen-Cilag. I. Glauche reports receiving a commercial research grant from Bristol-Myers Squibb. No potential conflicts of interest were disclosed by the other authors.

Conception and design: T. Hähnel, C. Baldow, I. Roeder, A.C. Fassoni, I. Glauche

Development of methodology: T. Hähnel, C. Baldow, I. Roeder, A.C. Fassoni, I. Glauche

Acquisition of data (provided animals, acquired and managed patients, provided facilities, etc.): J. Guilhot, F. Guilhot, S. Saussele, S. Mustjoki, S. Jilg, P.J. Jost, S. Dulucq, F.-X. Mahon

Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis): T. Hähnel, C. Baldow, I. Roeder, A.C. Fassoni, I. Glauche

Writing, review, and/or revision of the manuscript: T. Hähnel, C. Baldow, J. Guilhot, S. Saussele, S. Mustjoki, S. Dulucq, F.-X. Mahon, I. Roeder, A.C. Fassoni, I. Glauche

Administrative, technical, or material support (i.e., reporting or organizing data, constructing databases): S. Mustjoki, I. Glauche

Study supervision: C. Baldow, I. Roeder, A.C. Fassoni, I. Glauche

We thank all patients and hospital staff for providing this valuable data for scientific assessment. This work was supported by the German Federal Ministry of Education and Research (www.bmbf.de/en/), grant number 031A424 “HaematoOpt” (to I. Roeder) and grant number 031A315 “MessAge” (to I. Glauche), as well as the ERA-Net ERACoSysMed JTC-2 project “prediCt” (project number 031L0136A to I. Roeder). The research of A.C. Fassoni was supported by the Excellence Initiative of the German Federal and State Governments (Dresden Junior Fellowship) and by CAPES/Pós-Doutorado no Exterior Grant number 88881.119037/2016-01. S. Mustjoki was supported by Finnish Cancer Organizations, Sigrid Juselius Foundation, and Gyllenberg Foundation.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1.
Hochhaus
A
,
Saussele
S
,
Rosti
G
,
Mahon
F-X
,
Janssen
JJWM
,
Hjorth-Hansen
H
, et al
Chronic myeloid leukaemia: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up
.
Ann Oncol
2017
;
28
:
iv41
51
.
2.
Pasic
I
,
Lipton
JH
. 
Current approach to the treatment of chronic myeloid leukaemia
.
Leuk Res
2017
;
55
:
65
78
.
3.
Rosti
G
,
Castagnetti
F
,
Gugliotta
G
,
Baccarani
M
. 
Tyrosine kinase inhibitors in chronic myeloid leukaemia: which, when, for whom?
Nat Rev Clin Oncol
2017
;
14
:
141
54
.
4.
Apperley
JF
. 
Chronic myeloid leukaemia
.
Lancet North Am Ed
2015
;
385
:
1447
59
.
5.
Michor
F
,
Hughes
TP
,
Iwasa
Y
,
Branford
S
,
Shah
NP
,
Sawyers
CL
, et al
Dynamics of chronic myeloid leukaemia
.
Nature
2005
;
435
:
1267
70
.
6.
Roeder
I
,
Horn
M
,
Glauche
I
,
Hochhaus
A
,
Mueller
MC
,
Loeffler
M
. 
Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications
.
Nat Med
2006
;
12
:
1181
4
.
7.
Stein
AM
,
Bottino
D
,
Modur
V
,
Branford
S
,
Kaeda
J
,
Goldman
JM
, et al
BCR-ABL transcript dynamics support the hypothesis that leukemic stem cells are reduced during imatinib treatment
.
Clin Cancer Res
2011
;
17
:
6812
21
.
8.
Tang
M
,
Gonen
M
,
Quintas-Cardama
A
,
Cortes
J
,
Kantarjian
H
,
Field
C
, et al
Dynamics of chronic myeloid leukemia response to long-term targeted therapy reveal treatment effects on leukemic stem cells
.
Blood
2011
;
118
:
1622
31
.
9.
Fassoni
AC
,
Baldow
C
,
Roeder
I
,
Glauche
I
. 
Reduced tyrosine kinase inhibitor dose is predicted to be as effective as standard dose in chronic myeloid leukemia: a simulation study based on phase III trial data
.
Haematologica
2018
;
103
:
1825
34
.
10.
Cortes
JE
,
Saglio
G
,
Kantarjian
HM
,
Baccarani
M
,
Mayer
J
,
Boqué
C
, et al
Final 5-year study results of DASISION: the dasatinib versus imatinib study in treatment-naïve chronic myeloid leukemia patients trial
.
J Clin Oncol
2016
;
34
:
2333
40
.
11.
Saussele
S
,
Richter
J
,
Guilhot
J
,
Gruber
FX
,
Hjorth-Hansen
H
,
Almeida
A
, et al
Discontinuation of tyrosine kinase inhibitor therapy in chronic myeloid leukaemia (EURO-SKI): a prespecified interim analysis of a prospective, multicentre, non-randomised, trial
.
Lancet Oncol
2018
;
19
:
747
57
.
12.
Okada
M
,
Imagawa
J
,
Tanaka
H
,
Nakamae
H
,
Hino
M
,
Murai
K
, et al
Final 3-year results of the dasatinib discontinuation trial in patients with chronic myeloid leukemia who received dasatinib as a second-line treatment
.
Clin Lymphoma Myeloma Leuk
2018
;
18
:
353
360
.
13.
Mahon
F-X
,
Réa
D
,
Guilhot
J
,
Guilhot
F
,
Huguet
F
,
Nicolini
F
, et al
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
.
Lancet Oncol
2010
;
11
:
1029
35
.
14.
Rousselot
P
,
Charbonnier
A
,
Cony-Makhoul
P
,
Agape
P
,
Nicolini
FE
,
Varet
B
, et al
Loss of major molecular response as a trigger for restarting tyrosine kinase inhibitor therapy in patients with chronic-phase chronic myelogenous leukemia who have stopped imatinib after durable undetectable disease
.
J Clin Oncol
2014
;
32
:
424
30
.
15.
Caldemeyer
L
,
Dugan
M
,
Edwards
J
,
Akard
L
. 
Long-term side effects of tyrosine kinase inhibitors in chronic myeloid leukemia
.
Curr Hematol Malig Rep
2016
;
11
:
71
9
.
16.
Experts in Chronic Myeloid Leukemia
. 
The price of drugs for chronic myeloid leukemia (CML) is a reflection of the unsustainable prices of cancer drugs: from the perspective of a large group of CML experts
.
Blood
2013
;
121
:
4439
42
.
17.
Saussele
S
,
Richter
J
,
Hochhaus
A
,
Mahon
F-X
. 
The concept of treatment-free remission in chronic myeloid leukemia
.
Leukemia
2016
;
30
:
1638
47
.
18.
Takahashi
N
,
Kyo
T
,
Maeda
Y
,
Sugihara
T
,
Usuki
K
,
Kawaguchi
T
, et al
Discontinuation of imatinib in Japanese patients with chronic myeloid leukemia
.
Haematologica
2012
;
97
:
903
6
.
19.
Ross
DM
,
Branford
S
,
Seymour
JF
,
Schwarer
AP
,
Arthur
C
,
Yeung
DT
, et al
Safety and efficacy of imatinib cessation for CML patients with stable undetectable minimal residual disease: results from the TWISTER study
.
Blood
2013
;
122
:
515
22
.
20.
Schütz
C
,
Inselmann
S
,
Sausslele
S
,
Dietz
CT
,
Müller
MC
,
Eigendorff
E
, et al
Expression of the CTLA-4 ligand CD86 on plasmacytoid dendritic cells (pDC) predicts risk of disease recurrence after treatment discontinuation in CML
.
Leukemia
2017
;
31
:
829
36
.
21.
Ilander
M
,
Olsson-Strömberg
U
,
Schlums
H
,
Guilhot
J
,
Brück
O
,
Lähteenmäki
H
, et al
Increased proportion of mature NK cells is associated with successful imatinib discontinuation in chronic myeloid leukemia
.
Leukemia
2017
;
31
:
1108
16
.
22.
Mahon
F-X
. 
Treatment-free remission in CML: who, how, and why?
Hematology Am Soc Hematol Educ Program
2017
;
2017
:
102
9
.
23.
Altrock
PM
,
Liu
LL
,
Michor
F
. 
The mathematics of cancer: integrating quantitative models
.
Nat Rev Cancer
2015
;
15
:
730
45
.
24.
West
JB
,
Dinh
MN
,
Brown
JS
,
Zhang
J
,
Anderson
AR
,
Gatenby
RA
. 
Multidrug cancer therapy in metastatic castrate-resistant prostate cancer: an evolution-based strategy
.
Clin Cancer Res
2019
;
25
:
4413
21
.
25.
Brady
R
,
Enderling
H
. 
Mathematical models of cancer: when to predict novel therapies, and when not to
.
Bull Math Biol
2019
;
81
:
3722
31
.
26.
Park
DS
,
Robertson-Tessi
M
,
Maini
P
,
Bonsall
MB
,
Gatenby
RA
,
Anderson
AR
. 
The Goldilocks window of personalized chemotherapy: an immune perspective [Internet]
; 
2018
.
Available from
: http://biorxiv.org/lookup/doi/10.1101/495184.
27.
Komarova
NL
,
Wodarz
D
. 
Effect of cellular quiescence on the success of targeted CML therapy
.
PLoS One
2007
;
2
:
e990
.
28.
Komarova
NL
,
Wodarz
D
. 
Combination therapies against chronic myeloid leukemia: short-term versus long-term strategies
.
Cancer Res
2009
;
69
:
4904
10
.
29.
Glauche
I
,
Moore
K
,
Thielecke
L
,
Horn
K
,
Loeffler
M
,
Roeder
I
. 
Stem cell proliferation and quiescence–two sides of the same coin
.
PLoS Comput Biol
2009
;
5
:
e1000447
.
30.
Glauche
I
,
Horn
K
,
Horn
M
,
Thielecke
L
,
Essers
MA
,
Trumpp
A
, et al
Therapy of chronic myeloid leukaemia can benefit from the activation of stem cells: simulation studies of different treatment combinations
.
Br J Cancer
2012
;
106
:
1742
52
.
31.
Woywod
C
,
Gruber
FX
,
Engh
RA
,
Flå
T
. 
Dynamical models of mutated chronic myelogenous leukemia cells for a post-imatinib treatment scenario: Response to dasatinib or nilotinib therapy
.
PLoS One
2017
;
12
:
e0179700
.
32.
Nanda
S
,
Moore
H
,
Lenhart
S
. 
Optimal control of treatment in a mathematical model of chronic myelogenous leukemia
.
Math Biosci
2007
;
210
:
143
56
.
33.
Krishchenko
AP
,
Starkov
KE
. 
On the global dynamics of a chronic myelogenous leukemia model
.
Commun Nonlinear Sci Numer Simul
2016
;
33
:
174
83
.
34.
Schiffer
JT
,
Schiffer
CA
. 
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
.
Haematologica
2018
;
103
:
1756
7
.
35.
Kim
PS
,
Lee
PP
,
Levy
D
. 
Dynamics and potential impact of the immune response to chronic myelogenous leukemia
.
PLoS Comput Biol
2008
;
4
:
e1000095
.
36.
Wodarz
D
. 
Heterogeneity in chronic myeloid leukaemia dynamics during imatinib treatment: role of immune responses
.
Proc Biol Sci
2010
;
277
:
1875
80
.
37.
Clapp
GD
,
Lepoutre
T
,
El Cheikh
R
,
Bernard
S
,
Ruby
J
,
Labussiere-Wallet
H
, et al
Implication of the autologous immune system in BCR-ABL transcript variations in chronic myelogenous leukemia patients treated with imatinib
.
Cancer Res
2015
;
75
:
4053
62
.
38.
Besse
A
,
Clapp
GD
,
Bernard
S
,
Nicolini
FE
,
Levy
D
,
Lepoutre
T
. 
Stability analysis of a model of interaction between the immune system and cancer cells in chronic myelogenous leukemia
.
Bull Math Biol
2018
;
80
:
1084
110
.
39.
Fassoni
A
,
Roeder
I
,
Glauche
I
. 
To cure or not to cure: consequences of immunological interactions in CML treatment
.
Bull Math Biol
2019
;
81
:
2345
95
.
40.
Gottschalk
A
,
Glauche
I
,
Cicconi
S
,
Clark
RE
,
Roeder
I
. 
Molecular monitoring during dose reduction predicts recurrence after TKI cessation in CML
.
Blood
2020
;
135
:
766
9
.
41.
Hughes
A
,
Clarson
J
,
Tang
C
,
Vidovic
L
,
White
DL
,
Hughes
TP
, et al
CML patients with deep molecular responses to TKI have restored immune effectors and decreased PD-1 and immune suppressors
.
Blood
2017
;
129
:
1166
76
.
42.
Fassoni
AC
,
Yang
HM
. 
An ecological resilience perspective on cancer: insights from a toy model
.
Ecological Complexity
2017
;
30
:
34
46
.
43.
Clark
RE
,
Polydoros
F
,
Apperley
JF
,
Milojkovic
D
,
Rothwell
K
,
Pocock
C
, et al
De-escalation of tyrosine kinase inhibitor therapy before complete treatment discontinuation in patients with chronic myeloid leukaemia (DESTINY): a non-randomised, phase 2 trial
.
Lancet Haematol
2019
;
6
:
e375
83
.
44.
Clark
RE
,
Polydoros
F
,
Apperley
JF
,
Milojkovic
D
,
Pocock
C
,
Smith
G
, et al
De-escalation of tyrosine kinase inhibitor dose in patients with chronic myeloid leukaemia with stable major molecular response (DESTINY): an interim analysis of a non-randomised, phase 2 trial
.
Lancet Haematol
2017
;
4
:
e310
6
.
45.
Rea
D
,
Henry
G
,
Khaznadar
Z
,
Etienne
G
,
Guilhot
F
,
Nicolini
F
, et al
Natural killer-cell counts are associated with molecular relapse-free survival after imatinib discontinuation in chronic myeloid leukemia: the IMMUNOSTIM study
.
Haematologica
2017
;
102
:
1368
77
.
46.
Hughes
A
,
Yong
ASM
. 
Immune effector recovery in chronic myeloid leukemia and treatment-free remission
.
Front Immunol
2017
;
8
:
469
.
47.
Horn
M
,
Glauche
I
,
Muller
MC
,
Hehlmann
R
,
Hochhaus
A
,
Loeffler
M
, et al
Model-based decision rules reduce the risk of molecular relapse after cessation of tyrosine kinase inhibitor therapy in chronic myeloid leukemia
.
Blood
2013
;
121
:
378
84
.
48.
Ilander
M
,
Mustjoki
S
. 
Immune control in chronic myeloid leukemia
.
Oncotarget
2017
;
8
:
102763
4
.
49.
Brück
O
,
Blom
S
,
Dufva
O
,
Turkki
R
,
Chheda
H
,
Ribeiro
A
, et al
Immune cell contexture in the bone marrow tumor microenvironment impacts therapy response in CML
.
Leukemia
2018
;
32
:
1643
56
.
50.
Zhang
H
,
Chen
J
. 
Current status and future directions of cancer immunotherapy
.
J Cancer
2018
;
9
:
1773
81
.