Cause-specific hazard models with markovian elements to quantify the fludarabine exposure-response relationship: from learning to confirming in allogeneic hematopoietic cell transplantation
J.B. Langenhorst 1,2, T.P.C. Dorlo 3, C. van Kesteren1,2, E.M. van Maarseveen 4, S. Nierkens 2, M.A. De Witte 5, J.J Boelens 1,2, A.D.R. Huitema 3,4
1 Pediatric Blood and Marrow Transplant Program, University Medical Center Utrecht (UMCU), Utrecht University; 2 Laboratory of Translational Immunology, UMCU, Utrecht University; 3 Department of Pharmacy & Pharmacology, Antoni van Leeuwenhoek Hospital/Netherlands Cancer Institute, Amsterdam, The Netherlands; 4 Department of Clinical Pharmacy, UMCU, Utrecht University; 5 Department of Hematology, UMCU, Utrecht University
Allogeneic hematopoietic cell transplantation (HCT) is a potentially curative treatment for a variety of malignant and benign hematological disorders. Unfortunately, non-relapse mortality (NRM, 10-40%) and disease relapse (20-50%) remain major causes of therapy failure, thus further treatment optimization is potentially life-saving.
The conditioning regimen prior to HCT consists of a combination of cytotoxic agents (chemo- and serotherapy) administered to eradicate recipient’s bone marrow and immune system. Reducing the toxicity while maintaining the efficacy of such regimens is one of the key strategies to reduce NRM. Fludarabine combined with busulfan and anti-thymocyte globulin is a commonly used conditioning regimen for HCT and a profound influence of all these agents[3-5] on HCT outcomes has been established.
However, the relationship between fludarabine exposure and HCT’s main outcomes event-free survival (EFS: absence of NRM, relapse, and graft failure) and overall survival (OS) is complex. There is an increased probability of graft failure at low fludarabine exposures, an inverse relationship with NRM,[7, 8] and no relationship with relapse. In addition, NRM and OS are directly connected, but graft failure and relapse are not necessarily followed by death.
Therefore, this study aims to relate fludarabine exposure during conditioning to the separate outcomes measures, using parametric cause-specific hazard models (CSH-models). Models were expanded with Markovian elements, by adding a transition from event to death for relapse and graft failure.
Subsequently, clinical trial simulations (CTS) were performed of studies comparing conventional dosing to alternative dosing strategies in the most abundant group of HCT recipients: adult leukemia and lymphoma patients. The aim of CTS was to estimate the expected survival as a result of reducing exposure variability, and to find the optimal design of a prospective confirmatory study in this patient group.
Events considered were competing risks of graft failure, relapse, and NRM. Relapse was defined as disease recurrence, NRM as death while in complete remission. Both graft rejection and non-engraftment were considered graft failure.
Fludarabine cumulative area-under-the-curve for all doses (AUCT0-∞) was quantitatively linked to events using CSH-models. For relapse, the transition to death was modelled using a parametric survival model describing OS in relapsed patients with event-time as T0. For graft failure, a literature-derived 1-year-OS of 31%  was used as transition probability.
Optimal baseline hazards were selected per model. Covariates based on literature, as well as fludarabine AUCT0-∞, were evaluated as predictors. Evaluation of covariates was done by stepwise forward inclusion (p<0.15) and backward deletion (p>0.05). Continuous covariates were tested linearly and as a polynomial spline (3, 4 and 5 degrees of freedom).
The AUCT0-∞ resulting in maximum EFS probability, estimated by exponentiating the sum of the cumulative hazard for separate events, was henceforth regarded as the optimal exposure.
CSH-models were evaluated for predicting both EFS and OS, using a visual predictive check (VPC). The 95% confidence intervals and means of 1000 simulations were compared to the observed Kaplan-Meier estimates of both EFS and OS.
For the CTS, 1) the conventional 160 mg/m2 dose was compared to 2) dosing based on the predicted clearance (Clpred) by the pharmacokinetic (PK) model or 3) dosing based on therapeutic drug monitoring (TDM), both 2 and 3 targeted to the optimal exposure.
Patient variables were derived from an in-house database of HCT recipients (2005-2016). The PK model was used to derive individual exposures following the various dosing strategies and to simulate 5 observations (1, 4, 5, 6, 7-hour post-infusion) on day 1 as input for TDM. TDM samples were randomly excluded according to the previously observed distribution of missing samples.
The CTS were used to 1) determine the optimal trial design (dosing strategy, primary outcome, number of subjects, stratification) and 2) calculate the expected results of such trial.
Using baseline characteristics and fludarabine AUCT0-∞, daily event probabilities were estimated with the CSH-models. Events and OS were then simulated up to 1 year. Trial endpoints were: cumulative incidence of events and OS as calculated by the Kaplan-Meier method. To compare dosing strategies, p-values were calculated using Gray’s test (events) or the log-rank test (OS). Power was defined as the percentage of studies with p less than 0.05. The design resulting in at least 80% power with minimal subjects was considered optimal. During trial optimization, 100 trials were simulated per design and the proposed optimal trial was simulated 1000 times.
The CSH-models were based on 192 patients. Models were best described by a log-logistic- (relapse), exponential- (graft failure), and Gompertz- (NRM & post-relapse survival) distribution. Fludarabine AUCT0-∞ was included on NRM (polynomial spline, 4 degrees of freedom, p<0.001) and graft failure (linear, p=0.03) hazards. The target AUCT0-∞ was found at 20 mg*h/L, with increased graft failures below, and NRM above this exposure. In the VPC’s, simulated EFS and OS were in line with observations.
For CTS, 148 patients were selected. Missing data (weight/height: 33%) were imputed from the observed distribution per age quantile. 25 possible parameter vectors per subject were simulated with the PK model, to expand the dataset and account for uncertainty in expected clearance. Each derived set was then assessed as a new subject.
A design with 90 subjects randomized to either 160 mg/m2 or TDM, stratified on renal function (≥ 90 ml/min/1.73 m2) with NRM as a primary endpoint was found to be optimal. With a similar design, but Clpred-based dosing as a comparator, 80 more subjects per arm were necessary for sufficient power.
Simulations of the proposed optimal trial showed a decrease in median NRM from 27% in 160 mg/m2 dosing to 10% in TDM-based dosing. Relapse incidence and graft failure followed an inverse trend: there was 3% increase in relapse, due to more patients being at risk, and 2% more graft failures, as a result from the lower exposures following TDM-based dosing (median AUCT0-∞: 20 mg*h/L compared to 24 mg*h/L). Finally, OS increased from 57% (160 mg/m2) to 72% (TDM-based), although the power for this result was only 63%.
These results indicate that a substantial survival benefit may be achieved by individualizing the fludarabine dose prior to HCT. However, unpredicted variability and concomitant sub-/supra-optimal exposures in alternative dosing regimens decrease the power of a confirmatory trial for this effect. Therefore, TDM should be used as a comparator, to minimize remaining variability, and at least 90 patients per arm are necessary.
 Hahn, T. et al. Significant improvement in survival after allogeneic hematopoietic cell transplantation during a period of significantly increased use, older recipient age, and use of unrelated donors. J Clin Oncol 31, 2437-49 (2013).
 Gooley, T.A. et al. Reduced mortality after allogeneic hematopoietic-cell transplantation. N Engl J Med 363, 2091-101 (2010).
 Admiraal, R. et al. Association between anti-thymocyte globulin exposure and survival outcomes in adult unrelated haemopoietic cell transplantation: a multicentre, retrospective, pharmacodynamic cohort analysis. Lancet Haematol 4, e183-e91 (2017).
 Bartelink, I.H. et al. Association of busulfan exposure with survival and toxicity after haemopoietic cell transplantation in children and young adults: a multicentre, retrospective cohort analysis. Lancet Haematol 3, e526-e36 (2016).
 J.B. Langenhorst et al. High exposure to fludarabine in conditioning prior to allogeneic hematopoietic cell transplantation predicts impaired CD4 reconstitution and lower probability of survival. Abstract PAGE B-17, (2017).
 Ivaturi, V. et al. Pharmacokinetics and Model-Based Dosing to Optimize Fludarabine Therapy in Pediatric Hematopoietic Cell Transplant Recipients. Biol Blood Marrow Transplant 23, 1701-13 (2017).
 Sanghavi, K. et al. Personalized fludarabine dosing to reduce nonrelapse mortality in hematopoietic stem-cell transplant recipients receiving reduced intensity conditioning. Transl Res 175, 103-15 e4 (2016).
 Long-Boyle, J.R. et al. High fludarabine exposure and relationship with treatment-related mortality after nonmyeloablative hematopoietic cell transplantation. Bone Marrow Transplant 46, 20-6 (2011).
 Hinchliffe, S.R. & Lambert, P.C. Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions. BMC Med Res Methodol 13, 13 (2013).
 Rondon, G. et al. Long-term follow-up of patients who experienced graft failure postallogeneic progenitor cell transplantation. Results of a single institution analysis. Biol Blood Marrow Transplant 14, 859-66 (2008).