Using adaptive model predictive control to customize maintenance therapy chemotherapeutic dosing for childhood acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a common childhood cancer in which nearly one-quarter of patients experience a disease relapse. However, it has been shown that individualizing therapy for childhood ALL patients by adjusting doses based on the blood concentration of active drug metabolite could significantly improve treatment outcome. An adaptive model predictive control (MPC) strategy is presented in which maintenance therapy for childhood ALL is personalized using routine patient measurements of red blood cell mean corpuscular volume as a surrogate for the active drug metabolite concentration. A clinically relevant mathematical model is developed and used to describe the patient response to the chemotherapeutic drug 6-mercaptopurine, with some model parameters being patient-specific. During the course of treatment, the patient-specific parameters are adaptively identified using recurrent complete blood count measurements, which sufficiently constrain the patient parameter uncertainty to support customized adjustments of the drug dose. While this work represents only a first step toward a quantitative tool for clinical use, the simulated treatment results indicate that the proposed mathematical model and adaptive MPC approach could serve as valuable resources to the oncologist toward creating a personalized treatment strategy that is both safe and effective.     

Challenges in implementing individualized medicine illustrated by antimetabolite therapy of childhood acute lymphoblastic leukemia

Predicting the response to medical therapy and subsequently individualizing the treatment to increase efficacy or reduce toxicity has been a longstanding clinical goal. Not least within oncology, where many patients fail to be cured, and others are treated to or beyond the limit of acceptable toxicity, an individualized therapeutic approach is indicated. The mapping of the human genome and technological developments in DNA sequencing, gene expression profiling, and proteomics have raised the expectations for implementing genotype-phenotype data into the clinical decision process, but also multiplied the complex interaction of genetic and other laboratory parameters that can be used for therapy adjustments. Thus, with the advances in the laboratory techniques, post laboratory issues have become major obstacles for treatment individualization. Many of these challenges have been illustrated by studies involving childhood acute lymphoblastic leukemia (ALL), where each patient may receive up to 13 different anticancer agents over a period of 2-3 years. The challenges include i) addressing important, but low-frequency outcomes, ii) difficulties in interpreting the impact of single drug or single gene response data that often vary across treatment protocols, iii) combining disease and host genomics with outcome variations, and iv) physicians' reluctance in implementing potentially useful genotype and phenotype data into clinical practice, since unjustified downward or upward dose adjustments could increase the of risk of relapse or life-threatening complications. In this review we use childhood ALL therapy as a model and discuss these issues, and how they may be addressed.     

Micronucleus assays on 5-fluorouracil and 6-mercaptopurine with mouse peripheral blood reticulocytes.

As part of the 5th collaborative study of the Collaborative Study Group for the Micronucleus Test (CSGMT), the sensitivity and advantages of the micronucleus assay using mouse peripheral blood cells were evaluated using 5-fluorouracil (5-FU) and 6-mercaptopurine (6-MP). The peripheral blood cells were collected from a tail vein of CD-1 male mice just before and 24-120 h after intraperitoneal injection. At 24-h intervals. The maximum incidence of micronucleated reticulocytes (MNRETs) at 50 mg/kg 5-FU was observed 96 h after injection; at 100 mg/kg, the peak was delayed to 120 h, and followed severe bone marrow depression. With 6-MP, maximum MNRETs were observed 48 h after treatment at all doses tested. At dose levels higher than 50 mg/kg, severe bone marrow depression was observed after maximum MNRETs. Though the appearance patterns of MNRETs and the bone marrow depression were different between 5-FU and 6-MP, the positive response of both chemical could be detected with this assay system as well as with the micronucleus test using femoral bone marrow cells.     

Brain distribution of 6-mercaptopurine is regulated by the efflux transport system in the blood-brain barrier

6-mercaptopurine (6-MP) has been used clinically for 40 years to maintain remission in patients with acute lymphoblastic leukemia (ALL). However, central nervous system (CNS) relapses frequently occur in patients with ALL who continuously receive anticancer drugs, including 6-MP, during remission maintenance therapy. The cause of such CNS relapse is not well understood. One possible reason may involve the restricted distribution of 6-MP in the brain. This study, therefore, investigates the blood-brain barrier (BBB) transport which largely regulates 6-MP distribution in the brain using a quantitative microdialysis technique and centers on the efflux transport of 6-MP across the BBB. The brain tissue, cerebrospinal fluid (CSF), or hippocampal interstitial fluid (ISF) concentration of 6-MP was very low compared with the unbound plasma concentration, suggesting that 6-MP distribution in the brain is highly restricted. Kinetic analyses of this BBB transport showed that the efflux clearance from brain ISF to plasma across the BBB (CLout) is approximately 20-times greater than the influx clearance from plasma to brain (CLin). The CLout was significantly reduced by 1mM N-ethylmaleimide (NEM), a sulfhydryl-modifying agent, suggesting the participation of transport protein in the efflux of 6-MP across the BBB. In addition, efflux transport was inhibited by an intracerebral infusion of probenecid (1.5 mM), p-aminohippuric acid (PAH, 3.0 mM), benzoate (3.6 mM), or salicylate (3.7 mM) administered through a microdialysis probe, but neither choline (0.8 mM) nor tetraethylammonium (TEA, 0.7 mM) had any effect. These data suggest that the restricted 6-MP brain distribution may be ascribed to efficient efflux from the brain, possibly via both the organic anion transport system, shared with probenecid and PAH, and the monocarboxylic acid transport system, shared with benzoate and salicylate.     

A utility approach to individualized optimal dose selection using biomarkers

In many settings, including oncology, increasing the dose of treatment results in both increased efficacy and toxicity. With the increasing availability of validated biomarkers and prediction models, there is the potential for individualized dosing based on patient specific factors. We consider the setting where there is an existing dataset of patients treated with heterogenous doses and including binary efficacy and toxicity outcomes and patient factors such as clinical features and biomarkers. The goal is to analyze the data to estimate an optimal dose for each (future) patient based on their clinical features and biomarkers. We propose an optimal individualized dose finding rule by maximizing utility functions for individual patients while limiting the rate of toxicity. The utility is defined as a weighted combination of efficacy and toxicity probabilities. This approach maximizes overall efficacy at a prespecified constraint on overall toxicity. We model the binary efficacy and toxicity outcomes using logistic regression with dose, biomarkers and dose–biomarker interactions. To incorporate the large number of potential parameters, we use the LASSO method. We additionally constrain the dose effect to be non-negative for both efficacy and toxicity for all patients. Simulation studies show that the utility approach combined with any of the modeling methods can improve efficacy without increasing toxicity relative to fixed dosing. The proposed methods are illustrated using a dataset of patients with lung cancer treated with radiation therapy.     

Model-based approach for human kinematics reconstruction from markerless and marker-based motion analysis systems

Modeling tools related to the musculoskeletal system have been previously developed. However, the integration of the real underlying functional joint behavior is lacking and therefore available kinematic models do not reasonably replicate individual human motion. In order to improve our understanding of the relationships between muscle behavior, i.e. excursion and motion data, modeling tools must guarantee that the model of joint kinematics is correctly validated to ensure meaningful muscle behavior interpretation. This paper presents a model-based method that allows fusing accurate joint kinematic information with motion analysis data collected using either marker-based stereophotogrammetry (MBS) (i.e. bone displacement collected from reflective markers fixed on the subject's skin) or markerless single-camera (MLS) hardware. This paper describes a model-based approach (MBA) for human motion data reconstruction by a scalable registration method for combining joint physiological kinematics with limb segment poses. The presented results and kinematics analysis show that model-based MBS and MLS methods lead to physiologically-acceptable human kinematics. The proposed method is therefore available for further exploitation of the underlying model that can then be used for further modeling, the quality of which will depend on the underlying kinematic model.     

Modeling mechanisms of in vivo variability in methotrexate accumulation and folate pathway inhibition in acute lymphoblastic leukemia cells

Methotrexate (MTX) is widely used for the treatment of childhood acute lymphoblastic leukemia (ALL). The accumulation of MTX and its active metabolites, methotrexate polyglutamates (MTXPG), in ALL cells is an important determinant of its antileukemic effects. We studied 194 of 356 patients enrolled on St. Jude Total XV protocol for newly diagnosed ALL with the goal of characterizing the intracellular pharmacokinetics of MTXPG in leukemia cells; relating these pharmacokinetics to ALL lineage, ploidy and molecular subtype; and using a folate pathway model to simulate optimal treatment strategies. Serial MTX concentrations were measured in plasma and intracellular MTXPG concentrations were measured in circulating leukemia cells. A pharmacokinetic model was developed which accounted for the plasma disposition of MTX along with the transport and metabolism of MTXPG. In addition, a folate pathway model was adapted to simulate the effects of treatment strategies on the inhibition of de novo purine synthesis (DNPS). The intracellular MTXPG pharmacokinetic model parameters differed significantly by lineage, ploidy, and molecular subtypes of ALL. Folylpolyglutamate synthetase (FPGS) activity was higher in B vs T lineage ALL (p<0.005), MTX influx and FPGS activity were higher in hyperdiploid vs non-hyperdiploid ALL (p<0.03), MTX influx and FPGS activity were lower in the t(12;21) (ETV6-RUNX1) subtype (p<0.05), and the ratio of FPGS to γ-glutamyl hydrolase (GGH) activity was lower in the t(1;19) (TCF3-PBX1) subtype (p<0.03) than other genetic subtypes. In addition, the folate pathway model showed differential inhibition of DNPS relative to MTXPG accumulation, MTX dose, and schedule. This study has provided new insights into the intracellular disposition of MTX in leukemia cells and how it affects treatment efficacy.     

Handling modular hip implants in model-based RSA: combined stem-head models

Migration measurements of hip prostheses using marker-based Roentgen stereophotogrammetric analysis (RSA) require the attachment of markers to the prostheses. The model-based approach, which does not require these markers, is, however, less precise. One of the reasons may be the fact that the spherical head has not been modelled. Therefore, we added a 3D surface model of the spherical head and estimated the position and orientation of the combined stem-head model. The new method using a combined stem-head model was compared in a phantom study on five prostheses (of different types) and in a clinical study using double examinations of implanted hip prostheses, with two existing methods: a standard model-based approach and one using elementary geometrical shapes. The combined model showed the highest precision for the rotation about the longitudinal axis in the phantom experiments. With a standard deviation of 0.69 degrees it showed a significant improvement (p=0.02) over the model-based approach (0.96 degrees ) on the phantom data, but no improvement on the clinical data. Overall, the use of elementary geometrical shapes was worse with respect to the model-based approach, with a standard deviation of 1.02 degrees on the phantom data and 0.79 degrees on the clinical data. This decrease in precision was significant (p<0.01) on the clinical data. With relatively small differences in the other migration directions, these results demonstrate that the new method with a combined stem-head model can be a useful alternative to the standard model-based approach.     

Is Model Fitting Necessary for Model-Based fMRI?

Model-based analysis of fMRI data is an important tool for investigating the computational role of different brain regions. With this method, theoretical models of behavior can be leveraged to find the brain structures underlying variables from specific algorithms, such as prediction errors in reinforcement learning. One potential weakness with this approach is that models often have free parameters and thus the results of the analysis may depend on how these free parameters are set. In this work we asked whether this hypothetical weakness is a problem in practice. We first developed general closed-form expressions for the relationship between results of fMRI analyses using different regressors, e.g., one corresponding to the true process underlying the measured data and one a model-derived approximation of the true generative regressor. Then, as a specific test case, we examined the sensitivity of model-based fMRI to the learning rate parameter in reinforcement learning, both in theory and in two previously-published datasets. We found that even gross errors in the learning rate lead to only minute changes in the neural results. Our findings thus suggest that precise model fitting is not always necessary for model-based fMRI. They also highlight the difficulty in using fMRI data for arbitrating between different models or model parameters. While these specific results pertain only to the effect of learning rate in simple reinforcement learning models, we provide a template for testing for effects of different parameters in other models.     

O-acetyl sialic acid specific IgM in childhood acute lymphoblastic leukaemia

Initial studies have revealed an enhanced surface expression of O-acetylated sialoglycoconjugates (O-AcSGs) on lymphoblasts concomitant with high titres of IgG in childhood Acute Lymphoblastic Leukaemia (ALL) (Mandal C, Chatterjee M, Sinha D, Br J Haematol 110, 801–12, 2000). In our efforts to identify disease specific markers for ALL, we have affinity-purified IgM directed against O-AcSGs that reacts with three disease specific O-AcSGs present on membrane proteins derived from peripheral blood mononuclear cells (PBMC) of ALL patients. Antibody specificity towards O-AcSGs was confirmed by selective binding to erythrocytes bearing surface O-AcSGs, decreased binding with de-O-acetylated BSM and following pretreatment with O-acetyl esterase. Competitive inhibition ELISA demonstrated a higher avidity of IgM for O-AcSG than IgG. Flow cytometry demonstrated the diagnostic potential of purified O-AcSA IgM as binding was specific with ALL patients and minimal with other haematological disorders and normal individuals. It therefore may be adopted as a non-invasive approach for detection of childhood ALL. Taken together, the data indicates that carbohydrate epitopes having terminal O-AcSA 2 6 GalNAc determinants induce disease specific IgG and IgM, potentially useful molecular markers for childhood ALL.     

Combining multiple comparisons and modeling techniques in dose-response studies

The analysis of data from dose-response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. Model-based approaches assume a functional relationship between the response and the dose, taken as a quantitative factor, according to a prespecified parametric model. The fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose-response model. Multiple comparison procedures regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the family-wise error rate. Such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation. We describe a unified strategy to the analysis of data from dose-response studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose-response curve, while preserving the family-wise error rate. The selected model is then used to provide inference on adequate doses.     

Navigating the unknown: model selection in phylogeography. Models of population structure: tools for thinkers

Despite the widespread use and obvious strengths of model-based methods for phylogeographic study, a persistent concern for such analyses is related to the definition of the model itself. The study by Peter et al. (2010) in this issue of Molecular Ecology demonstrates an approach for overcoming such hurdles. The authors were motivated by a deceptively simple goal; they sought to infer whether a population has remained at a low and stable size or has undergone a decline, and certainly there is no shortage of software packages for such a task (e.g., see list of programs in Excoffier & Heckel 2006). However, each of these software packages makes basic assumptions about the underling population (e.g., is the population subdivided or panmictic); these assumptions are explicit to any model-based approach but can bias parameter estimates and produce misleading inferences if the model does not approximate the actual demographic history in a reasonable manner. Rather than guessing which model might be best for analyzing the data (microsatellite data from samples of chimpanzees), Peter et al. (2010) quantify the relative fit of competing models for estimating the population genetic parameters of interest. Complemented by a revealing simulation study, the authors highlight the peril inherent to model-based inferences that lack a statistical evaluation of the fit of a model to the data, while also demonstrating an approach for model selection with broad applicability to phylogeographic analysis.     

Model-based clustering and data transformations for gene expression data.

MOTIVATION: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications. RESULTS: We benchmarked the performance of model-based clustering on several synthetic and real gene expression data sets for which external evaluation criteria were available. The model-based approach has superior performance on our synthetic data sets, consistently selecting the correct model and the number of clusters. On real expression data, the model-based approach produced clusters of quality comparable to a leading heuristic clustering algorithm, but with the key advantage of suggesting the number of clusters and an appropriate model. We also explored the validity of the Gaussian mixture assumption on different transformations of real data. We also assessed the degree to which these real gene expression data sets fit multivariate Gaussian distributions both before and after subjecting them to commonly used data transformations. Suitably chosen transformations seem to result in reasonable fits. AVAILABILITY: MCLUST is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. CONTACT: kayee@cs.washington.edu. SUPPLEMENTARY INFORMATION: http://www.cs.washington.edu/homes/kayee/model.     

No induction of thiopurine methyltransferase during thiopurine treatment in inflammatory bowel disease

The aim of this study was to follow, during standardized initiation of thiopurine treatment, thiopurine methyltransferase (TPMT) gene expression and enzyme activity and thiopurine metabolite concentrations, and to study the role of TPMT and ITPA 94C > A polymorphisms for the development of adverse drug reactions. Sixty patients with ulcerative colitis or Crohn's disease were included in this open and prospective multi-center study. Thiopurine na?ve patients were prescribed azathioprine (AZA), patients previously intolerant to AZA received 6-mercaptopurine (6-MP). The patients followed a predetermined dose escalation schedule, reaching target dose at Week 3; 2.5 and 1.25 mg/kg body weight for AZA and 6-MP, respectively. The patients were followed every week during Weeks 1-8 from baseline and then every 4 weeks until 20 weeks. TPMT activity and thiopurine metabolites were determined in erythrocytes, TPMT and ITPA genotypes, and TPMT gene expression were determined in whole blood. One homozygous TPMT-deficient patient was excluded. Five non compliant patients were withdrawn during the first weeks. Twenty-seven patients completed the study per protocol; 27 patients were withdrawn because of adverse events. Sixty-seven percent of the withdrawn patients tolerated thiopurines at a lower dose at Week 20. There was no difference in baseline TPMT enzyme activity between individuals completing the study and those withdrawn for adverse events (p = 0.45). A significant decrease in TPMT gene expression (TPMT/huCYC ratio, p = 0.02) was found, however TPMT enzyme activity did not change. TPMT heterozygous individuals had a lower probability of remaining in the study on the predetermined dose (p = 0.039). The ITPA 94C > A polymorphism was not predictive of adverse events (p = 0.35).     

No Induction of Thiopurine Methyltransferase During Thiopurine Treatment in Inflammatory Bowel Disease

The aim of this study was to follow, during standardized initiation of thiopurine treatment, thiopurine methyltransferase (TPMT) gene expression and enzyme activity and thiopurine metabolite concentrations, and to study the role of TPMT and ITPA 94C > A polymorphisms for the development of adverse drug reactions. Sixty patients with ulcerative colitis or Crohn's disease were included in this open and prospective multi-center study. Thiopurine naïve patients were prescribed azathioprine (AZA), patients previously intolerant to AZA received 6-mercaptopurine (6-MP). The patients followed a predetermined dose escalation schedule, reaching target dose at Week 3; 2.5 and 1.25 mg/kg body weight for AZA and 6-MP, respectively. The patients were followed every week during Weeks 1–8 from baseline and then every 4 weeks until 20 weeks. TPMT activity and thiopurine metabolites were determined in erythrocytes, TPMT and ITPA genotypes, and TPMT gene expression were determined in whole blood. One homozygous TPMT-deficient patient was excluded. Five non compliant patients were withdrawn during the first weeks. Twenty-seven patients completed the study per protocol; 27 patients were withdrawn because of adverse events. Sixty-seven percent of the withdrawn patients tolerated thiopurines at a lower dose at Week 20. There was no difference in baseline TPMT enzyme activity between individuals completing the study and those withdrawn for adverse events (p = 0.45). A significant decrease in TPMT gene expression (TPMT/huCYC ratio, p = 0.02) was found, however TPMT enzyme activity did not change. TPMT heterozygous individuals had a lower probability of remaining in the study on the predetermined dose (p = 0.039). The ITPA 94C > A polymorphism was not predictive of adverse events (p = 0.35).     

Cluster-based network model for time-course gene expression data

We propose a model-based approach to unify clustering and network modeling using time-course gene expression data. Specifically, our approach uses a mixture model to cluster genes. Genes within the same cluster share a similar expression profile. The network is built over cluster-specific expression profiles using state-space models. We discuss the application of our model to simulated data as well as to time-course gene expression data arising from animal models on prostate cancer progression. The latter application shows that with a combined statistical/bioinformatics analyses, we are able to extract gene-to-gene relationships supported by the literature as well as new plausible relationships.     

Using a Bayesian Hierarchical Model for Identifying Single Nucleotide Polymorphisms Associated with Childhood Acute Lymphoblastic Leukemia Risk in Case-Parent Triads

Childhood acute lymphoblastic leukemia (ALL) is a condition that arises from complex etiologies. The absence of consistent environmental risk factors and the presence of modest familial associations suggest ALL is a complex trait with an underlying genetic component. The identification of genetic factors associated with disease is complicated by complex genetic covariance structures and multiple testing issues. Both issues can be resolved with appropriate Bayesian variable selection methods. The present study was undertaken to extend our hierarchical Bayesian model for case-parent triads to incorporate single nucleotide polymorphisms (SNPs) and incorporate the biological grouping of SNPs within genes. Based on previous evidence that genetic variation in the folate metabolic pathway influences ALL risk, we evaluated 128 tagging SNPs in 16 folate metabolic genes among 118 ALL case-parent triads recruited from the Texas Children’s Cancer Center (Houston, TX) between 2003 and 2010. We used stochastic search gene suggestion (SSGS) in hierarchical Bayesian models to evaluate the association between folate metabolic SNPs and ALL. Using Bayes factors among these variants in childhood ALL case-parent triads, two SNPs were identified with a Bayes factor greater than 1. There was evidence that the minor alleles of NOS3 rs3918186 (OR = 2.16; 95% CI: 1.51-3.15) and SLC19A1 rs1051266 (OR = 2.07; 95% CI: 1.25-3.46) were positively associated with childhood ALL. Our findings are suggestive of the role of inherited genetic variation in the folate metabolic pathway on childhood ALL risk, and they also suggest the utility of Bayesian variable selection methods in the context of case-parent triads for evaluating the role of SNPs on disease risk.