Bayesian modelling of response to therapy and drug-sensitivity in acute lymphoblastic leukemia

Acute lymphoblastic leukemia (ALL) is a heterogeneous haematologic malignancy involving the abnormal proliferation of immature lymphocytes and accounts for most paediatric cancer cases. The management of ALL in children has seen great improvement in the last decades thanks to greater understanding of the disease leading to improved treatment strategies evidenced through clinical trials. Common therapy regimens involve a first course of chemotherapy (induction phase), followed by treatment with a combination of anti-leukemia drugs. A measure of the efficacy early in the course of therapy is the presence of minimal residual disease (MRD). MRD quantifies residual tumor cells and indicates the effiectiveness of the treatment over the course of therapy. MRD positivity is defined for values of MRD greater than 0.01%, yielding left-censored MRD observations. We propose a Bayesian model to study the relationship between patient features (leukemia subtype, baseline characteristics, and drug sensitivity profile) and MRD observed at two time points during the induction phase. Specifically, we model the observed MRD values via an auto-regressive model, accounting for left-censoring of the data and for the fact that some patients are already in remission after the first stage of induction therapy. Patient characteristics are included in the model via linear regression terms. In particular, patient-specific drug sensitivity based on ex vivo assays of patient samples is exploited to identify groups of subjects with similar profiles. We include this information as a covariate in the model for MRD. We adopt horseshoe priors for the regression coefficients to perform variable selection to identify important covariates. We fit the proposed approach to data from three prospective paediatric ALL clinical trials carried out at the St. Jude Children's Research Hospital. Our results highlight that drug sensitivity profiles and leukemic subtypes play an important role in the response to induction therapy as measured by serial MRD measures.