title: Characterizing and quantifying the effects of breast cancer therapy using mathematical modeling.
abstract: We designed a mathematical model to describe and quantify the mechanisms and dynamics of tumor growth, cell-kill and resistance as they affect durations of benefit after cancer treatment. Our aim was to explore how treatment efficacy may be related to primary tumor characteristics, with the potential to guide future trial design and appropriate selection of therapy. Assuming a log-normal distribution of both resistant disease and tumor doubling times generates disease-free survival (DFS) or invasive DFS curves with specific shapes. Using a multivariate mathematical model, both treatment and tumor characteristics are related to quantified resistant disease and tumor regrowth rates by allowing different mean values for the influence of different treatments or clinical subtypes on these two log-normal distributions. Application of the model to the CALGB 9741 adjuvant breast cancer trial showed that dose-dense therapy was estimated to achieve an extra 3/4 log of cell-kill compared to standard therapy, but only in patients with more rapidly growing ER-negative tumors. Application of the model to the AZURE trial of adjuvant bisphosphonate treatment suggested that the 5-year duration of zoledronic acid was adequate for ER-negative tumors, but may not be so for ER-positive cases, with increased recurrences after ceasing the intervention. Mathematical models can identify different effects of treatment by subgroup and may aid in treatment design, trial analysis, and appropriate selection of therapy. They may provide a more appropriate and insightful tool than the conventional Cox model for the statistical analysis of response durations.
authors.affiliation: Leeds Institute for Clinical Trials Research (LICTR), University of Leeds, Clinical Trials Research House, 71-75 Clarendon Road, Leeds, LS2 9JT, UK. w.m.gregory@leeds.ac.uk.
authors.forename: Walter M
authors.initials: WM
authors.lastname: Gregory
authors.affiliation: Leeds Institute of Cancer and Pathology, University of Leeds, Leeds, UK.
authors.forename: Christopher J
authors.initials: CJ
authors.lastname: Twelves
authors.affiliation: Deakin University, Geelong, Australia.
authors.forename: Richard
authors.initials: R
authors.lastname: Bell
authors.affiliation: St. James's Academic Division of Medical Physics, University of Leeds, Leeds, UK.
authors.forename: Stephen W
authors.initials: SW
authors.lastname: Smye
authors.affiliation: Leeds Institute for Clinical Trials Research (LICTR), University of Leeds, Clinical Trials Research House, 71-75 Clarendon Road, Leeds, LS2 9JT, UK.
authors.forename: Dena R
authors.initials: DR
authors.lastname: Howard
authors.affiliation: Sheffield Cancer Research Centre, Sheffield, UK.
authors.forename: Robert E
authors.initials: RE
authors.lastname: Coleman
authors.affiliation: Edinburgh University, Edinburgh, Scotland.
authors.forename: David A
authors.initials: DA
authors.lastname: Cameron
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use*; D001943:Breast Neoplasms / Q000188:drug therapy* / Q000378:metabolism; D017024:Chemotherapy, Adjuvant / Q000379:methods; D004164:Diphosphonates / Q000627:therapeutic use; D018572:Disease-Free Survival; D005260:Female; D006801:Humans; D007093:Imidazoles / Q000627:therapeutic use; D008962:Models, Theoretical; D009364:Neoplasm Recurrence, Local / Q000188:drug therapy / Q000378:metabolism; D011960:Receptors, Estrogen / Q000378:metabolism; D000077211:Zoledronic Acid
chemical_list: D000970:Antineoplastic Agents; D004164:Diphosphonates; D007093:Imidazoles; D011960:Receptors, Estrogen; D000077211:Zoledronic Acid
keywords: Adjuvant therapy; Bisphosphonates; Cell-kill; Growth rate; Mathematical model; Resistance