Therapy operating characteristic curves: tools for precision chemotherapy

Abstract

The therapy operating characteristic (TOC) curve, developed in the context of radiation therapy, is a plot of the probability of tumor control versus the probability of normal-tissue complications as the overall radiation dose level is varied, e.g., by varying the beam current in external-beam radiotherapy or the total injected activity in radionuclide therapy. This paper shows how TOC can be applied to chemotherapy with the administered drug dosage as the variable. The area under a TOC curve (AUTOC) can be used as a figure of merit for therapeutic efficacy, analogous to the area under an ROC curve (AUROC), which is a figure of merit for diagnostic efficacy. In radiation therapy, AUTOC can be computed for a single patient by using image data along with radiobiological models for tumor response and adverse side effects. The mathematical analogy between response of observers to images and the response of tumors to distributions of a chemotherapy drug is exploited to obtain linear discriminant functions from which AUTOC can be calculated. Methods for using mathematical models of drug delivery and tumor response with imaging data to estimate patient-specific parameters that are needed for calculation of AUTOC are outlined. The implications of this viewpoint for clinical trials are discussed.

Physiological random processes in precision cancer therapy

“…So far we have considered the drug distribution c ( r , t ) within a tumor to be a general spatial random process that evolves in time. A more detailed treatment considers that the drug molecules may be in the capillaries, diffusing in the interstitial space, bound to surface receptors or internalized into the cytoplasm of malignant cells, so that the drug distribution can be decomposed as [ 49 – 52 ] …”

“…The first two terms in ( 22 ) are linked by the time-dependent diffusion equation for an inhomogeneous medium, given by [ 52 ] where D ( r ) is the diffusion coefficient and s ( r , t ) is the source of the diffusing species (e.g. drug molecules).…”

“…In several previous papers [ 9 , 52 , 61 – 63 ], we have considered the problem of optimizing a diagnostic imaging study or therapeutic regimen in order to get the best outcome for an individual patient. This would seem to be fundamentally impossible since both diagnostic and therapeutic efficacy are typically defined in terms of large groups of patients and evaluated by clinical trials, but we have developed rigorous mathematical methods for patient-specific optimization of SPECT imaging [ 9 ], radiation therapy [ 61 , 62 ] and chemotherapy [ 52 , 63 ]. None of these papers, however, makes use of random processes and characteristic functionals as in this paper.…”

“…The paradigm we consider for personalized cancer therapy is thus [ 52 , 64 ]: Obtain images, genomic data and other data for a specific patient; Optimize the therapy regimen using this information and supporting mathematical models; Evaluate the resulting patient-specific protocol with multiple patients as in conventional clinical trials. …”

“…The second step requires the application of mathematical or heuristic models for estimating the probability of tumor control and probability of normal tissue complication for each patient, and all of the expressions for Pr( TC ) given in this paper are potentially applicable. To optimize a treatment, we advocate using a curve-based analysis such as the Therapy Operating Characteristic (TOC) curve discussed below and elsewhere [ 52 ], which models the trade-off between tumor control and undesired side effects.…”