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.
There are two basic sources of uncertainty in cancer chemotherapy: how much of the therapeutic agent reaches the cancer cells, and how effective it is in reducing or controlling the tumor when it gets there. There is also a concern about adverse effects of the therapy drug. Similarly in external-beam radiation therapy or radionuclide therapy, there are two sources of uncertainty: delivery and efficacy of the radiation absorbed dose, and again there is a concern about radiation damage to normal tissues. The therapy operating characteristic (TOC) curve, developed in the context of radiation therapy, is a plot of the probability of tumor control vs. 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. The 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. In this paper we discuss the potential of using mathematical models of drug delivery and tumor response with imaging data to estimate AUTOC for chemotherapy, again for a single patient. This approach provides a basis for truly personalized therapy and for rigorously assessing and optimizing the therapy regimen for the particular patient. A key role is played by Emission Computed Tomography (PET or SPECT) of radiolabeled chemotherapy drugs.
Medical imaging is often performed for the purpose of estimating a clinically relevant parameter. For example, cardiologists are interested in the cardiac ejection fraction, the fraction of blood pumped out of the left ventricle at the end of each heart cycle. Even when the primary task of the imaging system is tumor detection, physicians frequently want to estimate parameters of the tumor, e.g. size and location. For signal-detection tasks, we advocate that the performance of an ideal observer be employed as the figure of merit for optimizing medical imaging hardware. We have examined the use
of the minimum variance of the ideal, unbiased estimator as a figure of merit for hardware optimization. The minimum variance of the ideal, unbiased estimator can be calculated using the Fisher information matrix. To account for both image noise and object variability, we used a statistical method known as Markov-chain Monte Carlo. We employed a lumpy object model and simulated imaging systems to compute our figures of merit. We have demonstrated the use of this method in comparing imaging systems for estimation tasks.
There are many methods to estimate, from ensembles of signal-present and signal-absent images, the area under the receiver operating characteristic curve for an observer in a detection task. For the ideal observer on realistic detection tasks, all of these methods are time consuming due to the difficulty in calculating the ideal-observer test statistic. There are relations, in the form of equations and inequalities, that can be used to check these estimates
by comparing them to other quantities that can also be estimated from the ensembles. This is especially useful for evaluating these estimates for any possible bias due to small sample sizes or errors in the calculation of the likelihood ratio. This idea is demonstrated with a simulation of an idealized single photon emission detector array viewing a possible signal in a two-dimensional lumpy activity distribution.
Imaging is often used for the purpose of estimating the value of some parameter of interest. For example, a cardiologist may measure the ejection fraction (EF) of the heart to quantify how much blood is being pumped out of the heart on each stroke. In clinical practice, however, it is difficult to evaluate an estimation method because the gold standard is not known, e.g., a cardiologist does not know the true EF of a patient. An estimation method is typically evaluated by plotting its results against the results of another (more accepted) estimation method. This approach results in the use of one set of estimates as the pseudo-gold standard. We have developed a maximum-likelihood approach for comparing different estimation methods to the gold standard without the use of the gold standard. In previous works we have displayed the results of numerous simulation studies indicating the method can precisely and accurately estimate the parameters of a regression line without a gold standard, i.e., without the x-axis. In an attempt to further validate our method we have designed an experiment performing volume estimation using a physical phantom and two imaging systems (SPECT< CT).