Clinical experience with positron emission tomography (PET) scanning of sarcoma, using fluorodeoxyglucose (FDG), has established spatial heterogeneity in the standardized uptake values within the tumor mass as a key prognostic indicator of patient survival. But it may be that a more detailed quantitation of the tumor FDG uptake pattern could provide additional insights into risk. The present work develops a statistical model for this purpose. The approach is based on a tubular representation of the tumor mass with a simplified radial analysis of uptake, transverse to the tubular axis. The technique provides novel ways of characterizing the overall profile of the tumor, including the introduction of an approach for the measurement of its phase of development. The phase measure can distinguish between early phase tumors, in which the uptake is highest at the core, and later stage masses, in which there can often be central voids in FDG uptake. Biologically, these voids arise from necrosis and fluid, fat or cartilage accumulations. The tumor profiling technique is implemented using open-source software tools and illustrations are provided with clinically representative scans. A series of FDG-PET studies from 185 patients is used to formally evaluate the prognostic benefit. Significant (p < 0.05) improvements in the prediction of patient survival and progression are obtained from the tumor profiling analysis. After adjustment for other factors including heterogeneity, a typical one standard deviation increase in phase (as determined by the analysis) is associated with close to 20% more risk of progression or death. The work confirms that more detailed quantitative assessments of the spatial pattern of PET imaging data of tumor masses, beyond the maximum FDG uptake (SUVmax) and previously considered measures of heterogeneity, provide improved prognostic information for potential input to treatment decisions for future patients.
Abstract. We consider semiparametric regression problems for which the response function is known up to some vector of parameters θ and the errors have an unknown density f , treated as an infinite-dimensional nuisance parameter for the estimation of θ. The maximum likelihood (ML) estimator is clearly unapplicable in this context, and classical approaches like least squares or M-estimation may perform poorly. Since the results of Stein in 1956, a large amount of work was dedicated to the construction of adaptive estimators that have the same asymptotic behavior as the ML estimator (asymptotic efficiency). The focus has been mainly set on the asymptotic theory and the practical results seem to be restricted to the case of scalar observations. We presented in an estimator that minimizes the entropy of the symmetrized sample of the residuals. In [Wolsztynski et al., 2005] we show the link between this Minimum Entropy (ME) estimator, the ML estimator, and the two-stage adaptive estimator of [Bickel, 1982]. Also, we show that the shiftinvariance property of entropy confers some robustness to ME estimation.Adaptive estimation has important applications in Signal and Image Processing. The present paper summarizes the theoretical aspects of the ME approach and focuses on such applications. Although asymptotic properties are commonly the main concern, we illustrate the performances of estimators for finite samples through simulations, including multidimensional situations. The examples we consider also illustrate the robustness of ME estimation.
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