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Cumulative Histograms under Uncertainty: An Application to Dose–Volume Histograms in Radiotherapy Treatment Planning

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  • Flavia Gesualdi

    (German Cancer Research Center—DKFZ, 69120 Heidelberg, Germany
    Institute for Astroparticle Physics (IAP), Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
    Instituto de Tecnologías en Detección y Astropartículas (Comisión Nacional de Energía Atómica, Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad Nacional de San Martín), Centro Atómico Constituyentes, San Martín B1650KNA, Argentina
    Radiation Oncology Department, Institut Curie, PSL Research University, 91898 Orsay, France)

  • Niklas Wahl

    (German Cancer Research Center—DKFZ, 69120 Heidelberg, Germany
    Heidelberg Institute of Radiation Oncology (HIRO), National Center for Radiation Oncology (NCRO), 69120 Heidelberg, Germany
    These authors contributed equally to this work.)

Abstract

In radiotherapy treatment planning, the absorbed doses are subject to executional and preparational errors, which propagate to plan quality metrics. Accurately quantifying these uncertainties is imperative for improved treatment outcomes. One approach, analytical probabilistic modeling (APM), presents a highly computationally efficient method. This study evaluates the empirical distribution of dose–volume histogram points (a typical plan metric) derived from Monte Carlo sampling to quantify the accuracy of modeling uncertainties under different distribution assumptions, including Gaussian, log-normal, four-parameter beta, gamma, and Gumbel distributions. Since APM necessitates the bivariate cumulative distribution functions, this investigation also delves into approximations using a Gaussian or an Ali–Mikhail–Haq Copula. The evaluations are performed in a one-dimensional simulated geometry and on patient data for a lung case. Our findings suggest that employing a beta distribution offers improved modeling accuracy compared to a normal distribution. Moreover, the multivariate Gaussian model outperforms the Copula models in patient data. This investigation highlights the significance of appropriate statistical distribution selection in advancing the accuracy of uncertainty modeling in radiotherapy treatment planning, extending an understanding of the analytical probabilistic modeling capacities in this crucial medical domain.

Suggested Citation

  • Flavia Gesualdi & Niklas Wahl, 2024. "Cumulative Histograms under Uncertainty: An Application to Dose–Volume Histograms in Radiotherapy Treatment Planning," Stats, MDPI, vol. 7(1), pages 1-17, March.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:1:p:17-300:d:1352088
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    References listed on IDEAS

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    1. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
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