Confidence intervals in dose volume histogram computation

Henríquez, Francisco Cutanda; Castrillón, Silvia

doi:10.1118/1.3355888

Cited by 6 publications

(15 citation statements)

References 18 publications

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“…Furthermore, a detailed comparison of α − DVHs and DVCMs is exercised to validate empirical percentiles against results from the respective quantile functions from Eq. and the previous works 27 …”

Section: Methodsmentioning

confidence: 63%

“…A subsequent work 27 (to Refs. [25,26]) already formulated an analytical calculation of α − DVHs as defined in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…In summary, their model is based on the definition of a “binary random variable” 27

T_{i}^{α, \overset{false^}{d}} = \{\begin{matrix} 1 & P (d_{i} \geq \overset{false^}{d}) > 1 - α \\ 0 & P (d_{i} \geq \overset{false^}{d}) \leq 1 - α \end{matrix}

interpreted as “the volume receiving a dose greater than

\overset{d}{true}

with a probability greater than 1− α ” 27 . This interpretation then leads them to define

T_{i}^{α, \overset{false^}{d}} = Θ false(1 - α - F_{d_{i}} (\overset{false^}{d}) false)

which, in analogy to Eq.…”

Section: Methodsmentioning

confidence: 99%

“…For all three patient cases, empirical estimates DVH,

{\overset{false¯}{σ}}_{DVH}^{2}

are obtained by computing 100×30 dose scenarios, that is, 100 sampled treatment scenarios with 30 fraction each, based on a Gaussian uncertainty model using the assumed setup and range errors from Table B.I as respective standard deviation with zero mean (compare to the description of the APM uncertainty model in Ref. [27]). Additionally, expected dose μ and covariance Σ within the respective VOIs was also computed with APM (see Section 2.D.2) for the same input uncertainty model, and then fed into the herein presented DVH‐models (by assuming a multivariate normal distribution as described in Section 2.D).…”

Section: Methodsmentioning

confidence: 99%

“…Along the lines of our validation campaign, we illustrate the shortcomings of previous work and highlight where wide approximations regarding the correlation models (as exercised by Ref. [27]) render meaningful quantification of DVH‐probabilities impossible.…”

Section: Introductionmentioning

confidence: 91%

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Analytical probabilistic modeling of dose‐volume histograms

et al. 2020

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Purpose: Radiotherapy, especially with charged particles, is sensitive to executional and preparational uncertainties that propagate to uncertainty in dose and plan quality indicators, for example, dose-volume histograms (DVHs). Current approaches to quantify and mitigate such uncertainties rely on explicitly computed error scenarios and are thus subject to statistical uncertainty and limitations regarding the underlying uncertainty model. Here we present an alternative, analytical method to approximate moments, in particular expectation value and (co)variance, of the probability distribution of DVH-points, and evaluate its accuracy on patient data. Methods: We use Analytical Probabilistic Modeling (APM) to derive moments of the probability distribution over individual DVH-points based on the probability distribution over dose. By using the computed moments to parameterize distinct probability distributions over DVH-points (here normal or beta distributions), not only the moments but also percentiles, that is, a À DVHs, are computed. The model is subsequently evaluated on three patient cases (intracranial, paraspinal, prostate) in 30-and single-fraction scenarios by assuming the dose to follow a multivariate normal distribution, whose moments are computed in closed-form with APM. The results are compared to a benchmark based on discrete random sampling. Results: The evaluation of the new probabilistic model on the three patient cases against a sampling benchmark proves its correctness under perfect assumptions as well as good agreement in realistic conditions. More precisely, ca. 90% of all computed expected DVH-points and their standard deviations agree within 1% volume with their empirical counterpart from sampling computations, for both fractionated and single fraction treatments. When computing a À DVH, the assumption of a beta distribution achieved better agreement with empirical percentiles than the assumption of a normal distribution: While in both cases probabilities locally showed large deviations (up to AE0.2), the respective À DVHs for a={0.05,0.5,0.95} only showed small deviations in respective volume (up to AE5% volume for a normal distribution, and up to 2% for a beta distribution). A previously published model from literature, which was included for comparison, exhibited substantially larger deviations. Conclusions: With APM we could derive a mathematically exact description of moments of probability distributions over DVH-points given a probability distribution over dose. The model generalizes previous attempts and performs well for both choices of probability distributions, that is, normal or beta distributions, over DVH-points.

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Section: Methodsmentioning

confidence: 63%

“…A subsequent work 27 (to Refs. [25,26]) already formulated an analytical calculation of α − DVHs as defined in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…In summary, their model is based on the definition of a “binary random variable” 27

T_{i}^{α, \overset{false^}{d}} = \{\begin{matrix} 1 & P (d_{i} \geq \overset{false^}{d}) > 1 - α \\ 0 & P (d_{i} \geq \overset{false^}{d}) \leq 1 - α \end{matrix}

interpreted as “the volume receiving a dose greater than

\overset{d}{true}

with a probability greater than 1− α ” 27 . This interpretation then leads them to define

T_{i}^{α, \overset{false^}{d}} = Θ false(1 - α - F_{d_{i}} (\overset{false^}{d}) false)

which, in analogy to Eq.…”

Section: Methodsmentioning

confidence: 99%

“…For all three patient cases, empirical estimates DVH,

{\overset{false¯}{σ}}_{DVH}^{2}

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

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Analytical probabilistic modeling of dose‐volume histograms

et al. 2020

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Quality Management and Safety in Radiation Oncology

et al. 2011

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The effect of slice thickness on target and organs at risk volumes, dosimetric coverage and radiobiological impact in IMRT planning

2015

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Estimation of a volume is dependent on CT slice thickness and the contouring algorithm in a TPS. During commissioning of TPS and for all clinical protocols, evaluation of volume should be included to provide the limit of accuracy in DVH from TPS, especially for small objects. A smaller slice thickness provides superior dosimetry with improved TCP. Thus, the smallest possible slice thickness should be used for IMRT planning, especially when smaller structures are present.

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Confidence intervals in dose volume histogram computation

Abstract: alpha-DVHs provide bounds for DVH values while dose expected volume histograms can be used as central estimates for DVH when uncertainty is taken into account. They are particularly useful when an optimization approach is necessary.

Cited by 6 publications

References 18 publications

Analytical probabilistic modeling of dose‐volume histograms

Analytical probabilistic modeling of dose‐volume histograms

Quality Management and Safety in Radiation Oncology

The effect of slice thickness on target and organs at risk volumes, dosimetric coverage and radiobiological impact in IMRT planning

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