A comparison of dose-response characteristics of four NTCP models using outcomes of radiation-induced optic neuropathy and retinopathy

Moiseenko Vitali, Song, Mell, Bhandare, Bhandare Niranjan

Description

Biological models are used to relate the outcome of radiation therapy to dose distribution. As use of biological models in treatment planning expands, uncertainties associated with the use of specific models for predicting outcomes should be understood and quantified. In particular, the question to what extent model predictions are data-driven or dependent on the choice of the model has to be explored. Methods Four dose-response models--logistic, log-logistic, Poisson-based and probit--were tested for their ability and consistency in describing dose-response data for radiation-induced optic neuropathy (RION) and retinopathy (RIRP). Dose to the optic nerves was specified as the minimum dose, D min , received by any segment of the organ to which the damage was diagnosed by ophthalmologic evaluation. For retinopathy, the dose to the retina was specified as the highest isodose covering at least 1/3 of the retinal surface ( D 33% ) that geometrically covered the observed retinal damage. Data on both complications were modeled separately for patients treated once daily and twice daily. Model parameters D 50 and γ and corresponding confidence intervals were obtained using maximum-likelihood method. Results Model parameters were reasonably consistent for RION data for patients treated once daily, D 50 ranging from 94.2 to 104.7 Gy and γ from 0.88 to 1.41. Similar consistency was seen for RIRP data which span a broad range of complication incidence, with D 50 from 72.2 to 75.0 Gy and γ from 1.51 to 2.16 for patients treated twice daily; 72.2-74.0 Gy and 0.84-1.20 for patients treated once daily. However, large variations were observed for RION in patients treated twice daily, D 50 from 96.3 to 125.2 Gy and γ from 0.80 to 1.56. Complication incidence in this dataset in any dose group did not exceed 20%. Conclusions For the considered data sets, the log-logistic model tends to lead to larger D 50 and lower γ compared to other models for all datasets. Statements regarding normal tissue radiosensitivity and steepness of dose-response, based on model parameters, should be made with caution as the latter are not only model-dependent but also sensitive to the range of complication incidence exhibited by clinical data.

Informations

• Publié par: biomed
• Publié le: 01 janvier 2011
• Nombre de lectures: 7
• Langue: English
• Poids de l'ouvrage: 2 Mo

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Moiseenko et al. Radiation Oncology 2011, 6:61
http://www.ro-journal.com/content/6/1/61
RESEARCH Open Access
A comparison of dose-response characteristics of
four NTCP models using outcomes of
radiationinduced optic neuropathy and retinopathy
1 2 2 3*Vitali Moiseenko , William Y Song , Loren K Mell and Niranjan Bhandare
Abstract
Background: Biological models are used to relate the outcome of radiation therapy to dose distribution. As use of
biological models in treatment planning expands, uncertainties associated with the use of specific models for
predicting outcomes should be understood and quantified. In particular, the question to what extent model
predictions are data-driven or dependent on the choice of the model has to be explored.
Methods: Four dose-response models–logistic, log-logistic, Poisson-based and probit–were tested for their ability
and consistency in describing dose-response data for radiation-induced optic neuropathy (RION) and retinopathy
(RIRP). Dose to the optic nerves was specified as the minimum dose, D , received by any segment of the organmin
to which the damage was diagnosed by ophthalmologic evaluation. For retinopathy, the dose to the retina was
specified as the highest isodose covering at least 1/3 of the retinal surface (D ) that geometrically covered the33%
observed retinal damage. Data on both complications were modeled separately for patients treated once daily and
twice daily. Model parameters D and g and corresponding confidence intervals were obtained using maximum-50
likelihood method.
Results: Model parameters were reasonably consistent for RION data for patients treated once daily, D ranging50
from 94.2 to 104.7 Gy and g from 0.88 to 1.41. Similar consistency was seen for RIRP data which span a broad
range of complication incidence, with D from 72.2 to 75.0 Gy and g from 1.51 to 2.16 for patients treated twice50
daily; 72.2-74.0 Gy and 0.84-1.20 for patients treated once daily. However, large variations were observed for RION
in patients treated twice daily, D from 96.3 to 125.2 Gy and g from 0.80 to 1.56. Complication incidence in this50
dataset in any dose group did not exceed 20%.
Conclusions: For the considered data sets, the log-logistic model tends to lead to larger D and lower g50
compared to other models for all datasets. Statements regarding normal tissue radiosensitivity and steepness of
dose-response, based on model parameters, should be made with caution as the latter are not only
modeldependent but also sensitive to the range of complication incidence exhibited by clinical data.
Background concept [1-3] to commercial implementation [4]. It is
Modeling of dose-volume response for normal tissues expected that biologically-based radiotherapy planning
has been used to establish correlation between toxicity will play a more prominent role. This could be
faciliand dose-volume parameters, determine safe dose distri- tated by expanding use of biological imaging intended
butions in organs at risk and make projections for risks to map biological properties of tumors and organs at
of adverse effects associated with dose escalation. Biolo- risk [5,6] thereby making planning not only
biologicallygically-based radiotherapy optimization has progressed based but also patient-specific [7].
in recent years from pioneering work presenting the The dose-response follows the basic sigmoid shape
and numerous models have been proposed based either
* Correspondence: [e-mail] on a purely statistical approach or assumptions
regard3University of Florida Health Sciences Center, P.O. Box 100385, Gainesville, FL, ing organ architecture and its influence on the
develop32610-0385, USA
ment of complications [8]. The popular choices toFull list of author information is available at the end of the article
© 2011 Moiseenko et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.Moiseenko et al. Radiation Oncology 2011, 6:61 Page 2 of 10
http://www.ro-journal.com/content/6/1/61
describe the sigmoid dose-response curves are: Poisson- Poisson-based, logistic and probit models. The authors
based, probit, logistic and log-logistic functions [9-12]. carefully considered the location of the maximum
doseDose-response can be plotted as a function of a dosi- response slope and maximum normalized dose-response
metric parameter deemed significant for a particular gradient for these models and relationships between
complication. This can be mean or maximum dose or measures describing the slope at various response levels.
equivalent uniform dose (also known as effective dose), Notably, Bentzen and Tucker, 1997 demonstrated that if
EUD [13]. If the intent of the model is to specifically logistic and Poisson models are forced to predict
identiaccount for volume effect, typically a parameter to cal D , dose corresponding to 10% response, and their10
account for this effect is introduced [9,10]. Fits to multi- slopes are matched at D , a substantial deviation in D10 50
ple models have been reported in the literature [14,15]. would be observed. Two clinical examples of fitting
The purpose of these studies is typically two-fold: 1) to these three models to describe tumor control probability
establish a model that provides the most accurate (TCP)datashowedminorvariationsin D and g.The50
description of clinical data and; 2) to test consistency of data used in their clinical example covered a broad
model predictions, e.g., strength of volume effects. range of local control including data points
correspondA sigmoid curve can be readily described by a two- ing to 50% TCP.
parameter function, one parameter describing the dose The emphasis of this report is on normal tissue
comat which 50% of patients exhibit complications, D , and plications, incidence of which is kept low. This often50
the second parameter, g, the normalized dose-response leaves the parameter D lying outside of the range of50
gradient [16]. Because all models follow a similar sig- clinical data. Despite the stipulations regarding
nonmoid shape it is generally acknowledged that fits to typi- transferability of model parameters and ambiguities in
cally noisy human data do not allow establishing quantifying dose-response slope uncovered by Bentzen
superiority of a particular model over other models [8]. and Tucker, 1997, the following statements or
observaIt is further acknowledged that different models with tions are often made in the literature: 1) organs are
clasthe same D and g would follow a similar dose- sified as radiosensitive or radioresistant based on D ;2)50 50
response. Figure 1 shows the dose - response relation- dose-response is described as shallow or steep based on
ship predicted by the four above-mentioned models g; 3) review articles interpret differences in D and g50
with matching D =80Gyand g = 1.5. The curves reported by various institutions as a reflection of differ-50
overlap around 50% incidence but separate in the low- ences in underlying data. This is based on an
assumpand high-dose regions. It is, therefore, also acknowl- tion that the parameters governing the dose-response
edged that model parameters are not interchangeable. would be reasonably consistent if fitting was performed
That is, D and g obtained following the fitting of one to the same data set.50
model to a specific data set should not be used with Plotting or tabulating model parameters from different
another model. (Figure 1) studiesisagoodwaytoobtainabroadoverviewof
Bentzen and Tucker, 1997, provided the most detailed dose-response data. A recently published special issue of
and insightful analysis of specific features of the the International Journal of Radiation Oncology Biology
Physics was dedicated to the Quantitative Analysis of
Normal Tissue Effects in the Clinic (QUANTEC). This
included 16 consistently structured organ-specific papers
[17] and a number of papers contained summarized
dose-response parameters in a form of a table or a
graph, typically showing a significant spread in these
parameters. These comparisons are usually presented in
a guarded manner. For example, in the QUANTEC
paper on salivary function [18], the plot showing D50
values for incidence of xerostomia is followed by a
qualifying statement that “The wide variation in the
reported TD50 values is unexplained but could result
from several factors, including differences in dose
distributions, salivary measurement methods, segmentation,
intragland sensitivity, and so forth”. It is, however,
notable that three particularly large values of D [19,20] are50
associated with the use of the log-logistic model,
Figure 1 Dose-response predicted by four studied models. whereas the probit model was used in other studies.
Model parameters were commonly set to D = 80 Gy and g = 1.5.50
Therefore, any systematic and predictable trends andMoiseenko et al. Radiation Oncology 2011, 6:61 Page 3 of 10
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biases in models should be determined and quantified. damage was diagnosed by ophthalmologic evaluation.
As will be shown in this work, for the considered data For retinopathy the dose to the retina was specified as
sets, the log-logistic model inde