Radiation induced lung damage - Chapter 5 Comparing different NTCP models that predict the incidence of radiation pneumonitis

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)

UvA-DARE (Digital Academic Repository)

Radiation induced lung damage

Seppenwoolde, Y.

Publication date

2002

Link to publication

Citation for published version (APA):

Seppenwoolde, Y. (2002). Radiation induced lung damage.

General rights

It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).

Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.

Chapterr 5

Comparingg different NTCP models

thatt predict the incidence

off radiation pneumonitis

Comparingg different NTCP models that predict the

incidencee of radiation pneumonitis

Dataa from 382 breast cancer, malignant lymphoma and inoperable non-smaH cell tung cancerr patients from two centers were studied to compare different normal tissue complicationn probabffity (NTCP) models to predict the incidence of radiation pneumonitis basedd on the dose distribution in Kmg. Radiation pneumonitis was scored using the SWOGG criteria. Dose-volume histograms (DVHs) of thé lungs were calculated from the dosee distributions. The DVH of each patient was reduced into a single parameter using differentt local dose effect relationships. Examples of single parameters were the mean kmgg dose (MLD) and the volume of lung receiving more than a threshold dose (Vom). Parameterss for me different NTCP models were fit to patient data using a maximum likelihoodd analysis. The MLD model was found to be significantly better than the VDth modell (p<0.03). However, for 85% of the studied patients the difference in NTCP calculatedd wfm boft models is less than 10%, because of the high correlation between the twoo parameters. For dose distributions outside the range of studied DVHs the difference inn NTCP, using the two models, could be higher than 35%. For arbitrary dose distributions, ann estimate of the uncertainty in the NTCP could be determined using the probability distributionn of the parameter values of me Lyman-Kutcher-Burman model.

Introduction n

Estimationoff the probability of developing radiation pneumonrtts after treatment with high dose radiotherapyy is important for patients with inoperable non-small cell lung cancer ( N S C t C ) , especiallyy for patients with a compromised lung function. Severe radiation pneumonitis during thee first 6 months after irradiation may be life threatening; the clinical symptoms range from fever,, dyspnea and cough to death from respiratory failure. In patients who survive the pneumonitiss phase, the type and severity of the early response may have a bearing on the typee and severity of the subsequent late response. These complications limit the maximum safee radiation dose that can be delivered to thoracic tumors. Knowledge about the relationship betweenn the 3D dose distribution and the incidence of radiation pneumonitis is essential for designingg a treatment plan that maximizes the tumor dose and minimizes the normal tissue complicationn probability (NTCP).

Severall theoretical models have been developed to estimate the risk of radiation pneumonitis basedd on the 3D dose distribution. In two of these models, the dose-volume histogram (DVH) iss first reduced to a single parameter, which is subsequently related to the NTCP by a sigmoid relation.. In the Lyman-Kutcher-Burman (LKB) model (Kutcher 1989, Lyman 1985), a power-laww relationship with a volume exponent n is used for the reduction into a single parameter, in thee critical volume or parallel model (Jackson 1993) a sigmoid function, characterized by a DQQ (thee local dose for 5 0 % local damage) and a steepness parameter k is used (Niemierko 1993, Yorkee 1993). This sigmoid function represents tor example the functional-sub-unit kill due to locallyy applied dose. The single parameters that result from the above-mentioned models can bee used as a predictor for the incidence of radiation pneumonitis. Single parameters can be, forr example, the mean lung dose (MLD) (Kwa 1998a) or the volume of lung receiving more thann a threshold dose (Vp^) (Armstrong 1997). Graham et al. (1999) investigated for 99 patientss irradiated for tung cancer, whether a straightforward parameter such as the relative

Chapters Chapters

lungg volume that received more than 20 Gy (V20) was related to the incidence of radiation pneumonitis.. Multivariate analysis revealed fine V20 to be the most significant predictor of radiationn pneumonitis. Simitar findings were reported by Marks et al. (1997) for the lung volumee receiving more than 30 Gy. Armstrong et al. (1997) found a higher incidence of grade 33 radiation pneumonitis for patients with more than 30% of their lungs irradiated with more than 255 Gy compared to patients with a smaller V25.

Inn a large mufti-center study (Kwa 1996a), data of 540 patients were pooled to study the dose-incidencee curve for radiation pneumonitis as a function of the mean lung dose (MLD). In all centers,, an increasing pneumonitis rate was observed with increasing MLD. The data were fittedd with a sigmoid function between the MLD and NTCP, characterized by TD» = 30.5 Gy andd m = 0.30 for all patients, and an offset of 0-11% for the lung group, depending on the center.. None of the studies described above used the full DVH information. Although all the studiedd parameters showed a good correlation with the incidence of radiation pneumonitis,

untill now no consensus has been reached about what the best model is to predict radiation pneumonitiss (Seppenwoolde 2001).

Thee purpose of this study was to determine the best NTCP model for radiation pneumonitis usingg the observed incidence of radiation pneumonitis, based on the full dose distributions in aa large group of patients, so that NTCP estimations in dose-escalation studies will improve.

Materialss and methods

Dataa from 382 breast cancer, malignant lymphoma and inoperable NSCLC patients from two centerss were studied (Table 1). CT-based dose calculations were performed as described previouslyy (Boersma 1994, Hayman 2001, Martel 1994), using a 3D treatment planning systemm (U-MPIan, University of Michigan) with a tissue inhomogenetty correction, according to ann equivalent path length algorithm (Van Dyk 1989). The physical dose distributions were correctedd for fractionation (Lebesque 1991), using the linear quadratic model with an a/p ratio off 2.5 - 3.0 Gy (Newcomb 1993), resulting in the normalized total dose distribution. All doses referredd to in this paper are corrected for fractionation.

Normall lung tissue was defined in the CT scan by binary thresholding (thus excluding the grosss tumor volume). The CT-defined lungs were considered as one organ. Dose-volume histogramss (DVHs) of the lungs with 1 Gy dose bins were calculated from the 3D dose distributionss of each patient

Complications s

Thee severity of radiation pneumonitis occurring in the first six months after treatment was scoredd according to the Southwest Oncology Group (SWOG) toxicity criteria where a grade 1 (mild)) radiation pneumonitis applies when radiographic changes (on chest radiographs or CT scans)) are observed but the symptoms do not require steroids. Grade 2 (moderate) is scored whenn steroids are required. For grade 3 (severe), oxygen is needed and for grade 4 (life threatening),, assisted ventilation is required. For all patients the follow-up time was at least 6 months.. Because the scoring of grade 1 radiation pneumonitis was found to be unreliable, the endpointt of the study was radiation pneumonitis grade 2 or higher.

DVHH reduction "Volume space"

GeneralGeneral parallel model

Inn a general parallel model, a DVH can be reduced to a single parameter by deriving an overall responsee parameter (Boersma 1995) that represents the relative damaged volume (rdV). The

RadiationRadiation pneumonitis and NTCP models

rdVV can be calculated when a relationship between the local dose and local damage is specified.. This local dose-effect relation E(D) can have arbitrary shapes. If an expression for E(D)) is known, rdV can be calculated by adding up all local radiation induced effects (Jackson 1993,1995). .

">V-ZE(Di)-^-- (1)

»» " t o t

wheree V( is the volume «radiated with dose D| in bin number i.

ParallelParallel Of critical volume model

Inn the parallel or critical volume model (Jackson 1993, Niemierko 1993), a logistic focal dose-effectt relation can be used. The rdV can be calculated using:

l d VV =

£ , /r, ^ ^ ^ 7 " <

>

characterizedd by a D^ (the local dose for 50% local damage) and a steepness parameter k. AA special case of the parallel model is the "volume above a threshold dose (Vo*)" model. Whenn k goes to infinity, the local dose-effect relationship becomes a step function:

E(D

)) = 0(D

-D

)=J ' *

andd the relative damaged volume becomes equal to the volume above a threshold dose:

r d V = 2 ] ® (

-

« . ) - ^ -- = %

= V

(4)

>> " t o t ^ t o t DVHH reduction "Dose space*

GeneralGeneral parallel model

Thee DVH of a 3D dose distribution of an organ at risk can also be replaced by a DVH of a uniformm dose distribution, where the whole organ is irradiated with a single dose; the equivalentt uniform dose (EUD, (Kwa 1998b)). This general EUD is the dose that, according to ann arbitrary underlying theoretical model, when given as a uniform dose to the entire organ wouldd produce the same NTCP and rdV as the original inhomogeneous dose distribution. Thee EUD can thus be calculated by:

^ E C D J - ^ X E C E U D ^ ^ E U D ))

ChapterChapter 5

resultingg in:

EUDD = E-

I

feE(D

i

).^-J

Lyman-Kutcher-BurmanLyman-Kutcher-Burman model

Inn the Lyman-Kutcher-Burman (LKB) model (Kutcher 1989, Lyman 1985) the DVH is reduced too the EUD with a power-law relationship (Figure 1) for E(Dj), using:

E U DL K BB =

4-- ' v

A.. 2 parameters B.. 3 parameters C.. 4 parameters D.. 3 parameters

D* *

FigureFigure 1. Different DVH-reductbn schemes using local dose^ffect relations with increasing complexity:

A.A. The local dose in the lungs is weighted with a linear dose-effect resulting in the mean lung dose (MLD). The Lyman modelmodel consists of 2 parameters (TD^ and m). B. The DVH is weighted with a power-law relation (LKB model) where

nisnis a measure for the steepness; the larger n, the steeper the curve. The 3 parameters of this model are n, TDX and

m.m. C. The DVH is weighted with a logistic relation that is characterized by a DM (the local dose at which a 50% effect

isis obtained) and a steepness parameter k. Together with TO» and m this makes 4 parameters. Instead of an EUD also thethe relative damaged volume (rdV) can be calculated. D. When the logistic model is used with a fixed high value ofk,

thethe local dose^ffect relation becomes a step-function with a variable Dft. Below Dth no damage will be caused, above

DDmm 100% damage is observed. The EUD cannot be calculated for this model and therefore the rdV, that is equal to Vm

inin this case, is calculated. Dft, rdV^ and m are the 3 parameters of this model. The arrows indicate how the different

I I

RadiationRadiation pneumonitis and NTCP modeis

Thiss EUDLKB has earlier been called the effective dose (D^) (Mohan 1992), the homogeneous dos®® (Dhom) (Damen 1994) or the equivalent uniform dose (EUD) (Kwa 1998b). In the 'new* definitionn of Niemierko (Niemierko 1999), the power-law exponent n in equation 7 was replacedd by 1/a.

MeanMean lung dose model

AA special case of the LKB model is the MLD model, when n equals one (Kwa 1998b):

EUD D

lKBIn=t t

-fe*fl--

MLD D

ParallelParallel or critical volume model

Inn the parallel or critical volume model the E U D p * ^ can be determined using:

rr

1 1

j T l + O V D jj V

_

- 1 1

0) )

SpecialSpecial cases of the parallel model

Inn the special case that DM - «> (or D -* 0), E U D ^ ^ ~ EUDLKB, with n = 1/k.

limfeuD D

1 1

V.. M '

II - (D»/Dj V„J

: :

».. v,

== EUD

Whenn D50 -» — and ateo n = 1/k = 1, the EUDparaKe, * EUDLKB = MLD.

AA large value for k in the parallel model results in a very steep dose-effect relation. This special casee of the parallel model corresponds to the V ^ model with D50 = CW Instead of an EUD (whichh cannot be calculated for k = <*>) the rdV is used to calculate an NTCP value.

Thee parallel model can be used to study the range of possible local dose-effect relations (from linearr (the MLD model) to a step-function (the Vj», model)) that can be used to calculate the NTCPP for radiation pneumonitis.

NTCP P

Thee NTCP is calculated from the EUD or rdV assuming a sigmoid (cumulative normal density) relationn between the complication and either EUD or rdV:

NTCPP =

11 i

=*-(2n =*-(2n

ƒ

dx x

,, EUD-TDso

m-TD D

rdV-rdV, ,

m-rdV V

Chapters Chapters

Thee NTCP relation is determined by two parameters: The TD^, (or rdV^) represents the dose (orr relative damaged volume) for a complication rate of 50%; m is the slope parameter (the steepnesss of the curve increases with decreasing m).

Statistics s

Forr each patient the DVH is reduced to a single parameter (EUD or rdV) according to the modell and the model fit parameters for the underlying local dose-effect. Based on this single parameter,, an NTCP value is calculated using the other two fit parameters.

Inn a maximum likelihood analysis (Clayton 1993) the best fitting parameter values are those forr which the likelihood function L is a maximum. The value of L is a measure for the agreementt between the measured results and the results as predicted by the model, which, in ourr case, are the NTCP values calculated from the associated DVHs. Each NTCP value predictedd from a DVH by the model depends on the shape of the DVH and on the values of thee modef parameters. Given the model parameter values for a data set containing N DVHs, thee N associated NTCP values Pt (i = 1..N) can be calculated for each model, using Equation

11.. Each DVH in the data set has an associated measured endpoint ep, which is either 0 or 1. Thee expression for the natural logarithm of the likelihood function L is:

ln(L)ln(L) = hif[lA = f > ( I , ; = £ [g>, ln(PJ + (l -epj&ifl - P,)] (13)

Fittingg of the model was performed by automatically adjusting the parameters to maximize ln(L). .

Too compare the different models, a Likelihood Ratio test was performed (Clayton 1993) by comparingg the maximum tog likelihood values of different models to that of a reference model. Wee used the most general model, i.e. the parallel model with optimal parameter values as a referencee model. The significance of the difference between the reference and the tested modelss was indicated by a p-value. Differences were considered significant when the p-value wass smaller than 0.05.

Thee statistical approach in this study was:

a.. To test whether the reference model could be simplified to one of the alternative models (LKB,, MLDorVoft).

b.. To test whether the parameters of the models differed between patient subgroups; the possiblee differences between the two institutes were evaluated, as well as the possible differencee between the tumor sites (NSCLC-patients versus malignant lymphoma and breast cancerr patients). Evaluation of smaller subgroups (i.e. based on age or tobacco use) was not possiblee because of the low statistical power of the remaining subsets.

ProfileProfile likelihood

Too express the uncertainty in the fitted parameters, confidence intervals (CI) around the fitted valuess were calculated using the profile likelihood method (Clinton 1993). The CI is found by findingg the points in the parameter space where the ln(L) values are Aln(L) lower than m ™ ^ . Byy changing only one parameter at the time, while the others were optimized, the confidence intervalss for all parameters were determined. The value of Atn(L) is one-half of the g2 value associatedd with the confidence level and the degrees of freedom of the model.

RadiationRadiation pneumonitis and NTCP models

ProbabilityProbability distribution of estimated NTCP values

Too be able to calculate the probability distribution of an estimated NTCP value for arbitrary DVHs,, the complete parameter probability distribution (PD) of the model parameters has to be calculatedd to account for deviations of normality of the fit parameters. The probability distributionn of the parameter space could be determined using a method that is described in detaill by Schilstra et at. (2001). For a grid of many possible combinations of model parameters, thee likelihood values (which are proportional to the probability) are calculated. For the same gridd of possible combinations of the model parameters, NTCPs are calculated. The range of thee combination of parameter values has to be appropriate, i.e. it should encompass the major partt of the PO with sufficient detail, but it should not be too large to restrict calculation time. Everyy grid point in the parameter space has both an NTCP value and a probability value relatedd to i t A histogram of NTCP values can be constructed by calculating the contents of eachh NTCP bin by adding alt the probabilities associated with the NTCP values falling into that bin.. This histogram is the probability distribution of the NTCP for the individual DVH. The uncertaintyy of the NTCP value is given by the 95% confidence interval. Once the parameter probabilityy distribution of a model is determined based on the data set, NTCP probability distributionss can be calculated for any individual DVH, resulting in NTCPs with varying uncertainty,, depending on the shape of the DVH.

Results s

Off the 382 patients, 37 developed radiation pneumonitis grade 2, seven patients grade 3 or higher.. The details of the patient groups from the two institutions are more or less similar (Tablee 1). All the breast cancer and malignantt lymphoma patients and 124 of the UM patientss were enrolled in previous studies (Kwa 1998a, Martel 1994). Sixty-four NSCLC-pafientss from the NKI were partly treated with conventional doses (49.5-70 Gy) and 39 were treatedd according to the protocol of a dose-escalation study (Belderbos 2000), with doses betweenn 70 and 102.9 Gy.

Tablee 1. Patient characteristics. Institute e NKt t NKI I NKI I UM M UM M Number r off patients 42* * 4 4 * * 103** * 22*** * Tumor r type e Breast t Lymphoma a NSCLC C Lymphoma a NSCLC C Prescribed d dose(Gy) ) 40-50 0 25-42 2 49.5-87.5 5 O O 63-102.9 9 Overall l treatment t timee (days) 21-35 5 21-35 5 4(M7 7 28-30 0 40-67 7 RP P 0 0 6 6 15 5 2 2 14 4 RP P grades s orr higher 0 0 0 0 3 3 1 1 3 3 Thesee patients were enrolled in a previous study (Kwa 1998a).

399 of the NKI patients and 47 of the UM patients were treated in ongoing dose-escalation trialss (Bekterbos 2000, Hayman 2001).

Somee of these patients were enrolled in previous studies (22 lymphoma and 42 NSCLC in (Martell 1994) and 22 lymphoma and 124 NSCLC in (Kwa 1998a)).

Chapters Chapters

Generall parallel model (4-parameter), reference fit

Thee parallel model with a logistic local dose-effect relation (Equation 4) resulted in an infinite D500 and 1/k = 0.99 (Tables 2 and 3). T D » was equal to 30.8 6 y and m was 0.37 (Tables 2 and 3)) with a maximum log likelihood value of -119.06.

Lyman-Kutcher-Burmann model (3-parameter fit)

Whenn one less parameter was used in the description of the local dose-effect relation, as in thee LKB model (Equation 2), the parameter value of n converged to 0.99. The values for T D ^ andd m were the same as in the reference model (Tables 2 and 3). The maximum tog likelihood valuee of this fit was equal to that of the reference fit (-119.06).

Vott,, model (3-parameter fit)

Whenn the Vm, model with k fixed at was evaluated, Dft converged to 13 Gy (Tables 2 and 3).. The maximum log likelihood value was -121.3. This fit was significantly worse than the referencee fit (likelihood Ratio test: p = 0.03).

Meann lung dose model (2-parameter fit)

Thee 2 parameter fit that was equal to the MLD model resulted in a TDgo of 30.8 Gy and m equalss 0.37 (Tables 2 and 3) with a maximum log likelihood value of -119.06.

Tablee 2. Parameter values for different models.

Parallell model Present t SPECT T LKBB model Present t Burman(1991)* * Martell (1994) MLDD model Present t Kwaa (1998a) VDthh model Present t Present t Grahamm (1999) Serialttyy model Gagliardii (2000)" Present t TD,o(Gy) ) 308 8 31.0 0 TD„(Gy) ) 30.8 8 24.5 5 28.0 0 TD„(Gy) ) 30.8 8 30.5 5 rdV»<%) ) 77 7 65 5 51.3 3 D „ ( 6 y ) ) 30.1 1 34 4 m m 0.37 7 0.32 2 m m 0.37 7 0.18 8 0.18 8 m m 0.37 7 0.33 3 m m 0.44 4 0.46 6 0.32 2 y y 0.97 7 0.9 9 n ** 1/k 0.99 9 0.67 7 n n 0.99 9 0.87 7 0.87 7 n n 1.0 0 1 1 s s 0.01 1 0.06 6 D»(Gy> > « 0 0 63 3 D*(Gy) ) 13 3 20 0 20 0 Logg likelihood -119.1 1 -119.4 4 -119.1 1 NE E -141.7 7 -119.1 1 -119.9 9 -121.3 -121.3 -123.4 4 -130.2 2 -119.3 3 -118.1 1 p-value e Reference e 0.7 7 1 1 NE E <0.001 1 1 1 0.4 4 0.03 3 0.003 3 <0.001 1 ME E NE E

Thee parameters that were optimized in the maximum likelihood analysis are bold. Significant differencess between the models relative to the reference model are determined by a p-value fc2 test).. NE: not evaluabte. * Without tissue inhomogeneity corrections. ** For radiation pneumonitiss grade >=1, lungs were considered as separate organs.

RadiationRadiation pneumonitis and NTCP models

Tablee 3. Parameter values for the various models with their confidence intervals.

Parallell model 95%CI I 68%% CI LKBB model 95%CI I 68%% CI MLD D 95%% CI 68%% CI Vw», , 95%% CI 68%% CI TDsofGy) ) 30.8 8 23-45 5 27-38 8 30.8 8 23-46 6 27-38 8 30.8 8 27-42 2 29-36 6 rdVBo(%) ) 77 7 62-107 7 68-87 7 m m 0.37 7 0.26-0.54 4 0.30-0.46 6 0.37 7 0.28-0.56 6 0.34-0.48 8 0.37 7 0.31-0.51 1 0.34-0.44 4 m m 0.44 4 0.36-0.54 4 0.40-0.48 8 nn (1/k) 0.99 9 0.4-2.4 4 0.6-1.8 8 0.99 9 0.6-2.8 8 0.8-1.6 6 1 1 DM(Gy) ) CO O 35-00 0 Dm(Gy) ) 13 3 7-19,, 26-31 9-17 7 Thee difference in the upper limit of n for the LKB and parallel model are probably due to sampling errorss because the distribution for n has a long shallow tail.

Thee parallel model, the LKB model and the MLD model all resulted in the same maximum likelihoodd value, indicating that the simplest model (MLD) gives an equally good description of thee data compared to the more complex models.

1 0

ll 1 i Üh

A.. Mean lung dose (Gy) B. V13 (%)

FigureFigure 2. The incidence of grade > 2 radiation pneumonitis as a function of A. the mean king dose (MLD), the line representrepresent the NTCP model with TDso = 30.8 Gy and m = 0.37. B. the V13, the line represent the NTCP model with rdVsordVso = 77% and m = 0.44. The data of all patients were pooled and sorted into dose-bins of 4 Gy for A and 10% intervalsintervals for B. The error bars represent the 68% confidence inten/als of the data in the bins. The grey areas represent thethe 68% confidence interval of the fitted NTCP curve.

ChapterChapter 5

Forr the MLD and the V13 model, the NTCP curves (Figure 2A and B) were calculated. The curvess look very similar, one can even have the impression that the NTCP curve for the V13 lookss better. However, detailed analysis on the individual data points showed that below a MLDD of 20 Gy or a V13 of 50%, the MLD is a better predictor for the incidence of radiation pneumonitis.. Above these values the V13 model is slightly better than the MLD model.

Subgroups s

Forr some subgroups the extended models yielded a little higher log likelihood value. The largestt differences were seen for the VDth model. For the breast cancer and malignant lymphomaa patients the NTCP relation was steeper (m = 0.23) than the relation for the NSCLC-patientss (m = 0.44). The D« (15 Gy versus 12 Gy) and rdV50 (68% versus 66%) were almost

1 . 0 0 CO O OO 0.8 E E CD D Q. . co.6 6 ^ ^ • o o 2 2 •RR 0.4

1 1

Ë Ö Ö

II ¥

x

FigureFigure 3. The incidence of grade > 2 radiation pneumonitis as a function of V13 for two subgroups: the breast cancer (B)(B) and malignant lymphoma (ML) patients (triangles and dotted line) compared to the NSCL&patients (circles and dasheddashed line). The difference in NTCP curves between both patient groups is not significant. The error bars represent thethe 68% confidence intervals of the data.

0.6 6 0.4 4 0.2 2 0.0 0 •• Grade RP>3

-I-I—r^y —r^y

4— —

3 0 0

FigureFigure 4. The incidence of grade > 3 radiation pneumonitis as a function of the mean lung dose (solid line). The incidenceincidence of grade > 3 radiation pneumonitis is less than half the incidence of grade > 2 radiation pneumonitis. The absoluteabsolute patient numbers in each dose interval with complications are indicated. The error bars represent the 68% confidenceconfidence intervals. The dotted line is the fitted NTCP curve for grade > 2 radiation pneumonitis.

RadiationRadiation pneumonitis and NTCP models

similar.. Although the log likelihood value was larger (-115.5) than that of the reference model, thiss improvement was not significant. The difference in steepness parameter between the two patientt groups is shown in Figure 3 for the V13 model only, because both values for Dth and bothh values for rdVso were almost similar for the two patient groups. For the LKB model, differencess were seen for the parameter n for both institutions: n was 0.5 for the NKI and 1.6 forr UM. However, these differences did not lead to a significant improvement of the fit. Gradee 3 or higher radiation pneumonitis

Onlyy 7 patients developed a grade 3 or 4 radiation pneumonitis. Although this incidence is low, thee MLD model could be fitted with a Dso of 43 Gy and an m of 0.28. Below a MLD of 15 Gy theree is no incidence at all (Figure 4) and between 15 and 28 Gy the incidence is less than Profilee likelihood

Forr a large number of combinations of D50 and k in the parallel model, the log-likelihood was optimizedd for the TDSQ and m. A 3D surface of the maximum likelihood for each combination off DM and k was the result (Figure 5A). The highest point in the likelihood surface is where D500 approached infinity (MLD). A ridge pointed towards a D50 of 13 Gy at an infinite k (Figure 5B),, indicating that this parameter combination has also a relatively high log-likelihood value.

M L D D Dso—>«>> k = 1.01

D5o:=Dthh = 1 3 G y

ö ö

-125 5

FigureFigure 5. A. The profile likelihood

surfacesurface of the parallel model. For D50 >

100100 Gy the shape of the surface is rather

invariantinvariant for 050. The value for k

convergesconverges to 1.01 (= MLD) when D50 - »

00.. When /f -»eo, Df t converges to 13 Gy

(V13).(V13). The likelihood value for a fit using

perfusionperfusion data with Dx = 63Gyandk =

1.7(Seppenwoolde1.7(Seppenwoolde 2000) is indicated by aa star. B. The tog likelihood values of

fitsfits of the Voft model for different values

forfor Dft. There is a local maximum for Dft

== 28 Gy and a global maximum for Dt t =

1313 Gy. The log likelihood values for the V20V20 and V30 model are indicated as well.well. The dashed lines indicate the 68% andand 95% confidence intervals for the V13 model.model. Note that this figure is a magnificationmagnification of a part of Figure 5A for thethe special case that /c-> «>.

ChapterChapter 5

Fromm Figure 5A can be concluded that the distribution of especially D50 is not entirely normal; beyondd a D50 of 100 Gy the maximum is constant and does not longer depend on D^. The outcomee of a Likelihood Ratio test is only valid when the distribution of the parameters of the testedd models is normal. Therefore we estimated the p-value for the difference between the Votf,, and the parallel model, both with optimall parameter values, with a Monte Carlo simulation methodd (see Appendix).

Inn none of 200 simulated cases, the difference in the maximum log likelihood between both modelss (Aln(L)s) was larger than the measured difference, but for 4 cases, Aln(L)s was comparablee to the measured difference, so the Monte Carlo p-value was estimated to be smallerr than 0.02.

Probabilityy distribution of estimated NTCP values

Thee LKB model is the simplest model that can account for the shape of the DVH in the calculationn of the uncertainty in the estimated NTCP values, by using the variation in the dose-weightingg factor n. With the full 3D parameter probability distribution of the LKB model, the uncertaintyy in NTCP values can be calculated for DVHs with arbitrary shape. As an example, thee DVHs of a lymphoma and a NSCLC patient (Figure 6A), combined with the probability distributionn of the LKB model, resulted in the probability distribution of the estimated NTCP (Figuree 6B). The MLD of both patients was equal (21 Gy). The difference between the NTCP

20 0 ^ "" 15 h 200 30 40 N T C P ( % ) ) 200 30 40 N T C P ( % ) )

FigureFigure 6. A. DVHs of a lymphoma (solid line) and a lung patient (dotted line) with the same MLD of 24 Gy. B. The

probabilityprobability distribution of the NTCP and its 95% confidence interval (bold lines) using the LKB model for the lymphoma (solid(solid line) and the king patient (dotted line) from Figure 6A. The star represents the NTCP value estimated with the MLDMLD model. C. The probability distributions of the NTCP value and its 95% confidence interval (bold lines) using the LKBLKB model for irradiation of 3/3 (dotted line), 2/3 (solid line) and 1/3 (dashed line) of the lung with the same MLD (24 Gy)Gy) as the patients from Figure 6A. The star represents the NTCP value estimated with the MLD model.

RadiationRadiation pneumonitis and NTCP models

valuess with the highest probability and the NTCP calculated with the MLD model (star in Figure 6BB and C), is caused by the distribution of parameter n that has a long tail towards 2.3; small differencess in the shape of the DVHs are then reflected in differences in the shape of the probabilityy distribution for the NTCP. For fictitious irradiation techniques (homogeneous irradiationn of 3/3, 2/3 and 1/3 of the lung) with a MLD of 23 Gy, the probability distributions for thee NTCP (Figure 6C) differ a lot and the uncertainty in the NTCP value is much larger for homogeneouss irradiation of 3/3 and 1/3 than for irradiation of 2/3 of the lungs. This means that thee DVH of irradiating 2/3 of the lungs with a MLD of 23 Gy comes closer to the DVHs that weree used in the study than the other two DVHs. Also for treatment plans with equal V13 but withh different DVHs, the NTCP (using the LKB model) will have a larger uncertainty for the DVHH that was unlike the studied ones.

Discussion n

Thee maximum likelihood method revealed that the underlying local dose-effect relation for radiationn pneumonitis was linear (equal to the MLD model), rather than a step-function (Vp^ model).. However, both models describe the data well and don't over-fit the data. This is causedd by the high correlation between the two parameters in our dataset: r2 = 0.82. In clinical practice,, both the MLD and the V13 can be used for the prediction of radiation pneumonitis, ass long as the MLD or V13 are in the same range of the studied data, because for 84% of the dose-distributionss in this study, the difference in NTCP calculated with both models is less than 10%% (Figure 7).

00 5 10 15 20 25 30 35 Meann Lung Dose (Gy)

FigureFigure 7. The V13 as a function of the MLD for the patient data of both institutions. The correlation between the V13

andand MLD is strong (r2

is 0.82). The solid circles represent patients who developed radiation pneumonitis, grade 2 or higher.higher. In solid lines the difference in the predicted NTCP value with both models is indicated. The grey regions representrepresent the regions where additional clinical data are needed to make differences between the V13 and MLD model clearer.clearer. The region left of the dotted line is theoretically unreachable

ChapterChapter 5

However,, for treatment plans with dose distributions that are different than the ones used in thiss study (i.e IMRT or proton irradiation), the outcome of both models can differ a lot (Figure 8).. For example irradiation of 1/3 of the lung with 80 Gy results in an NTCP of only 10% for thee V13 model, while the MLD is 27 Gy, resulting in an NTCP of 37% according to the MLD model.. When 100% of the lung is irradiated with the same uniform (mean) lung dose of 27 Gy, thee NTCP calculated with the MLD model is again 37% while the NTCP calculated with the V133 model is 76%. 100 0 80 0 60 0 40 0 20 0 as s — — / 3 / 3 3 // / / 2 / 3 3

-4 4

ft ft

FigureFigure 8. NTCP curves for uniform irradiation of the whole lung, 21/3 and 1/3 of the lung, using two models that predict

thethe incidence of radiation pneumonitis: the V13 model (solid line) and the MLD model (dashed line). The stars represent thethe NTCP values for 1/3 and 3/3 irradiation of the lung for the two models with an equal mean lung dose of 27 Gy. The NTCPNTCP for the MLD model is 37% for both volumes while the V13 model gives an NTCP of 76% for irradiating 3/3 with 2727 Gy and an NTCP of 10% for irradiating 1/3 of the lungs with 80 Gy.

Too be able to discriminate better between different models and to determine the exact shape off the local dose-effect relation for radiation pneumonitis, more clinical data are needed for whichh the differences between both models are large, for example dose distributions with a highh VDIh and a low MLD (like the mantle field irradiation; a large volume of lung irradiated with aa relatively uniform low dose), or with a low VDth and a high MLD (small lung volume to a high locall dose as in IMRT and dose-escalation studies). The problem is that some parts of the V13-MLDD space cannot be achieved theoretically (Figure 7) and a part of the space with a high MLDD and a low V13 cannot be covered by photon irradiation because, even with the highest conformity,, the multiple beams have to enter the lungs and deliver (some low) dose in a large volumee of the lungs. The light grey regions of the graph in Figure 5D represent regions that cann be covered with current dose-distributions but with only few available data.

Simplee parameters versus a more complicated model

AA model with more than two parameters, for example the LKB model, could be used to account forr the shape of the DVH in the calculation of the uncertainty in the NTCP value. Using the 3D parameterr probability distribution of the LKB model, based on the available data, the uncertaintyy in an NTCP value could be calculated for DVHs with arbitrary shape. This gives an indicationn for the uncertainty in the NTCP calculated for dose distributions of new treatment techniques. .

RadiationRadiation pneumonitis and NTCP models

Comparisonn wtth other models

Becausee the underlying local mechanism that induces radiation pneumonitis is unknown, the locall dose-effect relation for radiation induced changes in perfusion, as measured with perfusionn SPECT scans was determined (Seppenwootde 2000) to see if changes in focal perfusionn are related to the incidence of radiation pneumonitis. For a sigmoid dose-effect relationn that was fitted through measured perfusion-SPECT data with a DM = 63 Gy and

kk - 1.7 resulted in an accompanying TDm of 31 Gy and an m of 0.32. The maximum log

likelihoodd value for this fit was -119.4 (star in Figure 5A) and the corresponding p-value was 0.7,, indicating that the perfusion based model is not significantly different from the reference parallell model with optimal parameter values. Thus, a slightly curved (instead of a linear) underlyingg focal dose-effect relation is permitted within the confidence limits of the model. Inn a study of Kwa et al. (1998a), the MLD and complication data of 540 patients of 5 different institutess were pooled. The values for the TDgg and m in this study were 30.5 Gy and 0.3 respectively,, yielding a somewhat steeper curve than with the results of the present study. Althoughh in the present study fewer patients were included, the full 3D dose-distribution of eachh patient was considered, instead of sorting the data into dose bins of 4 Gy, thus enabling thee local dose-effects to be studied in much more detail.

Becausee in many studies the incidence of radiation pneumonitis is calculated using V20 (Grahamm 1999) or V30 (Marks 1997), these parameter values were tested as well. Forcing a valuee of 20 or 30 Gy for Vat, resulted in a fit with a lower log likelihood value than the reference fitt (Figure 5B, Table 2), indicating that V20 and V30 describe the data less adequately. When otherr values for Dm were tested (Figure 5B), a local (at D* - 28 Gy) and a global (at

Dg,, = 13 Gy) maximum in the log likelihood were found. The fits of V20, V28 and V30 all had aa significantly lower maximum log likelihood value than VI3 and the reference tit

Thee parameters D50, s and y of the serialfty model that was used in the study of Gagliardi et al.(2000)) were determined with the maximum likelihood method as well. The tog likelihood was littlee higher for this model than for the MLD. Although in this study the lungs were considered ass one organ, and as two organs in Gagliardi's study and the scoring of radiation pneumonitis wass different the parameter values were relatively simitar (Table 2).

Dosee calculations

Altt dose calculations were performed with tissue density inhomogenetty correction algorithms thatt do not explicitly take into account electron transfer. Such calculations systematically overestimatee the local dose in lung tissue, by an amount mat can be about 10% (Engelsman 2001),, mainly in the low-dose regions. The consequence of using more accurals dose calculationn algorithms for the results of this paper is currently being studied. In general, caution iss needed when the relations presented here are used for predicting the NTCP based on dose distributionss that are calculated with different dose calculation algorithms.

Inn conclusion, given the cautions stated above, the mean lung dose is, for our patient group, thee most accurate parameter that can be used to predict the incidence of radiation pneumonitis forr an individual patient, based on the 3D dose-distribution. To calculate the uncertainty in the estimatedd NTCP for dose distributions of new treatment techniques, the Lyman-Kutcher-Burmann mode) can be used.

Chapters Chapters

Appendix x

Thee Monte Carlo estimation method (parametric bootstrap)

Thee %2-test to determine the significance of the difference between two models is only valid whenn the likelihood function has a more or less normal shape. For the 4-parameter model this wass not necessarily true. Therefore, a Monte Carlo simulation was performed to determine the p-valuee for the difference between the 4-parameter reference model and the reduced 3-parameterr V ^ model.

Thee steps for performing a Monte Carlo procedure (Noreen 1989) are:

1.. The reduced V ^ model with the optimized parameters is set as the model of the population fromm which simulated samples are to be drawn (Manly 1991).

2.. A targe number N of simulated radiation pneumonitis cases for each DVH were generated fromm this reduced V ^ model in a way that the population average of these samples was in accordancee with the model (for example when for one DVH the incidence of radiation pneumonitiss was predicted to be 25% by model 1, on average in one of the four times radiation pneumonitiss was scored).

3.. For each of the N samples, the simulated difference between the maximum log likelihood valuess of both models Aln(L)s was calculated by optimizing the parameters of the reduced

modell and of the reference model, using the simulated radiation pneumonitis cases.

4.. The measured Aln(L)ffl is compared to the N calculated values of Aln(L)s to determine if it is

unusuallyy high or low. The percentile rank of Mn(L)m is the estimation of the p-value. For

example,, if 4 out of 100 values of Aln(L)s are larger than Aln(L)m, the difference between the

modelss is significant at p < 0.05.

Thiss p-value is the probability to find a difference in the fit between the 3-parameter Vpth mode] andd the more complicated 4-parameter model at least as large as in our own data, while in fact thee simpler model gives an adequate description of the data.