- Email: [email protected]
On the consistent use of organ definitions and radiobiological models for the evaluation of complication probabilities of “tubular” organs
1150
I. J. Radiation Oncology
● Biology ● Physics
Volume 52, Number 4, 2002
Table 3. Time to first Grade 3⫹ toxicity at various times after commencement of radiation (by Cumulative Incidence method) SFX % ⫾ SE 1 year 2 years 3 years 4 years 5 years Comparison with SFX (11)
17.2 ⫾ 2.5 22.2 ⫾ 2.8 25.6 ⫾ 3.0 27.1 ⫾ 3.1 27.1 ⫾ 3.1 —
HFX At risk 146 77 49 26 17
% ⫾ SE
At risk
16.9 ⫾ 2.5 23.3 ⫾ 2.8 26.5 ⫾ 3.0 26.5 ⫾ 3.0 26.5 ⫾ 3.0 p ⫽ 0.99
level of 0.05, the probability of finding one false-positive result increases with the number of tests performed. This probability increases from 0.098 with two tests, to 0.226 with 5 tests, and 0.460 with 12 tests. This problem, recognized by most statisticians, can be rectified by the Bonferroni correction (7), which calls for the desired overall significance level to be divided by the number of tests performed. To preserve an overall significance of 0.05 with the 12 pairwise tests of the prevalence rates here, the p value would have to be less than the adjusted value of 0.0042 (⫽0.05/12). We calculated all 12 p values and found the lowest to be 0.018, which is well above the adjusted critical value for statistical significance. More convincingly, however, Table 1 also shows no increase in the prevalence rates with HFX after 2.0 years and there is no statistical difference in the incidence rates computed using two different methodologies as presented in Tables 2 and 3. Finally, Dr. Logie recommends exploration of a combination of chemotherapy and radiation as a strategy specifically designed to avoid the late effects typical of radiation while maintaining a superior tumor cell kill compared to standard fractionation. In principle, it does make much more sense to design combined modality regimens based on specific mechanisms of radiation– drug interaction. In reality, however, knowledge on the exact mechanisms of drug–radiation interaction or the pharmacodynamics is limited for most cytotoxic agents. Consequently, most combined chemoradiation regimens evolved empirically simply by adding chemotherapy regimens showing some clinical activity, usually in patients with disseminated disease, to radiation. Therefore, most of the concurrent chemoradiation regimens turn out to have increased acute or late toxicity relative to radiation alone though some also yielded survival advantage (8). The data of a recently completed Intergroup Phase III trial enrolling patients with unresectable head-andneck squamous cell carcinoma, presented at the 2000 Annual Meeting of the American Society of Clinical Oncology, clearly illustrate this point (9). This trial randomized patients to radiation alone (70 Gy in 7 weeks), radiation (70 Gy) plus cisplatin (100 mg/m2 for 3 cycles), or split-course radiation (30 Gy ⫹ 30 – 40 Gy) given with the first and third cycles of cisplatin (75 mg/m2) plus fluorouracil (1000 mg/m2) given every 4 weeks. The 2- and 3-year actuarial survival rates were 30 –20% for radiation alone, 43–37% for radiation ⫹ cisplatin ( p ⫽ 0.016), and 40 –29% for split-course radiation plus cisplatin–fluorouracil ( p ⫽ 0.13). The Grade 3⫹ toxicity, however, occurred in 53%, 86% ( p ⬍ 0.0001), and 77% ( p ⬍ 0.001) of the patients, respectively. Fortunately, advances in understanding the biology of head-and-neck cancers have brought us a step forward in identifying specific molecular targets for therapeutic interventions, which hopefully will translate into a substantial therapeutic gain. K. KIAN ANG, M.D., PH.D. Department of Radiation Oncology University of Texas M. D. Anderson Cancer Center Houston, TX BRIAN A. BERKEY, M.S. THOMAS F. PAJAK, PH.D. RTOG Statistical Unit Philadelphia, PA KAREN K. FU, M.D. Department of Radiation Oncology University of California San Francisco San Francisco, CA PII S0360-3016(01)02777-8
AFX-S
144 90 58 35 24
% ⫾ SE
AFX-C At risk
16.0 ⫾ 2.4 21.6 ⫾ 2.7 24.9 ⫾ 2.9 27.7 ⫾ 3.1 28.5 ⫾ 3.1 p ⫽ 0.94
149 84 50 29 21
% ⫾ SE
At risk
17.6 ⫾ 2.5 25.2 ⫾ 2.9 29.0 ⫾ 3.1 31.6 ⫾ 3.2 34.9 ⫾ 3.6 p ⫽ 0.27
149 90 58 38 18
1. Dubben HH, Beck-Bornholdt HP. A Radiation Therapy Oncology Group (RTOG) Phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard-fractionation radiotherapy for head-and-neck squamous cell carcinomas: First report of RTOG 9003: In regard to Fu et al. IJROBP 2000;48: 7–16. Actuarial estimates of late normal-tissue effects . . . now! Int J Radiat Oncol Biol Phys 2001;51:563. 2. Logie MB. Regarding Fu et al., A Radiation Therapy Oncology Group (RTOG) phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard fractionation radiotherapy for head and neck squamous cell carcinomas: First report of RTOG 9003. Int J Radiat Oncol Biol Phys. In press. 3. Fu KK, Pajak TF, Trotti A, et al. A Radiation Therapy Oncology Group (RTOG) phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard fractionation radiotherapy for head and neck squamous cell carcinomas: First report of RTOG 9003. Int J Radiat Oncol Biol Phys 2000;48:7– 16. 4. Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc 1958;53:457– 481. 5. Kalbfleish J, Prentice R. The statistical analysis of failure time data. New York: John Wiley and Sons; 1980. 6. Baumann M, Bentzen SM, Ang KK. Hyperfractionated radiotherapy in head and neck cancer: A second look at the clinical data. Radiother Oncol 1998;46:127–130. 7. Bonferroni CE. Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze 1936;8:3– 62. 8. El-Sayed S, Nelson N. Adjuvant and adjunctive chemotherapy in the management of squamous cell carcinoma of the head and neck region: A meta-analysis of prospective and randomised trials. J Clin Oncol 1996;14:838 – 847. 9. Adelstein DJ, Adams GL, Li Y, et al. A phase III comparison of standard radiation therapy (RT) versus RT plus concurrent cisplatin (DDP) versus split-course RT plus concurrent DDP and 5-fluorouracil (5FU) in patients with unresectable squamous cell head and neck cancer (SCHNC): An intergroup study. (Abstract). Proceedings of ASCO 2000;19:411a. 10. Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother Rep 1966;5:163–170. 11. Gray RJ. A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 1988;16:1141–1154.
ON THE CONSISTENT USE OF ORGAN DEFINITIONS AND RADIOBIOLOGICAL MODELS FOR THE EVALUATION OF COMPLICATION PROBABILITIES OF “TUBULAR” ORGANS To the Editor: The advent of 3D conformal therapy has instigated an enormous interest in the application of radiobiological models for the purposes of treatment planning optimization and evaluation, mostly because of the potential of these models to summarize an abundance of dosimetric information into a single figure of merit (1). This figure of merit (whether tumor control probability [TCP] or normal tissue complication probability [NTCP]) depends on the functional form of the radiobiological model, organ definitions, planned dose distribution, and the values of the model free parameters. Figure 1a illustrates a parameter estimation procedure to emphasize that
Letters to the editor
1151
Fig. 1. (a) Procedure for estimating model parameters. After the selection of a consistent organ definition throughout the entire patient population and a functional form of the radiobiological model, the model parameters are derived from a fit to the outcome data. (b) Estimation of the outcome probability.
the estimated values of the radiobiological model parameters depend on the adopted definition of the organ under consideration. This definition can be rather ambiguous, especially for the case of “tubular” organs such as rectum, esophagus, bladder, etc. These organs could be represented either as 2D surface, 3D wall objects (the volume of the wall is defined on the bases of the thickness of the organ’s wall and its surface contours), or 3D solid volumes. Based on the underlying anatomy, some authors (2– 4) have a priori presumed the wall–volume definitions for bladder and rectum, whereas others (5–7) have applied various methods to estimate which organ definition (surface, wall–volume, or solid–volume) better suits NTCP estimations. In their investigations they have compared various indices derived from dose–volume histograms (DVHs) and dose–wall histograms (DWHs). (A DVH is calculated based on a solid body organ definition, whereas a DWH is calculated based on a wall–volume organ definition.) However, the results of these studies are in disaccord with respect to the question, “Does the DWH reflect better the organ response than DVH?” Here we do not attempt to advocate in favor of any of those organ definitions. All of them could be used for NTCP assessments,
providing the parameters of the applied NTCP model have been derived from data based on identical organ definition. One way to assess which is the proper organ definition can be based on how well could a certain radiobiological model fit sets of data (Dose– Volume, Outcome) based on the different organ definitions. For example, if for one and the same group of patients one has the DWHs and the DVHs for a given tubular organ, and also the outcome of the treatment, i.e., complication or noncomplication, the fit, let us say, of Lyman’s NTCP model to the set of data based on the wall–volume definition may result in considerably better fit than the one using the solid volume organ definition. It is quite possible, though, that for some organs both definitions (wall– volume and solid–volume), would lead to equally acceptable fits, meaning that both definitions should be considered sufficiently proper. It is important to emphasize that regardless of the particular organ definition, for subsequent applications of the radiobiological model to the evaluation of dose distributions, the combination model/organ definition/ parameter set should be identical to the combination model/organ definition/parameter set used in the estimation procedure as implied in Fig. 1.
1152
I. J. Radiation Oncology
● Biology ● Physics
Volume 52, Number 4, 2002 2. A model is used with organ definitions different from the ones used in the parameter estimation procedure (5, 6, 7, 11). This tends to be the case for “tubular” (hollow) organs, such as rectum, esophagus, bladder, etc. because, as noted by Lebesque et al. (6): “Emami et al. (12) and Burman et al. (8) did not specify whether the rectum and bladder should be considered as solid organs (contouring of the outer surface only) or hollow organs, which require contouring of the outer and internal surfaces.” We agree with Lebesque et al. (6) that the organs (rectum and bladder) were not exactly defined in the work by Emami et al. (12). On the other hand, given the reported total volume of the rectum and the fact that during the 1980s the 3D dose distributions were not a common tool, one can support the view of Dale et al. (5), that the rectum in the work of Emami et al. (12) was considered a solid body [although this was never stated by Emami et al. (12)], i.e., not a tubular one. To conclude, as illustrated in Fig. 1, we would like to reiterate that the predictive power of radiobiological models is based on consistent use of the parameter estimate and the outcome evaluation procedures. Note: This work is partially supported by MRC Grant MOP 36470. PAVEL V. STAVREV, PH.D. DIMITRE H. HRISTOV, PH.D. JAN P. SEUNTJENS, PH.D. Medical Physics Unit Montreal General Hospital and McGill University Montreal, Canada PII S0360-3016(01)02748-1
Fig. 2. The difference between the CE NTCP model (dashed line) used by Ting et al. (7) and Lyman’s NTCP model (solid line) for rectum and bladder. Both are using the Burman et al. (8) parameters. The three curves represent whole, 2/3, and 1/3 volume irradiation respectively, moving from left to right.
However, this somewhat obvious requirement is not always satisfied, and the following deviations can be noted in various studies reported in the literature: 1. A set of parameters estimated on the basis of one radiobiological model is used with another model. For instance, Ting et al. (7) use a two-parametric model with a set of parameters estimated on the bases of a three-parametric model. In their work the parameters {D50, m, n}, estimated by Burman et al. (8) using Lyman’s model were transformed to {D50, k (k ⫽ 1.6/m)}, and a Critical Element (CE) model, also referred to as Series Organ model, suggested by Schultheiss et al. (9) was used. Ting et al. (7) have used the Schultheiss, but not the CE model based on the functional subunit (FSU) ideology, both discussed by Niemierko and Goitein (10). The second model has at least three parameters—two (D50 and ␥50) describing the FSU response and the third being the number of FSU, while the first model has only two parameters—D50 and k (␥50) of the whole organ response. If the transformed parameters were consistent with the Schultheiss model, one would expect that both the Lyman and the Schultheiss models would result in similar dose–response curves for any partial irradiation. This is definitely the expectation, if both models were applied with their own parameters, properly deduced from fits to outcome data (see Fig. 1). For bladder and rectum, Fig. 2 demonstrates the partial organ— one-third, two-thirds, and whole— dose–response curves predicted by the Lyman model and the Schultheiss model. The differences result from the mismatched use of the estimated parameters. Only the whole, organ response curves coincide because the transformation k ⫽ 1.6/m is derived for this case. Hence, for each partial volume irradiation the value of k should be recalculated.
1. Brahme A. Individualizing cancer treatment: Biological optimization models in treatment planning and delivery. Int J Radiat Oncol Biol Phys 2001;49:327–337. 2. Hartford AC, Niemierko A, Adams JA, Urie MM, Shipley WU. Conformal irradiation of the prostate: Estimating long-term rectal bleeding risk using dose–volume histograms. Int J Radiat Oncol Biol Phys 1996;36:721–730. 3. Jackson A, Skwarchuk MW, Zelefsky MJ, Cowen DM, Venkatraman ES, Levegrun S, Burman CM, Kutcher GJ, Fuks Z, Liebel SA, Ling CC. Late rectal bleeding after conformal radiotherapy of prostate cancer. II. Volume effects and dose–volume histograms Int J Radiat Oncol Biol Phys 2001;49:685– 698. 4. Skwarchuk MW, Jackson A, Zelefsky MJ, Venkatraman ES, Cowen DM, Levegrun S, Burman CM, Fuks Z, Leibel SA, Ling CC. Late rectal toxicity after conformal radiotherapy of prostate cancer (I): Multivariate analysis and dose-response. Int J Radiat Oncol Biol Phys 2000;47:103–113. 5. Dale E, Olsen DR, Fossa SD. Normal tissue complication probabilities correlated with late effects in the rectum after prostate conformal radiotherapy. Int J Radiat Oncol Biol Phys 1999;43:385–391. 6. Lebesque JV, Bruce AM, Kroes AP, Touw A, Shouman RT, van Herk M. Variation in volumes, dose–volume histograms, and estimated normal tissue complication probabilities of rectum and bladder during conformal radiotherapy of T3 prostate cancer. Int J Radiat Oncol Biol Phys 1995;33:1109 –1119. 7. Ting JY, Wu X, Fiedler JA, Yang C, Watzich ML, Markoe A. Dose–volume histograms for bladder and rectum. Int J Radiat Oncol Biol Phys 1997;38:1105–1111. 8. Burman C, Kutcher GJ, Emami B, Goitein M. Fitting of normal tissue tolerance data to an analytic function. Int J Radiat Oncol Biol Phys 1991;21:123–135. 9. Schultheiss TE, Orton CG, Peck RA. Models in radiotherapy: Volume effects. Med Phys 1983;10:410 – 415. 10. Niemierko A, Goitein M. Calculation of normal tissue complication probability and dose–volume histogram reduction schemes for tissues with a critical element architecture. Radiother Oncol 1991;20:166 – 176. 11. Boersma LJ, van den Brink M, Bruce AM, Shouman T, Gras L, te Velde A, Lebesque JV. Estimation of the incidence of late bladder and rectum complications after high-dose (70 –78 Gy) conformal radiotherapy for prostate cancer, using dose–volume histograms. Int J Radiat Oncol Biol Phys 1998;41:83–92. 12. Emami B, Lyman J, Brown A, Coia L, Goitein M, Munzenrider JE, Shank B, Solin LJ, Wesson M. Tolerance of normal tissue to therapeutic irradiation. Int J Radiat Oncol Biol Phys 1991;21:109 –122.
I. J. Radiation Oncology
● Biology ● Physics
Volume 52, Number 4, 2002
Table 3. Time to first Grade 3⫹ toxicity at various times after commencement of radiation (by Cumulative Incidence method) SFX % ⫾ SE 1 year 2 years 3 years 4 years 5 years Comparison with SFX (11)
17.2 ⫾ 2.5 22.2 ⫾ 2.8 25.6 ⫾ 3.0 27.1 ⫾ 3.1 27.1 ⫾ 3.1 —
HFX At risk 146 77 49 26 17
% ⫾ SE
At risk
16.9 ⫾ 2.5 23.3 ⫾ 2.8 26.5 ⫾ 3.0 26.5 ⫾ 3.0 26.5 ⫾ 3.0 p ⫽ 0.99
level of 0.05, the probability of finding one false-positive result increases with the number of tests performed. This probability increases from 0.098 with two tests, to 0.226 with 5 tests, and 0.460 with 12 tests. This problem, recognized by most statisticians, can be rectified by the Bonferroni correction (7), which calls for the desired overall significance level to be divided by the number of tests performed. To preserve an overall significance of 0.05 with the 12 pairwise tests of the prevalence rates here, the p value would have to be less than the adjusted value of 0.0042 (⫽0.05/12). We calculated all 12 p values and found the lowest to be 0.018, which is well above the adjusted critical value for statistical significance. More convincingly, however, Table 1 also shows no increase in the prevalence rates with HFX after 2.0 years and there is no statistical difference in the incidence rates computed using two different methodologies as presented in Tables 2 and 3. Finally, Dr. Logie recommends exploration of a combination of chemotherapy and radiation as a strategy specifically designed to avoid the late effects typical of radiation while maintaining a superior tumor cell kill compared to standard fractionation. In principle, it does make much more sense to design combined modality regimens based on specific mechanisms of radiation– drug interaction. In reality, however, knowledge on the exact mechanisms of drug–radiation interaction or the pharmacodynamics is limited for most cytotoxic agents. Consequently, most combined chemoradiation regimens evolved empirically simply by adding chemotherapy regimens showing some clinical activity, usually in patients with disseminated disease, to radiation. Therefore, most of the concurrent chemoradiation regimens turn out to have increased acute or late toxicity relative to radiation alone though some also yielded survival advantage (8). The data of a recently completed Intergroup Phase III trial enrolling patients with unresectable head-andneck squamous cell carcinoma, presented at the 2000 Annual Meeting of the American Society of Clinical Oncology, clearly illustrate this point (9). This trial randomized patients to radiation alone (70 Gy in 7 weeks), radiation (70 Gy) plus cisplatin (100 mg/m2 for 3 cycles), or split-course radiation (30 Gy ⫹ 30 – 40 Gy) given with the first and third cycles of cisplatin (75 mg/m2) plus fluorouracil (1000 mg/m2) given every 4 weeks. The 2- and 3-year actuarial survival rates were 30 –20% for radiation alone, 43–37% for radiation ⫹ cisplatin ( p ⫽ 0.016), and 40 –29% for split-course radiation plus cisplatin–fluorouracil ( p ⫽ 0.13). The Grade 3⫹ toxicity, however, occurred in 53%, 86% ( p ⬍ 0.0001), and 77% ( p ⬍ 0.001) of the patients, respectively. Fortunately, advances in understanding the biology of head-and-neck cancers have brought us a step forward in identifying specific molecular targets for therapeutic interventions, which hopefully will translate into a substantial therapeutic gain. K. KIAN ANG, M.D., PH.D. Department of Radiation Oncology University of Texas M. D. Anderson Cancer Center Houston, TX BRIAN A. BERKEY, M.S. THOMAS F. PAJAK, PH.D. RTOG Statistical Unit Philadelphia, PA KAREN K. FU, M.D. Department of Radiation Oncology University of California San Francisco San Francisco, CA PII S0360-3016(01)02777-8
AFX-S
144 90 58 35 24
% ⫾ SE
AFX-C At risk
16.0 ⫾ 2.4 21.6 ⫾ 2.7 24.9 ⫾ 2.9 27.7 ⫾ 3.1 28.5 ⫾ 3.1 p ⫽ 0.94
149 84 50 29 21
% ⫾ SE
At risk
17.6 ⫾ 2.5 25.2 ⫾ 2.9 29.0 ⫾ 3.1 31.6 ⫾ 3.2 34.9 ⫾ 3.6 p ⫽ 0.27
149 90 58 38 18
1. Dubben HH, Beck-Bornholdt HP. A Radiation Therapy Oncology Group (RTOG) Phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard-fractionation radiotherapy for head-and-neck squamous cell carcinomas: First report of RTOG 9003: In regard to Fu et al. IJROBP 2000;48: 7–16. Actuarial estimates of late normal-tissue effects . . . now! Int J Radiat Oncol Biol Phys 2001;51:563. 2. Logie MB. Regarding Fu et al., A Radiation Therapy Oncology Group (RTOG) phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard fractionation radiotherapy for head and neck squamous cell carcinomas: First report of RTOG 9003. Int J Radiat Oncol Biol Phys. In press. 3. Fu KK, Pajak TF, Trotti A, et al. A Radiation Therapy Oncology Group (RTOG) phase III randomized study to compare hyperfractionation and two variants of accelerated fractionation to standard fractionation radiotherapy for head and neck squamous cell carcinomas: First report of RTOG 9003. Int J Radiat Oncol Biol Phys 2000;48:7– 16. 4. Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc 1958;53:457– 481. 5. Kalbfleish J, Prentice R. The statistical analysis of failure time data. New York: John Wiley and Sons; 1980. 6. Baumann M, Bentzen SM, Ang KK. Hyperfractionated radiotherapy in head and neck cancer: A second look at the clinical data. Radiother Oncol 1998;46:127–130. 7. Bonferroni CE. Teoria statistica delle classi e calcolo delle probabilita. Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze 1936;8:3– 62. 8. El-Sayed S, Nelson N. Adjuvant and adjunctive chemotherapy in the management of squamous cell carcinoma of the head and neck region: A meta-analysis of prospective and randomised trials. J Clin Oncol 1996;14:838 – 847. 9. Adelstein DJ, Adams GL, Li Y, et al. A phase III comparison of standard radiation therapy (RT) versus RT plus concurrent cisplatin (DDP) versus split-course RT plus concurrent DDP and 5-fluorouracil (5FU) in patients with unresectable squamous cell head and neck cancer (SCHNC): An intergroup study. (Abstract). Proceedings of ASCO 2000;19:411a. 10. Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother Rep 1966;5:163–170. 11. Gray RJ. A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 1988;16:1141–1154.
ON THE CONSISTENT USE OF ORGAN DEFINITIONS AND RADIOBIOLOGICAL MODELS FOR THE EVALUATION OF COMPLICATION PROBABILITIES OF “TUBULAR” ORGANS To the Editor: The advent of 3D conformal therapy has instigated an enormous interest in the application of radiobiological models for the purposes of treatment planning optimization and evaluation, mostly because of the potential of these models to summarize an abundance of dosimetric information into a single figure of merit (1). This figure of merit (whether tumor control probability [TCP] or normal tissue complication probability [NTCP]) depends on the functional form of the radiobiological model, organ definitions, planned dose distribution, and the values of the model free parameters. Figure 1a illustrates a parameter estimation procedure to emphasize that
Letters to the editor
1151
Fig. 1. (a) Procedure for estimating model parameters. After the selection of a consistent organ definition throughout the entire patient population and a functional form of the radiobiological model, the model parameters are derived from a fit to the outcome data. (b) Estimation of the outcome probability.
the estimated values of the radiobiological model parameters depend on the adopted definition of the organ under consideration. This definition can be rather ambiguous, especially for the case of “tubular” organs such as rectum, esophagus, bladder, etc. These organs could be represented either as 2D surface, 3D wall objects (the volume of the wall is defined on the bases of the thickness of the organ’s wall and its surface contours), or 3D solid volumes. Based on the underlying anatomy, some authors (2– 4) have a priori presumed the wall–volume definitions for bladder and rectum, whereas others (5–7) have applied various methods to estimate which organ definition (surface, wall–volume, or solid–volume) better suits NTCP estimations. In their investigations they have compared various indices derived from dose–volume histograms (DVHs) and dose–wall histograms (DWHs). (A DVH is calculated based on a solid body organ definition, whereas a DWH is calculated based on a wall–volume organ definition.) However, the results of these studies are in disaccord with respect to the question, “Does the DWH reflect better the organ response than DVH?” Here we do not attempt to advocate in favor of any of those organ definitions. All of them could be used for NTCP assessments,
providing the parameters of the applied NTCP model have been derived from data based on identical organ definition. One way to assess which is the proper organ definition can be based on how well could a certain radiobiological model fit sets of data (Dose– Volume, Outcome) based on the different organ definitions. For example, if for one and the same group of patients one has the DWHs and the DVHs for a given tubular organ, and also the outcome of the treatment, i.e., complication or noncomplication, the fit, let us say, of Lyman’s NTCP model to the set of data based on the wall–volume definition may result in considerably better fit than the one using the solid volume organ definition. It is quite possible, though, that for some organs both definitions (wall– volume and solid–volume), would lead to equally acceptable fits, meaning that both definitions should be considered sufficiently proper. It is important to emphasize that regardless of the particular organ definition, for subsequent applications of the radiobiological model to the evaluation of dose distributions, the combination model/organ definition/ parameter set should be identical to the combination model/organ definition/parameter set used in the estimation procedure as implied in Fig. 1.
1152
I. J. Radiation Oncology
● Biology ● Physics
Volume 52, Number 4, 2002 2. A model is used with organ definitions different from the ones used in the parameter estimation procedure (5, 6, 7, 11). This tends to be the case for “tubular” (hollow) organs, such as rectum, esophagus, bladder, etc. because, as noted by Lebesque et al. (6): “Emami et al. (12) and Burman et al. (8) did not specify whether the rectum and bladder should be considered as solid organs (contouring of the outer surface only) or hollow organs, which require contouring of the outer and internal surfaces.” We agree with Lebesque et al. (6) that the organs (rectum and bladder) were not exactly defined in the work by Emami et al. (12). On the other hand, given the reported total volume of the rectum and the fact that during the 1980s the 3D dose distributions were not a common tool, one can support the view of Dale et al. (5), that the rectum in the work of Emami et al. (12) was considered a solid body [although this was never stated by Emami et al. (12)], i.e., not a tubular one. To conclude, as illustrated in Fig. 1, we would like to reiterate that the predictive power of radiobiological models is based on consistent use of the parameter estimate and the outcome evaluation procedures. Note: This work is partially supported by MRC Grant MOP 36470. PAVEL V. STAVREV, PH.D. DIMITRE H. HRISTOV, PH.D. JAN P. SEUNTJENS, PH.D. Medical Physics Unit Montreal General Hospital and McGill University Montreal, Canada PII S0360-3016(01)02748-1
Fig. 2. The difference between the CE NTCP model (dashed line) used by Ting et al. (7) and Lyman’s NTCP model (solid line) for rectum and bladder. Both are using the Burman et al. (8) parameters. The three curves represent whole, 2/3, and 1/3 volume irradiation respectively, moving from left to right.
However, this somewhat obvious requirement is not always satisfied, and the following deviations can be noted in various studies reported in the literature: 1. A set of parameters estimated on the basis of one radiobiological model is used with another model. For instance, Ting et al. (7) use a two-parametric model with a set of parameters estimated on the bases of a three-parametric model. In their work the parameters {D50, m, n}, estimated by Burman et al. (8) using Lyman’s model were transformed to {D50, k (k ⫽ 1.6/m)}, and a Critical Element (CE) model, also referred to as Series Organ model, suggested by Schultheiss et al. (9) was used. Ting et al. (7) have used the Schultheiss, but not the CE model based on the functional subunit (FSU) ideology, both discussed by Niemierko and Goitein (10). The second model has at least three parameters—two (D50 and ␥50) describing the FSU response and the third being the number of FSU, while the first model has only two parameters—D50 and k (␥50) of the whole organ response. If the transformed parameters were consistent with the Schultheiss model, one would expect that both the Lyman and the Schultheiss models would result in similar dose–response curves for any partial irradiation. This is definitely the expectation, if both models were applied with their own parameters, properly deduced from fits to outcome data (see Fig. 1). For bladder and rectum, Fig. 2 demonstrates the partial organ— one-third, two-thirds, and whole— dose–response curves predicted by the Lyman model and the Schultheiss model. The differences result from the mismatched use of the estimated parameters. Only the whole, organ response curves coincide because the transformation k ⫽ 1.6/m is derived for this case. Hence, for each partial volume irradiation the value of k should be recalculated.
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