1095
CORRESPONDENCE RESPONSE
TO DR. LAWRENCE
ET AL.
To fhe Editor: In a recent letter, Dr. Gilbert A. Lawrence, Dr. Jerome D. Derdel, and Dr. Douglas Colkitt, have expressed their concerns about grouping of the two RTOC protocols 75-06 and 77-06, and a need for a radiobiological model of a “prostate cancer cell”. We agree with some of the comments that they made about adenocarcinoma of the prostate in general, but differ in their conclusion. The grouping of the two RTOG protocols were very reasonable because the analysis was done with appropriate stratification. It is clearly stated in the section under “Methods and Materials” that the patients who were accrued onto RTOG protocol 77-06 were either Tlb (A2) or T2 (B), while the majority of the patients who were accrued onto RTOG protocol 75-06 were primarily stage T3,4 (C) patients. There were very few patients with stage T1 b (A2) (3) T2 (B) (57) with lymphangiographically or histologically confirmed pelvic lymph node involvement. These 60 patients may be the source of concern to Dr. Lawrence et al., but the numbers were small and were evenly distributed among ah the subgroups. Furthermore, the analysis was stratified by stage Tlb (AZ), T2 (B), T3,4 (C) which essentially assigns patients to their respective prognostic subgroup. With regard to the statement in the last paragraph “radiation oncologists may be prudent to stay with the widely tested and accepted time, dose, and fractionation regimes for cancer of the prostate,” it was mentioned in the “Discussion” section that different clinical schedules have evolved empirically, but are centered around the balance between local tumor control, acute reactions, and late complications. Thus time, dose, fractionation schedules that cannot stand the test of time have been discarded. In our experience, prolongation of the treatment time does not seem to affect treatment outcome or treatment-related morbidity for adenocarcinoma ofthe prostate. After evaluation of the clinical outcome and the available tumor kinetics data on prostate adenocarcinoma, Dr. Fowler stated in the editorial “treatment of Ca prostate given in longer overall times than 8 or 9 weeks can give a good outcome, provided that adequately high doses (e.g., > 65 Gy) were given.” A radiobiological model of a “prostate cancer cell” would unify the clinical observation with the laboratory findings. Moreover, it would provide a theoretical basis that might define a subset of prostate cancer patients with poor prognostic factors who might be affected by prolongation ofoverall treatment time. Prostate adenocarcinoma, like other human tumors, is not a homogenous disease. By meticulous evaluation of available clinical data, coupled with strong theoretical construct, we are continuously sub classifying patients to provide them with individualized treatment, and hopefully to improve treatment outcome. Regarding their comment on post-irradiation prostate biopsy, we would like to emphasize that the time of post-irradiation biopsy is critical in correlating histologic findings with prognosis. Several authors ( 1,2) have reported a greater local recurrence rate, and decreased survival in patients with residual carcinoma of the prostate (positive biopsy) more than 18 months after completion of irradiation.
positive surgical margins are important factors related to risk of local relapse following radical surgery for prostate cancer. In their discussion, they mention some of the difficulties in analyzing local relapse including failure to state exactly how local recurrence is defined and how patients are counted who suffer other untoward events without prior evidence of local relapse. One might have expected that Anscher and Prosnitz would give a clear definition of local relapse and state exactly how patients were counted in their analysis who suffered other events (e.g., distant metastases or death) without having had local relapse. Unfortunately, Anscher and Prosnitz have contributed to the difficulties in analyzing local failure rates by not giving precise statements concerning these issues. While one cannot argue with the statement of Robey and Shellhammer (2) that they quote: “The efficacy of local definitive treatment is measured by success in achieving local control,” one should be sure that the whole patient is somehow not lost in this evaluation process. Thus, it would be desirable to present time to distant metastases and survival curves in addition to the time to local relapse curve. If a major cause of failure is evidence of distant metastases, then reducing the local relapse rate to 0% might not have much impact on the patient’s overall survival. Consequently, it would seem important to evaluate time to local relapse data in the context of data on distant metastases and survival. The authors do not consider the impact of the risk factors they have identified with local failure, namely elevated PAP, poorly differentiated tumors, and positive surgical margins on the incidence of systemic failure. If these factors, as one might expect, are associated with increased risk of systemic disease, then the addition of another local treatment modality would add little to the patient’s overall survival. The authors support this when they state that distant disease appeared shortly after local failure. Also, the authors do not address the incidence of either local or systemic failure in the 38% of patients who did undergo pelvic lymphadenectomy. The data analysis ofthe patients in this series is also somewhat difficult to interpret since 3 1% of their patients were considered to have received hormonal therapy, which could impact directly upon both local and systemic failure rates. The exclusion of post operative PSA data would be expected to result in an under estimate of both local and systemic failure which adds more confusion to the authors’ conclusion. Though the title of their paper implies that patients receiving radical prostatectomy might also receive postoperative radiotherapy, the authors unaccountably excluded from their analysis the 46 patients who received adjuvant postoperative irradiation. While 46 patients would not represent a definitive series, ifthey had good follow-up, estimates of the percentage of patients suffering local relapse, distant metastases, or death could be made with a maximum standard error of 7.4% based on 46 patients. Having such an estimate would provide some basis for evaluating the authors’ suggestion. It would be helpful to have a clarification of these issues to provide a more definitive evaluation of the results presented in the paper. EDMUND A. GEHAN, PH.D. RICHARD J. BABAIAN, M.D.
The University of Texas M. D. Anderson Cancer Center 15 I5 Holcombe Boulevard Houston, TX 77030
PETER P. LAI, PH.D., M.D. CARLOS A. PEREZ, M.D.
Mallinckrodt Institute of Radiology Washington Univ. Med. Ctr. 4939 Audubon Ave., Suite 5500 St. Louis, MO 63 110 1. Freiha, F. S.; Bagshaw, M. A. Carcinoma of the prostate: results of post-irradiation biopsy. Prostate 5:19-25;1984. 2. Scardino, P. T.; Wheeler, T. M. Local control of prostate cancer with radiotherapy: frequency and prognostic significance of positive results of postirradiation prostate biopsy. NC1 Monogr. 7:95103:1988.
RADICAL PROSTATECr’OMY-POSSIBLE INDICATIONS FOR POSTOPERATIVE RADIOTHERAPY To the Editor: The article by Anscher and Prosnitz (I) answers some questions about factors predicting local relapse after radical prostatectomy, but raises others that it would be desirable to have more information about. Based on their multivariate analysis, they establish that an elevated preoperative acid phosphatase, poorly differentiated histology, and/or
Anscher, M. S.; Prosnitz, L. R. Multivariate analysis of factors predicting local relapse after radical prostatectomy-possible indications for postoperative radiotherapy. Int. J. Radiation. Oncol. Biol. Phys. 21:941-948;1991. 2. Robey, E. L.; Shellhammer, P. F. Local failure after definitive therapy for prostate cancer. J. Urol. 137:613-619;1987. RESPONSE
TO DRS. GEHAN
AND BABAIAN
Our thanks to Drs. Gehan and Babaian for their thoughtful comments concerning our paper, “Multivariate analysis of factors predicting local relapse after radical prostatectomy. . “(2)Perhaps we can clarify some of the issues and questions raised in their letter. The goal of this study was to identify patients at high risk for local failure following radical prostatectomy who might benefit from the use of adjuvant radiotherapy. Patients undergoing radical prostatectomy at Duke University between 1970 and 1983 were studied. A small percentage of this group did undergo postoperative radiotherapy and has been the subject of a previous publication which demonstrated a marked reduction
1096
I. J. Radiation Oncology 0 Biology 0 Physics
in local failure rate and improvement in survival when compared with concurrent patients treated with surgery alone (1). This current study focused on risk factors for local failure among the patients who did not receive adjuvant radiotherapy. We do indicate in the method section of the study that local failure was histologically confirmed in all cases. Thus the current definition of local failure is a pathologic one. Local failure was the most common cause of initial relapse with actuarial local failure rates as the first sign of relapse at 5 and 10 years being 12 and 32 percent, respectively. In comparison, the rates of distant failure as a first sign of relapse were I2 and 20 percent at 5 and IO years, respectively. The great majority of the patients with initial local failure do go on to develop distant metastases, both in our series and others reported in the literature. One could take a nihilistic view of this and conclude that local therapy does not have much of an impact on ultimate survival. We prefer to reason that improved local treatment not only would prevent local relapse, but would also positively impact on the distant metastatic rate, ifthese local failures can serve as a nidus for subsequent disease dissemination. In our prior 1987 study, there was some evidence for this with apparent improved survival in patients who received adjuvant radiotherapy as well as much better local control than patients who were treated with surgery alone. The principle point is that there are patients undergoing radical prostatectomy who constitute a high risk group for recurrence locally, that such local failure is followed by distant metastases in the great majority of patients, and at the very least Phase III trails of postoperative radiotherapy in certain patients undergoing radical prostatectomy should be done in order to assess the impact of such radiation on local control, distant metastatic rate, and ultimate survival. Such a study is, of course, underway, sponsored primarily by the Eastern Cooperative Oncology group. We understand there has been some difficulty in accruing patients but would urge the support of this trial. MITCHELLS. ANSCHER,M.D. LEONARDR. PROSNITZ,M.D. Duke University Medical Center Box 3085 Durham. NC 277 10 I. Anscher, M. S.; Prosnitz, L. R. J. Ural. 138:1407;1987. 2. Gehan, E. A. Babaian, R. J. Int. J. Radiat. Oncol. Biol. Phys. 21: 941-947;1991. LATE EFFECTS AFTER RADIOTHERAPY
Volume 23, Number 5, 1992 If both sides of Equation 3 are multiplied by 01,then cvBED = aLQ dose - yT = and + /3nd2 - yT
The quantity /3,/p2 is an estimate of a/p. In Equation 4, T equals overall time minus T,, (starting time of compensatory proliferation). Biologically, the quantity @Z in Equation 2 is correlated to the natural logarithm of survival fraction after radiotherapy with daily dose d for n fractions in a time period T. The T in Dr. Taylor’s study has a different definition than that T in Dr. Fowler’s BED formulation. T in Dr. Taylor’s article is a covariate of n for BID and QD is radiation. T increases with the number of fractions n. When clinical data are used to fit the proportional hazards model to estimate &, & and &, the correlation between n and T in PZ, is likely to skew the true value of the p’s, The addition of P,T implies cell regeneration, incomplete damage repair, or cell death from other causes during the treatment period T. Clinically, it is extremely difficult to analyze the late complications, which may be co-presented with a variety of physical findings from different tissues such as mandible, mucous membrane, and soft tissues in the head and neck region. Each type of tissue may have its own characteristic a//3 value for the late effect. The authors categorized the late complications into two groups 2+ and 3+, which represents the combined late effects or even contains some acute effect, (2). This categorization is insufficient to determine a pure a/@ value for each particular late effect of a specific tissue. The two points mentioned above, perhaps, may explain the difference between the clinically derived @iI& (an estimate of (Y/P) and experimentally obtained (Y/P ( l-5 Gy) values for late effects (3). Assuming ps = 0, the proportional hazards model becomes:
h(Z, t) = ho(t)exp(PZ) PZ = B,*nd + /3z*nd2
h(Z, t)i9 = h,,(t)exp(0.4.68
TIME,
h(Z, t) = ho(t)exp(gZ)
+ 0.08-68. 1.9)
= h,,(t)exp(37.54)
To the Editor: Drs. Taylor, Mendenhall and Lavey (3), presented an excellent study of fractionation factors to evaluate the late effects after radiotherapy in head and neck squamous cell carcinoma. The proportional hazards analysis was used to estimate the late effects with the following equation of hazard.
(1)
(5)
IF pi = 0.4 Gy-‘, & = 0.08 Gym2,(a//3 = 5 Gy), the late complication for 68 Gy, given at 1.9 Gy per fraction, as mentioned in Dr. Taylor’s article, h(z, t), g becomes
IN HEAD AND
NECK MALIGNANCIES: OVERALL TREATMENT NUMBER OF FRACTIONS AND THE LINEAR-QUADRATIC MODEL
(4)
(6)
To compute D, 2 (the isoeffect dose for BID treatment, at I .2 Gy per fraction, as the regimen in Equation 6), the following relationship is used:
h(z, tl1.9= h(z. t),
2
(7)
Since h,,(t) can be removed from each side of Equation 7, after taking natural logarithm on the remaining term, the equation becomes
while, 13,*68+8z.68.1.9=B,.D,z+/3z.D,z.1.2=37.54 PZ = p,nd + &nd’ + &T
(8)
(2) Hence.
n = number of fractions Di.2 = 75.7 Gy
d = dose per fraction T = overall treatment time 4,, &, f13= coefficients obtained from fitting proportional hazards model. PZ has a similar form as the biological effective dose (BED) which was proposed by Dr. Fowler for evaluation of acute effect from radiotherapy ( 1). This resemblance can be shown in the following equations: BED = LQ dose - rTf 01
(3)
The difference between 75.7 Gy and 68 Gy falls into the 4-9 Gy range which was clinically observed by Dr. Taylor, and the /3i/& value is in the range I-5 Gy for late tissues. Similar results are obtained in the range of clinically used daily fractionation of 1.8 Gy to 2 Gy, if other PI/p2 values are used to compute the total isoeffect dose for late effects. For example, fli/& = 0.15/0.03 (oc/B = 5 Gy), given at 2 Gy per day to 68 Gy, the corresponding total isoeffect dose for I .2 Gy BID was 76.77 Gy; for pi/& = 0.12/0.03, (a/j3 = 4 Gy), I.8 Gy Q.D. to a total dose of 68 Gy, the 1.2 Gy BID regimen will require 75.85 Gy to produce the same late effects.
CORRESPONDENCE RESPONSE
TO DR. LAWRENCE
ET AL.
To fhe Editor: In a recent letter, Dr. Gilbert A. Lawrence, Dr. Jerome D. Derdel, and Dr. Douglas Colkitt, have expressed their concerns about grouping of the two RTOC protocols 75-06 and 77-06, and a need for a radiobiological model of a “prostate cancer cell”. We agree with some of the comments that they made about adenocarcinoma of the prostate in general, but differ in their conclusion. The grouping of the two RTOG protocols were very reasonable because the analysis was done with appropriate stratification. It is clearly stated in the section under “Methods and Materials” that the patients who were accrued onto RTOG protocol 77-06 were either Tlb (A2) or T2 (B), while the majority of the patients who were accrued onto RTOG protocol 75-06 were primarily stage T3,4 (C) patients. There were very few patients with stage T1 b (A2) (3) T2 (B) (57) with lymphangiographically or histologically confirmed pelvic lymph node involvement. These 60 patients may be the source of concern to Dr. Lawrence et al., but the numbers were small and were evenly distributed among ah the subgroups. Furthermore, the analysis was stratified by stage Tlb (AZ), T2 (B), T3,4 (C) which essentially assigns patients to their respective prognostic subgroup. With regard to the statement in the last paragraph “radiation oncologists may be prudent to stay with the widely tested and accepted time, dose, and fractionation regimes for cancer of the prostate,” it was mentioned in the “Discussion” section that different clinical schedules have evolved empirically, but are centered around the balance between local tumor control, acute reactions, and late complications. Thus time, dose, fractionation schedules that cannot stand the test of time have been discarded. In our experience, prolongation of the treatment time does not seem to affect treatment outcome or treatment-related morbidity for adenocarcinoma ofthe prostate. After evaluation of the clinical outcome and the available tumor kinetics data on prostate adenocarcinoma, Dr. Fowler stated in the editorial “treatment of Ca prostate given in longer overall times than 8 or 9 weeks can give a good outcome, provided that adequately high doses (e.g., > 65 Gy) were given.” A radiobiological model of a “prostate cancer cell” would unify the clinical observation with the laboratory findings. Moreover, it would provide a theoretical basis that might define a subset of prostate cancer patients with poor prognostic factors who might be affected by prolongation ofoverall treatment time. Prostate adenocarcinoma, like other human tumors, is not a homogenous disease. By meticulous evaluation of available clinical data, coupled with strong theoretical construct, we are continuously sub classifying patients to provide them with individualized treatment, and hopefully to improve treatment outcome. Regarding their comment on post-irradiation prostate biopsy, we would like to emphasize that the time of post-irradiation biopsy is critical in correlating histologic findings with prognosis. Several authors ( 1,2) have reported a greater local recurrence rate, and decreased survival in patients with residual carcinoma of the prostate (positive biopsy) more than 18 months after completion of irradiation.
positive surgical margins are important factors related to risk of local relapse following radical surgery for prostate cancer. In their discussion, they mention some of the difficulties in analyzing local relapse including failure to state exactly how local recurrence is defined and how patients are counted who suffer other untoward events without prior evidence of local relapse. One might have expected that Anscher and Prosnitz would give a clear definition of local relapse and state exactly how patients were counted in their analysis who suffered other events (e.g., distant metastases or death) without having had local relapse. Unfortunately, Anscher and Prosnitz have contributed to the difficulties in analyzing local failure rates by not giving precise statements concerning these issues. While one cannot argue with the statement of Robey and Shellhammer (2) that they quote: “The efficacy of local definitive treatment is measured by success in achieving local control,” one should be sure that the whole patient is somehow not lost in this evaluation process. Thus, it would be desirable to present time to distant metastases and survival curves in addition to the time to local relapse curve. If a major cause of failure is evidence of distant metastases, then reducing the local relapse rate to 0% might not have much impact on the patient’s overall survival. Consequently, it would seem important to evaluate time to local relapse data in the context of data on distant metastases and survival. The authors do not consider the impact of the risk factors they have identified with local failure, namely elevated PAP, poorly differentiated tumors, and positive surgical margins on the incidence of systemic failure. If these factors, as one might expect, are associated with increased risk of systemic disease, then the addition of another local treatment modality would add little to the patient’s overall survival. The authors support this when they state that distant disease appeared shortly after local failure. Also, the authors do not address the incidence of either local or systemic failure in the 38% of patients who did undergo pelvic lymphadenectomy. The data analysis ofthe patients in this series is also somewhat difficult to interpret since 3 1% of their patients were considered to have received hormonal therapy, which could impact directly upon both local and systemic failure rates. The exclusion of post operative PSA data would be expected to result in an under estimate of both local and systemic failure which adds more confusion to the authors’ conclusion. Though the title of their paper implies that patients receiving radical prostatectomy might also receive postoperative radiotherapy, the authors unaccountably excluded from their analysis the 46 patients who received adjuvant postoperative irradiation. While 46 patients would not represent a definitive series, ifthey had good follow-up, estimates of the percentage of patients suffering local relapse, distant metastases, or death could be made with a maximum standard error of 7.4% based on 46 patients. Having such an estimate would provide some basis for evaluating the authors’ suggestion. It would be helpful to have a clarification of these issues to provide a more definitive evaluation of the results presented in the paper. EDMUND A. GEHAN, PH.D. RICHARD J. BABAIAN, M.D.
The University of Texas M. D. Anderson Cancer Center 15 I5 Holcombe Boulevard Houston, TX 77030
PETER P. LAI, PH.D., M.D. CARLOS A. PEREZ, M.D.
Mallinckrodt Institute of Radiology Washington Univ. Med. Ctr. 4939 Audubon Ave., Suite 5500 St. Louis, MO 63 110 1. Freiha, F. S.; Bagshaw, M. A. Carcinoma of the prostate: results of post-irradiation biopsy. Prostate 5:19-25;1984. 2. Scardino, P. T.; Wheeler, T. M. Local control of prostate cancer with radiotherapy: frequency and prognostic significance of positive results of postirradiation prostate biopsy. NC1 Monogr. 7:95103:1988.
RADICAL PROSTATECr’OMY-POSSIBLE INDICATIONS FOR POSTOPERATIVE RADIOTHERAPY To the Editor: The article by Anscher and Prosnitz (I) answers some questions about factors predicting local relapse after radical prostatectomy, but raises others that it would be desirable to have more information about. Based on their multivariate analysis, they establish that an elevated preoperative acid phosphatase, poorly differentiated histology, and/or
Anscher, M. S.; Prosnitz, L. R. Multivariate analysis of factors predicting local relapse after radical prostatectomy-possible indications for postoperative radiotherapy. Int. J. Radiation. Oncol. Biol. Phys. 21:941-948;1991. 2. Robey, E. L.; Shellhammer, P. F. Local failure after definitive therapy for prostate cancer. J. Urol. 137:613-619;1987. RESPONSE
TO DRS. GEHAN
AND BABAIAN
Our thanks to Drs. Gehan and Babaian for their thoughtful comments concerning our paper, “Multivariate analysis of factors predicting local relapse after radical prostatectomy. . “(2)Perhaps we can clarify some of the issues and questions raised in their letter. The goal of this study was to identify patients at high risk for local failure following radical prostatectomy who might benefit from the use of adjuvant radiotherapy. Patients undergoing radical prostatectomy at Duke University between 1970 and 1983 were studied. A small percentage of this group did undergo postoperative radiotherapy and has been the subject of a previous publication which demonstrated a marked reduction
1096
I. J. Radiation Oncology 0 Biology 0 Physics
in local failure rate and improvement in survival when compared with concurrent patients treated with surgery alone (1). This current study focused on risk factors for local failure among the patients who did not receive adjuvant radiotherapy. We do indicate in the method section of the study that local failure was histologically confirmed in all cases. Thus the current definition of local failure is a pathologic one. Local failure was the most common cause of initial relapse with actuarial local failure rates as the first sign of relapse at 5 and 10 years being 12 and 32 percent, respectively. In comparison, the rates of distant failure as a first sign of relapse were I2 and 20 percent at 5 and IO years, respectively. The great majority of the patients with initial local failure do go on to develop distant metastases, both in our series and others reported in the literature. One could take a nihilistic view of this and conclude that local therapy does not have much of an impact on ultimate survival. We prefer to reason that improved local treatment not only would prevent local relapse, but would also positively impact on the distant metastatic rate, ifthese local failures can serve as a nidus for subsequent disease dissemination. In our prior 1987 study, there was some evidence for this with apparent improved survival in patients who received adjuvant radiotherapy as well as much better local control than patients who were treated with surgery alone. The principle point is that there are patients undergoing radical prostatectomy who constitute a high risk group for recurrence locally, that such local failure is followed by distant metastases in the great majority of patients, and at the very least Phase III trails of postoperative radiotherapy in certain patients undergoing radical prostatectomy should be done in order to assess the impact of such radiation on local control, distant metastatic rate, and ultimate survival. Such a study is, of course, underway, sponsored primarily by the Eastern Cooperative Oncology group. We understand there has been some difficulty in accruing patients but would urge the support of this trial. MITCHELLS. ANSCHER,M.D. LEONARDR. PROSNITZ,M.D. Duke University Medical Center Box 3085 Durham. NC 277 10 I. Anscher, M. S.; Prosnitz, L. R. J. Ural. 138:1407;1987. 2. Gehan, E. A. Babaian, R. J. Int. J. Radiat. Oncol. Biol. Phys. 21: 941-947;1991. LATE EFFECTS AFTER RADIOTHERAPY
Volume 23, Number 5, 1992 If both sides of Equation 3 are multiplied by 01,then cvBED = aLQ dose - yT = and + /3nd2 - yT
The quantity /3,/p2 is an estimate of a/p. In Equation 4, T equals overall time minus T,, (starting time of compensatory proliferation). Biologically, the quantity @Z in Equation 2 is correlated to the natural logarithm of survival fraction after radiotherapy with daily dose d for n fractions in a time period T. The T in Dr. Taylor’s study has a different definition than that T in Dr. Fowler’s BED formulation. T in Dr. Taylor’s article is a covariate of n for BID and QD is radiation. T increases with the number of fractions n. When clinical data are used to fit the proportional hazards model to estimate &, & and &, the correlation between n and T in PZ, is likely to skew the true value of the p’s, The addition of P,T implies cell regeneration, incomplete damage repair, or cell death from other causes during the treatment period T. Clinically, it is extremely difficult to analyze the late complications, which may be co-presented with a variety of physical findings from different tissues such as mandible, mucous membrane, and soft tissues in the head and neck region. Each type of tissue may have its own characteristic a//3 value for the late effect. The authors categorized the late complications into two groups 2+ and 3+, which represents the combined late effects or even contains some acute effect, (2). This categorization is insufficient to determine a pure a/@ value for each particular late effect of a specific tissue. The two points mentioned above, perhaps, may explain the difference between the clinically derived @iI& (an estimate of (Y/P) and experimentally obtained (Y/P ( l-5 Gy) values for late effects (3). Assuming ps = 0, the proportional hazards model becomes:
h(Z, t) = ho(t)exp(PZ) PZ = B,*nd + /3z*nd2
h(Z, t)i9 = h,,(t)exp(0.4.68
TIME,
h(Z, t) = ho(t)exp(gZ)
+ 0.08-68. 1.9)
= h,,(t)exp(37.54)
To the Editor: Drs. Taylor, Mendenhall and Lavey (3), presented an excellent study of fractionation factors to evaluate the late effects after radiotherapy in head and neck squamous cell carcinoma. The proportional hazards analysis was used to estimate the late effects with the following equation of hazard.
(1)
(5)
IF pi = 0.4 Gy-‘, & = 0.08 Gym2,(a//3 = 5 Gy), the late complication for 68 Gy, given at 1.9 Gy per fraction, as mentioned in Dr. Taylor’s article, h(z, t), g becomes
IN HEAD AND
NECK MALIGNANCIES: OVERALL TREATMENT NUMBER OF FRACTIONS AND THE LINEAR-QUADRATIC MODEL
(4)
(6)
To compute D, 2 (the isoeffect dose for BID treatment, at I .2 Gy per fraction, as the regimen in Equation 6), the following relationship is used:
h(z, tl1.9= h(z. t),
2
(7)
Since h,,(t) can be removed from each side of Equation 7, after taking natural logarithm on the remaining term, the equation becomes
while, 13,*68+8z.68.1.9=B,.D,z+/3z.D,z.1.2=37.54 PZ = p,nd + &nd’ + &T
(8)
(2) Hence.
n = number of fractions Di.2 = 75.7 Gy
d = dose per fraction T = overall treatment time 4,, &, f13= coefficients obtained from fitting proportional hazards model. PZ has a similar form as the biological effective dose (BED) which was proposed by Dr. Fowler for evaluation of acute effect from radiotherapy ( 1). This resemblance can be shown in the following equations: BED = LQ dose - rTf 01
(3)
The difference between 75.7 Gy and 68 Gy falls into the 4-9 Gy range which was clinically observed by Dr. Taylor, and the /3i/& value is in the range I-5 Gy for late tissues. Similar results are obtained in the range of clinically used daily fractionation of 1.8 Gy to 2 Gy, if other PI/p2 values are used to compute the total isoeffect dose for late effects. For example, fli/& = 0.15/0.03 (oc/B = 5 Gy), given at 2 Gy per day to 68 Gy, the corresponding total isoeffect dose for I .2 Gy BID was 76.77 Gy; for pi/& = 0.12/0.03, (a/j3 = 4 Gy), I.8 Gy Q.D. to a total dose of 68 Gy, the 1.2 Gy BID regimen will require 75.85 Gy to produce the same late effects.
