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The Effect of Radiotherapy on the Survival of Non-Small Cell Lung Cancer Patients
Int. J. Radiation Oncology Biol. Phys., Vol. 41, No. 2, pp. 291–298, 1998 Copyright © 1998 Elsevier Science Inc. Printed in the USA. All rights reserved 0360-3016/98 $19.00 1 .00
PII S0360-3016(98)00055-8
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Clinical Investigation THE EFFECT OF RADIOTHERAPY ON THE SURVIVAL OF NON-SMALL CELL LUNG CANCER PATIENTS JOSEPH SCHAAFSMA, PH.D.*
AND
PETER COY, M.B., B.CH., F.R.C.P.(C)†
*Department of Economics, University of Victoria, Victoria, British Columbia, V8W 3P5 Canada and †Vancouver Island Cancer Centre, British Columbia Cancer Agency, 1900 Fort Street, Victoria, British Columbia, V8R 1J8 Canada Purpose: To determine if thoracic radiotherapy improves the survival of non-small cell lung cancer (NSCLC) patients. Methods and Materials: A Cox proportional hazards model with prognostic and treatment covariates was estimated using prospective data for 129 NSCLC patients presenting at the Victoria Clinic (ViCC) of the British Columbia Cancer Agency (BCCA) 1990 –1991. The estimated model was simulated to predict survival curves for groups of patients with and without treatment. The difference between the predicted median survival with treatment and without treatment is the gain in survival attributable to treatment. Results: After adjusting for the effect of TNM staging, Karnofsky performance status, weight loss, tumor size, and tumor histology on survival, high-dose palliative radiotherapy (RT) (30 –50 Gy in 10 –20 fractions) increased median survival by 79 days (95% confidence interval: 31–106 days), and lowered the relative risk of death rate to 0.53 (95% confidence interval: 0.35– 0.85). Radical RT (50 or more Gy, in 20 or more fractions) increased median survival by 424 days (95% confidence interval: 302– 488 days), and lowered the relative risk of death to 0.24 (95% confidence interval: 0.14 – 0.43). Conclusion: Our results support the hypothesis that the increased survival of patients receiving aggressive palliative, or radical, RT is due not solely to patient selection, but also partly to a response to treatment. © 1998 Elsevier Science Inc. Non-small cell lung cancer, Radiotherapy, Survival.
There has been prolonged debate over the appropriate radiation schedules for the treatment of non-small cell lung cancer (NSCLC) (1–9). One aspect of the debate has focused on whether or not higher doses of radiotherapy produce survival benefits as well as local control. Ball et al. (10) show that, after adjusting for Eastern Cooperative Oncology Group (ECOG) performance status and the presence of any weight loss, the death rates for patients receiving aggressive palliative radiotherapy (30 or 36 Gy) and radical radiotherapy (60 Gy) are 79% and 53%, respectively, of what they would have been if these patients had received low-dose radiotherapy. They used a sample of 813 patients, a Cox proportional hazards model, and stepwise regression analysis to select the two statistically significant (p , 0.001) prognostic variables from the following list of patient characteristics and disease features: age at presentation, gender, tumor histology, smoking history, symptoms
of thoracic disease, malaise, paraneoplastic syndrome, superior vena caval obstructions, weight loss, ECOG performance status, side of tumor, site of tumor, and time from symptoms to diagnosis. Due to data limitations, Ball et al. did not include in their analysis tumor size and TNM staging (11), two prognostic variables that influence the choice of treatment aggressiveness (12). They acknowledge that their estimate of the survival response to treatment may be overstated, as a result of not fully adjusting for the fact that early stage NSCLC patients tend to select more aggressive treatment and also have a better survival prognosis, regardless of the treatment option selected. The purpose of this paper is to determine whether or not the survival effects they identified persist if TNM staging and tumor size are incorporated in an analysis that also includes weight loss, performance status, age at presentation, tumor histology, and the presence of malignant pleural effusion.
Reprint requests to: Joseph Schaafsma, Ph.D., Department of Economics, University of Victoria, P.O. Box 3050, Victoria, B.C. V8W 3P5 Canada. Acknowledgments—The authors acknowledge L. Blenkinsop, M. Boyle, J. Cawsey, S. Iwama, R. Kitching, E. Laukkanen, D. Linekin, P. McAllister, P. Nielson, G. Owen, M. Sauder, J. Schofield, A. Stewart, M. Thompson, M. Wehinger, K. Wilson,
and I. Yong, for their contribution to the design and compilation of the data base, and the many patients whose cooperation made this study possible. Any errors are our responsibility. Supported by the British Columbia Health Research Foundation and the Science Council of British Columbia Health Development Fund Grants HDF 70-89 and 14-90. Accepted for publication 3 July 1997.
INTRODUCTION
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METHODS AND MATERIALS Patients The data for our analysis were generated in the context of a prospective cost-effectiveness study of the treatment of NSCLC at the Vancouver Island Cancer Centre (ViCC) of the British Columbia Cancer Agency (BCCA), Canada. All Greater Victoria lung cancer patients presenting at the ViCC between February 1, 1990 and January 31, 1992 were invited to participate. Of the 241 lung cancer patients referred to ViCC during this period, who lived in the Victoria area, 162 (66%) agreed to enter the study. Our survival analysis excluded 33 of these 162 patients as follows: 23 small cell lung cancer patients, 1 NSCLC patient who received chemotherapy as a primary treatment, and 9 radical surgery patients. This left a useable sample of 129 patients. Participating patients gave informed consent and authorized access to all their medical records. Methods All patients were observed from the time of diagnosis. Diagnosis was usually made by a consulting thoracic surgeon or respirologist before the patient was referred to ViCC for assessment regarding additional treatment. With one exception, the patient’s survival time was measured from the assessment date, the date on which the prognostic variables were observed, to the date of death, or to the cutoff date, April 30, 1997, whichever occurred first. The exception was 1 patient who left Victoria and was lost to followup. The survival time for this patient was from the assessment date to the last contact date. The analysis of the effect of treatment on survival consisted of estimating a Cox proportional hazards model with covariates (13, 14) and using this model to predict survival curves with and without treatment. The difference between the medians for these predicted survival curves was the estimated effect of treatment on survival. The prognostic covariates in our survival model were the two found by Ball et al. to be statistically significant (i.e., performance status and weight loss), two variables found by Ball et al. not to be statistically significant (i.e., age at presentation and tumor histology), and three variables not included in their analysis (TNM staging, tumor size, and the presence of malignant pleural effusion). In our analysis, performance status was measured with the Karnofsky Performance Index (15). Age and weight loss were entered as continuous variables and tumor size was measured using the greatest diameter in centimeters, the method used in TNM staging. The format in which the seven prognostic variables enter the survival model and the mnemonics for them are given in Table 1. We combined some of the adjacent classes within the categorical variables to have a reasonable number of patients in each category. The treatment covariates in the model were binary variables for two primary treatment options: high-dose palliative radiotherapy and radical radiotherapy given with curative intent. The high-dose palliative radiotherapy group of
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patients received doses ranging from 30 Gy in 10 fractions in an overall time of 12 to 15 days to 52.5 Gy in 20 fractions in an overall time of 32 days, using parallel opposing fields from 8 3 8 cms to 22 3 20 cms. The ret values (16) range from 1281 to 1790. The dose was expressed as the central axis dose. No corrections were made for lung density. The patients in the radical group received 50 to 55 Gy in 20 fractions in an overall time of 26 to 36 days to a high-dose volume ranging in size from 7 3 7 3 10 cms to 10 3 11 3 16 cms. The ret values ranged from 1705 to 1875. The dose was expressed as the central axis dose and corrections were made for lung density. The treatment category was determined by the prescribed dose. All patients received the prescribed dose, although, in a few instances, overall treatment times were prolonged for medical reasons. The binary treatment variable equalled 1 if the patient was in the specified treatment category, and 0 otherwise. The two binary treatment variables and their mnemonics are shown in Table 1. The Cox proportional hazards model with all the prognostic variables in Table 1 and the two binary treatment variables as covariates was first fitted. Restrictions on coefficient estimates were then tested and the model was reestimated with the relevant restrictions in place to increase the power of the tests. The likelihood ratio (LR) and the t-ratio were used to test the statistical significance of sets of coefficients, and of individual coefficients, respectively (17). The models were estimated with LIMDEP™ (18). Censored patients (patients still alive on April 30, 1997 or lost to follow-up) were carried in the risk set until they exited as a result of censoring. When censored patients exited, they were not included in the computation of the hazard rate. In the second stage of the analysis, the survival benefit of a specific treatment was obtained by simulating the estimated Cox proportional hazards model twice, first with the binary variable for the specified treatment set equal to 1 and, then, with this binary variable set equal to 0. In these simulations, the values for the prognostic variables were specific to the treatment group (i.e., the average patient characteristics for that treatment group), and were the same in the simulations with and without treatment. These model simulations yielded two survival curves. The difference between the medians for these two survival curves was the estimated survival response to treatment. RESULTS Descriptive results The crude survival rates for the entire sample and by primary treatment option are shown in Table 2. The notreatment option category in our analysis included the patients who opted for low-dose palliative radiotherapy (less than 30 Gy in less than 10 fractions), as well as patients who opted to receive no primary treatment. The hypothesis that the survival experience of the low-dose palliative and of the no-treatment patients is the same, holding everything else
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Table 1. The format of the prognostic and treatment variables Variable
Format*
TNM staging T stage TX T1† T2 T3 T4‡ N stage NX N0 N1 N2 & N3‡ M stage MX M0 M1‡
5 5 5 5 5
1 1 1 1 1
if if if if if
T T T T T
5 5 5 5 5
TX T1 T2 T3 T4
5 5 5 5
1 1 1 1
if if if if
N N N N
5 5 5 5
NX N0 N1 N2 or N3
5 1 if M 5 MX 5 1 if M 5 M0 5 1 if M 5 M1
Karnofsky performance status (KPS) 5 5 5 5
1 1 1 1
SIZEZERO SIZELARGE OBSDSIZE
5 5 5 5
1 if the tumor is too small to be measured on the chest X ray 1 if the tumor is large and not measurable on the chest X ray 0 if SIZEZERO or SIZELARGE 5 1 observed tumor size in cm when SIZEZERO 5 SIZELARGE 5 0
Weight loss
5 weight loss in kilograms
Pleural
5 1 if malignant pleural effusion is present
Age
5 patient age in years at presentation
K910 K80 K70 K456‡
if if if if
the the the the
patient’s patient’s patient’s patient’s
KPS KPS KPS KPS
equals equals equals equals
90 or 100 80 70 40, 50 or 60§
Tumor size
Histology SQUAM ADENO‡ HISTOTH
5 1 for any squamous cell carcinoma 5 1 for any adenocarcinoma 5 1 if the histology is neither squamous cell nor adenocarcinoma
Treatment options NOTX‡ HPAL\ RADICAL¶
5 1 if the patient received no primary treatment or low-dose palliative treatment (less than 30 Gy in 1–6 fractions). 5 1 if the patient received high-dose palliative radiotherapy (30–50 Gy in 10–20 fractions, with palliative intent). 5 1 if the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent)
* Throughout the table, the variable equals 0 if the condition is not met. There were no patients with T stage of TO or TIS. ‡ This is the omitted category in the regression analysis. § There are no patients in our sample with a KPS less than 40. \ Includes 1 surgery patient who received adjuvant radiotherapy of this dosage for residual disease. ¶ Includes 4 surgery patients who received adjuvant radiotherapy of this dosage for residual disease. †
constant, was tested in the context of our Cox proportional hazards model and could not be rejected (p 5 0.7825). The 1-, 2-, and 3-year survival rates of 34.9%, 15.5%, and 10.9%, respectively, for the full sample conform to what is generally observed for NSCLC patients. The median survival for the full sample was 248 days. For the no-treatment, high-dose palliative, and radical radiotherapy options, median survival was 123, 266, and 651 days, respectively.
The p values for the log rank (LRK) and generalized Wilcoxon (GW) tests for the pairwise comparisons of the survival curves by treatment option are shown in Table 3. The consistently better survival experience of the radical radiotherapy (RADICAL) patients vs. the patients in the no-treatment (NOTX) and the high-dose palliative (HPAL) radiotherapy categories is statistically significant at p 5 0.001 using either test. The difference between the survival
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Table 4. Distribution of patients across the prognostic variables for the full sample and by treatment option*
Table 2. Crude survival rates for the full sample and by treatment option Radiotherapy
Variable†
Full sample
NOTX
HPAL
Survival duration (days)
Full sample
No treatment*
High-dose palliative†
Radical
TNM staging
0 91 183 274 365 730 1095 1460 1825 2190 Median survival (days) Cases: total died censored‡
1.0000 0.8061 0.5891 0.4651 0.3488 0.1550 0.1085 0.0835 0.0417 0.0334
1.0000 0.6304 0.3696 0.2391 0.1522 0.1087 0.0870 0.0290 0 0
1.0000 0.8889 0.6296 0.4815 0.3333 0.0556 0.0185 0.0185 0.0185 0.0185
1.0000 0.9310 0.8621 0.7931 0.6897 0.4138 0.3103 0.2759 0.2069 0.2069
248
123
266
651
129 125 4
46 45 1
54 54 0
29 26 3
T stage TX 0.1008 0.1522 0.0926 T1 0.1395 0.1087 0.0926 T2 0.4109 0.4130 0.3519 T3 0.2326 0.1957 0.3148 T4 0.1163 0.1304 0.1481 N stage NX 0.1550 0.1957 0.1481 N0 0.4884 0.5217 0.3889 N1 0.0620 0.0217 0.0926 N2 & N3‡ 0.2946 0.2609 0.3704 M stage MX 0.1008 0.1304 0.1111 M0 0.7597 0.6087 0.7778 M1 0.1395 0.2609 0.1111 Karnofsky PI K910§ 0.1783 0.1522 0.0926 K80 0.2481 0.1522 0.2593 K70 0.3721 0.3696 0.4815 K456\ 0.2016 0.3261 0.1667 Tumor size SIZEZERO 0.0233 0.0652 0.0000 SIZELARGE 0.0698 0.1087 0.0556 OBSDSIZE (cm)¶ 5.79 5.68 6.53 Weight loss (kg)¶ 3.36 4.30 2.98 Pleural 0.0310 0.0652 0.0185 Age¶ 70.12 70.26 70.15 Histology SQUAM 0.5659 0.3478 0.6667 ADENO 0.2093 0.2826 0.1852 HISTOTH 0.2248 0.3696 0.1481 Sample size 129 46 54
* No primary treatment and low-dose (less than 30 Gy in less than 10 fractions) palliative radiotherapy. † High-dose (30 –50 Gy in 10 –20 fractions) palliative radiotherapy. ‡ Patients still alive on the cutoff date (April 30, 1997) and 1 patient who exited the study before the cutoff date.
curves for the no-treatment and high-dose palliative categories is not as statistically significant (p 5 0.09176 and 0.00202, respectively, for the LRK and GW tests). The lower p value for the GW test is attributable to the fact that, in this test, early differences are particularly important (19) and, as shown in Table 2, it is in the first year that the survival experience of the high-dose palliative patients is consistently superior to the survival experience of the notreatment patients. The proportional distribution of the patients across the categorical prognostic variables used in the regression analysis is shown in Table 4 for the full sample and for the patients in each treatment category. The averages for the Table 3. The p values for the log rank and generalized Wilcoxon tests for the pairwise comparisons of the survival curves by treatment category p Values Pairwise comparisons of the treatment options
Log rank test
Gen. Wilcoxon test
RADICAL* vs. HPAL RADICAL vs. NOTX HPAL vs. NOTX
0.00002 0.00000 0.09176
0.00010 0.00000 0.00202
* RADICAL 5 Radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent); HPAL 5 High-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); NOTX 5 No primary treatment or low-dose palliative radiotherapy (less than 30 Gy in 1– 6 fractions).
RADICAL
0.0345 0.2759 0.5172 0.1379 0.0345 0.1034 0.6207 0.0690 0.2069 0.0345 0.9655 0.0000 0.3793 0.3793 0.1724 0.0690 0.0000 0.0345 4.57 2.55 0.0000 69.86 0.7241 0.1379 0.1379 29
* NOTX 5 the patient received either no treatment or low-dose palliative radiotherapy (less than 30 Gy in 1– 6 fractions); HPAL 5 the patient received high-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); RADICAL 5 the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent). † See Table 1 for the definitions of the variables. ‡ There were only 5 patients in the sample with N-stage N3. § There were only 4 patients in the sample with a KPS of 100. \ There were only 6 and 7 patients with a KPS of 40 and 50, respectively. ¶ The average for the group.
continuous variables (age, weight loss, and tumor size) are also shown in Table 4. The results in Table 4 conform to the expectation (12, 20) that patients with a superior prognosis tend to receive more aggressive treatment. Because patients with a superior prognosis can be expected to live longer without treatment than patients with a less-favorable prognosis, it is not surprising that median survival is shortest for the NOTX patients and longest for the RADICAL patients. Of interest is whether or not at least some of the observed differences in median survival can be attributed to the treatment selected. The data in Table 4 also indicate that, with only a few
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Table 5. The regression results for the Cox proportional hazards model Equation 1
Equation 2
Covariate
Coefficient
T-ratio
p Value*
Coefficient
T ratio
p Value*
HPAL RADICAL T1&T2 NX M0 ADENO K910 K78 SIZEZERO Wt loss Pleural Age Log likelihood Likelihood ratio
20.5970 21.4187 20.4337 20.3957 20.8923 0.6088 20.8270 20.3902 21.2772 0.0461 0.3868 20.0088
22.62 24.66 22.12 21.48 23.24 2.21 22.29 21.53 22.05 2.38 0.66 20.81 2456.6334 0.0779
0.0044 0.0000 0.0338 0.0701 0.0006 0.0136 0.0110 0.0632 0.0204 0.0088 0.2551 0.2077
20.6294 21.4277 20.4738 20.4162 20.8540 0.6523 20.7989 20.3767 21.3554 0.0472 – –
22.86 24.88 22.42 21.55 23.17 2.41 22.27 21.48 22.20 2.42 – – 2457.1640 0.0768
0.0021 0.0000 0.0079 0.0602 0.0008 0.0080 0.0116 0.0702 0.0140 0.0077 – –
* In a one-tail test. T1&T2 5 1 if T-stage equals T1 or T2; NX 5 1 if N-stage equals NX; M0 5 1 if M-stage equals M0; ADENO 5 1 for adenocarcinoma; K910 5 1 if the patient’s KPS equals 90 or 100; K78 5 1 if the patient’s KPS equals 70 or 80; SIZEZERO 5 1 if the tumor is too small to be measured on the chest X ray; Wt loss 5 weight loss in kg; HPAL 5 the patient received high-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); RADICAL 5 the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent).
exceptions, patients in any one of the prognostic categories are distributed across the full range of treatment options. The only exceptions are that no patient with a tumor too small to measure received high-dose palliative or radical radiotherapy, and no patient with M-stage M1 or with malignant pleural effusion, received radical radiotherapy. Thus, because the patient’s prognosis only partly determines the treatment option selected, multiple regression analysis can be used to analyze how a change in treatment affects survival, holding constant the values for the prognostic variables. Regression results The Cox proportional hazards model, fitted with the full set of prognostic and treatment variables shown in Table 1, was statistically significant (p , 0.000001). The coefficients of the two treatment variables HPAL and RADICAL were statistically significant individually (p 5 0.0388 and p 5 0.0001, respectively) and jointly (p 5 0.0004). Likelihood ratio tests of restrictions on the coefficients for subsets of regressors within prognostic categories did not reject the following hypotheses: the coefficients of K70 and K80 are the same (p 5 0.7696); the coefficients of T-stage categories T1 and T2 are the same, and categories T3 and TX can be combined with T4 (p 5 0.2725); N-stage categories N0 and N1 can be combined with N2 and N3 (p 5 0.4083); M-stage category MX can be combined with M1 (p 5 0.8541); there is no difference in the survival impact of tumor histology categories SQUAM and HISTOTH, and these two variables can be replaced with the variable ADENO (p 5 0.8805); the coefficients of SIZELARGE and OBSDSIZE are statistically insignificant individually (p 5 0.6736 and p 5 0.4994, respectively) and jointly (p 5 0.8307). The hypothesis that these restrictions apply simultaneously could not be rejected
(p 5 0.8535). The survival model was fitted with these restrictions in place and the results are shown as Eq. 1 in Table 5. Equation 1 in Table 5 fits the data almost as well as the full model; the log of the likelihood and the likelihood ratio index are 2456.63 and 0.0779, respectively, vs. 2453.87 and 0.0835, respectively, for the full model. The coefficients of the variables are jointly significant at p , 0.000001. Individually, the coefficients are all significant at p 5 0.07 or better in a one-tail test, except the coefficients of PLEURAL (p 5 0.2551) and AGE (p 5 0.2077). The regression results when these two variables are also dropped from the model are shown as Eq. 2 in Table 5. Dropping AGE and PLEURAL from the model had little impact on the results for the remaining variables. This was not surprising. Ball et al. also found that patient age at presentation was not a statistically significant prognostic variable. The coefficient for PLEURAL has the expected sign, but is not statistically significant, probably because there are only 4 patients with malignant pleural effusion in the sample. Equation 2 in Table 5 is our preferred set of regression results. This model was simulated twice to produce predicted survival curves with and without treatment for the patients receiving HPAL and RADICAL. The medians for the survival curves simulated with treatment applied are shown in Table 6. The actual median survival times are also shown. The simulated median survival times in the absence of treatment are shown as well in Table 6. The estimated effect of treatment on median survival is the difference between the two simulated medians. Median survival increased by an estimated 79 and 424 days as a result of high-dose palliative and radical radiotherapy treatment, respectively. With treatment, the death rates for the high-dose
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Table 6. The estimated effect of treatment on median survival, in days Median survival (days) With treatment Treatment category
Number of patients
Actual*
Simulated†
HPAL RADICAL
54 29
266 651
251 656
Simulated‡
Estimated gain in median survival (days) with rx - no rx
Death rate relative to no treatment
172 232
79 (31–106)§ 424 (302–488)§
0.53 (0.35–0.82)§ 0.24 (0.14–0.43)§
No treatment
* For the patients in the treatment group; HPAL 5 the patient received high-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); RADICAL 5 the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent). † Using the parameter estimates for the Cox proportional hazards model, the average values of the covariates for the patients in the treatment group, and the binary treatment variable set equal to 1. ‡ Produced as described in the preceding footnote, but with the binary treatment variable set equal to 0. § The 95% confidence interval is shown in parentheses.
palliative and radical radiotherapy patients were 53% and 24%, respectively, of what they would have been had these patients not received treatment (Table 6). DISCUSSION Ball et al. (10) showed that, after adjusting for survival differences attributable to ECOG performance status and the absence of any weight loss, high-dose palliative and radical radiotherapy increased the survival of NSCLC patients. We have extended their analysis by including TNM staging, tumor size, and malignant pleural effusion as additional potential prognostic variables in the Cox proportional hazards model. We also included, in the set of potential prognostic variables, age at presentation and tumor histology to determine whether the statistically insignificant results reported by Ball et al. for these two variables would also occur with our data set. Due to data availability, performance status in our analysis was measured using the Karnofsky, rather than the ECOG, scale. Weight loss entered our analysis as a continuous, rather than as a binary, variable. The two binary treatment variables in our model also differed somewhat from those reported by Ball et al. In their study, high-dose palliation consisted of 36 Gy in 10 or 12 fractions, as opposed to 30 –50 Gy in 10 to 20 fractions in our study, and radical radiotherapy in their study consisted of 60 Gy in 30 fractions, as opposed to 50 Gy or more in 20 or more fractions in our study. Despite the differences in variable definitions, the number of prognostic variables in the model, and patient sample, our estimates of the survival benefit attributable to treatment are qualitatively similar to those reported by Ball et al. Our regression results indicate that TNM staging, tumor size, and tumor histology are statistically significant prognostic variables (p 5 0.0010, 0.0140, and 0.0080, respectively) and that, after their addition to the model, weight loss continues to be a statistically significant predictor of survival (p 5 0.0077) and Karnofsky Performance Status marginally so (p 5 0.0735). With these variables in the model,
the inclusion of the pleural effusion binary variable and patient age at presentation did not add statistically significant explanatory power. After adjusting for survival differences attributable to differences in staging, weight loss, tumor size, tumor histology, and treatment, the death rates of high-performance (KPS 5 90 or 100) and good-performance (KPS 5 70 or 80) patients were 45.0% and 68.6%, respectively, of the death rate of poor-performance patients (KPS 5 40, 50 or 60). Similarly, holding everything else constant, weight losses of 5 or 10 kg increased the death rate by 26.6% and 60.3%, respectively, relative to patients who experienced no weight loss. Patients with adenocarcinoma experienced a 92.0% higher death rate than otherwise similar patients with squamous cell, or other nonadenocarcinomas. Our results show that TNM staging was not only a statistically significant prognostic variable, but was quantitatively also very important. After adjusting for survival differences attributable to differences in performance status, weight loss, tumor size, tumor histology, and treatment, the relative death rate of patients with T1 or T2 tumors was 62.3% of that for patients with tumors greater than T2, the relative death rate of patients with N-stage equal to NX was 66.0% of that of patients for whom N-stage does not equal NX, and the relative death rate of patients with M equal to M0 was 42.6% of that of patients for whom M does not equal M0. Thus, compared to patients with TNM staging any T, any N, and M1 (Stage IV), the relative death rates of patients with T1 or T2, N0 or N1, and M0 (Stages I and II), and of patients with T3 or T4, N0, N1, N2, or N3, and M0 (Stages IIIA and IIIB), were 26.5% and 42.6%, respectively. With respect to tumor size, our results show that when staging, performance status, tumor histology, and weight loss appear in the model, neither the size of a measurable tumor nor the binary variable for a large nonmeasurable tumor are statistically significant prognostic variables. However, our results do suggest that, if the patient’s tumor is too small to be measured on a chest X ray, the patient’s
Survival response to radiotherapy for NSCLC
death rate will be 25.6% of the death rate of an otherwise identical patient with a measurable or large nonmeasurable tumor. The regression results for the two binary treatment covariates indicate that high-dose palliative and radical radiotherapy produce a statistically significant improvement in survival (p 5 0.0021 and 0.0000, respectively, in upper tail tests), relative to opting for no treatment or low-dose palliative treatment. These improvements were observed after adjusting for survival differences across the treatment groups for differences in weight loss, performance status, staging, tumor histology, and tumor size. The estimated gain in median survival was 79 days (95% confidence interval: 31–106 days) for the high-dose palliative radiotherapy patients, and 424 days (95% confidence interval: 302– 488 days) for the radical radiotherapy patients (Table 6), where the confidence interval was computed using the endpoints of the 95% confidence interval for the estimated treatment coefficients. Ball et al. do not report the gains in median survival attributable to treatment. The relative risk of death over time for a treatment option, after adjusting for the survival effects of the prognostic variables, is the base of the natural log raised to the power b, where b is the estimated coefficient of the binary treatment variable (13). Thus, our results indicate that, relative to the no-treatment/low-dose palliative radiotherapy base group, and holding everything else constant, the relative death rates are 53% (95% confidence interval: 35%– 82%) and 24% (95% confidence interval: 14%– 43%) for the high-dose palliative and radical radiotherapy options, respectively (Table 6). These relative death rates are somewhat lower than those reported by Ball et al.: 71% (95% confidence interval: 57%– 88%) and 53% (95% confidence interval: 44%– 65%), for their high-dose palliative and radical radiotherapy treatment categories, respectively (10, Table 5). In this paper, we extended the Ball et al. analysis of the impact of radiotherapy treatment on the survival of NSCLC patients by adding TNM staging, tumor size, and
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malignant pleural effusion to the set of potential prognostic variables in the Cox proportional hazards regression model. The expanded model was then estimated with a patient sample drawn from an entirely different population: NSCLC patients living in Victoria, B.C., Canada, rather than in Melbourne, Australia. Despite these differences, our results confirm the Ball et al. finding that high-dose palliative and radical radiotherapy improve the survival prospects of NSCLC patients. Quantitatively, our results suggest a somewhat lower risk of death relative to the low-dose/no-treatment option than found by Ball et al., 53% compared to 71% for high-dose palliative radiotherapy, and 24% compared to 53% for radical radiotherapy. Finally, our model assumes that, if radiotherapy reduces the risk of death, it does so by a constant proportion regardless of the patient’s prognosis as determined by the prognostic factors in the survival model. Ideally, the analysis should test whether or not the proportionate reduction in the death rate as a result of treatment varies with the prognostic factors. However, this requires modeling interactions between the variables and, thus, a much larger data set than ours is needed if one is to have a meaningful number of patients in the cross tabulations. In conclusion, our prospective analysis illustrates how the Cox proportional hazards model with covariates can be used to estimate treatment effects on survival when a randomized clinical trial cannot be conducted for ethical reasons. Prognostic covariates are included in these models to capture systematic survival differences not attributable to treatment. Inevitably, the analysis omits more subtle comorbidity, performance, and other similar issues that affect both treatment selection and survival. The extent to which such omissions may have affected the survival response to treatment estimated in this paper after adjusting for survival differences attributable to TNM staging, Karnofsky Performance Status, tumor size, tumor histology, and weight loss will require further research with a much larger data set than was available for this paper.
REFERENCES 1. Durrant, K. R.; Ellis, F.; Black, J. M.; Berry, R. J.; Ridehalgh, F. R.; Hamilton, W. S. Comparison of treatment policies in operable bronchial carcinoma. Lancet 1:715–719; 1971. 2. Mackillop, W. J.; Ward, G. K.; O’Sullivan, B. The use of expert surrogates to evaluate clinical trials in non-small cell lung cancer. Br. J. Cancer. 54:661– 667; 1986. 3. Medical Research Council Lung Cancer Working Party. Inoperable non-small cell lung cancer (NSCLC): a medical research council non randomized trial of palliative radiotherapy with two fractions and ten fractions. Br. J. Cancer 63: 265–270; 1991. 4. Payne, D. G. Non-small cell lung cancer: -should unresectable stage IIIA patients routinely receive high dose radiotherapy? J. Clin. Oncol. 6:552–558; 1988. 5. Perez, C. A.; Stanley, K.; Grundy, G.; Hanson, W.; Rubin, P.; Kramer, S.; Brady, L. W.; Marks, J. E.; Perez-Tamayo, R.;
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Brown, S.; Concannon, J.; Rotman, M. Impact of irradiation technique and tumour extent in tumour control and survival of patients with unresectable non-oat cell carcinoma of the lung. Cancer 50:1091–1099; 1982. Priestman, T. J.; Bullimore, J. A.; Godden, T. P.; Deutsch, G. P. The royal college of radiologists fractionation survey. Clin. Oncol. 1:39 – 42; 1989. Seagren, S. L. Radical radiation therapy for lung cancer. Haematol. Oncol. Clin. North Am. 4:1093–1109; 1990. Simpson, J. R.; Francis, M. E.; Perez-Tamayo, R.; Marks, R. D.; Rao, D. V. Palliative radiotherapy for inoperable carcinoma of the lung: final report of an RTOG institutional trial. Intl. J. Radiat. Oncol. Biol. Phys. 11:751–719; 1985. Tannock, I. F. When is cancer treatment worthwhile? N. Engl. J. Med. 323:989 –990; 1990. Ball, D.; Matthews, J.; Worotniuk, V.; Crennan, E. Longer
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16. 17. 18. 19.
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J. H. The use of nitrogen mustards in the palliative treatment of carcinoma. Cancer 1:634 – 656; 1948. Orton, C.; Ellis, F. A simplification of the N.S.D. concept in practical radiotherapy. Br. J. Cancer 40:529 –537; 1973. Greene, W. H. Econometric analysis. 2nd ed. New York: Macmillan; 1993. Greene, W. H. LIMDEP version 6.0. Econometric Software, Inc.; 1992. Lagakos, S. W. Inference in survival analysis: Nonparametric tests to compare survival distributions. In Mike´, V.; Stanley, K. E., eds. Statistics in medical research: methods and issues, with applications in cancer research. New York: John Wiley & Sons; 1982:340 –364. Mayer, R. J.; Patterson, W. B. How is cancer treatment chosen? N. Engl. J. Med. 318:636 – 638; 1988.
PII S0360-3016(98)00055-8
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Clinical Investigation THE EFFECT OF RADIOTHERAPY ON THE SURVIVAL OF NON-SMALL CELL LUNG CANCER PATIENTS JOSEPH SCHAAFSMA, PH.D.*
AND
PETER COY, M.B., B.CH., F.R.C.P.(C)†
*Department of Economics, University of Victoria, Victoria, British Columbia, V8W 3P5 Canada and †Vancouver Island Cancer Centre, British Columbia Cancer Agency, 1900 Fort Street, Victoria, British Columbia, V8R 1J8 Canada Purpose: To determine if thoracic radiotherapy improves the survival of non-small cell lung cancer (NSCLC) patients. Methods and Materials: A Cox proportional hazards model with prognostic and treatment covariates was estimated using prospective data for 129 NSCLC patients presenting at the Victoria Clinic (ViCC) of the British Columbia Cancer Agency (BCCA) 1990 –1991. The estimated model was simulated to predict survival curves for groups of patients with and without treatment. The difference between the predicted median survival with treatment and without treatment is the gain in survival attributable to treatment. Results: After adjusting for the effect of TNM staging, Karnofsky performance status, weight loss, tumor size, and tumor histology on survival, high-dose palliative radiotherapy (RT) (30 –50 Gy in 10 –20 fractions) increased median survival by 79 days (95% confidence interval: 31–106 days), and lowered the relative risk of death rate to 0.53 (95% confidence interval: 0.35– 0.85). Radical RT (50 or more Gy, in 20 or more fractions) increased median survival by 424 days (95% confidence interval: 302– 488 days), and lowered the relative risk of death to 0.24 (95% confidence interval: 0.14 – 0.43). Conclusion: Our results support the hypothesis that the increased survival of patients receiving aggressive palliative, or radical, RT is due not solely to patient selection, but also partly to a response to treatment. © 1998 Elsevier Science Inc. Non-small cell lung cancer, Radiotherapy, Survival.
There has been prolonged debate over the appropriate radiation schedules for the treatment of non-small cell lung cancer (NSCLC) (1–9). One aspect of the debate has focused on whether or not higher doses of radiotherapy produce survival benefits as well as local control. Ball et al. (10) show that, after adjusting for Eastern Cooperative Oncology Group (ECOG) performance status and the presence of any weight loss, the death rates for patients receiving aggressive palliative radiotherapy (30 or 36 Gy) and radical radiotherapy (60 Gy) are 79% and 53%, respectively, of what they would have been if these patients had received low-dose radiotherapy. They used a sample of 813 patients, a Cox proportional hazards model, and stepwise regression analysis to select the two statistically significant (p , 0.001) prognostic variables from the following list of patient characteristics and disease features: age at presentation, gender, tumor histology, smoking history, symptoms
of thoracic disease, malaise, paraneoplastic syndrome, superior vena caval obstructions, weight loss, ECOG performance status, side of tumor, site of tumor, and time from symptoms to diagnosis. Due to data limitations, Ball et al. did not include in their analysis tumor size and TNM staging (11), two prognostic variables that influence the choice of treatment aggressiveness (12). They acknowledge that their estimate of the survival response to treatment may be overstated, as a result of not fully adjusting for the fact that early stage NSCLC patients tend to select more aggressive treatment and also have a better survival prognosis, regardless of the treatment option selected. The purpose of this paper is to determine whether or not the survival effects they identified persist if TNM staging and tumor size are incorporated in an analysis that also includes weight loss, performance status, age at presentation, tumor histology, and the presence of malignant pleural effusion.
Reprint requests to: Joseph Schaafsma, Ph.D., Department of Economics, University of Victoria, P.O. Box 3050, Victoria, B.C. V8W 3P5 Canada. Acknowledgments—The authors acknowledge L. Blenkinsop, M. Boyle, J. Cawsey, S. Iwama, R. Kitching, E. Laukkanen, D. Linekin, P. McAllister, P. Nielson, G. Owen, M. Sauder, J. Schofield, A. Stewart, M. Thompson, M. Wehinger, K. Wilson,
and I. Yong, for their contribution to the design and compilation of the data base, and the many patients whose cooperation made this study possible. Any errors are our responsibility. Supported by the British Columbia Health Research Foundation and the Science Council of British Columbia Health Development Fund Grants HDF 70-89 and 14-90. Accepted for publication 3 July 1997.
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METHODS AND MATERIALS Patients The data for our analysis were generated in the context of a prospective cost-effectiveness study of the treatment of NSCLC at the Vancouver Island Cancer Centre (ViCC) of the British Columbia Cancer Agency (BCCA), Canada. All Greater Victoria lung cancer patients presenting at the ViCC between February 1, 1990 and January 31, 1992 were invited to participate. Of the 241 lung cancer patients referred to ViCC during this period, who lived in the Victoria area, 162 (66%) agreed to enter the study. Our survival analysis excluded 33 of these 162 patients as follows: 23 small cell lung cancer patients, 1 NSCLC patient who received chemotherapy as a primary treatment, and 9 radical surgery patients. This left a useable sample of 129 patients. Participating patients gave informed consent and authorized access to all their medical records. Methods All patients were observed from the time of diagnosis. Diagnosis was usually made by a consulting thoracic surgeon or respirologist before the patient was referred to ViCC for assessment regarding additional treatment. With one exception, the patient’s survival time was measured from the assessment date, the date on which the prognostic variables were observed, to the date of death, or to the cutoff date, April 30, 1997, whichever occurred first. The exception was 1 patient who left Victoria and was lost to followup. The survival time for this patient was from the assessment date to the last contact date. The analysis of the effect of treatment on survival consisted of estimating a Cox proportional hazards model with covariates (13, 14) and using this model to predict survival curves with and without treatment. The difference between the medians for these predicted survival curves was the estimated effect of treatment on survival. The prognostic covariates in our survival model were the two found by Ball et al. to be statistically significant (i.e., performance status and weight loss), two variables found by Ball et al. not to be statistically significant (i.e., age at presentation and tumor histology), and three variables not included in their analysis (TNM staging, tumor size, and the presence of malignant pleural effusion). In our analysis, performance status was measured with the Karnofsky Performance Index (15). Age and weight loss were entered as continuous variables and tumor size was measured using the greatest diameter in centimeters, the method used in TNM staging. The format in which the seven prognostic variables enter the survival model and the mnemonics for them are given in Table 1. We combined some of the adjacent classes within the categorical variables to have a reasonable number of patients in each category. The treatment covariates in the model were binary variables for two primary treatment options: high-dose palliative radiotherapy and radical radiotherapy given with curative intent. The high-dose palliative radiotherapy group of
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patients received doses ranging from 30 Gy in 10 fractions in an overall time of 12 to 15 days to 52.5 Gy in 20 fractions in an overall time of 32 days, using parallel opposing fields from 8 3 8 cms to 22 3 20 cms. The ret values (16) range from 1281 to 1790. The dose was expressed as the central axis dose. No corrections were made for lung density. The patients in the radical group received 50 to 55 Gy in 20 fractions in an overall time of 26 to 36 days to a high-dose volume ranging in size from 7 3 7 3 10 cms to 10 3 11 3 16 cms. The ret values ranged from 1705 to 1875. The dose was expressed as the central axis dose and corrections were made for lung density. The treatment category was determined by the prescribed dose. All patients received the prescribed dose, although, in a few instances, overall treatment times were prolonged for medical reasons. The binary treatment variable equalled 1 if the patient was in the specified treatment category, and 0 otherwise. The two binary treatment variables and their mnemonics are shown in Table 1. The Cox proportional hazards model with all the prognostic variables in Table 1 and the two binary treatment variables as covariates was first fitted. Restrictions on coefficient estimates were then tested and the model was reestimated with the relevant restrictions in place to increase the power of the tests. The likelihood ratio (LR) and the t-ratio were used to test the statistical significance of sets of coefficients, and of individual coefficients, respectively (17). The models were estimated with LIMDEP™ (18). Censored patients (patients still alive on April 30, 1997 or lost to follow-up) were carried in the risk set until they exited as a result of censoring. When censored patients exited, they were not included in the computation of the hazard rate. In the second stage of the analysis, the survival benefit of a specific treatment was obtained by simulating the estimated Cox proportional hazards model twice, first with the binary variable for the specified treatment set equal to 1 and, then, with this binary variable set equal to 0. In these simulations, the values for the prognostic variables were specific to the treatment group (i.e., the average patient characteristics for that treatment group), and were the same in the simulations with and without treatment. These model simulations yielded two survival curves. The difference between the medians for these two survival curves was the estimated survival response to treatment. RESULTS Descriptive results The crude survival rates for the entire sample and by primary treatment option are shown in Table 2. The notreatment option category in our analysis included the patients who opted for low-dose palliative radiotherapy (less than 30 Gy in less than 10 fractions), as well as patients who opted to receive no primary treatment. The hypothesis that the survival experience of the low-dose palliative and of the no-treatment patients is the same, holding everything else
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Table 1. The format of the prognostic and treatment variables Variable
Format*
TNM staging T stage TX T1† T2 T3 T4‡ N stage NX N0 N1 N2 & N3‡ M stage MX M0 M1‡
5 5 5 5 5
1 1 1 1 1
if if if if if
T T T T T
5 5 5 5 5
TX T1 T2 T3 T4
5 5 5 5
1 1 1 1
if if if if
N N N N
5 5 5 5
NX N0 N1 N2 or N3
5 1 if M 5 MX 5 1 if M 5 M0 5 1 if M 5 M1
Karnofsky performance status (KPS) 5 5 5 5
1 1 1 1
SIZEZERO SIZELARGE OBSDSIZE
5 5 5 5
1 if the tumor is too small to be measured on the chest X ray 1 if the tumor is large and not measurable on the chest X ray 0 if SIZEZERO or SIZELARGE 5 1 observed tumor size in cm when SIZEZERO 5 SIZELARGE 5 0
Weight loss
5 weight loss in kilograms
Pleural
5 1 if malignant pleural effusion is present
Age
5 patient age in years at presentation
K910 K80 K70 K456‡
if if if if
the the the the
patient’s patient’s patient’s patient’s
KPS KPS KPS KPS
equals equals equals equals
90 or 100 80 70 40, 50 or 60§
Tumor size
Histology SQUAM ADENO‡ HISTOTH
5 1 for any squamous cell carcinoma 5 1 for any adenocarcinoma 5 1 if the histology is neither squamous cell nor adenocarcinoma
Treatment options NOTX‡ HPAL\ RADICAL¶
5 1 if the patient received no primary treatment or low-dose palliative treatment (less than 30 Gy in 1–6 fractions). 5 1 if the patient received high-dose palliative radiotherapy (30–50 Gy in 10–20 fractions, with palliative intent). 5 1 if the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent)
* Throughout the table, the variable equals 0 if the condition is not met. There were no patients with T stage of TO or TIS. ‡ This is the omitted category in the regression analysis. § There are no patients in our sample with a KPS less than 40. \ Includes 1 surgery patient who received adjuvant radiotherapy of this dosage for residual disease. ¶ Includes 4 surgery patients who received adjuvant radiotherapy of this dosage for residual disease. †
constant, was tested in the context of our Cox proportional hazards model and could not be rejected (p 5 0.7825). The 1-, 2-, and 3-year survival rates of 34.9%, 15.5%, and 10.9%, respectively, for the full sample conform to what is generally observed for NSCLC patients. The median survival for the full sample was 248 days. For the no-treatment, high-dose palliative, and radical radiotherapy options, median survival was 123, 266, and 651 days, respectively.
The p values for the log rank (LRK) and generalized Wilcoxon (GW) tests for the pairwise comparisons of the survival curves by treatment option are shown in Table 3. The consistently better survival experience of the radical radiotherapy (RADICAL) patients vs. the patients in the no-treatment (NOTX) and the high-dose palliative (HPAL) radiotherapy categories is statistically significant at p 5 0.001 using either test. The difference between the survival
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Table 4. Distribution of patients across the prognostic variables for the full sample and by treatment option*
Table 2. Crude survival rates for the full sample and by treatment option Radiotherapy
Variable†
Full sample
NOTX
HPAL
Survival duration (days)
Full sample
No treatment*
High-dose palliative†
Radical
TNM staging
0 91 183 274 365 730 1095 1460 1825 2190 Median survival (days) Cases: total died censored‡
1.0000 0.8061 0.5891 0.4651 0.3488 0.1550 0.1085 0.0835 0.0417 0.0334
1.0000 0.6304 0.3696 0.2391 0.1522 0.1087 0.0870 0.0290 0 0
1.0000 0.8889 0.6296 0.4815 0.3333 0.0556 0.0185 0.0185 0.0185 0.0185
1.0000 0.9310 0.8621 0.7931 0.6897 0.4138 0.3103 0.2759 0.2069 0.2069
248
123
266
651
129 125 4
46 45 1
54 54 0
29 26 3
T stage TX 0.1008 0.1522 0.0926 T1 0.1395 0.1087 0.0926 T2 0.4109 0.4130 0.3519 T3 0.2326 0.1957 0.3148 T4 0.1163 0.1304 0.1481 N stage NX 0.1550 0.1957 0.1481 N0 0.4884 0.5217 0.3889 N1 0.0620 0.0217 0.0926 N2 & N3‡ 0.2946 0.2609 0.3704 M stage MX 0.1008 0.1304 0.1111 M0 0.7597 0.6087 0.7778 M1 0.1395 0.2609 0.1111 Karnofsky PI K910§ 0.1783 0.1522 0.0926 K80 0.2481 0.1522 0.2593 K70 0.3721 0.3696 0.4815 K456\ 0.2016 0.3261 0.1667 Tumor size SIZEZERO 0.0233 0.0652 0.0000 SIZELARGE 0.0698 0.1087 0.0556 OBSDSIZE (cm)¶ 5.79 5.68 6.53 Weight loss (kg)¶ 3.36 4.30 2.98 Pleural 0.0310 0.0652 0.0185 Age¶ 70.12 70.26 70.15 Histology SQUAM 0.5659 0.3478 0.6667 ADENO 0.2093 0.2826 0.1852 HISTOTH 0.2248 0.3696 0.1481 Sample size 129 46 54
* No primary treatment and low-dose (less than 30 Gy in less than 10 fractions) palliative radiotherapy. † High-dose (30 –50 Gy in 10 –20 fractions) palliative radiotherapy. ‡ Patients still alive on the cutoff date (April 30, 1997) and 1 patient who exited the study before the cutoff date.
curves for the no-treatment and high-dose palliative categories is not as statistically significant (p 5 0.09176 and 0.00202, respectively, for the LRK and GW tests). The lower p value for the GW test is attributable to the fact that, in this test, early differences are particularly important (19) and, as shown in Table 2, it is in the first year that the survival experience of the high-dose palliative patients is consistently superior to the survival experience of the notreatment patients. The proportional distribution of the patients across the categorical prognostic variables used in the regression analysis is shown in Table 4 for the full sample and for the patients in each treatment category. The averages for the Table 3. The p values for the log rank and generalized Wilcoxon tests for the pairwise comparisons of the survival curves by treatment category p Values Pairwise comparisons of the treatment options
Log rank test
Gen. Wilcoxon test
RADICAL* vs. HPAL RADICAL vs. NOTX HPAL vs. NOTX
0.00002 0.00000 0.09176
0.00010 0.00000 0.00202
* RADICAL 5 Radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent); HPAL 5 High-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); NOTX 5 No primary treatment or low-dose palliative radiotherapy (less than 30 Gy in 1– 6 fractions).
RADICAL
0.0345 0.2759 0.5172 0.1379 0.0345 0.1034 0.6207 0.0690 0.2069 0.0345 0.9655 0.0000 0.3793 0.3793 0.1724 0.0690 0.0000 0.0345 4.57 2.55 0.0000 69.86 0.7241 0.1379 0.1379 29
* NOTX 5 the patient received either no treatment or low-dose palliative radiotherapy (less than 30 Gy in 1– 6 fractions); HPAL 5 the patient received high-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); RADICAL 5 the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent). † See Table 1 for the definitions of the variables. ‡ There were only 5 patients in the sample with N-stage N3. § There were only 4 patients in the sample with a KPS of 100. \ There were only 6 and 7 patients with a KPS of 40 and 50, respectively. ¶ The average for the group.
continuous variables (age, weight loss, and tumor size) are also shown in Table 4. The results in Table 4 conform to the expectation (12, 20) that patients with a superior prognosis tend to receive more aggressive treatment. Because patients with a superior prognosis can be expected to live longer without treatment than patients with a less-favorable prognosis, it is not surprising that median survival is shortest for the NOTX patients and longest for the RADICAL patients. Of interest is whether or not at least some of the observed differences in median survival can be attributed to the treatment selected. The data in Table 4 also indicate that, with only a few
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Table 5. The regression results for the Cox proportional hazards model Equation 1
Equation 2
Covariate
Coefficient
T-ratio
p Value*
Coefficient
T ratio
p Value*
HPAL RADICAL T1&T2 NX M0 ADENO K910 K78 SIZEZERO Wt loss Pleural Age Log likelihood Likelihood ratio
20.5970 21.4187 20.4337 20.3957 20.8923 0.6088 20.8270 20.3902 21.2772 0.0461 0.3868 20.0088
22.62 24.66 22.12 21.48 23.24 2.21 22.29 21.53 22.05 2.38 0.66 20.81 2456.6334 0.0779
0.0044 0.0000 0.0338 0.0701 0.0006 0.0136 0.0110 0.0632 0.0204 0.0088 0.2551 0.2077
20.6294 21.4277 20.4738 20.4162 20.8540 0.6523 20.7989 20.3767 21.3554 0.0472 – –
22.86 24.88 22.42 21.55 23.17 2.41 22.27 21.48 22.20 2.42 – – 2457.1640 0.0768
0.0021 0.0000 0.0079 0.0602 0.0008 0.0080 0.0116 0.0702 0.0140 0.0077 – –
* In a one-tail test. T1&T2 5 1 if T-stage equals T1 or T2; NX 5 1 if N-stage equals NX; M0 5 1 if M-stage equals M0; ADENO 5 1 for adenocarcinoma; K910 5 1 if the patient’s KPS equals 90 or 100; K78 5 1 if the patient’s KPS equals 70 or 80; SIZEZERO 5 1 if the tumor is too small to be measured on the chest X ray; Wt loss 5 weight loss in kg; HPAL 5 the patient received high-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); RADICAL 5 the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent).
exceptions, patients in any one of the prognostic categories are distributed across the full range of treatment options. The only exceptions are that no patient with a tumor too small to measure received high-dose palliative or radical radiotherapy, and no patient with M-stage M1 or with malignant pleural effusion, received radical radiotherapy. Thus, because the patient’s prognosis only partly determines the treatment option selected, multiple regression analysis can be used to analyze how a change in treatment affects survival, holding constant the values for the prognostic variables. Regression results The Cox proportional hazards model, fitted with the full set of prognostic and treatment variables shown in Table 1, was statistically significant (p , 0.000001). The coefficients of the two treatment variables HPAL and RADICAL were statistically significant individually (p 5 0.0388 and p 5 0.0001, respectively) and jointly (p 5 0.0004). Likelihood ratio tests of restrictions on the coefficients for subsets of regressors within prognostic categories did not reject the following hypotheses: the coefficients of K70 and K80 are the same (p 5 0.7696); the coefficients of T-stage categories T1 and T2 are the same, and categories T3 and TX can be combined with T4 (p 5 0.2725); N-stage categories N0 and N1 can be combined with N2 and N3 (p 5 0.4083); M-stage category MX can be combined with M1 (p 5 0.8541); there is no difference in the survival impact of tumor histology categories SQUAM and HISTOTH, and these two variables can be replaced with the variable ADENO (p 5 0.8805); the coefficients of SIZELARGE and OBSDSIZE are statistically insignificant individually (p 5 0.6736 and p 5 0.4994, respectively) and jointly (p 5 0.8307). The hypothesis that these restrictions apply simultaneously could not be rejected
(p 5 0.8535). The survival model was fitted with these restrictions in place and the results are shown as Eq. 1 in Table 5. Equation 1 in Table 5 fits the data almost as well as the full model; the log of the likelihood and the likelihood ratio index are 2456.63 and 0.0779, respectively, vs. 2453.87 and 0.0835, respectively, for the full model. The coefficients of the variables are jointly significant at p , 0.000001. Individually, the coefficients are all significant at p 5 0.07 or better in a one-tail test, except the coefficients of PLEURAL (p 5 0.2551) and AGE (p 5 0.2077). The regression results when these two variables are also dropped from the model are shown as Eq. 2 in Table 5. Dropping AGE and PLEURAL from the model had little impact on the results for the remaining variables. This was not surprising. Ball et al. also found that patient age at presentation was not a statistically significant prognostic variable. The coefficient for PLEURAL has the expected sign, but is not statistically significant, probably because there are only 4 patients with malignant pleural effusion in the sample. Equation 2 in Table 5 is our preferred set of regression results. This model was simulated twice to produce predicted survival curves with and without treatment for the patients receiving HPAL and RADICAL. The medians for the survival curves simulated with treatment applied are shown in Table 6. The actual median survival times are also shown. The simulated median survival times in the absence of treatment are shown as well in Table 6. The estimated effect of treatment on median survival is the difference between the two simulated medians. Median survival increased by an estimated 79 and 424 days as a result of high-dose palliative and radical radiotherapy treatment, respectively. With treatment, the death rates for the high-dose
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Table 6. The estimated effect of treatment on median survival, in days Median survival (days) With treatment Treatment category
Number of patients
Actual*
Simulated†
HPAL RADICAL
54 29
266 651
251 656
Simulated‡
Estimated gain in median survival (days) with rx - no rx
Death rate relative to no treatment
172 232
79 (31–106)§ 424 (302–488)§
0.53 (0.35–0.82)§ 0.24 (0.14–0.43)§
No treatment
* For the patients in the treatment group; HPAL 5 the patient received high-dose palliative radiotherapy (30 –50 Gy in 10 –20 fractions, with palliative intent); RADICAL 5 the patient received radical radiotherapy (50 Gy or more in 20 or more fractions, with curative intent). † Using the parameter estimates for the Cox proportional hazards model, the average values of the covariates for the patients in the treatment group, and the binary treatment variable set equal to 1. ‡ Produced as described in the preceding footnote, but with the binary treatment variable set equal to 0. § The 95% confidence interval is shown in parentheses.
palliative and radical radiotherapy patients were 53% and 24%, respectively, of what they would have been had these patients not received treatment (Table 6). DISCUSSION Ball et al. (10) showed that, after adjusting for survival differences attributable to ECOG performance status and the absence of any weight loss, high-dose palliative and radical radiotherapy increased the survival of NSCLC patients. We have extended their analysis by including TNM staging, tumor size, and malignant pleural effusion as additional potential prognostic variables in the Cox proportional hazards model. We also included, in the set of potential prognostic variables, age at presentation and tumor histology to determine whether the statistically insignificant results reported by Ball et al. for these two variables would also occur with our data set. Due to data availability, performance status in our analysis was measured using the Karnofsky, rather than the ECOG, scale. Weight loss entered our analysis as a continuous, rather than as a binary, variable. The two binary treatment variables in our model also differed somewhat from those reported by Ball et al. In their study, high-dose palliation consisted of 36 Gy in 10 or 12 fractions, as opposed to 30 –50 Gy in 10 to 20 fractions in our study, and radical radiotherapy in their study consisted of 60 Gy in 30 fractions, as opposed to 50 Gy or more in 20 or more fractions in our study. Despite the differences in variable definitions, the number of prognostic variables in the model, and patient sample, our estimates of the survival benefit attributable to treatment are qualitatively similar to those reported by Ball et al. Our regression results indicate that TNM staging, tumor size, and tumor histology are statistically significant prognostic variables (p 5 0.0010, 0.0140, and 0.0080, respectively) and that, after their addition to the model, weight loss continues to be a statistically significant predictor of survival (p 5 0.0077) and Karnofsky Performance Status marginally so (p 5 0.0735). With these variables in the model,
the inclusion of the pleural effusion binary variable and patient age at presentation did not add statistically significant explanatory power. After adjusting for survival differences attributable to differences in staging, weight loss, tumor size, tumor histology, and treatment, the death rates of high-performance (KPS 5 90 or 100) and good-performance (KPS 5 70 or 80) patients were 45.0% and 68.6%, respectively, of the death rate of poor-performance patients (KPS 5 40, 50 or 60). Similarly, holding everything else constant, weight losses of 5 or 10 kg increased the death rate by 26.6% and 60.3%, respectively, relative to patients who experienced no weight loss. Patients with adenocarcinoma experienced a 92.0% higher death rate than otherwise similar patients with squamous cell, or other nonadenocarcinomas. Our results show that TNM staging was not only a statistically significant prognostic variable, but was quantitatively also very important. After adjusting for survival differences attributable to differences in performance status, weight loss, tumor size, tumor histology, and treatment, the relative death rate of patients with T1 or T2 tumors was 62.3% of that for patients with tumors greater than T2, the relative death rate of patients with N-stage equal to NX was 66.0% of that of patients for whom N-stage does not equal NX, and the relative death rate of patients with M equal to M0 was 42.6% of that of patients for whom M does not equal M0. Thus, compared to patients with TNM staging any T, any N, and M1 (Stage IV), the relative death rates of patients with T1 or T2, N0 or N1, and M0 (Stages I and II), and of patients with T3 or T4, N0, N1, N2, or N3, and M0 (Stages IIIA and IIIB), were 26.5% and 42.6%, respectively. With respect to tumor size, our results show that when staging, performance status, tumor histology, and weight loss appear in the model, neither the size of a measurable tumor nor the binary variable for a large nonmeasurable tumor are statistically significant prognostic variables. However, our results do suggest that, if the patient’s tumor is too small to be measured on a chest X ray, the patient’s
Survival response to radiotherapy for NSCLC
death rate will be 25.6% of the death rate of an otherwise identical patient with a measurable or large nonmeasurable tumor. The regression results for the two binary treatment covariates indicate that high-dose palliative and radical radiotherapy produce a statistically significant improvement in survival (p 5 0.0021 and 0.0000, respectively, in upper tail tests), relative to opting for no treatment or low-dose palliative treatment. These improvements were observed after adjusting for survival differences across the treatment groups for differences in weight loss, performance status, staging, tumor histology, and tumor size. The estimated gain in median survival was 79 days (95% confidence interval: 31–106 days) for the high-dose palliative radiotherapy patients, and 424 days (95% confidence interval: 302– 488 days) for the radical radiotherapy patients (Table 6), where the confidence interval was computed using the endpoints of the 95% confidence interval for the estimated treatment coefficients. Ball et al. do not report the gains in median survival attributable to treatment. The relative risk of death over time for a treatment option, after adjusting for the survival effects of the prognostic variables, is the base of the natural log raised to the power b, where b is the estimated coefficient of the binary treatment variable (13). Thus, our results indicate that, relative to the no-treatment/low-dose palliative radiotherapy base group, and holding everything else constant, the relative death rates are 53% (95% confidence interval: 35%– 82%) and 24% (95% confidence interval: 14%– 43%) for the high-dose palliative and radical radiotherapy options, respectively (Table 6). These relative death rates are somewhat lower than those reported by Ball et al.: 71% (95% confidence interval: 57%– 88%) and 53% (95% confidence interval: 44%– 65%), for their high-dose palliative and radical radiotherapy treatment categories, respectively (10, Table 5). In this paper, we extended the Ball et al. analysis of the impact of radiotherapy treatment on the survival of NSCLC patients by adding TNM staging, tumor size, and
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malignant pleural effusion to the set of potential prognostic variables in the Cox proportional hazards regression model. The expanded model was then estimated with a patient sample drawn from an entirely different population: NSCLC patients living in Victoria, B.C., Canada, rather than in Melbourne, Australia. Despite these differences, our results confirm the Ball et al. finding that high-dose palliative and radical radiotherapy improve the survival prospects of NSCLC patients. Quantitatively, our results suggest a somewhat lower risk of death relative to the low-dose/no-treatment option than found by Ball et al., 53% compared to 71% for high-dose palliative radiotherapy, and 24% compared to 53% for radical radiotherapy. Finally, our model assumes that, if radiotherapy reduces the risk of death, it does so by a constant proportion regardless of the patient’s prognosis as determined by the prognostic factors in the survival model. Ideally, the analysis should test whether or not the proportionate reduction in the death rate as a result of treatment varies with the prognostic factors. However, this requires modeling interactions between the variables and, thus, a much larger data set than ours is needed if one is to have a meaningful number of patients in the cross tabulations. In conclusion, our prospective analysis illustrates how the Cox proportional hazards model with covariates can be used to estimate treatment effects on survival when a randomized clinical trial cannot be conducted for ethical reasons. Prognostic covariates are included in these models to capture systematic survival differences not attributable to treatment. Inevitably, the analysis omits more subtle comorbidity, performance, and other similar issues that affect both treatment selection and survival. The extent to which such omissions may have affected the survival response to treatment estimated in this paper after adjusting for survival differences attributable to TNM staging, Karnofsky Performance Status, tumor size, tumor histology, and weight loss will require further research with a much larger data set than was available for this paper.
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