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© 2000 American Society for Clinical Oncology Pretreatment Nomogram for Predicting the Outcome of Three-Dimensional Conformal Radiotherapy in Prostate CancerFrom the Departments of Urology, Epidemiology and Biostatistics, and Radiation Oncology, Memorial Sloan-Kettering Cancer Center, New York, NY, and the Cleveland Clinic, Cleveland, OH. Address reprint requests to Michael W. Kattan, PhD, Memorial Sloan-Kettering Cancer Center, 1275 York Ave C1068, New York, NY 10021; email kattanm{at}mskcc.org
PURPOSE: Several studies have defined risk groups for predicting the outcome after external-beam radiotherapy of localized prostate cancer. However, most models formed patient risk groups, and none of these models considers radiation dose as a predictor variable. The purpose of this study was to develop a nomogram to improve the accuracy of predicting outcome after three-dimensional conformal radiotherapy. MATERIALS AND METHODS: This study was a retrospective, nonrandomized analysis of patients treated at the Memorial Sloan-Kettering Cancer Center between 1988 and 1998. Clinical parameters of the 1,042 patients included stage, biopsy Gleason score, pretreatment serum prostate-specific antigen (PSA) level, whether neoadjuvant androgen deprivation therapy was administered, and the radiation dose delivered. Biochemical (PSA) treatment failure was scored when three consecutive rises of serum PSA occurred. A nomogram, which predicts the probability of remaining free from biochemical recurrence for 5 years, was validated internally on this data set using a bootstrapping method and externally using a cohort of patients treated at the Cleveland Clinic, Cleveland, OH. RESULTS: When predicting outcomes for patients in the validation data set from the Cleveland Clinic, the nomogram had a Somers’ D rank correlation between predicted and observed failure times of 0.52. Predictions from this nomogram were more accurate (P < .0001) than the best of seven published risk stratification systems, which achieved a Somers’ D coefficient of 0.47. CONCLUSION: The development process illustrated here produced a nomogram that seems to predict more accurately than other available systems and may be useful for treatment selection by both physicians and patients.
ONE OF THE FIRST nomograms for counseling patients with localized prostate cancer, developed by Partin et al,1 used clinical data of surgically treated patients to predict the final pathologic stage after radical prostatectomy. Pathologic stage had previously been shown to correlate independently with each of three clinical variables, clinical stage,2 Gleason score,3 and serum prostate-specific antigen (PSA) level.4 Partin et al demonstrated increased prediction accuracy when these variables were combined. This nomogram was later revised and validated.5,6 However, because this nomogram did not predict other outcome parameters, such as the risk of relapse, its clinical value has been limited.7 Addressing this concern, Kattan et al8-10 subsequently developed nomograms that predict the probability of PSA relapse-free survival after radical prostatectomy based on pre- and postsurgical variables. In the present study, we extend this paradigm, providing a nomogram that predicts the probability of PSA relapse-free survival after external-beam radiotherapy.
Several published models predict the outcome of radiotherapy in localized prostate cancer.11-19 These models combine prognostic variables to generate risk stratification groups, based on initial clinical stage, Gleason score, and pretreatment serum PSA levels. In general, these systems consist of three to five risk groups and are designed to predict the PSA relapse-free survival as a surrogate of tumor control after radiotherapy. However, their predictive accuracy may be limited, because all of these systems combine patients with similar, albeit not identical, variables to form a risk group. The use of inhomogeneous groups potentially results in suboptimal predictive accuracy. For example, most models consider the range of PSA values of Our research question was whether a nomogram, which is based on a continuous risk estimation model and includes the effect of dose as a variable, would improve the outcome prediction accuracy after radiotherapy in localized prostate cancer, using PSA relapse-free survival as an end point. To achieve this goal, several modeling techniques were tested on a large cohort of patients with prostate cancer treated at the Memorial Sloan-Kettering Cancer Center (MSKCC) with three-dimensional conformal radiotherapy (3D-CRT), which is considered state-of-the-art in the radiation management of prostate cancer. The Cox proportional hazards regression method21 with restricted cubic splines22 was found to be the most accurately predicting technique and thus was used to construct the nomogram. This nomogram seemed to yield the most accurate prediction of the outcome when tested on the MSKCC database and confirmed using a database of patients with prostate cancer treated at the Cleveland Clinic. The proposed nomogram significantly improves the prediction accuracy when compared with several published risk stratification models.
MSKCC Series From December 1988 through November 1998, 1,080 patients with prostate cancer were treated at MSKCC with 3D-CRT. Patients with missing data (PSA, n = 2; Gleason score, n = 9; recurrence status, n = 27) were excluded, leaving 1,042 patients available for the present analysis. The median age was 68 years (range, 46 to 86 years), and 94% of the patients were white. The clinical characteristics of this group of patients are listed in Table 1. Each patient was clinically staged by one of three of the authors (M.J.Z., Z.F., S.A.L.) according to the 1992 American Joint Committee on Cancer staging classification system.23 Those with T3a and T3b disease were combined into a single group because of the small frequencies of each. Serum PSA was measured by the Tosoh radioimmunoassay, with a normal range of  4.0 ng/mL, and modeled as its natural log. All patients had histologically confirmed adenocarcinoma of the prostate, classified according to the Gleason grading system3 by one of two pathologists at our institution. Radiation was planned and delivered using the MSKCC system for 3D-CRT or the intensity-modulated version of 3D-CRT, as previously described.24 Table 1 shows that since 1991, 387 patients (37.1%) with large-volume prostate glands, in whom the treatment-planning dose-volume histograms indicated that greater than 30% of the rectal wall and/or greater than 50% of the bladder wall might receive a dose of greater than 75 Gy, were treated with neoadjuvant androgen deprivation for 3 months before and during radiation.15 Hormone therapy was discontinued at the completion of radiotherapy. Radiation doses ranged between 64.8 and 86.4 Gy, delivered in daily dose fractions of 1.8 Gy, using a previously reported dose-escalation scheme that achieved a dose of 81 Gy in October 1992.15 Follow-up evaluations were performed at 3- to 6-month intervals.
The parameters selected as nomogram variables included the clinical stage, biopsy Gleason score, pretreatment serum PSA level, whether neoadjuvant androgen deprivation therapy was administered, and the radiation dose delivered. Variables that are not available before treatment, such as time to PSA nadir, or that do not have theoretical justification for independent predictive ability, such as patient age, were not included in the nomogram. Treatment failure was defined according to a modification14 of the American Society of Therapeutic Radiation Oncology consensus definition.25 It was based on the development of three consecutive rises of serum PSA level. The date of failure was defined as the midpoint between the last nonrising and the first rising PSA values. All patients were included with no minimum requirements for follow-up or number of PSAs. None of the patients received postirradiation hormonal or other anticancer therapy before documentation of PSA failure. The median follow-up time for the patients who did not relapse was 29 months (range, 6 to 113 months). The overall freedom from recurrence is illustrated in Fig 1. Removing from analysis the patients who were treated within the last 24 months14 affects the probability of remaining free from recurrence by less than 1%, so these patients were retained in the analysis. There were no recurrences beyond 63 months, and there were 649 patient-months of follow-up beyond 60 months.
Validation Data Set: The Cleveland Clinic Series The Cleveland Clinic data set included 1,030 patients treated between July 1986 and November 1998. Of these, 78 patients who received planned adjuvant hormonal therapy and another 40 in whom one or more predictor variables and/or follow-up information was missing were excluded from the current analysis. Of the remaining 912 patients, 529 received conventional external-beam radiotherapy and 383 received 3D-CRT. A Cox proportional hazards regression analysis did not disclose any adjusted impact of the treatment technique (conventional v 3D-CRT) on the therapeutic outcome in this series (P = .14). Therefore, the entire data set of the 912 patients was used for analysis in the present study. None of the patients received hormonal or other anticancer therapy before the demonstration of recurrence. The clinical characteristics of this group of patients are listed in Table 1, and overall freedom from recurrence is illustrated in Fig 1. The median follow-up time for the patients who did not recur was 25 months (range, 6 to 148 months).
Statistical Methods
When the prediction techniques were compared, the Cox proportional hazards model with restricted cubic splines produced the most accurate predictions. This Cox prediction model is illustrated graphically by the nomogram in Fig 2. Using bootstrapping to obtain unbiased estimates of expected future performance, this nomogram predicted the 5-year PSA relapse-free survival with a Somers’ D correlation coefficient of 0.46, and the performance across the spectrum of relapse probabilities was accurate to within 10% of the observed freedom from PSA relapse (Fig 3). The predictive accuracy of this nomogram was compared with the accuracy of the seven risk stratification schemes using the Cleveland Clinic data (Fig 4). For this comparison, each patient in the Cleveland Clinic series had his outcome independently predicted by the nomogram and each of the risk stratification schemes, and all of these predictions were compared with observed outcomes. The McNemar test indicated that the Somers’ D correlation coefficient of the nomogram (0.52) was higher (P = .0001) than that of the best risk stratification scheme tested (0.47), suggesting that the nomogram was more accurate than the risk stratification schemes in predicting the outcome.
The present study demonstrates that the nomogram developed here represents a valid and accurate method for predicting the outcome of external-beam radiotherapy in localized prostate cancer. Its advantage over the risk stratification prediction systems is likely associated with the use of continuous risk scales for relevant technique parameters as opposed to condensing sections of the risk spectra into heterogeneous risk groups. The inclusion of dose as a variable affecting outcome may have also contributed to the improved predictive accuracy. Definitive interpretations regarding the degree of the improvement in prediction are, however, difficult because the data are of the time-until-event type. Thus, although the nomogram was shown to predict better than the best of the risk stratification models (P < .05), the improvement is difficult to appreciate by interpreting the error measure used in this study, the Somers’ D correlation coefficient, which evaluates the strength of rank association between a prognostic model and the actual PSA, relapse-free survival. To address this concern, it is helpful to illustrate the use of the nomogram and compare its prediction with that of risk stratification by considering a specific patient from the Cleveland Clinic validation series. This patient had clinical stage T2c disease, a pretreatment PSA level of 6 ng/mL, a biopsy Gleason score of 9, and a planned dose of 66.6 Gy without use of neoadjuvant hormones. By a recently published risk stratification scheme,14 this patient would be classified into the most favorable group (group I), which has an associated freedom from recurrence prediction of 81% at 5 years. According to our nomogram, which was shown to predict more accurately on the Cleveland Clinic series, the same patient’s predicted probability of 5-year freedom from recurrence is 24%. With our previously reported preoperative surgery nomogram,8 the same patient’s predicted probability of 5-year freedom from recurrence is 68%. Thus, risk stratification may have influenced this man to choose radiation therapy over surgery, whereas with the nomogram approach, this particular patient’s better chance at freedom from progression would seem to have been with surgery rather than with low-dose radiation. As a second example, consider the Cleveland Clinic patient who had T1c disease with a PSA level of 21.4 and a biopsy Gleason sum of 7 who was treated with 78 Gy and neoadjuvant hormones. Risk stratification14 would have put him in the least favorable risk group, with a 29% 5-year freedom from recurrence prediction. The surgery nomogram8 predicts a 55% freedom from recurrence, whereas the radiation therapy nomogram predicts 82% freedom from recurrence, both at 5 years. Thus, risk stratification would have potentially directed this patient away from radiation therapy, which seems to be his better choice for preventing disease progression. Figure 5 compares the nomogram and risk stratification14 predictions for all patients in the Cleveland Clinic series. It is clear from this Figure that the risk stratification approach produces heterogeneous strata with respect to the nomogram predictions and, assuming the nomogram is indeed more accurate, could be misleading for the individual patient who is trying to decide on a treatment strategy. The latter is illustrated by the number of patients with low freedom from recurrence predictions by the nomogram despite favorable risk stratification and the number of patients with high freedom from recurrence predictions by the nomogram despite unfavorable risk stratification. Thus, risk stratification does not seem to provide these patients with the best estimates of treatment efficacy currently available and may lead to them making poor treatment choices as they compare treatments.
The Somers’ D method uses a range of coefficient values from -1 to +1 to test the predictive accuracy associated with a model. On this scale, 0 represents no association at all and 1 (or -1) represents perfect positive (or negative) association. The nomogram developed here performs near the center of this scale, discriminating significantly better than chance (P < .0001). Although it provides improved accuracy over the risk stratification models we tested, all of which had smaller D scores, it leaves a substantial degree of uncertainty in the prediction. It seems that an improved nomogram will have to be based on larger patient series, longer follow-up periods, and additional biologic and clinical markers with significant predictive potential. Although the follow-up in the validation data set was not as mature as that found in the nomogram derivation data set, Somers’ D is able to use all follow-up information, regardless of duration. Shorter follow-up in a series does not bias one prediction technique in favor of another; it simply reduces the statistical power to declare one technique superior to another. Fortunately, sample size and follow-up were adequate in the validation data set to provide sufficient power to declare one technique superior. To identify the best algorithm for nomogram design, we compared several statistical and machine learning models of outcome prediction. This trial-and-error approach was chosen because it was impossible to know in advance which method would provide the best prediction on a given set of data, because each technique has theoretical strengths and weaknesses.34 Of the techniques considered, the traditional Cox model is the most commonly used method for multivariable analysis of survival data. It assumes that continuous variables have linear effects (ie, linearly related to the log-hazard function), unless special modifications are made, such as restricted cubic splines. In fact, in the present study we used the restricted cubic splines approach for the PSA, Gleason, and dose variables, which improved the predictive accuracy (data not shown). This study was not an exhaustive comparison of the modeling techniques tested. Each technique has numerous options that may be varied, and most options were left at the software defaults. Thus, our results do not represent definitive comparisons of the techniques in a general sense, nor can it necessarily be concluded that the Cox model with restricted cubic splines is the best tool for the analysis of our data. Because a definitive comparison of techniques was not the focus of this study, we did not conduct statistical significance testing between techniques but merely selected the technique with the superior apparent accuracy. A thorough comparison of all the options for each technique would require an enormous study. Simply put, we carried out limited comparisons of each technique and found the Cox model with restricted cubic splines to be the most accurate. Others may find, by varying the options, that a different approach may further improve the predictive accuracy of the nomogram. Nonetheless, the Cox model with restricted cubic splines produced a nomogram that predicts more accurately than the risk stratification systems previously used for outcome prediction. We plan to facilitate the computations of the nomogram by adding it to our Palm Pilot (Palm, Inc, Santa Clara, CA) nomogram software application, which we distribute free of charge.9 In addition to serving as a prognostic tool, the nomogram in Fig 2 is also useful in interpreting the underlying Cox model. PSA seems to have a major impact across its spectrum. The clinical stage point assignment is intuitive except for, possibly, stage T2c, which is associated with a worse predicted prognosis than is T3ab. The difference likely results from estimation variability for the coefficient or variability in the digital rectal examination. However, the difference between these groups is not statistically significant at the 5% level. We have avoided combining groups after modeling to improve the appearance of the nomogram because such action can have a deleterious effect on performance.32 This is also the reason for not deleting the nomogram axis for "Hormones," which has a statistically insignificant impact on the outcome. When interpreting the nomogram, it is essential to consider possible changes in other variables (eg, PSA level and Gleason score) when comparing points across levels of a single variable (eg, dose). It is difficult to draw meaningful conclusions about the effect of a single variable in isolation when other variables of the nomogram may correlate with it, because moving a patient on one axis would likely affect the position of variables on other axes. Thus, whereas the nomogram indicates that dose may be a helpful predictor of patient outcome, this analysis is not a formal test of dose-response. It is also important to consider our selection criteria for neoadjuvant hormones when judging its effect on predicted probability. There are several potential applications for nomograms such as that developed in the present study.8,9 First, it may assist both physicians and patients in treatment selection. A patient weighing the risks and benefits of various treatments would value the most accurate predictions of treatment outcome currently available when he considers radiation therapy. It should, however, be emphasized that the development of the present nomogram was based on a cohort of patients treated with external-beam radiotherapy. Both physician and patient biases unquestionably affected the selection of treatment in this group of patients. Hence, the nomogram parameters may not be applicable to the population of patients with localized prostate cancer at large. It should, nonetheless, be noted that approximately 75% of the patients in the MSKCC series were stage T1 or T2 patients and that a majority of these patients were offered a surgical option. Whether simultaneous use of surgical and radiation nomograms would facilitate treatment selection in an individual candidate remains to be tested. The design of clinical trials may represent another application of nomograms. By quantifying the probability of treatment failure, prognostic nomograms also identify patients most likely to benefit from neoadjuvant or adjuvant treatments. Selection of candidates would be facilitated by specifying a risk cutoff (eg, at least 70% chance of treatment failure) rather than individual variable levels, which may not as easily produce homogenous groups of patients. A third use, also related to clinical trials, may be verification of adequate randomization. Traditionally, such verifications have been carried out by comparing the distribution of individual variables in each arm and recording differences. However, joint distribution differences may remain undetected by this procedure. Assessment of a predicted risk imbalance using all of the common prognostic factors would yield more relevant comparisons. There are several limitations to the present nomogram. The major limitation is the high level of uncertainty in prediction that still exists. In addition to the fact that the bootstrap-corrected Somers’ D correlation coefficient for the nomogram was 0.46, the confidence intervals at the various predicted probabilities of recurrence (Fig 3) were at some levels as high as ± 10%. Furthermore, as we state on the nomogram itself, disease may still recur in patients after the prediction time point of 5 years, although this has been shown to be rare.35 However, although the current nomogram may not represent the most optimal tool for prediction, it nonetheless provides an example of the appropriate methodology for development and evaluation of prognostic nomograms in general. Furthermore, the Somers’ D coefficient of 0.46 is near that of other prognostic models of survival data.36 Another limitation is that the nomogram is based on a single institution’s database and that the patients were treated with the sophisticated and technically advanced 3D-CRT technique. Despite the fact that it was validated by the Cleveland Clinic series of mixed modalities with dose escalation, its applicability to other centers and external-beam radiotherapy of localized prostate cancer in general require further testing. We encourage others to evaluate the accuracy of this nomogram and development approach on their series. The fact that patient evaluation with this nomogram encompasses commonly used pretreatment parameters, the planned dosage, and the decision regarding the frequently applied neoadjuvant androgen deprivation suggests that its usefulness in outcome prediction of radiotherapy in stages T1c to T3c NX MO prostate cancer can be rapidly assessed. It may provide a highly beneficial tool for physicians and patients in making decisions about treatment and in identifying patients at high risk of failure after radiotherapy who may benefit from adjuvant treatment protocols.
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ABSTRACT
INTRODUCTION
represents data set subcohorts. x represents the bootstrap-corrected estimate of nomogram.
