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© 2002 American Society for Clinical Oncology Nomogram for Overall Survival of Patients With Progressive Metastatic Prostate Cancer After CastrationByFrom the Genitourinary Oncology Service, Departments of Medicine, Epidemiology and Biostatistics, and Urology, Memorial Sloan-Kettering Cancer Center; Department of Medicine, Joan and Sanford Weill Medical College of Cornell University, New York, NY; and University of California at San Francisco, UCSF–Mount Sinai Cancer Center, San Francisco, CA. Address reprint requests to Howard I. Scher, MD, Memorial Sloan-Kettering Cancer Center, 1275 York Ave, New York, NY 10021; email: scherh{at}mskcc.org
PURPOSE: To develop a pretreatment prognostic model for survival of patients with progressive metastatic prostate cancer after castration using parameters that are measured during routine clinical management. PATIENTS AND METHODS: Pretreatment clinical and biochemical determinants from 409 patients enrolled onto 19 consecutive therapeutic protocols from June 1989 through January 2000 were evaluated. The factors selected were age, Karnofsky performance status (KPS), hemoglobin (HGB), prostate-specific antigen (PSA), lactate dehydrogenase (LDH), alkaline phosphatase (ALK), and albumin. These factors were combined in an accelerated failure time regression model to produce a nomogram to predict median, 1-year, and 2-year survival. The nomogram was validated internally and externally using data from a multicenter randomized trial of suramin plus hydrocortisone versus hydrocortisone alone. RESULTS: The median survival of the entire group was 15.8 months (range, 0.9 to 77.8 months); 87% have died. In multivariable analysis, KPS, HGB, ALK, albumin, and LDH were significantly associated with survival (P < .05), whereas age and PSA were not. All seven factors were included in the nomogram. When applied to the external validation data set, the nomogram achieved a concordance index of 0.67. Calibration plots suggested that the nomogram was well calibrated for all predictions. CONCLUSION: A nomogram derived from pretreatment parameters that are measured on a routine basis was constructed. It can be used to predict the median, 1-year, and 2-year survival of patients with progressive castrate metastatic disease with reasonable accuracy. The information is useful to assess prognosis, guide treatment selection, and design clinical trials.
IN A CLASSIC analysis of clinical trials evaluating nonhormonal cytotoxic agents for patients with progressive metastatic prostate cancers after castration, median survival ranged from 6 to 10 months.1 This contrasts with some contemporary trials in which median survivals in the range of 14 to 22 months are being reported,2-5 with the implication that current therapies may be more effective than those available in the past. The reported increase in overall response proportions is consistent with this view, even though many of the "responses" are prostate-specific antigen (PSA) based, and a definitive survival benefit has not been proven for any chemotherapy program in a prospective randomized trial. Nevertheless, more patients are now receiving chemotherapy, as the reluctance of physicians to administer, and patients to accept, this form of therapy is reduced. This includes patients with rising PSA levels without radiographic or clinical progression, raising the contribution of lead-time bias in the purported benefit of more contemporary regimens. Inclusion of the latter group of patients increases both the heterogeneity of the population and the importance of determining which patients are destined to do well and which are destined to do poorly. Having the ability to assess prognosis before therapy is critical to counsel patients about their long-term outlook, to guide treatment selection, and to compare outcomes of phase II trials so that only the most effective regimens are moved forward. Several groups have reported prognostic models for survival of patients with progressive disease after castration (Table 1). 6-13 Some consider only pretherapy factors, whereas others include both pretreatment parameters and a determinant that describes a specific pattern of change in PSA after treatment. The objective of the present study was to develop a nomogram to predict survival probabilities for the individual patient before treatment using clinical parameters and biologic determinants that are measured routinely in the course of patient management. The results were validated using an external database of patients treated on a prospective randomized trial of suramin plus hydrocortisone versus hydrocortisone alone.14
The study population included patients with progressive metastatic disease after castration enrolled onto protocols conducted from the time PSA measurements became available at Memorial Sloan-Kettering Cancer Center (MSKCC). Validation was performed using patients from a multicenter randomized trial.14 Each data set is described below, along with the statistical methods used for nomogram construction and validation.
The MSKCC Series The pretreatment evaluations were similar among the protocols and included a complete history and physical examination plus laboratory studies within 2 weeks before the start of treatment. The laboratory tests included a complete automated blood cell and platelet count; a comprehensive profile including alkaline phosphatase (ALK), lactate dehydrogenase (LDH), aspartate transglutaminase, blood urea nitrogen, creatinine, calcium, phosphorus, glucose, uric acid, total protein, albumin, and total bilirubin; in addition to the tumor markers serum PSA and acid phosphatase. Imaging studies (abdominal and pelvic computed tomography or magnetic resonance imaging and bone scan) were obtained within the 4 weeks before the treatment start date. The presence or absence of pain was not a uniform requirement for entry. In cases where a patient was entered on two or more protocols, only the pretreatment data from the initial protocol were included.
Validation Data Set
Statistical Methods Nomogram construction was carried out as described previously.16 Initially, a Cox regression model17 was fit containing all predictors, with no attempt at variable selection. Because of skewed distributions, PSA, LDH, and ALK were log transformed. Restricted cubic splines were used in the Cox model to accommodate potentially nonlinear effects. The model derived using a Cox regression analysis fit the data poorly, as several variables violated the proportional hazards assumption of a constant effect over time. Consequently, an accelerated failure time model,18 which models the log survival time as a function of the predictors and an error random variable, was constructed. Graphic examination of the residuals suggested the accelerated failure time model with a Gaussian error distribution fit the data well. Survival was also estimated using the Kaplan-Meier method.19 Nomogram validation consisted of three activities. First, a concordance index was estimated by bootstrapping with 200 resamples to calculate an unbiased measure of the ability of the nomogram to discriminate among patients. The concordance index is the probability that, given two randomly drawn patients, the patient who dies first had a higher probability of death. Next, the predicted probability of survival versus actual survival was compared. This examined the calibration of the nomogram, also using 200 bootstrap resamples. Finally, external validity of the nomogram was assessed using an external data set to compare nomogram predictions with observed survival. Nomogram predictions were assessed for discriminatory ability by quantifying the concordance index, and the predictions were assessed for calibration accuracy by plotting actual survival against predicted survival probabilities for patients stratified by predicted risk. All analyses were conducted with S-Plus 2000 Professional (Insightful Corp, Seattle, WA) with the Design and Hmisc libraries attached.20
Details of the accrual, the number of patients included and excluded from the analysis, and the reasons for exclusion are listed in Table 2.4,21-35 Overall, 519 patients were enrolled onto the 19 consecutive trials, of whom 110 were excluded for the following reasons: 93 (87%) were enrolled onto multiple protocols, eight proved to have testosterone levels outside the castrate range (more than 50 ng/dL), and nine had no evidence of metastatic disease on scan that was permitted for the specific study (high-dose bicalutamide, IRB 93-137). In the validation set, 25 of the 458 (6%) patients had missing values and were excluded, leaving 433 patients in the analysis.
Descriptive statistics of the patient populations for the nomogram development series and the validation series are listed in Table 3, and the 25% and 75% quartile ranges for each variable as used in the nomogram are listed in Table 4 and illustrated graphically in Fig 1. The median survival of patients in the MSKCC series was 15.8 months (range, 0.9 to 77.8 months) versus 10.3 months (range, 1.4 to 38.4 months) for the validation series. There were 357 deaths (87%) in the MSKCC series and 395 (91%) in the validation data set. The survival of MSKCC patients was longer than for those in the validation set as shown in Fig 2, which is consistent with the individual parameters listed in Tables 3 and 4, suggesting that the latter cohort included patients with more advanced disease. The results of the accelerated failure time regression model for the MSKCC group showed that KPS, HGB, ALK, albumin, and LDH were each associated with overall survival (P < .05), whereas age and PSA were not (Table 5).
The final nomogram including all seven parameters is illustrated in Fig 3. This is a points-based nomogram, where points are tallied for each of the patient’s predictor variables. It is used by first locating the patient’s position on each predictor variable scale (age through albumin). Each scale position has corresponding prognostic points located on the "points" scale. To determine the points associated with a KPS of 80%, a vertical line is drawn from the 80% on the KPS axis to the points axis, and the numeric score is read. A KPS of 80% contributes approximately 40 points. The point values for all clinical predictor variables are determined in a similar manner. They are then summed to arrive at a "total points" value, which is plotted on the total points axis (fourth from the bottom). A vertical line is then drawn from the total points axis down to the "1-year survival probability" and to the "2-year survival probability" to indicate the patient’s probability of being alive in 1 and 2 years, respectively. Drawing a vertical line from the total points axis down to the "median survival months" axis indicates the predicted median life expectancy for patients with identical characteristics.
Instructions for Physician: Locate the age on the Age axis. Draw a line straight upwards to the Points axis to determine how many points towards survival the patient receives for his age. Repeat this process for the other axes, each time drawing straight upwards to the Points axis. Sum the points achieved for each predictor and locate this sum on the Total Points Axis. Draw a line straight down to find the patient’s probability of survival for 1 year and 2 years and his median survival. Instructions for Patient: "Mr. X, if we had 100 men exactly like you, we would expect <nomogram prediction x 100> to be alive in 1 and 2 years, respectively, and we expect 50 of those to be alive after <median survival prediction> months." The nomogram includes the entire range of values for each of the variables evaluated, and the box plots (Fig 1) illustrate the median and 75% and 25% quartile ranges. Considering two hypothetical patients representing the 75% quartile (251 points) and the 25% quartile (186 points) for each of the variables, the predicted 1-year, 2-year, and median survivals are 87% versus 35%, 55% versus 9%, and 26 months versus 9 months, respectively. When subjected to internal validation, the nomogram achieved a bootstrap-corrected concordance index of 0.71, and internal calibration showed that the predictions reasonably approximate actual survival probabilities. External validation was accomplished by comparing the nomogram predictions for each patient in the validation data set with the actual outcome. In this analysis, the nomogram had an estimated concordance index of 0.67. Calibration plots suggested that the nomogram was well calibrated for all predictions and are presented in Fig 4. These are plots of nomogram-predicted probabilities against observed survival proportions in the validation data set. The survival of patients, grouped by quartiles of their median survival time predictions, is illustrated in Fig 5. The quartiles of nomogram-predicted median survival are associated with different observed survival (ie, the curves in Fig 6 are significantly different, P < .0001). Table 6 lists details for each quartile of median survival in the validation data set. For each quartile, the actual and predicted median survival estimates and confidence intervals show good agreement, suggesting the survival predictions from the nomogram are well calibrated externally. Figure 6 shows a comparison of predicted median survival versus actual survival for the patients who died in the validation data set. The figure suggests substantial variability in the actual survival among patients with similar median predicted survival. This plot must be interpreted cautiously, because the analysis was restricted to patients who died, who tend to have survivals that are lower than expected.
Patients with progressive metastatic prostate cancer after castration are destined to die of disease. Nevertheless, the prognosis of individual patients within this clinical state varies greatly. Knowing whether the prognosis is months or years is important to the individual facing a lethal illness.36 It is also useful to physicians to guide treatment selection, and in the design of clinical trials. The present study reports a prognostic nomogram for survival that can be applied easily in the clinic because it is derived from pretreatment parameters that are measured in the context of routine clinical practice. It includes seven factors, of which KPS, HGB, and LDH had the largest impact on outcome when considered for the range of values commonly encountered in this patient population. For most of the factors, the direction of the predictive effect, positive or negative, was consistent with what one might expect clinically. Indices of more advanced disease such as a low KPS, low albumin and HGB, and high LDH and ALK produced a lower overall prognostic score. Although higher age was associated with better survival, the overall contribution of age within a range of 40 to 85 years was modest (total of 20 points). In contrast, a change in performance status of 30%, from 60% (symptomatic) to 90% (asymptomatic), contributed over 45 prognosis points. These results are consistent with reports showing associations between performance status and outcome whether measured on the Karnofsky37 or the Eastern Cooperative Oncology Group/World Health Organization scale,7,38-41 and the adverse effect of anemia on survival.9,42-44 Anemia may reflect advanced disease (ie, myelophthisis), the effect of prior interventions (hormones, chemotherapy, and radiation therapy), and/or the nutritional status of a patient. Markers of tumor burden such as a higher LDH8,10,42 and ALK10,43 have been found to be predictive in many studies.39,41 It was of interest that the impact of ALK on survival was modest, which may reflect the fact that some elevations in ALK are the result of bone healing and not progressive disease. The predictive effect of two variables, PSA and albumin, were not intuitive. For PSA, the implication is that high levels may be protective, as suggested in a report showing that the protease action of PSA may have an antiangiogenic effect.45 However, a close inspection shows that the overall effect of PSA is not significantly different from zero and that an increase in PSA from 0 to 100 ng/mL contributed only "8" points. This is more consistent with our previous reports10,11 but contrasts with that of others.43,46 Alterna tively, increases in PSA do not occur independently, and may be associated with changes in other predictors. For example, the higher tumor burden associated with a higher PSA may be associated with a decrease in KPS and HGB, and an increase in LDH. Changes in these variables would create a large negative effect on outcome, negating any seemingly "protective" effect of PSA. With respect to albumin, it appears that values above 4.2 g/dL were associated with an inferior outcome. This affected 158 (39%) patients who met this criterion. There is no plausible biologic explanation. When developing a nomogram, variable selection is performed somewhat differently from the procedures typically used to develop prognostic models in that we defined our list before data analysis. A more common approach is to assess each variable in univariable analysis, and to build a multivariable model using predictors that are significant. These approaches may be suboptimal for maximizing predictive accuracy,47 as both lead to predictor variable coefficients that are biased in high absolute value and confidence intervals that are falsely narrow. Other analyses place patients into risk groups, which has the potential to force heterogeneity and result in lost information. Another method is to count risk factors and group patients on the basis of the number of factors. This assumes that each factor has equal weight, and places continuous predictors in discrete ranges for counting purposes. This may diminish predictive accuracy relative to simple fitting of the full model, as was done in the present study, retaining all predictors as long as the number of events in the data set is sufficient.47 Using an external data set for validation,14 the estimated concordance index for the nomogram was 0.67, suggesting adequate discrimination, as shown by the actual and predicted median survivals with confidence intervals by quartile in Fig 4. Figure 6 shows the predicted median survival versus actual survival for patients who died. It suggests substantial variability in actual survival among patients with similar median predicted survival. However, the plot must be interpreted cautiously, because this analysis is restricted to patients who died, who tend to have survivals that are lower than expected. Performing such an analysis on all patients requires grouping the patients in order to obtain an observed median survival figure. This is illustrated in Fig 5 and Table 6. Patients in both data sets are often interchangeably categorized as "androgen-independent," or "hormone refractory." At MSKCC, we favor assigning these patients to a single clinical state: "castrate metastatic" disease when they show progression after their first androgen ablative therapy.6 In this way, the specific therapy administered can be evaluated independently on the basis of the point in the natural history of the disease in which the patient currently resides, rather than on the number of prior therapies a patient may or may not have received. This is underscored by the external validation of the nomogram. A 5-month difference in median survival between the derivation and the validation data sets suggests that the latter has more advanced disease, as evidenced by higher median ALK, LDH, and PSA and lower HGB and albumin (Tables 3 and 4). The fact that the nomogram remained accurate in prediction shows that it can absorb the 5-month median survival discrepancy and demonstrates its ability to accommodate differences in baseline factors. Reports of prognostic factors for survival of patients with progressive disease after castration can be categorized into two distinct types. The first, like the current report, include only pretreatment factors; the second type requires factors only available after therapy has been initiated. The latter models were developed to assess the prognostic significance of a predefined pattern of change in PSA after treatment,10,11,36,39,41,48 and require that the patient or patient population be treated first and the outcome observed. This is a different question, and the results obtained cannot be used to address issues of treat- ment selection or determining prognosis before treatment. Table 1 lists published reports of prognostic models for survival of patients with progressive prostate cancer after castration. It includes the characteristics of the population studied, the factors considered, and whether the model was validated on an independent data set. Some antedate the PSA era,7,8 and include a wide range of patient profiles and variable factors. Some factors are subjective and may be difficult to quantify, such as voiding symptoms7 and fatigue.9 Others are no longer measured routinely (eg, acid phosphatase).7 Progression of disease was not a uniform entry criterion, as some included patients who were "stable" on hormones.7 The methods of analysis also differed. Some included a percentage change in posttherapy change in PSA,10,11 others included PSA kinetics,12,13 and others included a count of the number of adverse features to assign risk strata.38 Few included a validation set. The unique aspects of the model reported here is that it includes parameters that are measured routinely, that each variable was considered on a continuous basis, and that prognostic scores can be calculated easily in the course of daily patient management. This affords the model several applications. A role for counseling is shown by the consideration of two hypothetical patients representing the upper and lower quartile of risk who differed significantly in predicted median, 1-year, and 2-year survival. In practice, a patient in the upper quartile might be considered for an aggressive approach with a higher potential for long-term benefit, the toxicities of which may be prohibitive for a low-risk patient. Alternatively, a high 1-year survival probability can be viewed as a window in which to explore less toxic alternatives that might modulate tumor growth before a more aggressive approach is tried. Another advantage of a pretherapy model is that it can be used to define entry criteria for a clinical trial. Limiting entry on a protocol to patients with a given range of prognosis reduces the heterogeneity of patients treated, and can be used to adjust risk strata in reported trials with seemingly disparate results.49 This is useful to determine whether some of the differences in reported outcomes can be explained simply by the enrollment of a group of patients with an inherently better or worse prognosis independent of therapy. As an example, the median survival of patients enrolled onto the first 10 protocols in the series was 11.8 months (range, 0.9 to 77 months); for the last nine, median survival was 16.4 months (range, 1.1 to 71.3 months). The nomogram has limitations. First, it was developed using the individual data from highly selected patients meeting the eligibility criteria for phase I and phase II trials. These patients tend to have a better performance status with limited, if any, organ dysfunction. Second, the predictions of the bootstrap-corrected concordance index, 0.71 for this nomogram, suggests that for 29% of patient pairs, the patient predicted to have a better prognosis actually died first. This highlights the need to continue the search for additional predictors. These might include more quantitative measures of extent of disease in bone,44,50 circulating cytokine levels such as interleukin-651 or vascular endothelial growth factor,52 the presence or absence of circulating cells in the peripheral blood detected by reverse-transcriptase polymerase chain reaction,53,54 or the expression of specific biologic determinants, such as HER2, on tumor cells. The latter would require a biopsy of a relapsed tumor as opposed to diagnostic biopsy of the primary tumor obtained before treatment, as the expression of many determinants changes as the disease progresses.55 Despite these limitations, a concordance index of 0.67 to 0.71 is statistically better than chance (P < .0001) and represents a good starting point, given the lack of established prognostic models in this setting. The purpose of this study was to design a prognostic model that clinicians could apply easily in the clinic. It was achieved by using parameters that are measured on a routine basis in a points-based nomogram.
Supported by grant nos. CA 05826 and CA92629, CaPCURE, PepsiCo Foundation, grant no. RPG-00-202-01-CCE from the American Cancer Society, and Parke-Davis Pharmaceutical Research, Division of Warner-Lambert Co.
Presented in part at the Thirty-Seventh Annual Meeting of the American Society of Clinical Oncology, San Francisco, CA, May 12-15, 2001.
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ABSTRACT
INTRODUCTION
