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© 2003 American Society for Clinical Oncology Using the Expected Survival to Explain Differences Between the Results of Randomized Trials: A Case in Advanced Ovarian CancerFrom the International Drug Development Institute, Cambridge, MA; Limburgs Universitair Centrum, Center for Statistics, Diepenbeek; University Hospital Antwerp, Edegem, Belgium; Medical Research Council Clinical Trials Office, London; Cochrane Collaboration, Oxford, United Kingdom; Istituto di Ricerche Farmacologiche Mario Negri; European Institute of Oncology, Milan; Azienda Ospedaliera Pisana, Pisa, Italy; and University of Alabama at Birmingham, Birmingham, AL. Address reprint requests to Marc Buyse, ScD, IDDI Inc, American Twine Office Park, 222 Third St, Suite 0342, Cambridge, MA 02142; email: marc.buyse{at}iddi.com.
Purpose: A meta-analysis of randomized trials in advanced ovarian cancer showed a longer survival with cyclophosphamide, doxorubicin, and cisplatin (CAP) than with cyclophosphamide and cisplatin (CP; P = .009). In contrast, the results of the large International Collaborative Ovarian Neoplasm Study (ICON2) showed no survival difference between CAP and carboplatin (P = .98). In this article, we show how these discrepant results can be reconciled through the estimation of expected survival curves. Materials and Methods: A proportional hazards model, fitted to the meta-analysis data, was used to construct the expected survival curve for each treatment arm of the ICON2 trial. Expected survival curves were compared with observed survival curves in the ICON2 trial at all time points using a nonparametric test. Results: The prognostic model for survival obtained in the meta-analysis included extent of residual disease, age, histologic grade, and International Federation of Gynecology and Obstetrics stage. When this model was applied to the ICON2 data, there was no difference between the expected and observed curves in the CAP arm. In contrast, the observed survival curve for carboplatin was far superior to the expected survival curve for CP (P < .01). Conclusion: These analyses provide indirect evidence that better results are achieved with carboplatin alone at an optimally tolerated dose, compared with the CP combination at a cisplatin dose of 50 to 60 mg/m2. The expected survival may provide valuable insight when direct comparisons between randomized groups yield discrepant results across different studies.
OFTEN, THE results of different studies addressing similar therapeutic questions yield conflicting results, which makes it difficult to draw any definite conclusion about the therapies under investigation. For instance, one experiment may show survival benefit from a certain therapy, whereas another similar experiment may fail to do so. Meta-analysis has been advocated as a way to combine evidence from several experiments addressing the same therapeutic question.1 Critics of meta-analysis have pointed out that results of trials were sometimes contradicted by those of subsequent large confirmatory trials.2,3 Although this observation invalidates neither the meta-analysis nor the randomized trial, contradictory results are unsettling and deserve to be investigated further.4,5 In this article, we consider such a situation in advanced ovarian cancer. A meta-analysis was undertaken in 1989 to evaluate the role of anthracyclines in the treatment of women with advanced ovarian tumors. Six randomized trials compared a standard regimen consisting of cyclophosphamide and cisplatin (CP) with cyclophosphamide and cisplatin plus the anthracycline doxorubicin (CAP). The meta-analysis of these trials, which is based on individual patient data supplied by the principal investigators, showed that CAP yielded a higher rate of tumor response and a longer survival than CP.6 These results, which seemed to warrant the use of anthracyclines in the treatment of advanced ovarian cancer, led to a multinational randomized trial that was started in 1991 to compare CAP (the better regimen in the meta-analysis) with carboplatin alone. In this trial, known as the Second International Collaborative Ovarian Neoplasm Study (ICON2), carboplatin was chosen instead of CP because it was believed that an optimally tolerated dose of a single-agent platinum would give results similar to those of platinum-based combinations.7 In addition, carboplatin (the most widely used platinum salt in the United Kingdom) was likely to have an efficacy similar to that of cisplatin, with far less toxicity.8 An update of the meta-analysis, performed after a median follow-up of more than 10 years in the four larger trials, confirmed the survival benefit of CAP over CP (hazard ratio [HR] = 0.84; P = .009).9 In contrast, the results of the ICON2 trial, after a median follow-up of approximately 2.5 years, showed no survival difference between CAP and carboplatin (HR = 1.0; P = .98).10 An obvious explanation for these apparently conflicting results is that single-agent carboplatin, at an optimally tolerated dose, is better in terms of overall survival than cyclophosphamide combined with cisplatin at the dose of 50 mg/m2. However, there are alternative possible explanations for the discrepancy, including differences in prognostic mix between the two patient series, imbalances with respect to important prognostic factors in either series, shorter follow-up time in the ICON2 trial, better treatments after disease progression in the more recent ICON2 trial, unreliability of the results of either the meta-analysis or the ICON2 trial, or simply the play of chance. Therefore, without additional analyses, there may be doubts about the proper interpretation of the discrepancy. In this article, we show how the discrepancy can be explored through the estimation of the expected survival that takes into account patient prognostic features in both the meta-analysis and the randomized trial.
Patient Data We used individual patient data from the meta-analysis and from the ICON2 trial, both of which are described in detail in previous publications.6,9,10 All patients were considered in the present article, whether eligible or not and whether properly treated or not. Items requested for every patient included baseline clinical characteristics (patient identification, institution, date of random assignment to treatment, age, performance status [not available in ICON2], extent of residual disease after debulking surgery, histologic cell type, histologic grade (cell differentiation), and International Federation of Gynecology and Obstetrics [FIGO] stage), treatment assigned by randomization, and the outcome of interest (date of death or last visit and survival status). Survival time was considered from the day of random treatment assignment to the day of death regardless of the cause of death. Table 1  compares some characteristics of the meta-analysis9 with the ICON2 trial.10 The dose of carboplatin in the ICON2 study was determined using the area under the curve method of Calvert et al11 to find the optimally tolerated dose for each patient.
Statistical Analysis All analyses were based on individual patient data using an intent-to-treat approach. Observed survival curves were estimated using the product-limit method and compared using the log-rank test, as in the original publications on the meta-analysis and the ICON2 trial.6,10 For the meta-analysis, the log-rank test was stratified by trial. A proportional hazards regression model was fitted on the data of the meta-analysis, starting from the full model with all baseline characteristics and treatment, and eliminating covariates from the model using a step-down procedure.12 Patients with missing values for the retained covariates were excluded from the estimation of the model parameters. The model was then used to construct the expected survival curve for each treatment arm of the ICON2 trial; that is, the curve one would have observed if the estimated model were correct and the mortality rate of the corresponding treatment arm of the meta-analysis were operating.13,14 The expected survival curve was calculated by integrating the expected hazard rate over time, with the expected hazard rate at time t defined as the average of the hazards of all individuals who were still under observation at that time.14,15 The expected survival curve was compared with the observed survival curve at each time point through a nonparametric test.16 A Kolmogorov-Smirnov type test was used to assess the overall significance of any difference between the observed and expected curve.17 The level of statistical significance was set at P = .01.
Observed Survival Curves Figure 1 shows the survival curves for CP and CAP in the meta-analysis. The difference between the curves was statistically significant (HR = 0.84; P = .009). Figure 2 shows the survival curves for carboplatin and CAP in the ICON2 trial. There was no apparent difference between the curves (HR = 1.00; P = .98).
Prognostic Model for Survival Table 2 shows the distribution of prognostic factors in the meta-analysis and the ICON2 trial. The prognostic mix differed somewhat between the meta-analysis and the ICON2 trial, but treatment arms seemed to be well balanced with respect to all prognostic factors in both patient series. When all patients included in the meta-analysis were used, the prognostic model for survival included the following factors (P < .01): extent of residual disease (HR = 1.54; SE = 0.08), age as a continuous variable (HR = 1.018; SE = 0.003), histologic grade (HR = 1.17; SE = 0.06), FIGO stage (HR = 1.36; SE = 0.12), and treatment (HR = 0.83; SE = 0.06). Performance status was also significant (P < .01) but was not retained in the model because it had not been collected in the ICON2 trial. No interaction term between any of the factors was statistically significant. Of the 1,198 patients included in the meta-analysis, 1,054 had complete data for the factors included in the model.
Expected Survival Curves With this prognostic model for survival, expected survival curves could be constructed for any combination of the prognostic factors retained as significant in the model. Figure 3 shows the expected survival curves for 1,387 patients entered on the ICON2 trial, under three different assumptions: (1) who had complete data for the factors used in the model, using actually observed values of the prognostic factors (actual); (2) if all the patients had the best possible values for all prognostic factors in the model: no residual disease, age of 18 years, well-differentiated histology, and FIGO stage I (best); and (3) if all the patients had the worst possible values for all prognostic factors in the model: bulky residual disease, age of 85 years, poorly differentiated histology, and FIGO stage IV (worst). In all three cases, the original treatment assignment of the patients was used. Figure 3 illustrates that the expected survival curve depends heavily on the prognostic factors. The actual curve reflects the distribution of the prognostic factors in the ICON2 study presented in Table 2 . Both the worst and best curves are markedly different from the actual curve; the 5-year survival probabilities are 30% for the patients actually entered onto the ICON2 trial (Table 2) versus 85% for a patient with the best characteristics and close to 0% for a patient with the worst characteristics.
Comparison of Observed and Expected Survival Curves Expected survival curves were also constructed separately for each treatment arm of the ICON2 trial for the combination of the prognostic factors actually observed in that arm of the trial. Figure 4 shows the observed and expected survival curve in the CAP arm of the ICON2 trial. There was relatively little difference between the expected and observed curves. Figure 5 shows the observed survival curve in the carboplatin arm of the ICON2 trial and the expected survival curve using the CP arm of the meta-analysis. There was a large difference between the expected and the observed curves in favor of the carboplatin arm of the ICON2 trial. Figure 6 shows the test statistic comparing the observed and the expected survival curves over time. There was a tendency for the observed and expected survival curves for CAP to differ between 1 and 3 years, but the separation between them was not statistically significant. In contrast, the observed survival curve for carboplatin and the expected survival curve for CP differed significantly at all times after approximately 1.25 years (P < .01).
These analyses provide highly suggestive evidence that the difference between the survival comparisons in the meta-analysis and in the ICON2 trial is because of the better results achieved with carboplatin alone at an optimally tolerated dose compared with the CP combination at a cisplatin dose of 50 to 60 mg/m2. Indeed, after all known covariates were taken into account, the survival curve of the CAP arm in the ICON2 trial was close to the curve that would have been expected had the mortality rates seen in the CAP arm of the meta-analysis been operating (Fig 4 ). The two curves were only slightly separated by the play of chance between 1 and 3 years. In contrast, the survival curve of the carboplatin arm in the ICON2 trial was much better than the curve that would have been expected had the mortality rates seen in the CP arm of the meta-analysis been operating (Fig 5). The separation between the two curves was highly significant at all times after 1.25 years (P < .01; Fig 6). Although the comparison between carboplatin and CP is indirect and, therefore, far less reliable than a direct comparison between randomized arms, it is calibrated by the presence of a common CAP arm that exhibited similar survival in both the meta-analysis and the ICON2 trial. Taken together, the results of the meta-analysis and of the ICON2 trial indicate that the dose of platinum may be important. Direct evidence from randomized trials comparing doses of platinum, however, is inconclusive because of major differences between the trials, insufficient numbers of observations, and the play of chance.18 Our results also indicate that the addition of an anthracycline to CP might compensate for the insufficient dose of platinum in the CP arm. Other trials that are ongoing will provide further evidence on any added benefits of anthracyclines.19
The comparison of survival curves across different experiments requires knowledge of prognostic factors for individual patients in both experiments.20 Indeed, as shown in Fig 3
The data available in this study included survival as well as important prognostic information in both the meta-analysis and the ICON2 trial. Without such data, there would have been no reliable way of comparing the survival results of the meta-analysis with the results of the ICON2 trial because these series had different distributions of prognostic factors known to have a major impact on survival (Table 2
Although the results presented here may be particularly clear-cut because the two CAP groups exhibited almost identical results, the expected survival approach may provide a generally useful approach to reconcile the results of independent randomized trials of similar therapies. This approach may provide valuable insight when direct comparisons between randomized groups yield ambiguous or discrepant results. A case in point concerns the role of taxanes in the treatment of advanced ovarian cancer. Two trials, one conducted by the Gynecologic Oncology Group in the United States21 and the other conducted by a European Canadian Intergroup,22 showed that the combination of cisplatin and paclitaxel was superior to CP. The recently published ICON3 trial23 found no benefit of the combination of carboplatin and paclitaxel over either carboplatin alone or CAP (Table 3
We thank Bent Nielsen and Erik Christensen for useful advice, the ICON Collaborators and the Ovarian Cancer Meta-Analysis Project for sharing individual patient data on which all analyses presented in this article were based, and two reviewers for numerous useful comments. The SAS programs used to calculate expected survival curves and to test these against observed survival curves are available from the second author, Tomasz Burzykowski (email: tomasz.burzykowski{at}luc.ac.be).
1. Collins R, Gray R, Godwin J, et al: Avoidance of large biases and large random errors in the assessment of moderate treatment effects: The need for systematic overviews. Stat Med 6:245–250, 1987[Medline] 2. Villar J, Carroli G, Belizan JM: Predictive ability of meta-analyses of randomised controlled trials. Lancet 345:772–776, 1995[CrossRef][Medline]
3. LeLorier J, Grégoire G, Benhaddad A, et al: Discrepancies between meta-analyses and subsequent large randomized, controlled trials. N Engl J Med 337:536–542, 1997
4. Cappelleri JC, Ioannidis JPA, Schmid CH, et al: Large trials vs meta-analysis of smaller trials: How do their results compare? J Am Med Assoc 276:1332–1338, 1996
5. Ioannidis JPA, Cappelleri JC, Lau J: Meta-analyses and large randomized, controlled trials. N Engl J Med 338:59, 1998 (letter) 6. Ovarian Cancer Meta-Analysis Project: Cyclophosphamide plus cisplatin versus cyclophosphamide, doxorubicin and cisplatin chemotherapy of ovarian carcinoma: A meta-analysis. J Clin Oncol 9:1668–1674, 1991[Abstract] 7. Ghersi D, Parmar MKB, Stewart LA, et al: Early ovarian cancer and the ICON trials. Eur J Cancer 28A:1297, 1992[CrossRef][Medline]
8. Advanced Ovarian Cancer Trialists Group: Chemotherapy in advanced ovarian cancer: An overview of randomised clinical trials. Br Med J 303:884–893, 1991 9. Ovarian Cancer Meta-Analysis Project: Cyclophosphamide plus cisplatin versus cyclophosphamide, doxorubicin and cisplatin chemotherapy of ovarian carcinoma: A meta-analysis. Classic Papers Current Comments 3:237–243, 1998 10. The ICON Collaborators: ICON-2: A randomised trial of single-agent carboplatin against the 3-drug combination of CAP (cyclophosphamide, doxorubicin and cisplatin) in women with ovarian cancer. Lancet 352:1571–1576, 1998[CrossRef][Medline] 11. Calvert AH, Newell DR, Gumbrell LA, et al: Carboplatin dosage: Prospective evaluation of simple formula based on renal function. J Clin Oncol 7:1748–1756, 1989[Abstract] 12. Cox DR: Regression models and life tables. J R Stat Soc B 34:187–220, 1972 13. Thomsen BL, Keiding N, Altman DG: A note on the calculation of expected survival. Stat Med 10:733–738, 1991[Medline] 14. Therneau TM, Grambsch PM: Expected survival, in Modelling Survival Data: Extending the Cox Model. New York, NY, Springer-Verlag, 2000 15. Andersen PK, Vaeth M: Simple parametric and nonparametric models for excess and relative mortality. Biometrics 45:523–535, 1989[CrossRef][Medline] 16. Nielsen B: Expected survival in the Cox model. Scand J Stat 24:275–287, 1997[CrossRef] 17. Schumacher M: Two sample tests of Cramér-von Mises and Kolmogorov-Smirnov type for randomly censored data. Int Stat Rev 52:263–281, 1984
18. Thigpen JT: Dose-intensity in ovarian carcinoma: Hold, enough? J Clin Oncol 15:1291–1293, 1997 19. Vermorken JB, Harper PG, Buyse M: The role of anthracyclines in epithelial ovarian cancer. Ann Oncol 10:S43–S50, 1999 (suppl 1)[CrossRef] 20. Simon R: Importance of prognostic factors in cancer clinical trials. Cancer Treat Rep 68:185–192, 1984[Medline]
21. McGuire WP, Hoskins WJ, Brady MF, et al: Cyclophosphamide and cisplatin compared with paclitaxel and cisplatin in patients with stage 3 and 4 ovarian cancer. N Engl J Med 334:1–6, 1996
22. Piccart MJ, Bertelsen K, James K, et al: Randomized Intergroup trial of cisplatin-paclitaxel versus cisplatin-cyclophosphamide in women with advanced epithelial ovarian cancer. J Natl Cancer Inst 92:699–708, 2000 23. The International Collaborative Ovarian Neoplasm (ICON) Group: Paclitaxel plus carboplatin versus standard chemotherapy with either carboplatin or cyclophosphamide, doxorubicin and cisplatin in women with ovarian cancer: The ICON3 randomized trial. Lancet 360:505–515, 2002[CrossRef][Medline] 24. Sandercock J, Parmar MKB, Torri V, et al: First-line treatment for advanced ovarian cancer: Paclitaxel, platinum and the evidence. Br J Cancer 87:815–824, 2002[CrossRef][Medline] Submitted April 17, 2001; accepted December 30, 2002.
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Copyright © 2003 by the American Society of Clinical Oncology, Online ISSN: 1527-7755. Print ISSN: 0732-183X
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ABSTRACT
INTRODUCTION
