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Journal of Clinical Oncology, Vol 26, No 24 (August 20), 2008: pp. 3913-3915 © 2008 American Society of Clinical Oncology. DOI: 10.1200/JCO.2008.16.1000
Analysis of Survival by Tumor Response and Other Comparisons of Time-to-Event by Outcome VariablesUniversity of Nebraska College of Public Health, Omaha, NE
University of Washington, Seattle, WA
Dana-Farber Cancer Institute and Harvard School of Public Health, Boston, MA Twenty-five years ago, in its first volume, the Journal of Clinical Oncology published our methodologic article,1 which highlighted an inappropriate analytic approach then in common use and suggested alternative unbiased techniques. Cited more than 380 times, this article and similar ones by other authors have had a large impact on how results from early-phase clinical trials are reported, almost completely eliminating so-called survival by tumor response analyses from the oncology literature. The success of treatments for patients with advanced cancers at diagnosis or recurrence is often assessed by computing overall response rates and survival from the start of treatment. Before 1983, analysis of survival by tumor response category was commonly included as part of the reports of these treatments. Patients were characterized as responders or nonresponders, estimates of survival from the start of treatment were calculated for each responder category, and differences in survival by these tumor response categories were compared using a significance test appropriate for time-to-event data. These analyses had been used to bolster the claim of benefit for the treatment, often as a surrogate for a randomized trial. Responders benefited from the therapy and thus constituted the treatment group. Nonresponders did not benefit, and thus their survival could be considered similar to that for untreated patients. Similarly, these analyses had also been used to argue that therapies that increase the response rate should necessarily result in increased survival. In March 1983, Weiss et al2 reported the results of a review of articles published in Cancer or Cancer Treatment Reports and found 228 articles presenting data on responders and nonresponders, with 61% containing formal statistical comparisons of survival by tumor response category. They identified problems in the interpretation of these comparisons. In November 1983, our article in the Journal of Clinical Oncology, "Analysis of Survival by Tumor Response," was published. We showed that the usual methods of comparing responders with nonresponders were wrong, leading to biased estimates of the survival distributions, invalid statistical tests, and misleading conclusions. This bias results in part from the fact that responders must live long enough for response to be observed; there is no such requirement for nonresponders. We described several valid approaches to comparing survival by response category. One approach, the landmark method, determines each patient's response at some fixed time point, with survival estimates calculated from that time point and associated statistical tests being conditional on patients’ landmark responses. Note that in this method, patients who die before the landmark time point are excluded from the analysis. An alternative approach treats response status as a time-dependent covariate, where all patients begin in the nonresponse state and patients move to the response state at the time of their response. Shortly thereafter, Simon and Makuch3 proposed a method of obtaining estimates of survival probabilities for responders and nonresponders, combining ideas from the landmark and time-dependent covariate approaches. Even when these analyses were performed appropriately, we argued that longer survival for responders, as compared with nonresponders, could not be used to conclude that response caused longer survival. Response might act as a surrogate marker for prognostically favorable patients. Thus responders may survive longer than nonresponders, not because of an effect of response on survival, but because response identifies patients with pretreatment characteristics that favor longer survival. It is generally difficult to distinguish between cases where response prolongs survival and cases where it simply acts as a marker for favorable-prognosis patients. In 1985, Cancer Treatment Reports indicated it would not publish comparisons of survival by tumor response.4 Notwithstanding the reports by Weiss et al2 and us, Anderson and Davis5 showed that between July 1984 and June 1985, the Journal of Clinical Oncology published 18 articles that included analyses of survival by tumor response, 10 of which provided inappropriate statistical comparisons of survival of responders and nonresponders. They suggested that the Journal of Clinical Oncology follow the lead of Cancer Treatment Reports and no longer publish articles that include survival by tumor response. An editorial accompanying the letter by the then-editor of the Journal of Clinical Oncology, Joseph Bertino, MD, indicated that "authors should not compare survival of responders and nonresponders without discussing the limitations of such a comparison".6 Although inappropriate analysis of survival by tumor response rarely appears in the current cancer literature, a few are still published (7; see also the letter to the editor and the authors’ response8). More often, assessment of the impact of response on outcome is made using appropriate statistical methods. For example, Bruzzi et al9 evaluated response to chemotherapy as a potential surrogate for survival in metastatic breast cancer. The authors used response as a time-dependent covariate in a proportional hazards model and generated survival curves using the method of Simon and Makuch.3 More recently, Lara et al10 from the Southwest Oncology Group assessed 8-week disease control as a predictor of clinical benefit in advanced non–small-cell lung cancer using landmark analyses and proportional hazards models to adjust for other prognostic factors. Analysis of survival by tumor response is an example of a wider class of analyses in which comparisons of survival or other time-to-event distributions are compared among patient subsets defined by other treatment outcome variables. Examples include comparisons by measures of treatment compliance (for instance, chemotherapy dose-intensity delivered (Bonadonna and Valagussa11) and by adverse event experience (eg, Sorensen et al12). Such comparisons of outcome by other outcomes of treatment share the same problems as analyses of survival by tumor response; the statistical issues inherent in these analyses have been previously addressed.13-15 Recent efforts by one of us (R.D.G.) to study the relationship of the length of adjuvant trastuzumab therapy to outcome in HER2-positive breast cancer illustrate some of the issues outlined here. Four large randomized trials have demonstrated that prescribing 1 year of adjuvant trastuzumab therapy significantly improves disease-free survival and overall survival compared with observation for patients with HER2-positive, early breast cancer.16-18 A small randomized trial suggested that adjuvant trastuzumab administered for as little as 9 weeks provides substantial efficacy of similar magnitude to that obtained from the longer duration regimen.19 In the HERA trial,16 approximately 8.5% of the 3,404 patients who were randomly assigned to receive at least 1 year of trastuzumab began therapy but discontinued early for reasons other than recurrence of disease (primarily related to decreases in left ventricular ejection fraction). Comparing patients who received shorter duration treatment with those who received the full regimen with respect to disease-free survival would be subject to bias similar to that seen with survival according to tumor response. A landmark analysis (with the landmark set at 1 year from study entry) was performed. However, many of the disease-free survival events occurred in the first year after randomization, and the trastuzumab treatment effect compared with observation was substantial during the first year.20 Thus the landmark analysis comparing short-term with longer-term trastuzumab had limited power, both because of the events lost in setting the landmark at 1 year and the small number of patients who received short-term trastuzumab treatment. Further complicating this analysis is the possibility that patients who discontinued trastuzumab may be either more or less at risk for treatment failure. Analysis of survival by tumor response and similar analyses in which the primary outcome is compared among patients defined by some other outcome (dose-intensity, compliance to treatment, adverse event experience) using standard statistical approaches measuring outcome from the start of treatment are statistically invalid and should not be used. Although appropriate statistical methods for investigating these relationships exist, they are no substitute for properly designed and conducted randomized trials. From the very beginning, the Journal of Clinical Oncology has been an important venue for methodologic articles such as ours related to the design, analysis, and interpretation of cancer clinical trials. Close collaboration between clinical and statistical scientists is essential to produce reliable evidence useful for patient care and future progress. We and our cancer biostatistician colleagues are grateful to the Journal of Clinical Oncology for the opportunity to contribute to this collaboration. AUTHORS’ DISCLOSURES OF POTENTIAL CONFLICTS OF INTEREST The author(s) indicated no potential conflicts of interest. AUTHOR CONTRIBUTIONS Conception and design: James R. Anderson, Richard D. Gelber Provision of study materials or patients: James R. Anderson, Richard D. Gelber Collection and assembly of data: James R. Anderson, Richard D. Gelber Data analysis and interpretation: James R. Anderson, Kevin Cain, Richard D. Gelber Manuscript writing: James R. Anderson, Kevin Cain, Richard D. Gelber Final approval of manuscript: James R. Anderson, Kevin Cain, Richard D. Gelber REFERENCES 1. Anderson JR, Cain KC, Gelber RD: Analysis of survival by tumor response. J Clin Oncol 1:710-719, 1983[Abstract] 2. Weiss GB, Bunce H III, Hokanson JA: Comparing survival of responders and non-responders after treatment: A potential source of confusion in interpreting cancer clinical trials. Control Clin Trials 4:43-52, 1983[Medline] 3. Simon R, Makuch RW: A non-parametric graphical representation of the relationship between survival and the occurrence of an event: Application to responder versus non-responder bias. Stat Med 3:35-44, 1984[Medline] 4. Simon R, Wittes RE: Methodologic guidelines for reports of clinical trials. Cancer Treat Rep 69:1-3, 1985[Medline] 5. Anderson JR, Davis RB: Analysis of survival by tumor response. J Clin Oncol 4:115-117, 1998 6. Bertino JR: Guidelines for reporting clinical trials. J Clin Oncol 4:1, 1986 7. Moreton P, Kennedy B, Lucas G, et al: Eradication of minimal residual disease in B-cell chronic lymphocytic leukemia after alemtuzumab therapy is associated with prolonged survival. J Clin Oncol 23:2971-2979, 2005 8. Anderson JR, Neuberg DS: Analysis of outcome by response flawed. J Clin Oncol 23:8122-8123, 2005 9. Bruzzi P, Del Mastro LD, Sormani MP, et al: Objective response to chemotherapy as a potential surrogate end point of survival in metastatic breast cancer. J Clin Oncol 23:5117-5125, 2005 10. Lara PN Jr, Redman MW, Kelly K, et al: Disease control rate at 8 weeks predicts clinical benefit in advanced non-small-cell lung cancer: Results from Southwest Oncology Group randomized trials. J Clin Oncol 26:463-467, 2008 11. Bonadonna G, Valagussa P: Dose-response effect of adjuvant chemotherapy in breast cancer. N Engl J Med 304:10-15, 1981[Abstract] 12. Sørensen JB, Hansen HH, Dombernowsky P, et al: Chemotherapy for adenocarcinoma of the lung (WHO III): A randomized study of vindesine versus lomustine, cyclophosphamide, and methotrexate versus all four drugs. J Clin Oncol 5:1169-1177, 1987 13. Henderson IC, Hayes DF, Gelman R: Dose-response in the treatment of breast cancer: A critical review. J Clin Oncol 6:1501-1515, 1988 14. Propert KJ, Anderson JR: Assessing the effect of toxicity on prognosis: Methods of analysis and interpretation. J Clin Oncol 6:868-870, 1988 15. Shuster JJ, Lieser PW: In reply to: Radiation in pediatric Hodgkin's disease. J Clin Oncol 16:393, 1998 16. Smith I, Procter M, Gelber RD, et al: 2-year follow-up of trastuzumab after adjuvant chemotherapy in HER2-positive breast cancer: A randomized controlled trial. Lancet 369:29-36, 2007[CrossRef][Medline] 17. Romond EH, Perez EA, Bryant J, et al: Trastuzumab plus adjuvant chemotherapy for operable HER2-positive breast cancer. N Engl J Med 353:1673-1684, 2005 18. Slamon D, Eiermann W, Robert N, et al: BCIRG 006: 2nd interim analysis phase III randomized trial comparing doxorubicin and cyclophosphamide followed by docetaxel with doxorubicin and cyclophosphamide followed by docetaxel and trastuzumab with docetaxel, carboplatin, and trastuzumab (TCH) in Her2neu positive early breast cancer patients. 29th Annual San Antonio Breast Cancer Symposium, December 14-17, 2006, San Antonio, TX (abstr 52). http://www.abstracts2view.com/sabcs06/view.php?nu=SABCS06L_78 19. Joensuu H, Kellokumpu-Lehtinen PL, Bono P, et al: Adjuvant docetaxel or vinorelbine with or without trastuzumab for breast cancer. N Engl J Med 354:809-820, 2006 20. Untch M, Gelber RD, Jackisch C, et al: Estimating the magnitude of trastuzumab effects within patient subgroups in the HERA trial. Ann Oncol [epub ahead of print on February 21, 2008]
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Copyright © 2008 by the American Society of Clinical Oncology, Online ISSN: 1527-7755. Print ISSN: 0732-183X
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