A, Kaplan-Meier curves of progression-free survival (PFS) for chemotherapy and crizotinib. B, Restricted mean P/D event-free time up to month 30: the shaded area under the Kaplan-Meier curve of PFS for crizotinib. C, Restricted mean P/D/R event-free time up to month 30: the shaded area under the Kaplan-Meier curve of time to P/D/R for crizotinib. D: Restricted mean DOR for crizotinib up to month 30: the shaded area between the 2 Kaplan-Meier curves in panels B and C.
Possible patterns (without censoring) of times to response (R) and progression/death (P/D) up to month 30.
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Huang B, Tian L, Talukder E, Rothenberg M, Kim DH, Wei L. Evaluating Treatment Effect Based on Duration of Response for a Comparative Oncology Study. JAMA Oncol. 2018;4(6):874–876. doi:10.1001/jamaoncol.2018.0275
Quantitative procedures for analyzing data for progression-free survival (PFS) and overall survival are generally well established. However, it is not clear how to analyze data efficiently for duration of response (DOR), a clinically important end point that is related to quality of life and is endorsed by regulatory agencies for drug evaluation.1,2 Duration of response is the time from response (R) to progression/death (P/D). The existing statistical procedures for DOR are valid when certain model assumptions are correctly specified.3 Therefore, in a typical report of a clinical study, DOR is summarized descriptively. Moreover, the Kaplan-Meier curves (KMCs) to estimate the distribution of DOR are generally based on observations from responders and may be biased owing to dependent censoring.2 Here, we present a simple, intuitive procedure to estimate mean DOR in a time window for which KMCs for PFS are well defined. We illustrate this method with data from a clinical trial, PROFILE-1014, to evaluate crizotinib vs chemotherapy for patients with ALK-positive lung cancer.4
In Figure 1A, we present KMCs of PFS. The PFS was significantly longer with crizotinib than with chemotherapy (F, 0.45; 95% CI, 0.35-0.60; P < .001). Furthermore, the objective response rates for crizotinib and chemotherapy were 74% and 45%, respectively. Because there is little information regarding PFS beyond month 30 for either arm, we analyzed data by month 30. When a PFS time is not censored before month 30, possible patterns of time to R and P/D and the corresponding DORs are shown in Figure 2. For case 1, R and P/D occurred at month 3 and month 12, and the DOR was 9 months. For case 2, R occurred at month 9 and the patient was P/D-free at month 30, DOR before month 30 was 21 months. For cases 3 and 4, patients did not respond during the study, therefore, DOR was 0. In general, if we let P/D/R be a composite endpoint (ie, first of progression, death, or response), DOR is PFS time minus P/D/R event-free time and its mean can be estimated over 30 months accordingly.
For crizotinib, the restricted mean PFS time up to month 30 was the area under the KMC for PFS in Figure 1B. Likewise, the counterpart for P/D/R-free was the area under the KMC in Figure 1C. This simple estimation procedure for restricted mean event-free time has been discussed extensively.5,6 The restricted mean DOR for crizotinib was therefore the area between 2 KMC’s in Figure 1D, which was 10.4 months. That is, on average, future patients treated by crizotinib would have 10.4-month DOR over a 30-month follow-up. The corresponding DOR for chemotherapy would be 3.0 months. Over 30-month follow-up, the mean difference of DOR was 7.4 months (95% CI, 6.0-8.8 months; P < .001). This result, coupled with the mean DOR of 3.0 months for chemotherapy as reference, provides clinically interpretable treatment effect for crizotinib.
The DOR, which collectively uses information from R and P/D, is underused in practice partly owing to lack of a reliable estimation procedure that does not require strong modeling assumptions. If we compare DOR times between crizotinib and chemotherapy among responders, owing to the higher objective response rate in the crizotinib arm, it would undermine the treatment benefit with respect to DOR. A caveat for our proposal is that mean DOR depends on a specific time window that can be preselected based on clinical consideration. Empirically one may choose the largest possible time window beyond which a small proportion of patients (eg, 2%) remain at risk for P/D. Like other procedures such as hazard ratio estimation, this time window constraint may not be avoidable without a parametric model for extrapolation. Lastly, it can be quite informative to examine the temporal treatment effect profile by choosing several time windows to estimate restricted mean differences in DOR.
Corresponding Author: Lee-Jen Wei, PhD, Department of Biostatistics, Harvard University, 655 Huntington Ave, Boston, MA 02115 (firstname.lastname@example.org).
Accepted for Publication: January 22, 2018.
Published Online: April 19, 2018. doi:10.1001/jamaoncol.2018.0275
Author Contributions: Dr Huang had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Drs Huang and Tian contributed equally to the work.
Study concept and design: Wei, Huang, Tian, Rothenberg.
Acquisition, analysis, or interpretation of data: All authors.
Drafting of the manuscript: Wei, Huang, Tian, Talukder, Rothenberg.
Critical revision of the manuscript for important intellectual content: Wei, Huang, Tian, Rothenberg, Kim.
Statistical analysis: Wei, Huang, Tian.
Administrative, technical, or material support: Huang, Talukder.
Study supervision: Wei, Rothenberg.
Conflict of Interest Disclosures: Drs Huang, Talukder, and Rothenberg are employees and stock holders of Pfizer Inc. No other conflicts are reported.
Funding/Support: This research was partially supported by US National Institutes of Health grants and contracts. The procedure presented here is implemented via computer code available in (https://web.stanford.edu/~lutian/Software.HTML).
Role of the Funder/Sponsor: The National Institutes of Health had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.
Additional Contributions: We thank Timothy Kluge, MS, Tiziana Usari, BS, and Paulina Selaru, MS, all at Pfizer, for providing the PROFILE-1014 data. None were compensated.
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