Relapse-Free Survival

Relapse-Free Survival as a Trial Endpoint and Model Input

Relapse-free survival (RFS) is the endpoint most adjuvant and curative-intent trials use to show that a treatment keeps disease away, and it often reaches a result years before overall survival does. For economic evaluation it supplies the curve that separates patients who remain free of disease from those who relapse, which drives costs, quality of life and survival in the model. Its value depends on a clear time origin and a clear list of events, because trials differ on both, and an RFS curve that starts the clock at a different point from the model can misstate the benefit.

Time origin and events in relapse-free survival

In a randomised trial the clock starts at randomisation. The FDA guidance on clinical trial endpoints for cancer drugs defines disease-free survival, the closely related endpoint that many trials report under the name relapse-free or recurrence-free survival, as the time from randomisation until disease recurrence or death from any cause. Starting at randomisation keeps the comparison fair, since both arms are followed from the same point and every patient counts, including those who relapse or die during treatment. In non-randomised studies the start must be another stated event, such as the date of surgery or the start of treatment, and it should be the same for every group compared.

Starting the clock when treatment ends is not the standard origin. It drops patients who relapse or die during treatment and makes arms with treatments of different length incomparable. The events also need stating. Trials differ on whether second primary cancers and deaths without relapse count as events, which is why consensus projects such as STEEP in breast cancer and DATECAN across cancers have proposed standard definitions.

How RFS is estimated

RFS is a time-to-event outcome, so it is estimated with survival methods that allow for censoring. The survival function gives the probability of remaining alive and free of relapse beyond each time.

$$S_{\text{RFS}}(t) = \Pr(T > t), \qquad T = \min(T_{\text{relapse}}, T_{\text{death}})$$

where $T$ is the time from the origin to the first of relapse or death, and patients who are alive and relapse-free at their last assessment are censored at that time. The Kaplan-Meier estimator gives the curve, a hazard ratio from a Cox model summarises the comparison between arms, and median RFS or RFS at fixed times such as three years summarise each arm.

Worked example of how the time origin changes RFS

The figures in this example are illustrative. A trial randomises 500 patients to six months of adjuvant treatment. During treatment 20 patients relapse or die, and 36 months after randomisation 390 patients are alive and free of relapse, with no censoring for simplicity.

$$S_{\text{RFS}}(36 \text{ months from randomisation}) = \frac{390}{500} = 0.78$$

where every randomised patient is in the denominator. Counting instead from the end of treatment, only the 480 patients who finished treatment free of relapse are followed, and the same 390 patients are relapse-free 30 months later.

$$\frac{390}{480} = 0.8125$$

where the 20 early events have disappeared from the analysis. The same patients give an RFS about 3 percentage points higher, and if a comparator arm had a shorter treatment period the two arms would be measured from different points. Using the randomisation origin avoids both problems.

RFS in economic models

In a partitioned survival model for an adjuvant setting, the RFS curve gives the proportion relapse-free at each cycle, the overall survival curve gives the proportion alive, and the gap between them is the post-relapse state. In a state transition model, RFS data are split into transitions to relapse and to death without relapse. Either way the RFS curve usually has to be extrapolated beyond the trial, and Latimer sets out how parametric survival models should be fitted, compared and checked for plausibility for that purpose.

The model's time origin should match the trial's. If the model starts at the decision to treat, which in a trial corresponds to randomisation, an RFS curve measured from the end of treatment would overstate time relapse-free. Some adjuvant settings show a plateau in RFS, which may suggest cure for part of the cohort, and a cure model can then describe the curve better than standard parametric forms.

RFS and related endpoints

RFS combines relapse and death, so it differs from overall survival, which counts deaths only, and from the time to recurrence, which counts relapse only and censors deaths without relapse. Event-free survival in the FDA guidance applies when randomisation takes place before surgery or radiotherapy and also counts progression that rules out surgery. Progression-free survival is the counterpart for patients with disease already present, and the endpoint names are not used consistently across trials, so the protocol definition matters more than the label.

Limitations of relapse-free survival

RFS is a surrogate endpoint for overall survival in many settings, and a gain in RFS does not always become a gain in survival, for example when effective treatment after relapse is available. Detection of relapse depends on how often patients are assessed, so different follow-up schedules between arms can bias the comparison. Treating RFS from different trials as comparable without checking their origins and event lists is a frequent error in evidence synthesis and modelling.

Sources

• US Food and Drug Administration. Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics. Guidance for Industry. December 2018.
• Hudis CA, Barlow WE, Costantino JP, et al. Proposal for standardized definitions for efficacy end points in adjuvant breast cancer trials: the STEEP system. Journal of Clinical Oncology. 2007;25(15):2127-2132.
• Bellera CA, Pulido M, Gourgou S, et al. Protocol of the Definition for the Assessment of Time-to-event Endpoints in CANcer trials (DATECAN) project: formal consensus method for the development of guidelines for standardised time-to-event endpoints' definitions in cancer clinical trials. European Journal of Cancer. 2013;49(4):769-781.
• Latimer NR. Survival analysis for economic evaluations alongside clinical trials: extrapolation with patient-level data. Medical Decision Making. 2013;33(6):743-754.
• Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. Journal of the American Statistical Association. 1958;53(282):457-481.