Rank Preserving Structural Failure Time Model (RPSFTM) to account for treatment crossover

In a previous post "Treatment crossover in parallel-group, randomized, controlled clinical trials", treatment crossover was discussed. Treatment crossover (or treatment switching) occurs when patients switch from their randomized arm to the other treatment during the study. In handling the treatment crossover, the naïve approaches (such as ITT analysis, exclusion of the treatment crossover subjects, and censoring at the time of the crossover) can cause a biased estimate of the treatment difference. More sophisticated approaches are needed to handle the treatment crossover. One of these approaches is called 'Rank Preserving Structure Failure Time Model (RPSFTM)". 

RPSFTM method was proposed by Robins and Tsiatis (1991) in their paper "Correcting for Non-Compliance in Randomized Trials Using Rank Preserving Structure Failure Time Models". The RPSFTM is a method used to adjust for treatment switching in trials with survival outcomes. The method is randomization based and uses only the randomized treatment group, observed event times and treatment history in order to estimate a causal treatment effect. The treatment effect is estimated by balancing counter-factual event times (i.e. the time that would be observed if no treatment were received) between treatment groups. 

We are seeing examples of RPSFTM application in oncology trials (especially open-label randomized trials) and in rare disease clinical trials. 

Hussain et al (2022) published a paper on NEJM "Survival with Olaparib in Metastatic Castration-Resistant Prostate Cancer". The results were from an open-label, phase 3 trial where patients were randomly assigned in 2:1 ratio to receive olaparib or physician's choice of enzalutamide or abiraterone plus prednisone as the control therapy. Patients in the control therapy group were allowed to be crossed over to olaparib after imaging-based disease progression criteria were met. Overall survival was analyzed using the naïve approach (intention-to-treat approach). Sensitivity analysis using the RPSFTM method was then performed to adjust for control patient crossover to olaparib.  Kaplan-Meier plots for the observed data and for crossover-adjusted analysis were depicted below: 

EISAI's Lenvatinib was approved for the treatment of patients with progressive, radioiodinerefractory differentiated thyroid cancer. The NDA approval was based on a pivotal study (Study 303). Study 303 is an international, double-blind, randomized 2:1, placebo-controlled, parallel-group, 2-arm trial. Patients would receive lenvatinib or placebo daily and could be treated until disease progression confirmd by IIR (RECIST v1.1) or unacceptable toxicity. The primary endpoint was progression-free survival with secondary endpoints of ORR and overall survival. Patients randomized to the placebo arm who had confirmed progression could choose to cross over and receive open-label lenvatinib. Overall survival was analyzed with the pooled data from the randomized portion of the study and the optional open-label extension phase. The effect of lenvatinib on overall survival was potentially confounded by the crossover of 83% of patients on the placebo arm to receive lenvatinib in the optional open-label (OOL) extension Phase.

The rank preserving structural failure time (RPSFT) model was then used in OS analysis to correct the bias introduced by cross-over and estimate the true treatment effect on OS. Here is the reference of RPSFT in the FDA's statistical review:

Amylyx's RELYVRIO was approved by FDA for the treatment of ALS. The approval was based on a pivotal study (CENTAUR) and its open-label extension study (CENTAUR-OLE). The pivotal CENTAUR study was a randomized, placebo-controlled, double-blind, 24-weeks study in patients with ALS. Patients who completed 24-week randomized treatment were rolled over to an open-label extension study where all patients received the active drug. Patients in the active drug group in the randomized trial would continue with the active drug in the open-label extension study; patients in the placebo group in the randomized trial would switch or cross over to the active drug. To provide substantial evidence of the effectiveness of the active drug, the sponsor performed the analyses for long-term overall survival with the combined data from the randomized study and the open-label extension study. RPSFTM method was employed to handle the switch or crossover of the placebo patients in the randomized study to active drug in the OLE. Here is the description of the RPSFTM analysis from the briefing book for FDA Adcom. 

The drug Uptravi was approved for the treatment of pulmonary arterial hypertension. The efficacy and safety were based on a pivotal study followed by an open-label extension study. The pivotal study was designed as an event-driven study where patients who had clinical worsening events would be rolled over to the open-label extension study. The placebo patients in the randomized study would switch or cross over the active drug in the open-label extension study. While the randomized study showed the treatment benefit in reducing the risk of clinical worsening events, there was an imbalance in the number of deaths (more death events in active drug group than the placebo group).  The analyses for long-term overall survival with the combined data from the randomized study and the open-label extension study became necessary to mitigate the concern about the imbalance in the number of deaths observed in the randomized trial. RPSFTM method was employed to handle the switch or crossover of the placebo patients in the randomized study to the active drug in the OLE. EMA's assessment report described the RPSFTM analyses. 

An add-on package (RPSFTM) publically available for fitting rank preserving structural failure time models is available for R (Bond and Allison, 2017), and can be installed from the CRAN web portal. A SAS program was written by Bradford J. Danner and Indrani Sarkarto to perform RPSFTM analysis
 

• R-package: https://cran.r-project.org/web/packages/rpsftm/vignettes/rpsftm_vignette.html
• Paper about R-package: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5858764/
• Danner and Sarkarto (2018) Implementing the Rank-Preserving Structural Failure Time Model in SAS® and R 

 Additional References: 

• Hollaender (2014) Methods to estimate survival time after treatment switching in oncology - overview and practical considerations
• Paganoni et al (2022) Survival analyses from the CENTAUR trial in amyotrophic lateral sclerosis: Evaluating the impact of treatment crossover on outcomes
• Latimer et al (2016) Adjusting for treatment switching in the METRIC study shows further improved overall survival with trametinib compared with chemotherapy
• Latimer and Abrams (2014) NICE DSU Technical Support Document 16: Adjusting Survival Time Estimantes in the Presence of Treatment Switching
• Korhonen et al (2012) Correcting Overall Survival for the Impact of Crossover via a Rank-Preserving Structural Failure Time (RPSFT) Model in the RECORD-1 Trial of Everolimus in Metastatic Renal-cell Carcinoma
• White et al (1999) Randomization-based Methods for Correcting for Treatment Changes: Examples from the CONCORDE Trial
• Locke et al (2022) Axicabtagene Ciloleucel as Second-Line Therapy for Large B-Cell Lymphoma
• Bidard et al (2022) Switch to fulvestrant and palbociclib versus no switch inadvanced breast cancer with rising ESR1 mutation duringaromatase inhibitor and palbociclib therapy (PADA-1):a randomised, open-label, multicentre, phase 3 trial
• Turner et al (2018) Overall Survival with Palbociclib and Fulvestrant in Advanced Breast Cancer
• Zhu et al (2021) Final Overall Survival Efficacy Results of Ivosidenib for Patients With Advanced Cholangiocarcinoma With IDH1 Mutation

Treatment crossover in parallel-group, randomized, controlled clinical trials

Randomized, controlled clinical trial (RCT) is the golden standard in drug development. RCTs are usually designed as parallel-group to compare the experimental treatment with a control group (usually the placebo). Eligible patients are randomized to one of the treatment arms (the experimental treatment or placebo). The patients who are randomized to the experimental treatment arm will receive the experimental treatment for the duration of the study and patients who are randomized to the placebo arm will receive the placebo for the duration of the study. 

There are situations where the treatment crossover is allowed by the protocol and the treatment crossover is usually one-sided (i.e., patients on the placebo arm crossed over to the experimental treatment arm, not patients on the experimental treatment arm crossed over to the placebo arm). Treatment crossover can be seen in oncology clinical trials (especially the open-label, randomized trials) or in rare disease clinical trials where the RCT is followed by an open-label extension study. 

In EMA's scientific guidance "Question and answer on adjustment for cross-over in estimating effects in oncology trials", the treatment crossover was described as the following:

In oncology trials, one-sided cross-over of control patients to the experimental treatment may occur, e.g. after progression. No objections from a methodological perspective exist against systematic crossover, where systematic means that there is an objective criterion which determines whether a control patient will cross over to the experimental treatment, or not. One example is when all control patients switch to experimental treatment at the same calendar time (e.g. after an interim analysis declaring superiority); however, this is provided that unconfounded overall survival (OS) data are not considered necessary to evaluate efficacy or safety. Another example of systematic cross-over is when by design a control patient must switch to experimental treatment when that patient experiences progression and the outcome is another measure than progression, e.g. OS, if it is justified to use this design. Nonsystematic cross-over can occur, for instance, when the study protocol allows cross-over after progression at the discretion of the investigator. This document addresses the situation where crossover of control patients is not systematic and there is interest in estimating the effect in the (hypothetical) situation that no cross-over would have occurred in the trial, under the assumption that the experimental treatment cannot introduce harm or deterioration of the condition under investigation in the control patients who cross over. In particular, it should be fully justified that this hypothetical effect is a relevant one for regulatory decision making. It should be noted that due to the uncertainties involved in the methods described below, such estimations should, at present, be used primarily as supportive or sensitivity analyses. 

The guidance defines the treatment crossover as systematic crossover and nonsystematic crossover:

• Systematic crossover is for clinical trials where there is an objective criterion which determines whether a control patient will cross over to the experimental treatment, or not
• Nonsystematic cross-over can occur, for instance, when the study protocol allows cross-over after progression at the discretion of the investigator

Systematic crossover can be seen in the following situations: 

• all control patients switch to experimental treatment at the same calendar time (e.g. after an interim analysis declaring superiority; at the time of study closure)
• individual patients switch to experimental treatment at a different time when patient experiences an event (progression, clinical worsening event, or complete the scheduled treatment duration)
• or a mixture of both situations above

In rare disease areas, the clinical development program usually includes an RCT followed by an open-label study. Because of the rarity of the patients and lack of alternative treatment options, clinical trial participants who complete the randomized portion of the study will be rolled over to an open-label extension (OLE) study where all patients receive experimental treatment. To consider the RCT portion and OLE portion of the study as a whole, the patients in the control arm are crossed over to the experimental treatment arm and the patients in the experimental treatment arm continue the experimental treatment (no crossover). By design, patients who receive the control in the RCT portion of the study cross over to experimental treatment in the OLE portion of the study, which is a perfect example of a systematic crossover. 

Amylyx conducted a phase 2 RCT with a fixed treatment duration (24 weeks) "Trial of Sodium Phenylbutyrate–Taurursodiol for Amyotrophic Lateral Sclerosis". Patients who completed 24 weeks of study treatment (Sodium Phenylbutyrate–Taurursodiol or placebo) were then rolled over a separate open-label extension study where all patients received Sodium Phenylbutyrate–Taurursodiol. Overall survival was analyzed using the combined data from both the RCT and the OLE studies. This can also be viewed as a one-sided crossover where all patients in the placebo arm crossed over to the experimental treatment arm in the OLE. In this case, individual patients switch to experimental treatment at different calendar times, but all after the scheduled RCT duration of 24 weeks. 

The RCT could also be designed as an event-driven study, patients who experienced an event would then be rolled over to the OLE study. Patients who do not experience an event would also be rolled over the OLE study at the RCT study closure when the total number of events was reached. This situation can also be viewed as a one-sided crossover where all patients in the placebo arm crossed over to the experimental treatment arm when they are rolled over to the OLE study. In this case, individual patients who experience an event switch to experimental treatment at different calendar times, but individual patients who do not experience an event switch to experimental treatment at the same calendar time after the total number of events are reached and the study is closed.  See the following examples: 

• Selexipag (ACT-293987) in Pulmonary Arterial Hypertension (GRIPHON)
• Long-term Single-arm Open-label Study, to Assess the Safety and Tolerability of ACT-293987 in Patients With Pulmonary Arterial Hypertension
• Phase III Clinical Worsening Study of UT-15C in Subjects With PAH Receiving Background Oral Monotherapy (FREEDOM-EV)
• An Open-Label, Long-Term Study of Oral Treprostinil in Subjects With Pulmonary Arterial Hypertension

Different approaches can be employed to analyze the data from clinical trials with one-sided treatment crossover. 

EMA's scientific guidance "Question and answer on adjustment for cross-over in estimating effects in oncology trials" mentioned the following methods:

Different statistical methods have been proposed to adjust overall survival for cross-over, including analysis censoring at time of cross-over, Inverse Probability of Censoring Weighting (IPCW), Rank Preserving Structural Failure Time models (RPSFT), and ‘two-stage’ methods.

In principle, these methods can (be adapted to) address different questions by formulating distinct estimands. For example, IPCW estimates the effect of the experimental treatment versus control as if cross-over by control group patients to the experimental treatment was absent but still includes subsequent therapies. Using RPSFT the analyst could choose the estimate to aim at the effect of experimental therapy only (effect of being ‘on experimental treatment’), but in practice the effect of experimental therapy and subsequent therapies (effect of ‘ever being treated’) is often estimated.

In a presentation by Norbert Hollaender "Methods to estimate survival time after treatment switching in oncology– overview and practical considerations", the following simple('naive') methods and complex methods were discussed:

Simple (‘naive’) methods 

• Intent to treat analysis: as randomized and ignoring that some patients switched
• Exclude treatment switchers: small sample size for control group; destroying the randomization; may produce biased results
• Censor switches at time of ‘cross-over’: informative censoring -> results may be biased
• Time-varying treatment variable: No longer a comparison between randomized Treatment vs. Control arm, more difficult interpretation

Complex methods 

• Inverse-probability-of-censoring weighting (IPCW) :
• Switchers are censored at ‘time point of cross-over’, but patients are weighted according to their probability to switch treatment.
• IPCW method artifically increases weights for patients with low probability of treatment switch and decreases weights for patients with high probability of treatment switch
• Rank Preserving Structural Failure Time (RPSFT) Model
• The RPSFTM models the counter-factual or treatment-free event time
• Estimate the survival time gained/lost by receiving active treatment

In practice, for clinical trial data containing patients with one-sided treatment crossover, the overall survival data may be analyzed using both RPSFT and IPCW methods. The results from different methods can then be compared. For example, in EMA's assessment report for Uptravi (selexipag), both RPSFT and IPCW methods were used to evaluate overall survival with the data from the RCT and the OLE studies. 

The applicant presented two analyses to explore the impact of cross-over from the placebo arm and treatment discontinuations in the selexipag arm on the mortality up to study closure. These are a Rank Preserving Structural Accelerated Failure Time Model (RPSFT Model) and an approach using a Marginal Structural Cox Proportional Hazards Model with time-dependent weights according to the Inverse Probability of Censoring Weighting (IPCW) scheme. For both approaches, the RPSFT and Structural Proportional Hazards Model analyses, patients were considered on “active treatment” if they were treated with selexipag or with an agent targeting the same pathway as selexipag. The number of patients in both treatment arms receiving prostacyclin and analogues with the same target as selexipag after study drug discontinuation was similar (40 in the selexipag arm, 44 in the placebo arm). Considering selexipag and agents targeting the same pathway as selexipag as “active treatment”, patients in the selexipag arm were about 85% of their observation time on active treatment and patients in the placebo arm were about 16% on active treatment.

The results RPSFT Model provide a valuable estimate of relative survival on active treatment compared to no treatment of 1.19 with a quite wide 95% confidence interval of (0.56, 2.05).

Using the Structural Proportional Hazards Model with IPCW weighting the estimate for the hazard ratio for death as if all patients had received active treatment compared to the situation if all patients had never received active treatment was 0.92 with a 95% confidence interval of (0.58, 1.47) for the 1 month time intervals, showing a slight advantage for treatment with selexipag. Both estimations with models with longer time intervals show non-significant lower hazard ratios (0.79 and 0.75).