Key points for decision makers
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• In 168 pivotal oncology RCTs (270 contrasts), landmark analyses at 2, 3, 4, and 5 years showed that post-landmark HRs generally remained below 1 and corresponding median RMSTRs remained above 1 for both OS and non-OS end points.
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• RMSTR showed lower dispersion than HR across long-term landmarks and greater stability across data updates, especially when proportional hazards was violated. As an RMST-based relative measure, it is naturally aligned with cost-effectiveness modeling and provides a more reliable basis for extrapolation and TEW specification than the HR.
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• Longer-term RMSTR was accurately predictable from early trial data using regularized models, with conformal 90-percent prediction intervals achieving 91 percent (OS) and 96 percent (non-OS) coverage. This allows analysts to derive an empirically grounded “update expectation” at the time of initial HTA submission, replacing arbitrary waning rules with data-driven uncertainty bounds.
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• We provide a stepwise workflow that uses the predicted RMSTR interval as an external anchor to screen extrapolation models and calibrate TEW assumptions, supporting a shift from precedent-driven hazard-scale convergence rules toward transparent, evidence-based survival extrapolation in oncology economic evaluations.
Introduction
In oncology health technology assessment (HTA), the validity of cost-effectiveness results depends heavily on how survival is projected beyond the trial period, since much of the additional cost and health benefit occurs after observed follow-up and substantially shapes estimated quality-adjusted life years (QALYs) and the incremental cost-effectiveness ratio (ICER) (Reference Latimer1;Reference Ouwens, Mukhopadhyay, Zhang, Huang, Latimer and Briggs2). In practice, coverage and reimbursement decisions are frequently taken while randomized controlled trials (RCTs) still have limited survival maturity, leaving extrapolation models to extend outcomes past the data and to impose assumptions about whether the comparative effect is maintained over time (Reference Latimer1;3).
One particularly influential – and often debated – assumption concerns treatment effect waning (TEW), whereby the initial relative benefit diminishes with time and outcomes in the intervention and comparator arms tend to converge, creating material uncertainty for decision making (Reference Taylor, Latimer and Douglas4;Reference Trigg, Melendez-Torres, Abdelsabour and Lee5). Findings from the National Institute for Health and Care Excellence (NICE) appraisal programme suggest that TEW is frequently raised in deliberations, yet handled in a non-standardized manner. In Trigg et al.’s review of 104 NICE appraisals, TEW was incorporated in the base case in 27.9 percent of evaluations; when TEW was discussed, 93.2 percent assessed at least one TEW scenario analysis (Reference Trigg, Melendez-Torres, Abdelsabour and Lee5). Across appraisals, TEW was operationalized in diverse ways, including stepwise versus gradual waning and application to different end points and patient subgroups. The landmark (switch-point) used to impose TEW, often by setting the HR to 1 beyond about 2–5 years, has typically been chosen on pragmatic grounds rather than empirical evidence (Reference Taylor, Latimer and Douglas4;Reference Trigg, Melendez-Torres, Abdelsabour and Lee5). TEW remains contentious in oncology partly because successive trial updates often show HRs moving toward the null (“slippage”). Slippage can reflect several non-exclusive processes – including depletion of susceptibles, treatment resistance, fixed-duration stopping rules, and differential access to effective subsequent therapies – so it does not, by itself, confirm a biological waning mechanism. Nonetheless, it highlights substantial uncertainty in long-term comparative effectiveness and motivates explicit consideration of TEW in extrapolation modeling (Reference Hernán6).
Restricted mean survival time (RMST) is the mean time survived up to a prespecified truncation horizon τ, which directly yields difference in RMST (RMSD; experimental/control) and RMST ratio (RMSTR; experimental/control) (Reference Royston and Parmar7;Reference Uno, Claggett and Tian8). Although TEW modeling in oncology HTA is most often implemented on the hazard scale (Trigg et al.), oncology economic evaluations typically fit survival models separately for each arm and derive mean life-years from the resulting survival functions (3), making RMST-based summaries closely aligned with the quantities used in cost-effectiveness models. Methodological work has also noted that the HR can suggest a larger treatment effect than RMSTR and may appear large even when the absolute effect is small, while HR estimates can be unstable when evidence is immature (Reference Trinquart, Jacot, Conner and Porcher9;Reference Lin, Hsu and Chiou10). Evidence specifically assessing the stability of RMSTR remains limited.
This study had three objectives. First, we examined long-term treatment-effect patterns in the context of TEW modeling, providing the HR-based evidence for subsequent comparison with RMSTR. Second, we compared HR- versus RMSTR-based evidence under longer follow-up by evaluating the dispersion of the estimands and the stability of their update-related changes, with the aim of identifying a more reliable metric to inform survival extrapolation and TEW specification in economic models. Third, building on these findings, we developed prediction models for longer-term RMSTR across time-to-event end points (e.g., OS) to provide a practical, data-driven basis for extrapolation model selection and TEW modeling in future oncology cost-effectiveness evaluations.
Method
Evidence identification and study selection
Using the FDA Hematology/Oncology Approvals Database, we enumerated all US FDA oncology drug approvals issued between January 2006 and September 2025 and identified the phase II/III randomized controlled trials underpinning each approval. To study how efficacy estimates evolve with longer follow-up, we required that each trial had at least one later results update; if several updates were available, we analyzed only the latest report.
We focused on overall survival (OS) and other time-to-event efficacy outcomes, including progression-free survival and disease-free/relapse-free/event-free survival (combined as non-OS). Studies were not eligible if they provided hazard ratios without Kaplan–Meier plots, or if Kaplan–Meier plots were shown without accompanying numbers at risk, because both components are needed to support reconstruction of individual patient-level time-to-event data. We also removed approvals outside oncology and those pertaining to supportive care or diagnostic indications.
Trial reports and registry entries were identified through searches of MEDLINE and ClinicalTrials.gov using NCT identifiers, drug names, and disease indications. Two investigators (MZ and HS) independently screened all records using prespecified criteria, resolving any discrepancies by consensus.
Database assembly and IPD reconstruction
Data were abstracted in parallel by six investigators (MZ, HQ, YJ, YN, LY, and HF). For each eligible trial, we captured core design characteristics (trial phase, blinding, allowance of crossover, and whether the experimental regimen included a prespecified fixed-duration stopping plan), treatment groups, cancer type/indication, sample size, follow-up duration, and time-to-event results reported at both the initial and the latest updated analyses. We further derived the information fraction (IF) as the ratio of observed events to the target number of events specified in the original sample-size/power assumptions.
Kaplan–Meier plots were digitized using DigitizeIt (v2.0.4), and individual patient-level time-to-event data were reconstructed following the method proposed by Guyot et al. (Reference Guyot, Ades, Ouwens and Welton11). Reconstruction quality was evaluated by comparing reconstructed and published numbers at risk and survival probabilities across follow-up. Reconstructions were required to meet all prespecified accuracy thresholds: root mean square error < .01, mean absolute error < .005, maximum absolute error < .01, and Kolmogorov–Smirnov test p > .9. These criteria were set more stringently than in prior work to enhance fidelity (Reference Liu, Zhou and Lee12). As an additional check, we required agreement between reconstructed and reported HRs using the absolute log (HR_reconstructed/HR_reported) ≤ .1. Two reviewers (MZ and HS) independently verified the reconstructed Kaplan–Meier curves against the source publications. If any criterion was not satisfied, digitization and reconstruction were repeated until all thresholds were met. The reconstructed IPD have been deposited at https://doi.org/10.17605/OSF.IO/X3TYV.
Post-landmark HR and RMSTR estimation and treatment effect changes
For the primary analysis, RMST was calculated separately for the experimental and control arms at each data cut using a data-cut-specific truncation time τ, defined as the earlier of the last observed event time in either arm. Accordingly, the initial and updated RMSTR estimates could be based on different values of τ. As a sensitivity analysis, we used the initial-data-cut τ as a common within-trial truncation horizon and recalculated the updated RMSTR at this horizon. Treatment effect was summarized using the RMSTR, with values greater than 1 indicating longer average survival (up to τ) in the experimental arm (Reference Royston and Parmar13).
Because the trial-level distributions of HRs and RMSTRs were non-normal, we summarized them using the median and interquartile range (IQR). Between-trial relative dispersion was compared using the coefficient of quartile relative dispersion (CQR) (Reference Bonett14). All landmark analyses were based on the updated reconstructed IPD. To evaluate potential late treatment effects, we prespecified landmark times at 2, 3, 4, and 5 years (chosen to align with commonly used time-to-event landmarking in HTA) (Reference Taylor, Latimer and Douglas4). For each landmark time t0 and within each trial, we implemented a delayed-entry (left-truncation) design: analyses were restricted to participants who remained event-free and under observation beyond t0 (i.e. T > t0), and time was re-indexed to start at t0 (Reference Klein and Moeschberger15). Each analysis used the remaining available follow-up after t0; observations were not censored at the next landmark, and the resulting estimates did not represent mutually exclusive intervals.
For post-landmark HRs, we fit a Cox proportional hazards model in the post-t0 risk set with treatment group as the sole covariate; ties were handled using the Efron method. This yielded an HR for the period from t0 to the end of available follow-up (Reference Therneau and Grambsch16). For post-landmark RMSTRs, we estimated the RMST for each arm over [t0, τ] and summarized the treatment effect as the RMST ratio over the same interval. Trial-specific post-landmark HRs and RMSTRs at 2, 3, 4, and 5 years were then described across trials. Because the amount of late follow-up information differed substantially between trials, cross-trial summaries were weighted by the number of observed events occurring after each landmark. RMSTR was pre-specified as the primary relative-effect anchor because it is dimensionless and facilitates cross-trial comparison when interpreted at the corresponding trial-specific truncation horizon, and because it provides a ratio-scale counterpart to the HR. RMSD is measured in months and can be zero or negative, precluding the ratio-based stability metrics used in the primary framework, and was therefore reported as a complementary absolute-scale result.
Treatment-effect change was assessed at the trial level using two ratios: (i) updated-to-initial HR (rHR; > 1 indicates TEW with longer follow-up) and (ii) updated-to-initial RMSTR (rRMSTR; values < 1 are consistent with TEW). Because late follow-up information varied across trials, all analyses were weighted by the number of events accrued during the update segment. We summarized rHR and rRMSTR using event-weighted quartiles and CQR to compare their update stability. In addition to analyses in the overall cohort, we conducted prespecified subgroup analyses (Supplementary Methods S1).
Long-term RMSTR prediction modeling and implications for TEW modeling
Association between initial and updated RMSTR was examined after log transformation. We quantified concordance using the Pearson correlation coefficient and derived 95-percent confidence intervals via trial-level nonparametric bootstrapping (2,000 replicates). Correlations exceeding .80 were defined a priori as reflecting strong agreement (Reference Mukaka17). Linearity between the log-transformed initial and updated RMSTR estimates was assessed by fitting an ordinary least squares linear regression model and testing for nonlinearity using an added quadratic term and the Ramsey Regression Equation Specification Error Test (see details in Supplementary Methods S2) (Reference Ramsey18).
We developed a multivariable model to predict updated RMSTR on the log scale using elastic-net regularized linear regression (glmnet) (Reference Zou and Hastie19;Reference Friedman, Hastie and Tibshirani20). The outcome was the updated RMSTR estimated at the updated data cut’s own truncation horizon. All predictors were quantities observable at the initial data cut. The log-transformed initial RMSTR was forced into the model (penalty factor = 0), whereas all other candidate covariates were penalized and could be shrunk toward zero (with some coefficients set exactly to zero), providing data-driven variable selection (Reference Zou and Hastie19). Tuning considered α∈{0,.25,.5,.75,1} and selected λ using the one-standard error rule within inner cross-validation (Reference Zou and Hastie19;Reference Friedman, Hastie and Tibshirani20). Covariates are described in Supplementary Methods S3. Model development and internal validation were conducted using nested cross-validation (10 outer folds with 10-fold inner tuning) to generate out-of-fold predictions and reduce optimism in performance estimates (Reference Stone21). Predictive accuracy was quantified using mean absolute error (MAE), root mean squared error (RMSE), and R2; 95-percent confidence intervals for performance metrics were obtained by nonparametric bootstrap resampling of the out-of-fold pairs (2,000 resamples) (Reference Efron and Tibshirani22). After evaluation, the final model was refit on the full data set and split-conformal 90-percent prediction intervals were constructed using a held-out calibration split based on the empirical quantile of absolute calibration residuals (Reference Romano and Patterson23). Prediction “correctness” was defined as the proportion of observations for which the observed updated RMSTR fell within the corresponding 90-percent prediction interval, with uncertainty quantified by bootstrap resampling (Reference Efron and Tibshirani22).
Complementary analyses using RMSD
Using the updated reconstructed IPD and the same post-landmark risk sets as for RMSTR, we described post-landmark RMSD dispersion using event-weighted IQR width and MAD. Using the same data-cut-specific τ as for RMSTR, we calculated RMSD at the initial and updated cuts and ΔRMSD (updated minus initial), summarized overall and by prespecified subgroup. Predictability of updated RMSD was assessed primarily using Spearman correlation, with Pearson correlation reported secondarily, and using the same nested-cross-validated elastic-net framework as for RMSTR. All analyses used the original month scale, and no numerical comparison was made between RMSD dispersion and ratio-scale CQR. Baseline dependence was examined by mapping RMSTR to RMSD using comparator-arm RMST. Full methods are provided in Supplementary Methods S4.
Results
We identified 524 records; 168 randomized trials met the inclusion criteria for analysis, contributing 270 treatment comparisons (150 OS and 120 non-OS). Study selection and baseline characteristics are presented in Supplementary Figure S1 and Table S1. Within the OS set, most trials did not report a prespecified discontinuation strategy (92), and immunotherapy-containing regimens were common (76). First-line therapy was evaluated in 89 trials, and 114 were conducted in metastatic settings. Blinding was implemented in 51 trials, and crossover was allowed in 59. The most represented indications were lung cancer (n = 25), leukemia (n = 18), and breast cancer (n = 18) (Supplementary Table S2). Characteristics for non-OS end points are summarized in Supplementary Table S3.
Across landmark analyses at 2, 3, 4, and 5 years, post-landmark HRs generally remained below 1, providing limited evidence of the convergence to the null assumed in some HTA TEW models (Reference Taylor, Latimer and Douglas4;Reference Trigg, Melendez-Torres, Abdelsabour and Lee5). Median post-landmark HRs, estimated from each landmark to the end of available follow-up, ranged from .73 to .79 for OS and from .65 to .77 for non-OS across the 2-, 3-, 4-, and 5-year landmarks. For OS, the corresponding IQRs remained below 1 at all four landmarks. For non-OS, the IQRs remained below 1 at the 2-, 3-, and 4-year landmarks but included 1 at 5 years, possibly because of the smaller sample size and fewer late events. Overall, the direction of the post-landmark treatment effects was broadly consistent across OS and non-OS, although uncertainty was greater at the latest non-OS landmark. More information is in Figure 1 and Supplementary Table S4.
Post-landmark HRs and RMSTRs at 2, 3, 4, and 5 years. Note: At each landmark t0, estimates were based on the remaining observed follow-up after t0; observations were not censored at the next landmark. Abbreviations: HR, hazard ratio; RMSTR, restricted mean survival time ratio; OS, overall survival; non-OS, non–overall survival time-to-event end points (e.g., progression-free survival, disease-free survival, relapse-free survival, event-free survival); IQR, interquartile range; CQR, coefficient of quartile relative dispersion; Y, year(s).
Figure 1. Long description
The image consists of two main sections, A and B, each containing a 2 by 4 grid of scatter plots.
Section A: Hazard ratio (H R)
* The Y-axis ranges from 0.0 to 3.0. A dashed horizontal line is at 1.0. A solid red line represents the event-weighted median, surrounded by a light red band for the I Q R.
* Top Row (O S): Shows data for 2 Y (N=141, Median 0.787), 3 Y (N=118, Median 0.780), 4 Y (N=84, Median 0.732), and 5 Y (N=51, Median 0.789). Points are clustered below the 1.0 line.
* Bottom Row (non-O S): Shows data for 2 Y (N=103, Median 0.652), 3 Y (N=79, Median 0.684), 4 Y (N=53, Median 0.733), and 5 Y (N=35, Median 0.765). The red median line is lower than in the O S row.
Section B: R M S T R
* The Y-axis ranges from 0.8 to 1.5. A dashed horizontal line is at 1.0.
* Top Row (O S): Shows data for 2 Y (N=110, Median 1.049), 3 Y (N=91, Median 1.036), 4 Y (N=70, Median 1.037), and 5 Y (N=49, Median 1.022). Points are clustered slightly above the 1.0 line.
* Bottom Row (non-O S): Shows data for 2 Y (N=71, Median 1.079), 3 Y (N=60, Median 1.055), 4 Y (N=48, Median 1.032), and 5 Y (N=35, Median 1.023).
In all plots, teal circles represent individual trials, with size proportional to the number of events. C Q R values are provided in the top right of each panel, generally decreasing as time increases in section B.
As shown in Figure 1, across the 2-, 3-, 4-, and 5-year landmark analyses, RMSTR consistently showed lower dispersion than HR for both OS and non-OS end points. For OS, median RMSTRs were 1.049, 1.036, 1.037, and 1.022, with CQRs of .043, .030, .036, and .019, respectively, substantially lower than the corresponding HR CQRs of .186, .204, .216, and .275. For non-OS, median RMSTRs were 1.079, 1.055, 1.032, and 1.023, with CQRs of .069, .035, .023, and .019, respectively, consistently lower than the corresponding HR CQRs of .226, .217, .182, and .176. Subgroup analyses across prespecified trial- and treatment-level factors were consistent with the primary results: RMSTR generally showed lower dispersion than HR across strata. Occasional departures were observed only in strata with limited numbers of trials at later landmarks, where HR dispersion increased markedly, while RMSTR remained comparatively stable. Detailed post-landmark results are provided in Table 1.
Summary of post-landmark RMSTRs at 2, 3, 4, and 5 years
Table 1. Long description
The table is divided into two main vertical sections: O S (post-landmark R M S T R, median [I Q R], C Q R) and Non-O S (post-landmark R M S T R, median [I Q R], C Q R). The columns represent time intervals: 2-year, 3-year, 4-year, and 5-year.
Section 1: O S (Overall Survival)
* Overall: 2-year 1.049 (N = 110); 3-year 1.036 (N = 91); 4-year 1.037 (N = 70); 5-year 1.022 (N = 49).
* Planned treatment discontinuation: No planned discontinuation shows a 2-year R M S T R of 1.078 (N = 65) decreasing to 1.010 at 5 years (N = 23). Planned discontinuation shows 1.041 at 2 years (N = 45) and 1.022 at 5 years (N = 26).
* Treatment crossover: No crossover ranges from 1.041 (2-year) to 1.022 (5-year). Crossover allowed ranges from 1.078 (2-year) to 1.010 (5-year).
* Immunotherapy (I C I): Non-I C I regimen ranges from 1.070 (2-year) to 1.037 (5-year). I C I-based regimen ranges from 1.041 (2-year) to 1.009 (5-year).
* Line of therapy: First-line ranges from 1.049 (2-year) to 1.022 (5-year). Second-line or later ranges from 1.070 (2-year) to 0.940 (5-year).
* Metastatic disease: Non-metastatic ranges from 1.049 (2-year) to 1.022 (5-year). Metastatic ranges from 1.054 (2-year) to 1.026 (5-year).
* Proportional hazards (P H): P H satisfied ranges from 1.049 (2-year) to 1.019 (5-year). P H violated ranges from 1.088 (2-year) to 1.026 (5-year).
Section 2: Non-O S
* Overall: 2-year 1.079 (N = 71); 3-year 1.055 (N = 60); 4-year 1.032 (N = 48); 5-year 1.023 (N = 35).
* Planned treatment discontinuation: No planned discontinuation ranges from 1.119 (2-year) to 0.985 (5-year). Planned discontinuation ranges from 1.079 (2-year) to 1.023 (5-year).
* Immunotherapy (I C I): Non-I C I ranges from 1.065 (2-year) to 1.023 (5-year). I C I-based ranges from 1.119 (2-year) to 0.985 (5-year).
* Line of therapy: First-line ranges from 1.079 (2-year) to 1.023 (5-year). Second-line or later ranges from 1.057 (2-year) to 1.071 (5-year).
* Metastatic disease: Non-metastatic ranges from 1.079 (2-year) to 1.023 (5-year). Metastatic ranges from 1.057 (2-year) to 0.956 (5-year).
* Proportional hazards (P H): P H satisfied ranges from 1.083 (2-year) to 1.035 (5-year). P H violated ranges from 1.079 (2-year) to 1.023 (5-year).
Note: At each landmark t0, RMSTR was estimated over the remaining observed follow-up after t0; observations were not censored at the next landmark.
CQR, Coefficient of Quartile Relative Dispersion; ICI, immune checkpoint inhibitor; IQR, Interquartile Range; OS, Overall Survival; PH, Proportional Hazards; RMSTR, restricted mean survival time ratio.
Across end points (Table 2 and Supplementary Figure S2), rRMSTR was more stable across data updates than rHR, with consistently smaller CQRs overall and in most subgroups. In OS, the overall rRMSTR was 1.04 (IQR 1.02–1.08; CQR .028) and showed lower dispersion than rHR (CQR .071); this pattern persisted across prespecified strata, and the clearest divergence was seen when PH was violated, where rHR dispersion increased substantially (CQR .119) compared with rRMSTR (CQR .046). In non-OS, dispersion was higher for both metrics, but rRMSTR remained at least as stable as rHR overall (CQR .079 vs .099) and in most subgroups; a notable exception was immunotherapy-based subgroup, where rHR was more concentrated (CQR .055) than rRMSTR (CQR .073), while several disease strata showed comparable or greater variability for rHR than rRMSTR. In the sensitivity analysis using a common within-trial truncation horizon, the overall rRMSTR was 1.00 (IQR 1.00–1.01; CQR .006) for OS and 1.00 (IQR .98–1.01; CQR .015) for non-OS ( Supplementary Table S5). Common-horizon rRMSTR remained less dispersed than rHR overall and across all prespecified subgroups.
Update stability of rRMSTR and rHR and corresponding absolute changes in RMSD
Table 2. Long description
The table is divided into two primary sections: O S (Overall Survival) and Non-O S.
For the O S group (N = 150):
* Overall: r R M S T R median is 1.04 (I Q R 1.02, 1.08) with a C Q R of .028. r H R C Q R is .071. Delta R M S D median is 2.04 months.
* Planned treatment discontinuation: No discontinuation (N = 92) shows r R M S T R 1.04; Planned discontinuation (N = 58) shows r R M S T R 1.05.
* Treatment crossover: No crossover (N = 91) r R M S T R 1.03; Crossover allowed (N = 59) r R M S T R 1.05.
* Immunotherapy: Non-immunotherapy (N = 74) r R M S T R 1.04; I C I-based (N = 76) r R M S T R 1.06.
* Line of therapy: First-line (N = 89) r R M S T R 1.04; Second-line or later (N = 61) r R M S T R 1.04.
* Metastatic disease: Non-metastatic (N = 36) r R M S T R 1.03; Metastatic (N = 114) r R M S T R 1.05.
* P H assumption: P H satisfied (N = 110) r R M S T R 1.04; P H violated (N = 40) r R M S T R 1.08.
* Disease types: Breast Cancer (1.02), Digestive System (1.03), Genitourinary (1.04), Head Neck Skin Endocrine (1.07), Hematologic (1.04), and Thoracic Respiratory (1.07).
For the Non-O S group (N = 120):
* Overall: r R M S T R median is 1.08 (I Q R 1.04, 1.21) with a C Q R of .079. r H R C Q R is .099. Delta R M S D median is 3.33 months.
* Planned treatment discontinuation: No discontinuation (N = 63) r R M S T R 1.14; Planned discontinuation (N = 57) r R M S T R 1.05.
* Immunotherapy: Non-immunotherapy (N = 54) r R M S T R 1.05; I C I-based (N = 66) r R M S T R 1.10.
* Line of therapy: First-line (N = 74) r R M S T R 1.06; Second-line or later (N = 46) r R M S T R 1.10.
* Metastatic disease: Non-metastatic (N = 27) r R M S T R 1.04; Metastatic (N = 93) r R M S T R 1.10.
* P H assumption: P H satisfied (N = 58) r R M S T R 1.10; P H violated (N = 62) r R M S T R 1.07.
* Disease types: Breast Cancer (1.04), Digestive System (1.01), Genitourinary (1.07), Head Neck Skin Endocrine (1.16), Hematologic (1.11), and Thoracic Respiratory (1.17).
Note: Summary statistics were calculated using event-weighted distributions. ΔRMSD was calculated as updated RMSD minus initial RMSD and is reported in months. CQR was used to compare the relative-scale dispersion of rRMSTR and rHR; because RMSD is an additive measure that may be zero or negative, its dispersion was not directly compared with ratio-scale CQR. rHR medians and IQRs are presented in Supplementary Figure S2.
CQR, coefficient of quartile relative dispersion; ICI, immune checkpoint inhibitor; IQR, interquartile range; non-OS, non-overall-survival time-to-event end points; OS, overall survival; PH, proportional hazards; RMSD, restricted mean survival time difference; rHR, updated-to-initial hazard ratio; rRMSTR, updated-to-initial restricted mean survival time ratio.
Figure 2 indicates that, with accumulating follow-up, the update ratios were more stable and more tightly distributed for RMSTR than for HR; for OS, rRMSTR was dominated by 1.0-1.1 and 1.1-1.2 (7.7 and 14.9 percent, respectively), whereas rHR was more dispersed across .8-.9, .9-1.0, 1.0-1.1, 1.1-1.2, and 1.2–1.5 (1.4, 25.3, 34.1, 17.5, and 9.1 percent, respectively). For non-OS, rRMSTR similarly concentrated in 1.0-1.1, 1.1-1.2, and 1.2-1.3 (52.9, 17.3, and 15.7 percent, respectively), while rHR showed a broader spread across < .9, .9-1.0, 1.0-1.1, 1.1-1.2, and 1.2-1.3 (8.6, 24.2, 32.1, 18.4, and 11.5 percent, respectively); subgroup patterns were broadly consistent with these overall distributions, with any visible deviations mainly observed in smaller disease strata. A complementary presentation of the observed ranges and event-weighted medians and IQRs is provided in Supplementary Figure S3.
Distributions of rHR and rRMSTR. Abbreviations: ICI, immune checkpoint inhibitor; OS, Overall Survival; PH, Proportional Hazards; rHR, updated-to-initial hazard ratio; rRMSTR, updated-to-initial restricted mean survival time ratio.
Figure 2. Long description
A four-panel set of heatmaps. Each panel shares a vertical axis listing clinical subgroups including Disease types (Thoracic Respiratory, Hematologic Malignancy, Head Neck Skin Endocrine, Genitourinary, Digestive System, Breast), P H status (Yes, No), Metastatic status (Yes, No), Treatment line (Subsequent-line, First-line), I C I use (Yes, No), Crossover (Yes, No), Fixed stopping (Yes, No), and an Overall row.
1. Top-Left Panel (r R M S T R, O S): The horizontal axis shows weighted r R M S T R ranges from 0-0.5 to 1.5 plus. Most data is concentrated in the 1-1.1 column, with percentages ranging from 45.3 percent to 94.8 percent across subgroups.
2. Top-Right Panel (r H R, O S): The horizontal axis shows weighted r H R ranges. Data is more dispersed compared to r R M S T R, with peaks in the 0.9-1 and 1-1.1 columns, often exceeding 30 percent or 40 percent.
3. Bottom-Left Panel (r R M S T R, Non-O S): The horizontal axis ranges from 0-0.9 to 1.5 plus. High concentrations are visible in the 1-1.1 column, particularly for Breast Cancer at 84.7 percent.
4. Bottom-Right Panel (r H R, Non-O S): The horizontal axis ranges from 0-0.9 to 1.5 plus. This panel shows the highest variance, with significant density in the 0.9-1 and 1-1.1 columns, and some subgroups like Digestive System Cancer peaking at 55.7 percent in the 1-1.1 range.
A color scale on the right indicates that darker blue represents higher Weighted percentage, from 0 percent to 50 percent.
The correlation analysis (Supplementary Figure S4) showed high concordance of RMSTR before and after data updates for both end points. Specifically, RMSTR was strongly correlated for non-OS (r = .82, 95-percent CI .76–.88) and even more so for OS (r = .87, 95-percent CI .78–.93), indicating that RMSTR estimates remain highly consistent across successive data updates.
For OSTable 3, using complete cases (n = 147) and 49 trial-level predictors (after one-hot encoding), the elastic-net model showed great discrimination and low error for predicting long-term updated RMSTR (R2 = .75, MAE = .041, RMSE = .058), with negligible bias and near-ideal calibration (intercept = .002, p = .805; slope = .985, p < .001). The final model fitted on all data selected α = 0 (ridge), and essentially retained initial RMSTR as the dominant predictor; the fitted equation was:
Where
$ {\overline{RMSTR}}_{updated} $
denotes the predicted updated RMSTR and
$ RMST{R}_{pre} $
denotes initial RMSTR. A split-conformal 90-percent prediction interval achieved a prediction success rate of 91 percent prediction success rate; the observed updated RMSTR fell within the interval for 90.5 percent of trials (95-percent CI, 86–95 percent), corresponding to an approximate multiplicative factor of [.916,1.092] around the point prediction.
Predictive accuracy and uncertainty of the elastic-net model for long-term updated RMSTR
Table 3. Long description
The table contains 10 columns and 2 data rows.
Columns include: Outcome group, Number of trials (complete cases), Explained variance (R super 2, cross-validated), Mean absolute error (cross-validated), Root mean squared error (cross-validated), Calibration: intercept (p-value), Calibration: slope (p-value), Final prediction equation, Prediction interval width, and Prediction success rate (95% C I).
Row 1: O S group.
- Number of trials: 147.
- Explained variance: .748.
- Mean absolute error: .041.
- Root mean squared error: .058.
- Calibration intercept: .002 (p = .805).
- Calibration slope: .985 (p < .001).
- Final prediction equation: log (R M S T R_updated) = .0323 + 1.1775 times log (R M S T R_pre).
- Prediction interval width: times [.916, 1.092].
- Prediction success rate: .905 (95% C I: .857–.952).
Row 2: Non-O S group.
- Number of trials: 120.
- Explained variance: .663.
- Mean absolute error: .09.
- Root mean squared error: .116.
- Calibration intercept: .0028 (p = .909).
- Calibration slope: .990 (p < .001).
- Final prediction equation: log (R M S T R_updated) = .0913 + 1.0994 times log (R M S T R_pre).
- Prediction interval width: times [.790, 1.265].
- Prediction success rate: .958 (95% C I: .917–.992).
Footnote: R M S T R stands for restricted mean survival time ratio; O S stands for overall survival.
RMSTR, restricted mean survival time ratio; RMSTRpre, initial RMSTR; RMSTRupdated, updated RMSTR; OS, overall survival.
For non-OS, using complete cases (n = 120) and 46 trial-level predictors (after one-hot encoding), the elastic-net model showed good discrimination for predicting long-term updated RMSTR (R2 = .663, MAE = .09, RMSE = .116), with negligible bias and near-ideal calibration (intercept = .003, p = .909; slope = .99, p < .001). The final model fitted on all data selected α = .5 and essentially retained initial RMSTR as the dominant predictor; the fitted equation was:
$ \log \left({\overline{RMSTR}}_{updated}\right)=.0913+1.0994\times \log \left( RMST{R}_{pre}\right) $
. A split-conformal 90-percent prediction interval achieved a 96 percent prediction success rate (95-percent CI, 92–99 percent), corresponding to an approximate multiplicative factor of [.790,1.265] around the point prediction. More details are in Supplementary Table S6.
Because rRMSTR quantifies the relative change from initial RMSTR to updated RMSTR, we assessed whether the magnitude of updating depended on the follow-up duration. Event-weighted regressions of
log(rRMSTR) on follow-up duration yielded slope estimates close to zero and non-significant for both OS (β = 1.000, 95-percent CI 1.000–1.001, p = .56) and non-OS (β = 1.000, 95-percent CI .999–1.001, p = .43). Details are in Supplementary Figure S5. This provides no evidence that follow-up duration systematically affects the updating magnitude, supporting the use of the initial RMSTR as the primary predictor of the updated RMSTR.
Ultimately, we developed a practical methodological workflow for selecting extrapolation models and implementing TEW in oncology, incorporating our predicted RMSTR anchor; details are presented in Supplementary Table S7.
Complementary analysis of absolute RMSD
Complementary RMSD analyses are detailed in Supplementary Figure S6, Table 2, Supplementary Results S1 and Supplementary Tables S8–S10. Post-landmark RMSD distributions varied across landmarks and subgroups. Median RMSD increased by 2.04 months in OS and 3.33 months in non-OS between cuts; initial and updated RMSD were associated (Spearman rho = .59 and .76), and nested-cross-validated models yielded R2 values of .43 and .44, respectively. At RMSTR=1.10, implied disease-level RMSDs ranged from 1.45 to 4.22 months for OS and from .75 to 4.20 months for non-OS.
Discussion
In this comprehensive cohort of pivotal oncology RCTs, post-landmark HR distributions generally remained centered below 1 across the 2- to 5-year landmarks. In the present study, these HR patterns were considered alongside RMSTR to compare the dispersion and update stability of the two measures in the context of TEW modeling. Across the same long-term landmarks, RMSTR was consistently less dispersed than HR, and this advantage persisted across prespecified strata, suggesting that RMSTR is less sensitive to late-follow-up sparsity and non-proportional hazards. Likewise, rRMSTR was more stable than rHR overall and in most subgroups. RMSTR therefore provides a dimensionless anchor for relative comparison, whereas RMSD more directly reflects absolute survival gain. The complementary difference-scale analyses showed that RMSD distributions varied by landmark and subgroup, absolute gains generally increased between data cuts, and early RMSD retained useful predictive information. Thus, RMSTR stability should not be interpreted as invariant economically meaningful absolute benefit; both measures should inform extrapolation and TEW assessment.
Finally, RMSTR showed strong agreement between initial and updated analyses, and longer-term RMSTR could be predicted with good accuracy using parsimonious regularized models in which the initial RMSTR dominated. This is practically important for HTA because decisions are often made when evidence is still immature: our findings suggest that a data-driven “update expectation” for RMSTR is feasible, and that TEW can be handled as an empirically informed uncertainty problem rather than a deterministic rule that imposes full waning at an arbitrarily chosen time. In addition, our results provide an additional, clinically interpretable criterion to support extrapolation model selection.
The contrast in dispersion and stability between effect measures also clarifies why prediction was more feasible for RMSTR in this setting. RMST-based estimands summarize survival as an integrated quantity up to a prespecified horizon and do not require PH, so they tend to be less sensitive to time-varying hazards and thinning late risk sets, while remaining clinically interpretable under non-PH (Reference Uno, Claggett and Tian8;Reference Royston and Parmar13). By comparison, HRs are harder to interpret as a single effect when hazards are non-proportional, and can become unstable in late follow-up when information is sparse, limiting their value as a reliable modeling target (Reference Hernán6;Reference Royston and Parmar13). Consistent with these properties, we observed greater dispersion and later-landmark instability for HR than for RMSTR, especially when PH was violated. We therefore did not build prediction models for long-term HR, and instead modeled updated RMSTR, where estimates were more consistent across updates, and the early-to-late relationship was sufficiently stable to support out-of-sample prediction.
Predicting longer-term updated RMST/RMSTR directly addresses a well-described weakness in current TEW practice: HTA reviews show TEW is often implemented as a time-based, hazard-scale rule (frequently setting HR = 1 at a chosen landmark), with substantial heterogeneity and switch-point choices commonly justified by precedent rather than evidence (Reference Taylor, Latimer and Douglas4;Reference Trigg, Melendez-Torres, Abdelsabour and Lee5). Taylor et al. further note that, even in immuno-oncology, the external clinical literature rarely provides evidence that maps cleanly to TEW because TEW is defined in terms of relative effects over time, not absolute long-term survival, leaving analysts without an empirical basis to parameterize waning (Reference Taylor, Latimer and Douglas4). The RMSTR prediction model provides a dimensionless update anchor rather than a direct estimate of absolute benefit. For economic evaluation, the predicted RMSTR and its interval should be combined with the modeled comparator-arm RMST to obtain disease-specific RMSD inputs for survival and outcome projections. This is also practically usable because we found no quantitative relationship between follow-up duration and rRMSTR, implying that the magnitude of RMSTR updating is not systematically time-driven, so early RMSTR can serve as a stable anchor for predicting updated RMSTR across varying trial maturities; in contrast, recent work highlights how HR “slippage” across data cuts can materially distort survival projections and economic conclusions, reinforcing the need for more stable targets than HR for long-term modeling (Reference Lee, Ahmad, Farmer, Barnish, Lovell and Melendez-Torres24).
Our prediction model provides an external constraint for both extrapolation-model selection and TEW parameterization in oncology economic evaluations. Although independent arm modeling is standard, extrapolation uncertainty is substantial, and in-sample fit criteria – such as Akaike information criterion (AIC) and Bayesian information criterion (BIC) – are often weakly related to long-term predictive performance, motivating clinically grounded constraints to exclude implausible projections (Reference Lee, Ahmad, Farmer, Barnish, Lovell and Melendez-Torres24). Current TEW practice in HTA is frequently coarse and precedent-driven (e.g., assuming hazard equalization after an arbitrary time), with heterogeneous implementation and limited empirical support for the waning specification (Reference Taylor, Latimer and Douglas4;Reference Trigg, Melendez-Torres, Abdelsabour and Lee5). Using early trial evidence, our model predicts the long-term RMSTR, which can be operationalized by fitting multiple candidate extrapolation models, deriving each model’s implied long-term RMSTR, and selecting/validating models whose implied RMSTR is consistent with our prediction (and prediction interval), thereby complementing AIC/BIC-based selection (Reference Latimer1). Where TEW must be imposed, a pragmatic alternative to assuming no long-term relative effect is to use the interval of our predicted long-term RMSTR as the waning constraint, which is clinically more plausible and is supported by the empirical coverage of our prediction intervals (91 percent for OS and 96 percent for non-OS outcomes).
Limitations
Several limitations should be noted. Our cohort was restricted to FDA-approved trials with sufficient Kaplan–Meier reporting to support IPD reconstruction, which may limit generalizability. Although we applied stringent reconstruction checks, reconstructed IPD remains approximate. Because the primary rRMSTR analysis used data-cut-specific truncation horizons, it may reflect both treatment-effect change and extension of the integration horizon. The common-horizon sensitivity analysis produced estimates closer to 1 but confirmed the lower dispersion of rRMSTR relative to rHR. “Longer-term” RMSTR was defined by the latest available update and truncation at the last observed event time, so our prediction performance is not validated for true lifetime horizons; late landmark estimates (especially at 5 years and for non-OS end points) may also be imprecise due to sparse information. Finally, the prediction models were internally validated but not externally validated, and their use to support extrapolation selection and TEW should be interpreted as decision support rather than definitive evidence on long-term comparative effectiveness.
Conclusion
Across a large cohort of pivotal oncology RCTs, RMSTR showed lower dispersion than HR across long-term landmarks and remained strongly concordant between initial and updated analyses. The greater dispersion of late-follow-up HRs suggests that reliance on HR-based convergence rules alone may be insufficient to fully characterize long-term treatment-effect uncertainty. Leveraging this stability, we developed parsimonious regularized models that accurately predicted longer-term RMSTR from early evidence, enabling a practical, data-driven “update expectation” that can inform extrapolation model selection and parameterize TEW as an empirically grounded uncertainty problem in future oncology cost-effectiveness evaluations. Predicted RMSTR should be interpreted alongside RMSD when translating relative update stability into economically meaningful absolute survival benefit.
Supplementary material
The supplementary material for this article can be found at http://doi.org/10.1017/S026646232610422X.
Author contribution
Prof. Tang had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Zhao and H. Shao contributed equally to this work. Tang, Zhao, and H. Shao conceived and designed the study. Zhao, H. Shao, Y. Jiang, Yu. Jiang, Li, and Fang collected and extracted the data. Zhao, H. Shao, and Fang performed data analysis and drafted the manuscript. Tang, Zhao, Y. Jiang, and T. Shao critically revised the manuscript for important intellectual content. Zhao, H. Shao, T. Shao, Fang, Li, and Y. Jiang conducted the statistical analyses. Tang obtained funding, provided administrative and technical support, and supervised the study.
Funding statement
This work was supported by the General Program of National Natural Science Foundation of China (grant no. 72174207). The funders 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.
Competing interests
The authors have no competing interests to declare.
Ethics approval
This study does not involve human participants or animal subjects.
Patient consent for publication
Not required.
Provenance and peer review
Not commissioned; externally peer reviewed.
Data sharing statement
Full data set is available, on request from the corresponding author.
Patient and public involvement
No patient involved
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