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Colorectal Cancer Phase 3 Time-to-Event Analysis NCT05064059

A Study of Coformulated Favezelimab/Pembrolizumab (MK-4280A) Versus Standard of Care in Subjects With Previously Treated Metastatic PD-L1 Positive Colorectal Cancer (MK-4280A-007): Complete Statistical Analysis

This page examines the randomized comparison of favezelimab/pembrolizumab with investigator-selected standard of care in previously treated metastatic PD-L1 positive colorectal cancer. It focuses on overall survival and the registry’s posted secondary, safety, and planning information.

Trial start: 2021-11-10  ·  Enrollment: 441  ·  Sponsor: Merck Sharp & Dohme LLC
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for A Study of Coformulated Favezelimab/Pembrolizumab (MK-4280A) Versus Standard of Care in Subjects With Previously Treated Metastatic PD-L1 Positive Colorectal Cancer (MK-4280A-007) (NCT05064059), a randomized phase 3 study. The primary outcome is Overall Survival (OS).

441
Enrollment
Phase 3
2
Arms
In the primary outcome
0.98
Hazard ratio
Favezelimab/Pembrolizumab vs Standard of
0.80–1.20
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT05064059
PhasePhase 3
ConditionColorectal Cancer
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment441
Arms in the primary outcome2
Lead sponsorMerck Sharp & Dohme LLC
Results postedYes

2. Clinical Question

Population

Participants had previously treated metastatic PD-L1 positive colorectal cancer. The registry describes the primary analysis population as all randomized participants; the trial enrolled 441 participants.

Intervention

The experimental group received coformulated favezelimab/pembrolizumab, also identified as MK-4280A. The listed regimen was 800 mg/200 mg intravenously on Day 1, then every 3 weeks, for up to 35 infusions.

Comparator

The comparison was standard of care, chosen by the investigator: regorafenib or TAS-102, also called trifluridine and tipiracil. These were not combined treatments; the registry describes a choice between them.

Primary question

The primary question was whether favezelimab/pembrolizumab was superior to standard of care for overall survival. Overall survival was defined as time from randomization to death due to any cause.

This is a direct randomized comparison, but the control group represents a choice of two treatments rather than a single uniform drug. The primary endpoint is time-to-event: each participant contributes information about how long they were followed before death or censoring. The posted results summarize this endpoint with medians and a hazard ratio. Those summaries answer related, but not identical, questions. The median describes the time by which half of the analyzed group had experienced the event, while the hazard ratio compares event rates over follow-up under the model used for the analysis.

The registry reports an overall-survival median of 7.3 months for favezelimab/pembrolizumab and 8.5 months for standard of care. The reported hazard ratio was 0.98, with a 95% confidence interval from 0.80 to 1.20 and p = 0.418. The interpretation should therefore consider the interval and the sponsor’s reported comparison, not just compare the two medians. The posted results describe the data from this trial; they do not establish what would happen for every patient or in a different population.

3. Trial Design

This was a Phase 3, randomized, open-label, parallel-group study sponsored by Merck Sharp & Dohme LLC. The registry lists enrollment of 441 and status as completed. The recorded start date was 2021-11-10 and primary completion date was 2024-08-15. The study compared coformulated favezelimab/pembrolizumab with standard of care in participants with previously treated metastatic PD-L1 positive colorectal cancer.

The experimental group received favezelimab/pembrolizumab at 800 mg/200 mg intravenously on Day 1, then every 3 weeks for up to 35 infusions. In the standard-of-care group, the investigator selected either regorafenib, 160 mg orally daily on Days 1-12 of each 28-day cycle, or TAS-102, 35 mg/m^2 orally twice daily on Days 1-5 and Days 8-12 of each 28-day cycle. Thus, the comparator reflects a treatment strategy with investigator choice, not a single fixed comparator regimen.

Random allocation helps make the groups comparable at the start on average, although it does not guarantee identical groups in every characteristic. Because masking was listed as none, this was an open-label study. The registry record does not report the allocation ratio, details of random sequence generation, stratification factors, or procedures for concealing allocation. Those design details are not reported in the registry record.

The primary outcome was overall survival, analyzed in all randomized participants. It was defined as time from randomization to death due to any cause, with a timeframe of up to approximately 33 months. The listed secondary outcomes include progression-free survival, objective response rate, duration of response, adverse events, discontinuations due to adverse events, and patient-reported quality-of-life measures. The registry has 14 outcome measures and 11 analyses recorded, with 13 secondary outcomes posted. The protocol’s planned analysis schedule, stopping rules, interim analyses, and original sample-size justification are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

StageFavezelimab/PembrolizumabStandard of Care (Regorafenib or TAS-102)
STARTED221220
Treated221210
COMPLETED00
NOT COMPLETED221220

Reasons for not completing this period:

ReasonFavezelimab/PembrolizumabStandard of Care (Regorafenib or TAS-102)
Death199196
Physician Decision42
Sponsor Decision1411
Withdrawal by Subject411

Analysis population for the primary outcome, as defined in the registry: All randomized participants were analyzed.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

CharacteristicUnitFavezelimab/PembrolizumabStandard of Care (Regorafenib or TAS-102)Total
Participants analysed221220441
Age, ContinuousYears59.9 (SD 11.3)57.6 (SD 11.4)58.8 (SD 11.4)
Sex: Female, Male: FemaleParticipants8381164
Sex: Female, Male: MaleParticipants138139277
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants191736
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants197196393
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants5712
Race (NIH/OMB): American Indian or Alaska NativeParticipants000
Race (NIH/OMB): AsianParticipants6765132
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants549
Race (NIH/OMB): WhiteParticipants145147292
Race (NIH/OMB): More than one raceParticipants022
Race (NIH/OMB): Unknown or Not ReportedParticipants426
Geographic Region: Asia PacificParticipants7170141
Geographic Region: EMEA/AmericasParticipants150150300
Presence of Liver Metastasis: YesParticipants172173345
Presence of Liver Metastasis: NoParticipants494796
Time from Initial Diagnosis of Metastatic Disease to Randomization: ≥18 monthsParticipants144150294
Time from Initial Diagnosis of Metastatic Disease to Randomization: <18 monthsParticipants7770147

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival (OS), measured over Up to approximately 33 months.

ElementRegistry entry
Result typeMedian
Measure of spread95% Confidence Interval
UnitMonths
Endpoint classificationTime-to-Event Analysis

Overall survival measures the time from randomization until death due to any cause. It is a time-to-event endpoint: the analysis uses both whether an event occurred and the timing of that event, while accounting for participants whose event time is not observed during follow-up. The registry reports that all randomized participants were analyzed and gives a timeframe of up to approximately 33 months.

Overall survival is used because it describes time to death directly, without requiring attribution of the cause of death to the cancer or treatment. In a randomized comparison, it can summarize how the groups fare over follow-up. The median is the time at which the estimated survival curve reaches the halfway point. It is not the average survival time, and it does not say when any particular participant will experience an event.

The posted medians were 7.3 months for favezelimab/pembrolizumab and 8.5 months for standard of care. The sponsor also reported a hazard ratio of 0.98, with a 95% confidence interval from 0.80 to 1.20. The hazard ratio compares the event rates over follow-up rather than comparing only the two median values. Its interpretation depends on the assumptions and analysis method used. The registry does not report the survival-curve estimates at other specific times or the details needed to assess all modeling assumptions.

7. Results Posted in the Registry

Hazard ratio: Favezelimab/Pembrolizumab vs Standard of Care (Regorafenib or TAS-102)

0.98

95% CI: 0.80 to 1.20

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Favezelimab/Pembrolizumab vs …0.770.850.931.031.131.24hazard ratio (as reported) vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Progression-Free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as Assessed by Blinded Independent Central Review (BICR)Time-to-Event AnalysisHazard ratio1.34 (1.09 to 1.64)367 events
Objective Response Rate (ORR) Per RECIST 1.1 as Assessed by BICRBinary EndpointRisk difference+5.9 pts (2.3 to 9.4)167 per arm
Time to Deterioration (TTD) in EORTC QLQ-C30 GHS (Item 29) and QoL (Item 30) Combined ScoreTime-to-Event AnalysisHazard ratio1.00 (0.64 to 1.58)n/a

Progression-Free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as Assessed by Blinded Independent Central Review (BICR)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Favezelimab/Pembrolizumab vs …0.961.081.211.361.521.71hazard ratio (as reported) vs control (95% CI)

Objective Response Rate (ORR) Per RECIST 1.1 as Assessed by BICR

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Favezelimab/Pembrolizumab-0.751.433.625.807.9910risk difference (percentage points) vs control (95% CI)

Time to Deterioration (TTD) in EORTC QLQ-C30 GHS (Item 29) and QoL (Item 30) Combined Score

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Favezelimab/Pembrolizumab vs …0.600.730.911.121.381.70hazard ratio (as reported) vs control (95% CI)

Across the posted secondary outcomes, the registry shows a mixed pattern rather than a uniform direction of results. The measures cover tumor response and progression, time to deterioration in quality of life, adverse events, treatment discontinuation, and patient-reported functioning and symptoms. Each captures a different aspect of the trial, and each has its own analysis population, measurement process, and uncertainty.

These outcomes can add context to the primary overall-survival result, but they do not alter what the primary endpoint estimates. A response outcome asks whether a response was recorded; progression-free survival concerns time to progression or death under its definition; patient-reported outcomes address reported health status or symptoms. Differences across these measures are possible because they measure different things and use different follow-up and assessment procedures. They should not be combined into a single claim about overall benefit or harm.

The registry lists 13 posted secondary outcomes, including outcomes for which the record gives no result in the information. Values or analyses not included in the posted results are not reported in the registry record. The secondary results that are available should be considered alongside their confidence intervals and analysis methods, rather than treated as a substitute for the primary analysis.

Multiplicity is an important reason for caution. When several outcomes or comparisons are examined, the chance of at least one apparently unusual result can increase. In general, a prespecified correction or testing hierarchy can address this issue, but the registry record does not report whether or how multiplicity was controlled. Accordingly, nominal p-values for secondary outcomes carry less weight than a result interpreted within a fully reported prespecified testing plan. They can be informative signals, but should not automatically be treated as confirmatory evidence. The registry also does not report the complete endpoint hierarchy or the role assigned to each secondary measure in the trial’s formal conclusions.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

The primary endpoint results show an overall-survival median of 7.3 months in the favezelimab/pembrolizumab group and 8.5 months in the standard-of-care group. The reported hazard ratio for favezelimab/pembrolizumab versus standard of care was 0.98, with a 95% confidence interval from 0.80 to 1.20 and p = 0.418. The confidence interval includes values on both sides of 1.00, so the posted estimate is compatible with a range of relative event-rate differences. The p-value does not provide evidence against the null hypothesis at conventional thresholds, but it is not a probability that the null hypothesis is true.

The median values and hazard ratio are different summaries of time-to-event data. The medians describe points on each group’s survival distribution; the hazard ratio is the sponsor’s reported relative comparison over follow-up. These summaries need not move in perfect correspondence, and neither alone captures every feature of the survival curves. The registry does not provide the curves or enough detail to judge whether the relative event rates changed over time.

The posted secondary results add context but do not replace the primary overall-survival analysis. Progression-free survival had medians of 2.1 months and 2.6 months, and a reported hazard ratio of 1.34 with a 95% confidence interval from 1.09 to 1.64. Objective response was reported in 6.8% and 0.9% of participants, with a sponsor-reported difference of 5.9 percentage points and p < 0.001. The quality-of-life deterioration comparison had a reported hazard ratio of 1.00 with a 95% confidence interval from 0.64 to 1.58. These outcomes describe distinct domains and have their own uncertainty and analysis considerations.

Secondary endpoints may be exploratory or may be part of a larger testing plan. The registry record does not report a multiplicity adjustment plan, so a statistically significant result among secondary outcomes should not automatically be read as confirmatory. Likewise, a result with a non-significant p-value does not establish that groups are equivalent. The interpretation rests on the sizes and uncertainty of the posted estimates, the endpoint hierarchy, and the analysis plan; the latter is not reported in the registry record.

The result is a comparison among the randomized participants and treatments studied, using the definitions and follow-up recorded. It does not establish a treatment effect for other populations, comparator choices, or follow-up periods. The registry record also does not provide all information needed to assess the handling of missing observations, censoring, protocol deviations, or every prespecified analysis. Those gaps limit how fully an external reader can reconstruct the analysis.

10. Statistical Methods Explained

The primary result is a time-to-event analysis. Each participant’s follow-up begins at randomization, and the event is death due to any cause. A participant who has not had a recorded event by the end of observed follow-up may be censored: their available follow-up still contributes information, but their later event time is unknown. This is a general explanation of survival analysis; the registry does not report detailed censoring rules or the exact data cut used for the posted analysis.

What does the median summarize?

The median survival time is a point on an estimated survival distribution: it is the time by which half the group is estimated to have experienced the event. It is distinct from the mean and from an individual’s expected outcome. The registry reports median overall survival of 7.3 months for favezelimab/pembrolizumab and 8.5 months for standard of care. These are summaries of the observed trial groups, not guarantees about future outcomes or a complete description of the survival curves.

What does the hazard ratio summarize?

The sponsor reported a hazard ratio of 0.98 for favezelimab/pembrolizumab versus standard of care, using a Log Rank method for the reported comparison. In general, a hazard ratio compares the event rates between groups over time. A value of 1.00 indicates no relative difference in the modeled comparison; values below or above 1.00 indicate different directions for the comparison as defined. The reported 95% confidence interval, from 0.80 to 1.20, includes 1.00. The registry does not report enough information to establish whether the proportional-hazards assumption was evaluated or how any departure from it was handled.

The Log Rank procedure is a general method for comparing time-to-event experience between groups. It uses the ordering and timing of events across follow-up, including information from participants who are censored. A hazard ratio is commonly presented alongside such a comparison to express the relative contrast. The registry lists the Log Rank method and reports the hazard ratio, but does not give a full statistical analysis plan or detailed model specification. For that reason, the estimate should be read as the sponsor’s reported analysis rather than as a fully reproducible calculation from the registry summary alone.

How should the p-value be read?

The primary comparison has p = 0.418. In general, a p-value describes how unusual results at least as incompatible with a specified null model would be if that model and the test assumptions were correct. It does not measure the probability that the treatment effect is zero, and it does not quantify the importance of the estimate. Here, the confidence interval and the point estimate convey information about effect size and precision that a p-value alone cannot provide.

The registry reports a superiority analysis. A superiority test assesses whether the results support a difference in the stated direction or a difference between groups according to the analysis plan. A non-significant result is not proof that treatments are equivalent or that a clinically important difference has been ruled out. Equivalence or non-inferiority would require an appropriate design and prespecified margin; such a margin is not reported in the registry record.

Why can a confidence interval be more informative?

A confidence interval expresses uncertainty around an estimate under the method used. In general, a 95% confidence interval is generated by a procedure that, under its assumptions and repeated use, would cover the target parameter in 95% of such intervals. It is not a statement that there is a 95% probability that this particular interval contains the true effect. The primary interval extends from 0.80 to 1.20, showing that the estimate is not precise enough to isolate a narrow range of relative effects.

The secondary outcomes use different measures. Progression-free survival is another time-to-event endpoint, assessed by blinded independent central review under RECIST 1.1. Its reported hazard ratio is 1.34 with a 95% confidence interval from 1.09 to 1.64. Objective response rate is a binary endpoint: each participant is classified according to whether a response was recorded under RECIST 1.1, with the assessment by blinded independent central review. The sponsor reported a difference in percentage of 5.9, with a 95% confidence interval from 2.5 to 10.1 and p < 0.001.

In general, binary outcomes can be summarized by proportions and differences between proportions, while time-to-event outcomes use timing and censoring. The sponsor’s objective-response comparison used the Miettinen & Nurminen method. These methods answer different questions, and their estimates should not be treated as interchangeable. The registry does not report all endpoint-specific missing-data rules, analysis populations, or details of multiplicity handling.

These methods explanations are general descriptions of statistical concepts. The registry lists the sponsor’s reported methods and estimates, but does not report a complete statistical analysis plan, so any additional assumptions or implementation details are not reported in the registry record.

11. Confidence Intervals and Precision

Precision is reflected in the range of values compatible with the data under the interval method. The primary overall-survival hazard ratio was 0.98, with a 95% confidence interval from 0.80 to 1.20. The point estimate is close to 1.00, while the interval extends on both sides of 1.00. This means the posted result does not pin down a narrow relative effect. The reported p-value, 0.418, is consistent with the sponsor’s superiority test not providing strong evidence against its null hypothesis, but it does not demonstrate that the groups are equivalent.

The medians also have uncertainty intervals: 5.8 to 8.8 months for favezelimab/pembrolizumab and 7.5 to 9.9 months for standard of care. These are intervals around the group medians, not confidence intervals for the difference between medians. The registry’s reported hazard-ratio interval addresses the relative time-to-event comparison under the sponsor’s analysis. Readers should not infer a formal comparison simply from whether the median intervals overlap or from the order of the median point estimates.

In general, confidence intervals are affected by the amount and distribution of information available and by the analysis method. They do not account automatically for bias, unmeasured differences, or selective reporting. They also do not show the range of individual participant outcomes. The registry record does not report enough methodological detail to independently assess all sources of uncertainty, including censoring assumptions and the effect of missing data.

The secondary estimates vary in precision. For example, the progression-free survival hazard-ratio interval is 1.09 to 1.64, while the objective-response difference interval is 2.5 to 10.1 percentage points. The quality-of-life deterioration hazard-ratio interval is 0.64 to 1.58. These intervals refer to different estimands and should be interpreted within their respective outcome definitions. Their widths reflect uncertainty in each specific estimate; they do not establish the reliability of another endpoint.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

Effect to detect (log scale)Hazard ratioEvents, 80% powerEvents, 90% power
100% of the observed effect0.9876,922102,977
75% of the observed effect0.98136,750183,069
50% of the observed effect0.99307,687411,905
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect50,000100,000200,000500,0001,000,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Favezelimab/Pembrolizumab vs Standard of Care (Regorafenib or TAS-102).

The sample-size table and curve are planning illustrations based on the observed effect, not a record of the trial’s original design calculation. For the time-to-event primary analysis, the table expresses requirements as total events, not participants per arm. Its rows describe planning for 100%, 75%, and 50% of the observed effect. For example, the entry for 100% of the observed effect gives 76,922 total events for 80% power and 102,977 total events for 90% power. The table also shows 136,750 and 183,069 total events for planning for 75% of the observed effect, and 307,687 and 411,905 for 50%.

For binary outcomes, the displayed quantities are participants per arm. The objective-response illustration gives 167 participants per arm for 80% power and 223 participants per arm for 90% power when planning for 100% of the observed effect. The corresponding entries for 75% of the observed effect are 243 and 325 participants per arm, and for 50% are 421 and 563 participants per arm.

The assumptions for these illustrations are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The time-to-event calculations use the Schoenfeld method. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

In plain language, the 80% and 90% power columns describe the amount of information a hypothetical study would need to have the stated chance of detecting the specified effect under the planning assumptions, if that effect and assumptions were correct. Smaller effects require more participants or events to detect with the same target power. This is not observed power.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

  1. Hazard ratio HR = 0.980, so ln(HR) = -0.0202.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.980)]2 = 76,921.6, rounded up to 76,922 events in total for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
hr <- 0.98                              # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6))   # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))

# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(5064059)
d    <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z  <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))

Output from running the code

100% of observed effect: events = 76,922 (80% power), 102,977 (90% power)
 75% of observed effect: events = 136,750 (80% power), 183,069 (90% power)
 50% of observed effect: events = 307,687 (80% power), 411,905 (90% power)
Simulated power with 76,922 events: 0.802 (20000 replicates)

The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.

14. Group-Sequential Design Analysis

Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.

Under these assumptions the design needs about 116,289 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 115.734,7303.7100.00010.0001
Look 224.869,4612.5110.00600.0060
Look 360.0104,1911.9930.02310.0250
01234z = 3.7116 mo34730 eventsz = 2.5125 mo69461 eventsz = 1.9960 mo104191 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%76,92185,85260.0
Two looks, O'Brien-Fleming80%77,20786,17260.0
Three looks, O'Brien-Fleming80%77,90186,94660.0
Three looks, Pocock80%90,030100,48360.0
Fixed design, one analysis90%102,975114,93260.0
Two looks, O'Brien-Fleming90%103,327115,32560.0
Three looks, O'Brien-Fleming90%104,191116,28960.0
Three looks, Pocock90%118,856132,65660.0

Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.

Sensitivity to a smaller true effect

Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.

True effect assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.980104,191116,289
75% of the observed effect0.985185,229206,666
50% of the observed effect0.990416,767464,844

For context, this trial enrolled 441 participants.

Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.

R code and output

suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 7.3          # control-arm median, months (converted from the posted unit)
hr          <- 0.98          # hazard ratio used for planning
lambdaC     <- log(2) / med_control
eta         <- 0.01               # dropout hazard per month (assumption)
acc_months  <- 24                 # accrual duration (assumption)
study_months<- 60                 # total study duration (assumption)

design <- function(k, sfu, beta, h = hr) gsSurv(k = k, test.type = 1, alpha = 0.025, beta = beta, sfu = sfu,
  lambdaC = lambdaC, hr = h, hr0 = 1, eta = eta, gamma = 1, R = acc_months, T = study_months, minfup = study_months - acc_months)

# Main design: 3 looks, Lan-DeMets O'Brien-Fleming spending, one-sided alpha 0.025, 90% power
x <- design(3, sfLDOF, 0.10)
cat(sprintf("N_TOTAL|%s\n", format(ceiling(sum(x$gamma * x$R)), big.mark = ",")))
for (i in 1:3) cat(sprintf("GS|%d|%.1f|%.0f|%.3f|%.5f|%.5f\n", i, x$T[i], x$n.I[i], x$upper$bound[i], pnorm(-x$upper$bound[i]), cumsum(x$upper$spend)[i]))
cat("\n"); print(gsBoundSummary(x))

# Comparison of designs
cmp <- list(list("Fixed design, one analysis", 1, sfLDOF), list("Two looks, O'Brien-Fleming", 2, sfLDOF),
            list("Three looks, O'Brien-Fleming", 3, sfLDOF), list("Three looks, Pocock", 3, sfLDPocock))
cat("\n")
for (b in c(0.20, 0.10)) for (d in cmp) {
  y <- design(d[[2]], d[[3]], b)
  cat(sprintf("DES|%s|%d|%.0f|%s|%.1f\n", d[[1]], round(100 * (1 - b)), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ","), tail(y$T, 1)))
}

# Sensitivity: what if the true effect is smaller than the observed one? (3 looks, O'Brien-Fleming, 90% power)
cat("\n")
for (fr in c(1, 0.75, 0.5)) {
  y <- design(3, sfLDOF, 0.10, exp(log(hr) * fr))
  cat(sprintf("SENS|%.2f|%.3f|%.0f|%s\n", fr, exp(log(hr) * fr), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ",")))
}

# Independent cross-check of the boundaries with rpact
r <- getDesignGroupSequential(kMax = 3, alpha = 0.025, beta = 0.10, sided = 1, typeOfDesign = "asOF", informationRates = x$timing)
cat(sprintf("\nCross-check, upper boundaries: gsDesign %s | rpact %s\n", paste(round(x$upper$bound, 3), collapse = ", "), paste(round(r$criticalValues, 3), collapse = ", ")))

Method: LachinFoulkes 
       Analysis               Value Efficacy
      IA 1: 33%                   Z   3.7103
       N: 75874         p (1-sided)   0.0001
  Events: 34731        ~HR at bound   0.9610
      Month: 16    P(Cross) if HR=1   0.0001
                P(Cross) if HR=0.98   0.0338
      IA 2: 67%                   Z   2.5114
      N: 116290         p (1-sided)   0.0060
  Events: 69461        ~HR at bound   0.9811
      Month: 25    P(Cross) if HR=1   0.0060
                P(Cross) if HR=0.98   0.5603
          Final                   Z   1.9930
      N: 116290         p (1-sided)   0.0231
 Events: 104192        ~HR at bound   0.9877
      Month: 60    P(Cross) if HR=1   0.0250
                P(Cross) if HR=0.98   0.9000



Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993

15. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.980.80 to 1.200.418

The primary result includes a sponsor-reported analysis: a Log Rank comparison with hazard ratio 0.98, 95% confidence interval from 0.80 to 1.20, and p = 0.418. The posted medians are 7.3 months for favezelimab/pembrolizumab and 8.5 months for standard of care. The registry’s reported analysis and the displayed summary values are consistent in their stated direction and do not show a discrepancy requiring a separate recalculation.

Where a sponsor’s analysis is reported, it is the main inferential result to use. A simple recalculation from summary statistics, when available, is not a replacement for that analysis: it may not reproduce the prespecified model, event-time data, censoring, stratification, or other details. In this record, the hazard ratio and p-value are explicitly reported by the sponsor. The confidence interval and p-value should therefore be understood as the sponsor’s analysis, not as a calculation reconstructed from the two median values.

The same distinction matters for secondary endpoints. For objective response, the registry reports the Miettinen & Nurminen comparison, a difference in percentage of 5.9, 95% confidence interval from 2.5 to 10.1, and p < 0.001. A simple unadjusted comparison derived from posted counts may differ because it uses a different calculation. The sponsor’s own analysis takes precedence. Neither a recalculation nor the sponsor’s inferential result resolves questions that depend on the unreported protocol, multiplicity plan, or missing-data rules.

16. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when statistical conclusions are drawn across several outcomes, time points, or comparisons. In general, the more opportunities there are to find a result that crosses a chosen threshold, the more important it is to specify in advance how the tests will be interpreted. Possible approaches include a prespecified hierarchy, adjustment of significance thresholds, or treating some analyses as exploratory. The registry record does not report whether a multiplicity procedure was planned or used, how the primary and secondary tests were ordered, or whether any secondary findings were confirmatory.

This uncertainty matters because the record contains a primary endpoint and numerous secondary outcomes, with 14 outcome measures and 11 analyses recorded. A nominal p-value for a secondary measure should not be interpreted as though it necessarily accounted for all the other tests. The posted objective-response result includes p < 0.001, but the registry does not report whether that p-value was adjusted for multiplicity. The unadjusted result can be described as posted; its place in a formal family of tests is not reported in the registry record.

The record states that all randomized participants were analyzed for the primary endpoint. It does not give further details about the analysis population definitions for every outcome, protocol deviations, or the handling of missing observations. For patient-reported measures, missing questionnaires can affect who contributes to a particular analysis. For binary outcomes, missing or unevaluable assessments can affect the denominator or classification. The exact approaches are not reported in the registry record.

For time-to-event endpoints, censoring is part of the analysis because follow-up may end before an event is recorded. In general, validity depends on how censoring occurs and on the assumptions used to interpret incomplete follow-up. The registry identifies the overall-survival definition and the Log Rank method, but does not report detailed censoring rules or diagnostics. It also does not report whether interim analyses occurred, how they were handled, or whether the analysis plan changed. These omissions limit an external reader’s ability to reproduce the full statistical interpretation and distinguish prespecified analyses from analyses added later.

17. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Favezelimab/Pembrolizumab7522133.9%
Standard of Care (Regorafenib or TAS-102)5621026.7%
Participants with at least one serious adverse event
Serious adverse events by armFavezelimab/Pembrolizumab33.9%Standard of Care (Regorafenib…26.7%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Favezelimab/Pembrolizumab202 of 221
Standard of Care (Regorafenib or TAS-102)203 of 220

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Favezelimab/Pembrolizumab193 of 221
Standard of Care (Regorafenib or TAS-102)187 of 210

Most frequent serious adverse event terms

Event termOrgan systemFavezelimab/PembrolizumabStandard of Care (Regorafenib or TAS-102)
PyrexiaGeneral disorders6 of 2213 of 210
PneumoniaInfections and infestations4 of 2212 of 210
AnaemiaBlood and lymphatic system disorders3 of 2212 of 210
ColitisGastrointestinal disorders5 of 2210 of 210
Intestinal obstructionGastrointestinal disorders2 of 2213 of 210
SepsisInfections and infestations3 of 2212 of 210
AscitesGastrointestinal disorders2 of 2212 of 210
Infusion related reactionInjury, poisoning and procedural complications4 of 2210 of 210
HyponatraemiaMetabolism and nutrition disorders4 of 2210 of 210
Pleural effusionRespiratory, thoracic and mediastinal disorders1 of 2213 of 210

Most frequent non-serious adverse event terms

Event termOrgan systemFavezelimab/PembrolizumabStandard of Care (Regorafenib or TAS-102)
FatigueGeneral disorders53 of 22143 of 210
NauseaGastrointestinal disorders35 of 22148 of 210
AnaemiaBlood and lymphatic system disorders33 of 22148 of 210
DiarrhoeaGastrointestinal disorders36 of 22142 of 210
Decreased appetiteMetabolism and nutrition disorders48 of 22124 of 210
Aspartate aminotransferase increasedInvestigations30 of 22122 of 210
ConstipationGastrointestinal disorders20 of 22129 of 210
AstheniaGeneral disorders26 of 22121 of 210
Palmar-plantar erythrodysaesthesia syndromeSkin and subcutaneous tissue disorders2 of 22145 of 210
VomitingGastrointestinal disorders22 of 22124 of 210

Serious events with the highest arm-level rate: pyrexia (2.7%), colitis (2.3%), pneumonia (1.8%), infusion related reaction (1.8%), hyponatraemia (1.8%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The posted safety summary records serious adverse events in 75 of 221 participants at risk in the favezelimab/pembrolizumab group and 56 of 210 participants at risk in the standard-of-care group. Participants with at least one adverse event of any kind are listed as 193 of 221 and 187 of 210, respectively. These are counts from the registry’s safety summary; they do not by themselves establish that treatment caused an event or permit a causal comparison between groups.

The listed serious adverse-event terms include pyrexia at 2.7%, colitis at 2.3%, pneumonia at 1.8%, infusion related reaction at 1.8%, hyponatraemia at 1.8%, and intestinal obstruction at 1.4%. The registry also lists deaths of 202 and 203 in the two groups. The record information does not specify that these deaths were caused by treatment, nor does it provide a causal attribution for each event.

Safety counts should be read with their denominators, the event definitions, follow-up duration, and the criteria used to collect and classify events. The registry summary does not report all those details here, including exposure-adjusted rates or a complete event listing. Counts alone are not a measure of comparative risk, and differences in time on treatment or observation may affect how many events are recorded.

18. What the Result Does, and Does Not, Mean

The posted primary result describes overall survival in the randomized groups enrolled in this trial. The median was 7.3 months with favezelimab/pembrolizumab and 8.5 months with standard of care. The sponsor-reported hazard ratio was 0.98, with a 95% confidence interval from 0.80 to 1.20 and p = 0.418. Taken together, these summaries do not provide strong evidence of a difference in overall survival in the sponsor’s superiority analysis, while the interval leaves uncertainty about the relative effect.

This is not proof that the treatments are equivalent. The confidence interval includes values below and above 1.00, and the registry does not report an equivalence or non-inferiority design with a prespecified margin. A non-significant p-value cannot establish that any difference is absent or too small to matter. It indicates that the analysis did not meet its specified statistical criterion for superiority, as reported.

The results also do not determine an individual participant’s outcome. Group medians and hazard ratios are summaries across participants and follow-up; they do not predict the time to an event for a particular person. Nor can the result be assumed to apply to populations, treatment settings, or comparator choices outside the trial’s described population and regimens.

The secondary outcomes address additional questions, but they do not replace the primary endpoint. Their interpretation depends on endpoint definitions, missing-data handling, multiplicity, and the analysis plan. Some of these details are not reported in the registry record. The safety summary lists events but does not by itself establish causation. Overall, the posted data support a precise description of the recorded estimates and their uncertainty, not a broad conclusion beyond the trial and its reported analyses.

19. Why This Trial Matters Statistically

This trial is statistically informative because it compares a randomized treatment strategy with a standard-of-care strategy in previously treated metastatic PD-L1 positive colorectal cancer, using overall survival as its primary endpoint. Randomization supports a direct group comparison by reducing systematic differences at allocation in expectation. The open-label design and the investigator’s choice between regorafenib and TAS-102 are also important features to keep in view when interpreting the comparison.

The record illustrates why a time-to-event result should not be reduced to the two median values. The medians are 7.3 months and 8.5 months, while the reported hazard ratio is 0.98 with a 95% confidence interval from 0.80 to 1.20. These measures summarize different aspects of the data. Their joint reading foregrounds uncertainty and makes clear why neither a visual comparison of medians nor a single p-value is a complete account.

The trial also shows the distinction between a primary endpoint and a larger set of secondary outcomes. Response, progression, quality of life, and safety can all matter to the statistical description, but each has a separate estimand and method. Multiple analyses create a need for a transparent testing plan, which is not reported in the registry record. The record’s missing detail about multiplicity and other analysis choices is therefore relevant to the weight assigned to secondary findings.

Finally, the planning illustrations demonstrate how assumed effect size influences event or participant requirements. They are not the trial’s original design calculation. Keeping that distinction clear helps prevent a post hoc planning table from being mistaken for evidence about the trial’s design or achieved power. The record offers useful reported estimates, while leaving some protocol and analysis details unavailable for independent reconstruction.

20. Limitations

The registry record does not report a complete statistical analysis plan, including the original sample-size justification, target effect, allocation ratio, randomization details, stratification factors, or any interim-analysis plan. The planning illustrations displayed with the results are based on the observed effect and should not be mistaken for the assumptions used to design this completed trial.

The primary result is summarized with medians and a sponsor-reported hazard ratio, but the record does not give detailed information about survival curves, censoring rules, model diagnostics, or whether the proportional-hazards assumption was assessed. It also does not report a full account of missing data, protocol deviations, or sensitivity analyses. These omissions make it harder for an external reader to reproduce the analysis or assess how robust it is to alternative reasonable assumptions.

The open-label design means participants and investigators were not masked. This is particularly relevant to outcomes involving investigator assessment, treatment decisions, adverse-event reporting, and patient-reported measures. Some tumor outcomes were assessed by blinded independent central review, as stated for the RECIST 1.1 secondary measures, but this does not mean all trial procedures or outcomes were blinded.

The standard-of-care arm allowed investigator choice between regorafenib and TAS-102. The registry record does not provide the number of participants receiving each option or their separate outcomes, so the posted comparison cannot be separated into drug-specific comparisons from this information. The record also does not report details needed to assess whether treatment exposure and follow-up differed between groups.

Finally, multiplicity procedures for secondary outcomes are not reported. The record lists multiple outcomes, but does not make clear which were intended as confirmatory or how their statistical errors were controlled. Results should therefore be interpreted in the scope of the specific posted analyses, with particular caution about drawing broad conclusions from isolated secondary findings.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

24. Record Summary

NCT05064059 is a completed, randomized, open-label, parallel-group Phase 3 study of favezelimab/pembrolizumab versus investigator-selected standard of care in previously treated metastatic PD-L1 positive colorectal cancer. The registry lists enrollment of 441 and identifies overall survival as the primary endpoint, defined as time from randomization to death due to any cause.

The posted overall-survival medians were 7.3 months and 8.5 months. The sponsor-reported hazard ratio was 0.98, with a 95% confidence interval from 0.80 to 1.20 and p = 0.418. Secondary outcomes covered progression, response, quality of life, and safety. Their interpretation is limited by the absence of a reported multiplicity plan and by other analysis details not reported in the registry record.

The record supports describing the posted estimates and their uncertainty. It does not provide a complete basis for reconstructing all trial analyses or extending conclusions beyond the participants and treatment strategies studied.

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