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Head and Neck Neoplasms Phase 3 Time-to-Event Analysis NCT03765918

Study of Pembrolizumab Given Prior to Surgery and in Combination With Radiotherapy Given Post-surgery for Advanced Head and Neck Squamous Cell Carcinoma (MK-3475-689): Complete Statistical Analysis

This randomized phase III study compares pembrolizumab given before and after surgery with postoperative standard care for resectable, locoregionally advanced head and neck squamous cell carcinoma. The primary outcome is event-free survival, with secondary outcomes including pathological response.

Trial start: 2018-12-17  ·  Enrollment: 714  ·  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 Study of Pembrolizumab Given Prior to Surgery and in Combination With Radiotherapy Given Post-surgery for Advanced Head and Neck Squamous Cell Carcinoma (MK-3475-689) (NCT03765918), a randomized phase 3 study. The primary outcome is Event-free Survival (EFS).

714
Enrollment
Phase 3
2
Arms
In the primary outcome
0.73
Hazard ratio
Pembrolizumab + Standard of Care (SOC) v
0.58–0.92
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03765918
PhasePhase 3
ConditionHead and Neck Neoplasms
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment714
Arms in the primary outcome2
Lead sponsorMerck Sharp & Dohme LLC
Results postedYes

2. Clinical Question

Population

Participants had newly diagnosed, treatment-naïve stage III-IVA resectable locoregionally advanced head and neck squamous cell carcinoma. The registry record identifies the condition more broadly as head and neck neoplasms. The efficacy analysis included all randomized participants.

Intervention

The experimental strategy combined pembrolizumab before surgery with pembrolizumab and standard-of-care postoperative treatment. Before surgery, participants received pembrolizumab 200 mg intravenously on Day 1 of each 21-day cycle for 2 cycles, up to 6 weeks. Postoperative standard care included radiotherapy, with or without cisplatin. The complete adjuvant schedule for the pembrolizumab arm is not reported in the registry record.

Comparator

The active comparator was postoperative standard care after surgical resection: radiotherapy, with or without cisplatin 100 mg/m^2 intravenously on Day 1 of a 21-day cycle for 3 cycles, up to 9 weeks. Two participants assigned to this arm received neoadjuvant treatment in error and remained in the standard-care arm for efficacy analysis.

Primary question

Does the strategy of pembrolizumab before surgery and pembrolizumab with postoperative radiotherapy, with or without cisplatin, change event-free survival compared with postoperative radiotherapy, with or without cisplatin, alone? Event-free survival counts specified progression or recurrence events and death from any cause; a secondary malignancy is not counted as an event. The registry’s primary comparison is the sponsor-reported hazard ratio.

3. Trial Design

This is a phase III, randomized, open-label, parallel-group, active-controlled study. The registry record lists an enrollment of 714 participants. Participants were allocated to pembrolizumab plus standard of care or standard of care after surgery. Masking is listed as none. The study began on 2018-12-17, and the primary completion date is listed as 2024-07-25. Its status is active, not recruiting.

The treatment strategies differ in whether pembrolizumab is added before surgery and during postoperative treatment. In the pembrolizumab arm, participants received 200 mg intravenously on Day 1 of each 21-day cycle for 2 cycles before surgery, up to 6 weeks. After resection, the strategy included pembrolizumab with standard-of-care radiotherapy, with or without cisplatin. The registry description of that arm is incomplete, so its full postoperative schedule is not reported in the registry record. In the standard-care arm, postoperative treatment was radiotherapy, with or without cisplatin 100 mg/m^2, administered on Day 1 of a 21-day cycle for 3 cycles, up to 9 weeks.

The primary efficacy analysis included all randomized participants. The registry specifies that two participants in the standard-care arm received neoadjuvant treatment in error and were analyzed in the arm to which they were assigned. This is an assignment-based analysis despite those protocol deviations. The trial was open-label, but event-free survival was assessed using blinded independent central review. The registry describes efficacy outcomes as stratified by PD-L1 combined positive score status; the exact stratification factors used in the primary comparison 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.

Before assignment: Two participants in the SOC arm received neoadjuvant treatment in error (protocol deviations). One of the participants (who received one cycle of neoadjuvant treatment) was included in the SOC arm for the efficacy and safety analyses per protocol. The other participant (who received 2 cycles of neoadjuvant treatment) was included in the SOC arm for efficacy analysis and in the Pembrolizumab + SOC arm for the safety analysis per protocol.

Overall Study

StagePembrolizumab + Standard of Care (SOC)Standard of Care (SOC)
STARTED363351
Treated360316
Safety Analysis Population361315
Efficacy Analysis Population363351
Neoadjuvant Treatment Period: Participants Who Took EORTCQLQ-C30 GHS/QoL (Items 29 & 30) Assessment3540
Adjuvant Treatment Period: Participants Who Took EORTCQLQ-C30 GHS/QoL (Items 29 and 30) Assessment356306
Neoadjuvant Treatment Period: Participants Who Took EORTCQLQ-C30 (Items 1-5) Assessment3540
Adjuvant Treatment Period: Participants Who Took EORTCQLQ-C30 (Items 1-5) Assessment356306
Neoadjuvant Treatment Period: Participants Who Took EORTCQLQ-H&N35 (Items 35-38) Assessment3540
Adjuvant Treatment Period: Participants Who Took EORTCQLQ-H&N35 (Items 35-38) Assessment356306
Neoadjuvant Treatment Period: Participants Who Took EORTCQLQ-H&N35 (Items 46, 53-54) Assessment3540
Adjuvant Treatment Period: Participants Who Took EORTCQLQ-H&N35 (Items 46, 53-54) Assessment356306

Reasons for not completing this period:

ReasonPembrolizumab + Standard of Care (SOC)Standard of Care (SOC)
Death109127
Lost to Follow-up23
Withdrawal by Subject1216
Participants Ongoing240205

Analysis population for the primary outcome, as defined in the registry: Efficacy analysis population, which included all randomized participants. Per protocol, two participants in the SOC arm received neoadjuvant treatment in error (protocol deviations) and were included in the SOC arm for efficacy analysis.

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.

CharacteristicUnitPembrolizumab + Standard of Care (SOC)Standard of Care (SOC)Total
Participants analysed363351714
Age, ContinuousYears59.4 (SD 10.0)60.6 (SD 10.0)59.9 (SD 10.0)
Sex: Female, Male: FemaleParticipants7774151
Sex: Female, Male: MaleParticipants286277563
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants5546101
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants300298598
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants8715
Race (NIH/OMB): American Indian or Alaska NativeParticipants011
Race (NIH/OMB): AsianParticipants514495
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants112
Race (NIH/OMB): Black or African AmericanParticipants9918
Race (NIH/OMB): WhiteParticipants284270554
Race (NIH/OMB): More than one raceParticipants92029
Race (NIH/OMB): Unknown or Not ReportedParticipants9615
Primary Tumor Site: OropharynxParticipants353873
Primary Tumor Site: Oral CavityParticipants219213432
Primary Tumor Site: LarynxParticipants8173154
Primary Tumor Site: HypopharynxParticipants282654
Primary Tumor Site: MissingParticipants011
Overall Cancer Staging at Baseline: IIIParticipants9093183
Overall Cancer Staging at Baseline: IVAParticipants271257528
Overall Cancer Staging at Baseline: IVBParticipants202
Overall Cancer Staging at Baseline: MissingParticipants011
Programmed Cell Death Ligand 1 (PD-L1) Status by Tumor Proportion Score (TPS): TPS <50%Participants257242499
Programmed Cell Death Ligand 1 (PD-L1) Status by Tumor Proportion Score (TPS): TPS ≥50%Participants103107210
Programmed Cell Death Ligand 1 (PD-L1) Status by Tumor Proportion Score (TPS): MissingParticipants325
PD-L1 Status by Combined Positive Score (CPS; CPS10): CPS <10Participants126118244
PD-L1 Status by Combined Positive Score (CPS; CPS10): CPS ≥10Participants234231465
PD-L1 Status by Combined Positive Score (CPS; CPS10): MissingParticipants325
PD-L1 Status by CPS (CPS1): CPS <1Participants131427
PD-L1 Status by CPS (CPS1): CPS ≥1Participants347335682
PD-L1 Status by CPS (CPS1): MissingParticipants325

6. Primary Endpoint

The registry lists the primary outcome as Event-free Survival (EFS), measured over Up to ~66 months.

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

Event-free survival measures the time from randomization until the first qualifying event. In this study, qualifying events included radiographic disease progression, progression during neoadjuvant treatment that prevented surgery, local or distant progression or recurrence, and death from any cause. A secondary malignancy was not counted as an event. The progression and recurrence assessments used imaging or biopsy as indicated. For radiographic progression, a definitive biopsy showing no histologic evidence of invasive cancer did not meet the event definition.

The endpoint was assessed using RECIST 1.1 by blinded independent central review. The protocol modified RECIST 1.1 to allow up to 10 target lesions in total, with up to 5 per organ. Event-free survival is a time-to-event outcome: it incorporates both whether an event occurred and when it occurred, rather than reducing follow-up to a simple count of participants with events.

General explanation: a time-to-event endpoint can use information from participants followed for different lengths of time, including those who have not had an event by the end of their observed follow-up. This makes the timing of events and the handling of incomplete follow-up important to interpretation. The registry definition identifies the events counted, but details of censoring and missing-data handling are not reported in the registry record.

7. Results Posted in the Registry

Hazard ratio: Pembrolizumab + Standard of Care (SOC) vs Standard of Care (SOC)

0.73

95% CI: 0.58 to 0.92

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Pembrolizumab + Standard of C…0.560.630.710.810.921.04hazard 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
Major Pathological Response (mPR) RateBinary EndpointRisk difference-9.4 pts (-12.4 to -6.4)n/a
mPR Rate in Participants With PD-L1 CPS ≥10Binary EndpointRisk difference-13.7 pts (-18.1 to -9.3)n/a
mPR Rate in Participants With PD-L1 CPS ≥1Binary EndpointRisk difference-9.8 pts (-12.9 to -6.7)n/a

Major Pathological Response (mPR) Rate

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Standard of Care (SOC)-13-10-7.62-4.75-1.880.99risk difference (percentage points) vs control (95% CI)

mPR Rate in Participants With PD-L1 CPS ≥10

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Standard of Care (SOC)-20-15-11-6.94-2.751.45risk difference (percentage points) vs control (95% CI)

mPR Rate in Participants With PD-L1 CPS ≥1

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Standard of Care (SOC)-14-11-7.96-4.96-1.961.03risk difference (percentage points) vs control (95% CI)

The secondary outcomes cover pathological response, including major pathological response and pathological complete response, with some analyses defined for PD-L1 CPS subgroups. The registry also lists quality-of-life change outcomes during neoadjuvant treatment. These outcomes address different aspects of the study: pathological response concerns findings in surgical tissue, while quality-of-life measures concern participants’ reported health status. They are not alternative definitions of event-free survival.

For the pathological response comparisons with numerical results, the overall pattern is that responses were reported in the pembrolizumab-plus-standard-care group and not in the standard-care group. This provides a distinct response-based perspective that is directionally compatible with the primary comparison, but it does not establish that pathological response explains or causes the event-free survival result. The relationship between response outcomes and later event times is not reported in the registry record.

Secondary outcomes generally carry less inferential weight than the primary outcome when many outcomes are examined. General explanation: testing multiple outcomes creates more opportunities for apparently noteworthy results, even when no adjustment is made. The registry record does not report a multiplicity-control procedure, so secondary p-values should not be treated as if they necessarily preserve the same overall error rate as a single prespecified primary test.

The record lists 74 outcome measures, and 71 secondary outcomes are posted. The specific numerical details included in the registry record cover only some of the listed secondary outcomes; results for other measures are not reported in the registry record. Subgroup findings should also be interpreted in light of their smaller analysis populations and the absence of reported multiplicity procedures. These outcomes can inform context, but the primary event-free survival comparison remains the central efficacy analysis.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The sponsor-reported primary comparison gives a hazard ratio of 0.73 for pembrolizumab plus standard of care versus standard of care, with a 95% confidence interval from 0.58 to 0.92 and p = 0.004. In this comparison, a hazard ratio below 1 corresponds to a lower estimated event hazard in the pembrolizumab strategy arm during follow-up. The confidence interval excludes 1, and the reported p-value is below 0.05. These are features of the registry’s reported statistical comparison, not a guarantee about outcomes for any individual participant.

The posted median event-free survival is 51.8 months in the pembrolizumab plus standard-of-care arm and 30.4 months in the standard-of-care arm. For the first estimate, the lower confidence limit is 37.5 months and an upper limit is not reported in the registry record. For standard care, the 95% confidence interval is 21.8 to 50.1 months. The median is the time by which the estimated event-free survival curve has reached the halfway point. It does not describe every participant’s time to an event, and it is not interchangeable with the hazard ratio, which uses information across follow-up.

The hazard ratio and the medians answer related but different questions. The hazard ratio summarizes the relative event rate over observed follow-up under the analysis approach; the medians identify a point on each estimated survival curve. They need not express the same feature of the data. Neither statistic by itself conveys all variation in event timing, follow-up, or participant characteristics.

The registry also reports pathological response outcomes among secondary outcomes. Those outcomes concern response in surgical tissue, rather than the duration until progression, recurrence, or death. They can add context about treatment response but do not replace the primary time-to-event analysis. Their interpretation also depends on their analysis methods and on how multiple outcomes are handled; multiplicity procedures are not reported in the registry record.

The result is specific to the enrolled population and the trial’s treatment strategies: resectable stage III-IVA locoregionally advanced head and neck squamous cell carcinoma, with surgery and postoperative care. The open-label design, use of blinded central review for the primary assessment, treatment deviations in the standard-care arm, and incomplete reporting of some analysis details all matter when reading the estimate. The posted statistics describe the trial comparison; they do not establish an individual prognosis or settle how the regimen should be used in other settings.

10. Statistical Methods Explained

What does the hazard ratio summarize? The primary comparison uses a hazard ratio reported by the sponsor. General explanation: a hazard is the rate at which an event occurs among participants who have not yet had that event. A hazard ratio compares these rates between treatment strategies over follow-up, according to the analysis model. A value below 1 indicates a lower estimated event hazard in the first named arm relative to the second; it is not a ratio of median survival times and does not mean that the same relative difference applies at every time point.

What does the stratified log-rank method do? The reported method is the stratified log-rank method. General explanation: a log-rank test compares event-time patterns between groups while accounting for the timing of events and participants’ follow-up. Stratification can preserve comparisons within defined groups before combining evidence across them. The registry says outcomes were stratified by PD-L1 CPS status, but the exact strata and the details of how stratification entered the primary model are not reported in the registry record. The registry identifies a stratified log-rank analysis for the hazard ratio and reports a superiority analysis.

Why use a blinded independent review? The study is open-label, meaning treatment assignment was not masked. The primary endpoint was assessed by blinded independent central review using RECIST 1.1. General explanation: independent review by assessors unaware of treatment assignment can reduce the opportunity for knowledge of treatment to influence radiographic assessment. It does not remove every possible source of bias, and the registry does not report additional details about the review process beyond the endpoint definition and method.

What does the median convey? The primary endpoint is also summarized by median event-free survival in months, with a 95% confidence interval where reported. General explanation: the median is the time at which an estimated time-to-event curve reaches 50%. It is one summary of the curve, while the hazard ratio uses event-time information across the follow-up period. The median is not the average event-free time, and it does not show the full shape of the curve. The upper confidence limit for the pembrolizumab-arm median is not reported in the registry record.

What is a confidence interval? General explanation: a confidence interval describes statistical uncertainty around an estimate under the assumptions of the method used. A narrower interval indicates greater precision than a wider interval on the same scale, while an interval’s compatibility with a reference value can inform interpretation. The 95% interval for the hazard ratio ranges from 0.58 to 0.92. It describes uncertainty in the estimated relative hazard, not the range of individual participants’ outcomes and not a probability that the true value lies within the particular interval.

How should p-values be read? The sponsor reports p = 0.004 for the primary comparison. General explanation: a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the analysis assumptions held. It is not the probability that the null hypothesis is true, nor does it measure the magnitude or clinical importance of an effect. The p-value should be considered alongside the estimated hazard ratio, its confidence interval, the endpoint definition, and the analysis population.

Why is the primary outcome time-to-event? General explanation: time-to-event analysis can account for the order and timing of events and for differing follow-up, rather than treating all participants as if they had identical observation time. Participants without an event by the end of their recorded follow-up may contribute information up to that point. This approach relies on rules for censoring and follow-up. The exact censoring rules, missing-data procedures, and handling of participants lost to follow-up are not reported in the registry record.

How do the pathological response comparisons differ? The secondary pathological response outcomes are percentages of participants, and their sponsor-reported comparisons use the stratified Miettinen and Nurminen method. General explanation: methods for comparing proportions estimate a difference between groups and can account for the structure of a stratified analysis. These outcomes are binary at the participant level, unlike event-free survival, which incorporates event timing. The specific response definitions and any multiplicity adjustment for secondary outcomes are not reported in the registry record.

What does over-dispersion mean in general? General explanation: over-dispersion occurs when observed variability is greater than a statistical model expects. It can affect uncertainty estimates when the model assumes less variability than the data contain. The primary endpoint is analyzed as time-to-event, and no over-dispersion adjustment is reported in the registry record; therefore, this concept is not an identified feature of the posted primary analysis.

11. Confidence Intervals and Precision

The primary hazard ratio is 0.73, with a 95% confidence interval from 0.58 to 0.92. The interval lies below 1, the reference value for equal hazards, and gives a range of values compatible with the estimate under the analysis method and its assumptions. It still spans a range of possible relative hazard magnitudes, so the point estimate should not be read as exact. The sponsor-reported p-value is 0.004.

The medians give another view of the endpoint, but the amount of reported uncertainty differs between arms. The median is 51.8 months for pembrolizumab plus standard of care, with a lower limit of 37.5 months; its upper confidence limit is not reported in the registry record. For standard care, the median is 30.4 months and the 95% confidence interval is 21.8 to 50.1 months. The incomplete interval for the first median limits a direct comparison of precision between the two median estimates.

General explanation: confidence intervals quantify uncertainty in an estimate, not the spread of outcomes among individual participants. Precision depends on the information available to the analysis, including the number and timing of events and the length of follow-up. The registry gives an endpoint timeframe of up to ~66 months, but the exact data cutoff and detailed follow-up distribution are not reported in the registry record. The interval therefore should be interpreted with the endpoint and follow-up details available, rather than as a complete description of every source of uncertainty.

Precision is also distinct from importance. A confidence interval can indicate how narrowly an effect is estimated, but it does not determine whether the effect is meaningful for every participant or applicable outside the study population. The hazard-ratio interval and the median intervals summarize different quantities and should not be treated as interchangeable measures of uncertainty.

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 effect0.73317425
75% of the observed effect0.79564755
50% of the observed effect0.851,2681,698
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,0005,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
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: Pembrolizumab + Standard of Care (SOC) vs Standard of Care (SOC).

Read each planning row as an illustration based on a stated fraction of the observed effect. The time-to-event entries are total events, not participants per arm. For 100% of the observed effect, the planning figures are 317 total events for 80% power and 425 total events for 90% power. For 75% of the observed effect, they are 564 and 755 total events. For 50% of the observed effect, they are 1,268 and 1,698 total events.

The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The event-count calculations use the Schoenfeld approach. The trial’s original design assumptions and sample-size justification are not reported in the registry record; these planning figures are illustrations rather than a reconstruction of that original design.

In plain language, the 80% power column gives the total number of events the illustration estimates would be needed for an analysis to have an 80% chance of detecting the specified effect under its assumptions. The 90% power column gives the corresponding event total for a 90% chance. These are planning concepts, not probabilities that the reported result is correct. This is not observed power.

As the assumed effect becomes smaller, more information is needed to detect it under the same planning framework. The row using 50% of the observed effect therefore has larger event requirements than the row using 100%. Event totals are not equivalent to enrollment totals: the number of participants needed depends in part on how many experience an event and how long follow-up continues. The registry does not report the original assumptions used to set the trial enrollment.

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 = 0.730, so ln(HR) = -0.3147.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.730)]2 = 317.0, rounded up to 317 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 <- 0.73                              # 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(3765918)
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 = 317 (80% power), 425 (90% power)
 75% of observed effect: events = 564 (80% power), 755 (90% power)
 50% of observed effect: events = 1,268 (80% power), 1,698 (90% power)
Simulated power with 317 events: 0.816 (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 863 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 122.31433.7100.00010.0001
Look 236.22862.5110.00600.0060
Look 360.04291.9930.02310.0250
01234z = 3.7122 mo143 eventsz = 2.5136 mo286 eventsz = 1.9960 mo429 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%31763760.0
Two looks, O'Brien-Fleming80%31863960.0
Three looks, O'Brien-Fleming80%32164560.0
Three looks, Pocock80%37074560.0
Fixed design, one analysis90%42485360.0
Two looks, O'Brien-Fleming90%42685660.0
Three looks, O'Brien-Fleming90%42986360.0
Three looks, Pocock90%49098560.0

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 effect0.730429863
75% of the observed effect0.7907631,498
50% of the observed effect0.8541,7173,289

For context, this trial enrolled 714 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 <- 30.4          # control-arm median, months (converted from the posted unit)
hr          <- 0.73          # 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: 804         p (1-sided)   0.0001
 Events: 144        ~HR at bound   0.5378
   Month: 22    P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.73   0.0338
   IA 2: 67%                   Z   2.5114
      N: 864         p (1-sided)   0.0060
 Events: 287        ~HR at bound   0.7431
   Month: 36    P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.73   0.5603
       Final                   Z   1.9930
      N: 864         p (1-sided)   0.0231
 Events: 430        ~HR at bound   0.8250
   Month: 60    P(Cross) if HR=1   0.0250
             P(Cross) if HR=0.73   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
Stratified Log RankHazard Ratio (HR) 0.730.58 to 0.920.004

The primary time-to-event comparison is represented by the sponsor’s reported hazard ratio, 0.73, with a 95% confidence interval from 0.58 to 0.92 and p = 0.004. Its reported method is the stratified log-rank method. The posted median event-free survival estimates complement that relative comparison but are not a recalculation of the hazard ratio.

No simple unadjusted recalculation of the primary hazard ratio is used. A hazard ratio depends on participant-level event and follow-up information and the specified analysis method; it cannot be reproduced from the posted medians alone. The registry’s sponsor analysis is therefore the relevant reported comparison for the primary time-to-event outcome. The record does not flag a discrepancy between sponsor and recalculated results.

General explanation: a recalculation from summary statistics, when one is available, may not match an analysis using the trial’s stratification or other modeling details. Such a recalculation would be a check based on limited aggregate information, not a substitute for the sponsor’s prespecified analysis. In this case, the primary comparison should be read as reported by the sponsor, with its confidence interval and p-value, and alongside the endpoint definition and analysis population.

16. Multiplicity, Missing Data and Analysis Populations

The registry record identifies event-free survival as the primary outcome and lists numerous secondary outcome measures. It does not report a procedure for controlling multiplicity across secondary outcomes, across PD-L1 CPS subgroup analyses, or across other analyses. Without such a procedure, secondary findings should be read as supportive or exploratory rather than assumed to have the same confirmatory status as the primary analysis. The precise hierarchy of hypotheses and any prespecified testing sequence are not reported in the registry record.

The efficacy analysis population included all randomized participants. Two participants assigned to standard care received neoadjuvant treatment in error, but the registry states that they were included in the standard-care arm for efficacy analysis. This preserves their assigned-group classification for that analysis, while the treatment deviations remain relevant context for interpreting the comparison.

The record says the primary endpoint was assessed by blinded independent central review, despite the trial’s open-label design. It describes RECIST 1.1 as modified to allow up to 10 target lesions total, with up to 5 per organ. The record does not report further detail about endpoint adjudication, the exact stratification variables for the primary analysis, or how protocol deviations other than the two identified participants were handled.

Missing-data methods, censoring rules, and procedures for participants with incomplete endpoint assessments are not reported in the registry record. Their absence from the record does not establish that no such procedures were used; it means they cannot be evaluated from the reported details. The data cutoff, follow-up completeness, and handling of missing secondary outcome assessments are also not reported in the registry record. These omissions limit a full assessment of how incomplete observations may affect the estimates, particularly for outcomes requiring follow-up or participant reports.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Pembrolizumab + Standard of Care (SOC)17936149.6%
Standard of Care (SOC)11631536.8%
Participants with at least one serious adverse event
Serious adverse events by armPembrolizumab + Standard of C…49.6%Standard of Care (SOC)36.8%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Pembrolizumab + Standard of Care (SOC)113 of 363
Standard of Care (SOC)131 of 351

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
Pembrolizumab + Standard of Care (SOC)335 of 361
Standard of Care (SOC)290 of 315

Most frequent serious adverse event terms

Event termOrgan systemPembrolizumab + Standard of Care (SOC)Standard of Care (SOC)
PneumoniaInfections and infestations13 of 36118 of 315
Acute kidney injuryRenal and urinary disorders6 of 3619 of 315
Postoperative wound infectionInfections and infestations5 of 3619 of 315
Pneumonia aspirationInfections and infestations8 of 3612 of 315
Wound dehiscenceInjury, poisoning and procedural complications8 of 3612 of 315
DysphagiaGastrointestinal disorders7 of 3612 of 315
StomatitisGastrointestinal disorders6 of 3612 of 315
PyrexiaGeneral disorders7 of 3611 of 315
Septic shockInfections and infestations4 of 3614 of 315
Pulmonary embolismRespiratory, thoracic and mediastinal disorders6 of 3612 of 315

Most frequent non-serious adverse event terms

Event termOrgan systemPembrolizumab + Standard of Care (SOC)Standard of Care (SOC)
StomatitisGastrointestinal disorders144 of 361170 of 315
Radiation skin injuryInjury, poisoning and procedural complications144 of 361150 of 315
AnaemiaBlood and lymphatic system disorders121 of 361102 of 315
Weight decreasedInvestigations129 of 36186 of 315
DysphagiaGastrointestinal disorders99 of 36198 of 315
NauseaGastrointestinal disorders87 of 36184 of 315
ConstipationGastrointestinal disorders96 of 36170 of 315
Dry mouthGastrointestinal disorders81 of 36181 of 315
FatigueGeneral disorders84 of 36152 of 315
DysgeusiaNervous system disorders55 of 36160 of 315

Serious events with the highest arm-level rate: pneumonia (5.7%), postoperative wound infection (2.9%), acute kidney injury (2.9%), pneumonia aspiration (2.2%), wound dehiscence (2.2%).

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 serious adverse event figures are counts of participants at risk and participants affected, reported separately by treatment arm. In the pembrolizumab plus standard-of-care arm, 361 participants were at risk and 179 were affected by a serious adverse event. In the standard-care arm, 315 were at risk and 116 were affected. These are participant counts, not counts of separate serious-event episodes, and they should be read using the reported at-risk denominators for each arm.

The registry also reports other adverse events for 335 of 361 participants in the pembrolizumab-plus-standard-care arm and 290 of 315 in the standard-care arm. Deaths are listed as 113 and 131, respectively. The record does not provide the cause of each death in these figures, so they should not be interpreted as counts of deaths caused by treatment. The listed serious-event terms include pneumonia, postoperative wound infection, acute kidney injury, aspiration pneumonia, wound dehiscence, and dysphagia, with term-specific percentages reported in the safety results.

These safety counts are descriptive. They do not by themselves establish that treatment caused an event or explain differences between arms. The groups have different at-risk denominators, and the registry entries given do not describe exposure-adjusted comparisons, event duration, severity grading beyond serious-event classification, or causal adjudication. No treatment recommendation follows from these figures.

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

The posted primary analysis indicates a lower estimated event hazard for the pembrolizumab-plus-standard-care strategy than for standard care alone, with a sponsor-reported hazard ratio of 0.73 and a 95% confidence interval from 0.58 to 0.92. The p-value is 0.004. The median event-free survival estimates are 51.8 months and 30.4 months, respectively, although the upper confidence limit for the first median is not reported in the registry record. These statistics describe the randomized comparison under the study’s endpoint definition and analysis.

They do not show that every participant in one group had a better outcome than every participant in the other. Group-level estimates summarize patterns across participants; individual outcomes vary. The hazard ratio does not mean that each participant’s time to an event changes by the same amount, and the medians do not predict an individual participant’s course.

The comparison is between treatment strategies, not between pembrolizumab and no postoperative care. Both arms involved surgery and postoperative treatment, and the standard-care regimen could include radiotherapy with or without cisplatin. The experimental strategy added pembrolizumab before surgery and as part of postoperative treatment. Because the trial is open-label, participants and treating teams knew the assigned strategy, though the primary endpoint used blinded independent central review.

The results pertain to participants with newly diagnosed, treatment-naïve stage III-IVA resectable locoregionally advanced head and neck squamous cell carcinoma. They do not automatically generalize to other disease stages, unresectable disease, other tumor types, or treatment settings. The record also does not report all details needed to assess missing data, multiplicity, or the full adjuvant schedule in the pembrolizumab arm. The statistics describe the evidence recorded for this trial and are not individual medical advice.

19. Why This Trial Matters Statistically

Statistically, the study combines a randomized comparison with a time-to-event primary outcome. Randomization supports a group comparison by treatment assignment, while the event-free survival definition captures progression, recurrence, and death over time. This is more informative about event timing than a single end-of-study proportion, but it requires clear rules for event assessment and follow-up. The registry defines qualifying events and identifies blinded independent central review, allowing readers to understand important parts of the endpoint construction.

The reported hazard ratio, confidence interval, and p-value make it possible to distinguish the estimated direction and magnitude of the primary comparison from its uncertainty. The median estimates add a more directly time-based summary, although one median confidence interval is incomplete in the registry record. Reading both types of summary avoids reducing a survival curve to a single statistic.

The study also illustrates the difference between a primary endpoint and multiple secondary outcomes. Pathological response and quality-of-life outcomes can provide additional context, but multiple analyses create interpretive challenges when multiplicity procedures are not reported. The subgroup outcomes by PD-L1 CPS further emphasize the need to distinguish a prespecified primary comparison from analyses in narrower groups.

Finally, the trial’s open-label design and use of blinded central endpoint review show how assessment procedures can address some, but not all, sources of bias. Reporting the two standard-care participants who received neoadjuvant treatment in error also helps readers understand the efficacy analysis population. The record supports a focused statistical reading while leaving several design and analysis details unavailable.

20. Limitations

The registry record identifies the study as open-label, so participants and clinical teams were not masked to treatment assignment. Blinded independent central review was used for the primary event assessment, but this does not remove all possible influences of an unmasked treatment strategy, including those affecting care or follow-up. The exact safeguards beyond central review are not reported in the registry record.

The reported median for the pembrolizumab-plus-standard-care group has a lower confidence limit of 37.5 months, but its upper limit is not reported in the registry record. This makes the uncertainty around that median less complete than for the standard-care median. The exact data cutoff, the number of events at analysis, and follow-up completeness are not reported in the registry record, although the outcome timeframe is listed as up to ~66 months.

The efficacy population included all randomized participants, including two in the standard-care arm who received neoadjuvant treatment in error. Their inclusion in the assigned arm is reported, but detailed sensitivity analyses addressing these deviations are not reported in the registry record. The full postoperative schedule for the pembrolizumab arm is also not available in the arm description.

Multiplicty adjustment, missing-data handling, censoring rules, and the exact primary-analysis stratification factors are not reported in the registry record. Those details would help assess the interpretation of secondary findings and the effects of incomplete follow-up. Generalizability is also limited by the study population: newly diagnosed, treatment-naïve stage III-IVA resectable locoregionally advanced disease. The results should not be assumed to apply to populations or treatment settings not represented by that description.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

NCT03765918 is a randomized, phase III, open-label, parallel-group study of pembrolizumab before surgery and with postoperative standard care versus postoperative standard care alone for stage III-IVA resectable locoregionally advanced head and neck squamous cell carcinoma. Enrollment is listed as 714. The primary endpoint is event-free survival assessed by blinded independent central review using RECIST 1.1, with a protocol modification to the target-lesion limit.

The sponsor reports a hazard ratio of 0.73, with a 95% confidence interval from 0.58 to 0.92 and p = 0.004. Median event-free survival is reported as 51.8 months and 30.4 months in the respective arms; an upper confidence limit for the first median is not reported in the registry record. The study status is active, not recruiting, and the record lists the primary completion date as 2024-07-25. Some analysis details, including multiplicity control and missing-data methods, are not reported in the registry record.

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