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Nonsquamous Non-small Cell Lung Cancer Phase 3 Time-to-Event Analysis NCT03829319

Safety and Efficacy Study of Pemetrexed + Platinum Chemotherapy + Pembrolizumab (MK-3475) With or Without Lenvatinib (MK-7902/E7080) as First-line Intervention in Adults With Metastatic Nonsquamous Non-small Cell Lung Cancer (MK-7902-006/E7080-G000-315/LEAP-006): Complete Statistical Analysis

This analysis examines progression-free survival in the randomized, placebo-controlled LEAP-006 trial of first-line pemetrexed, platinum chemotherapy and pembrolizumab with lenvatinib or matching placebo. It also explains the registry’s reported secondary outcomes, safety counts, and statistical uncertainty.

Trial start: 2019-03-25  ·  Enrollment: 761  ·  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 Safety and Efficacy Study of Pemetrexed + Platinum Chemotherapy + Pembrolizumab (MK-3475) With or Without Lenvatinib (MK-7902/E7080) as First-line Intervention in Adults With Metastatic Nonsquamous Non-small Cell Lung Cancer (MK-7902-006/E7080-G000-315/LEAP-006) (NCT03829319), a randomized phase 3 study. The primary outcome is Part 2: Progression-free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1).

761
Enrollment
Phase 3
2
Arms
In the primary outcome
0.88
Hazard ratio
Part 2 First Course: Pembrolizumab+Chemo
0.74–1.05
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03829319
PhasePhase 3
ConditionNonsquamous Non-small Cell Lung Cancer
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment761
Arms in the primary outcome2
Lead sponsorMerck Sharp & Dohme LLC
Results postedYes

2. Clinical Question

Population

Adults with metastatic nonsquamous non-small cell lung cancer receiving first-line intervention. The primary-outcome analysis population is described as randomized Part 2 participants who received at least one dose of study intervention and were evaluable for response.

Intervention

Pemetrexed plus platinum chemotherapy and pembrolizumab, with lenvatinib. The platinum option was carboplatin or cisplatin.

Comparator

The same pemetrexed, platinum chemotherapy and pembrolizumab regimen, with matching placebo in place of lenvatinib.

Primary question

In Part 2, how did progression-free survival assessed by blinded independent central review differ between the lenvatinib and placebo groups?

The trial’s brief summary describes hypotheses about both progression-free survival (PFS) and overall survival (OS). The posted primary outcome is PFS, defined from randomization until documented progression or death from any cause, whichever occurred first. Progression was assessed using RECIST 1.1 criteria. The primary comparison therefore concerns the time-to-event experience of participants, rather than simply the proportion with a response at a particular visit.

The registry identifies this as a first-line study in adults with metastatic nonsquamous non-small cell lung cancer. It was randomized, double-masked, parallel-group and placebo-controlled. These features establish the basic comparison, but the registry record does not report every detail that would be needed to assess how randomization was implemented or what information participants and investigators could access during the study.

The central question is whether the reported PFS data distinguish the lenvatinib-containing regimen from the matching-placebo regimen with useful precision. The estimated medians and hazard ratio describe different aspects of the time-to-event results; neither alone establishes a treatment effect. The confidence interval and the sponsor’s reported analysis are important parts of interpreting the comparison.

3. Trial Design

LEAP-006 (NCT03829319) is a Phase 3 randomized, double-masked, parallel-group, placebo-controlled study. It evaluated first-line pemetrexed plus platinum chemotherapy and pembrolizumab, with either lenvatinib or matching placebo, in adults with metastatic nonsquamous non-small cell lung cancer. The registry lists enrollment as 761. The study status is completed.

The Part 2 groups compared pembrolizumab plus chemotherapy with lenvatinib against pembrolizumab plus chemotherapy with matching placebo. The chemotherapy backbone used pemetrexed with either carboplatin or cisplatin. The registry’s arm descriptions also specify treatment cycles and durations, but the descriptions are truncated in the record; any further regimen details are not reported in the registry record.

The primary outcome listed is PFS per RECIST 1.1, with blinded independent central review (BICR) assessment reported in the outcome description. The primary outcome timeframe is up to approximately 36 months. The registry also lists secondary outcomes covering objective response rate (ORR), duration of response, adverse events, discontinuations due to adverse events, and patient-reported health status and symptoms. The listed symptom and quality-of-life measures include global health status, cough, chest pain and dyspnea.

The registry lists a start date of 2019-03-25 and a primary completion date of 2023-08-11. Those dates describe the registry record; they do not establish when every analysis was conducted or reported. Detailed information about the randomization procedure, allocation concealment, stratification factors, and the trial’s original statistical design assumptions is 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: Per protocol, Part 1 participants were excluded from all Part 2 efficacy and safety outcome measures. China participants randomized during the global study phase (134 participants) were included in all global study analyses. China participants randomized during the China extension phase were excluded from all global study analyses and were included in the China-specific analyses in the extension study (NCT04716933).

Overall Study

StagePart 1 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+Placebo
STARTED13375373
Treated During First Course13373372
Treated During Second Course135
COMPLETED000
NOT COMPLETED13375373

Reasons for not completing this period:

ReasonPart 1 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+Placebo
Sponsor's Decision490102
Withdrawal by Subject154
Physician Decision030
Lost to Follow-up001
Death8277266

Analysis population for the primary outcome, as defined in the registry: The analysis population consisted of all participants enrolled in Part 1 who received at least 1 dose of study intervention.

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.

CharacteristicUnitPart 1 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+PlaceboTotal
Participants analysed13375373761
Age, ContinuousYears64.2 (SD 7.6)62.0 (SD 9.9)63.0 (SD 9.7)62.5 (SD 9.8)
Sex: Female, Male: FemaleParticipants6121126253
Sex: Female, Male: MaleParticipants7254247508
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants07577152
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants13291279583
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants091726
Race (NIH/OMB): American Indian or Alaska NativeParticipants0011
Race (NIH/OMB): AsianParticipants5116114235
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0213
Race (NIH/OMB): Black or African AmericanParticipants0033
Race (NIH/OMB): WhiteParticipants8248237493
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants091726
Eastern Cooperative Oncology Group (ECOG) Performance Status: ECOG = 0Participants8135133276
Eastern Cooperative Oncology Group (ECOG) Performance Status: ECOG = 1Participants5240240485
Programmed Cell Death Ligand 1 (PD-L1) Status at Baseline: TPS = < 50%Participants10272269551
Programmed Cell Death Ligand 1 (PD-L1) Status at Baseline: TPS = ≥ 50%Participants39091184
Programmed Cell Death Ligand 1 (PD-L1) Status at Baseline: Not EvaluableParticipants0131326
Geographic Region: East AsiaParticipants3111112226
Geographic Region: Non-East AsiaParticipants10264261535

6. Primary Endpoint

The registry lists the primary outcome as Part 2: Progression-free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1), measured over Up to approximately 36 months.

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

PFS is a time-to-event endpoint. For each participant, the outcome is the time from randomization to the first documented progressive disease or death from any cause, whichever occurred first. Participants who have not had a recorded event by the end of their available follow-up can contribute censored information rather than being treated as though an event occurred at that time.

The registry defines progressive disease using RECIST 1.1. The description specifies an increase of at least 20% in the sum of target-lesion diameters and an absolute increase of at least 5 mm; the appearance of one or more new lesions also qualifies as progression. PFS is reported from the product-limit, or Kaplan-Meier, method for censored data, and the assessment is attributed to BICR.

As a general statistical concept, a time-to-event endpoint can use information about both when events occur and how long participants remain under observation without an event. This can be useful when follow-up time varies or when some participants have no observed event during follow-up. The Kaplan-Meier method estimates the event-free pattern over time while accounting for censoring under its assumptions.

The median PFS is the estimated time at which the event-free curve reaches the halfway point. It is not the average follow-up time and does not describe every participant’s experience. The hazard ratio provides a relative comparison of event rates over follow-up under the model and analysis used; it is not a direct comparison of median times. The registry’s PFS estimates and hazard ratio should therefore be read together, with their confidence intervals.

7. Results Posted in the Registry

Hazard ratio: Part 2 First Course: Pembrolizumab+Chemotherapy+Lenvatinib vs Part 2 First Course: Pembrolizumab+Chemotherapy+Placebo

0.88

95% CI: 0.74 to 1.05

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Part 2 First Course: Pembroli…0.720.780.850.921.001.08hazard 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
Part 2: Objective Response Rate (ORR) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1)Binary EndpointRisk difference+6.4 pts (-3.1 to 15.8)962 per arm
Part 2: Time to True Deterioration (TTD) Based on Change From Baseline in Global Health Status (GHS)/Quality of Life (QoL) (EORTC QLQ-C30 Items 29 and 30) ScoreTime-to-Event AnalysisHazard ratio1.16 (0.92 to 1.47)1,426 events
Part 2: TTD Based on Change From Baseline in Cough EORTC QLQ-LC13 (Item 31) ScoreTime-to-Event AnalysisHazard ratio1.41 (1.02 to 1.94)266 events

Part 2: Objective Response Rate (ORR) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Part 2 First Course: Pembroli…-4.63-0.234.168.561317risk difference (percentage points) vs control (95% CI)

Part 2: Time to True Deterioration (TTD) Based on Change From Baseline in Global Health Status (GHS)/Quality of Life (QoL) (EORTC QLQ-C30 Items 29 and 30) Score

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Part 2 First Course: Pembroli…0.890.991.101.231.371.53hazard ratio (as reported) vs control (95% CI)

Part 2: TTD Based on Change From Baseline in Cough EORTC QLQ-LC13 (Item 31) Score

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Part 2 First Course: Pembroli…0.951.111.291.501.752.05hazard ratio (as reported) vs control (95% CI)

The posted secondary outcomes span response, duration of response, adverse events, discontinuation due to adverse events, quality of life and symptoms. The available numerical results include ORR and TTD measures for global health status and cough. These outcomes address distinct questions from PFS: response concerns tumor response classification, while TTD concerns deterioration in reported health or symptoms.

Across these available results, the point estimates do not present one uniform pattern across all outcome types. The ORR group estimates and its sponsor-reported comparison are not the same measure as the time-to-deterioration hazard ratios. The registry also posts fewer secondary numerical results than the number of secondary outcomes it lists; results for the other secondary endpoints are not reported in the registry record in the registry record for this analysis.

Secondary results help describe the trial beyond its primary endpoint, but they do not replace the primary PFS analysis. Their interpretation also depends on endpoint definitions, follow-up, missing assessments and the analysis method. The registry record does not report a complete multiplicity plan. When many outcomes are examined, the chance of at least one apparently unusual result can increase if each is interpreted without adjustment. Unadjusted secondary findings therefore carry less confirmatory weight than a prespecified primary analysis with a defined testing strategy.

These considerations do not make secondary outcomes irrelevant. They can identify patterns that warrant careful evaluation and provide information about different aspects of the study. They should be treated as complementary evidence, interpreted in context and with appropriate caution rather than as independent proof of a treatment effect.

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

9. Statistical Interpretation

Clinical Biostats interpretation

In Part 2, the reported median PFS was 12.1 months with pembrolizumab, chemotherapy and lenvatinib, with a 95% confidence interval (CI) of 10.4 to 14.1 months. With matching placebo, the reported median was 9.5 months, with a 95% CI of 8.3 to 10.7 months. These estimates describe the Kaplan-Meier curves; they do not by themselves quantify the full difference between groups or establish that the groups differ.

The sponsor-reported hazard ratio was 0.88, with a 95% CI of 0.74 to 1.05, using a stratified log-rank analysis. A hazard ratio below 1 is in the direction of a lower event hazard in the lenvatinib group under the reported comparison. However, the confidence interval includes 1, so the data are compatible with a range of relative effects that includes no hazard difference. The reported p-value was 0.080. These statistics do not establish that the treatment caused a difference, nor do they prove that the groups are equivalent.

The median estimates and hazard ratio answer related but distinct questions. Medians identify a point on each estimated event-free curve. The hazard ratio summarizes a relative comparison across follow-up, subject to the analysis assumptions. A difference between the displayed medians should not be substituted for the hazard ratio, and no new difference is calculated.

The registry brief summary identifies both PFS and OS hypotheses, but the posted outcome results in this record do not include an OS estimate. The PFS result therefore cannot answer the OS question. Other posted results include ORR and time to true deterioration (TTD) outcomes. Their estimates do not replace the primary PFS comparison, and their interpretation is affected by their own endpoint definitions, uncertainty and the number of outcomes assessed.

For ORR, the posted group estimates are percentages with confidence intervals, while the sponsor also reports a stratified percent-difference analysis. An unadjusted recalculation from posted summary statistics is a separate analysis and need not reproduce the sponsor’s method or estimate. The record does not flag a discrepancy for the primary PFS result. A result’s numerical direction, confidence interval and analysis method all matter; none should be treated as a standalone verdict about clinical benefit or harm.

Overall, the PFS point estimates favor the lenvatinib group in direction, while the hazard-ratio interval remains compatible with no difference. The posted results are therefore best read as an estimate with uncertainty, not as conclusive proof of an effect or of no effect. The registry record does not report the full statistical analysis plan needed to assess all prespecified testing and analysis decisions.

10. Statistical Methods Explained

The primary outcome uses a time-to-event framework. The event is the first occurrence of progressive disease or death from any cause. Each participant contributes follow-up time until an event or censoring. Censoring means that the event was not observed during the participant’s available follow-up; it is not the same as confirming that the participant would never experience the event. As a general statistical concept, valid time-to-event estimates depend on assumptions about censoring and follow-up.

The registry says PFS was summarized using the product-limit method, also known as the Kaplan-Meier method. In general, this method estimates the probability of remaining event-free over time while accounting for censored observations. It produces a curve rather than a single summary. The median is the time at which the estimated curve reaches one-half, if that point can be estimated. A median is one feature of the curve and does not convey its entire shape.

The sponsor’s reported comparison is a hazard ratio analyzed by a stratified log-rank method. A hazard is an instantaneous event rate among participants still at risk at a given time. As a general explanation, a hazard ratio compares the hazards between groups over follow-up, according to the analysis model. A hazard ratio of 1 corresponds to equal hazards in the comparison; values below or above 1 indicate direction relative to the order of groups. The interpretation depends on which group is the numerator and on the analysis assumptions. The registry does not report the stratification factors or enough detail to assess the model assumptions fully.

A log-rank procedure compares time-to-event experience while accounting for the ordering of observed events and the time participants remain at risk. Stratification means the analysis accounts for specified strata, but the strata used are not reported in the registry record. The sponsor-reported PFS hazard ratio is 0.88, with a 95% CI of 0.74 to 1.05; the reported p-value is 0.080. The CI describes uncertainty in the estimate under the method used. Because it includes 1, the estimate is not precise enough to rule out equal hazards at that interval level.

A p-value is a measure of how compatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor the probability that the result occurred “by chance.” The registry reports the PFS p-value but does not provide a complete account of the testing hierarchy, adjustment for multiple comparisons, or the prespecified decision rules. The p-value should therefore be interpreted alongside the effect estimate, interval, endpoint and available design information.

The PFS medians are reported with 95% confidence intervals. In general, a confidence interval describes the range of estimates reasonably compatible with the data and the method, subject to the model’s assumptions. It is not a range containing a fixed proportion of individual participants’ outcomes. The intervals for the two groups overlap, but a visual comparison of separate intervals is not a substitute for the sponsor’s direct between-group analysis.

The ORR outcome is a binary endpoint: participants are classified according to whether they meet the response criteria. The registry reports group percentages and confidence intervals. It also reports a sponsor analysis using a stratified Miettinen and Nurminen method, with a percent-difference estimate. A separate unadjusted recalculation from the posted summary statistics is not the same as that stratified analysis. Differences can arise because methods may use different adjustments or inferential procedures; the record does not establish the cause of any particular difference. No discrepancy is flagged in the record.

The TTD outcomes are time-to-event measures based on changes from baseline in quality-of-life or symptom scores. Their interpretation depends on how deterioration and censoring are defined. The registry supplies outcome labels and some analysis results, but does not report the complete scoring thresholds, missing-questionnaire rules, or detailed handling of participants who discontinue or miss assessments. Those details are not reported in the registry record.

Safety outcomes are counts of participants with events in the listed registry groups. Serious and other adverse events are different categories of event reporting; neither category alone establishes that an event was caused by study treatment. As a general statistical point, safety counts need context about the analysis population, exposure time, event definitions and collection period. The registry gives group counts but does not supply all those details in the registry record for these results.

The trial’s original statistical plan, sample-size justification, interim-analysis procedures and multiplicity strategy are not reported in the registry record. The sample-size illustrations are planning calculations based on observed effects, not reconstructions of the trial’s design. Their assumptions and interpretation are described separately.

11. Confidence Intervals and Precision

The primary PFS hazard ratio is 0.88, with a 95% CI from 0.74 to 1.05. The interval communicates uncertainty around the estimated relative hazard. Values below 1 favor the lenvatinib group in this comparison, while 1 corresponds to equal hazards. Because the interval extends across 1, the posted estimate does not rule out equal hazards, and it also includes values in the direction of a lower hazard with lenvatinib.

The group median estimates have their own intervals: 12.1 months (10.4 to 14.1) for the lenvatinib group and 9.5 months (8.3 to 10.7) for the placebo group. These intervals describe precision for each group’s median, not a direct interval for the difference between medians. The sponsor’s hazard-ratio analysis is the reported direct comparison for PFS.

As a general statistical explanation, greater precision usually corresponds to a narrower confidence interval, while less precision corresponds to a wider interval. Precision is affected by the amount and distribution of event information, follow-up, censoring and variability, as well as the analysis method. A confidence interval does not account for every possible bias or limitation; it reflects uncertainty under the analysis used.

The PFS estimate should not be reduced to whether a confidence interval crosses a reference value. The point estimate conveys the observed direction and magnitude on the hazard-ratio scale; the interval conveys the range of effects compatible with the data and method. The reported p-value adds a related test-based summary but does not replace the interval. The registry does not report enough detail to evaluate all sources of uncertainty, including the prespecified analysis plan, missing-data procedures and multiplicity handling.

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 effect0.881,9222,572
75% of the observed effect0.913,4164,573
50% of the observed effect0.947,68510,288
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00040%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: Part 2 First Course: Pembrolizumab+Chemotherapy+Lenvatinib vs Part 2 First Course: Pembrolizumab+Chemotherapy+Placebo.

The planning illustrations use assumptions stated in the registry-derived analysis: a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They use a target effect equal to a stated fraction of the observed effect. These are planning assumptions for the illustration; the trial’s own original design assumptions are not reported in the registry record.

For binary outcomes such as ORR, the figures are participants per arm. For time-to-event outcomes such as PFS and TTD, the figures are total events across the comparison, not participants per arm. The PFS planning illustration lists 1,922 total events for 80% power and 2,572 total events for 90% power when planning for 100% of the observed effect. For ORR, planning for 100% of the observed effect gives 962 participants per arm for 80% power and 1,288 participants per arm for 90% power.

In general, an 80% power target means the calculation is designed to have an 80% chance of detecting the specified effect under the assumptions if that effect is real; a 90% target uses a higher detection probability and therefore generally requires more information. The figures are not observed trial outcomes. Smaller target effects require more participants or events to detect with the same power, which is why the illustrations increase as the targeted fraction of the observed effect decreases.

These calculations are planning illustrations based on the observed effect, not observed power. The registry’s original sample-size justification and its assumptions are not reported in the registry record.

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 = 0.880, so ln(HR) = -0.1278.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.880)]2 = 1,921.2, rounded up to 1,922 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 <- 0.88                              # 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(3829319)
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 = 1,922 (80% power), 2,572 (90% power)
 75% of observed effect: events = 3,416 (80% power), 4,573 (90% power)
 50% of observed effect: events = 7,685 (80% power), 10,288 (90% power)
Simulated power with 1,922 events: 0.804 (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 3,065 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 117.28673.7100.00010.0001
Look 227.21,7342.5110.00600.0060
Look 360.02,6011.9930.02310.0250
01234z = 3.7117 mo867 eventsz = 2.5127 mo1734 eventsz = 1.9960 mo2601 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%1,9202,26360.0
Two looks, O'Brien-Fleming80%1,9272,27160.0
Three looks, O'Brien-Fleming80%1,9452,29260.0
Three looks, Pocock80%2,2472,64860.0
Fixed design, one analysis90%2,5713,02960.0
Two looks, O'Brien-Fleming90%2,5793,04060.0
Three looks, O'Brien-Fleming90%2,6013,06560.0
Three looks, Pocock90%2,9673,49660.0

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 effect0.8802,6013,065
75% of the observed effect0.9094,6255,430
50% of the observed effect0.93810,40812,178

For context, this trial enrolled 761 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 <- 9.5          # control-arm median, months (converted from the posted unit)
hr          <- 0.88          # 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: 2200         p (1-sided)   0.0001
  Events: 868        ~HR at bound   0.7772
    Month: 17    P(Cross) if HR=1   0.0001
              P(Cross) if HR=0.88   0.0338
    IA 2: 67%                   Z   2.5114
      N: 3066         p (1-sided)   0.0060
 Events: 1735        ~HR at bound   0.8864
    Month: 27    P(Cross) if HR=1   0.0060
              P(Cross) if HR=0.88   0.5603
        Final                   Z   1.9930
      N: 3066         p (1-sided)   0.0231
 Events: 2602        ~HR at bound   0.9248
    Month: 60    P(Cross) if HR=1   0.0250
              P(Cross) if HR=0.88   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) 0.880.74 to 1.050.080

The primary PFS comparison is the sponsor-reported stratified log-rank analysis: hazard ratio 0.88, 95% CI 0.74 to 1.05, and p-value 0.080. The time-to-event analysis uses the sponsor’s reported hazard ratio; no separate unadjusted hazard-ratio recalculation is presented as a replacement. The registry record does not flag a discrepancy for this result.

For ORR, the sponsor reports a stratified Miettinen and Nurminen analysis of percent difference: 6.3, with a 95% CI from -2.8 to 15.4 and p-value 0.086. The unadjusted recalculation from posted summary statistics is a different analysis and has a different estimate and interval. It is useful as a check based on the posted counts, but it does not supersede the sponsor’s method or result. The record does not flag a discrepancy.

In general, recalculations based on summary statistics may differ from a trial analysis because the sponsor may use stratification or other prespecified procedures not represented in a simple unadjusted calculation. The registry record does not provide enough detail to attribute the ORR difference to a particular analytic choice. The sponsor’s reported analysis should be read as the trial’s reported comparison, while an unadjusted recalculation is supplementary context rather than a substitute.

16. Multiplicity, Missing Data and Analysis Populations

The registry brief summary describes primary hypotheses for both PFS and OS. The outcome results presented in this record include a PFS comparison, but an OS estimate is not reported in the registry record. The record does not explain how the two hypotheses were ordered, whether testing was controlled across them, or what decision rules governed interpretation. The full prespecified multiplicity strategy is not reported in the registry record.

This matters because testing several outcomes can increase the chance of observing a result that appears notable even when there is no underlying effect. As a general statistical concept, multiplicity procedures can control error rates across a family of tests or define a hierarchy in which later tests depend on earlier results. Without the planned procedure, readers should not treat each secondary p-value as though it were the only test conducted. The record does not establish whether any particular secondary result was adjusted for multiple comparisons.

The registry identifies the primary PFS analysis population as all randomized participants in Part 2 who received at least one dose of study intervention and were evaluable for response. This description does not give a complete account of the analysis population rules or explain how participants who were not evaluable were handled. The exact number of participants included in every outcome analysis may vary; the registry record does not provide a complete account of those decisions in the registry record.

The record gives PFS definitions and states that the Kaplan-Meier method was used, but detailed rules for censoring, missing assessments, loss to follow-up and sensitivity analyses are not reported in the registry record. For quality-of-life and symptom outcomes, the rules for incomplete questionnaires and missed visits are also not reported. These omissions limit the ability to assess whether missing observations could affect estimates or whether conclusions are robust to alternative assumptions.

The trial’s interim-analysis plan, stopping rules, complete statistical analysis plan and original sample-size justification are not reported in the registry record. Their absence does not show that such procedures were or were not used; it means their details cannot be assessed from this record.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Part 1 First Course: Pembrolizumab+Chemotherapy+Lenvatinib71353.8%
Part 2 First Course: Pembrolizumab+Chemotherapy+Lenvatinib23237362.2%
Part 2 First Course: Pembrolizumab+Chemotherapy+Placebo18937250.8%
Part 1 Second Course: Pembrolizumab Only From Pembrolizumab+Chemotherapy+Lenvatinib11100.0%
Part 2 Second Course: Pembrolizumab+Chemotherapy+Lenvatinib1333.3%
Part 2 Second Course: Pembrolizumab+Chemotherapy+Placebo3742.9%
Participants with at least one serious adverse event
Serious adverse events by armPart 1 First Course: Pembroli…53.8%Part 2 First Course: Pembroli…62.2%Part 2 First Course: Pembroli…50.8%Part 1 Second Course: Pembrol…100.0%Part 2 Second Course: Pembrol…33.3%Part 2 Second Course: Pembrol…42.9%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Part 1 First Course: Pembrolizumab+Chemotherapy+Lenvatinib9 of 13
Part 2 First Course: Pembrolizumab+Chemotherapy+Lenvatinib278 of 375
Part 2 First Course: Pembrolizumab+Chemotherapy+Placebo266 of 373
Part 1 Second Course: Pembrolizumab Only From Pembrolizumab+Chemotherapy+Lenvatinib0 of 1
Part 2 Second Course: Pembrolizumab+Chemotherapy+Lenvatinib3 of 3
Part 2 Second Course: Pembrolizumab+Chemotherapy+Placebo3 of 7

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
Part 1 First Course: Pembrolizumab+Chemotherapy+Lenvatinib13 of 13
Part 2 First Course: Pembrolizumab+Chemotherapy+Lenvatinib366 of 373
Part 2 First Course: Pembrolizumab+Chemotherapy+Placebo363 of 372
Part 1 Second Course: Pembrolizumab Only From Pembrolizumab+Chemotherapy+Lenvatinib1 of 1
Part 2 Second Course: Pembrolizumab+Chemotherapy+Lenvatinib2 of 3
Part 2 Second Course: Pembrolizumab+Chemotherapy+Placebo4 of 7

Most frequent serious adverse event terms

Event termOrgan systemPart 1 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+PlaceboPart 1 Second Course: Pembrolizumab Only From Pembrolizumab+Chemotherapy+LenvatinibPart 2 Second Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 Second Course: Pembrolizumab+Chemotherapy+Placebo
PneumoniaInfections and infestations2 of 1328 of 37336 of 3720 of 10 of 31 of 7
PneumonitisRespiratory, thoracic and mediastinal disorders1 of 1314 of 37315 of 3720 of 10 of 30 of 7
AnaemiaBlood and lymphatic system disorders1 of 1317 of 3739 of 3720 of 10 of 30 of 7
Pleural effusionRespiratory, thoracic and mediastinal disorders1 of 1310 of 3739 of 3720 of 10 of 31 of 7
Pulmonary embolismRespiratory, thoracic and mediastinal disorders0 of 1311 of 3738 of 3720 of 10 of 31 of 7
Platelet count decreasedInvestigations0 of 1310 of 3738 of 3720 of 10 of 30 of 7
Febrile neutropeniaBlood and lymphatic system disorders0 of 1312 of 3735 of 3720 of 10 of 30 of 7
DeathGeneral disorders0 of 1310 of 3735 of 3720 of 10 of 30 of 7
COVID-19 pneumoniaInfections and infestations0 of 135 of 37310 of 3720 of 10 of 30 of 7
DiarrhoeaGastrointestinal disorders0 of 137 of 3734 of 3720 of 10 of 30 of 7

Most frequent non-serious adverse event terms

Event termOrgan systemPart 1 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 First Course: Pembrolizumab+Chemotherapy+PlaceboPart 1 Second Course: Pembrolizumab Only From Pembrolizumab+Chemotherapy+LenvatinibPart 2 Second Course: Pembrolizumab+Chemotherapy+LenvatinibPart 2 Second Course: Pembrolizumab+Chemotherapy+Placebo
AnaemiaBlood and lymphatic system disorders1 of 13192 of 373220 of 3720 of 11 of 30 of 7
Neutrophil count decreasedInvestigations4 of 13188 of 373154 of 3720 of 10 of 30 of 7
NauseaGastrointestinal disorders10 of 13148 of 373137 of 3720 of 10 of 30 of 7
Alanine aminotransferase increasedInvestigations0 of 13132 of 373119 of 3720 of 10 of 30 of 7
Platelet count decreasedInvestigations1 of 13148 of 37398 of 3720 of 10 of 30 of 7
Decreased appetiteMetabolism and nutrition disorders3 of 13130 of 373112 of 3720 of 10 of 31 of 7
ConstipationGastrointestinal disorders7 of 13120 of 373110 of 3720 of 11 of 30 of 7
Aspartate aminotransferase increasedInvestigations0 of 13127 of 373108 of 3720 of 10 of 30 of 7
AstheniaGeneral disorders2 of 13108 of 373110 of 3720 of 10 of 30 of 7
White blood cell count decreasedInvestigations0 of 13119 of 37395 of 3720 of 10 of 30 of 7

Serious events with the highest arm-level rate: hyponatraemia (100.0%), cardiac arrest (33.3%), syncope (33.3%), pneumonia (15.4%), sensory disturbance (14.3%).

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 registry lists serious adverse-event counts for the Part 2 first-course groups: 232 of 373 participants in the lenvatinib group and 189 of 372 participants in the matching-placebo group. For other adverse events, it lists 366 of 373 and 363 of 372, respectively. These are counts in the registry’s listed groups and should be read with their denominators, not as evidence that an event was caused by treatment.

The registry also lists deaths in those groups: 278 in the lenvatinib group and 266 in the matching-placebo group. The record does not establish from these counts whether deaths were attributed to study treatment, nor does it provide the exposure-adjusted rates needed to account for time on treatment or follow-up. Serious adverse events, other adverse events and deaths are separate reporting categories; they should not be combined or treated as interchangeable.

As a general statistical point, safety comparisons require context about event definitions, collection periods, exposure, and analysis populations. The registry record gives counts but does not report all of these details in the registry record for this analysis. The counts describe reported events and do not, by themselves, establish comparative safety.

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

The posted PFS results describe the time-to-event comparison in Part 2. The lenvatinib group had a reported median PFS of 12.1 months, compared with 9.5 months for the matching-placebo group. The sponsor-reported hazard ratio was 0.88, with a 95% CI of 0.74 to 1.05. The estimate is in the direction of a lower event hazard with lenvatinib, but its confidence interval includes equal hazards. The data therefore do not establish a precise relative difference.

These results do not prove that the regimens are equivalent, because an interval that includes 1 can still be compatible with effects in either direction. They also do not prove that lenvatinib caused an improvement. The registry presents an estimate with uncertainty from a trial comparison; causal interpretation depends on the trial’s conduct, analysis choices and assumptions, some of which are not detailed in the record.

PFS is not the same as overall survival, symptom relief, quality of life, or a participant’s individual prognosis. Although the brief summary identifies an OS hypothesis, an OS result is not reported in the registry record. The posted secondary outcomes address other measures, but their interpretation is limited by uncertainty and by the lack of a reported complete multiplicity strategy.

As a general explanation, statistical evidence is not a substitute for clinical judgment. No single p-value, confidence interval or median can determine the importance of an outcome for every patient or setting. The results should be understood as the findings recorded for this study population and these specified outcomes, not as a guarantee about what will happen to an individual.

19. Why This Trial Matters Statistically

This trial illustrates why time-to-event results should be read using more than a single summary. The group medians describe where the estimated PFS curves reach their halfway point, while the hazard ratio summarizes a relative comparison over follow-up. The confidence interval shows that the hazard-ratio estimate remains uncertain and includes equal hazards. Considering these statistics together gives a more complete account than focusing only on the difference in medians or the p-value.

The study also highlights the distinction between a sponsor’s reported analysis and an unadjusted calculation based on posted summaries. Stratification and other analysis choices can matter, particularly when the registry does not report the complete analysis plan. Recalculations can offer a check, but they do not reproduce every feature of a trial’s prespecified method.

Finally, the record contains several types of outcomes: PFS, response, patient-reported measures and safety counts. These endpoints answer different questions, and interpreting many outcomes raises multiplicity concerns. The absence of a reported testing hierarchy, missing-data rules and original sample-size justification limits how fully those results can be evaluated. These are important statistical considerations when interpreting complex randomized trials.

20. Limitations

The registry outcome description states that the primary analysis population included randomized Part 2 participants who received at least one dose of study intervention and were evaluable for response. It does not give a detailed account of how this population was defined in practice or how participants outside it were handled. That makes it difficult to assess how closely the analyzed population corresponds to the randomized population.

The registry lists both PFS and OS hypotheses in its brief summary, but the posted results summarized in this record do not include an OS estimate. The PFS results alone cannot answer the OS question. Likewise, the registry lists more secondary outcomes than it reports numerical results for in the registry record; results for the remaining outcomes are not reported in the registry record.

The complete statistical analysis plan, original design assumptions, interim-analysis procedures, multiplicity adjustments and detailed handling of missing data are not reported in the registry record. The stratification factors for the reported stratified analyses are also not reported. For patient-reported outcomes, detailed deterioration thresholds and rules for incomplete assessments are not included in the available record.

Safety counts are presented without all the context needed to compare event rates over exposure time or establish attribution. The registry reports group counts, but the registry entries available do not provide the full event collection and follow-up details needed for a complete safety analysis. These limitations constrain interpretation; they do not, by themselves, determine whether the trial methods were appropriate.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

LEAP-006 (NCT03829319) is a completed Phase 3 randomized, double-masked, parallel-group, placebo-controlled study sponsored by Merck Sharp & Dohme LLC. It enrolled 761 participants and compared first-line pemetrexed, platinum chemotherapy and pembrolizumab with lenvatinib against the same backbone with matching placebo in adults with metastatic nonsquamous non-small cell lung cancer.

The posted primary outcome is Part 2 PFS per RECIST 1.1, assessed by BICR and analyzed using Kaplan-Meier estimates and a sponsor-reported stratified log-rank comparison. The reported hazard ratio is 0.88, with a 95% CI of 0.74 to 1.05 and p-value of 0.080. The registry also lists response, quality-of-life, symptom and safety outcomes. Detailed multiplicity, missing-data and original design procedures are not reported in the registry record.

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