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Carcinoma, Hepatocellular Phase 3 Time-to-Event Analysis NCT04246177

Safety and Efficacy of Lenvatinib (E7080/MK-7902) With Pembrolizumab (MK-3475) in Combination With Transarterial Chemoembolization (TACE) in Participants With Incurable/Non-metastatic Hepatocellular Carcinoma (MK-7902-012/E7080-G000-318/LEAP-012): Complete Statistical Analysis

A randomized Phase 3 trial compared lenvatinib plus pembrolizumab with TACE against placebo plus TACE for incurable, non-metastatic hepatocellular carcinoma. The registry reports progression-free survival results assessed by blinded independent central review, alongside secondary outcomes and safety information.

Trial start: 2020-05-22  ·  Enrollment: 480  ·  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 of Lenvatinib (E7080/MK-7902) With Pembrolizumab (MK-3475) in Combination With Transarterial Chemoembolization (TACE) in Participants With Incurable/Non-metastatic Hepatocellular Carcinoma (MK-7902-012/E7080-G000-318/LEAP-012) (NCT04246177), a randomized phase 3 study. The primary outcome is Progression Free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as Assessed by Blinded Independent Central Review (BICR).

480
Enrollment
Phase 3
2
Arms
In the primary outcome
0.66
Hazard ratio
Lenvatinib + Pembrolizumab + TACE vs Pla
0.51–0.84
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT04246177
PhasePhase 3
ConditionCarcinoma, Hepatocellular
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment480
Arms in the primary outcome2
Lead sponsorMerck Sharp & Dohme LLC
Results postedYes

2. Clinical Question

Population

Participants with incurable, non-metastatic hepatocellular carcinoma. The primary analysis population was all randomized participants.

Intervention

Lenvatinib plus pembrolizumab in combination with transarterial chemoembolization (TACE).

Comparator

Oral placebo plus intravenous placebo in combination with TACE.

Primary question

How did progression-free survival, measured from first dose to documented progression or death, compare between the two randomized groups?

The study also assessed overall survival as a primary hypothesis, according to the brief summary. However, the posted primary outcome results concern progression-free survival (PFS); an overall survival result is not reported in the registry record. The PFS assessment used RECIST 1.1 and blinded independent central review (BICR). The registry describes the study as randomized, parallel-group, and quadruple-masked, while the official title calls it double-blinded. Its stated purpose was to evaluate efficacy and safety, not simply to compare a drug regimen with no treatment: TACE was included in both groups.

3. Trial Design

This was a Phase 3, multicenter, randomized, parallel-group, active-controlled study of lenvatinib and pembrolizumab combined with TACE versus placebo combined with TACE. The registry lists 480 participants enrolled. The primary PFS analysis included all randomized participants: 237 in the lenvatinib, pembrolizumab, and TACE group and 243 in the placebo and TACE group.

Both groups received TACE. The treatment group also received lenvatinib and pembrolizumab, while the comparison group received matching oral and intravenous placebos. The registry describes masking as quadruple; the official title describes the study as double-blinded. Details about who was masked, how masking was maintained, and how treatment allocation was concealed are not reported in the registry record.

The registry lists the status as terminated and gives a primary completion date. The reason for termination, whether it was related to efficacy, safety, recruitment, or another matter, is not reported in the registry record. The trial's original sample-size justification and planned number of events are also not reported in the registry record. Planning illustrations based on the observed effect are separate from the trial's original design assumptions.

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: 480 participants were enrolled. Of the 480 enrolled participants 1 participant was enrolled in the study in error and did not receive study treatment and 1 participant withdrew from the study and subsequently died without receiving study treatment.

Overall Study

StageLenvatinib Plus Pembrolizumab Plus TACEOral Placebo Plus IV Placebo Plus TACE
STARTED237243
Treated237241
Participants Ongoing105114
COMPLETED00
NOT COMPLETED237243

Reasons for not completing this period:

ReasonLenvatinib Plus Pembrolizumab Plus TACEOral Placebo Plus IV Placebo Plus TACE
Death124122
Randomized By Mistake Without Study Treatment01
Withdrawal by Subject86
Participants Ongoing105114

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

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.

Population: The baseline analysis population consisted of all randomized participants. Participants will be analyzed in the treatment group to which they are randomized.

CharacteristicUnitLenvatinib + Pembrolizumab + TACEPlacebo + TACETotal
Participants analysed237243480
Age, ContinuousYears63.8 (SD 10.7)65.2 (SD 10.4)64.5 (SD 10.6)
Sex: Female, Male: FemaleParticipants453782
Sex: Female, Male: MaleParticipants192206398
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants313364
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants193199392
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants131124
Race (NIH/OMB): American Indian or Alaska NativeParticipants325
Race (NIH/OMB): AsianParticipants168179347
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants224
Race (NIH/OMB): WhiteParticipants514798
Race (NIH/OMB): More than one raceParticipants7714
Race (NIH/OMB): Unknown or Not ReportedParticipants6612
Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) at Baseline: ECOG= 0Participants216213429
Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) at Baseline: ECOG= 1Participants213051
Geographic Region: Asia without JapanParticipants135137272
Geographic Region: Non-Asia with JapanParticipants102106208
Serum Albumin (ALBI) Grade: Grade 1Participants171174345
Serum Albumin (ALBI) Grade: Grade 2Participants6569134
Serum Albumin (ALBI) Grade: MissingParticipants101
Tumor Burden Stratum per Investigator: ≤ 6Participants112116228
Tumor Burden Stratum per Investigator: > 6 and ≤ 12Participants120117237
Tumor Burden Stratum per Investigator: > 12Participants51015
Alpha Fetoprotein at Screening Lab: > 400 ng/mLParticipants374077
Alpha Fetoprotein at Screening Lab: ≤ 400 ng/mLParticipants200203403

6. Primary Endpoint

The registry lists the primary outcome as Progression Free Survival (PFS) Per Response Evaluation Criteria in Solid Tumors Version 1.1 (RECIST 1.1) as Assessed by Blinded Independent Central Review (BICR), measured over Up to approximately 43.5 Months.

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

The primary endpoint was PFS per RECIST 1.1, assessed by BICR. It measures the time from the first dose of study intervention until the first documented progressive disease or death from any cause, whichever occurs first. The analysis therefore combines radiographic progression and death into one time-to-event outcome; it does not measure either event in isolation.

The registry gives study-specific RECIST 1.1 rules. Progression could be based on an increase in the sum of target-lesion diameters, subject to both a relative and an absolute increase, or the appearance of a new lesion. The study allowed a maximum of 10 target lesions and 5 per organ. These definitions determine which observations count as progression and are important to interpreting the endpoint.

PFS is used in trials to assess how long participants remain alive without documented progression. General statistical context: it can capture disease progression earlier than an endpoint that waits for death, but it depends on assessment timing, imaging rules, and censoring. Central review can apply a consistent assessment process across participants, though the registry does not report further details of the review procedures. The primary outcome timeframe was up to approximately 43.5 months.

7. Results Posted in the Registry

Hazard ratio: Lenvatinib + Pembrolizumab + TACE vs Placebo + TACE

0.66

95% CI: 0.51 to 0.84

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Lenvatinib + Pembrolizumab + …0.480.560.660.770.901.06hazard 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
PFS Per Modified RECIST (mRECIST) as Assessed by BICRTime-to-Event AnalysisHazard ratio0.63 (0.49 to 0.81)148 events
Objective Response Rate (ORR) Per mRECIST as Assessed by BICRBinary EndpointRisk difference+21.9 pts (13.4 to 30.5)77 per arm
Disease Control Rate (DCR) Per mRECIST as Assessed by BICRBinary EndpointRisk difference+8.4 pts (2.3 to 14.5)266 per arm

PFS Per Modified RECIST (mRECIST) as Assessed by BICR

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Lenvatinib + Pembrolizumab + …0.460.550.640.760.901.06hazard ratio (as reported) vs control (95% CI)

Objective Response Rate (ORR) Per mRECIST as Assessed by BICR

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Lenvatinib + Pembrolizumab + …-2.444.6312192633risk difference (percentage points) vs control (95% CI)

Disease Control Rate (DCR) Per mRECIST as Assessed by BICR

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Lenvatinib + Pembrolizumab + …-1.162.215.588.961216risk difference (percentage points) vs control (95% CI)

The registry lists secondary outcomes spanning time-to-event measures, tumor response, disease control, and safety. The posted efficacy results include PFS assessed by mRECIST and response outcomes assessed by BICR. In broad terms, the reported secondary efficacy pattern aligns with the primary result in favor of the lenvatinib, pembrolizumab, and TACE group. These outcomes nevertheless use different definitions and should be interpreted as complementary rather than as repeated measurements of precisely the same endpoint.

mRECIST PFS uses modified response criteria, whereas the primary endpoint uses RECIST 1.1. ORR and DCR describe response categories rather than time until progression or death. Other listed outcomes include duration of response and time to progression. They address different features of disease course and apply to different analysis questions. The registry lists 13 secondary outcomes as posted, but numerical results for every listed outcome are not reported in the registry record.

General statistical context: when a study evaluates multiple outcomes, the chance of obtaining at least one apparently unusual result can increase if each is tested separately without adjustment. The registry does not report a multiplicity adjustment or a prespecified hierarchy for the secondary outcomes. Consequently, unadjusted secondary findings carry less confirmatory weight than a result supported by a prespecified testing strategy with control of the overall error rate. The secondary findings can inform interpretation and future questions, but should not be read as independent confirmation of the primary result without those details.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The registry reports median PFS of 14.6 months for lenvatinib plus pembrolizumab plus TACE, with a 95% confidence interval from 12.6 to 16.7 months. For placebo plus TACE, the median was 10.0 months, with a 95% confidence interval from 8.1 to 12.2 months. These are group-level summaries of the time-to-event outcome; they do not mean that every participant experienced progression or death at the median time.

The reported hazard ratio was 0.66, with a 95% confidence interval from 0.51 to 0.84, and p < 0.001. The registry identifies the comparison as a superiority analysis using a re-randomization test. In general, a hazard ratio compares event rates over follow-up, rather than comparing the two medians directly. The reported estimate is below 1, and its confidence interval does not include 1. The reported p-value is evidence against the null hypothesis used for this comparison, under the analysis method stated in the record.

This is statistical evidence about the endpoint and trial groups, not proof that the result applies to every participant or every setting. The confidence interval expresses uncertainty in the hazard-ratio estimate; it does not remove uncertainty about study conduct, endpoint assessment, or how results might generalize. The registry reports the primary PFS result but does not report an overall survival result, despite naming overall survival as part of the study's primary hypotheses.

The secondary results use other outcome definitions, including PFS under mRECIST and response measures. Their broad direction is compatible with the primary PFS result, but these outcomes are not interchangeable: they use different definitions and may answer different questions. The registry record does not report a complete statistical testing strategy for the secondary outcomes, so they should not be treated as equivalent in confirmatory strength to the stated primary analysis.

10. Statistical Methods Explained

The primary result is a time-to-event analysis. The event was the first documented RECIST 1.1 progression by BICR or death from any cause, whichever came first. The endpoint starts at first dose of study intervention. Its reported summary includes a median for each group and a hazard ratio for the comparison. The registry names a re-randomization test for the hazard-ratio analysis.

What does a median PFS represent?

In general, the median time-to-event value is the time by which half of the participants in the analyzed group have had the event, according to the analysis and follow-up data. It is not an average, and it does not describe the time for every individual. Participants who have not had an event by their last available assessment can contribute information up to that point through censoring, but the registry record does not report the censoring rules or detailed missing-data procedures.

What does a hazard ratio represent?

In general, a hazard ratio compares the event rates between groups over follow-up, conditional on the analysis framework. It is not a ratio of median PFS values and should not be translated directly into a difference in months. The reported estimate is 0.66, with a 95% confidence interval from 0.51 to 0.84. The registry reports p < 0.001 and names the re-randomization test as the method. The test's detailed implementation and any stratification factors are not reported in the registry record.

Why does endpoint definition matter?

Progression was determined using RECIST 1.1 as adapted for the study, with BICR. According to the registry description, progression involved a specified increase in the sum of target-lesion diameters or the appearance of one or more new lesions. In general, a defined assessment rule helps make event classification more consistent. However, outcome timing and classification still depend on assessments and the rules governing them. The registry does not report the imaging schedule, adjudication procedures beyond BICR, or how unavailable assessments were handled.

The analysis population is described as all randomized participants. This identifies who was included in the primary outcome population, but it does not by itself specify every analysis detail. The registry record does not report whether additional populations were analyzed, the detailed statistical model, treatment of protocol deviations, or the handling of participants who discontinued assigned treatment. These omissions limit independent assessment of those aspects of the analysis.

General statistical context: a p-value summarizes how compatible the observed data are with a null hypothesis under the test's assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The confidence interval provides a range of values compatible with the data under the method used, while also reflecting sampling uncertainty. Neither statistic addresses every possible source of bias or uncertainty.

The registry identifies a superiority analysis for the primary comparison. It does not report whether the primary test was adjusted for other hypotheses or whether an interim analysis was planned or conducted. A stated test method and a reported p-value are therefore not enough to reconstruct the full prespecified analysis plan. Additional details about the statistical analysis plan are not reported in the registry record.

11. Confidence Intervals and Precision

The 95% confidence interval for median PFS in the lenvatinib, pembrolizumab, and TACE group is 12.6 to 16.7 months. In the placebo and TACE group, it is 8.1 to 12.2 months. The reported hazard-ratio interval is 0.51 to 0.84. These intervals communicate uncertainty around the estimates, rather than a range containing every participant's outcome.

General explanation: a confidence interval is constructed by a statistical procedure that, under its assumptions, would cover the underlying parameter at the stated rate across repeated studies. It is not a guarantee that the true value lies within this particular interval. Its width reflects precision under the model and available data; narrower intervals generally indicate greater statistical precision than wider intervals.

The hazard-ratio interval does not include 1, and the reported p-value is < 0.001. Together, these summarize the strength and precision of the primary comparison under the reported method. They do not establish that the estimate is free of bias, nor do they address whether the effect is important to patients. The registry does not provide a clinical threshold for interpreting the size of the PFS difference.

Precision also depends on trial conduct and the information available for analysis. The registry reports the analysis population and outcome definitions, but detailed information about missing assessments, censoring, follow-up completeness, and the number of endpoint events is not reported in the registry record. Those details would help readers assess how the observed precision relates to the underlying data and analysis assumptions.

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 effect0.66182244
75% of the observed effect0.73324433
50% of the observed effect0.81728974
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%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: Lenvatinib + Pembrolizumab + TACE vs Placebo + TACE.

The planning illustrations are not the trial's original design calculations. For binary outcomes, the entries are participants per arm; for time-to-event outcomes, they are total events. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect used for each illustration is a stated fraction of the observed effect. The original trial's sample-size assumptions are not reported in the registry record.

The 80% power column describes the number of participants per arm, or total events for a time-to-event endpoint, that the illustration estimates would be needed to detect the specified effect with 80% power under those assumptions. The 90% power column gives the corresponding planning amount for 90% power. In general, power is the chance that a study will reject the null hypothesis when the specified effect is present, conditional on the model and assumptions used for planning. Higher planned power generally requires more information.

Rows based on 100%, 75%, and 50% of the observed effect illustrate how the planning requirement changes as the target effect becomes smaller. Smaller effects need more participants or events to distinguish them from random variation at the same significance level and target power. These calculations use observed results as inputs, so they are illustrations of possible planning requirements rather than evidence about the trial's design or its operating characteristics before the results were known.

These figures are not observed power. They should not be read as a retrospective measure of whether the trial was adequately powered. The registry record does not report the original sample-size justification, planned event target, or the assumptions used in the trial's design.

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 = 0.660, so ln(HR) = -0.4155.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.660)]2 = 181.8, rounded up to 182 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 <- 0.66                              # 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(4246177)
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 = 182 (80% power), 244 (90% power)
 75% of observed effect: events = 324 (80% power), 433 (90% power)
 50% of observed effect: events = 728 (80% power), 974 (90% power)
Simulated power with 182 events: 0.783 (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 305 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 118.1823.7100.00010.0001
Look 228.61632.5110.00600.0060
Look 360.02451.9930.02310.0250
01234z = 3.7118 mo82 eventsz = 2.5129 mo163 eventsz = 1.9960 mo245 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%18122560.0
Two looks, O'Brien-Fleming80%18122560.0
Three looks, O'Brien-Fleming80%18322860.0
Three looks, Pocock80%21126360.0
Fixed design, one analysis90%24230160.0
Two looks, O'Brien-Fleming90%24330260.0
Three looks, O'Brien-Fleming90%24530560.0
Three looks, Pocock90%27934760.0

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 effect0.660245305
75% of the observed effect0.732437534
50% of the observed effect0.8129841,185

For context, this trial enrolled 480 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 <- 10          # control-arm median, months (converted from the posted unit)
hr          <- 0.66          # 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: 230         p (1-sided)   0.0001
  Events: 82        ~HR at bound   0.4399
   Month: 18    P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.66   0.0338
   IA 2: 67%                   Z   2.5114
      N: 306         p (1-sided)   0.0060
 Events: 164        ~HR at bound   0.6750
   Month: 29    P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.66   0.5603
       Final                   Z   1.9930
      N: 306         p (1-sided)   0.0231
 Events: 245        ~HR at bound   0.7752
   Month: 60    P(Cross) if HR=1   0.0250
             P(Cross) if HR=0.66   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
Re-randomization testHazard Ratio (HR) 0.660.51 to 0.84< 0.001

The sponsor-reported primary comparison gives a hazard ratio of 0.66, a 95% confidence interval from 0.51 to 0.84, and p < 0.001 using a re-randomization test. The posted primary summary reports the same hazard-ratio estimate and interval, and the registry indicates no discrepancy for that result. The sponsor's analysis is therefore the relevant reported inferential result for the primary endpoint.

Some secondary outcomes also have sponsor-reported analyses. For example, the registry reports a sponsor estimate for the mRECIST PFS comparison using a Log Rank method. For ORR, the sponsor reports a difference in percentage with its confidence interval and p-value. The recalculated summaries are simple, unadjusted calculations from posted group summaries and are not substitutes for the sponsor's analysis, which may use a different analytical procedure.

Where a recalculated value does not match a sponsor-reported value exactly, the registry does not report a reason for the difference. The estimates should not be treated as interchangeable without knowing whether they target the same estimand and use the same method. The record does not provide enough detail to resolve every such methodological distinction. Recalculations can serve as descriptive checks, while the sponsor's reported analysis remains the primary source for the trial's stated inferential result.

16. Multiplicity, Missing Data and Analysis Populations

The registry identifies primary hypotheses involving PFS and overall survival in the brief summary, while the posted primary outcome result is PFS per RECIST 1.1. The record does not report an overall survival result. It also does not report how the two stated hypotheses were ordered, whether testing was hierarchical, or how the overall type I error rate was controlled across them.

Multiplicity matters when several hypotheses are tested. General explanation: if each test is judged independently at a chosen significance level, the chance of at least one false-positive result across the set can be higher than the chance for a single test. Prespecified procedures, such as a testing hierarchy or adjustment, can address this issue. Whether such a procedure was used for this study is not reported in the registry record. The same limitation applies to the secondary outcomes; an adjustment or formal testing sequence is not reported.

The registry does not report whether interim analyses were planned or conducted, how interim results would affect statistical thresholds, or whether a data monitoring committee reviewed accumulating data. The reason for the terminated status is also not reported. These absences prevent conclusions about the role of interim monitoring or termination in the observed result.

The primary outcome population is all randomized participants. Detailed missing-data methods, censoring rules, sensitivity analyses, and handling of incomplete assessments are not reported in the registry record. Nor are detailed subgroup analyses or model specifications reported. These are important for judging robustness, especially for a time-to-event endpoint that depends on follow-up and event ascertainment. The available record supports interpretation of the posted estimate and its reported test, but not reconstruction of the complete statistical analysis plan.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Lenvatinib + Pembrolizumab + TACE12223751.5%
Placebo + TACE6224125.7%
Participants with at least one serious adverse event
Serious adverse events by armLenvatinib + Pembrolizumab + …51.5%Placebo + TACE25.7%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Lenvatinib + Pembrolizumab + TACE126 of 237
Placebo + TACE127 of 243

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
Lenvatinib + Pembrolizumab + TACE234 of 237
Placebo + TACE229 of 241

Most frequent serious adverse event terms

Event termOrgan systemLenvatinib + Pembrolizumab + TACEPlacebo + TACE
Hepatic encephalopathyNervous system disorders12 of 2372 of 241
Liver abscessInfections and infestations3 of 2376 of 241
DiarrhoeaGastrointestinal disorders8 of 2370 of 241
Oesophageal varices haemorrhageGastrointestinal disorders5 of 2373 of 241
Blood bilirubin increasedInvestigations8 of 2370 of 241
Platelet count decreasedInvestigations3 of 2375 of 241
AscitesGastrointestinal disorders7 of 2370 of 241
SepsisInfections and infestations3 of 2374 of 241
PneumoniaInfections and infestations4 of 2372 of 241
Gastrointestinal haemorrhageGastrointestinal disorders4 of 2371 of 241

Most frequent non-serious adverse event terms

Event termOrgan systemLenvatinib + Pembrolizumab + TACEPlacebo + TACE
HypertensionVascular disorders126 of 23753 of 241
Alanine aminotransferase increasedInvestigations94 of 23779 of 241
Aspartate aminotransferase increasedInvestigations92 of 23777 of 241
Platelet count decreasedInvestigations96 of 23763 of 241
Blood bilirubin increasedInvestigations84 of 23756 of 241
ProteinuriaRenal and urinary disorders105 of 23727 of 241
Post embolisation syndromeInjury, poisoning and procedural complications52 of 23766 of 241
Abdominal painGastrointestinal disorders61 of 23756 of 241
Decreased appetiteMetabolism and nutrition disorders83 of 23731 of 241
PyrexiaGeneral disorders55 of 23756 of 241

Serious events with the highest arm-level rate: hepatic encephalopathy (5.1%), diarrhoea (3.4%), blood bilirubin increased (3.4%), ascites (3.0%), liver abscess (2.5%).

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 reports serious adverse events in 122 participants in the lenvatinib, pembrolizumab, and TACE group, among 237 at risk, and in 62 participants in the placebo and TACE group, among 241 at risk. These are participant counts, not event counts: a participant with more than one serious event may still be counted once in an outcome defined as experiencing at least one serious adverse event.

The record also lists serious adverse event terms and their reported percentages, including hepatic encephalopathy, diarrhoea, increased blood bilirubin, ascites, liver abscess, and oesophageal varices haemorrhage. These terms describe events recorded in the trial; they do not establish that the assigned regimen caused each event. The registry does not provide a causal attribution for the overall serious adverse event counts.

General context: safety comparisons require attention to time at risk, event definitions, follow-up, and how events were collected. The registry reports the groups at risk but does not provide detailed exposure-adjusted analyses or the full event narratives in the information. Counts should therefore be read as descriptive trial results, not as a complete account of comparative safety or individual risk.

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

The posted primary result indicates a difference between randomized groups in the reported PFS analysis, with the hazard-ratio estimate below 1 and a 95% confidence interval that does not include 1. The group medians and the reported inferential analysis describe the trial participants and endpoint under the registry's stated definitions. They do not establish a treatment effect for every individual or for populations not represented in the trial.

The comparison was between two regimens that both included TACE: lenvatinib plus pembrolizumab plus TACE versus placebo plus TACE. It does not isolate the separate contribution of lenvatinib, pembrolizumab, or TACE, and it does not compare TACE with no TACE. The result should be understood as a comparison of the assigned combinations.

The finding is specific to PFS per RECIST 1.1 assessed by BICR. It is not itself an overall survival result, and the registry does not report the overall survival result despite identifying OS as part of the study's primary hypotheses. PFS is also distinct from response rate, duration of response, and other secondary outcomes. Different endpoints can provide complementary evidence, but they do not answer identical questions.

Statistical significance does not by itself establish clinical importance. The registry does not report a threshold for a clinically meaningful difference or patient-reported outcomes in the information summarized. Nor does the reported result eliminate uncertainty from missing assessments, unreported analysis details, or the trial's terminated status. The record does not state why the trial was terminated, so that status should not be interpreted as evidence for or against the result.

No treatment recommendation follows from these statistics alone. They describe a randomized trial comparison and its reported precision; clinical decisions require broader evidence and patient-specific judgment.

19. Why This Trial Matters Statistically

This trial offers a randomized comparison of a combination regimen against placebo-containing treatment while keeping TACE in both groups. That design makes the assigned treatment strategies directly comparable within the trial, while defining the question as the added regimen in the context of TACE rather than the effect of TACE itself.

The primary endpoint is a time-to-event outcome with a prespecified clinical definition and central review. Reporting both group medians and a hazard ratio gives readers complementary summaries: the medians describe the timing of events within each group, while the hazard ratio compares event rates over follow-up under the reported analysis. The confidence interval and p-value communicate precision and statistical evidence, not clinical importance on their own.

The record also illustrates why endpoint families need to be distinguished. PFS under RECIST 1.1 and mRECIST, response measures, and safety outcomes represent different questions. Their results can provide context for the primary finding, but interpretation depends on analysis plans and multiplicity handling, which are not reported in detail. The registry's missing overall survival result also matters because OS was part of the stated primary hypotheses.

Finally, the record demonstrates the limits of a registry summary. It provides the principal result, group sizes, endpoint definitions, and some safety findings, but not the full statistical analysis plan, missing-data approach, interim analysis details, or reason for termination. Recognizing both the reported evidence and the unreported details is essential to a balanced statistical reading.

20. Limitations

The registry lists the study as terminated, but the reason for termination is not reported in the registry record. Without that information, it is not possible to determine whether termination affected follow-up, outcome collection, or the planned analysis. The record also does not report an overall survival result, although OS appears among the primary hypotheses in the brief summary.

Several details needed to assess the primary analysis are not reported: the original sample-size justification, the planned event target, interim analysis plans, censoring rules, missing-data procedures, and detailed model specifications. The registry identifies the primary analysis population as all randomized participants and names a re-randomization test, but does not provide enough detail to reconstruct the complete analysis.

The registry does not report a multiplicity strategy for the stated primary hypotheses or the secondary outcomes. This limits the degree to which secondary p-values can be viewed as confirmatory. It also does not provide detailed information about subgroup analyses, imaging schedules, or the handling of protocol deviations.

The primary endpoint is PFS assessed by BICR under RECIST 1.1. Such a result depends on the event definition and assessment process; the registry gives the progression criteria but not the full procedures for assessment timing and missing scans. The secondary mRECIST endpoint uses a different response framework, so its results are not directly interchangeable with the primary outcome.

Finally, the comparison tests two combinations in which both groups received TACE. It cannot identify the separate effect of each component. The registry record also does not report a clinical-importance threshold, which limits interpretation of whether the statistical difference meets a particular patient-centered benchmark.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

NCT04246177 is a randomized, parallel-group Phase 3 study in participants with incurable, non-metastatic hepatocellular carcinoma. It compared lenvatinib plus pembrolizumab plus TACE with placebo plus TACE. The registry lists 480 participants enrolled and the status as terminated.

The posted primary result is PFS per RECIST 1.1 assessed by BICR. The reported hazard ratio was 0.66, with a 95% confidence interval from 0.51 to 0.84 and p < 0.001 using a re-randomization test. The registry also reports secondary efficacy and safety outcomes, but does not report an overall survival result or the reason for termination.

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