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Lung Cancer Phase 2 Binary Endpoint NCT03322566

A Study of Pembrolizumab Plus Epacadostat With Platinum-based Chemotherapy Versus Pembrolizumab Plus Platinum-based Chemotherapy Plus Placebo in Metastatic Non-Small Cell Lung Cancer (KEYNOTE-715-06/ECHO-306-06): Complete Statistical Analysis

This randomized phase 2 trial compared pembrolizumab plus epacadostat and platinum-based chemotherapy with pembrolizumab plus platinum-based chemotherapy and placebo as first-line treatment for metastatic non-small cell lung cancer. The primary outcome was confirmed objective response; the registry also reports survival and safety outcomes.

Trial start: 2018-01-09  ·  Enrollment: 233  ·  Sponsor: Incyte Corporation
Scope of this record

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

1. Trial at a Glance

This page covers the registry results for A Study of Pembrolizumab Plus Epacadostat With Platinum-based Chemotherapy Versus Pembrolizumab Plus Platinum-based Chemotherapy Plus Placebo in Metastatic Non-Small Cell Lung Cancer (KEYNOTE-715-06/ECHO-306-06) (NCT03322566), a randomized phase 2 study. The primary outcome is Objective Response Rate (ORR) of Pembrolizumab + Chemotherapy + Epacadostat Versus Pembrolizumab + Chemotherapy + Placebo.

233
Enrollment
Phase 2
2
Arms
In the primary outcome
-18.5 pts
Risk difference
Pembrolizumab + Chemotherapy + Epacadost
-32.3 to -4.6 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03322566
PhasePhase 2
ConditionLung Cancer
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment233
Arms in the primary outcome2
Lead sponsorIncyte Corporation
Results postedYes

2. Clinical Question

Population

Participants with metastatic non-small cell lung cancer receiving first-line treatment. The primary outcome population is described as the ITT population of participants randomized to the pembrolizumab plus epacadostat plus chemotherapy arm or the pembrolizumab plus chemotherapy arm. The third treatment arm was not part of this primary outcome comparison.

Intervention

Pembrolizumab plus epacadostat and platinum-based chemotherapy. The arm description specifies pembrolizumab 200 mg intravenously every 3 weeks and epacadostat 100 mg orally twice daily, with platinum-doublet chemotherapy. The listed treatment courses could continue for up to 35 cycles.

Comparator

Pembrolizumab plus platinum-based chemotherapy and matching placebo. Pembrolizumab was given every 3 weeks; the placebo was taken orally twice daily. The registry describes this arm as the comparator for the primary outcome.

Primary question

What percentage of participants in each of these two groups had a confirmed complete or partial response, assessed under RECIST 1.1 by blinded independent central review? The registry specifies assessment every 12 weeks up to 24 months. The comparison concerns response proportions, not a direct measure of how long a response lasted.

The trial was designed to evaluate efficacy and safety. Its primary outcome is an objective response measure: it records whether participants had a confirmed complete or partial response, rather than relying on a subjective symptom rating. The registry also lists progression-free survival, overall survival, duration of response, and safety outcomes. Those endpoints address different aspects of the treatment experience and should not be treated as interchangeable with the primary response question.

3. Trial Design

The registry describes NCT03322566 as a randomized, quadruple-masked, parallel-group phase 2 study. Its stated objective was to evaluate pembrolizumab plus epacadostat with platinum-based chemotherapy against pembrolizumab plus platinum-based chemotherapy plus placebo as first-line therapy for participants with metastatic non-small cell lung cancer. The record lists an enrollment of 233 and a completed status.

The primary response comparison was between the pembrolizumab, chemotherapy, and epacadostat group and the pembrolizumab, chemotherapy, and placebo group. The primary outcome description says the ITT population included participants randomized to those two treatment arms, and explicitly states that this outcome was not a primary measure for the pembrolizumab plus epacadostat arm. A third arm, pembrolizumab plus epacadostat without chemotherapy, is also described in the record. It is distinct from the two-arm primary comparison.

The registry describes the experimental regimen as pembrolizumab 200 mg intravenously every 3 weeks, epacadostat 100 mg orally twice daily, and platinum-doublet chemotherapy. The comparator used pembrolizumab, matching placebo, and platinum-doublet chemotherapy. Both descriptions refer to treatment for up to 35 cycles. The chemotherapy details in the arm descriptions are truncated in the registry record, so the full regimen details are not reported in the registry record.

The primary outcome was objective response rate, assessed every 12 weeks up to 24 months. Response was defined as a confirmed complete response or partial response according to RECIST 1.1, based on blinded independent central review. The record lists progression-free survival, overall survival, duration of response, and safety outcomes as secondary measures. The original sample-size justification, planned interim analyses, and full statistical analysis plan are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: Phase 3 design of the study has been amended soon after it had started to a prospectively randomized phase 2 study. At the time of amendment existing participants were given a choice to move/participate in the new phase 2 study, and some participants who chose to discontinue the study at phase 3 were assigned to "study terminated by sponsor" as the reason for not completing the study in disposition table. The results posted are combined in the prospectively redesigned phase 2 trial.

Overall Study

StagePembrolizumab + Chemotherapy + EpacadostatPembrolizumab + Chemotherapy + PlaceboPembrolizumab + Epacadostat
STARTED918755
COMPLETED464222
NOT COMPLETED454533

Reasons for not completing this period:

ReasonPembrolizumab + Chemotherapy + EpacadostatPembrolizumab + Chemotherapy + PlaceboPembrolizumab + Epacadostat
Death343523
Physician Decision672
Withdrawal by Subject436
Lost to Follow-up001
Study terminated by sponsor101

Analysis population for the primary outcome, as defined in the registry: ITT population consisted of all participants randomized in treatment arm Pembrolizumab+Epacadostat+Chemotherapy and treatment arm Pembrolizumab+Chemothrapy. This is not a primary outcome measure for treatment arm Pembrolizumab+Epacadostat per protocol.

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: Intent-to-treat (ITT) population included all participants who were randomized to study intervention.

CharacteristicUnitPembrolizumab + Chemotherapy + EpacadostatPembrolizumab + Chemotherapy + PlaceboPembrolizumab + EpacadostatTotal
Participants analysed918755233
Age, Continuousyears63.0 (SD 11.7)63.6 (SD 8.8)62.8 (SD 8.4)63.2 (SD 9.9)
Sex: Female, Male: FemaleParticipants33301679
Sex: Female, Male: MaleParticipants585739154
Race/Ethnicity, Customized: Race – American Indian Or Alaska NativeParticipants1001
Race/Ethnicity, Customized: Race – AsianParticipants1110223
Race/Ethnicity, Customized: Race – Black Or African AmericanParticipants1102
Race/Ethnicity, Customized: Race – WhiteParticipants787553206
Race/Ethnicity, Customized: Race – MissingParticipants0101
Race/Ethnicity, Customized: Ethnicity – Hispanic or LatinoParticipants3115
Race/Ethnicity, Customized: Ethnicity – Not Hispanic or LatinoParticipants868552223
Race/Ethnicity, Customized: Ethnicity – UnknownParticipants2114
Race/Ethnicity, Customized: Ethnicity – Not ReportedParticipants0011

6. Primary Endpoint

The registry lists the primary outcome as Objective Response Rate (ORR) of Pembrolizumab + Chemotherapy + Epacadostat Versus Pembrolizumab + Chemotherapy + Placebo, measured over Assessed every 12 weeks up to 24 months.

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is objective response rate (ORR), expressed as the percentage of participants with a confirmed complete response or partial response. Responses were assessed using RECIST 1.1 and blinded independent central review, with assessments every 12 weeks up to 24 months. Complete and partial responses are distinct response categories, but both count toward this endpoint when confirmed.

As a binary endpoint, ORR classifies each participant as having or not having a qualifying response within the endpoint's assessment framework. The resulting percentage gives a straightforward summary of how often a response was recorded in each group. Comparing those percentages can help describe whether observed response frequency differed between the treatment groups. It does not by itself describe the duration of response, progression-free survival, overall survival, or adverse effects; these are separate outcomes in the registry.

Central review provides an assessment process separate from the treating site, and masking is intended to reduce the influence of knowledge about treatment assignment. The registry identifies the outcome assessment as blinded independent central review. The precise review procedures beyond that description are not reported in the registry record.

ORR is useful as a measure of tumor response, but a response proportion is not a complete account of clinical benefit or harm. The registry’s other endpoints cover different questions, and their results require separate interpretation. No medical conclusion follows from the endpoint definition alone; interpretation depends on the observed estimates, their uncertainty, and the analysis methods.

7. Results Posted in the Registry

Risk difference: Pembrolizumab + Chemotherapy + Epacadostat

-18.5

95% CI: -32.3 to -4.6 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals14.723.632.441.350.159.0Pembrolizumab + Chemotherapy … (n=91)Pembrolizumab + Chemotherapy … (n=87)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Pembrolizumab + Chemotherapy …-35-27-20-12-4.912.58risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Progression-free Survival of Pembrolizumab + Chemotherapy + Epacadostat Versus Pembrolizumab + Chemotherapy + PlaceboTime-to-Event AnalysisHazard ratio1.47 (0.91 to 2.36)212 events
Overall Survival of Pembrolizumab + Chemotherapy + Epacadostat Versus Pembrolizumab + Chemotherapy + PlaceboTime-to-Event AnalysisHazard ratio1.90 (0.93 to 3.90)77 events

Progression-free Survival of Pembrolizumab + Chemotherapy + Epacadostat Versus Pembrolizumab + Chemotherapy + Placebo

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Pembrolizumab + Chemotherapy …0.841.051.311.642.042.55hazard ratio (as reported) vs control (95% CI)

Overall Survival of Pembrolizumab + Chemotherapy + Epacadostat Versus Pembrolizumab + Chemotherapy + Placebo

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Pembrolizumab + Chemotherapy …0.831.161.612.253.144.37hazard ratio (as reported) vs control (95% CI)

The secondary endpoints address several different questions: time to progression or death, time to death, duration of response, and safety. The registry includes reported comparative analyses for progression-free and overall survival. Detailed numerical results for duration of response and all listed safety outcomes are not available in the registry record. Thus, the secondary evidence is incomplete and does not form a single, uniform set of findings.

The posted survival estimates do not provide a clear, precise basis for a firm conclusion about differences between groups. Their hazard-ratio confidence intervals include 1, and the overall survival medians are not reported in the registry record. These survival outcomes are related to the primary response endpoint but measure different aspects of disease course. A response percentage describes whether a qualifying response was recorded; it does not determine how long participants remained progression-free or how long they lived.

Secondary endpoints commonly involve multiple comparisons. When many outcomes are examined, the chance of at least one apparently unusual result can increase if no adjustment is made. The registry record does not report whether a multiplicity adjustment was prespecified or applied. Accordingly, secondary results should be treated as less confirmatory than a clearly specified primary analysis, particularly when the statistical plan and adjustment procedures are not available.

It is also important not to infer that endpoints with unreported estimates had no events or no difference. The record simply does not report those detailed results. The secondary findings can add context to the primary response comparison, but they do not resolve the discrepancy in the sponsor's primary analysis or replace the need for clear reporting of analysis methods and uncertainty.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary comparison, the registry reports an ORR of 26.4% in the pembrolizumab plus chemotherapy plus epacadostat group and 44.8% in the pembrolizumab plus chemotherapy plus placebo group. The corresponding reported 95% confidence intervals are 17.7% to 36.7% and 34.1% to 55.9%. These are estimates of response frequency in the two analyzed groups, not guarantees about the response rate in another population.

A simple unadjusted recalculation from the posted counts estimates a risk difference of -0.184 for epacadostat plus chemotherapy relative to placebo plus chemotherapy, with a 95% confidence interval from -0.323 to -0.046. The recalculated, unadjusted p-value is 0.01. Because the registry record contains a discrepancy between this recalculation and the sponsor's reported analysis, the sponsor's own analysis takes precedence. The sponsor reports a difference in percentages of -18.5, with a 95% confidence interval from -32.0 to -4.3, and p = 0.995. The registry's reported p-value and confidence interval should be presented as recorded; their apparent inconsistency is not resolved by the information in the registry record.

The sponsor-reported confidence interval for the difference is entirely below zero, while the reported p-value is 0.995. Those two entries do not convey a consistent statistical signal under the usual interpretation of a two-sided test and confidence interval. The registry does not explain this mismatch. It is therefore important not to substitute the recalculated test result for the sponsor's result or to treat the p-value in isolation as a reliable summary of the comparison. The available record does not establish why the entries differ.

For progression-free survival, the reported median estimates are 8.0 months for epacadostat plus chemotherapy and 8.2 months for placebo plus chemotherapy. The reported hazard ratio is 1.47, with a 95% confidence interval from 0.91 to 2.36; the reported p-value is 0.943. For overall survival, median estimates and their confidence intervals are not reported in the registry record. The reported hazard ratio is 1.90, with a 95% confidence interval from 0.93 to 3.90; the reported p-value is 0.963. The registry reports these as Cox regression analyses. These estimates are imprecise, and their confidence intervals include 1.

The registry also lists duration of response and safety outcomes among the secondary measures, but detailed results for all listed secondary outcomes are not available in the registry entries. The evidence should therefore be read as a set of endpoint-specific estimates with limitations, rather than as a single definitive summary. The primary comparison concerns response frequency; survival and safety results address distinct questions.

10. Statistical Methods Explained

The primary endpoint is a binary outcome: a participant either had a confirmed complete or partial response under the stated assessment criteria or did not. For a binary outcome, the observed response percentage is the number of participants with a qualifying response relative to the number assessed in the relevant group. The posted arm sizes for the primary comparison are 91 and 87. The displayed response percentages and confidence intervals describe each arm separately; the comparison estimate describes the difference between the groups.

What a risk difference represents

A risk difference subtracts one group's response proportion from the other's. The recalculated estimate is -0.184 for epacadostat plus chemotherapy relative to placebo plus chemotherapy. In plain language, the negative sign indicates that the estimated response proportion was lower in the first-named group in this unadjusted comparison. This recalculation uses the posted summary counts and is not the sponsor's reported analysis. Because the registry record flags a discrepancy, the sponsor's own analysis takes precedence.

Why the analysis method matters

The sponsor reports a stratified Miettinen and Nurminen method for the difference in percentages. This is a method for estimating and testing a difference between proportions. The term “stratified” indicates that the analysis accounts for strata, but the registry record does not identify those strata or explain their role. The sponsor's reported difference, confidence interval, and p-value are the registry's own analysis results. The unadjusted recalculation is not a replacement for that analysis and does not reproduce the stated method.

The recalculated confidence interval and p-value are derived from an unadjusted comparison of the posted response summaries. A confidence interval describes a range of values compatible with the data and method under its assumptions; it is not a probability statement that a particular fixed effect lies within the observed interval. A p-value measures how unusual the data would be under a specified null model, given the test's assumptions. Neither statistic measures the probability that a treatment is effective, nor does either determine the practical importance of an outcome.

How to read the survival analyses

Progression-free survival and overall survival are time-to-event outcomes. Their reported hazard ratios come from Cox regression. A hazard ratio compares event rates over follow-up under the model; it is not a ratio of median survival times. A value of 1 represents equal hazards in the comparison parameterization, while values on either side represent different estimated hazards. The estimates need to be considered alongside their confidence intervals and the analysis assumptions. The registry record does not report diagnostics or details about the Cox model beyond its method label.

The progression-free survival medians are reported with 95% confidence intervals, though the upper limit for the placebo group is not reported in the registry record. The overall survival medians and their interval limits are not reported in the registry record. Missing median estimates do not mean that the underlying outcome was absent; they mean that the values are not available in the registry results. The reported hazard ratios and p-values remain the registry's posted comparative statistics.

Confidence intervals and uncertainty

A confidence interval communicates estimation uncertainty as a range produced by a statistical procedure. Wider intervals indicate less precision than narrower intervals, all else equal. For the response percentages, the intervals reflect uncertainty in each arm's estimate. The sponsor's interval for the difference concerns the contrast between arms and should not be confused with the separate arm-specific intervals. Overlap or non-overlap of separate arm intervals is not a substitute for evaluating a formal between-arm contrast.

The interval for a hazard ratio is interpreted relative to 1, while the interval for a risk difference is interpreted relative to 0. The progression-free survival and overall survival intervals include 1. The sponsor-reported response difference interval is wholly below 0, but its accompanying p-value is inconsistent with that interval under standard two-sided interpretation. The record does not provide enough detail to reconcile this discrepancy.

Planning illustrations

The posted sample-size illustrations use the observed effect as a starting point and consider planning for 100%, 75%, or 50% of that effect. For the binary primary endpoint, the illustrations give participants per arm. For time-to-event endpoints, they give total events. They use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the time-to-event illustrations use the Schoenfeld approach. These are planning illustrations, not the original trial design calculations. The trial's original sample-size assumptions are not reported in the registry record.

Power is the probability, under a specified planning model and assumed effect, of detecting that effect at the selected significance level. The 80% and 90% columns describe two target probabilities under those assumptions. These targets are not probabilities that a result is true and are not estimates of the power achieved by the completed trial. The trial's observed power is not calculated from its results. Because the illustrations scale the effect downward, the smaller assumed effects require more participants or events to reach the same target power.

The registry's record of methods is incomplete for several important details. The treatment of missing endpoint data, any multiplicity adjustment, prespecified analysis populations beyond the primary ITT description, and the full statistical analysis plan are not reported in the registry record. Those omissions limit how fully the posted estimates can be independently assessed.

11. Confidence Intervals and Precision

Precision concerns how much uncertainty surrounds an estimate. For the primary response endpoint, the registry reports 95% confidence intervals for each arm: 17.7% to 36.7% for pembrolizumab plus chemotherapy plus epacadostat, and 34.1% to 55.9% for pembrolizumab plus chemotherapy plus placebo. These intervals show that the response percentages are estimated with meaningful uncertainty; the point estimates should not be read as exact population values.

The recalculated unadjusted risk difference is -0.184, with a 95% confidence interval from -0.323 to -0.046. The sponsor-reported difference is -18.5, with a 95% confidence interval from -32.0 to -4.3. These are separate presentations: the recalculation is unadjusted, while the sponsor reports a stratified method. The registry's stated discrepancy means the sponsor analysis takes precedence, and its p-value does not align with its confidence interval under standard two-sided interpretation. The record does not resolve that issue.

For progression-free survival, the hazard ratio is 1.47, with a 95% confidence interval from 0.91 to 2.36. For overall survival, the hazard ratio is 1.90, with a 95% confidence interval from 0.93 to 3.90. Both intervals span 1, indicating considerable uncertainty about the relative hazard represented by each estimate. The overall survival medians and confidence intervals are not reported in the registry record. The upper confidence limit for the placebo group's progression-free survival median is also not reported in the registry record.

A confidence interval is not a range containing most individual participants' outcomes. It is a range of plausible values for the underlying parameter under the statistical method and assumptions. It does not establish equivalence when it includes a null value, and it does not by itself establish a meaningful difference when it excludes one. Precision and clinical importance are related but distinct considerations.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect105140
75% of the observed effect192257
50% of the observed effect443592
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,0002,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Pembrolizumab + Chemotherapy + Epacadostat.

The planning illustrations are calculated from the observed effect; they are not the trial's original design calculations. The assumptions listed are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation, with the effect to detect set to the stated fraction of the observed effect. The time-to-event illustrations use the Schoenfeld approach. The original trial design assumptions and sample-size justification are not reported in the registry record.

For the primary binary outcome, the figures are participants per arm for 80% power and participants per arm for 90% power. For time-to-event outcomes, the figures are total events, not participants per arm. These quantities answer different planning questions: a per-arm participant count concerns the number assigned to each of two groups, while an event target concerns the number of observed events across the time-to-event comparison.

The 80% and 90% power columns represent alternative planning targets: under the stated assumptions, the higher target is a greater chance of detecting the assumed effect if that effect is present. The figures are not guarantees of detection and should not be interpreted as the probability that a finding is correct. They are planning illustrations, not observed power.

The illustrations also show how the assumed effect size changes the required scale of a study. Planning for a smaller fraction of the observed effect requires more participants per arm or more total events to reach a given power target. This is a general feature of statistical planning: smaller differences are harder to distinguish from random variation. The observed effect is only a reference point for these calculations, and it may not be a reliable estimate of the effect that a future study should expect.

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

n = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

  1. Control proportion p0 = 0.448; treatment proportion p1 = 0.264; average p̄ = 0.356.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6771 = 1.3272.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6645 = 0.5592.
  4. n = (1.3272 + 0.5592)2 / (-0.1845)2 = 104.5, rounded up to 105 participants per arm 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
p0 <- 0.448275862068966                          # control proportion
p1 <- 0.263736263736264                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(3322566)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 105 (80% power), 140 (90% power)
 75% of observed effect: n per arm = 192 (80% power), 257 (90% power)
 50% of observed effect: n per arm = 443 (80% power), 592 (90% power)
power.prop.test: 104.5 
Simulated power at n = 105 per arm: 0.801 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Stratified Miettinen and Nurminen methodDifference in Percentages -18.5-32.0 to -4.30.995
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The registry reports a sponsor analysis using the stratified Miettinen and Nurminen method. It gives a difference in percentages of -18.5, with a 95% confidence interval from -32.0 to -4.3, and p = 0.995. Separately, a simple unadjusted recalculation from the posted response counts gives a risk difference of -0.184, a 95% confidence interval from -0.323 to -0.046, and an unadjusted p-value of 0.01.

These are not identical analyses: the recalculation is unadjusted, whereas the sponsor reports a stratified method. The registry record flags a discrepancy, so the sponsor's own analysis takes precedence over the simple recalculation. However, the sponsor's reported p-value is not consistent with its reported confidence interval under standard two-sided interpretation. The registry does not explain this mismatch, and the posted results do not establish its cause.

The recalculated result can help readers see how the posted summary counts compare under a simple unadjusted approach, but it should not be substituted for the sponsor's result or treated as the definitive test. The correct reading is to report the sponsor's analysis as recorded, note the inconsistency in its entries, and avoid drawing a conclusion from the recalculated p-value alone.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study evaluates more than one endpoint, comparison, time point, or subgroup. Each additional statistical test can increase the chance of obtaining at least one apparently significant result by chance if the tests are considered together without adjustment. This is why interpretation often distinguishes a prespecified primary endpoint from secondary or exploratory outcomes.

The registry identifies objective response rate as the primary outcome for the comparison between pembrolizumab plus chemotherapy plus epacadostat and pembrolizumab plus chemotherapy plus placebo. It also lists progression-free survival, overall survival, duration of response, and safety outcomes. The record does not state whether the study controlled the overall type I error rate across these endpoints, whether a hierarchical testing strategy was used, or whether any adjustment for multiple comparisons was applied. These procedures are not reported in the registry record.

The primary outcome description identifies an ITT population consisting of participants randomized to the two treatment arms in the primary comparison. It also says that the outcome was not a primary outcome measure for the pembrolizumab plus epacadostat arm. Details of other analysis populations, any per-protocol analyses, or how participants were handled in the analysis are not reported in the registry record.

Missing-data methods are also not reported in the registry record. The posted description does not explain how unavailable response assessments, withdrawal, or other missing endpoint information were handled. It does not state how censoring was defined for the time-to-event analyses or describe sensitivity analyses for missing data. Those omissions matter because analysis choices can affect estimates and uncertainty, especially when follow-up or assessment information is incomplete.

The trial's full statistical analysis plan, planned interim analyses, and original sample-size justification are not reported in the registry record. Without these details, readers cannot verify the complete prespecified testing framework, determine whether analyses changed, or assess whether all relevant outcomes and analyses are represented. This is a limitation in interpretation, not evidence that a particular procedure was or was not used.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Pembrolizumab + Chemotherapy + Epacadostat479052.2%
Pembrolizumab + Chemotherapy + Placebo418647.7%
Pembrolizumab + Epacadostat205238.5%
Total10822847.4%
Participants with at least one serious adverse event
Serious adverse events by armPembrolizumab + Chemotherapy …52.2%Pembrolizumab + Chemotherapy …47.7%Pembrolizumab + Epacadostat38.5%Total47.4%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Pembrolizumab + Chemotherapy + Epacadostat38 of 90
Pembrolizumab + Chemotherapy + Placebo35 of 86
Pembrolizumab + Epacadostat26 of 52
Total99 of 228

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Pembrolizumab + Chemotherapy + Epacadostat87 of 90
Pembrolizumab + Chemotherapy + Placebo81 of 86
Pembrolizumab + Epacadostat51 of 52
Total219 of 228

Most frequent serious adverse event terms

Event termOrgan systemPembrolizumab + Chemotherapy + EpacadostatPembrolizumab + Chemotherapy + PlaceboPembrolizumab + EpacadostatTotal
PneumoniaInfections and infestations5 of 9012 of 864 of 5221 of 228
Malignant neoplasm progressionNeoplasms benign, malignant and unspecified (incl cysts and polyps)5 of 902 of 868 of 5215 of 228
Febrile neutropeniaBlood and lymphatic system disorders5 of 900 of 860 of 525 of 228
Pleural effusionRespiratory, thoracic and mediastinal disorders2 of 901 of 862 of 525 of 228
BronchitisInfections and infestations3 of 901 of 860 of 524 of 228
DiarrhoeaGastrointestinal disorders2 of 902 of 860 of 524 of 228
Lower respiratory tract infectionInfections and infestations3 of 901 of 860 of 524 of 228
PneumonitisRespiratory, thoracic and mediastinal disorders1 of 903 of 860 of 524 of 228
SepsisInfections and infestations3 of 900 of 861 of 524 of 228
Atrial fibrillationCardiac disorders1 of 902 of 860 of 523 of 228

Most frequent non-serious adverse event terms

Event termOrgan systemPembrolizumab + Chemotherapy + EpacadostatPembrolizumab + Chemotherapy + PlaceboPembrolizumab + EpacadostatTotal
NauseaGastrointestinal disorders38 of 9037 of 8610 of 5285 of 228
AnaemiaBlood and lymphatic system disorders24 of 9037 of 868 of 5269 of 228
FatigueGeneral disorders28 of 9025 of 8614 of 5267 of 228
DiarrhoeaGastrointestinal disorders23 of 9023 of 8614 of 5260 of 228
ConstipationGastrointestinal disorders26 of 9023 of 868 of 5257 of 228
RashSkin and subcutaneous tissue disorders22 of 9018 of 8610 of 5250 of 228
Decreased appetiteMetabolism and nutrition disorders19 of 9020 of 868 of 5247 of 228
AstheniaGeneral disorders12 of 9018 of 866 of 5236 of 228
VomitingGastrointestinal disorders19 of 9011 of 866 of 5236 of 228
DizzinessNervous system disorders16 of 9013 of 865 of 5234 of 228

Serious events with the highest arm-level rate: malignant neoplasm progression (15.4%), pneumonia (14.0%), febrile neutropenia (5.6%), death (3.8%), pleural effusion (3.8%).

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

The registry reports serious adverse event figures for three treatment groups and a total group. In the epacadostat plus chemotherapy group, 47 participants were at risk for serious adverse events and 90 were at risk for other adverse events; the reported number of deaths is 38. In the placebo plus chemotherapy group, the corresponding figures are 41, 86, and 35. For pembrolizumab plus epacadostat without chemotherapy, the figures are 20, 52, and 26. The total group reports 108 participants affected by serious adverse events, 219 affected by other adverse events, and 99 deaths, with 228 at risk for each adverse-event category.

The listed serious adverse event terms include malignant neoplasm progression at 15.4%, pneumonia at 14.0%, febrile neutropenia at 5.6%, death at 3.8%, pleural effusion at 3.8%, and pneumonitis at 3.5%. These are registry-listed terms and percentages; the record does not provide additional detail about event timing, recurrent events, or the denominator used for each term.

These figures are descriptive and include all three treatment groups for the overall safety record. They should not be read as a direct statistical comparison of the two primary-outcome arms. The registry's definitions and detailed methods for classifying adverse events are not reported in the registry record.

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

The posted primary outcome estimates describe different observed response percentages in the two treatment groups: 26.4% with pembrolizumab plus chemotherapy plus epacadostat and 44.8% with pembrolizumab plus chemotherapy plus placebo. The arm-specific confidence intervals indicate uncertainty in both estimates. The sponsor's reported difference is -18.5, with a 95% confidence interval from -32.0 to -4.3, but the accompanying p-value of 0.995 is inconsistent with that interval under standard two-sided interpretation. The registry does not explain the discrepancy.

Because the record identifies a discrepancy between the sponsor analysis and an unadjusted recalculation, the sponsor's own analysis takes precedence. The unadjusted recalculation can be described as a separate calculation from the posted summary statistics, not as a replacement for the sponsor's method. Neither the endpoint estimate nor a p-value alone establishes a treatment's overall benefit or harm.

The secondary survival results address outcomes distinct from response. The progression-free and overall survival hazard-ratio intervals include 1, and the overall survival median estimates are not reported in the registry record. The registry also lists safety outcomes, but the posted event figures are descriptive and do not by themselves establish comparative safety. The record does not give full results for every listed secondary endpoint.

These findings do not establish that one regimen is effective or ineffective, nor do they show that the treatments are equivalent. They describe the registry's reported results and their uncertainty for this study population and analysis. The available information does not support claims beyond those outcomes and comparisons, and it does not provide a complete account of the prespecified statistical plan, missing-data handling, or multiplicity procedures.

Clinical decisions require broader evidence and individual context; the statistics are not medical advice. The statistical reading is narrower: distinguish response frequency from survival and safety, consider intervals as well as point estimates, and take account of the unresolved inconsistency in the sponsor's primary analysis.

18. Why This Trial Matters Statistically

This trial illustrates why statistical interpretation requires more than reading a point estimate or a p-value. Its primary response percentages differ, while the sponsor's reported confidence interval and p-value do not give a consistent conventional account of the same comparison. The registry's discrepancy flag and the unadjusted recalculation make that issue visible, but the recalculation does not replace the sponsor's analysis. Transparent reporting of the analysis method and internally consistent results is essential for readers to evaluate evidence.

The study also shows why endpoints must be interpreted according to what they measure. ORR records the proportion with a confirmed response; progression-free survival and overall survival are time-to-event outcomes; safety summaries count adverse-event experience. A result on one endpoint cannot stand in for results on the others. The registry's incomplete reporting for some secondary outcomes makes it especially important to avoid treating the primary endpoint as a complete summary of all outcomes.

Uncertainty also matters. Confidence intervals communicate the range of estimates compatible with the data and method, while the planning illustrations show how assumed effect size affects required sample size or event counts. Those planning figures are not evidence of the trial's achieved power and are not the original design justification. The original sample-size assumptions are not reported in the registry record.

Finally, this is a randomized phase 2 comparison in metastatic non-small cell lung cancer, with a specified two-arm primary response question and a separate third arm in the wider study record. Clear identification of the population and comparator is necessary to understand which participants and outcomes the estimates describe. The record offers useful statistical information, but missing analysis details and the reported discrepancy limit how fully the findings can be evaluated.

19. Limitations

A key limitation is the inconsistency between the sponsor's reported primary analysis and the simple unadjusted recalculation from posted response summaries. The sponsor's confidence interval for the difference lies below zero, while the reported p-value is 0.995. The registry does not explain the discrepancy. Although the record flags it, the available information does not identify its source or provide a way to resolve it.

The record does not report the original sample-size justification or design assumptions. The posted sample-size figures are planning illustrations based on the observed effect, not the trial's own design calculations. The planned interim analyses and full statistical analysis plan are also not reported in the registry record.

Important analytical details are absent, including whether multiplicity was controlled, how missing outcome data were handled, which additional analysis populations were used, and the detailed censoring rules or model diagnostics for survival analyses. These omissions make it difficult to assess all assumptions behind the estimates.

Not all secondary results are reported in detail. Overall survival medians and their confidence intervals are not reported in the registry record, and the upper confidence limit for the placebo group's progression-free survival median is not reported. Detailed numerical findings for duration of response are not available in the registry entries. The safety summary provides group counts and selected serious event terms but does not report the event-classification methods or all details needed for a direct comparative assessment.

The primary comparison includes the two specified chemotherapy-containing groups; the study record also describes a third treatment arm. The primary result should not be generalized to that third arm. The registry records enrollment of 233, while the primary comparison and safety summaries use their own stated group counts; the record does not explain every difference in denominators.

20. Related Tutorials

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23. Record Summary

NCT03322566 is a completed randomized, quadruple-masked, parallel-group phase 2 study in metastatic non-small cell lung cancer. The primary comparison was pembrolizumab plus epacadostat and platinum-based chemotherapy versus pembrolizumab plus platinum-based chemotherapy and placebo. The primary endpoint was confirmed objective response rate assessed by blinded independent central review under RECIST 1.1, every 12 weeks up to 24 months.

The registry reports response percentages of 26.4% and 44.8%, respectively. The sponsor reports a difference of -18.5, a 95% confidence interval from -32.0 to -4.3, and p = 0.995. The registry record flags a discrepancy with a simple unadjusted recalculation; the sponsor's own analysis takes precedence, but the reported p-value and confidence interval are not consistent under standard two-sided interpretation. Survival and safety outcomes provide additional, distinct information, with important results and analysis details not reported in the registry record.

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