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Squamous Cell Carcinoma of the Head and Neck Phase 3 Time-to-Event Analysis NCT02105636

Trial of Nivolumab vs Therapy of Investigator's Choice in Recurrent or Metastatic Head and Neck Carcinoma (CheckMate 141): Complete Statistical Analysis

This analysis examines overall survival in CheckMate 141, a randomized phase 3 trial of nivolumab versus investigator’s choice therapy for recurrent or metastatic platinum-refractory squamous cell carcinoma of the head and neck. It also considers the posted progression-free survival, response, planning illustrations, and serious adverse event data.

Trial start: 2014-05-29  ·  Enrollment: 361  ·  Sponsor: Bristol-Myers Squibb
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 Trial of Nivolumab vs Therapy of Investigator's Choice in Recurrent or Metastatic Head and Neck Carcinoma (CheckMate 141) (NCT02105636), a randomized phase 3 study. The primary outcome is Overall Survival (OS).

361
Enrollment
Phase 3
2
Arms
In the primary outcome
0.70
Hazard ratio
Nivolumab 3mg/kg vs Investigators Choice
0.53–0.92
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02105636
PhasePhase 3
ConditionSquamous Cell Carcinoma of the Head and Neck
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment361
Arms in the primary outcome2
Lead sponsorBristol-Myers Squibb
Results postedYes

2. Clinical Question

Population

The trial concerned participants with recurrent or metastatic squamous cell carcinoma of the head and neck. Its official title specifies platinum-refractory disease. The primary outcome population was all randomized participants.

Intervention

Participants assigned to the experimental arm received nivolumab 3mg/kg as an intravenous solution every 2 weeks until disease progression.

Comparator

The comparison was with investigator’s choice of cetuximab, methotrexate, or docetaxel. The registry record describes the listed drugs and some administration details, but does not give complete dosing information for every option in the arm description.

Primary question

The primary question was whether nivolumab would significantly improve overall survival compared with investigator’s choice therapy. Overall survival was measured from randomization until death from any cause, with participants censored when last known alive or, when no follow-up was available, at randomization.

This was an open-label randomized comparison, so the assigned treatments were not masked. The central statistical question is about the time-to-event outcome: how the observed survival distributions and the reported hazard ratio compare between the randomized arms. The registry record reports median overall survival and a hazard ratio with a confidence interval, along with a log-rank p-value. Those statistics describe the trial’s posted result; they do not by themselves establish how the result applies to people outside the trial population.

The trial also posted investigator-assessed progression-free survival and objective response rate as secondary outcomes. These outcomes address different aspects of the disease course than overall survival. They can add context, but they do not replace the prespecified primary question, and the registry record does not report whether any adjustment for multiple outcome testing was used.

3. Trial Design

CheckMate 141 (NCT02105636) was a phase 3, randomized, parallel-group, open-label clinical trial sponsored by Bristol-Myers Squibb. The registry lists enrollment of 361 and a completed status. The study started on 2014-05-29, and primary completion was recorded as 2015-11-06. Its official title describes a comparison of nivolumab with therapy of investigator’s choice in recurrent or metastatic platinum-refractory squamous cell carcinoma of the head and neck.

One arm received nivolumab 3mg/kg intravenously every 2 weeks until disease progression. The other arm allowed investigator’s choice among cetuximab, methotrexate, or docetaxel. The registry describes cetuximab as an intravenous solution, with a first dose of 400 mg/m2 followed by 250 mg/m2 weekly until disease progression. It describes methotrexate as an intravenous solution at 40 or 60 mg/m2 weekly until disease progression. The docetaxel description begins with 30 or 40 mg/m2 weekly, but the posted arm description is incomplete, so further dosing details are not reported in the registry record.

For the primary outcome, the posted analysis includes 240 participants in the nivolumab arm and 121 in the investigator’s choice arm. These are the analysis group sizes listed for overall survival, whose stated population is all randomized participants. The registry record does not report the rationale for the allocation proportions, the original sample-size justification, or the protocol’s planned statistical details beyond the posted endpoint and analyses.

The primary endpoint was overall survival, defined as time from randomization to death from any cause. The primary timeframe is described as up to approximately 18 months. The posted secondary outcomes were investigator-assessed progression-free survival and objective response rate; their timeframe descriptions extend to up to approximately 87 months. A longer listed timeframe does not by itself indicate how much follow-up was available for every participant.

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.

Pre-Treatment

StageNivolumab 3mg/kgInvestigators Choice
STARTED240121
COMPLETED236111
NOT COMPLETED410

Reasons for not completing this period:

ReasonNivolumab 3mg/kgInvestigators Choice
Disease Progression10
Participant request to discontinue study treatment12
Participant withdrew consent06
Participant no longer meets study criteria22

Treatment

StageNivolumab 3mg/kgInvestigators Choice
STARTED236111
COMPLETED10
NOT COMPLETED235111

Reasons for not completing this period:

ReasonNivolumab 3mg/kgInvestigators Choice
Study Drug Toxicity1410
Adverse event unrelated to study drug193
Participant request to discontinue study treatment86
Participant withdrew consent51
Lost to Follow-up10
Maximum Clinical Benefit13
Poor/Non-compliance01
Participant no longer meets study criteria10
Other reasons10
Disease Progression18587

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.

CharacteristicUnitNivolumab 3mg/kgInvestigators ChoiceTotal
Participants analysed240121361
Age, Continuousyears59.0 (SD 10.15)59.4 (SD 11.00)59.1 (SD 10.43)
Age, Customized: < 65 yearsParticipants17276248
Age, Customized: >=65 and <75 yearsParticipants563995
Age, Customized: >=75 yearsParticipants12618
Sex: Female, Male: FemaleParticipants431861
Sex: Female, Male: MaleParticipants197103300
Race/Ethnicity, Customized: WhiteParticipants196104300
Race/Ethnicity, Customized: Black or African AmericanParticipants10313
Race/Ethnicity, Customized: AsianParticipants291443
Race/Ethnicity, Customized: OtherParticipants505
Race/Ethnicity, Customized: Hispanic/LatinoParticipants9413
Race/Ethnicity, Customized: Not Hispanic/LatinoParticipants13260192
Race/Ethnicity, Customized: Not ReportedParticipants9957156

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival (OS), measured over From date of randomization to date of death (Up to approximately 18 months).

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

Overall survival measures the time from randomization until death from any cause. In this trial, participants who were still known to be alive were censored at the date they were last known alive. Participants who were randomized but had no follow-up were censored at randomization. The registry states that median overall survival was calculated using the Kaplan-Meier method.

Overall survival is useful in a time-to-event comparison because it incorporates both the timing of events and the experience of participants who have not had an observed event by the end of their available follow-up. A median summarizes the estimated time by which half of the survival distribution has experienced the event, rather than describing the outcome for every participant. A hazard ratio offers a relative comparison of the event rates over follow-up, subject to the assumptions and interpretation of that measure.

Death from any cause is the event specified for this endpoint, rather than a cause-specific death category. This definition makes the endpoint distinct from progression-free survival, which counts disease progression or death, whichever occurs first. The posted primary outcome therefore addresses survival directly, while secondary outcomes provide information about progression and tumor response.

The endpoint’s stated timeframe is up to approximately 18 months. That wording does not mean that every participant was followed for that duration, and the registry record does not report participant-level follow-up distributions in the registry record presented. The event and censoring rules matter when interpreting the Kaplan-Meier median and its confidence interval, because estimates depend on the observed follow-up and censoring pattern.

7. Results Posted in the Registry

Hazard ratio: Nivolumab 3mg/kg vs Investigators Choice

0.70

95% CI: 0.53 to 0.92

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Nivolumab 3mg/kg vs Investiga…0.500.580.680.780.911.05hazard 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
Investigator-Assessed Progression-Free Survival (PFS)Time-to-Event AnalysisHazard ratio0.86 (0.68 to 1.10)1,381 events
Investigator-Assessed Objective Response Rate (ORR)Binary EndpointRisk difference-7.5 pts (-13.5 to -1.6)238 per arm

Investigator-Assessed Progression-Free Survival (PFS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Nivolumab 3mg/kg vs Investiga…0.650.730.820.911.021.14hazard ratio (as reported) vs control (95% CI)

Investigator-Assessed Objective Response Rate (ORR)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Investigators Choice-15-11-8.34-5.20-2.061.08risk difference (percentage points) vs control (95% CI)

The secondary endpoints broaden the clinical and statistical picture, but they do not all point to the same kind of measurement. Progression-free survival concerns time to progression or death, whereas objective response rate records whether a response was observed during the stated assessment period. These outcomes are related to disease course but are not equivalent to overall survival, the primary endpoint. Their results therefore add context rather than serving as direct replications of the primary survival comparison.

The posted progression-free survival comparison is less conclusive in its interval-based interpretation than the primary overall-survival comparison: its hazard-ratio confidence interval includes 1. The response outcome has a higher posted percentage in the nivolumab arm, but its estimates are based on a different endpoint and scale. This general pattern does not establish that one secondary endpoint confirms another; the questions, measurements, and statistical uncertainty differ.

Secondary analyses carry less confirmatory weight when the registry does not report whether multiplicity was addressed. Testing several outcomes can increase the chance that at least one appears statistically notable by chance. Adjustments or a prespecified testing hierarchy can manage that issue, but such procedures are not reported in the registry record. The response analyses also include more than one comparative measure, which reinforces the need to interpret each estimate in its stated context rather than select the most favorable result.

The primary endpoint remains the principal basis for evaluating the trial’s stated survival question. Secondary results can help describe other observed outcomes and identify questions for further study, but they should not be used to override the primary result or to claim broader certainty than the posted evidence supports. The registry does not report enough of the statistical plan to determine the intended confirmatory status of each secondary analysis.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted primary result reports median overall survival of 7.49 months for nivolumab and 5.06 months for investigator’s choice. The corresponding 95% confidence intervals are 5.49 to 9.1 months and 4.04 to 6.05 months. These medians describe each arm separately; their difference should not be treated as the trial’s principal comparative estimate. The reported hazard ratio for nivolumab versus investigator’s choice is 0.70, with a 95% confidence interval from 0.53 to 0.92 and a reported log-rank p-value of 0.010.

The hazard ratio is the registry’s relative time-to-event comparison. Its point estimate is below 1, and its confidence interval does not include 1. The reported p-value is evidence against the no-difference null hypothesis under the stated log-rank analysis. These statistics describe the observed randomized comparison; they do not establish a treatment effect for every patient or settle how the result applies beyond the trial population. No causal explanation for the outcome can be established from these summary statistics alone.

Precision is relevant to the size of the estimated association. The confidence interval spans values from 0.53 to 0.92, so the result is not a single exact value. Although the interval is on one side of 1, it still includes a range of possible relative effects. Median confidence intervals likewise give ranges of uncertainty around each arm’s estimated median. They should be read as uncertainty intervals rather than as ranges containing a fixed proportion of individual survival times.

The secondary outcomes offer a broader but not identical picture. For investigator-assessed progression-free survival, the posted medians are 2.04 months for nivolumab and 2.33 months for investigator’s choice, and the reported hazard ratio is 0.86 with a 95% confidence interval of 0.68 to 1.10. For objective response rate, the posted percentages are 13.3% and 5.8%, respectively. These outcomes do not reproduce the primary endpoint: progression-free survival includes progression, and response is a binary measure. The progression-free survival interval includes 1, while the response estimates have their own uncertainty. The registry does not report multiplicity adjustment, so secondary comparisons should not be treated as equally confirmatory as the primary analysis.

The reported results are based on the posted analysis methods and populations. The record does not report detailed censoring diagnostics, the number of primary endpoint events, or a full statistical analysis plan. Those omissions limit assessment of assumptions and analysis choices, but they do not alter the interpretation of the summary statistics as posted. Overall, the primary endpoint’s reported comparison is more directly relevant to the stated trial question than the secondary outcomes, while all estimates remain subject to uncertainty and the limits of the record.

10. Statistical Methods Explained

Time-to-event outcomes require methods that account for when an event occurs and for participants whose event time is not observed during their available follow-up. In this trial, overall survival time began at randomization and ended at death from any cause. The registry specifies censoring at the last date known alive, or at randomization for participants with no follow-up. Censoring means that the event time is not observed after a participant’s last known status; it does not mean that the participant experienced the event at that time.

What does the Kaplan-Meier median represent?

The Kaplan-Meier method estimates the survival distribution while accounting for censored observations. The median is the time at which the estimated survival curve reaches the halfway point. It is an arm-specific summary, not a direct estimate of the comparative effect between arms. The posted medians should therefore be read alongside the hazard ratio and its confidence interval. The method relies on censoring being appropriately handled; the registry record does not report diagnostics or further detail about the censoring pattern.

How should the hazard ratio be read?

A hazard ratio compares event rates between groups over follow-up. The reported primary estimate is 0.70 for nivolumab versus investigator’s choice. A value of 1 corresponds to no relative difference in the hazard under this measure; values on either side indicate a lower or higher relative hazard for the numerator group, respectively. This is a general interpretation of hazard ratios, not a claim that the relative hazard is constant at every time. The registry reports a log-rank method for the primary analysis, but does not report further details about the model or proportional-hazards assessment. The analysis description also labels the result as a superiority analysis.

The confidence interval communicates uncertainty around the estimated hazard ratio. The reported 95% interval is 0.53 to 0.92. It is an interval for the comparative parameter under the analysis, not a range of individual outcomes. The p-value of 0.010 summarizes how compatible the observed data are with the null hypothesis under the reported test; it is not the probability that the null hypothesis is true, nor does it measure the clinical importance of the estimate.

Why can over-dispersion matter?

General statistical context: in count outcomes, over-dispersion means that variation is greater than a model assumes. Ignoring it can make uncertainty appear smaller than it is. The primary endpoint is a time-to-event outcome, and the registry does not report a count model for it. The posted methods information does not establish that over-dispersion was a concern or that a correction was used. It is therefore not appropriate to attribute a specific over-dispersion adjustment to this trial.

What do the secondary outcome methods add?

Progression-free survival is also a time-to-event endpoint, defined by progression or death, whichever occurs first. Its posted hazard ratio is 0.86, with a 95% confidence interval of 0.68 to 1.10. The registry does not state a method or p-value for that comparison. Objective response rate is a binary outcome reported as a percentage of participants, with arm-specific confidence intervals. The posted sponsor analyses also include a difference in response rates and a common odds ratio estimated by the CMH method. The record does not provide additional details about stratification variables or the specific adjustment strategy for that analysis.

A simple unadjusted recalculation from posted summary statistics is distinct from the sponsor’s full analysis. It can describe a basic contrast but cannot recreate unreported stratification, covariate adjustment, censoring methods, or other protocol-defined procedures. The primary comparison uses the sponsor’s reported hazard ratio and log-rank result, rather than a new estimate from summary data. For secondary outcomes, the posted sponsor estimates and the simpler recalculated contrasts should be understood according to their respective methods, not treated as interchangeable.

What can be inferred from the reported test?

The primary log-rank p-value evaluates the survival distributions under the test’s null hypothesis. A confidence interval and p-value address statistical uncertainty from different angles: the interval gives a range of parameter values compatible with the analysis, while the p-value measures evidence against the null under that analysis. Neither statistic provides a probability that a particular participant will experience an outcome, and neither substitutes for assessing design, follow-up, missing data, or generalizability.

The registry identifies the primary population as all randomized participants. It does not provide a full account of exclusions, treatment discontinuations, crossover, missing endpoint assessments, or sensitivity analyses. It also does not report whether interim analyses were planned or conducted, the original sample-size calculation, or the complete analysis plan. Those details are not reported in the registry record. The methods available support interpretation of the posted summary estimates, but not reconstruction of every analysis decision.

11. Confidence Intervals and Precision

The primary overall-survival hazard ratio is 0.70, with a 95% confidence interval from 0.53 to 0.92. This interval conveys uncertainty around the comparative estimate: the point estimate is not exact, and values across the interval remain compatible with the analysis at the stated confidence level. The interval lies below 1, the value corresponding to no relative difference under the hazard-ratio measure. It therefore aligns with the reported log-rank p-value of 0.010, while still allowing a range of possible effect sizes.

Confidence intervals are not ranges that contain a fixed fraction of participants’ outcomes. The arm-specific median overall survival estimates are 7.49 months and 5.06 months, with intervals of 5.49 to 9.1 months and 4.04 to 6.05 months, respectively. These intervals describe uncertainty in the estimated medians, not the spread of individual survival times. Overlap or lack of overlap between separate arm-specific intervals is not a substitute for the trial’s direct comparative analysis.

The secondary estimates have their own levels of precision. The progression-free survival hazard ratio is 0.86, with a 95% confidence interval of 0.68 to 1.10, which includes 1. The response percentages have arm-specific 95% confidence intervals of 9.3% to 18.3% and 2.4% to 11.6%. The registry also posts a response-rate difference and a common odds ratio, each with its own confidence interval. Different measures express comparisons on different scales, so their intervals should not be compared as if they estimated the same quantity.

Interval width reflects statistical uncertainty but does not by itself capture all limitations. Interpretation also depends on the analysis population, follow-up, censoring, outcome assessment, and the trial’s design. Several of those details are not reported in the registry record. The intervals support a careful reading of the posted estimates, rather than a claim of certainty about the true effect or about outcomes for individuals.

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 effect0.70247331
75% of the observed effect0.77439588
50% of the observed effect0.849881,322
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: Nivolumab 3mg/kg vs Investigators Choice.

The planning illustrations show the event counts or participant counts that would be needed under specified assumptions to detect a fraction of the observed effect. For the time-to-event outcomes, the figures are total events, not participants per arm. For objective response rate, the figures are participants per arm. The displayed planning scenarios use the observed effect, then consider 75% and 50% of that effect; those smaller effects require more information to detect.

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

The 80% power column gives the illustrated total event count or participants per arm under which a study would have an 80% probability of detecting the assumed effect if that effect were the true one, under the listed assumptions. The 90% power column gives the corresponding planning quantity for a higher probability of detection. Greater power generally requires more information, and detecting a smaller effect requires more participants or events than detecting a larger one. These quantities are planning illustrations based on the observed estimates, not observed power.

For example, the overall-survival illustration lists 247 total events for planning at 100% of the observed effect and 80% power, and 331 total events for 90% power. For the response outcome, the corresponding 100%-effect illustrations are 238 participants per arm for 80% power and 317 participants per arm for 90% power. The additional rows show how those requirements rise when planning for 75% or 50% of the observed effect. These scenarios are sensitive to their assumptions and should not be read as proof that a future study will achieve the stated power.

13. How the Sample Size Is Derived

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

Formula

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

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

Worked calculation for this trial

  1. Hazard ratio HR = 0.700, so ln(HR) = -0.3567.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.700)]2 = 246.8, rounded up to 247 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 <- 0.7                              # 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(2105636)
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 = 247 (80% power), 331 (90% power)
 75% of observed effect: events = 439 (80% power), 588 (90% power)
 50% of observed effect: events = 988 (80% power), 1,322 (90% power)
Simulated power with 247 events: 0.809 (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 365 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 114.71113.7100.00010.0001
Look 223.52222.5110.00600.0060
Look 360.03341.9930.02310.0250
01234z = 3.7115 mo111 eventsz = 2.5124 mo222 eventsz = 1.9960 mo334 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%24627060.0
Two looks, O'Brien-Fleming80%24727160.0
Three looks, O'Brien-Fleming80%24927360.0
Three looks, Pocock80%28831660.0
Fixed design, one analysis90%33036160.0
Two looks, O'Brien-Fleming90%33136260.0
Three looks, O'Brien-Fleming90%33436560.0
Three looks, Pocock90%38141760.0

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 effect0.700334365
75% of the observed effect0.765594646
50% of the observed effect0.8371,3371,448

For context, this trial enrolled 361 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 <- 5.06          # control-arm median, months (converted from the posted unit)
hr          <- 0.7          # 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: 224        p (1-sided)   0.0001
 Events: 112       ~HR at bound   0.4947
   Month: 15   P(Cross) if HR=1   0.0001
             P(Cross) if HR=0.7   0.0338
   IA 2: 67%                  Z   2.5114
      N: 358        p (1-sided)   0.0060
 Events: 223       ~HR at bound   0.7140
   Month: 24   P(Cross) if HR=1   0.0060
             P(Cross) if HR=0.7   0.5603
       Final                  Z   1.9930
      N: 366        p (1-sided)   0.0231
 Events: 334       ~HR at bound   0.8039
   Month: 60   P(Cross) if HR=1   0.0250
             P(Cross) if HR=0.7   0.9000



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

15. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.700.53 to 0.920.010

The sponsor’s reported primary analysis is a log-rank comparison with a hazard ratio of 0.70, a 95% confidence interval of 0.53 to 0.92, and p = 0.010. The posted arm-specific overall-survival medians are 7.49 months for nivolumab and 5.06 months for investigator’s choice. The sponsor’s reported hazard ratio is the appropriate comparative estimate to emphasize for the primary time-to-event outcome; a comparison of the two medians is not a substitute for that analysis.

The registry indicates no discrepancy between the reported primary analysis and the posted result. The sponsor’s own analysis therefore takes precedence over a simple recalculation from summary statistics. A recalculation using only arm-level summaries cannot reproduce the complete time-to-event analysis or any details not included in those summaries. In this case, the reported estimate and its stated method provide the primary inferential result.

For the secondary response outcome, the registry posts sponsor analyses of the difference in response rates and the CMH estimate of a common odds ratio. It also contains simple unadjusted recalculations based on summary counts. Those are different types of analysis and need not have identical estimates or uncertainty. The registry record does not report enough details to reconstruct every aspect of the sponsor’s secondary analyses, including any stratification details. The posted sponsor results should be interpreted as the trial’s reported analysis, while unadjusted recalculations remain descriptive checks rather than replacements for that analysis.

16. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when multiple outcomes, comparisons, subgroups, or analyses are tested. If each is interpreted using an unadjusted significance threshold, the chance of a false-positive finding across the collection can increase. Statistical plans often address this through procedures such as adjustment, a testing hierarchy, or clear designation of exploratory analyses. These are general approaches; the registry record does not report which, if any, were used for this trial’s secondary outcomes.

The record lists investigator-assessed progression-free survival and objective response rate as secondary outcomes, and it posts analyses for both. It does not report a multiplicity adjustment or a prespecified hierarchy linking these outcomes to the primary endpoint. Consequently, the secondary findings should be interpreted with caution and should not be treated as having the same confirmatory status as the primary overall-survival analysis unless further protocol information establishes that status.

The primary analysis population is stated as all randomized participants. The record does not report detailed accounting of missing data, participant withdrawals, treatment discontinuations, crossover, or endpoint-specific analysis populations beyond the group counts shown for the outcomes. It also does not describe sensitivity analyses for missing or censored observations. For overall survival, the censoring rules are stated, but the registry does not provide further diagnostics about censoring or follow-up completeness.

The registry record also does not report the complete statistical analysis plan, interim-analysis procedures, subgroup analysis plan, or the original sample-size justification. These omissions limit the ability to assess whether all analyses followed prespecified procedures, how missing observations were handled beyond the endpoint definitions, and whether multiplicity was managed elsewhere in the protocol. Absence of these details in the registry record does not establish that the procedures were absent from the study; it means that they cannot be assessed from the record presented.

These uncertainties do not invalidate the reported primary comparison, but they define the limits of interpretation. The posted result can be described using its stated population, endpoint definition, method, and uncertainty interval. Claims about unreported analysis choices or about the behavior of missing data would go beyond what the registry record documents.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Nivolumab 3mg/kg16523669.9%
Investigator Choice8711178.4%
Participants with at least one serious adverse event
Serious adverse events by armNivolumab 3mg/kg69.9%Investigator Choice78.4%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Nivolumab 3mg/kg220 of 240
Investigator Choice119 of 121

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
Nivolumab 3mg/kg210 of 236
Investigator Choice108 of 111

Most frequent serious adverse event terms

Event termOrgan systemNivolumab 3mg/kgInvestigator Choice
Malignant neoplasm progressionNeoplasms benign, malignant and unspecified (incl cysts and polyps)94 of 23655 of 111
PneumoniaInfections and infestations17 of 2365 of 111
Pneumonia aspirationRespiratory, thoracic and mediastinal disorders10 of 2364 of 111
DyspnoeaRespiratory, thoracic and mediastinal disorders11 of 2362 of 111
SepsisInfections and infestations6 of 2364 of 111
PyrexiaGeneral disorders5 of 2364 of 111
AnaemiaBlood and lymphatic system disorders2 of 2364 of 111
DysphagiaGastrointestinal disorders3 of 2363 of 111
Lower respiratory tract infectionInfections and infestations3 of 2363 of 111
Respiratory tract infectionInfections and infestations5 of 2361 of 111

Most frequent non-serious adverse event terms

Event termOrgan systemNivolumab 3mg/kgInvestigator Choice
FatigueGeneral disorders67 of 23637 of 111
AnaemiaBlood and lymphatic system disorders53 of 23642 of 111
NauseaGastrointestinal disorders55 of 23637 of 111
DiarrhoeaGastrointestinal disorders47 of 23627 of 111
Decreased appetiteMetabolism and nutrition disorders46 of 23621 of 111
ConstipationGastrointestinal disorders43 of 23621 of 111
Weight decreasedInvestigations35 of 23619 of 111
PyrexiaGeneral disorders37 of 23616 of 111
AstheniaGeneral disorders27 of 23624 of 111
CoughRespiratory, thoracic and mediastinal disorders37 of 23613 of 111

Serious events with the highest arm-level rate: malignant neoplasm progression (49.5%), pneumonia (7.2%), dyspnoea (4.7%), pneumonia aspiration (4.2%), anaemia (3.6%).

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

The registry lists serious adverse events for each safety group, with 236 participants at risk in the nivolumab group and 111 at risk in the investigator choice group. Serious adverse events affected 165 and 87 participants, respectively. The figures for participants at risk differ from the primary outcome group counts, and the record does not explain the reason for that difference. These are safety summaries, not the primary efficacy analysis.

The most frequently listed serious event term is malignant neoplasm progression at 49.5%. Other listed terms are pneumonia at 7.2%, dyspnoea at 4.7%, pneumonia aspiration at 4.2%, anaemia at 3.6%, and pyrexia at 3.6%. The registry also reports other adverse events affecting 210 participants in the nivolumab group and 108 in the investigator choice group. It lists deaths for 220 and 119 participants, respectively. These death counts are reported in the safety data; the record does not identify them as treatment-caused deaths.

Event terms and participant counts do not, by themselves, establish causation or comparative risk. The registry record does not provide further detail about severity grading, exposure-adjusted rates, event timing, attribution, or how the listed percentages were calculated. The safety figures should therefore be read as descriptive summaries with those limits, not as a basis for inferring that treatment caused a particular event or that the arms differ in safety.

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

The posted data show that the sponsor’s primary analysis estimated a hazard ratio of 0.70 for overall survival, comparing nivolumab with investigator’s choice. Its 95% confidence interval is 0.53 to 0.92, and the reported log-rank p-value is 0.010. The arm-specific median estimates are 7.49 months and 5.06 months. Taken together, these are the trial’s reported statistical findings for the primary endpoint in the randomized population.

This result does not mean that every participant in one arm lived longer than every participant in the other arm, or that an individual’s outcome can be predicted from the group estimate. A median is a summary of a survival distribution, and a hazard ratio is a relative comparison over follow-up. Both are population-level measures. The confidence interval also makes clear that the estimated comparative effect has uncertainty.

The result does not resolve every question about treatment choice, safety, quality of life, or effects in populations not represented by the trial. The registry record identifies recurrent or metastatic platinum-refractory squamous cell carcinoma of the head and neck; conclusions should remain tied to that trial context. It does not provide all details needed to evaluate every subgroup, analysis assumption, or missing-data issue.

The secondary endpoints do not change the definition of the primary result. Progression-free survival and objective response address different outcomes, and the record does not report whether multiplicity was adjusted. Their estimates can add context, but should not be treated as independent confirmation of the primary finding. Similarly, the listed adverse-event summaries describe observed safety data but do not establish the cause of individual events.

Statistical evidence and clinical meaning are related but distinct. The reported p-value is not the probability that the null hypothesis is true, and statistical significance does not by itself measure the importance of an effect. The posted estimates, their intervals, the trial population, and the limits of the registry information all matter to a balanced interpretation. The data support describing the reported randomized comparison; they do not justify an unqualified claim about outcomes beyond the evidence recorded.

19. Why This Trial Matters Statistically

This trial is statistically notable for its clear primary time-to-event question and a reported comparative analysis rather than relying only on arm-specific summaries. Overall survival was defined from randomization to death from any cause, and the registry identifies the analysis population as all randomized participants. The sponsor reports a log-rank hazard ratio with a confidence interval and p-value, giving readers a direct estimate of the primary comparison alongside the Kaplan-Meier medians.

It also illustrates why endpoint choice matters. The primary endpoint measures survival, while progression-free survival combines progression and death and objective response measures a different clinical event. A result on one scale does not automatically predict the result on another. The secondary findings are informative context, but their statistical weight depends in part on the analysis plan and multiplicity procedures, which are not reported in the registry record.

The planning illustrations provide a separate statistical lesson: sample-size requirements depend on the effect a study aims to detect and the desired probability of detection under specified assumptions. Smaller effects require more information. Those illustrations use stated generic planning assumptions and the observed effects; they do not reveal the trial’s original design justification or show that the observed study had a particular power.

Finally, the record shows the value and limits of registry reporting. It supplies endpoint definitions, group estimates, confidence intervals, and selected adverse-event summaries, but leaves several analysis details unreported. Careful interpretation distinguishes the sponsor’s reported result from a simple recalculation and distinguishes descriptive safety counts from evidence of causation. This approach makes the statistical evidence useful without overstating what the record can establish.

20. Limitations

The registry record does not report the complete statistical analysis plan, the original sample-size justification, or interim-analysis procedures. It also does not describe whether multiplicity was controlled for secondary outcomes, how secondary outcomes were prioritized, or whether subgroup analyses were prespecified. These omissions limit evaluation of the confirmatory status of analyses beyond the primary endpoint.

Although the primary endpoint definition includes censoring rules and the primary population is identified as all randomized participants, the record does not report detailed follow-up distributions, event counts, censoring diagnostics, or sensitivity analyses. The primary timeframe is stated as up to approximately 18 months, while secondary timeframes are stated as up to approximately 87 months. These descriptions do not establish that each participant had the same length of follow-up.

The study was open-label, and progression-free survival and response were investigator-assessed. The record does not provide enough information to assess how knowledge of treatment assignment may have affected those assessments or whether independent review was used. For the investigator’s choice arm, the registry lists several possible therapies, but does not provide complete details of how the choice was made or how many participants received each option. The docetaxel arm description is incomplete.

Safety summaries are limited to the counts and event terms posted. The registry record does not report the attribution, timing, exposure-adjusted rates, or complete detail needed to make causal comparisons from those summaries. These limitations call for restraint in interpreting secondary and safety findings, while the primary result can still be described according to its posted analysis and confidence interval.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

CheckMate 141 (NCT02105636) was a completed, randomized, open-label, parallel-group phase 3 trial sponsored by Bristol-Myers Squibb. It compared nivolumab with investigator’s choice of cetuximab, methotrexate, or docetaxel in recurrent or metastatic platinum-refractory squamous cell carcinoma of the head and neck. The registry lists enrollment of 361.

The primary endpoint was overall survival among all randomized participants. The sponsor reported a log-rank hazard ratio of 0.70, with a 95% confidence interval of 0.53 to 0.92 and p = 0.010. Median overall survival was 7.49 months for nivolumab and 5.06 months for investigator’s choice. Secondary outcomes were investigator-assessed progression-free survival and objective response rate.

Interpretation is limited by analysis details not reported in the registry record, including the complete statistical plan, multiplicity procedures, and original sample-size justification. The posted findings describe the randomized comparison and its uncertainty; they do not establish effects beyond the trial context or causation for the listed adverse events.

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