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Squamous Cell Carcinoma, Non-Small-Cell Lung Phase 3 Time-to-Event Analysis NCT02027428

Safety and Efficacy Study of Abraxane as Maintenance Treatment After Abraxane Plus Carboplatin in 1st Line Stage IIIB / IV Squamous Cell Non-small Cell Lung Cancer: Complete Statistical Analysis

This analysis examines the randomized maintenance comparison of nab-paclitaxel plus best supportive care with best supportive care alone after induction treatment for advanced squamous cell non-small-cell lung cancer. It focuses on progression-free survival from randomization into maintenance and places the registry’s secondary outcomes, safety counts, and statistical uncertainty in context.

Trial start: 2014-02-11  ·  Enrollment: 427  ·  Sponsor: Celgene
Scope of this record

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

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy Study of Abraxane as Maintenance Treatment After Abraxane Plus Carboplatin in 1st Line Stage IIIB / IV Squamous Cell Non-small Cell Lung Cancer (NCT02027428), a randomized phase 3 study. The primary outcome is Kaplan-Meier Estimate of Progression-Free Survival (PFS) From Randomization Into Maintenance.

427
Enrollment
Phase 3
2
Arms
In the primary outcome
0.85
Hazard ratio
Nab-Paclitaxel + Best Supportive Care (B
0.61–1.19
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02027428
PhasePhase 3
ConditionSquamous Cell Carcinoma, Non-Small-Cell Lung
AllocationRandomized
Design modelCrossover
MaskingNone (open label)
Enrollment427
Arms in the primary outcome2
Lead sponsorCelgene
Results postedYes

2. Clinical Question

Population

People with stage IIIB or IV squamous cell non-small-cell lung cancer who had a complete response, partial response, or stable disease after induction with nab-paclitaxel plus carboplatin. The primary analysis population was the intent-to-treat population randomized into maintenance, including participants regardless of whether they received study drug or had efficacy assessments.

Intervention

Nab-paclitaxel with best supportive care as maintenance after induction with nab-paclitaxel plus carboplatin. The registry describes the study as a phase III, randomized, open-label, multicenter trial.

Comparator

Best supportive care alone as maintenance, following the same induction treatment with nab-paclitaxel plus carboplatin. The maintenance comparison therefore concerns treatment after induction, not the induction regimens.

Primary question

Among participants randomized into maintenance, how did progression-free survival compare between nab-paclitaxel plus best supportive care and best supportive care alone? Progression-free survival was measured from maintenance randomization to investigator-assessed disease progression or death from any cause.

3. Trial Design

The registry describes a phase III, randomized, open-label, multicenter study of nab-paclitaxel maintenance after induction with nab-paclitaxel plus carboplatin. The registry lists 427 participants enrolled. The maintenance comparison was between nab-paclitaxel plus best supportive care and best supportive care alone. Masking was listed as none. The registry also labels the model as crossover, but crossover sequence, timing, and analysis details are not reported in the registry record.

Both groups received induction with nab-paclitaxel plus carboplatin. At the end of 4 cycles, participants with complete response, partial response, or stable disease could continue to maintenance. The primary outcome population was the intent-to-treat population randomized into maintenance: the registry specifies that this included all randomized participants regardless of study-drug receipt or collection of efficacy assessments. The listed maintenance group sizes for the primary outcome were 136 and 66.

The primary outcome was progression-free survival from randomization into maintenance. The registry describes progression using investigator assessment under RECIST Version 1.1, based on CT imaging, and includes death from any cause as an event. Secondary outcomes included overall survival from maintenance randomization, response and disease-control outcomes, and progression-free survival and overall survival over the entire study.

The registry lists the study as completed. Its summary describes follow-up after maintenance discontinuation and continued survival follow-up by phone approximately every 90 days, for a minimum of 18 months and up to approximately 5 years after the last participant was randomized. The trial’s original sample-size justification, allocation sequence details, and any interim-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: Participants with a response or stable disease during Induction were randomised 2:1 into investigative treatment (nab-paclitaxel plus best supportive care \[BSC\] or BSC only) stratified by disease stage, response during induction and Eastern Cooperative Oncology Group (ECOG) performance status.

Induction

StageAll Participants - InductionNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)
STARTED42700
Received Study Drug42000
COMPLETED20200
NOT COMPLETED22500

Reasons for not completing this period:

ReasonAll Participants - InductionNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)
Never treated700
Progressive disease7700
Adverse Event5100
Withdrawal by Subject2200
Death2100
Symptomatic deterioration1600
Study terminated by sponsor1200
Protocol Violation100
Miscellaneous1400
Induction Treatment Ongoing400

Maintenance

StageAll Participants - InductionNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)
STARTED013666
COMPLETED0126
NOT COMPLETED012460

Reasons for not completing this period:

ReasonAll Participants - InductionNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)
Death032
Adverse Event0211
Progressive disease08447
Symptomatic deterioration041
Withdrawal by Subject065
Protocol Violation001
Other063

Survival Follow-up

StageAll Participants - InductionNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)
STARTED011755
COMPLETED0389
NOT COMPLETED07946

Reasons for not completing this period:

ReasonAll Participants - InductionNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)
Death07845
Lost to Follow-up011

Analysis population for the primary outcome, as defined in the registry: Intent to treat (ITT) population of participants randomized to Maintenance. The ITT population in the Maintenance part included all randomized subjects regardless of whether the subject received any study drug or had any efficacy assessments collected.

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: Induction includes participants who were enrolled and treated however, baseline characteristics (BLC) for non-randomised participants is not displayed. The total number represents the ITT population in the maintenance phase.

CharacteristicUnitNab-Paclitaxel + Best Supportive Care (BSC)Best Supportive Care (BSC)Total
Participants analysed13666202
Age, Continuousyears67.1 (SD 9.02)66.8 (SD 8.06)67.0 (SD 8.70)
Age, Customized: <65 yearsParticipants482775
Age, Customized: >=65 yearsParticipants8839127
Age, Customized: <70 yearsParticipants7941120
Age, Customized: >=70 yearsParticipants572582
Age, Customized: <75 yearsParticipants11055165
Age, Customized: >=75 yearsParticipants261137
Sex: Female, Male: FemaleParticipants492372
Sex: Female, Male: MaleParticipants8743130
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants358
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants13261193
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants101
Race/Ethnicity, Customized: American Indian or Alaska NativeParticipants101
Race/Ethnicity, Customized: AsianParticipants101
Race/Ethnicity, Customized: Black or African AmericanParticipants9211
Race/Ethnicity, Customized: WhiteParticipants12562187
Race/Ethnicity, Customized: OtherParticipants022
Eastern Cooperative Oncology Group (ECOG) Performance Status (PS): 0=fully active, no restrictionParticipants411960
Eastern Cooperative Oncology Group (ECOG) Performance Status (PS): 1=fully ambulatory; restricted strenuous activityParticipants9547142
Eastern Cooperative Oncology Group (ECOG) Performance Status (PS): >=2=ambulatory/self care; no work or worseParticipants000
Overall Tumor Response at End of Induction: Complete responseParticipants123
Overall Tumor Response at End of Induction: Partial responseParticipants9242134
Overall Tumor Response at End of Induction: Stable diseaseParticipants412162
Overall Tumor Response at End of Induction: Progressive diseaseParticipants202
Overall Tumor Response at End of Induction: Not evaluableParticipants011
Confirmed Histology: Squamous cell carcinomaParticipants13666202
Confirmed Histology: Squamous cell carcinoma not confirmedParticipants000
Disease Stage at Enrollment: Stage IIIBParticipants18826
Disease Stage at Enrollment: Stage IVParticipants11858176

6. Primary Endpoint

The registry lists the primary outcome as Kaplan-Meier Estimate of Progression-Free Survival (PFS) From Randomization Into Maintenance, measured over From the date of randomization to the date of disease progression or death of any cause; up to data cut off date of 15 September 2017; up to 27.6 months.

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

The primary endpoint, progression-free survival, measures the time from randomization into maintenance until disease progression or death from any cause. Progression was based on the investigator’s assessment using RECIST Version 1.1 criteria and CT imaging; symptomatic deterioration alone was not included in the stated progression definition. The registry’s description says that progression or death was counted as an event.

Time-to-event outcomes are useful when participants can have different lengths of follow-up and when the timing of an event matters. A median gives a point on the estimated survival curve: it is the time by which the estimated proportion remaining free of progression or death has reached one half. The registry reports median progression-free survival and a hazard ratio, which summarizes the relative event rate over follow-up under the analysis used. These measures answer related but different questions: the median describes a time point on each group’s curve, while the hazard ratio compares the groups across the observed follow-up.

The primary timeframe is described as extending from maintenance randomization to progression or death, up to the stated data cutoff and maximum follow-up. The registry’s outcome description also refers to events on or before 01 Aug 2019, while its timeframe lists a data cutoff of 15 September 2017. The relationship between those dates is not explained in the registry record.

7. Results Posted in the Registry

Hazard ratio: Nab-Paclitaxel + Best Supportive Care (BSC) vs Best Supportive Care (BSC)

0.85

95% CI: 0.61 to 1.19

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Nab-Paclitaxel + Best Support…0.580.680.790.921.081.26hazard 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
Kaplan-Meier Estimate of Overall Survival (OS) From Randomization Into MaintenanceTime-to-Event AnalysisHazard ratio0.68 (0.47 to 0.98)212 events
Percentage of Participants Who Achieved a Confirmed Overall Response of Complete Response or Partial Response (Overall Response Rate) Over Entire StudyBinary EndpointRisk difference-11.5 pts (-25.8 to 2.7)273 per arm
Kaplan-Meier Estimate of Progression-Free Survival (PFS) Over Entire StudyTime-to-Event AnalysisHazard ratio0.87 (0.62 to 1.22)1,619 events

Kaplan-Meier Estimate of Overall Survival (OS) From Randomization Into Maintenance

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Nab-Paclitaxel + Best Support…0.440.530.630.750.891.06hazard ratio (as reported) vs control (95% CI)

Percentage of Participants Who Achieved a Confirmed Overall Response of Complete Response or Partial Response (Overall Response Rate) Over Entire Study

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)BSC: Induction + Maintenance-28-21-15-8.24-1.644.96risk difference (percentage points) vs control (95% CI)

Kaplan-Meier Estimate of Progression-Free Survival (PFS) Over Entire Study

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Nab-Paclitaxel + BSC: Inducti…0.590.690.800.941.101.29hazard ratio (as reported) vs control (95% CI)

The secondary outcomes broaden the description beyond the primary maintenance progression-free survival comparison. They include overall survival from maintenance randomization, response and disease-control measures, and progression-free survival and overall survival over the entire study. The overall-study outcomes begin during induction and therefore address a broader treatment period than the primary endpoint. The secondary set also includes duration and timing of response.

Across these outcomes, the pattern is mixed rather than uniformly decisive. The overall-survival comparison from maintenance randomization has a hazard-ratio confidence interval that does not include 1, while the reported overall response and whole-study progression-free survival comparisons have confidence intervals that include their respective no-difference values. These outcomes differ in definition, follow-up period, and analysis method, so they should not be collapsed into a single conclusion or used to override the primary endpoint.

Multiplicity matters because evaluating many outcomes creates more opportunities for a result to appear noteworthy by chance. Unless the testing plan accounts for that, an individual secondary p-value may overstate the strength of evidence when viewed in isolation. The registry lists multiple secondary outcomes and analyses, but whether a formal hierarchy, adjustment, or confirmatory testing strategy was used is not reported in the registry record. The analysis plan and handling of multiplicity are not reported there either.

Secondary results can be useful for understanding what was measured and for identifying questions that may merit further study. Their interpretation should consider the primary result, the outcomes’ differing time scopes, and the lack of reported multiplicity procedures. They are supportive context, not independent confirmation simply because they point in a particular direction.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For progression-free survival from maintenance randomization, the reported median was 3.12 months (95% confidence interval 2.73 to 4.6) with nab-paclitaxel plus best supportive care, and 2.6 months (95% confidence interval 1.64 to 3.45) with best supportive care alone. The sponsor-reported hazard ratio was 0.85, with a 95% confidence interval from 0.61 to 1.19. The estimate points toward a lower event hazard in the nab-paclitaxel group, but the interval includes 1 and is compatible with no difference as well as effects in either direction. The registry-reported test does not establish a clear difference in this primary comparison.

The medians are estimates, not guaranteed times for an individual participant. Their confidence intervals overlap, and the hazard-ratio interval is broad enough to include both a potentially lower and a potentially higher event hazard in the nab-paclitaxel group. Reading the median values alone would not convey that uncertainty. The hazard ratio and its interval provide a group-level comparison over follow-up, subject to the model and analysis used.

The secondary outcomes do not all measure the same period or construct. Outcomes assessed over the entire study include the induction period, while the primary endpoint begins at maintenance randomization. Overall survival from maintenance randomization has a reported hazard ratio of 0.68 (95% confidence interval 0.47 to 0.98); this is a secondary outcome and should be interpreted in light of the overall set of outcomes and the analysis plan, which is not reported in the registry record. The overall response rate analysis over the entire study and progression-free survival over the entire study have estimates with confidence intervals that include no difference under their respective measures.

Those secondary findings can add context, but they do not replace the primary result. Outcomes defined over the entire study mix experience from induction and maintenance, whereas the primary endpoint isolates follow-up after maintenance randomization. The registry reports multiple secondary outcomes and analyses, but does not report whether or how their significance levels were adjusted for multiple testing. Without that information, isolated secondary findings warrant caution.

The results describe the posted analyses in the randomized maintenance population. They do not establish what would have happened under different induction regimens, in people who did not reach maintenance eligibility, or in other clinical settings. No treatment recommendation follows from the statistical comparison alone.

10. Statistical Methods Explained

Time-to-event analysis accounts for both whether an event was observed and how long each participant was followed. Participants who have not had progression or died by the end of their available follow-up contribute information up to that point; they are not treated as if an event occurred at the end of follow-up. Kaplan-Meier estimates are used to describe the event-free proportion over time, and the median is read from that estimated curve when it reaches one half. General explanation: censoring allows incomplete follow-up to contribute information, provided the assumptions behind the analysis are reasonable. The registry record does not report detailed censoring rules.

What does the hazard ratio represent?

The hazard ratio compares the event rates between groups over the analysis period. A value below 1 points toward a lower event hazard in the first-named group, while a value above 1 points toward a higher event hazard. This is a relative, time-to-event measure; it is not a ratio of median survival times and does not directly give the probability that an individual will remain progression-free. The primary reported hazard ratio was 0.85. Its 95% confidence interval, 0.61 to 1.19, includes 1, so the data are compatible with no difference as well as a range of relative effects. The hazard ratio was reported from a stratified log-rank test analysis.

Why use a stratified log-rank analysis?

A log-rank test compares time-to-event experience between groups while accounting for follow-up times and censoring. Stratification can account for specified grouping factors in the comparison. The registry identifies the method as a stratified log-rank test but does not report the stratification factors, the model specification, or diagnostics. Those details are not reported in the registry record, so the method cannot be independently reconstructed from the outcome summary alone.

What does the median add?

The median progression-free survival gives a time-based summary for each group, while the hazard ratio gives a relative comparison using event timing across follow-up. Neither summary contains the full survival curve. Medians can be unstable when the curve is estimated imprecisely near the point where it crosses one half, and hazard ratios may not capture changing differences over time if the relative event rate is not approximately constant. The registry does not report a proportional-hazards assessment or other diagnostics. General explanation: when the relative hazard changes over time, a single hazard ratio can compress that variation into one overall estimate.

How should the response outcomes be understood?

Overall response rate counts participants with a confirmed complete or partial response according to the outcome definition. This is a binary outcome, unlike progression-free survival, which uses event timing. The sponsor reported a Cochran-Mantel-Haenszel analysis for overall response rate. Such an analysis can account for strata in a comparison of categorical outcomes, but the registry does not identify the strata used. The response analysis over the entire study covers induction and subsequent treatment, and therefore has a different time scope from the primary maintenance endpoint.

General explanation: binary outcome comparisons may be expressed using a risk difference, risk ratio, odds ratio, or a model-based estimate. These are not interchangeable measures, and their interpretation depends on the analysis method. A recalculation from posted group summaries is unadjusted; it need not match an analysis that accounts for strata or uses a different estimand. For this reason, the sponsor-reported result should be distinguished from simple recalculations based on summary counts.

Why can over-dispersion matter?

General explanation: over-dispersion occurs when the variability in data exceeds what a simple statistical model assumes. If it is ignored, uncertainty can be understated and tests can appear more conclusive than warranted. The registry does not identify an over-dispersion adjustment for the primary time-to-event outcome, and this issue is not necessary to infer from the posted summaries. The registry does not report detailed model diagnostics or an analysis plan sufficient to evaluate whether over-dispersion was relevant to any secondary outcome.

What cannot be determined from the posted summaries?

Participant-level event times, censoring indicators, covariates, and stratification details are not reported in the registry record. Consequently, the survival curves, hazard-ratio analysis, and uncertainty estimates cannot be independently reproduced from the summary values alone. The record also does not report whether the analyses followed a prespecified statistical analysis plan, how protocol deviations were handled, or how missing outcome assessments were addressed. General statistical explanations describe the methods, not unreported features of this trial.

11. Confidence Intervals and Precision

A confidence interval communicates uncertainty around an estimated effect. The primary hazard-ratio estimate is 0.85, with a 95% confidence interval from 0.61 to 1.19. The interval includes 1, the value corresponding to equal hazards under this measure. Thus, although the point estimate is below 1, the observed data do not pin down the direction and size of the relative effect precisely enough to rule out no difference under the reported analysis.

The median estimates also have uncertainty. For nab-paclitaxel plus best supportive care, the median was 3.12 months, with a 95% confidence interval from 2.73 to 4.6. For best supportive care alone, the median was 2.6 months, with a 95% confidence interval from 1.64 to 3.45. These intervals describe uncertainty in each group’s median; they are not a confidence interval for the difference between medians.

In general, a 95% confidence interval is produced by a procedure that, under its assumptions, would cover the true parameter in 95% of repeated applications. It does not mean there is a 95% probability that the fixed parameter lies in this particular interval. Interval width reflects both the information available and the variability of the data. The maintenance group sizes listed for the primary outcome were 136 and 66, and the registry does not provide participant-level data or detailed event counts for reconstructing the interval.

Precision should therefore be judged from the interval as well as the point estimate. The estimate is not a definitive statement that the groups differ, and the interval does not prove that they are identical. It shows that the primary comparison leaves meaningful uncertainty about the size and direction of the effect.

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 effect0.851,1891,592
75% of the observed effect0.892,1142,829
50% of the observed effect0.924,7556,366
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1,0002,0005,00010,00020,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: Nab-Paclitaxel + Best Supportive Care (BSC) vs Best Supportive Care (BSC).

The planning figures are illustrations based on the observed effect, not the trial’s original design justification. The original design assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to a stated fraction of the observed effect.

For time-to-event outcomes, the figures refer to the total number of events required, using the Schoenfeld method. They are not participants per arm. For the other outcomes, the figures refer to participants per arm. The primary progression-free survival planning illustration lists 1,189 total events for 80% power when planning for 100% of the observed effect, and 1,592 total events for 90% power under that same effect assumption. Planning for 75% or 50% of the observed effect requires more events.

In plain terms, 80% power describes the chance that a study designed under the stated assumptions would detect an effect of the assumed size using the specified test, if that effect were truly present. The 90% column describes a higher target chance of detection under those same assumptions. Neither is a guarantee that a future study will produce a particular result. The planning figures are illustrations, not a statement about the power achieved in this completed trial.

Smaller effects are harder to distinguish from random variation, so they require more information: more events for time-to-event outcomes or more participants per arm for other outcomes. The planning curve represents that same relationship across the effect assumptions. These calculations use the observed effect as a starting point, so they should not be read as evidence that the observed estimate is the true effect or as a substitute for a prospective design justification.

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 = 0.850, so ln(HR) = -0.1625.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.850)]2 = 1,188.7, rounded up to 1,189 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 <- 0.85                              # 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(2027428)
d    <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z  <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))

Output from running the code

100% of observed effect: events = 1,189 (80% power), 1,592 (90% power)
 75% of observed effect: events = 2,114 (80% power), 2,829 (90% power)
 50% of observed effect: events = 4,755 (80% power), 6,366 (90% power)
Simulated power with 1,189 events: 0.792 (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 1,676 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 111.75373.7100.00010.0001
Look 219.91,0732.5110.00600.0060
Look 360.01,6101.9930.02310.0250
01234z = 3.7112 mo537 eventsz = 2.5120 mo1073 eventsz = 1.9960 mo1610 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%1,1881,23760.0
Two looks, O'Brien-Fleming80%1,1931,24260.0
Three looks, O'Brien-Fleming80%1,2041,25360.0
Three looks, Pocock80%1,3911,44860.0
Fixed design, one analysis90%1,5911,65760.0
Two looks, O'Brien-Fleming90%1,5961,66260.0
Three looks, O'Brien-Fleming90%1,6101,67660.0
Three looks, Pocock90%1,8361,91260.0

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 effect0.8501,6101,676
75% of the observed effect0.8852,8622,977
50% of the observed effect0.9226,4406,692

For context, this trial enrolled 427 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 <- 2.6          # control-arm median, months (converted from the posted unit)
hr          <- 0.85          # 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: 820         p (1-sided)   0.0001
  Events: 537        ~HR at bound   0.7259
    Month: 12    P(Cross) if HR=1   0.0001
              P(Cross) if HR=0.85   0.0338
    IA 2: 67%                   Z   2.5114
      N: 1390         p (1-sided)   0.0060
 Events: 1074        ~HR at bound   0.8579
    Month: 20    P(Cross) if HR=1   0.0060
              P(Cross) if HR=0.85   0.5603
        Final                   Z   1.9930
      N: 1676         p (1-sided)   0.0231
 Events: 1610        ~HR at bound   0.9054
    Month: 60    P(Cross) if HR=1   0.0250
              P(Cross) if HR=0.85   0.9000



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

15. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
stratified log-rank testHazard Ratio (HR) 0.850.61 to 1.190.349

The registry reports the primary hazard ratio from the sponsor’s stratified log-rank analysis: 0.85, with a 95% confidence interval from 0.61 to 1.19. The interval includes 1, so the primary result is not a clear separation of the groups. The sponsor-reported analysis is the relevant inferential result for this endpoint; no independently recalculated hazard ratio is used for the time-to-event outcome.

For overall response rate, the sponsor reported a Cochran-Mantel-Haenszel analysis with an overall response rate ratio of 1.20 and a 95% confidence interval from 0.948 to 1.519. A simple unadjusted recalculation from posted summary statistics uses a different method and need not match a stratified analysis. These results should not be treated as interchangeable estimates of exactly the same analysis.

No discrepancy is flagged between the registry’s reported analyses and the recalculation status recorded for this trial. Where a sponsor analysis is reported, it remains distinct from a simple recalculation based on group summaries. The registry does not report the detailed strata or participant-level data needed to reproduce the sponsor’s adjusted analyses independently.

16. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary endpoint and multiple secondary outcomes, including several time-to-event and response measures. Testing multiple outcomes increases the chance of at least one apparently unusual result when each is assessed separately. A prespecified hierarchy or multiplicity adjustment can help control that risk, but neither a testing hierarchy nor an adjustment procedure is reported in the registry record. The trial’s statistical analysis plan and whether the secondary analyses were intended to be confirmatory are also not reported in the registry record.

The primary outcome population is described as the intent-to-treat population randomized into maintenance. It included randomized participants regardless of whether they received study drug or had efficacy assessments collected. This definition clarifies who was intended for the primary analysis, but it does not explain how participants with missing assessments or incomplete follow-up were handled. Missing-data methods, censoring details, and sensitivity analyses are not reported in the registry record.

The registry provides group-level outcome summaries and sponsor-reported analyses, but not participant-level records, detailed event data, or the full analysis specification. Stratification factors for the reported stratified analyses are not reported. The original sample-size justification, allocation sequence details, and any interim-analysis plan are not reported in the registry record. These omissions limit assessment of whether analysis choices were prespecified and how robust the results are to alternative assumptions.

These limitations do not by themselves show that the analyses are invalid. They define what cannot be assessed from the registry report: the full multiplicity strategy, the handling of missing observations, and the reproducibility of adjusted analyses. Interpretation should remain tied to the outcomes and methods that are actually described.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
All Participants - Induction17742042.1%
Nab-Paclitaxel + Best Supportive Care (Maintenance)3213024.6%
Best Supportive Care (Maintenance)136221.0%
Participants with at least one serious adverse event
Serious adverse events by armAll Participants - Induction42.1%Nab-Paclitaxel + Best Support…24.6%Best Supportive Care (Mainten…21.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
All Participants - Induction80 of 420
Nab-Paclitaxel + Best Supportive Care (Maintenance)82 of 130
Best Supportive Care (Maintenance)48 of 62

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
All Participants - Induction417 of 420
Nab-Paclitaxel + Best Supportive Care (Maintenance)122 of 130
Best Supportive Care (Maintenance)45 of 62

Most frequent serious adverse event terms

Event termOrgan systemAll Participants - InductionNab-Paclitaxel + Best Supportive Care (Maintenance)Best Supportive Care (Maintenance)
PneumoniaInfections and infestations24 of 4204 of 1303 of 62
AnaemiaBlood and lymphatic system disorders17 of 4203 of 1300 of 62
DehydrationMetabolism and nutrition disorders14 of 4201 of 1300 of 62
DyspnoeaRespiratory, thoracic and mediastinal disorders15 of 4200 of 1300 of 62
DiarrhoeaGastrointestinal disorders11 of 4201 of 1301 of 62
NeutropeniaBlood and lymphatic system disorders12 of 4200 of 1300 of 62
SepsisInfections and infestations9 of 4203 of 1300 of 62
Pulmonary embolismRespiratory, thoracic and mediastinal disorders9 of 4202 of 1300 of 62
HypotensionVascular disorders11 of 4200 of 1300 of 62
Febrile neutropeniaBlood and lymphatic system disorders8 of 4201 of 1300 of 62

Most frequent non-serious adverse event terms

Event termOrgan systemAll Participants - InductionNab-Paclitaxel + Best Supportive Care (Maintenance)Best Supportive Care (Maintenance)
AnaemiaBlood and lymphatic system disorders256 of 42024 of 1306 of 62
NeutropeniaBlood and lymphatic system disorders225 of 42014 of 1300 of 62
Peripheral sensory neuropathyNervous system disorders152 of 42056 of 1306 of 62
NauseaGastrointestinal disorders191 of 42016 of 1302 of 62
FatigueGeneral disorders175 of 42024 of 1300 of 62
DiarrhoeaGastrointestinal disorders158 of 42018 of 1304 of 62
ThrombocytopeniaBlood and lymphatic system disorders163 of 4209 of 1302 of 62
ConstipationGastrointestinal disorders130 of 42014 of 1300 of 62
Decreased appetiteMetabolism and nutrition disorders101 of 42017 of 1303 of 62
AlopeciaSkin and subcutaneous tissue disorders105 of 4206 of 1302 of 62

Serious events with the highest arm-level rate: pneumonia (5.7%), anaemia (4.0%), dyspnoea (3.6%), dehydration (3.3%), general physical health deterioration (3.2%).

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

The registry reports serious adverse events during induction for 420 participants at risk, with 177 affected and 80 deaths listed. During nab-paclitaxel plus best supportive care maintenance, 130 were at risk, 32 were affected by serious adverse events, and 82 deaths were listed. During best supportive care maintenance, 62 were at risk, 13 were affected by serious adverse events, and 48 deaths were listed. These are counts from the reported safety groups, not adjusted comparisons between treatment groups.

The registry also lists other adverse events affecting 417 participants at risk during induction, 122 during nab-paclitaxel plus best supportive care maintenance, and 45 during best supportive care maintenance. The most frequently listed serious adverse-event terms include pneumonia (5.7%), anaemia (4.0%), dyspnoea (3.6%), dehydration (3.3%), general physical health deterioration (3.2%), and chronic obstructive pulmonary disease (3.2%).

Counts at risk and counts affected should be read within each treatment period. They do not, by themselves, establish that treatment caused an event or provide an exposure-adjusted comparison. Event definitions, duration of exposure by group, attribution, and methods for comparing safety outcomes are not reported in the registry record. The maintenance groups are also different in size, so raw counts alone are not a fair measure of relative risk.

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

The primary result describes progression-free survival after randomization into maintenance among participants who had reached that stage of the study. The estimated median was 3.12 months with nab-paclitaxel plus best supportive care and 2.6 months with best supportive care alone. The reported hazard ratio was 0.85, but its 95% confidence interval, 0.61 to 1.19, includes 1. The data therefore leave uncertainty about the size and direction of the relative difference; the point estimate alone should not be treated as a definitive answer.

This comparison does not estimate the effect of nab-paclitaxel for everyone beginning induction. Participants entered maintenance after induction and had complete response, partial response, or stable disease at the end of 4 cycles. The primary analysis population was randomized into maintenance. The results therefore concern this maintenance comparison and do not directly answer questions about people who did not proceed to maintenance, other induction regimens, or other populations.

The outcome is a statistical measure of time to progression or death, not a direct measure of symptoms, quality of life, or the experience of an individual participant. Those outcomes are not reported as part of the primary endpoint. A median is a group summary and does not predict an individual’s course. A hazard ratio is a relative measure and should be read with its confidence interval and the analysis assumptions.

The secondary outcomes supply additional context, but their time periods and methods differ, and the registry does not report a multiplicity strategy. The safety counts are descriptive and do not establish causality. Taken together, the posted results support cautious interpretation of the randomized maintenance comparison; they do not justify a medical recommendation or a claim that one treatment works or does not work.

19. Why This Trial Matters Statistically

This trial illustrates why the target population and the point of randomization matter. Although induction treatment preceded the comparison, the primary question concerns maintenance after participants had completed induction and met the response or stable-disease condition described in the registry. The primary endpoint begins at maintenance randomization, so its interpretation should not be extended to the full pathway from initial treatment without qualification.

It also shows why a point estimate is not enough. The primary hazard ratio is below 1, but its confidence interval includes 1 and covers a range of possible effects. The median values give an intuitive time-based description, yet they do not replace the relative time-to-event analysis or its uncertainty. Reading these summaries together avoids treating a numerical direction as conclusive evidence.

The secondary outcomes further demonstrate that endpoint definitions shape interpretation. An outcome measured over the entire study includes induction as well as maintenance, while the primary outcome starts at maintenance randomization. A favorable-looking estimate in a secondary outcome is not automatically equivalent to confirmation of the primary endpoint, particularly when many outcomes are reported and the multiplicity plan is unavailable.

Finally, the registry record makes clear that planning illustrations based on observed effects are different from the trial’s original design justification. Distinguishing post hoc planning calculations from prospective assumptions prevents readers from mistaking an illustrative calculation for achieved power or a prespecified design target. These are broadly useful habits for interpreting randomized trials with multiple treatment periods and endpoints.

20. Limitations

The open-label design means masking was listed as none. The primary outcome includes investigator-assessed progression using imaging criteria, so knowledge of assigned maintenance treatment could potentially influence assessment or care processes. The registry does not report blinded central review, investigator assessment procedures beyond the stated criteria, or safeguards against assessment bias.

The comparison applies to participants randomized into maintenance after induction, not necessarily to all participants enrolled at the start of the study. The groups listed for the primary endpoint were 136 and 66, and the registry does not explain in the posted outcome description why these group sizes differ or provide detailed recruitment and disposition information for this analysis. The primary population definition includes randomized participants regardless of treatment receipt or efficacy assessments, but the handling of missing outcomes is not reported.

The registry describes the primary timeframe with a data cutoff of 15 September 2017 and a maximum follow-up of 27.6 months, while the endpoint definition refers to progression or death on or before 01 Aug 2019. The relationship between these dates is not explained in the registry record. This makes the precise analysis cutoff difficult to interpret from the outcome descriptions alone.

Other trial-specific details that would aid appraisal are not reported in the registry record, including stratification factors, the statistical analysis plan, the handling of protocol deviations, and any interim analyses. The registry’s crossover model label is not accompanied by crossover sequence or analysis details. These limitations constrain independent assessment and should be considered alongside the uncertainty in the primary confidence interval.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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24. Record Summary

NCT02027428 is a completed phase III, randomized, open-label, multicenter study of nab-paclitaxel maintenance after induction with nab-paclitaxel plus carboplatin for stage IIIB or IV squamous cell non-small-cell lung cancer. The primary outcome was progression-free survival from randomization into maintenance. The reported median was 3.12 months with nab-paclitaxel plus best supportive care and 2.6 months with best supportive care alone; the sponsor-reported hazard ratio was 0.85, with a 95% confidence interval from 0.61 to 1.19.

The primary estimate points toward a lower event hazard in the nab-paclitaxel group, but the interval includes 1 and leaves substantial uncertainty. Secondary outcomes cover both maintenance and the entire study and should be interpreted in light of their different definitions and the unreported multiplicity plan. Safety counts are descriptive, not adjusted comparisons. Missing-data methods, detailed analysis specifications, and the original sample-size justification are not reported in the registry record.

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