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Neoplasms, Breast Phase 3 Time-to-Event Analysis NCT00075270

Paclitaxel With / Without GW572016 (Lapatinib) As First Line Therapy For Women With Advanced Or Metastatic Breast Cancer: Complete Statistical Analysis

This analysis examines the registry results for a randomized phase III comparison of lapatinib plus paclitaxel with placebo plus paclitaxel in advanced or metastatic breast cancer. It focuses on investigator-assessed time to progression and the precision and limits of the posted estimates.

Trial start: 2004-01  ·  Enrollment: 580  ·  Sponsor: GlaxoSmithKline
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 Paclitaxel With / Without GW572016 (Lapatinib) As First Line Therapy For Women With Advanced Or Metastatic Breast Cancer (NCT00075270), a randomized phase 3 study. The primary outcome is Time to Progression as Evaluated by the Investigator.

580
Enrollment
Phase 3
2
Arms
In the primary outcome
0.87
Hazard ratio
Lapatinib With Paclitaxel vs Placebo Wit
0.72–1.05
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00075270
PhasePhase 3
ConditionNeoplasms, Breast
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment580
Arms in the primary outcome2
Lead sponsorGlaxoSmithKline
Results postedYes

2. Clinical Question

Population

Women with advanced or metastatic breast cancer who had not previously received treatment for that setting, as described in the registry record. The primary outcome population is identified as the Intent-to-Treat population: randomized participants who received at least one dose of randomized therapy. The record does not give further eligibility criteria in the posted outcome description.

Intervention

Lapatinib, identified in the record as GW572016, with paclitaxel. The arm description specifies lapatinib 1500 mg once daily and paclitaxel 175 mg/m intravenously over 3 hours every 3 weeks.

Comparator

Placebo with paclitaxel. The arm description specifies paclitaxel 175 mg/m intravenously over 3 hours every 3 weeks, together with placebo.

Primary question

Does investigator-assessed time to progression differ between the combination arm and the placebo-plus-paclitaxel arm? The record defines this outcome by the interval from randomization to progression or death due to breast cancer, with progression assessed using radiological and clinical information. The reported comparison is expressed as a hazard ratio and a log-rank test result.

The study was randomized, double-blind, placebo-controlled, and parallel-group. Its stated purpose was to evaluate the efficacy and safety of adding the oral dual tyrosine kinase inhibitor to paclitaxel. The posted results describe an estimate of the relative timing of progression-related events, not a definitive statement about benefit for an individual participant. The outcome definition and the uncertainty around the estimate matter when interpreting the comparison.

3. Trial Design

This is a phase III, randomized, multicenter, double-blind, placebo-controlled, parallel-group study. The registry record lists enrollment as 580 and describes two treatment arms. The study is marked completed. Its listed start is 2004-01 and its primary completion is 2006-10. These registry dates describe the study record, not necessarily the timing of each participant’s follow-up.

Participants were assigned to lapatinib with paclitaxel or placebo with paclitaxel. The lapatinib arm description gives lapatinib 1500 mg once daily and paclitaxel 175 mg/m by intravenous administration over 3 hours every 3 weeks. The comparator arm received paclitaxel at the same stated dose and schedule with placebo. The record describes masking as double and allocation as randomized; further operational details about how allocation was generated or concealed are not reported in the registry record.

The primary outcome is investigator-assessed time to progression. The outcome population is described as randomized participants who received at least one dose of randomized therapy. The record also posts secondary outcomes covering tumor response, clinical benefit, response timing, duration of response, progression-free survival, and overall survival. Additional posted measures include the number of participants who progressed or died by 6 months and a baseline ErbB2 ratio.

The registry record does not report the original sample-size justification, the detailed randomization procedure, or the full statistical analysis plan. It also does not report whether interim analyses were planned or performed. The posted study enrollment should not be confused with the analysis counts reported for individual outcomes, which may differ because outcome populations and available measurements can vary.

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: A total of 580 participants were enrolled and randomized to treatment; however one participant withdrew from the study before taking any medication. Thus, only 579 participants were included in the Intent-to-Treat Population (comprised of all randomized participants who had received at least one dose of randomized therapy \[lapatinib or placebo\]).

Overall Study

StageLapatinib With PaclitaxelPlacebo With Paclitaxel
STARTED291288
Missing2613
COMPLETED54
NOT COMPLETED286284

Reasons for not completing this period:

ReasonLapatinib With PaclitaxelPlacebo With Paclitaxel
Withdrawal by Subject2821
Lost to Follow-up2528
Protocol Violation02
Death198215
Other/Unknown95
Missing2613

Analysis population for the primary outcome, as defined in the registry: Intent-to-Treat (ITT) Population: all randomized participants who had received at least one dose of randomized therapy (lapatinib or placebo)

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.

CharacteristicUnitLapatinib With PaclitaxelPlacebo With PaclitaxelTotal
Participants analysed291288579
Age, ContinuousYears51.3 (SD 10.45)52.4 (SD 10.98)51.8 (SD 10.72)
Sex: Female, Male: FemaleParticipants291288579
Sex: Female, Male: MaleParticipants000
Race/Ethnicity, Customized: Whiteparticipants190182372
Race/Ethnicity, Customized: Blackparticipants101020
Race/Ethnicity, Customized: Asianparticipants303565
Race/Ethnicity, Customized: American Hispanicparticipants5453107
Race/Ethnicity, Customized: Unknownparticipants7815

6. Primary Endpoint

The registry lists the primary outcome as Time to Progression as Evaluated by the Investigator, measured over Randomization until the date of disease progression or death (average of 26 weeks).

ElementRegistry entry
Result typeMedian
Measure of spreadInter-Quartile Range
Unitweeks
Endpoint classificationTime-to-Event Analysis

The primary endpoint is time to progression as evaluated by the investigator. It measures the interval beginning at randomization and ending at the earliest recorded progression or death due to breast cancer. Progression was assessed from radiological findings and clinical symptomatic progress. The registry description refers to RECIST criteria, including growth in the sum of the largest diameters of target lesions or new lesions, and progression involving non-target lesions.

Time-to-event endpoints are used when the question concerns how long participants remain without a specified event, while allowing the analysis to incorporate participants whose event time is not observed during follow-up. The registry description says that the last radiographic assessment was used for participants without a documented progression date or death due to breast cancer. Such observations are treated as censored: their recorded follow-up contributes information up to the last assessment, without claiming that an event occurred then.

The endpoint is useful for comparing the timing of progression-related events across randomized groups. It is not identical to tumor response: a response records a change in disease status, while time to progression concerns the interval until an event. The record’s timeframe also refers to progression or death and gives an average of 26 weeks, while its detailed definition specifies death due to breast cancer. The registry record does not explain this wording distinction further.

7. Results Posted in the Registry

Hazard ratio: Lapatinib With Paclitaxel vs Placebo With Paclitaxel

0.87

95% CI: 0.72 to 1.05

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Lapatinib With Paclitaxel vs …0.700.760.830.910.991.08hazard ratio (as reported) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Percentage of Participants With Clinical Benefit (CB) as Assessed by the InvestigatorBinary EndpointRisk difference+8.6 pts (0.8 to 16.4)489 per arm
Number of Participants Who Progressed or Died at or Prior to 6 Months, as a Measure of Six Months Progression-free Survival (PFS)Binary EndpointRisk difference-7.4 pts (-15.5 to 0.7)712 per arm
ErbB2 RatioContinuous EndpointMean difference0.09 (-0.34 to 0.52)9,899 per arm

Percentage of Participants With Clinical Benefit (CB) as Assessed by the Investigator

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Lapatinib With Paclitaxel-1.312.496.30101418risk difference (percentage points) vs control (95% CI)

Number of Participants Who Progressed or Died at or Prior to 6 Months, as a Measure of Six Months Progression-free Survival (PFS)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Lapatinib With Paclitaxel-17-13-9.30-5.54-1.772.00risk difference (percentage points) vs control (95% CI)

ErbB2 Ratio

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Lapatinib With Paclitaxel-0.41-0.21-0.010.190.390.59mean difference vs control (95% CI)

The secondary outcomes address several related but distinct aspects of disease status and follow-up: tumor response, clinical benefit, timing and duration of response, progression-free survival, overall survival, and a baseline ErbB2 measure. This collection provides broader context than the primary time-to-progression outcome alone. However, the registry record posts numerical results for only some secondary outcomes in the available results summarized for this analysis; details for the other listed outcomes are not reported in the registry record.

The posted secondary summaries do not change the primary analysis. Clinical benefit and tumor response describe disease status, while progression-free survival and overall survival use time-to-event concepts or event counts. These outcomes may be related to progression, but they are not interchangeable with investigator-assessed time to progression. Differences in endpoint definition, assessment, and follow-up can lead to different estimates without implying that one result invalidates another.

The secondary findings should be interpreted as exploratory context unless the analysis plan and testing strategy establish otherwise. When many outcomes are examined, some estimates may appear notable by chance even if there is no underlying difference. Unadjusted p-values do not account for the number of outcomes or comparisons considered, so they generally carry less confirmatory weight than a designated primary analysis. The registry record does not report a multiplicity adjustment or a hierarchy of secondary hypotheses.

Accordingly, the overall secondary pattern should be considered alongside the primary hazard-ratio estimate and its uncertainty, not treated as an independent verdict. The registry record does not report enough detail to establish that secondary results were prespecified, adequately powered, or adjusted for multiple testing. A complete account of the secondary endpoint findings and their analysis methods is not reported in the registry record.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The median investigator-assessed time to progression was 29.0 weeks in the lapatinib-with-paclitaxel arm, with an inter-quartile range of 13.9 to 46.9 weeks. In the placebo-with-paclitaxel arm, the median was 22.9 weeks, with an inter-quartile range of 12.0 to 38.3 weeks. These summaries describe the observed event-time distributions; the inter-quartile ranges show the spread of the middle portion of those distributions.

The reported hazard ratio for lapatinib with paclitaxel versus placebo with paclitaxel was 0.87, with a 95% confidence interval from 0.72 to 1.05 and a log-rank p-value of 0.142. Under the conventional hazard-ratio interpretation, a value below 1 points toward a lower event hazard in the lapatinib arm during the observed follow-up, but the confidence interval includes 1. The estimate is therefore compatible with a range of relative event hazards that includes no difference as well as values on either side of it. The registry’s reported test does not provide strong evidence against the no-difference hypothesis at commonly used thresholds, but the record does not state a threshold or adjustment plan for this outcome.

The median values and the hazard ratio answer related but different questions. The medians describe the time by which half of the relevant event-time distribution has reached the endpoint, whereas the hazard ratio summarizes relative event rates over follow-up under the time-to-event analysis. The medians alone do not establish the size or certainty of a treatment effect, and their difference should not be treated as a substitute for the reported hazard-ratio analysis.

The result should be read as an estimate with uncertainty, not as proof that the regimens are equivalent or that one is superior. The confidence interval is wide enough to include both a potentially lower event hazard and a modestly higher one for the lapatinib arm. The registry record does not post further details about the shape of the event-time curves, proportional-hazards assessment, or adjusted analyses. Those omissions limit how fully the hazard-ratio model and the consistency of the comparison over time can be evaluated.

The trial also reports secondary outcomes, but they do not replace the primary endpoint. A coherent interpretation weighs the prespecified primary question, the size and precision of its estimate, and the context of the other outcomes. The secondary findings have their own uncertainty and multiplicity concerns, so isolated favorable or unfavorable results should not be treated as independent confirmation of the primary comparison.

10. Statistical Methods Explained

Time-to-event analysis is appropriate when the outcome is the time until an event, such as progression or a defined death. Unlike a simple comparison of event counts, it can use information from participants whose follow-up ends before the event is documented. The registry’s primary outcome description says that participants without a documented progression date or death due to breast cancer were censored at their last radiographic assessment. Censoring does not mean that an event was absent indefinitely; it means that the event was not observed by the last recorded assessment.

What does the median describe?

The median time to progression is the point in the estimated event-time distribution at which half of the distribution has experienced the event and half has not yet done so. The registry reports medians with inter-quartile ranges. An inter-quartile range describes the span between the lower and upper quartiles, giving information about the distribution’s spread without assuming that event times follow a symmetric or normal distribution. It is not a confidence interval for the median.

The reported medians are 29.0 weeks for lapatinib with paclitaxel and 22.9 weeks for placebo with paclitaxel. Their inter-quartile ranges are 13.9 to 46.9 weeks and 12.0 to 38.3 weeks, respectively. The medians are compact summaries; they do not capture every feature of the event-time curves. Different curves can have similar medians but differ at other follow-up times, and the medians do not by themselves quantify the uncertainty in the comparison.

What does the hazard ratio describe?

A hazard is an event rate among participants who have not yet experienced the event, considered over time. A hazard ratio compares those rates between groups. A value of 1 represents equal hazards under the model; a value below 1 indicates a lower estimated hazard for the group named first, and a value above 1 indicates a higher estimated hazard for that group. This is a relative comparison, not a direct measure of the absolute probability that an individual will experience progression.

The registry reports a hazard ratio of 0.87 for lapatinib with paclitaxel versus placebo with paclitaxel. Its confidence interval is 0.72 to 1.05. Interpretation of a single hazard ratio generally relies on the groups’ relative hazards being sufficiently stable over time, or on the summary remaining useful despite variation. The registry record does not report whether proportional hazards were assessed, or whether another time-to-event summary was used to address changing relative hazards.

What does the log-rank test contribute?

The log-rank test compares event-time experience between groups while taking account of when events occurred and which participants remained at risk at different times. The registry identifies the comparison method as Log Rank and reports p = 0.142. The p-value measures how incompatible the observed test result is with a specified null model, assuming that model and the test’s conditions. It is not the probability that the null hypothesis is true, nor does it measure the probability that the result occurred by chance in a general sense.

The p-value is not a measure of clinical importance. The hazard ratio and its confidence interval communicate the estimated direction, relative magnitude, and uncertainty more directly. In this record, the confidence interval includes 1, while the point estimate lies below 1. These registry entries support a cautious reading: the observed estimate favors a lower event hazard in the lapatinib group, but the posted analysis does not precisely rule out no difference or a modestly higher hazard.

Why does censoring matter?

Time-to-event methods depend on how censoring occurs. In general, censoring is most straightforward to handle when the reason follow-up ends is not related to the participant’s underlying event risk after accounting for information in the analysis. If participants with worsening disease are more likely to miss assessments, for example, recorded event times may not fully represent the intended outcome. This is a general statistical consideration, not a claim about what happened in this trial. The registry record gives the last-radiographic-assessment rule but does not report the amount, reasons, or group distribution of censoring.

The endpoint definition names death due to breast cancer, while the timeframe phrase refers to progression or death. The posted material does not resolve whether this reflects a difference in wording or another operational detail. The registry record also does not report the number of primary-endpoint events, follow-up completeness, or any sensitivity analysis for censoring.

Why is the analysis population important?

The primary outcome population is described as an Intent-to-Treat population consisting of randomized participants who received at least one dose of randomized therapy. This definition is narrower than a formulation that includes every randomized participant regardless of treatment receipt. The registry record does not report further details about exclusions, missing outcome assessments, or how all randomized participants were handled in the reported analysis. Such details help readers assess whether the analysis retains the protection of randomization and how complete the observed outcome data are.

11. Confidence Intervals and Precision

The 95% confidence interval for the reported hazard ratio extends from 0.72 to 1.05 around a point estimate of 0.87. A confidence interval gives a range of estimates compatible with the observed data and the analysis procedure, under its assumptions. It is not a guarantee that the true value lies in that particular interval, nor is it a range containing 95% of individual participants’ outcomes.

The interval includes 1, the value corresponding to equal hazards. It also includes values below 1 and a value above 1. Thus, the data are consistent with a lower event hazard in the lapatinib arm, with little or no difference, and with a modestly higher event hazard. The interval does not support a sharply determined estimate of the relative effect. The p-value of 0.142 is consistent with this uncertainty: the reported log-rank test does not distinguish the observed comparison from the null at commonly used significance thresholds.

The inter-quartile ranges accompanying the medians describe the spread of event times, not uncertainty in the medians or the hazard ratio. They overlap substantially, but visual overlap of these ranges is not itself a formal test of the treatment comparison. The hazard-ratio confidence interval is the direct uncertainty summary for the reported relative comparison.

Precision depends on the amount of event information and the pattern of follow-up, among other features. The registry record does not report the primary event count or enough detail to independently assess the source of the interval’s width. A confidence interval that includes the null does not establish equivalence; demonstrating equivalence requires an appropriate design and margin, neither of which is reported in the registry record.

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 effect0.871,6192,168
75% of the observed effect0.902,8783,853
50% of the observed effect0.936,4768,669
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: Lapatinib With Paclitaxel vs Placebo With Paclitaxel.

The planning figures are illustrations based on the observed effect, not the trial’s original design calculation. For the primary time-to-event comparison, the figures are total events, not participants per arm. The listed event totals are 1,619 for 80% power and 2,168 for 90% power when planning for 100% of the observed effect; 2,878 and 3,853 when planning for 75% of the observed effect; and 6,476 and 8,669 when planning for 50% of the observed effect.

The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The time-to-event figures use the Schoenfeld method and express the requirement as a total number of events. The other planning displays express participants per arm. These are planning illustrations, not observed power.

The 80% power column represents a planning target under which a study with the stated assumed effect would have an 80% chance of detecting that effect using the specified test and assumptions. The 90% power column uses a higher chance-of-detection target under those same assumptions. Neither column describes the probability that the posted result is correct, or the chance that this completed trial detected an effect after the fact.

The effect fractions refer to a fraction of the observed effect, not a fraction of participants or events. Planning for a smaller effect requires more information, so the illustrated event or participant requirements rise as the assumed effect becomes smaller. The original trial’s sample-size assumptions are not reported in the registry record. The illustrated requirements should therefore not be read as the basis on which this trial was designed or as evidence that the trial did or did not meet its original target.

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 = 0.870, so ln(HR) = -0.1393.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.870)]2 = 1,618.8, rounded up to 1,619 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 <- 0.87                              # 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(75270)
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 = 1,619 (80% power), 2,168 (90% power)
 75% of observed effect: events = 2,878 (80% power), 3,853 (90% power)
 50% of observed effect: events = 6,476 (80% power), 8,669 (90% power)
Simulated power with 1,619 events: 0.802 (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 2,379 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 114.47313.7100.00010.0001
Look 223.21,4612.5110.00600.0060
Look 360.02,1921.9930.02310.0250
01234z = 3.7114 mo731 eventsz = 2.5123 mo1461 eventsz = 1.9960 mo2192 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%1,6181,75660.0
Two looks, O'Brien-Fleming80%1,6241,76360.0
Three looks, O'Brien-Fleming80%1,6391,77860.0
Three looks, Pocock80%1,8942,05560.0
Fixed design, one analysis90%2,1672,35160.0
Two looks, O'Brien-Fleming90%2,1742,35960.0
Three looks, O'Brien-Fleming90%2,1922,37960.0
Three looks, Pocock90%2,5012,71360.0

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 effect0.8702,1922,379
75% of the observed effect0.9013,8984,222
50% of the observed effect0.9338,7709,484

For context, this trial enrolled 580 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 <- 5.28461538461538          # control-arm median, months (converted from the posted unit)
hr          <- 0.87          # 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: 1428         p (1-sided)   0.0001
  Events: 731        ~HR at bound   0.7599
    Month: 14    P(Cross) if HR=1   0.0001
              P(Cross) if HR=0.87   0.0338
    IA 2: 67%                   Z   2.5114
      N: 2296         p (1-sided)   0.0060
 Events: 1462        ~HR at bound   0.8769
    Month: 23    P(Cross) if HR=1   0.0060
              P(Cross) if HR=0.87   0.5603
        Final                   Z   1.9930
      N: 2380         p (1-sided)   0.0231
 Events: 2193        ~HR at bound   0.9184
    Month: 60    P(Cross) if HR=1   0.0250
              P(Cross) if HR=0.87   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, log 0.870.72 to 1.050.142

The registry reports the sponsor’s primary comparison as a log-rank analysis with a hazard ratio of 0.87, a 95% confidence interval of 0.72 to 1.05, and p = 0.142. The posted median time-to-progression estimates and inter-quartile ranges describe the two groups separately; they do not replace the sponsor’s comparison of event-time distributions.

The recalculated summaries use the posted arm-level results and are unadjusted. For this primary endpoint, the reported comparison is the analysis to prioritize. The hazard ratio and p-value are the registry’s reported inferential results; a simple re-calculation from summary statistics cannot reproduce all participant-level features of a time-to-event analysis, including event timing and censoring. The record marks no discrepancy between the sponsor’s reported analysis and the available recalculation information.

The sponsor’s result does not establish that the groups are equivalent. Its confidence interval includes 1 and spans estimates on both sides of that value. The reported p-value also does not indicate a clear difference under the log-rank test. Interpretation should remain centered on the estimate and its uncertainty rather than treating a significance threshold as the only relevant finding.

For secondary outcomes without a sponsor-reported inferential comparison, any recalculated comparison is an unadjusted analysis of posted summary data. It may help describe how the group summaries relate, but it is not a substitute for the sponsor’s full analysis plan or participant-level analysis. The registry record does not report adjusted secondary analyses or the procedures used to control multiplicity.

16. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary endpoint and a broad set of secondary outcomes, including response, clinical benefit, progression-free survival, overall survival, and other measures. Testing or estimating many outcomes creates a multiplicity issue: even when no genuine effect exists, repeated analyses increase the opportunity for some results to look unusually strong. This is a general statistical concern, not evidence that any particular posted result is spurious.

The registry record does not report whether the secondary endpoints were organized into a prespecified testing hierarchy, whether multiplicity adjustments were planned, or whether confirmatory claims were restricted to particular outcomes. It also does not report a complete statistical analysis plan. Consequently, unadjusted secondary comparisons should be treated as descriptive or exploratory rather than as independent confirmation of efficacy. The reported primary log-rank result remains the central inferential comparison in the registry record.

Missing data and censoring also affect interpretation. For the primary time-to-progression endpoint, the record states that participants without a documented progression date or death due to breast cancer were censored at the last radiographic assessment. It does not report the extent of censoring, reasons for missed assessments, or whether these features differed between groups. In general, time-to-event analysis requires assumptions about the relationship between censoring and future event risk. The record does not provide enough information to evaluate those assumptions fully.

The primary outcome population is described as randomized participants who received at least one dose of randomized therapy. The registry record does not report a complete account of outcome missingness, exclusions, or sensitivity analyses. It also does not describe how missing measurements were handled for each secondary endpoint. These omissions limit assessment of whether missingness could have influenced the comparisons.

The timeframe language refers to progression or death, while the detailed endpoint description specifies death due to breast cancer. The registry record does not explain the distinction. Further details about endpoint adjudication, the completeness of follow-up, and any alternative analyses are not reported in the registry record.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Lapatinib With Paclitaxel10329335.2%
Placebo With Paclitaxel6328622.0%
Participants with at least one serious adverse event
Serious adverse events by armLapatinib With Paclitaxel35.2%Placebo With Paclitaxel22.0%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

ArmParticipants affected of at risk
Lapatinib With Paclitaxel287 of 293
Placebo With Paclitaxel278 of 286

Most frequent serious adverse event terms

Event termOrgan systemLapatinib With PaclitaxelPlacebo With Paclitaxel
NeutropeniaBlood and lymphatic system disorders22 of 29314 of 286
DiarrheaGastrointestinal disorders24 of 2932 of 286
Febrile neutropeniaBlood and lymphatic system disorders10 of 2933 of 286
Ejection fraction decreasedInvestigations5 of 2935 of 286
PyrexiaGeneral disorders7 of 2932 of 286
VomitingGastrointestinal disorders4 of 2934 of 286
Mucosal inflammationGeneral disorders6 of 2931 of 286
HypercalcemiaMetabolism and nutrition disorders4 of 2933 of 286
DyspneaRespiratory, thoracic and mediastinal disorders3 of 2933 of 286
PneumoniaInfections and infestations3 of 2932 of 286

Most frequent non-serious adverse event terms

Event termOrgan systemLapatinib With PaclitaxelPlacebo With Paclitaxel
AlopeciaSkin and subcutaneous tissue disorders153 of 293183 of 286
DiarrheaGastrointestinal disorders171 of 29373 of 286
RashSkin and subcutaneous tissue disorders145 of 29366 of 286
NauseaGastrointestinal disorders100 of 29385 of 286
MyalgiaMusculoskeletal and connective tissue disorders94 of 29374 of 286
NeutropeniaBlood and lymphatic system disorders76 of 29358 of 286
ArthralgiaMusculoskeletal and connective tissue disorders70 of 29358 of 286
FatigueGeneral disorders65 of 29361 of 286
VomitingGastrointestinal disorders74 of 29348 of 286
Peripheral sensory neuropathyNervous system disorders48 of 29354 of 286

Serious events with the highest arm-level rate: diarrhea (8.2%), neutropenia (7.5%), febrile neutropenia (3.4%), pyrexia (2.4%), mucosal inflammation (2.0%).

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 posts serious adverse event figures for each arm. For lapatinib with paclitaxel, 103 participants with serious adverse events are reported among 293 at risk. For placebo with paclitaxel, 63 are reported among 286 at risk. These are counts of participants affected, not counts of all serious-event episodes; the registry record does not state whether a participant could contribute more than one event to other summaries.

The most frequently listed serious adverse event terms include diarrhea at 8.2%, neutropenia at 7.5%, febrile neutropenia at 3.4%, pyrexia at 2.4%, mucosal inflammation at 2.0%, and decreased ejection fraction at 1.7%. These are reported as serious-event terms, and the registry record does not give further detail about their event definitions, timing, duration, or attribution. The record lists other adverse-event counts of 287 among 293 at risk in the lapatinib arm and 278 among 286 at risk in the placebo arm.

These figures describe reported safety events in the registry; they do not by themselves establish causality or provide a complete assessment of comparative safety. Death counts are not reported in the registry record. The safety follow-up window and detailed method for collecting adverse events are also not reported in the registry record.

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

The primary result describes a randomized comparison of lapatinib plus paclitaxel with placebo plus paclitaxel for investigator-assessed time to progression. The estimated median was 29.0 weeks in the lapatinib arm and 22.9 weeks in the placebo arm. The reported hazard ratio was 0.87, with a 95% confidence interval from 0.72 to 1.05 and p = 0.142. Together, these results indicate that the point estimate favored a lower event hazard with lapatinib, while the uncertainty includes no difference and a modestly higher hazard.

This does not establish that the combination improves outcomes, nor does it show that the regimens are equivalent. A nonsignificant test is not proof of no effect. Conversely, the point estimate below 1 is not proof of a benefit. The interval and the study’s analysis assumptions should be considered alongside the estimate. The registry record does not provide the details needed to evaluate every time-to-event assumption or the original design rationale.

The finding applies to the endpoint and analysis population as defined in the registry record. It does not automatically answer questions about tumor response, overall survival, quality of life, or safety. Secondary outcomes may offer additional context, but their interpretation is limited by the lack of reported multiplicity procedures and, for some listed outcomes, the absence of posted numerical results in the record summarized for this analysis.

The safety figures should also be read as registry summaries rather than a complete causal comparison. Serious adverse events are reported in both arms, with particular event terms listed, but event collection details and deaths are not reported in the registry record. The statistics therefore describe the posted results and their limits; they are not individualized predictions or medical advice.

19. Why This Trial Matters Statistically

This trial illustrates why a time-to-event result needs more than a single median. The medians summarize the event-time distributions, while the hazard ratio compares relative event rates over follow-up and the confidence interval communicates uncertainty in that comparison. In this study, those complementary summaries point to a lower estimated event hazard in the lapatinib arm, but the interval includes the no-difference value and extends to a modestly higher hazard. That combination calls for a measured interpretation rather than a binary conclusion.

The record also demonstrates the difference between statistical and clinical questions. A log-rank p-value evaluates compatibility with a null model under the test assumptions; it does not quantify the importance of an effect or prove the absence of one. A confidence interval helps show which relative effects remain compatible with the analysis, but it cannot resolve questions beyond the endpoint, population, and follow-up represented in the study.

Multiple secondary outcomes create another important interpretive challenge. Response, clinical benefit, progression-free survival, overall survival, and safety each contribute different information. Without a reported multiplicity strategy, unadjusted secondary findings have less confirmatory weight, even when they appear to align with the primary estimate. The record’s limited reporting of missingness, censoring, and analysis details further shows why registry results are best read as evidence with defined boundaries rather than as a complete clinical account.

Finally, planning illustrations based on an observed effect are distinct from a trial’s original design assumptions and from observed power. Keeping these concepts separate helps prevent retrospective planning calculations from being mistaken for evidence that the completed study was adequately or inadequately powered under its actual design.

20. Limitations

The registry record provides limited detail on the statistical plan. The original sample-size justification, interim analyses, and any prespecified multiplicity strategy are not reported in the registry record. The record also does not report whether proportional hazards were assessed, the number of primary endpoint events, or sensitivity analyses for the primary time-to-event comparison. These omissions restrict independent assessment of the model and the precision of the analysis.

For the primary endpoint, the registry gives a censoring rule based on the last radiographic assessment, but does not report the amount or reasons for censoring, follow-up completeness, or whether these differed by arm. The timeframe wording refers to progression or death, while the detailed definition specifies death due to breast cancer; the registry record does not explain this distinction. The outcome population is described as participants randomized and treated with at least one dose, but further details on exclusions and missing outcome data are not reported.

The registry lists many secondary outcomes, but does not report a testing hierarchy or adjustment for multiple comparisons. Some listed outcomes do not have numerical results in the posted information summarized for this analysis. For those outcomes, the full result and its uncertainty are not reported in the registry record. The registry also does not give enough detail about endpoint adjudication or the operational conduct of response assessments to independently assess consistency across assessors.

Safety reporting is also limited: detailed adverse-event collection methods, the safety follow-up window, and death counts are not reported in the registry record. The listed serious adverse-event terms and counts therefore cannot support a complete comparative safety assessment on their own.

21. Related Tutorials

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23. Sources

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24. Record Summary

The registry record describes a completed, randomized, double-blind, placebo-controlled, phase III parallel-group study of lapatinib with paclitaxel versus placebo with paclitaxel in advanced or metastatic breast cancer. Enrollment is listed as 580. The primary endpoint is investigator-assessed time to progression in an Intent-to-Treat population defined as randomized participants who received at least one dose of randomized therapy.

Median time to progression was 29.0 weeks with lapatinib and 22.9 weeks with placebo. The reported hazard ratio was 0.87, with a 95% confidence interval of 0.72 to 1.05 and p = 0.142. The estimate points toward a lower event hazard in the lapatinib arm, but its interval includes no difference and a modestly higher hazard. The record also posts secondary and safety results, with important limitations in multiplicity, missing-data, and analysis-plan reporting.

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