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Breast Cancer Phase 3 Time-to-Event Analysis NCT03337724

A Study of Ipatasertib in Combination With Paclitaxel as a Treatment for Participants With PIK3CA/AKT1/PTEN-Altered, Locally Advanced or Metastatic, Triple-Negative Breast Cancer or Hormone Receptor-Positive, HER2-Negative Breast Cancer: Complete Statistical Analysis

The completed randomized phase III study assessed ipatasertib with paclitaxel against placebo with paclitaxel in biomarker-altered advanced breast cancer. The primary result is Cohort A progression-free survival, with secondary outcomes and precision considered in the context of the registry record.

Trial start: 2018-01-06  ·  Enrollment: 579  ·  Sponsor: Hoffmann-La Roche
Scope of this record

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

1. Trial at a Glance

This page covers the registry results for A Study of Ipatasertib in Combination With Paclitaxel as a Treatment for Participants With PIK3CA/AKT1/PTEN-Altered, Locally Advanced or Metastatic, Triple-Negative Breast Cancer or Hormone Receptor-Positive, HER2-Negative Breast Cancer (NCT03337724), a randomized phase 3 study. The primary outcome is Cohort A: Progression-Free Survival (PFS).

579
Enrollment
Phase 3
2
Arms
In the primary outcome
1.02
Hazard ratio
Cohort A: Placebo + Paclitaxel vs Cohort
0.71–1.45
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03337724
PhasePhase 3
ConditionBreast Cancer
AllocationRandomized
Design modelParallel
MaskingTriple
Enrollment579
Arms in the primary outcome2
Lead sponsorHoffmann-La Roche
Results postedYes

2. Clinical Question

Population

The study included participants with PIK3CA/AKT1/PTEN-altered, locally advanced or metastatic breast cancer. The registry describes participants with triple-negative breast cancer and participants with hormone receptor-positive, HER2-negative breast adenocarcinoma who were not suitable for endocrine therapy. The primary outcome concerns Cohort A; the registry’s primary population definition says it included all randomized participants in that cohort, whether or not they received assigned treatment.

Intervention

Ipatasertib was given in combination with paclitaxel. The registry lists the study as randomized, parallel-group, placebo-controlled and triple-masked. It does not provide further details of the treatment schedules in the arm descriptions.

Comparator

The comparison for the primary outcome was placebo with paclitaxel. The primary Cohort A results include 87 participants in the placebo-plus-paclitaxel group and 168 in the ipatasertib-plus-paclitaxel group.

Primary question

The primary statistical question was whether Cohort A progression-free survival differed between the two treatment groups. Progression-free survival was measured from randomization until disease progression determined by the investigator using RECIST v.1.1, or death from any cause, whichever occurred first. The reported median was 6.1 months with placebo plus paclitaxel and 7.4 months with ipatasertib plus paclitaxel. The sponsor-reported hazard ratio was 1.02, with a 95% confidence interval from 0.71 to 1.45 and p = 0.924. These estimates describe the recorded comparison; they do not by themselves establish the size or certainty of an effect beyond the interval shown.

3. Trial Design

NCT03337724 is recorded as a completed phase III study sponsored by Hoffmann-La Roche. The registry reports randomized allocation, a parallel-group model, triple masking and placebo control. Enrollment is listed as 579. The study evaluated ipatasertib plus paclitaxel against placebo plus paclitaxel in participants with locally advanced or metastatic breast cancer with PIK3CA/AKT1/PTEN alterations. The record describes triple-negative disease and hormone receptor-positive, HER2-negative disease in participants not suitable for endocrine therapy.

The primary outcome is Cohort A progression-free survival. Its analysis population is defined as all randomized participants in Cohort A, regardless of whether assigned treatment was received. The primary outcome’s timeframe is from randomization up to 27 months. The outcome definition uses investigator-assessed disease progression under RECIST v.1.1 or death from any cause, whichever came first. The registry also lists outcomes for Cohorts A, B and C, including response, clinical benefit, overall survival and quality of life. The arm descriptions do not give more detail on treatment administration.

The recorded primary comparison includes 87 participants in the placebo-plus-paclitaxel group and 168 in the ipatasertib-plus-paclitaxel group. Cohort A adverse-event reporting lists 87 participants at risk for the placebo group and 166 for the ipatasertib group; these denominators differ from the primary outcome group sizes. The registry does not report why the analyzed or at-risk denominators differ. The study’s original sample-size justification, intended allocation ratio, recruitment target by cohort, and detailed protocol assumptions are not reported in the registry record. The listed planning illustrations based on observed effects are not descriptions of the trial’s original design.

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 TNBC or hormone receptor positive(HR+)/human epidermal growth factor receptor 2 negative(HER2-) breast adenocarcinoma with phosphatidylinositol-4,5-bisphosphate3-kinase,catalytic subunit, alpha(PIK3CA)/serine-threonine kinase(AKT1)/phosphatase \& tensin homolog (PTEN)-altered tumor were randomized to ipatasertib 400 mg+paclitaxel or placebo+paclitaxel (Cohorts A,B) \& those with TNBC without PIK3CA/ AKT1/PTEN-altered tumor received ipatasertib+atezolizumab+paclitaxel (Cohort C).

Overall Study

StageCohort A: Placebo + PaclitaxelCohort A: Ipatasertib + PaclitaxelCohort B: Placebo + PaclitaxelCohort B: Ipatasertib + PaclitaxelCohort C: Ipatasertib + Atezolizumab + Paclitaxel
STARTED8716876146102
Safety Evaluable Population8716675145102
COMPLETED00000
NOT COMPLETED8716876146102

Reasons for not completing this period:

ReasonCohort A: Placebo + PaclitaxelCohort A: Ipatasertib + PaclitaxelCohort B: Placebo + PaclitaxelCohort B: Ipatasertib + PaclitaxelCohort C: Ipatasertib + Atezolizumab + Paclitaxel
Reason not Specified12219929
Withdrawal by Subject13154156
Protocol Deviation01110
Adverse Event11010
Death4089437650
Lost to Follow-up55474
Physician Decision1634143413
Progressive Disease02120
Symptomatic Deterioration00010

Analysis population for the primary outcome, as defined in the registry: ITT Population included all randomized participants in Cohorts A regardless of whether the participants received the assigned treatment.

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: Intention-to-treat (ITT) Population included all randomized participants in Cohorts A and B regardless of whether the participants received the assigned treatment. For Cohort C, the ITT population consisted of all enrolled participants in Cohort C.

CharacteristicUnitCohort A: Placebo + PaclitaxelCohort A: Ipatasertib + PaclitaxelCohort B: Placebo + PaclitaxelCohort B: Ipatasertib + PaclitaxelCohort C: Ipatasertib + Atezolizumab + PaclitaxelTotal
Participants analysed8716876146102579
Age, Continuousyears54.2 (SD 12.6)54.6 (SD 12.8)54.5 (SD 11.3)57.2 (SD 11.1)54.6 (SD 11.7)55.2 (SD 12.0)
Sex: Female, Male: FemaleParticipants8716776144102576
Sex: Female, Male: MaleParticipants010203
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants2959132936166
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants571016211558393
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants1812820
Race (NIH/OMB): American Indian or Alaska NativeParticipants131534540
Race (NIH/OMB): AsianParticipants1737223812126
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000011
Race (NIH/OMB): Black or African AmericanParticipants1532920
Race (NIH/OMB): WhiteParticipants5199459355343
Race (NIH/OMB): More than one raceParticipants0420511
Race (NIH/OMB): Unknown or Not ReportedParticipants58191538

6. Primary Endpoint

The registry lists the primary outcome as Cohort A: Progression-Free Survival (PFS), measured over From randomization up to 27 months.

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

Progression-free survival (PFS) is the time from randomization until the first of disease progression or death from any cause. In this study, progression was determined locally by the investigator using RECIST v.1.1. The registry describes progression as a specified increase in the sum of target-lesion diameters, or the appearance of one or more new lesions. This endpoint combines an assessment of tumor progression with death, so a participant’s follow-up can end at either event.

PFS is used in clinical trials as a time-to-event outcome. It captures when an event occurs, rather than treating all participants as if they had the same follow-up duration. That distinction is useful when some participants have not experienced progression or death by the end of the recorded observation period. Such participants contribute information up to their last available assessment, subject to the analysis approach; the registry record does not provide further detail on censoring rules.

The reported median is the time by which half of the relevant event-time distribution has had an event, under the survival-analysis estimate. It is not the average follow-up time or a description of every participant’s experience. The primary outcome timeframe was from randomization up to 27 months. A median and a hazard ratio address different aspects of the time-to-event comparison: the median describes each group’s event-time distribution at its midpoint, while the hazard ratio compares event rates over the observed period under the analysis model. Neither measure alone gives the full course of the survival curves.

7. Results Posted in the Registry

Hazard ratio: Cohort A: Placebo + Paclitaxel vs Cohort A: Ipatasertib + Paclitaxel

1.02

95% CI: 0.71 to 1.45

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Cohort A: Placebo + Paclitaxe…0.670.790.931.101.301.54hazard 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
Cohort A and B: Objective Response Rate (ORR)Binary EndpointRisk difference+4.0 pts (-8.5 to 16.5)2,241 per arm
Cohort A and B: Clinical Benefit Rate (CBR)Binary EndpointRisk difference+1.4 pts (-11.6 to 14.3)21,153 per arm
Overall Survival (OS)Time-to-Event AnalysisHazard ratio1.08 (0.73 to 1.58)5,301 events

Cohort A and B: Objective Response Rate (ORR)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Cohort A: Ipatasertib + Pacli…Cohort B: Placebo + Paclitaxel-11-3.085.13132230risk difference (percentage points) vs control (95% CI)

Cohort A and B: Clinical Benefit Rate (CBR)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Cohort A: Ipatasertib + Pacli…Cohort B: Placebo + Paclitaxel-15-4.516.31172839risk difference (percentage points) vs control (95% CI)

Overall Survival (OS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Cohort A: Placebo + Paclitaxe…Cohort B: Placebo + Paclitaxe…0.610.740.911.121.381.70hazard ratio (as reported) vs control (95% CI)

The secondary outcomes add several kinds of context to the primary PFS comparison. Objective response and clinical benefit describe whether participants met outcome criteria within the stated timeframes. Overall survival addresses time until death, while the quality-of-life outcome listed for Cohorts A and B concerns change in global health status and health-related quality of life. These outcomes address related but distinct aspects of the study and should not be treated as interchangeable measures of the primary endpoint.

Across the posted arm estimates, the Cohort A response and clinical-benefit percentages are broadly similar between the two treatment groups. Cohort B has response and clinical-benefit estimates for both treatment groups, and Cohort C has a reported overall-survival median for the ipatasertib, atezolizumab and paclitaxel combination. Cohort C is not a randomized comparison in the outcome details; a corresponding comparator estimate is not shown. Cohort A and B overall-survival medians are also reported, with sponsor hazard ratios for those comparisons but no p-values in the record.

This pattern should be read alongside, not in place of, the primary PFS result. Secondary endpoints can clarify whether observed outcomes align across different domains, but they do not independently redefine the primary analysis. The registry lists 23 outcome measures and 5 analyses, and multiple cohorts and outcomes create opportunities for chance findings. The record does not report a multiplicity adjustment for the secondary outcomes. Unadjusted secondary results therefore carry less confirmatory weight than the prespecified primary comparison, particularly when no sponsor-reported inferential analysis is listed for them.

The registry includes a quality-of-life outcome in its secondary-outcome list, but the outcome results included in the posted data summarized in this record do not give a result for that measure. Its findings should not be inferred from the other outcomes. More generally, an outcome’s presence in the registry is not evidence that it showed a particular result.

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

9. Statistical Interpretation

Clinical Biostats interpretation

In Cohort A, the registry reports median PFS of 6.1 months for placebo plus paclitaxel and 7.4 months for ipatasertib plus paclitaxel. The sponsor’s reported stratified hazard ratio for the comparison, expressed as placebo plus paclitaxel versus ipatasertib plus paclitaxel, is 1.02. Its 95% confidence interval is 0.71 to 1.45, and the reported p-value is 0.924. The direction and scale of the hazard ratio should be read according to that stated comparison order. The estimate is close to 1, while the interval includes values on either side of 1 and spans a range of possible relative event rates.

The medians are point estimates and do not show how the event-time distributions behave throughout follow-up. The reported hazard ratio is the principal comparative statistic for the primary time-to-event outcome. The confidence interval indicates substantial uncertainty about the relative hazard compatible with the analysis. The p-value is not a measure of the probability that either treatment is better, nor does it indicate the probability that the null hypothesis is true. It summarizes the compatibility of the observed data with a specified no-difference hypothesis under the analysis procedure.

Other reported measures provide context but should not be treated as interchangeable with PFS. For example, Cohort A objective response rates are 34.9% with placebo plus paclitaxel and 38.9% with ipatasertib plus paclitaxel; the registry lists 95% confidence intervals for both. Clinical benefit rates are 45.3% and 46.7%, respectively. These binary outcomes reflect whether a response or clinical benefit was recorded, rather than when progression or death occurred. Overall survival medians are also reported for Cohort A, but the registry does not give a p-value for that comparison.

The posted primary comparison is the sponsor’s analysis, not a substitute for a new analysis based only on the arm medians. The registry identifies a Log Rank method for the primary analysis and reports a stratified hazard ratio. Because the record does not give the stratification factors or a full statistical analysis plan, the exact model specification cannot be reconstructed from the posted information. The result should therefore be read as a reported trial estimate with its stated uncertainty, population and endpoint definition, not as an isolated verdict about treatment or as a result that automatically applies to other cohorts or patient groups.

10. Statistical Methods Explained

What does a time-to-event analysis use?

General statistical explanation: A time-to-event method uses both the timing of an event and the information available from participants who have not yet had the event. Those participants may have follow-up that ends before an event is observed, so the analysis can use their observed time without labeling them as having had the event. This is commonly handled through censoring. The registry defines PFS as time from randomization to progression or death, but it does not report the detailed censoring rules or how assessments after missed visits were handled.

The PFS endpoint is composite: an event is either progression or death, whichever happens first. For this study, progression was locally assessed by the investigator using RECIST v.1.1. The endpoint therefore depends both on the timing of events and on the assessment process used to determine progression. The record does not report independent central review for this primary measure, and no such review should be assumed.

How should the median and hazard ratio be distinguished?

The median PFS is a time summary for each group. It locates the midpoint of the estimated event-time distribution; it does not state that every participant had an event at that time. A hazard ratio is a relative comparison of event rates between groups over follow-up, as defined by the analysis. The primary reported hazard ratio is 1.02 for placebo plus paclitaxel versus ipatasertib plus paclitaxel, with a 95% confidence interval of 0.71 to 1.45. The comparison order matters when describing its direction.

General statistical explanation: A hazard ratio near 1 indicates that the estimated event rates are similar under the model’s comparison, while values below or above 1 indicate different directions according to which group is in the numerator. A hazard ratio is not a ratio of the reported medians, and it does not directly express a difference in months. Interpreting it as a constant relative effect throughout follow-up requires assumptions about the pattern of hazards. The registry record does not report whether proportional hazards were assessed or whether the sponsor considered alternative time-to-event summaries.

What role does the Log Rank method have?

The primary comparison lists a Log Rank method. General statistical explanation: A log-rank test compares event-time experience across groups while accounting for the observed ordering of events over follow-up. It is a test of evidence against a no-difference hypothesis, not an estimate of the size of a treatment effect. The hazard ratio and its confidence interval provide an estimated relative effect and its uncertainty; the reported p-value supplies a separate test summary. The record does not report whether the Log Rank test was stratified, although the reported effect measure is named a stratified hazard ratio. The stratification variables are not reported in the registry record.

What does the analysis population tell us?

The primary outcome population is the intention-to-treat population for Cohort A: all randomized participants in that cohort, irrespective of whether they received assigned treatment. General statistical explanation: An intention-to-treat approach preserves the randomized group comparison and can limit bias that may arise when participants are reassigned according to treatment received or excluded after randomization. The exact handling of missing outcome assessments and other intercurrent events is not reported in the registry record. The primary group sizes are 87 and 168, while the Cohort A safety groups list 87 and 166 at risk. The registry does not explain the difference in these denominators.

How should the binary outcomes be read?

Objective response rate and clinical benefit rate are reported as percentages with 95% confidence intervals. These outcomes classify participants according to whether an outcome occurred during the stated observation timeframe. General statistical explanation: A proportion is a snapshot of the fraction meeting a criterion, whereas PFS accounts for event timing. Confidence intervals for proportions describe uncertainty in the underlying response or benefit rate under the corresponding method. The registry does not state the methods used to construct those intervals, or the detailed rules for missing response assessments.

The posted results also include unadjusted calculations for some binary contrasts, but no sponsor-reported analyses are listed for these secondary comparisons. They are descriptive calculations from posted summary information and do not replace a prespecified, adjusted analysis. A nominal p-value from an unadjusted comparison does not account for testing several outcomes or cohorts, and it should not be interpreted as confirmatory evidence on its own.

What is not documented?

The registry record does not report the detailed statistical analysis plan, the original sample-size justification, the allocation ratio assumed for planning, the stratification factors, any interim analyses, or a multiplicity procedure. It also does not provide full details of missing-data handling, sensitivity analyses, or model diagnostics. Those omissions limit how far readers can reproduce or evaluate the analysis beyond the reported estimates. The analysis methods that are explicitly named are the Log Rank method and a stratified hazard ratio for the primary PFS comparison.

11. Confidence Intervals and Precision

The primary PFS estimate is a hazard ratio of 1.02, with a 95% confidence interval from 0.71 to 1.45. The interval is the key precision summary: it represents a range of effect estimates compatible with the data under the analysis method and its assumptions. It includes 1, the value corresponding to equal hazards in the comparison, and also allows estimates on either side of that value. The point estimate alone therefore should not be read as a precise estimate of the relative event rate.

The 95% confidence intervals around the Cohort A median PFS estimates are 5.5 to 9.0 months for placebo plus paclitaxel and 5.6 to 8.5 months for ipatasertib plus paclitaxel. These intervals describe uncertainty around each group’s median separately; they are not themselves the confidence interval for the difference between groups. The sponsor-reported hazard-ratio interval is the direct comparative interval for the primary analysis.

For the listed binary outcomes, the estimates also have 95% confidence intervals. The breadth of an interval indicates how precisely a proportion is estimated, with wider intervals reflecting greater uncertainty. Differences in interval widths can arise from the amount of information and the observed outcome frequency. General statistical explanation: Confidence intervals are not guarantees that a particular interval contains the true value, nor do overlapping separate intervals provide a formal test of the difference between groups. A direct comparison requires its own estimate and uncertainty calculation.

Overall survival confidence intervals are available for the listed medians, including a Cohort C upper bound that is not reported. The Cohort A and B sponsor-reported hazard-ratio intervals also span 1. The registry does not provide p-values for those OS comparisons. Precision should be considered together with the endpoint, population, follow-up timeframe and analysis method; it is not captured by the point estimate alone.

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 effect1.0280,062107,180
75% of the observed effect1.01142,332190,541
50% of the observed effect1.01320,245428,717
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect50,000100,000200,000500,0001,000,00040%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: Cohort A: Placebo + Paclitaxel vs Cohort A: Ipatasertib + Paclitaxel.

The planning illustrations translate an observed effect into hypothetical sample-size or event-count requirements under stated assumptions. For binary outcomes, the figures are participants per arm for 80% power and participants per arm for 90% power. For time-to-event outcomes, the figures are total events, not participants per arm. The primary PFS illustration and the listed overall-survival illustrations therefore report total-event targets. The binary outcome illustrations report per-arm participant targets.

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

The 80% power column means the hypothetical design would have an 80% chance of detecting the specified effect under the stated assumptions if that effect were the true one. The 90% power column uses a higher target probability of detection under those same assumptions. Greater power generally requires more information, which can mean more participants for a binary endpoint or more observed events for a time-to-event endpoint. The fractions of the observed effect represent different hypothetical effect sizes; smaller effects need more participants or events to detect at the same power target.

These figures are planning illustrations, not observed power. They do not tell whether the completed trial was adequately powered under its original design, nor do they estimate the probability that the observed result is true. Their interpretation depends on the assumptions and the observed effect used to generate each scenario.

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 = 1.020, so ln(HR) = 0.0198.
  2. d = 4 × (1.96 + 0.842)2 / [ln(1.020)]2 = 80,061.2, rounded up to 80,062 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 <- 1.02                              # 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(3337724)
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 = 80,062 (80% power), 107,180 (90% power)
 75% of observed effect: events = 142,332 (80% power), 190,541 (90% power)
 50% of observed effect: events = 320,245 (80% power), 428,717 (90% power)
Simulated power with 80,062 events: 0.799 (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. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankStratified Hazard Ratio 1.020.71 to 1.450.924

The primary PFS result is reported by the sponsor as a stratified hazard ratio of 1.02, with a 95% confidence interval of 0.71 to 1.45 and p = 0.924. The registry also identifies the Log Rank method. This is the sponsor’s own reported analysis and is the appropriate reference for describing the primary comparison.

Recalculated summaries based on posted arm-level results are simple, unadjusted calculations. They do not reproduce the stratified analysis unless the necessary participant-level data, stratification factors and analysis details are available. For that reason, they should not be treated as a correction to or replacement for the sponsor’s reported estimate. The record does not indicate a discrepancy between the posted calculations and the sponsor analysis.

The secondary outcome comparisons do not have sponsor-reported analyses listed in the record. Any unadjusted comparisons shown for those outcomes are consequently descriptive and should be distinguished from the sponsor-reported primary analysis. The registry does not report the full analysis plan needed to establish whether other analyses were prespecified or how they were adjusted.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists multiple outcomes across Cohorts A, B and C, including response, duration of response, clinical benefit, overall survival and a quality-of-life measure. The primary PFS analysis is identified separately, but the registry record does not report a multiplicity adjustment or a hierarchy governing interpretation of the secondary outcomes. When many statistical comparisons are examined, the chance of at least one apparently notable result can increase even if no underlying differences exist. General statistical explanation: adjustment procedures or prespecified testing hierarchies can help control that risk, but no particular procedure should be attributed to this trial unless it is documented.

The record does not report whether interim analyses were planned or conducted, whether any stopping boundaries were used, or how the overall type I error was controlled across endpoints and cohorts. It also does not provide the original sample-size justification or a complete statistical analysis plan. These omissions mean the listed p-values should be interpreted only in the context of the analyses explicitly described, not as a full account of the trial’s confirmatory testing strategy.

The primary analysis population is stated as the Cohort A intention-to-treat population, including randomized participants whether or not they received assigned treatment. This makes the randomized assignment the basis of the primary group comparison. Details on missing PFS assessments, censoring, withdrawals, protocol deviations, and sensitivity analyses are not reported in the registry record. The record also does not describe how missing values were treated for the binary secondary outcomes or the quality-of-life measure.

These gaps do not erase the reported results, but they limit independent assessment of robustness and reproducibility. In particular, readers cannot determine from the registry record whether missing-data assumptions or multiple testing procedures materially affected the reported inferential conclusions. The primary estimate and its interval remain interpretable as reported, with these documentation limits kept in view.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
COHORT A Placebo + Paclitaxel208723.0%
COHORT A Ipatasertib + Paclitaxel3416620.5%
COHORT B Placebo + Paclitaxel117514.7%
COHORT B Ipatasertib + Paclitaxel3014520.7%
COHORT C Ipatasertib + Atezolizumab + Paclitaxel2910228.4%
Participants with at least one serious adverse event
Serious adverse events by armCOHORT A Placebo + Paclitaxel23.0%COHORT A Ipatasertib + Paclit…20.5%COHORT B Placebo + Paclitaxel14.7%COHORT B Ipatasertib + Paclit…20.7%COHORT C Ipatasertib + Atezol…28.4%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
COHORT A Placebo + Paclitaxel41 of 87
COHORT A Ipatasertib + Paclitaxel91 of 168
COHORT B Placebo + Paclitaxel44 of 76
COHORT B Ipatasertib + Paclitaxel78 of 146
COHORT C Ipatasertib + Atezolizumab + Paclitaxel50 of 102

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
COHORT A Placebo + Paclitaxel82 of 87
COHORT A Ipatasertib + Paclitaxel161 of 166
COHORT B Placebo + Paclitaxel72 of 75
COHORT B Ipatasertib + Paclitaxel141 of 145
COHORT C Ipatasertib + Atezolizumab + Paclitaxel101 of 102

Most frequent serious adverse event terms

Event termOrgan systemCOHORT A Placebo + PaclitaxelCOHORT A Ipatasertib + PaclitaxelCOHORT B Placebo + PaclitaxelCOHORT B Ipatasertib + PaclitaxelCOHORT C Ipatasertib + Atezolizumab + Paclitaxel
DiarrhoeaGastrointestinal disorders0 of 876 of 1661 of 754 of 1454 of 102
PneumoniaInfections and infestations4 of 872 of 1661 of 752 of 1453 of 102
Febrile neutropeniaBlood and lymphatic system disorders0 of 873 of 1660 of 752 of 1452 of 102
Urinary tract infectionInfections and infestations0 of 871 of 1661 of 750 of 1453 of 102
Pleural effusionRespiratory, thoracic and mediastinal disorders2 of 871 of 1660 of 751 of 1451 of 102
Pulmonary embolismRespiratory, thoracic and mediastinal disorders0 of 873 of 1661 of 750 of 1451 of 102
NeutropeniaBlood and lymphatic system disorders1 of 871 of 1660 of 752 of 1450 of 102
VomitingGastrointestinal disorders0 of 872 of 1660 of 750 of 1452 of 102
FatigueGeneral disorders0 of 871 of 1661 of 750 of 1452 of 102
PyrexiaGeneral disorders0 of 870 of 1660 of 750 of 1454 of 102

Most frequent non-serious adverse event terms

Event termOrgan systemCOHORT A Placebo + PaclitaxelCOHORT A Ipatasertib + PaclitaxelCOHORT B Placebo + PaclitaxelCOHORT B Ipatasertib + PaclitaxelCOHORT C Ipatasertib + Atezolizumab + Paclitaxel
DiarrhoeaGastrointestinal disorders28 of 87138 of 16629 of 75125 of 14586 of 102
AlopeciaSkin and subcutaneous tissue disorders38 of 8778 of 16644 of 7575 of 14542 of 102
NauseaGastrointestinal disorders22 of 8766 of 16617 of 7560 of 14542 of 102
ConstipationGastrointestinal disorders31 of 8749 of 16626 of 7542 of 14513 of 102
AnaemiaBlood and lymphatic system disorders23 of 8743 of 16615 of 7545 of 14534 of 102
Neuropathy peripheralNervous system disorders20 of 8739 of 16612 of 7546 of 14530 of 102
VomitingGastrointestinal disorders8 of 8753 of 1666 of 7545 of 14528 of 102
NeutropeniaBlood and lymphatic system disorders20 of 8728 of 16618 of 7536 of 14525 of 102
FatigueGeneral disorders15 of 8730 of 16619 of 7529 of 14523 of 102
RashSkin and subcutaneous tissue disorders11 of 8726 of 1669 of 7531 of 14529 of 102

Serious events with the highest arm-level rate: pneumonia (4.6%), diarrhoea (3.9%), pyrexia (3.9%), urinary tract infection (2.9%), pleural effusion (2.3%).

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

The registry lists serious adverse events and other adverse events by cohort and treatment group. In Cohort A, serious adverse events were recorded for 20 of 87 participants at risk in the placebo-plus-paclitaxel group and 34 of 166 at risk in the ipatasertib-plus-paclitaxel group. The corresponding other-adverse-event counts are 82 of 87 and 161 of 166. These are descriptive counts, and the safety denominators are not identical to the primary PFS group sizes.

For other cohorts, the serious-event counts are 11 of 75 for Cohort B placebo plus paclitaxel, 30 of 145 for Cohort B ipatasertib plus paclitaxel, and 29 of 102 for Cohort C ipatasertib plus atezolizumab plus paclitaxel. The registry also lists serious-event terms and frequencies, including pneumonia at 4.6%, diarrhoea at 3.9% and pyrexia at 3.9%. The displayed term list does not establish a treatment-specific comparison or causal attribution.

Counts alone do not account for exposure duration, event recurrence, severity beyond the serious-event classification, or differences between cohorts. The listed deaths are not interchangeable with a formal overall-survival comparison. Safety figures should be understood as recorded adverse-event summaries, not as a causal estimate of risk from the drug combination.

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

The primary result describes the Cohort A comparison of ipatasertib plus paclitaxel with placebo plus paclitaxel for PFS. The sponsor-reported hazard ratio is 1.02, with a 95% confidence interval of 0.71 to 1.45 and p = 0.924. The interval shows that the estimate is not precise enough to isolate a narrow range of relative hazards. The reported medians provide a group-level summary of event timing, but they do not capture all features of the event-time distributions.

The result does not prove that the treatments are identical. A non-significant p-value is not proof of no difference, and a confidence interval that includes 1 can remain compatible with a range of possible relative effects. Conversely, the point estimate and secondary outcome patterns do not establish a treatment benefit. Statistical estimates describe evidence and uncertainty under the specified design and analysis; they are not medical advice or a recommendation for an individual.

Interpretation is limited to the study population, endpoint definitions, follow-up and analysis reported. The primary estimate applies to Cohort A, rather than automatically to every cohort or to all people with breast cancer. The registry describes a biomarker-altered advanced-disease population, and the primary outcome is investigator-assessed progression or death. Results for response, clinical benefit and overall survival measure different outcomes and should not be substituted for PFS.

The record does not report the full analysis plan, missing-data procedures, multiplicity approach, interim analyses or original sample-size justification. These are relevant to understanding how the analysis was planned and how secondary evidence should be weighed. The central conclusion from the posted primary statistic is therefore descriptive: the reported estimate is near 1, its confidence interval is broad and includes 1, and the registry reports p = 0.924. Claims beyond those features would require evidence not documented in the registry record.

18. Why This Trial Matters Statistically

This study illustrates why a clinical trial result should be read through its endpoint definition, analysis population and comparative estimate rather than through a single arm-level median. PFS combines progression and death, uses investigator assessment under RECIST v.1.1, and is analyzed as a time-to-event outcome. The accompanying hazard ratio and confidence interval address a comparative question that the medians alone cannot answer.

It also demonstrates the distinction between a sponsor-reported analysis and a simple recalculation from summary values. A stratified hazard ratio reflects an analysis whose details cannot be fully reconstructed from the registry record. Arm-level summaries can help readers understand the data, but they are not a substitute for the sponsor’s analysis or the underlying participant-level information.

The record spans several cohorts and secondary outcomes. That breadth can be informative, but it also makes clear why outcome hierarchy and multiplicity matter: a result on one secondary measure does not automatically confirm a primary finding, and a collection of unadjusted comparisons can be difficult to interpret as a set. The absence of a documented multiplicity procedure means those secondary findings require particular restraint.

Finally, the planning illustrations help distinguish design calculations from trial results. Hypothetical participant or event requirements derived from observed effects are not evidence of the trial’s original assumptions and are not observed power. Together, these points make the trial useful for understanding how statistical precision, analysis choices and registry reporting shape the interpretation of a complex randomized study.

19. Limitations

The registry record does not include the full protocol or statistical analysis plan. The original sample-size justification, planned allocation ratio, stratification factors, interim analyses, multiplicity procedure and details of model diagnostics are not reported. Without those details, readers cannot fully reconstruct the primary analysis or evaluate the broader confirmatory testing strategy.

The primary endpoint relies on local investigator assessment of progression under RECIST v.1.1. The registry record does not report whether progression was independently reviewed, nor does it provide additional detail on assessment timing, censoring rules or handling of missed assessments. The primary analysis population is defined, but the record does not explain why safety denominators differ from the primary outcome group sizes in Cohort A.

Several secondary outcomes are listed across cohorts, but sponsor-reported inferential analyses are not included for the listed response and clinical-benefit comparisons. The registry record also does not report a multiplicity adjustment. The Cohort C overall-survival estimate has an upper confidence limit that is not reported, and the record gives no p-values for the listed overall-survival comparisons. These details limit the strength of conclusions that can be drawn from secondary findings.

Finally, serious adverse-event counts do not provide a complete comparative safety analysis. The registry summaries do not give exposure-adjusted rates or detailed information about event duration, recurrence or causal attribution. The available record supports description of the posted outcomes, but not a comprehensive independent assessment of all design, analysis and safety considerations.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT03337724 is a completed randomized, triple-masked, placebo-controlled phase III study of ipatasertib plus paclitaxel versus placebo plus paclitaxel in participants with PIK3CA/AKT1/PTEN-altered, locally advanced or metastatic breast cancer. The primary outcome is Cohort A PFS, measured from randomization to investigator-assessed progression or death. The reported medians are 6.1 months and 7.4 months, respectively; the sponsor-reported stratified hazard ratio is 1.02, with a 95% confidence interval of 0.71 to 1.45 and p = 0.924.

Secondary outcomes include response, clinical benefit, overall survival and quality of life across the listed cohorts. The record does not report the full statistical analysis plan, original sample-size justification, multiplicity procedure, interim analyses or detailed missing-data methods. The primary estimate should be read with its confidence interval and with those documentation limits in mind.

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