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Breast Cancer Phase 2 Binary Endpoint NCT02301988

A Study of Ipatasertib (GDC-0068) in Combination With Paclitaxel as Neoadjuvant Treatment for Participants With Early Stage Triple Negative Breast Cancer: Complete Statistical Analysis

This analysis examines a randomized, double-blind Phase II trial of ipatasertib plus paclitaxel compared with placebo plus paclitaxel as neoadjuvant treatment for early-stage triple-negative breast cancer. The primary outcome was pathological complete response in both breast and axilla at surgery.

Trial start: 2015-02-17  ·  Enrollment: 151  ·  Sponsor: Genentech, Inc.
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 (GDC-0068) in Combination With Paclitaxel as Neoadjuvant Treatment for Participants With Early Stage Triple Negative Breast Cancer (NCT02301988), a randomized phase 2 study. The primary outcome is Percentage of Participants With Pathological Complete Response (pCR) in Breast and Axilla as Defined by ypT0/Tis ypN0 in the American Joint Committee on Cancer Staging System (in All Participants).

151
Enrollment
Phase 2
2
Arms
In the primary outcome
+3.8 pts
Risk difference
Ipatasertib + Paclitaxel
-7.7 to 15.2 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02301988
PhasePhase 2
ConditionBreast Cancer
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment151
Arms in the primary outcome2
Lead sponsorGenentech, Inc.
Results postedYes

2. Clinical Question

Population

Women with Stage Ia–IIIa triple-negative breast adenocarcinoma were eligible according to the registry summary. The primary outcome population was the intention-to-treat (ITT) population, defined in the registry record as all randomized participants.

Intervention

Ipatasertib was given with paclitaxel as pre-operative treatment. The registry describes oral ipatasertib daily on Days 1–21 of each 28-day cycle for 3 cycles, alongside weekly intravenous paclitaxel for 3 cycles, described as 12 total doses.

Comparator

The comparison was matching placebo with the same paclitaxel schedule. The study was randomized, double-blind, placebo-controlled, multicenter, and parallel-group.

Primary question

At the surgery visit, approximately Weeks 14 to 19, what percentage of participants had a pathological complete response in both breast and axilla, defined as ypT0/Tis ypN0? The registry outcome compares the ipatasertib-plus-paclitaxel group with the placebo-plus-paclitaxel group.

This is an add-on comparison: both groups received paclitaxel, while the assigned oral treatment differed. The primary endpoint is a binary response outcome, classified as either meeting the stated pathological definition or not meeting it. The trial was designed to estimate efficacy in this setting; the registry does not report that the trial was intended to establish a definitive treatment effect. The registry record lists enrollment of 151 and reports results for 76 participants in the ipatasertib group and 75 in the placebo group. Those recorded group sizes describe the analysis results, not a basis for inferring details about recruitment or missing outcomes.

3. Trial Design

The registry identifies NCT02301988 as a randomized, double-blind, parallel-group Phase II study. It was placebo-controlled and multicenter, and compared ipatasertib plus paclitaxel with matching placebo plus paclitaxel in participants with early-stage triple-negative breast cancer. The study status is completed. The registry lists enrollment of 151, a start date of 2015-02-17, and primary completion on 2017-08-02.

The treatment period was described as approximately 12 weeks. Participants in the ipatasertib group received oral ipatasertib daily on Days 1–21 of each 28-day cycle for 3 cycles, together with weekly intravenous paclitaxel for 3 cycles, described as 12 total doses. Participants in the comparator group received matching oral placebo on the same schedule with weekly intravenous paclitaxel. This common chemotherapy background means the randomized contrast concerns adding ipatasertib rather than comparing paclitaxel with no paclitaxel.

The primary outcome was assessed at the surgery visit, approximately Weeks 14 to 19. The registry defines the primary ITT population as all randomized participants. It reports 76 in the ipatasertib group and 75 in the placebo group for this endpoint. Although the record labels the study randomized and double-blind, further operational details about the randomization procedure, allocation ratio, concealment, and who was masked are not reported in the registry record. The original sample-size rationale and any planned interim analyses are also not reported in the registry record. Consequently, the observed group results can be described, but the record does not establish how the original design assumptions shaped the planned enrollment.

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.

Overall Study

StageIpatasertib + PaclitaxelPlacebo + Paclitaxel
STARTED7675
COMPLETED6666
NOT COMPLETED109

Reasons for not completing this period:

ReasonIpatasertib + PaclitaxelPlacebo + Paclitaxel
Withdrawal by Subject21
Physician Decision22
Unknown Reason13
Lack of Efficacy32
Death10
Adverse Event11

Analysis population for the primary outcome, as defined in the registry: The ITT population included all randomized participants.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: The intent-to-treat (ITT) population included all randomized participants, with participants allocated to the treatment arms to which they were randomized.

CharacteristicUnitIpatasertib + PaclitaxelPlacebo + PaclitaxelTotal
Participants analysed7675151
Age, Continuousyears53.8 (SD 10.9)53.8 (SD 12.0)53.8 (SD 11.5)
Sex: Female, Male: FemaleParticipants7675151
Sex: Female, Male: MaleParticipants000
Race (NIH/OMB): American Indian or Alaska NativeParticipants000
Race (NIH/OMB): AsianParticipants011
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants101
Race (NIH/OMB): Black or African AmericanParticipants235
Race (NIH/OMB): WhiteParticipants7170141
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants213

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With Pathological Complete Response (pCR) in Breast and Axilla as Defined by ypT0/Tis ypN0 in the American Joint Committee on Cancer Staging System (in All Participants), measured over Surgery visit (at approximately Weeks 14 to 19).

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

The primary endpoint is the percentage of participants with a pathological complete response (pCR) in both breast and axilla at surgery. The registry defines pCR as ypT0/Tis ypN0 under the American Joint Committee on Cancer staging system. In the registry description, T0 means no evidence of primary tumor; Tis means early cancer that has not spread to neighboring tissue; and N0 means no cancer found in the lymph nodes. The assessment was based on local pathology laboratory evaluation, at the surgery visit, approximately Weeks 14 to 19.

This endpoint converts the pathology assessment into a binary outcome: a participant either meets the stated response definition or does not. The percentage summarizes the proportion meeting that definition in each randomized group. A pathological response at surgery is used in neoadjuvant studies to describe what is found in the tumor and lymph nodes after pre-operative treatment. It is distinct from outcomes that track recurrence, survival, symptoms, or longer-term health; those are not the primary endpoint.

The registry also lists breast-only pCR as a secondary outcome. That definition excludes the axillary requirement used for the primary endpoint, so the two response measures should not be treated as interchangeable. The distinction matters when interpreting percentages: the primary result specifically concerns response in both breast and axilla, while the breast-only result answers a narrower pathology question.

7. Results Posted in the Registry

Risk difference: Ipatasertib + Paclitaxel

+3.8

95% CI: -7.7 to 15.2 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals5.410.214.919.624.329.1Ipatasertib + Paclitaxel (n=76)Placebo + Paclitaxel (n=75)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ipatasertib + Paclitaxel-9.50-4.191.126.431217risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Percentage of Participants With pCR in Breast as Defined by ypT0/Tis in the American Joint Committee on Cancer Staging System (in All Participants)Binary EndpointRisk difference+7.7 pts (-4.6 to 20.0)399 per arm
Percentage of Participants With pCR in Breast as Defined by ypT0/Tis in the American Joint Committee on Cancer Staging System (in Participants Who Have PTEN-low Tumors)Binary EndpointRisk difference-3.0 pts (-28.2 to 22.2)2,558 per arm
Percentage of Participants With Objective Tumor Response by Magnetic Resonance Imaging (MRI), As Assessed by Investigator Per the Modified Response Evaluation Criteria in Solid Tumors (RECIST) (in All Participants)Binary EndpointRisk difference+11.1 pts (-4.3 to 26.5)301 per arm

Percentage of Participants With pCR in Breast as Defined by ypT0/Tis in the American Joint Committee on Cancer Staging System (in All Participants)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ipatasertib + Paclitaxel-6.59-0.884.84111622risk difference (percentage points) vs control (95% CI)

Percentage of Participants With pCR in Breast as Defined by ypT0/Tis in the American Joint Committee on Cancer Staging System (in Participants Who Have PTEN-low Tumors)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ipatasertib + Paclitaxel-32-20-8.802.881526risk difference (percentage points) vs control (95% CI)

Percentage of Participants With Objective Tumor Response by Magnetic Resonance Imaging (MRI), As Assessed by Investigator Per the Modified Response Evaluation Criteria in Solid Tumors (RECIST) (in All Participants)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ipatasertib + Paclitaxel-6.780.377.53152229risk difference (percentage points) vs control (95% CI)

The secondary outcomes broaden the assessment beyond the primary breast-and-axilla pathology definition. They include breast-only pCR, MRI-assessed objective tumor response, response outcomes in PTEN-low tumors and Akt diagnostic-positive participants, pCR by breast cancer subtype, and response to breast-conserving surgery among participants with T2 or T3 tumors. These outcomes address different dimensions of response and different analysis populations; they should not be treated as interchangeable confirmations of the primary result.

Among the posted all-participant secondary results, the breast-only pCR and MRI response point estimates are directionally higher in the ipatasertib-plus-paclitaxel group. The posted PTEN-low breast-only result does not follow that direction. This variation illustrates why a collection of secondary point estimates does not yield one uniform conclusion. The secondary results do not overturn or replace the primary breast-and-axilla comparison, which remains the main endpoint defined for the trial.

Secondary analyses generally carry less weight than the primary analysis when many outcomes or subgroups are examined. With multiple comparisons, some apparent differences can arise by chance even when no real effect exists. This issue is especially relevant when analyses involve different definitions, subgroup selections, or timeframes. The registry record does not report a multiplicity adjustment or a complete prespecified analysis hierarchy for the secondary outcomes. Therefore, individual secondary p-values should be regarded as exploratory unless additional analysis documentation establishes otherwise.

Secondary findings can still be useful for generating questions and describing patterns, but they require confirmation in appropriately designed research. The registry lists 12 secondary outcomes as posted, while the record does not provide full result detail for every listed outcome in the information available. Conclusions should be limited to the endpoints with posted results and should not imply that every secondary question was resolved.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, pCR in breast and axilla was recorded for 17.1% of participants in the ipatasertib-plus-paclitaxel group and 13.3% in the placebo-plus-paclitaxel group. The registry’s reported analysis gives a difference in response rates of 3.77, with a 95% confidence interval from -8.99 to 16.54 and p = 0.519. The interval includes values on both sides of no difference, and the reported p-value does not provide strong evidence against the no-difference hypothesis under the analysis used. These results are estimates from this trial; they do not establish that the treatments are equivalent or that a treatment effect is absent.

An unadjusted recalculation from the posted summary statistics gives a risk difference of 0.038, with a 95% confidence interval from -0.077 to 0.152 and p = 0.519. The recalculation is close in its central estimate and p-value to the registry analysis, while its interval limits differ. The sponsor’s reported analysis remains the registry’s own inferential result; the recalculation is a simple unadjusted comparison and does not replace that analysis. The registry lists a chi-squared method for the reported comparison.

The point estimates are not precise enough to distinguish a small difference from a more substantial difference in either direction. The confidence interval’s breadth is important: a near-zero estimate alone does not tell readers that the true difference is near zero. The posted results are compatible with a range of possible response-rate differences, including no difference. The p-value is not the probability that the treatments are the same, nor is it a measure of the clinical importance of the estimate.

The primary outcome is binary, so the comparison focuses on the proportion meeting a defined pathology criterion. It does not measure how quickly response occurred, whether a response persisted, or subsequent clinical outcomes. The result applies to the endpoint and analysis population recorded for this study. It should not be generalized automatically to other patient groups, treatment schedules, or outcomes. Information needed to assess those extensions is not reported in the registry record.

Secondary results provide additional descriptions of tumor response, but they do not change the primary endpoint’s role. Secondary outcomes include breast-only pCR, MRI-assessed objective response, and outcomes in selected subgroups. Because multiple outcomes and subgroups are considered, isolated secondary comparisons are less persuasive unless their analysis and multiplicity handling were prespecified and clearly reported. The registry record does not report enough information to establish that context for every posted secondary result.

10. Statistical Methods Explained

The primary endpoint is binary: each participant is classified according to whether the pathology meets the pCR definition. A response percentage is the proportion of participants in a group who meet that definition. The registry reports percentages with 95% confidence intervals, and its primary comparison is a difference in response rates assessed with a chi-squared method.

What does a group percentage describe?

A group percentage describes the observed frequency of the endpoint among participants included in the group’s analysis. It is not a measure of the size of a tumor change or the time until an event. For the primary endpoint, the definition requires both breast and axillary pathology criteria. The group percentages are therefore tied to that specific definition and to the surgery assessment timeframe. A different endpoint definition, such as breast-only pCR, can produce a different group percentage without contradicting the primary result.

What does the risk difference mean?

A risk difference expresses the contrast between two group proportions on the absolute probability scale. A value of zero corresponds to equal proportions in the groups. Positive and negative values indicate different directions depending on which group is subtracted from which. The recalculated risk difference in this analysis is 0.038; its 95% confidence interval ranges from -0.077 to 0.152. Because the interval includes zero, the recalculated result is compatible with no difference as well as with differences in either direction. This is an unadjusted calculation from the posted summary statistics, not an adjustment for participant characteristics or other covariates.

The posted results also contain relative measures, including risk ratios and odds ratios. These express contrasts on scales different from the risk-difference scale. A risk ratio compares the proportions directly, while an odds ratio compares the odds of the outcome. Relative and absolute measures answer related but not identical questions; they can convey different impressions when the underlying event frequency is not high. These measures are estimates, and their uncertainty should be considered alongside their point estimates. They do not remove the limitations of the underlying data or analysis.

How should a confidence interval be read?

A confidence interval describes the statistical uncertainty around an estimate under the method used to calculate it. In repeated use of the same method under its assumptions, intervals constructed at the stated confidence level would contain the underlying value at that rate. For an individual trial, the interval is best read as a range of values reasonably compatible with the observed data and method, rather than as a guarantee that the true value lies within it. A wide interval signals limited precision; an interval that includes the no-difference value indicates that the data do not rule out no difference at the stated confidence level.

What does the p-value assess?

A p-value measures how unusual data at least as incompatible with the null hypothesis would be if that hypothesis and the analysis assumptions were true. It does not measure the probability that the null hypothesis is true, nor does it quantify the probability that the result will replicate. The registry reports p = 0.519 for the primary comparison. Interpreted alongside the estimate and interval, this does not provide strong statistical evidence against no difference under the reported test. It is not proof of no effect, equivalence, or lack of clinical importance.

The chi-squared test is a general method for comparing proportions across groups. It assesses whether the observed distribution of the binary outcome differs from what would be expected under no association between group and outcome. Its use does not account automatically for covariate adjustment, repeated measurements, or multiple testing. The registry identifies the method as chi-squared and the parameter as difference in response rates; whether any additional analytic details were used is not reported in the registry record.

Randomization supports a fair comparison by assigning participants to groups without choosing treatment according to their prognosis, on average. Double-blinding and placebo control can also reduce some forms of differential behavior or assessment, but the record does not report detailed masking procedures. Randomization does not ensure that every source of bias or uncertainty is eliminated. Interpretation still depends on outcome ascertainment, adherence, missing data, and the analysis population.

The registry defines the primary ITT population as all randomized participants. An ITT approach generally preserves randomized group assignment for analysis, which supports interpretation of the randomized comparison. However, the registry does not describe how participants with missing pathology assessments were handled, whether all randomized participants contributed to each endpoint estimate, or what sensitivity analyses were undertaken. Those details are not reported in the registry record, so the potential influence of missing outcome data cannot be assessed from the stated definition alone.

Finally, statistical significance and clinical importance are separate considerations. A p-value reflects compatibility with a statistical null under specified assumptions; it does not identify whether a difference matters to patients or clinicians. Clinical interpretation would also require context about benefits, harms, other outcomes, and the intended treatment decision. The primary endpoint and its uncertainty are evidence about one defined response outcome, not a complete assessment of treatment value.

11. Confidence Intervals and Precision

The primary group estimates are 17.1% for ipatasertib plus paclitaxel and 13.3% for placebo plus paclitaxel. Their reported 95% confidence intervals are 9.82 to 27.25 and 6.58 to 22.86, respectively. These intervals show uncertainty around each group’s response percentage; they are not intervals for the difference between groups. The registry’s comparison interval for the difference in response rates is -8.99 to 16.54. The unadjusted recalculation gives a risk-difference interval from -0.077 to 0.152.

For the comparison, the interval extends below and above the no-difference value. That means the observed data do not precisely locate the between-group effect in one direction. The positive point estimate is only one part of the result; uncertainty around it is substantial relative to the estimate. The data remain compatible with no difference and with differences in either direction. A non-significant result does not establish that the groups are equivalent, because equivalence requires a prespecified margin and an analysis designed to evaluate it. Such a margin is not reported in the registry record.

Confidence intervals describe uncertainty under the statistical method and its assumptions. They do not account for every possible source of bias, including outcome measurement issues, missing data, or selective reporting. The registry’s stated ITT population and endpoint definition help describe what was analyzed, but details about missing pathology assessments are not reported in the registry record. Precision should therefore be read together with the limitations of the analysis information available.

The secondary subgroup estimates are also imprecise. For example, the posted PTEN-low breast-only response estimates have broad intervals, as reflected in their reported limits. Such subgroup estimates are based on smaller analysis groups than the overall primary comparison and should not be interpreted as firm evidence of a subgroup-specific effect. A formal test that treatment effect differs across subgroups is not 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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect1,4231,904
75% of the observed effect2,4653,300
50% of the observed effect5,4007,229
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: participants per arm)
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, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Ipatasertib + Paclitaxel.

The sample-size illustrations are planning calculations based on the observed effect, not the original trial’s design rationale. For these binary outcomes, the figures are participants per arm. The calculations assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect. The original sample-size assumptions and justification are not reported in the registry record.

The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under its assumptions. The 90% power column describes the corresponding number per arm for a 90% chance. These are design-planning quantities for a hypothetical study, not measures of how much power the completed trial had after observing its results.

Rows for planning for 100%, 75%, and 50% of the observed effect use progressively smaller target effects. Smaller effects are harder to distinguish from random variation, so the required number of participants per arm increases as the target effect becomes smaller. The calculations also depend on the assumed event rates and other stated planning conditions; changing those assumptions would change the estimates.

These figures are not observed power. They do not establish that a planned study would produce a significant result, and they should not be read as evidence that the observed trial was underpowered or that a future study should enroll a particular number. They are illustrations of the relationship between a target effect, a desired probability of detection, and the planning sample size, under the stated assumptions.

13. How the Sample Size Is Derived

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

Formula

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

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

Worked calculation for this trial

  1. Control proportion p0 = 0.133; treatment proportion p1 = 0.171; average p̄ = 0.152.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5080 = 0.9957.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5073 = 0.4270.
  4. n = (0.9957 + 0.4270)2 / (0.0377)2 = 1,422.5, rounded up to 1,423 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.133333333333333                          # control proportion
p1 <- 0.171052631578947                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

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

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(2301988)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 1,423 (80% power), 1,904 (90% power)
 75% of observed effect: n per arm = 2,465 (80% power), 3,300 (90% power)
 50% of observed effect: n per arm = 5,400 (80% power), 7,229 (90% power)
power.prop.test: 1422.5 
Simulated power at n = 1,423 per arm: 0.802 (20000 replicates)

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

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Chi-squaredDifference in Response Rates 3.77-8.99 to 16.540.519

The registry’s reported primary analysis uses a chi-squared method and gives a difference in response rates of 3.77, a 95% confidence interval from -8.99 to 16.54, and p = 0.519. The unadjusted recalculation from the posted summary statistics gives a risk difference of 0.038, a 95% confidence interval from -0.077 to 0.152, and p = 0.519. These are not identical presentations: the sponsor’s analysis reports the difference on a percentage-point scale, while the recalculation reports the risk difference as a proportion. The interval limits also differ.

The central estimates and p-values are closely aligned, but the recalculation remains a simple unadjusted analysis of posted group summaries. It cannot reproduce analysis details that are not reported in the registry record. The registry’s own reported analysis is the primary record of the sponsor’s inferential result; the recalculation is a supplementary check, not a replacement. The registry indicates no discrepancy flag for the primary comparison, and no reason to treat the recalculation as a correction to the sponsor’s result is stated.

Both analyses support a cautious reading: the estimated contrast is uncertain, and the reported p-value does not provide strong statistical evidence against no difference under the stated test. Neither the sponsor analysis nor the recalculation demonstrates equivalence or rules out potentially meaningful effects. The confidence interval and trial context remain essential to interpretation.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes, subgroups, or statistical comparisons are examined. Even if each test is conducted at a conventional significance threshold, the chance of at least one apparently unusual result can increase as the number of tests grows. This is why a primary endpoint is important: it identifies the principal confirmatory question, while secondary outcomes can be interpreted as supporting, complementary, or exploratory evidence depending on the analysis plan.

The registry lists multiple secondary outcomes, including response measures with different definitions and analyses in selected populations. A multiplicity adjustment, hierarchical testing strategy, or other prespecified method for controlling the overall error rate is not reported in the registry record. The absence of that information does not prove that no such strategy was used; it means the registry entry does not document it. Accordingly, isolated secondary p-values should not be read as if they were the only test conducted.

The registry defines the primary ITT population as all randomized participants. It does not report how missing primary pathology assessments were handled, whether participants without an evaluable surgery assessment were included in a particular category, or whether sensitivity analyses addressed missing outcomes. These details matter because the percentage estimate depends on who contributes to the numerator and denominator and on the assumptions used for absent outcome data. No imputation procedure or missing-data assumption is reported in the registry record.

The sponsor’s primary analysis is identified as chi-squared, but further details about covariate adjustment, protocol deviations, analysis populations for every secondary endpoint, or robustness checks are not reported in the registry record. The original sample-size justification and interim-analysis plan are also not reported. These omissions limit assessment of whether the analysis followed a prespecified hierarchy and how sensitive the conclusions are to alternative assumptions. They do not alter the posted estimates, but they narrow what can be concluded about their statistical context.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Ipatasertib + Paclitaxel107613.2%
Placebo + Paclitaxel3754.0%
Participants with at least one serious adverse event
Serious adverse events by armIpatasertib + Paclitaxel13.2%Placebo + Paclitaxel4.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Ipatasertib + Paclitaxel1 of 76
Placebo + Paclitaxel0 of 75

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
Ipatasertib + Paclitaxel76 of 76
Placebo + Paclitaxel73 of 75

Most frequent serious adverse event terms

Event termOrgan systemIpatasertib + PaclitaxelPlacebo + Paclitaxel
Device related infectionInfections and infestations2 of 760 of 75
PneumoniaInfections and infestations1 of 761 of 75
PyrexiaGeneral disorders1 of 761 of 75
Atypical pneumoniaInfections and infestations1 of 760 of 75
Chest painGeneral disorders1 of 760 of 75
Complication associated with deviceGeneral disorders1 of 760 of 75
General physical health deteriorationGeneral disorders0 of 761 of 75
Sickle cell anaemia with crisisBlood and lymphatic system disorders1 of 760 of 75
DiarrhoeaGastrointestinal disorders1 of 760 of 75
DehydrationMetabolism and nutrition disorders1 of 760 of 75

Most frequent non-serious adverse event terms

Event termOrgan systemIpatasertib + PaclitaxelPlacebo + Paclitaxel
DiarrhoeaGastrointestinal disorders66 of 7624 of 75
AlopeciaSkin and subcutaneous tissue disorders40 of 7640 of 75
AstheniaGeneral disorders32 of 7629 of 75
NauseaGastrointestinal disorders36 of 7623 of 75
FatigueGeneral disorders23 of 7624 of 75
DysgeusiaNervous system disorders18 of 7617 of 75
RashSkin and subcutaneous tissue disorders19 of 7614 of 75
InsomniaPsychiatric disorders15 of 7615 of 75
HeadacheNervous system disorders14 of 7615 of 75
Neuropathy peripheralNervous system disorders14 of 7614 of 75

Serious events with the highest arm-level rate: device related infection (2.6%), pneumonia (1.3%), pyrexia (1.3%), general physical health deterioration (1.3%), atypical pneumonia (1.3%).

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 reports serious adverse events in 10 participants in the ipatasertib-plus-paclitaxel group, among 76 at risk, and in 3 participants in the placebo-plus-paclitaxel group, among 75 at risk. It reports deaths of 1 in the ipatasertib group and 0 in the placebo group. These are descriptive counts recorded for the study groups; they do not by themselves establish that a treatment caused an event or difference.

The most frequently listed serious-event terms include device related infection at 2.6%, and pneumonia, pyrexia, general physical health deterioration, atypical pneumonia, and chest pain at 1.3% each. These terms describe the registry’s listed serious adverse events; they should not be interpreted as a complete account of all possible harms or as treatment-attributed effects. The record also gives other adverse-event counts of 76 among 76 at risk and 73 among 75 at risk, but the summarized information does not provide event-level detail for those counts.

Safety comparisons require context about event definitions, severity, duration of exposure, attribution, and completeness of follow-up. These details are not reported in the registry record in the information. The counts therefore describe what was recorded, rather than providing a causal or exposure-adjusted comparison.

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

The primary result describes the percentage meeting a defined pathological response criterion in breast and axilla at surgery. The observed estimates were 17.1% with ipatasertib plus paclitaxel and 13.3% with placebo plus paclitaxel. The registry’s comparison has a 95% confidence interval that includes the no-difference value, and p = 0.519. This means the trial result does not provide strong statistical evidence against no difference under the reported analysis. It does not prove that the treatments have the same effect.

The result also does not establish that ipatasertib improves response, that it has no effect, or that it is equivalent to placebo. The estimate is uncertain, and the interval accommodates a range of possible differences. The trial’s endpoint is a pathology finding at surgery; it is not a direct measure of survival, recurrence, quality of life, or long-term outcomes. Those outcomes cannot be inferred from this primary response result.

Both groups received paclitaxel, so the comparison concerns ipatasertib added to paclitaxel versus placebo added to paclitaxel. It does not answer what would happen with ipatasertib alone, without paclitaxel, or under a different treatment schedule. The study population was women with Stage Ia–IIIa triple-negative breast adenocarcinoma as described in the registry summary. Results should not be assumed to apply to other populations or disease settings without supporting evidence.

Clinical importance cannot be decided from a p-value alone. It requires consideration of the size and precision of the effect, the endpoint’s relevance, potential harms, other outcomes, and treatment context. The registry’s serious adverse-event and death counts provide descriptive safety information, but they do not establish causation. The posted record is therefore one source of evidence about a specific randomized comparison and response outcome, not a complete basis for treatment decisions.

18. Why This Trial Matters Statistically

This trial illustrates the distinction between an observed difference and a precise estimate of a treatment effect. The group response percentages are numerically different, but the primary comparison is uncertain: the sponsor-reported confidence interval includes no difference, and the p-value is 0.519. A point estimate should not be read alone. Its uncertainty determines how strongly the observed data distinguish among plausible effects.

It also shows why endpoint definitions matter. The primary outcome requires pCR in both breast and axilla, whereas a listed secondary outcome counts breast-only pCR. Those definitions address related but distinct questions. A result for one cannot substitute for the other, and a response measure at surgery does not stand in for longer-term outcomes.

The randomized, double-blind, placebo-controlled design provides a structured basis for comparing the assigned regimens. At the same time, interpretation depends on details such as missing outcome handling, multiplicity, and the original analysis plan. When these are not documented in the registry record, the limits of the available information should be made explicit rather than filled in by assumption.

Finally, the planning illustrations show how power calculations depend on the effect a future study aims to detect and on stated assumptions. They are not evidence about the probability that this completed study’s result is true or about what a future study will find. Together, these points make the trial useful for teaching careful interpretation: identify the target outcome, distinguish the primary comparison from secondary exploration, and read effect estimates with their uncertainty and documentation limits.

19. Limitations

The registry provides a concise record, not a complete protocol or statistical analysis plan. The original sample-size justification, allocation procedure, masking details, interim-analysis plan, multiplicity strategy, and any equivalence margin are not reported in the registry record. These omissions limit assessment of the design rationale and the extent to which the posted analyses were prespecified.

The record defines the primary population as ITT but does not describe missing pathology assessments or their handling. It does not report whether sensitivity analyses assessed the effect of missing data or whether the primary result was robust to alternative analysis choices. The local pathology assessment is described, but procedures for central review or consistency across sites are not reported in the registry record.

The primary endpoint is a short-term pathological response at surgery. The registry summary does not establish whether differences in this endpoint translate into differences in recurrence, survival, quality of life, or other longer-term outcomes. The available safety summary likewise gives event counts and selected serious-event terms, but not detailed attribution, exposure-adjusted rates, or complete event narratives.

Secondary outcomes cover several definitions and subgroups, while complete result detail is not reported in the registry record for every listed outcome. Without documentation of multiplicity handling and prespecified subgroup hypotheses, subgroup patterns should be treated cautiously. The population and regimen are also specific to this study; the results should not be extended to other settings without evidence.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT02301988 is a completed randomized, double-blind, placebo-controlled, multicenter Phase II study of ipatasertib plus paclitaxel versus placebo plus paclitaxel as neoadjuvant treatment for early-stage triple-negative breast cancer. The registry lists enrollment of 151 and describes treatment for approximately 12 weeks.

The primary endpoint was pCR in breast and axilla at surgery, defined as ypT0/Tis ypN0. The reported response percentages were 17.1% and 13.3%, respectively. The registry analysis reported a difference in response rates of 3.77, with a 95% confidence interval from -8.99 to 16.54 and p = 0.519. The estimate is uncertain, and the registry does not report evidence establishing equivalence or a definitive treatment effect.

The registry also lists secondary response outcomes and descriptive adverse-event counts. Details about multiplicity, missing outcome handling, original sample-size justification, and several other statistical design features are not reported in the registry record.

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