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 PALbociclib CoLlaborative Adjuvant Study (NCT02513394), a randomized phase 3 study. The primary outcome is Invasive Disease Free Survival (iDFS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02513394 |
| Phase | Phase 3 |
| Condition | Breast Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 5796 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Alliance Foundation Trials, LLC. |
| Results posted | Yes |
2. Clinical Question
Population
The primary outcome concerns patients with histologically confirmed hormone receptor-positive, HER2-negative invasive early breast cancer. The registry describes the study as international and multicenter. Further eligibility details are not reported in the registry record.
Intervention
Arm A received palbociclib in addition to standard adjuvant endocrine therapy. The protocol description specifies palbociclib for 2 years and endocrine therapy for at least 5 years.
Comparator
Arm B received standard adjuvant endocrine therapy alone, for at least 5 years. The contrast is therefore the addition of palbociclib to the endocrine-therapy regimen, rather than a comparison of endocrine therapy with no treatment.
Primary question
At 4 years, what proportion of participants was considered invasive disease-free in each arm, and how did the time to an invasive disease-free survival event compare between the randomized groups? The registry defines an event to include specified invasive recurrences, a second primary invasive cancer of non-breast origin, or death from any cause.
The study is a randomized Phase III trial with a parallel-group comparison. Its central question is whether adding palbociclib to standard adjuvant endocrine therapy changes invasive disease-free survival in the stated population. The primary registry result is a four-year percentage, while the sponsor also reports a time-to-event comparison. These summaries address related but not identical aspects of the outcome: the percentage describes the estimated status at a stated time, whereas a time-to-event analysis uses the timing of events across follow-up.
The trial's stated purpose also includes assessment of correlative analyses, including effects in genomically defined tumor subgroups. The registry record does not report subgroup results in the primary outcome information. The population definition, treatment contrast, event definition, and follow-up point provide the context needed to interpret the reported estimates without inferring treatment benefit from a single percentage or test result.
3. Trial Design
The PALbociclib CoLlaborative Adjuvant Study is a randomized, open-label, parallel-group Phase III trial. Its registry enrollment is 5796. The record identifies Alliance Foundation Trials, LLC. as sponsor and gives the study status as active, not recruiting. The recorded start is 2015-08 and primary completion is 2020-11.
Arm A received palbociclib alongside standard adjuvant endocrine therapy. The treatment description specifies palbociclib at 125 mg orally once daily from Day 1 to Day 21, followed by 7 days off treatment in a 28-day cycle, for a total duration of 2 years. Standard endocrine therapy in this arm was planned for at least 5 years. Arm B received standard adjuvant endocrine therapy alone for at least 5 years.
The study is described as prospective, international, and multicenter. Masking is listed as none, so the registry characterizes the trial as open-label. The record does not report details of sequence generation, allocation concealment, site-level procedures, adherence, treatment discontinuation, or protocol deviations. Those details should not be inferred from the randomized designation alone.
The primary outcome is invasive disease-free survival (iDFS), reported as a percentage of participants at 4 years. The registry also gives secondary results for iDFS excluding second primary invasive cancers of non-breast origin, distant recurrence-free survival, and overall survival. A further secondary outcome, locoregional recurrence-free survival, appears in the outcome list, but its result is not included among the posted secondary results. The registry record does not report the original sample-size justification or the trial's complete statistical analysis plan.
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
| Stage | Palbociclib Plus Endocrine Therapy (Arm A) | Endocrine Therapy Alone (Arm B) |
|---|---|---|
| STARTED | 2896 | 2900 |
| COMPLETED | 2884 | 2877 |
| NOT COMPLETED | 12 | 23 |
Reasons for not completing this period:
| Reason | Palbociclib Plus Endocrine Therapy (Arm A) | Endocrine Therapy Alone (Arm B) |
|---|---|---|
| Withdrawal by Subject | 11 | 23 |
| Ineligible | 1 | 0 |
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.
| Characteristic | Unit | Palbociclib Plus Endocrine Therapy (Arm A) | Endocrine Therapy Alone (Arm B) | Total |
|---|---|---|---|---|
| Participants analysed | 2884 | 2877 | 5761 | |
| Age, Continuous | years | 52 (25 to 90) | 52 (22 to 85) | 52 (22 to 90) |
| Sex: Female, Male: Female | Participants | 2867 | 2858 | 5725 |
| Sex: Female, Male: Male | Participants | 17 | 19 | 36 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 138 | 127 | 265 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 2504 | 2532 | 5036 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 242 | 218 | 460 |
| Race/Ethnicity, Customized: Race – Asain | Participants | 138 | 141 | 279 |
| Race/Ethnicity, Customized: Race – Black or African American/African Heritage | Participants | 74 | 75 | 149 |
| Race/Ethnicity, Customized: Race – White | Participants | 2521 | 2498 | 5019 |
| Race/Ethnicity, Customized: Race – Native Hawaiian or other Pacific Islander | Participants | 4 | 8 | 12 |
| Race/Ethnicity, Customized: Race – American Indian or Alaska Native | Participants | 14 | 22 | 36 |
| Race/Ethnicity, Customized: Race – Other | Participants | 37 | 36 | 73 |
| Race/Ethnicity, Customized: Race – Unknown | Participants | 96 | 97 | 193 |
6. Primary Endpoint
The registry lists the primary outcome as Invasive Disease Free Survival (iDFS), measured over 4 years.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is invasive disease-free survival (iDFS) at 4 years. The registry defines iDFS as the time from randomization to the first of the listed events: local or regional invasive ipsilateral recurrence, contralateral invasive breast cancer, distant recurrence, a second primary invasive cancer of non-breast origin, or death from any cause. The posted percentages represent participants considered iDFS at the stated time.
This endpoint combines several clinically relevant events into one time-to-event outcome. In general, a composite endpoint can capture more kinds of unfavorable outcomes than a single-event endpoint, but its interpretation depends on the event definition and on which components occur. The registry lists the components, but the primary result does not provide component-specific counts or estimates. It is therefore not possible from that result alone to identify which event types contributed most to the overall endpoint.
The registry states that medians had not yet been achieved and therefore reports the percentage considered iDFS at 4 years. A fixed-time percentage offers a direct description at that follow-up point, while the sponsor's log-rank analysis uses time to iDFS events. Neither summary should be treated as interchangeable with the other: the percentage does not show the full timing pattern, and a hazard ratio does not directly state the proportion event-free at 4 years.
The endpoint is used to compare the randomized groups on a defined outcome over follow-up. Its meaning is bounded by the registry's event definition, time point, and available analysis details. The record does not give additional information about censoring rules or handling of missing outcome assessments.
7. Results Posted in the Registry
- Endocrine Therapy Alone (Arm B): 84.5% (2431/2877) versus 84.2% (2428/2884) on control; risk difference 0.3 percentage points (95% CI -1.6 to 2.2), risk ratio 1.00 (0.98–1.03); unadjusted two-proportion z-test p = 0.747.
Risk difference: Endocrine Therapy Alone (Arm B)
95% CI: -1.6 to 2.2 percentage points
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Invasive Disease Free Survival (iDFS) Excluding Second Primary Invasive Cancers of Non-breast Origin. | Binary Endpoint | Risk difference | +0.6 pts (-1.2 to 2.4) | 55,248 per arm |
| Distant Recurrence-free Survival (DRFS) | Binary Endpoint | Risk difference | +1.6 pts (-0.1 to 3.3) | 6,934 per arm |
| Overall Survival (OS) | Binary Endpoint | Risk difference | +1.4 pts (0.2 to 2.6) | 4,104 per arm |
Invasive Disease Free Survival (iDFS) Excluding Second Primary Invasive Cancers of Non-breast Origin.
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Endocrine Therapy Alone (Arm B): 86.0% (2474/2877) versus 85.4% (2463/2884) on control; risk difference 0.6 percentage points (95% CI -1.2 to 2.4), risk ratio 1.01 (0.99–1.03); unadjusted two-proportion z-test p = 0.522.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Endocrine Therapy Alone (Arm B) and the control. The interval gives the range of effects that remain compatible with the data.
Distant Recurrence-free Survival (DRFS)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Endocrine Therapy Alone (Arm B): 87.8% (2526/2877) versus 86.2% (2486/2884) on control; risk difference 1.6 percentage points (95% CI -0.1 to 3.3), risk ratio 1.02 (1.00–1.04); unadjusted two-proportion z-test p = 0.071.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Endocrine Therapy Alone (Arm B) and the control. The interval gives the range of effects that remain compatible with the data.
Overall Survival (OS)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Endocrine Therapy Alone (Arm B): 95.2% (2739/2877) versus 93.8% (2705/2884) on control; risk difference 1.4 percentage points (95% CI 0.2 to 2.6), risk ratio 1.02 (1.00–1.03); unadjusted two-proportion z-test p = 0.019.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Endocrine Therapy Alone (Arm B) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry posts secondary results for iDFS excluding second primary invasive cancers of non-breast origin, distant recurrence-free survival, and overall survival. It also lists locoregional recurrence-free survival among the planned secondary outcomes, but a result for that endpoint is not reported in the registry record. The posted secondary estimates do not form a uniformly consistent pattern across outcomes: some comparisons are close to no difference, while others are more separated. They should be read according to each endpoint's own event definition and time-to-event estimate, rather than combined into a single claim.
These outcomes complement the primary iDFS result by examining narrower or different event groupings and an overall survival outcome. The primary endpoint already includes several invasive events and death, while a secondary endpoint can exclude or focus on particular components. Such outcomes can help describe where results may differ, but the registry does not provide component-level results that would explain those patterns. The secondary findings therefore do not establish a mechanism for the primary result or resolve its uncertainty.
The registry presents unadjusted re-calculations and sponsor-reported HR analyses for the posted secondary outcomes. Unadjusted tests do not account for the possibility of chance findings across a set of outcomes. In general, the more hypotheses examined, the more important a prespecified multiplicity strategy becomes for confirmatory interpretation. Whether an adjustment or hierarchy was planned is not reported in the registry record. The secondary p-values should consequently carry less inferential weight than a prespecified primary analysis and should be treated as exploratory evidence unless additional analysis-plan information is available.
The broad message is that the secondary results add context but do not provide a substitute primary endpoint. Their interpretation is limited by the absence of reported multiplicity procedures and by the fact that one listed endpoint has no posted result. They should be considered alongside, not in place of, the primary comparison and its confidence interval.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Invasive Disease Free Survival (iDFS) Excluding Second Primary Invasive Cancers of Non-breast Origin.
- Distant Recurrence-free Survival (DRFS)
- Overall Survival (OS)
- Locoregional Recurrences-free Survival (LRRFS)
9. Statistical Interpretation
At 4 years, the registry reports iDFS of 84.2% in the palbociclib-plus-endocrine-therapy arm and 84.5% in the endocrine-therapy-alone arm. These are descriptive estimates at the stated time point. The posted primary comparison also includes a sponsor-reported time-to-event analysis: hazard ratio (HR) 0.96, 95% confidence interval (CI) 0.81 to 1.14, p = 0.65. The interval includes the value corresponding to no relative difference in hazard, and the reported p-value does not provide strong statistical evidence against that null comparison under the test used. It does not establish that the regimens are equivalent.
A simple unadjusted re-calculation from the posted summary statistics gives a risk difference of 0.003, with a 95% CI from -0.016 to 0.022 and p = 0.747. In that calculation, the difference is expressed as the endocrine-therapy-alone percentage minus the palbociclib-plus-endocrine-therapy percentage. Its interval includes no difference and spans values in either direction. It is a re-calculation of the fixed-time summaries, not a replacement for the sponsor's time-to-event analysis.
Across these primary summaries, the estimates are close and the uncertainty does not support a precise claim about the direction or size of a difference. The time-to-event HR and the fixed-time risk difference use different summaries of the outcome and different methods. They should be read alongside their own confidence intervals rather than treated as duplicate estimates. The sponsor's analysis is the registry's reported analysis; the unadjusted calculation is a supplementary statistical description.
The secondary outcomes provide additional perspectives, but they do not change the definition or priority of the primary endpoint. Their estimates vary, and the registry does not state whether secondary-outcome tests were adjusted for multiplicity. Consequently, individual secondary p-values should be interpreted cautiously and should not be used alone to override the primary result.
The record also reports safety counts by arm. These counts describe recorded adverse-event information and should be distinguished from efficacy outcomes. They do not, by themselves, establish that an event was caused by study treatment or characterize the full clinical context of each event.
Overall, the posted results describe four-year outcome estimates and a sponsor-reported time-to-event comparison, with uncertainty around the comparative estimates. They do not establish a definitive benefit, harm, or equivalence claim. Important details about the analysis population, missing data, censoring, multiplicity, and the trial's original design assumptions are not reported in the registry record.
10. Statistical Methods Explained
The trial's randomized, parallel-group design assigns participants to compare palbociclib added to endocrine therapy with endocrine therapy alone. Randomization is intended, in general, to make treatment groups comparable with respect to measured and unmeasured baseline characteristics on average. That design supports a comparative interpretation, but it does not eliminate uncertainty or substitute for information about the analysis population and follow-up. The registry does not report those analysis details in full.
What does the fixed-time percentage describe?
The primary outcome is reported as a percentage of participants considered iDFS at 4 years. This is a fixed-time summary: it communicates the estimated outcome status at the specified time rather than a mean duration or a median time. The registry says the medians had not yet been achieved, which is why it reports the percentage at 4 years. In general, a fixed-time percentage is easy to relate to a stated follow-up point, but it does not reveal when events occurred during follow-up or how the estimate was affected by censoring.
The displayed arm percentages are 84.2% and 84.5%. A simple unadjusted re-calculation compares the underlying posted event proportions as a risk difference. The resulting estimate is 0.003, with a 95% CI from -0.016 to 0.022 and p = 0.747. This calculation uses the posted summaries and does not reproduce the sponsor's time-to-event method. A risk difference is an absolute contrast on the proportion scale; its sign depends on the subtraction order, which is endocrine therapy alone minus palbociclib plus endocrine therapy for this comparison.
Why use a time-to-event analysis?
The registry describes direct comparison of the arms using time to iDFS events and Kaplan-Meier log-rank analysis. In general, time-to-event methods use information about when an event occurs and can account for participants whose follow-up ends before an event is observed, subject to assumptions and the analysis rules. The Kaplan-Meier method estimates the event-free pattern over time; the log-rank test compares the observed event patterns between groups. The registry's posted primary sponsor analysis reports an HR of 0.96, a 95% CI from 0.81 to 1.14, and p = 0.65.
A hazard ratio summarizes the relative event rate over follow-up under the model or comparison used. It is not a risk difference, a ratio of the four-year percentages, or a direct estimate of the probability of remaining event-free. General interpretation of a hazard ratio also relies on assumptions about how the relative hazards behave over time; whether those assumptions were checked is not reported in the registry record. A CI expresses uncertainty in the estimate under the analysis, rather than the range containing most individual participant outcomes.
What is the role of the re-calculation?
The re-calculated risk difference and its p-value are simple unadjusted calculations from posted summary statistics. They offer a transparent comparison of the fixed-time percentages but do not reproduce the sponsor's event-time analysis. The two approaches can differ because one summarizes status at a time point and the other analyzes event timing. The registry record does not describe a formal reconciliation between them. The discrepancy indicator is false, so the posted sponsor analysis is not flagged as discrepant; where a discrepancy is not flagged, the sponsor's reported analysis remains the principal reported inferential result.
For general statistical interpretation, a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be under the test's assumptions. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. A non-small p-value is not proof of no effect; the estimate and its CI are also needed to understand what magnitudes remain compatible with the data.
How should secondary outcomes be treated?
The registry posts four secondary results. Their definitions and time point are outcome-specific, and the sponsor's reported analyses use HRs. The registry also presents re-calculated fixed-time risk differences and unadjusted p-values for posted binary summaries. These are additional analyses rather than independent confirmation of the primary result. In general, testing multiple outcomes can increase the chance that at least one result appears statistically notable by chance. No multiplicity adjustment is reported in the registry record, so the posted unadjusted secondary p-values do not by themselves establish confirmatory evidence.
The registry describes the primary log-rank approach but does not report a full statistical analysis plan, adjustment variables, the exact analysis population, censoring rules, missing-data procedures, interim analyses, or the handling of multiple comparisons. These absent details limit reconstruction of the analysis and should remain distinct from details that are explicitly reported. No assumption about those procedures is warranted from the outcome estimates alone.
11. Confidence Intervals and Precision
The sponsor's primary time-to-event estimate is HR 0.96 with a 95% CI from 0.81 to 1.14. The interval communicates uncertainty around the estimated relative hazard under the reported analysis. It includes the no-relative-difference value, so the data are compatible with a range of relative effects on either side of that value. The interval does not prove that the true effect is zero, nor does it show that all effects within the interval are equally plausible.
The unadjusted fixed-time re-calculation gives a risk difference of 0.003, with a 95% CI from -0.016 to 0.022. This interval also includes no difference and spans both negative and positive values under the stated subtraction order. It illustrates that the fixed-time estimate is imprecise enough to leave uncertainty about direction as well as magnitude. The interval and point estimate belong to this re-calculation, not to the sponsor's log-rank analysis.
In general, a confidence interval is a range generated by a method that, under repeated use and its assumptions, would cover the target parameter at the stated rate. It is not a guarantee that the parameter lies in the particular interval, and it is not a prediction interval for participant outcomes. Interval width reflects statistical precision in relation to the model, data, and analysis choices. It does not account for every possible source of bias or uncertainty.
The registry provides no confidence interval alongside the displayed four-year arm percentages themselves. The comparative re-calculation supplies an interval for a risk difference, while the sponsor supplies an interval for the HR. Keeping those scales separate is important: neither interval can be substituted for the other. The record does not report additional precision measures for the primary percentages or information sufficient to independently assess all modeling assumptions.
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 | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 216,947 | 290,429 |
| 75% of the observed effect | 386,458 | 517,357 |
| 50% of the observed effect | 871,273 | 1,166,387 |
The sample-size figures are planning illustrations based on the observed effect, not the trial's original design calculation. For the posted binary outcomes, the figures are participants per arm, not a total across arms and not a count of events. The record's planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses the stated fraction of the observed effect: 100%, 75%, or 50%.
The 80% power column gives the illustrative participants per arm needed for an analysis to have 80% power under those assumptions and the selected effect size. The 90% power column gives the corresponding planning figure for 90% power. Power is the probability, under a specified statistical model and assumed effect, of rejecting the null hypothesis when that effect is present. It is not a property of the observed result by itself.
Smaller effects are harder to distinguish from random variation, so planning to detect a smaller fraction of the observed effect requires more participants per arm in these illustrations. The table's values should be read as conditional planning scenarios, not as forecasts of what this trial would have found. The record does not report the original protocol's sample-size assumptions or justification, and these illustrations should not be mistaken for those design decisions.
This is not observed power. Observed power is not a useful substitute for interpreting the estimate and its confidence interval; the planning values instead show how assumed effect size and target power relate to illustrative sample requirements. For time-to-event outcomes, the registry's general note says such planning figures would be total event counts, but the binary outcome figures are participants per arm.
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 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
- Control proportion p0 = 0.842; treatment proportion p1 = 0.845; average p̄ = 0.843.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5139 = 1.0073.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5139 = 0.4325.
- n = (1.0073 + 0.4325)2 / (0.0031)2 = 216,946.2, rounded up to 216,947 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 <- 0.841886269070735 # control proportion
p1 <- 0.844977407021203 # 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(2513394)
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 = 216,947 (80% power), 290,429 (90% power)
75% of observed effect: n per arm = 386,458 (80% power), 517,357 (90% power)
50% of observed effect: n per arm = 871,273 (80% power), 1,166,387 (90% power)
power.prop.test: 216946.2
Simulated power at n = 216,947 per arm: 0.801 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 0.96 | 0.81 to 1.14 | 0.650 |
The sponsor's posted primary analysis is a log-rank time-to-event comparison. It reports HR 0.96, a 95% CI from 0.81 to 1.14, and p = 0.65. The result uses the timing of iDFS events, as described in the registry record. This is the sponsor's own inferential analysis and should be kept distinct from the fixed-time percentage comparison.
The unadjusted re-calculation from the posted summary statistics gives a risk difference of 0.003, a 95% CI from -0.016 to 0.022, and p = 0.747. It compares the four-year proportions rather than reproducing the log-rank test. Because an HR and a risk difference summarize different features of the outcome, numerical agreement between their estimates or p-values is not expected, and one cannot be converted into the other from the posted information alone.
The record does not flag a discrepancy between the sponsor result and the re-calculation. The sponsor's analysis remains the reported primary inferential result; the re-calculation is a supplementary, unadjusted check based on summary data. Neither result should be interpreted without its uncertainty, and the re-calculation does not replace details of the sponsor's analysis or provide an adjusted analysis.
15. Multiplicity, Missing Data and Analysis Populations
The registry record does not report whether the trial used a multiplicity adjustment, a hierarchical testing strategy, or another procedure to control error across the primary and secondary outcomes. This matters because multiple statistical tests create more opportunities for apparently notable findings to arise by chance. The posted secondary p-values are unadjusted re-calculations, and the record does not identify them as multiplicity-controlled. They therefore warrant cautious interpretation rather than confirmatory conclusions.
The registry does not report the precise analysis populations used for the posted efficacy results. Although the study is randomized, it is not appropriate to assume from that fact alone that every analysis followed an intention-to-treat principle, or to infer how participants with deviations or incomplete follow-up were handled. The record also does not report the missing-data procedures, censoring rules, or the number and timing of participants lost from outcome follow-up.
For the primary outcome, the registry says the analysis used time to iDFS events and Kaplan-Meier log-rank analysis, and it reports that medians had not yet been achieved. It does not provide the full analysis plan, details of assumptions about censoring, model diagnostics, or interim analyses. The original trial sample-size justification and design assumptions are also not reported in the registry record. The separate planning illustration is not a substitute for those protocol details.
These omissions do not invalidate the posted estimates, but they limit independent assessment of how the analyses were conducted and how robust they are to alternative choices. They also constrain interpretation of the secondary results and of the relationship between the fixed-time summaries and sponsor time-to-event analyses. Conclusions should remain limited to the analyses and information that the registry actually reports.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Palbociclib Plus Endocrine Therapy (Arm A) | 369 | 2841 | 13.0% |
| Endocrine Therapy Alone (Arm B) | 229 | 2902 | 7.9% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Palbociclib Plus Endocrine Therapy (Arm A) | 99 of 2841 |
| Endocrine Therapy Alone (Arm B) | 76 of 2902 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Palbociclib Plus Endocrine Therapy (Arm A) | 2824 of 2841 |
| Endocrine Therapy Alone (Arm B) | 2600 of 2902 |
Most frequent serious adverse event terms
| Event term | Organ system | Palbociclib Plus Endocrine Therapy (Arm A) | Endocrine Therapy Alone (Arm B) |
|---|---|---|---|
| Cellulitis | Infections and infestations | 24 of 2841 | 9 of 2902 |
| Breast cellulitis | Infections and infestations | 16 of 2841 | 10 of 2902 |
| Mastitis | Infections and infestations | 13 of 2841 | 10 of 2902 |
| Pneumonia | Infections and infestations | 16 of 2841 | 7 of 2902 |
| Influenza | Infections and infestations | 16 of 2841 | 2 of 2902 |
| Pulmonary embolism | Respiratory, thoracic and mediastinal disorders | 13 of 2841 | 5 of 2902 |
| Wound dehiscence | Injury, poisoning and procedural complications | 9 of 2841 | 5 of 2902 |
| Febrile neutropenia | Blood and lymphatic system disorders | 13 of 2841 | 0 of 2902 |
| Sepsis | Infections and infestations | 8 of 2841 | 3 of 2902 |
| Urinary tract infection | Infections and infestations | 8 of 2841 | 3 of 2902 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Palbociclib Plus Endocrine Therapy (Arm A) | Endocrine Therapy Alone (Arm B) |
|---|---|---|---|
| Arthralgia | Musculoskeletal and connective tissue disorders | 1087 of 2841 | 1305 of 2902 |
| Fatigue | General disorders | 1163 of 2841 | 560 of 2902 |
| Hot flush | Vascular disorders | 702 of 2841 | 849 of 2902 |
| Neutrophil count decreased | Investigations | 1344 of 2841 | 67 of 2902 |
| White blood cell count decreased | Investigations | 1187 of 2841 | 155 of 2902 |
| Neutropenia | Blood and lymphatic system disorders | 1125 of 2841 | 76 of 2902 |
| Nausea | Gastrointestinal disorders | 552 of 2841 | 241 of 2902 |
| Headache | Nervous system disorders | 445 of 2841 | 338 of 2902 |
| Anaemia | Blood and lymphatic system disorders | 634 of 2841 | 147 of 2902 |
| Insomnia | Psychiatric disorders | 383 of 2841 | 357 of 2902 |
Serious events with the highest arm-level rate: cellulitis (0.8%), breast cellulitis (0.6%), influenza (0.6%), pneumonia (0.6%), febrile neutropenia (0.5%).
The registry records serious adverse events for participants listed as at risk in each arm. The serious-event counts are 369 for the palbociclib-plus-endocrine-therapy arm and 229 for the endocrine-therapy-alone arm; the corresponding at-risk counts are 2841 and 2902. These are registry safety counts, not comparative efficacy outcomes. The posted information does not provide a causal assessment for each event or an adjusted comparison of safety risk.
The registry also lists other adverse-event counts of 2824 and 2600, with at-risk counts of 2841 and 2902, respectively. Deaths are recorded as 99 and 76. These fields should not be added together or treated as interchangeable categories: the registry presents them separately, and the record does not explain their overlap or provide additional contextual analyses. The counts alone do not establish that treatment caused an event.
The serious-event terms listed include cellulitis (0.8%), breast cellulitis (0.6%), influenza (0.6%), pneumonia (0.6%), febrile neutropenia (0.5%), and mastitis (0.5%). These are the reported leading terms, not a complete description of all safety events. The registry record does not provide further details about severity grading, duration, management, or participant-level event patterns. Interpretation should therefore remain descriptive and confined to the recorded counts and terms.
17. What the Result Does, and Does Not, Mean
The results describe the four-year iDFS percentages and a sponsor-reported comparison of time to iDFS events in a randomized trial of palbociclib added to standard adjuvant endocrine therapy versus endocrine therapy alone. The primary percentages are close, and the sponsor's HR confidence interval includes the no-relative-difference value. The unadjusted risk-difference interval also includes no difference and spans both directions. Together, these findings indicate uncertainty in the comparative effect, not proof that the regimens are identical.
The results do not establish equivalence or non-inferiority. Such conclusions require a defined margin and a design and analysis intended to test that question; those details are not reported in the registry record. A non-significant p-value does not show that an effect is absent, just as a point estimate by itself does not establish a clinically important effect. Confidence intervals help show which effect sizes remain compatible with each analysis, subject to its assumptions.
The secondary outcomes add descriptive information but are not a basis for selectively claiming an overall conclusion, particularly because multiplicity procedures are not reported. Safety counts likewise describe recorded events without proving causation or supplying a complete risk comparison. The registry outcome data do not provide the detailed analyses needed to assess every component, missing observation, or subgroup.
These statistics are not individual predictions and do not determine what treatment is appropriate for any person. They do not replace clinical judgment or the full trial report. Their meaning is limited to the registered population, treatment strategies, event definitions, follow-up point, and analyses recorded. Further details about missing data, analysis populations, multiplicity, and the original design assumptions are not reported in the registry record.
18. Why This Trial Matters Statistically
This trial raises a central statistical challenge in adjuvant research: evaluating a treatment added to an existing standard regimen when the outcome is time to a set of clinically relevant events. Randomization provides a structured comparison, while the open-label design and the endpoint definition are important features of the context in which results are interpreted. The primary outcome combines multiple event types, so a single overall estimate may not describe the pattern for every component.
The registry reports both a fixed-time iDFS percentage and a sponsor time-to-event analysis. Reading these together illustrates why the choice of statistical summary matters. A percentage at a specified follow-up point is directly interpretable at that time, whereas a time-to-event analysis uses event timing and follow-up. The summaries answer related questions but operate on different scales and should not be merged into one estimate.
The reported confidence intervals also show why a point estimate alone is insufficient. Estimates close to no difference can still leave uncertainty about the size and direction of an effect. Conversely, a secondary result with a more separated estimate should not be treated as decisive without considering its uncertainty, outcome definition, and the unreported multiplicity strategy.
Finally, the registry's planning illustration distinguishes hypothetical sample-size requirements from the trial's original design. Keeping that distinction clear prevents retrospective calculations from being mistaken for the assumptions that guided enrollment. The record offers useful outcome and safety summaries, while important elements of the full statistical plan are not reported. This makes careful separation of reported analyses, re-calculations, and unanswered questions essential.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The registry provides a concise record rather than a complete statistical report. The primary result includes four-year percentages and a sponsor-reported HR analysis, but details needed to reproduce the full time-to-event analysis are not reported. These include the analysis population, censoring rules, missing-data handling, and checks of model assumptions. The registry also does not report the original sample-size justification, interim analyses, or a complete statistical analysis plan.
The primary endpoint is composite, combining recurrence, second primary invasive cancer of non-breast origin, and death. Component-specific primary estimates are not reported in the result information, so the overall result cannot identify which event types drive the summary. The registry lists locoregional recurrence-free survival as a secondary outcome but does not report its result among the posted secondary results.
The fixed-time re-calculation is unadjusted and uses posted summary statistics. It does not reproduce the sponsor's Kaplan-Meier log-rank analysis or account for unreported analysis choices. Secondary re-calculations are also unadjusted, and the registry does not report multiplicity procedures. Accordingly, secondary p-values should not be treated as confirmatory findings.
The study is open-label, and the registry does not describe procedures that might address possible effects of knowledge of treatment assignment on outcome assessment or reporting. Further eligibility details, adherence information, treatment discontinuation, and protocol deviations are also not reported in the record. Safety information is presented as counts and selected terms, without enough context to establish causation or fully compare event profiles. These limitations constrain interpretation but do not justify assuming that unreported procedures were absent or present.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: PALbociclib CoLlaborative Adjuvant Study — NCT02513394.
- Registry record last updated 2026-06-15; status last verified 2026-06.
- Results first posted 2022-04-13.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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23. Record Summary
The PALbociclib CoLlaborative Adjuvant Study is a randomized, open-label, parallel-group Phase III trial in HR-positive, HER2-negative early breast cancer. It compares palbociclib added to standard adjuvant endocrine therapy with endocrine therapy alone. Registry enrollment is 5796; the recorded status is active, not recruiting.
The primary endpoint is iDFS at 4 years. The registry reports 84.2% for palbociclib plus endocrine therapy and 84.5% for endocrine therapy alone. The sponsor's time-to-event analysis reports HR 0.96, 95% CI 0.81 to 1.14, and p = 0.65. A simple unadjusted re-calculation gives risk difference 0.003, 95% CI -0.016 to 0.022, and p = 0.747. Secondary outcomes and safety counts provide additional descriptive information, with interpretation limited by unreported analysis details.