← Clinical Trials
Breast Cancer Phase 3 Binary Endpoint NCT01349322

Higher Per Daily Treatment-Dose Radiation Therapy or Standard Per Daily Treatment Radiation Therapy in Treating Patients With Early-Stage Breast Cancer That Was Removed by Surgery: Complete Statistical Analysis

NCT01349322 compares hypofractionated whole-breast irradiation with a concurrent boost against standard fractionation with a sequential boost after surgery for early-stage breast cancer. The primary outcome is five-year in-breast recurrence, with registry-reported time-to-event analysis and posted secondary outcomes also considered.

Trial start: 2011-05-24  ·  Enrollment: 2354  ·  Sponsor: Radiation Therapy Oncology Group
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 Higher Per Daily Treatment-Dose Radiation Therapy or Standard Per Daily Treatment Radiation Therapy in Treating Patients With Early-Stage Breast Cancer That Was Removed by Surgery (NCT01349322), a randomized phase 3 study. The primary outcome is Percentage of Participants With In-breast Recurrence (Local Failure).

2354
Enrollment
Phase 3
2
Arms
In the primary outcome
-0.0 pts
Risk difference
Hypofractionated Whole Breast Irradiatio
-1.2 to 1.1 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01349322
PhasePhase 3
ConditionBreast Cancer
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment2354
Arms in the primary outcome2
Lead sponsorRadiation Therapy Oncology Group
Results postedYes

2. Clinical Question

Population

Patients with early-stage breast cancer that was removed by surgery. The primary endpoint describes the eligible population; further eligibility details are not reported in the registry record.

Intervention

Hypofractionated whole-breast irradiation with a concurrent boost: the accelerated radiation course studied in the trial.

Comparator

Standard-fractionation whole-breast irradiation with a sequential boost.

Primary question

How does the five-year rate of in-breast recurrence compare between the two radiation approaches? The trial's reported primary analysis is a non-inferiority analysis, but the non-inferiority margin and the protocol's decision criterion are not reported in the registry record.

The clinical contrast is between treatment schedules and boost timing, not between radiation and no radiation. In the accelerated approach, the boost is concurrent with hypofractionated whole-breast treatment; in the comparator, the boost follows standard-fractionation whole-breast treatment. The primary endpoint is a local recurrence in the treated breast, including events within or outside the treatment field and invasive or non-invasive recurrence.

The primary result is expressed as a five-year cumulative incidence, with follow-up extending from randomization to last follow-up. Death without in-breast recurrence is treated as a competing event in the endpoint definition. The registry also reports a Cox-model hazard ratio and a non-inferiority analysis. Those time-to-event results address a different statistical summary from a simple comparison of the two five-year percentages.

The question is therefore not answered by the percentages alone. Interpretation also depends on the time-to-event analysis, its uncertainty, and the trial's non-inferiority framework. The margin and the detailed decision rules are not reported in the registry record, so the posted information does not support reconstructing that framework independently.

3. Trial Design

This is a randomized phase III trial with a parallel-group design and no masking. The registry lists enrollment of 2354 participants and identifies the Radiation Therapy Oncology Group as sponsor. The trial concerns breast cancer after surgery and compares two whole-breast radiation strategies with different fractionation and boost schedules.

One arm received standard-fractionation whole-breast irradiation with a sequential boost. The other received hypofractionated whole-breast irradiation with a concurrent boost. Because both the fractionation schedule and the timing of the boost differ, the contrast is between the treatment strategies as a whole. The record does not permit separating the contribution of fractionation from the contribution of boost timing.

The listed start date is 2011-05-24, and primary completion is recorded as 2022-01-25. The status is active, not recruiting. The maximum follow-up at the time of analysis was 10.1 years, while the primary and listed survival outcomes report five-year rates. The registry describes follow-up assessments during radiation treatment, after treatment, and annually; the detailed primary-endpoint schedule is stated in its outcome description.

Randomization supports comparison of assigned strategies, but the registry record does not report details such as the randomization sequence, allocation concealment, stratification factors, adherence, treatment crossovers, or the primary analysis population. Masking is recorded as NONE. This is relevant context for outcomes that might be assessed subjectively, although it does not by itself establish the presence or direction of bias.

The record lists 12 outcome measures, including survival, disease outcomes, adverse events, cosmetic outcomes, and translational research. Nine secondary outcomes are posted. The registry does not report the original sample-size justification or enough detail to reconstruct all aspects of the prespecified 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

StageWhole Breast Irradiation + Sequential BoostHypofractionated Whole Breast Irradiation + Concurrent Boost
STARTED11691185
Eligible population11241138
Adverse event population11001123
Quality of Life Population429449
COMPLETED11241138
NOT COMPLETED4547

Reasons for not completing this period:

ReasonWhole Breast Irradiation + Sequential BoostHypofractionated Whole Breast Irradiation + Concurrent Boost
Protocol Violation4547

Analysis population for the primary outcome, as defined in the registry: Eligible population

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: Eligible population

CharacteristicUnitWhole Breast Irradiation + Sequential BoostHypofractionated Whole Breast Irradiation + Concurrent BoostTotal
Participants analysed112411382262
Age, Continuousyears55 (47 to 64)55 (47 to 64)55 (47 to 64)
Age, Customized: < 50 yearsParticipants403400803
Age, Customized: ≥ 50 yearsParticipants7217381459
Sex: Female, Male: FemaleParticipants112411382262
Sex: Female, Male: MaleParticipants000
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants5772129
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants104610512097
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants211536
Race (NIH/OMB): American Indian or Alaska NativeParticipants8816
Race (NIH/OMB): AsianParticipants6562127
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants325
Race (NIH/OMB): Black or African AmericanParticipants135131266
Race (NIH/OMB): WhiteParticipants8879091796
Race (NIH/OMB): More than one raceParticipants279
Race (NIH/OMB): Unknown or Not ReportedParticipants241943
Zubrod Performance Status: 0Participants8969431839
Zubrod Performance Status: 1Participants222190412
Zubrod Performance Status: 2Participants6511
Resection Margin Status: Negative margins (no tumor at the resected specimen edge)Participants9429421884
Resection Margin Status: Close resection margins (>0mm to ≤2mm / Focally positive resection margin)Participants182196378
Axillary Staging Method: Sentinel node biopsy aloneParticipants8839341817
Axillary Staging Method: Sentinel node biopsy alone or followed by axillary node dissectionParticipants183163346
Axillary Staging Method: Sentinel node biopsy followed by axillary dissection/minimum 6 axillary nodesParticipants131124
Axillary Staging Method: Axillary dissection alone (with a minimum 6 axillary nodes)Participants302252
Axillary Staging Method: None: non-invasive breast cancerParticipants15823
Radiation Therapy Technique (plan at randomization): 3D-CRTParticipants8878881775
Radiation Therapy Technique (plan at randomization): IMRTParticipants237250487
Received Chemotherapy: YesParticipants6786971375
Received Chemotherapy: NoParticipants446441887
Estrogen receptor (ER) Status: NegativeParticipants335350685
Estrogen receptor (ER) Status: PositiveParticipants7897881577
Histologic Grade: 1-2Participants5355451080
Histologic Grade: 3Participants5895931182
Pathologic Stage: Stage 0 (Tis, N0, M0)Participants363470
Pathologic Stage: Stage I (T1/T1mi, N0, M0 or T0/T1/T1mi, N1mi, M0)Participants6837271410
Pathologic Stage: Stage II (T0/T1/T1mi, N1, M0 or T2, N0, M0 or T2, N1, M0 or T3, N0, M0)Participants399376775
Pathologic Stage: Stage III (T0/T1/T1mi/T2, N2, M0 or T3, N1/N2, M0 or T4, N0/N1/N2, M0 or Any T,N3,M0)Participants202
Pathologic Stage: Stage IV (Any T, Any N, M1)Participants415
Oncotype recurrence score > 25: NoParticipants103010142044
Oncotype recurrence score > 25: YesParticipants94124218

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With In-breast Recurrence (Local Failure), measured over From randomization to last follow-up. Evaluated weekly during radiation therapy (RT), last day of RT, 1, 6, and 12 months after RT completion, then annually. Maximum follow-up at time of analysis was 10.1 years. Five-year rates are reported here..

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

The primary endpoint is the percentage of participants with in-breast recurrence, also called local failure. A recurrence can be invasive or non-invasive and can occur within or outside the treatment field in the ipsilateral breast. The endpoint is time from randomization to the first qualifying recurrence. Participants without a recorded recurrence are followed to last known follow-up, and death without recurrence is treated as a competing risk.

This endpoint is relevant to the trial because it measures recurrence in the breast treated by the radiation strategies under comparison. It focuses on local control rather than survival or distant spread, which are reported as separate outcomes. The registry reports five-year cumulative-incidence rates, estimated with the cumulative incidence method. That method is appropriate to the stated competing-risk definition because a death without recurrence prevents a later observation of in-breast recurrence.

The record also says treatment comparisons are based on cause-specific hazards and that distributions of failure times are compared between arms. These analyses use the timing of events, rather than only whether an event was recorded by a fixed point. A five-year percentage and a hazard ratio therefore convey related but not identical information: one describes estimated cumulative incidence at a specified time, while the other summarizes the relative event hazard over follow-up under the model.

The endpoint's assessment schedule and the maximum follow-up are stated in the registry, but the registry record does not report all operational details of endpoint review or adjudication.

7. Results Posted in the Registry

Risk difference: Hypofractionated Whole Breast Irradiation + Concurrent Boost (Arm 2)

-0.0

95% CI: -1.2 to 1.1 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals1.11.51.92.32.73.1Whole Breast Irradiation + Se… (n=1124)Hypofractionated Whole Breast… (n=1138)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Hypofractionated Whole Breast…-1.34-0.82-0.290.240.771.30risk 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 AliveBinary EndpointRisk difference-0.7 pts (-2.4 to 1.1)16,267 per arm
Percentage of Participants Alive Without DiseaseBinary EndpointRisk difference-1.7 pts (-4.3 to 0.8)5,019 per arm
Percentage of Participants Alive Without Distant DiseaseBinary EndpointRisk difference-1.3 pts (-3.7 to 1.1)7,741 per arm

Percentage of Participants Alive

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Hypofractionated Whole Breast…-2.65-1.85-1.05-0.250.551.35risk difference (percentage points) vs control (95% CI)

Percentage of Participants Alive Without Disease

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Hypofractionated Whole Breast…-4.67-3.49-2.31-1.140.041.22risk difference (percentage points) vs control (95% CI)

Percentage of Participants Alive Without Distant Disease

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Hypofractionated Whole Breast…-4.06-2.96-1.85-0.750.361.46risk difference (percentage points) vs control (95% CI)

The posted secondary outcomes cover survival, disease-free and distant-disease-free status, adverse events, cosmetic assessments, and translational research. Nine secondary outcomes are posted out of 12 outcome measures listed in the registry. The three posted time-to-event outcomes show a broadly similar pattern in the arm-level estimates, with the comparator estimates numerically higher. Their tests do not establish a difference merely because the point estimates are not identical.

These outcomes add context to the primary local-recurrence result by addressing broader outcomes than recurrence in the treated breast. Survival and disease outcomes reflect different event definitions and can have different precision and clinical interpretations. Cosmetic and adverse-event outcomes address other aspects of treatment, while the listed dose-volume and genetic analyses concern associations or translational questions. They should not be treated as substitutes for the primary endpoint.

The registry reports superiority-type log-rank tests for the posted survival outcomes. Those tests answer whether the observed event-time patterns are inconsistent with a no-difference null under the test assumptions; they do not establish equivalence or non-inferiority. The registry does not report a multiplicity adjustment or a hierarchy of secondary hypotheses. When multiple outcomes are tested, unadjusted results carry less weight because the chance of at least one apparently notable result can rise across a collection of tests.

Secondary findings are therefore best viewed as supportive context, not as a set of separate definitive conclusions. Results not posted among the listed secondary outcomes are not reported in the registry record, and the record does not provide enough information to infer their direction or statistical significance.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted five-year in-breast recurrence estimates are 2.0% for standard-fractionation whole-breast irradiation with sequential boost and 1.9% for hypofractionated whole-breast irradiation with concurrent boost. Their 95% confidence intervals are 1.4% to 2.9% and 1.3% to 2.7%, respectively. These arm-level intervals overlap substantially, but overlap alone is not a formal test of equivalence or non-inferiority.

A simple unadjusted re-calculation from the posted summary statistics gives a risk difference of -< 0.001, with a 95% confidence interval from -0.012 to 0.011 and p = 0.967. This calculation treats the posted percentages as a binary comparison. It is not the same analysis as the registry's time-to-event model and should not replace it. The discrepancy is flagged in the record, so the sponsor's own analysis takes precedence.

The sponsor-reported analysis is a Cox regression non-inferiority analysis. It reports a hazard ratio of 1.32, with a 90% confidence interval from 0.84 to 2.05 and p = 0.039. The registry does not report the non-inferiority margin or the decision rule needed to interpret that p-value against the trial's design criterion. The result should therefore be read as the reported analysis, not as an independently verified non-inferiority conclusion. The confidence interval also indicates considerable uncertainty about the hazard ratio.

The statistical contrast is between two complete treatment strategies. It cannot isolate whether any difference is attributable to hypofractionation, boost timing, or both. The rates describe the posted five-year estimates, while the maximum follow-up at the time of analysis was 10.1 years; they should not be mistaken for estimates at the maximum follow-up time.

The registry posts three secondary time-to-event outcomes: alive, alive without disease, and alive without distant disease. Across these outcomes, the arm-level estimates show a generally similar pattern, with the comparator estimates numerically higher. These outcomes provide broader context but do not change the definition or analysis of the primary endpoint. Their reported superiority tests are not evidence that one strategy is superior simply because an estimate is numerically higher or lower.

Overall, the posted data show low five-year recurrence estimates in both arms, but the primary interpretation depends on the sponsor's time-to-event analysis and the unreported non-inferiority framework. The registry record does not establish equivalence, and a large p-value from the unadjusted re-calculation is not proof that the strategies have identical effects.

10. Statistical Methods Explained

The primary outcome combines an event definition, a follow-up period, and a statistical method. Keeping these components distinct helps prevent the five-year rates, the re-calculated risk difference, and the sponsor's hazard-ratio analysis from being treated as interchangeable.

What does the cumulative incidence estimate describe?

The cumulative incidence method estimates the probability of experiencing the event of interest by a specified time while accounting for a competing event. For this endpoint, the event of interest is in-breast recurrence and death without recurrence is the competing event. A competing event matters because a participant who dies without recurrence can no longer experience a later recurrence. Treating that death as though it were ordinary loss to follow-up could misrepresent the event probability.

The registry reports five-year cumulative-incidence estimates for the two arms. These are time-specific estimates, not simple counts divided by the number assigned to each arm. Follow-up can vary, and the method uses the recorded event and follow-up times. The arm-level 95% confidence intervals express uncertainty in each estimated rate.

Why are cause-specific hazards also reported?

A cause-specific hazard describes the instantaneous rate of the event of interest among participants who remain at risk, under the time-to-event model. The registry says comparisons are based on cause-specific hazards and reports a Cox regression hazard ratio. A hazard ratio summarizes the modeled relative event hazard between arms over follow-up. It is not a ratio of the five-year percentages, nor does it directly give an absolute difference in recurrence probability.

The Cox model uses event timing and the risk sets formed during follow-up. Its interpretation relies on the model's assumptions, including the proportional-hazards structure for a single summary hazard ratio. The registry record does not report diagnostics or further details that would allow those assumptions to be assessed from the posted summary alone. The stated protocol comparison of failure-time distributions is also not fully described in the registry record beyond the reported analysis.

What does the unadjusted re-calculation test?

The re-calculated risk difference and p-value use posted summary statistics for a simple, unadjusted comparison of the two arm-level percentages. They do not account for event timing in the same way as the cumulative-incidence and Cox analyses. They are useful as a transparent check on the posted percentages, but they are not a substitute for the sponsor's prespecified time-to-event analysis. Because the record flags a discrepancy, the sponsor's own analysis takes precedence.

A p-value measures how incompatible the observed data are with a specified null model, subject to the test's assumptions. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. A non-significant result in a conventional superiority test would not establish equivalence. Non-inferiority requires a prespecified margin and a decision rule; those details are not reported in the registry record.

Why do confidence intervals matter?

A confidence interval gives a range of effect estimates compatible with the data and analysis procedure at the stated confidence level. A narrow interval indicates greater precision than a wide interval, while the location of the interval indicates which effect values remain plausible. The 95% intervals around arm-level rates and the 90% interval around the sponsor-reported hazard ratio describe uncertainty for different quantities and use different confidence levels.

The sponsor's hazard-ratio interval includes values on either side of 1.00, so the posted interval allows a range of relative effects. It should not be recast as proof of no effect. For a non-inferiority question, the interval's relation to the prespecified margin is central, but that margin is not reported in the registry record. Without it, readers cannot independently apply the trial's non-inferiority criterion.

How should the secondary tests be read?

The registry reports log-rank tests for the posted survival outcomes. A log-rank test compares event-time distributions between groups under its assumptions; it does not by itself give the size of an effect. The registry does not report a single multiplicity-adjusted interpretation for the family of secondary outcomes. When many outcomes are examined, unadjusted p-values should be treated as exploratory or supportive rather than as a set of independent confirmatory findings.

General statistical principles explain why these methods differ; the registry record does not report every model specification, diagnostic, missing-data procedure, or analysis-population definition needed to reproduce the analyses in full.

11. Confidence Intervals and Precision

The arm-level recurrence estimates are 2.0% and 1.9%, with 95% confidence intervals of 1.4% to 2.9% and 1.3% to 2.7%. Each interval shows uncertainty in its own arm's estimated five-year cumulative incidence. The intervals overlap, but this does not itself quantify the uncertainty in the between-arm contrast or demonstrate equivalence.

The unadjusted re-calculated risk difference is -< 0.001, with a 95% confidence interval from -0.012 to 0.011. The interval spans values on either side of zero, meaning the simple comparison is compatible with more than one direction of difference. Its width is important: the point estimate is close to zero, but the interval does not restrict the effect to a single precise value. This calculation is distinct from the sponsor's time-to-event analysis.

The sponsor-reported hazard ratio is 1.32, and its 90% confidence interval runs from 0.84 to 2.05. This interval is broad relative to the point estimate and includes a range of possible relative hazards. Since it is a 90% interval rather than a 95% interval, it should not be directly compared with the arm-level 95% intervals as though they represented the same quantity and confidence level. The margin needed to judge non-inferiority is not reported in the registry record.

Confidence intervals describe statistical uncertainty under the relevant analysis; they do not capture every source of uncertainty, such as incomplete reporting or limitations in model assumptions. The registry provides a maximum follow-up of 10.1 years, but the primary result under discussion is the five-year rate. Precision at that time point does not establish what an estimate would be at a later time.

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 effect5,164,1486,913,328
75% of the observed effect9,194,63112,309,001
50% of the observed effect20,719,24527,737,189
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5,000,00010,000,00020,000,00050,000,00040%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: Hypofractionated Whole Breast Irradiation + Concurrent Boost (Arm 2).

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

The 80% power column gives the illustrative number of participants per arm needed for an analysis to have an 80% chance of rejecting its null hypothesis if the assumed effect and other planning conditions hold. The 90% power column gives the corresponding illustration for a 90% chance. These are planning quantities, not guarantees about a future study, and they depend on the effect size and assumptions used in the calculation.

Rows describing planning for 75% or 50% of the observed effect assume a smaller effect than the row using 100% of the observed effect. Smaller effects are harder to distinguish from random variation, so the illustrations require more participants per arm. The figures should be read as hypothetical planning scenarios under stated assumptions, not as a retrospective evaluation of whether this trial had enough participants.

This is not observed power. It is a prospective planning illustration derived from the observed estimate, and it does not describe the probability that the completed trial's result is correct. For any time-to-event illustration explicitly based on a Schoenfeld calculation, the stated unit would instead be total events; that is distinct from the participants-per-arm figures for percentage-based outcomes.

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 = 0.020; treatment proportion p1 = 0.019; average p̄ = 0.019.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.1953 = 0.3828.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.1953 = 0.1644.
  4. n = (0.3828 + 0.1644)2 / (-0.0002)2 = 5,164,147.1, rounded up to 5,164,148 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 <- 0.0195729537366548                          # control proportion
p1 <- 0.0193321616871705                          # 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(1349322)
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 = 5,164,148 (80% power), 6,913,328 (90% power)
 75% of observed effect: n per arm = 9,194,631 (80% power), 12,309,001 (90% power)
 50% of observed effect: n per arm = 20,719,245 (80% power), 27,737,189 (90% power)
power.prop.test: 5164147 
Simulated power at n = 5,164,148 per arm: 0.805 (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
Regression, CoxHazard Ratio (HR) 1.320.84 to 2.050.039
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The registry's sponsor-reported primary analysis is a Cox regression non-inferiority analysis, with hazard ratio 1.32, 90% confidence interval 0.84 to 2.05, and p = 0.039. It uses time-to-event information and is not the same as an unadjusted comparison of the posted five-year percentages.

The simple re-calculation from the percentages gives a risk difference of -< 0.001, 95% confidence interval -0.012 to 0.011, and p = 0.967. The record flags a discrepancy between the sponsor's result and the simple re-calculation. In that situation, the sponsor's own analysis takes precedence; the recalculation is a separate, unadjusted check and should not be used to overturn the reported analysis.

The two analyses differ in both their statistical quantity and their treatment of follow-up. The risk difference compares percentages at a specified time using posted summaries. The Cox analysis compares hazards over time and is reported as the trial's non-inferiority analysis. The registry does not report the non-inferiority margin or the criterion used to make a formal conclusion, so the reported p-value and interval cannot be independently translated into a declaration that non-inferiority was established.

For the sponsor result, readers should retain the reported model, confidence level, and non-inferiority framing. The re-calculation can help clarify how the arm-level percentages compare, but it answers a narrower question and does not reproduce the sponsor's analysis.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 12 outcome measures and reports nine secondary outcomes. It does not report how the trial handled multiplicity across the primary and secondary outcomes, whether outcomes were ordered in a formal testing hierarchy, or whether p-values were adjusted. Without that information, separate unadjusted secondary p-values should not be treated as if each were an isolated confirmatory test. Multiple testing can increase the chance of a nominally unusual result across a family of analyses.

The primary analysis is identified as non-inferiority, but the non-inferiority margin, the rationale for that margin, and the exact decision rule are not reported in the registry record. Those details are necessary to assess whether the reported hazard-ratio interval meets the trial's non-inferiority criterion. The original sample-size assumptions and design justification are also not reported; the planning illustrations based on observed effects are not a substitute for those original assumptions.

The record describes censoring at last known follow-up and death without in-breast recurrence as a competing event for the primary endpoint. It does not report detailed procedures for other missing outcome data, loss to follow-up by arm, or sensitivity analyses. The registry also does not identify the analysis population used for each result, such as whether analyses followed intention-to-treat principles or a different population definition. These omissions limit independent assessment of the handling of missingness and protocol deviations.

Randomization and parallel allocation are reported, but the record does not provide details of allocation concealment, stratification, adherence, crossovers, or the full statistical analysis plan. No assumption should be made about interim analyses or their boundaries; such details are not reported in the registry record.

These limitations do not establish that the analyses were conducted improperly. They identify information needed to judge the strength and reproducibility of the inferences. The posted results can be described as reported, while conclusions about multiplicity control, missing-data robustness, and the non-inferiority decision framework remain constrained by what the registry records.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Whole Breast Irradiation + Sequential Boost1811001.6%
Hypofractionated Whole Breast Irradiation + Concurrent Boost2011231.8%
Participants with at least one serious adverse event
Serious adverse events by armWhole Breast Irradiation + Se…1.6%Hypofractionated Whole Breast…1.8%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Whole Breast Irradiation + Sequential Boost87 of 1124
Hypofractionated Whole Breast Irradiation + Concurrent Boost86 of 1138

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
Whole Breast Irradiation + Sequential Boost866 of 1100
Hypofractionated Whole Breast Irradiation + Concurrent Boost910 of 1123

Most frequent serious adverse event terms

Event termOrgan systemWhole Breast Irradiation + Sequential BoostHypofractionated Whole Breast Irradiation + Concurrent Boost
Dermatitis radiationInjury, poisoning and procedural complications3 of 11002 of 1123
Localized edemaGeneral disorders and administration site conditions2 of 11001 of 1123
Breast infectionInfections and infestations1 of 11002 of 1123
SeromaInjury, poisoning and procedural complications1 of 11002 of 1123
Breast painReproductive system and breast disorders0 of 11003 of 1123
PneumonitisRespiratory, thoracic and mediastinal disorders1 of 11002 of 1123
Skin hyperpigmentationSkin and subcutaneous tissue disorders1 of 11002 of 1123
LymphedemaVascular disorders1 of 11002 of 1123
FatigueGeneral disorders and administration site conditions0 of 11002 of 1123
PainGeneral disorders and administration site conditions1 of 11001 of 1123

Most frequent non-serious adverse event terms

Event termOrgan systemWhole Breast Irradiation + Sequential BoostHypofractionated Whole Breast Irradiation + Concurrent Boost
Skin hyperpigmentationSkin and subcutaneous tissue disorders464 of 1100458 of 1123
FatigueGeneral disorders and administration site conditions435 of 1100427 of 1123
Dermatitis radiationInjury, poisoning and procedural complications399 of 1100384 of 1123
Breast painReproductive system and breast disorders325 of 1100320 of 1123
Hot flashesVascular disorders204 of 1100190 of 1123
Skin and subcutaneous tissue disorders - Other, specifySkin and subcutaneous tissue disorders191 of 1100172 of 1123
PainGeneral disorders and administration site conditions160 of 1100144 of 1123
ArthralgiaMusculoskeletal and connective tissue disorders116 of 1100124 of 1123
Localized edemaGeneral disorders and administration site conditions123 of 1100116 of 1123
Superficial soft tissue fibrosisMusculoskeletal and connective tissue disorders123 of 1100105 of 1123

Serious events with the highest arm-level rate: dermatitis radiation (0.3%), breast pain (0.3%), localized edema (0.2%), lung infection (0.2%), fatigue (0.2%).

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

For the standard-fractionation arm, the registry reports 18 participants with a serious adverse event among 1100 at risk. For the hypofractionated arm, it reports 20 participants with a serious adverse event among 1123 at risk. These are counts of participants affected, not counts of every event, and the record describes the adverse-event outcome as events definitely, probably, or possibly related to protocol treatment.

The record also reports other adverse-event counts of 866 among 1100 at risk in the standard-fractionation arm and 910 among 1123 at risk in the hypofractionated arm. These should be read separately from the serious adverse-event figures. The registry lists dermatitis radiation and breast pain at 0.3% each among the top serious terms; localized edema, lung infection, fatigue, and breast infection are each listed at 0.2%.

These summaries do not show event timing, duration, recurrence, or severity distributions beyond the recorded categories. The reported deaths are 87 and 86, but the registry summary does not establish that these deaths were adverse events related to protocol treatment. The figures should not be interpreted as proof that one treatment strategy is safer.

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

The results describe two randomized radiation strategies and their posted outcomes; they do not establish that the strategies are identical. The five-year in-breast recurrence estimates are close in the posted summaries, and the unadjusted re-calculation produces a risk-difference interval that includes zero. Neither observation is, by itself, a formal demonstration of equivalence or non-inferiority.

The sponsor reports a Cox regression non-inferiority analysis with hazard ratio 1.32, 90% confidence interval 0.84 to 2.05, and p = 0.039. Because the non-inferiority margin and decision criterion are not reported in the registry record, readers cannot independently determine from that summary whether the protocol's criterion was met. The flagged discrepancy also means the sponsor's own analysis takes precedence over the simple recalculation.

The result applies to the treatment strategies as compared in this trial: hypofractionated whole-breast irradiation with concurrent boost versus standard-fractionation whole-breast irradiation with sequential boost. It does not isolate the separate effects of fractionation and boost timing. The listed population is patients with early-stage breast cancer removed by surgery; the registry does not provide enough detail in this summary to extend the conclusions to other populations or treatment settings.

Five-year estimates should not be mistaken for outcomes at the maximum follow-up of 10.1 years. Nor do the posted summaries establish long-term patterns beyond the reported analyses. Secondary outcomes broaden the context but have their own definitions and statistical limitations, including the absence of reported multiplicity handling.

Statistical results do not determine an individual's care. They summarize outcomes in the trial population under the analyses reported in the registry. The evidence supports describing the observed estimates and their uncertainty; stronger claims about equivalence, non-inferiority, or comparative safety require details that are not reported in the registry record.

18. Why This Trial Matters Statistically

This trial presents several statistical issues common in comparative clinical research. The primary outcome is a time-to-event endpoint with a competing event, so the analysis must account for more than a simple comparison of event percentages. The cumulative incidence estimate addresses the event probability in the presence of competing deaths, while the Cox analysis summarizes relative cause-specific hazards. Understanding which quantity answers which question is essential to interpreting the result.

The trial also illustrates why a close pair of point estimates does not automatically establish that two strategies are equivalent. Non-inferiority requires a margin set in advance, along with a compatible analysis and decision rule. The registry reports a non-inferiority analysis but does not report the margin, leaving an important part of the interpretation unavailable to readers.

The contrast combines two treatment features: fractionation and boost timing. This makes the randomized comparison clinically coherent as a strategy-level contrast, but it limits statistical attribution. The results cannot identify the independent contribution of each feature from the posted comparison alone.

Finally, the difference between the sponsor's time-to-event analysis and a simple re-calculation from the five-year summaries shows why analysis methods matter. The re-calculation is not a replacement for the sponsor analysis, particularly when the record flags a discrepancy. Secondary outcomes and safety summaries also require careful treatment because multiple endpoints, different event definitions, and incomplete reporting can affect how much weight a result deserves.

These features make the record useful for learning how endpoint definition, competing risks, non-inferiority, confidence intervals, and analysis transparency shape interpretation. They also show why statistical conclusions should be tied to the exact estimand and analysis reported, rather than inferred from a point estimate alone.

19. Limitations

The registry reports no non-inferiority margin or formal decision rule for the primary analysis. As a result, the sponsor's non-inferiority conclusion cannot be independently assessed from the posted summary, despite the reported hazard ratio, confidence interval, and p-value. The record also flags a discrepancy between the sponsor analysis and a simple unadjusted re-calculation; the sponsor's own analysis takes precedence, but the available record does not explain the discrepancy in detail.

The randomized comparison changes both fractionation and boost timing. Any observed contrast therefore pertains to the combined strategies, not the isolated effect of either treatment component. The record identifies no masking, which may be relevant for assessment of outcomes such as cosmetic ratings, but the registry summary does not establish whether or how this affected measurement.

Although maximum follow-up at analysis was 10.1 years, the reported primary estimates are five-year rates. The registry summary does not provide arm-specific follow-up distributions, detailed loss-to-follow-up information, or missing-data sensitivity analyses. It also does not report the analysis population, adherence, crossovers, endpoint adjudication procedures, or diagnostic checks for the reported models.

Nine secondary outcomes are posted out of 12 listed outcome measures. The registry does not report multiplicity procedures or a testing hierarchy, which limits the strength of interpretation for secondary p-values. The original sample-size assumptions and justification are not reported; retrospective planning illustrations based on observed effects do not recover that information.

These are limitations of the information available in the registry record, not proof that the trial lacked procedures or analyses. They constrain what can be independently concluded from the posted summary.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

NCT01349322 is a randomized phase III parallel-group trial, with no masking, comparing hypofractionated whole-breast irradiation plus concurrent boost with standard-fractionation whole-breast irradiation plus sequential boost after surgery for early-stage breast cancer. The primary outcome is five-year in-breast recurrence, estimated using the cumulative incidence method with death without recurrence treated as a competing event.

The registry reports arm-level five-year recurrence estimates of 2.0% and 1.9%. The sponsor's primary analysis is a Cox regression non-inferiority analysis, reporting hazard ratio 1.32, 90% confidence interval 0.84 to 2.05, and p = 0.039. The non-inferiority margin is not reported. A discrepancy is flagged, so the sponsor's analysis takes precedence over the unadjusted re-calculation.

The record lists 12 outcome measures and posts nine secondary outcomes. Important details about multiplicity, missing-data procedures, analysis populations, and original sample-size justification are not reported in the registry record.

Clinical Biostats