Prone Partial Breast Irradiation (PBI): a Prospective Randomized Trial: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Prone Partial Breast Irradiation (PBI): a Prospective Randomized Trial (NCT02276885), a randomized na study. The primary outcome is Percentage of Participants With Grade 2 or 3 Fibrosis.

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group trial comparing two schedules of prone partial breast irradiation. The 6 Gy group was scheduled to receive treatment on five consecutive days. The 8 Gy group was scheduled to receive three treatments over five days, every other day. The record lists masking as none, so the study is described as unmasked. It lists the phase as not applicable.

The registry records enrollment of 284 participants. The primary outcome is the percentage of participants with grade 2 or 3 fibrosis, assessed at 60 months. The arm-level primary outcome results are reported for 137 participants in the 6 Gy group and 138 in the 8 Gy group. The registry does not explain the difference between the recorded enrollment and these outcome denominators, or specify the analysis population used for this result.

The record lists six secondary outcome entries concerning isolated local or regional recurrences and concomitant local or regional and distant recurrences. It reports seven outcome measures overall, but no analyses are posted. The recurrence outcomes therefore cannot be interpreted from the results presented in the registry record.

The study is listed as active, not recruiting. Its recorded start date is 2014-10-28, and its primary completion date is 2023-12-07. The registry record does not report the planned statistical analysis, the original sample-size justification, interim analyses, or how the primary endpoint was to be analyzed. The planning figures discussed separately are illustrations based on the observed effect and should not be mistaken for the trial's original design assumptions.

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

Reasons for not completing this period:

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: Baseline data was collected and analyzed for all participants.

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With Grade 2 or 3 Fibrosis, measured over 60 months.

The primary endpoint is the percentage of participants with grade 2 or 3 fibrosis at 60 months. It describes the proportion of participants in each group who met the specified fibrosis grade threshold by that assessment time. The posted values are 18.3% for the 6 Gy schedule and 12.3% for the 8 Gy schedule.

A graded endpoint focuses on events meeting a stated severity threshold rather than combining every possible change into a single measure. Reporting the percentage makes the outcome interpretable as a proportion of participants assessed in each group. The timeframe matters: this result concerns the 60-month assessment, not an unspecified point during follow-up.

Fibrosis is the primary endpoint named in the registry record, but the record does not define the grading procedure, describe who assessed it, or explain how missing 60-month assessments were handled. Those details are not reported in the registry record. The endpoint also does not encompass all dimensions of safety or effectiveness mentioned in the study description. In particular, recurrence is listed among the secondary outcomes, but the registry has no posted analyses for those outcomes. The fibrosis percentages should therefore be read as a specific outcome result, not as a complete account of every trial question.

7. Results Posted in the Registry

• PBI Radiotherapy 8 Gy: 12.3% (17/138) versus 18.2% (25/137) on control; risk difference -5.9 percentage points (95% CI -14.4 to 2.5), risk ratio 0.68 (0.38–1.19); unadjusted two-proportion z-test p = 0.172.

8. Statistical Interpretation

9. Statistical Methods Explained

What does randomization contribute?

Random allocation is intended to create groups that are comparable on average at the start of a trial, including with respect to measured and unmeasured characteristics. It supports a causal comparison when the allocation process is implemented as planned and outcome data are analyzed appropriately. The registry identifies the study as randomized, but does not describe the sequence-generation method, allocation concealment, or other implementation details. Those details are not reported in the registry record.

The study is listed as parallel-group: participants were assigned to one schedule or the other, rather than crossing between schedules. Masking is listed as none. This means the registry does not describe masked assessment or treatment, but it does not establish exactly which staff or participants knew assignment or whether outcome assessors were independent. Those specifics are not reported in the registry record.

What does the risk difference describe?

The risk difference compares the event proportions in the two groups by subtracting one group's proportion from the other's, using the stated comparison direction. A value of zero corresponds to equal proportions. Values on opposite sides of zero represent differences in opposite directions. The posted estimate is negative for the 8 Gy group compared with the 6 Gy control group, consistent with the lower observed percentage in the 8 Gy group. Its confidence interval crosses zero, so the data remain compatible with no difference under this measure.

General: the risk difference is an absolute measure. It helps express how far apart event proportions are on the percentage scale, while relative measures describe a proportional contrast. These measures answer different descriptive questions and should not be treated as interchangeable.

How should the p-value be understood?

The registry reports an unadjusted p-value of 0.172 for the primary comparison. General: a p-value measures how unusual data at least as incompatible with a null hypothesis would be if that null model and the test assumptions held. It is not a measure of effect size, clinical importance, or the probability that the null hypothesis is true. A result above a conventional significance threshold does not prove equivalence or absence of an effect.

The record does not report the original statistical analysis plan or the exact test used for the primary comparison. It also does not report whether the analysis was adjusted for other variables. Those methods are not reported in the registry record, so the p-value should be described as posted rather than attributed to an undocumented model.

What do relative measures add?

The comparison also reports a risk ratio and an odds ratio. A risk ratio compares the event proportions directly as a ratio, whereas an odds ratio compares event odds. General: odds and risks are distinct quantities, particularly when events are not rare, so an odds ratio should not automatically be read as a risk ratio. Relative measures can be useful for describing the direction and scale of a contrast, but absolute percentages remain important for understanding the observed groups.

The confidence intervals for the reported relative measures include the value representing no relative difference. This agrees with the lack of a clearly separated result in the risk-difference interval, though each measure has its own scale and interpretation. The intervals do not establish equivalence; they show that the estimates are uncertain across values compatible with both directions of association.

Why does analysis population matter?

The registry records overall enrollment of 284, while the primary outcome denominators are 137 and 138. The record does not explain why the denominators differ from overall enrollment, identify whether all randomized participants were analyzed in their assigned groups, or describe handling of missing outcome data. Such information is important because exclusions or unobserved outcomes can affect the interpretation of a randomized comparison. No specific explanation should be inferred from the count difference alone.

General: a complete-case analysis uses participants with observed outcomes, while an intention-to-treat analysis generally aims to retain participants in their randomized groups. These approaches can differ when outcomes are missing or participants do not follow their assigned schedule. The registry does not identify which approach was used for this endpoint.

Why can over-dispersion matter?

General: over-dispersion occurs when observed variability is greater than a statistical model expects. It can make standard errors and confidence intervals too small if the model does not account for that extra variability. The posted primary result is a binary percentage comparison, and the registry does not report a model involving a dispersion parameter or any over-dispersion assessment. This concept is therefore general context, not a claim about an analysis used in this trial.

10. Confidence Intervals and Precision

The confidence interval for the primary risk difference includes zero. That means the posted data are compatible with no difference between the groups, as well as with differences in either direction within the interval. The interval is broad enough that the point estimate should not be read as a precise estimate of the contrast.

General: a confidence interval describes a range of values that are reasonably compatible with the data under the statistical method used. It reflects sampling uncertainty, not every possible source of uncertainty. It does not account automatically for missing outcomes, measurement differences, or departures from the analysis assumptions. The registry record does not provide enough methodological detail to evaluate those issues for this comparison.

The unadjusted p-value is 0.172, and the reported relative-effect intervals also include their respective null values. Taken together, these results do not provide a clear statistical distinction between the schedules on the primary endpoint. They also do not demonstrate that the schedules are equivalent: a conclusion of equivalence or non-inferiority requires a prespecified margin and an appropriate analysis, neither of which is reported in the registry record.

Precision is also affected by the number of observed outcomes and the analysis denominator. The primary results include 25 events among 137 participants in the 6 Gy group and 17 among 138 in the 8 Gy group. The registry does not report how missing assessments were treated or whether the reported denominators represent all participants eligible for the 60-month assessment. The confidence interval should be interpreted as the uncertainty represented by the posted comparison, not as a complete accounting of all design and measurement uncertainty.

11. 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.

The planning entries are illustrations based on the observed effect, not a record of the trial's original design calculation. They use a two-sided significance level of 0.05, equal allocation between groups, and a normal approximation. Each scenario considers an effect equal to 100%, 75%, or 50% of the observed effect. The listed figures are participants per arm for 80% power and participants per arm for 90% power. They are not total enrollment targets.

For example, planning for 100% of the observed effect gives 577 participants per arm for 80% power and 772 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,067 participants per arm for 80% power and 1,428 participants per arm for 90% power. Planning for 50% of the observed effect gives 2,492 participants per arm for 80% power and 3,335 participants per arm for 90% power. Smaller effects need more participants to distinguish them from the null under the stated assumptions. The 90% power target requires more participants per arm than the 80% target for each effect scenario.

General: power is the probability that a study will detect an effect of a specified size under the assumed model and threshold if that effect is truly present. These planning figures are not observed power and should not be interpreted as a retrospective measure of the completed trial. The registry record does not report the original sample-size justification or assumptions used to plan enrollment.

12. 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 z_1−α/2 = 1.960) and the desired power (z_1−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

1. Control proportion p₀ = 0.182; treatment proportion p₁ = 0.123; average p̄ = 0.153.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5089 = 0.9974.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5071 = 0.4268.
4. n = (0.9974 + 0.4268)² / (-0.0593)² = 576.9, rounded up to 577 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 <- 0.182481751824818                          # control proportion
p1 <- 0.123188405797101                          # 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(2276885)
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 = 577 (80% power), 772 (90% power)
 75% of observed effect: n per arm = 1,067 (80% power), 1,428 (90% power)
 50% of observed effect: n per arm = 2,492 (80% power), 3,335 (90% power)
power.prop.test: 576.9 
Simulated power at n = 577 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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists six secondary outcome entries concerning isolated local or regional recurrences and concomitant local or regional and distant recurrences. It records seven outcome measures overall and no posted analyses. There are therefore no secondary outcome estimates or tests to interpret from the registry results.

Multiplicity arises when several outcomes, time points, or comparisons are tested. General: as the number of statistical tests increases, the chance of obtaining at least one apparently notable result can increase unless the analysis plan addresses that issue. The registry record does not report whether multiplicity adjustments were planned for the primary or secondary outcomes, or whether a hierarchy of tests was specified. The posted p-value for the primary comparison is identified as unadjusted; no adjustment strategy is described.

The record also does not report a missing-data method for the primary endpoint, the number of participants with missing 60-month assessments, or sensitivity analyses. Those details are not reported in the registry record. Missing outcome data can affect a percentage comparison if the participants with observed outcomes differ systematically from those without observed outcomes. The available denominators alone do not establish why any participants may be absent from the endpoint analysis.

The registry does not identify the analysis population or state whether participants were analyzed according to randomized assignment. It also does not describe a per-protocol population or another analysis set. These omissions limit assessment of how the posted comparison relates to the randomized design. They do not justify assuming that a particular analysis approach was used.

Finally, the record does not report interim analyses, stopping rules, or a prespecified statistical analysis plan. These items are not reported in the registry record. Without those details, the multiplicity and missing-data procedures cannot be reconstructed, and the posted results should be interpreted as the results recorded rather than as a fully documented analysis strategy.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hip fracture (0.7%).

The serious adverse event figures are reported separately from the primary fibrosis outcome. The 6 Gy group lists 0 serious adverse events among 144 participants at risk, and the 8 Gy group lists 1 among 140 at risk. The record lists 4 deaths in each group. These counts should be read as the posted safety summaries, not combined with the fibrosis percentages.

The registry also lists hip fracture at 0.7% among the top serious adverse event terms. It does not provide further detail in the record about the event's relationship to treatment or its timing. The other-adverse-event entries report 144 participants affected among 144 at risk in the 6 Gy group and 140 among 140 at risk in the 8 Gy group. The record does not provide additional event-level descriptions in the posted summary.

These summaries do not establish comparative safety on their own. The serious-event counts are sparse, and the registry does not report definitions, attribution procedures, duration of safety follow-up, or statistical comparisons for adverse events. Those details are not reported in the registry record.

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

The registry results show that the posted percentage with grade 2 or 3 fibrosis at 60 months was 18.3% in the 6 Gy group and 12.3% in the 8 Gy group. The comparison's risk-difference interval includes zero, and its unadjusted p-value is 0.172. The posted evidence therefore does not establish a clear difference between the schedules for this endpoint, while also not establishing that their effects are identical.

The result is specific to the fibrosis endpoint, its 60-month timeframe, and the participants represented by the reported denominators. The registry does not report enough detail to determine how participants without an observed outcome were handled or precisely how the endpoint was assessed. The result should not be extended to all safety outcomes or to recurrence outcomes. Recurrence measures are listed as secondary outcomes, but no analyses are posted for them.

General: a failure to demonstrate a statistically clear difference is not the same as evidence of equivalence. Equivalence or non-inferiority questions require an explicit margin defining what difference would be acceptable, along with a suitable prespecified analysis. Such a margin and analysis are not reported in the registry record.

The trial description frames the schedules in terms of safety and effectiveness, but the posted primary result alone cannot settle that broader question. The adverse-event summaries are descriptive and do not include a reported comparative analysis. The available results support a careful account of what was observed and how uncertain the comparison is; they do not support a blanket conclusion that either schedule is preferable, safer, or more effective.

16. Why This Trial Matters Statistically

This trial offers a direct randomized comparison of two schedules for prone partial breast irradiation, with differences in the number and spacing of treatments. Statistically, the comparison illustrates why the observed arm percentages should be considered alongside the contrast estimate and its uncertainty. A lower observed percentage in one group is a descriptive finding; it is not, by itself, evidence of a reliable difference.

The primary result is especially instructive because the confidence interval includes the null value and the unadjusted p-value is 0.172. The outcome percentages may look separated, but the comparison remains imprecise. This distinction matters in clinical research: estimation asks what range of differences remains compatible with the data, while a significance test addresses a narrower question about compatibility with a null model.

The registry also highlights the importance of complete reporting. Enrollment is recorded as 284, while the primary outcome denominators are 137 and 138. Without an explanation of the analysis population and missing assessments, readers cannot fully connect enrollment to the analyzed endpoint. Similarly, the trial description includes recurrence outcomes, but their results are not posted. A randomized design is valuable, but interpretation still depends on transparent outcome and analysis reporting.

Finally, illustrative planning scenarios show how the required sample size depends on the effect size one wants to detect and the desired power. They are distinct from the trial's original design assumptions and do not demonstrate the study's observed power. Separating prospective planning from retrospective interpretation helps prevent over-reading an uncertain result.

17. 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 record leaves several trial-specific details unclear. It does not describe eligibility criteria, baseline participant characteristics, the randomization procedure, or allocation concealment. Masking is listed as none, but the record does not identify who knew treatment assignment or whether outcome assessment was standardized or independent. These details are not reported in the registry record.

The primary outcome denominators total less than the recorded enrollment, but the record does not explain the difference. It does not identify the primary analysis population, describe missing 60-month outcome data, or state how missing assessments were handled. Consequently, the posted percentages cannot be assumed to represent every randomized participant.

The record provides no definition of fibrosis grading, no information about who assigned grades, and no account of whether assessment procedures were prespecified. It also does not report the statistical analysis plan, the original sample-size justification, interim analyses, or multiplicity procedures. These missing details limit assessment of how the reported p-value and interval were generated and how the primary endpoint was selected or analyzed.

Only the primary fibrosis outcome has a posted comparison. Although recurrence outcomes are listed, no analyses are posted for them. The adverse-event summary provides counts, but does not report attribution, event timing, or a comparative safety analysis. These limitations constrain interpretation to the reported endpoint and descriptive safety figures; they do not imply that unreported analyses were or were not performed.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Prone Partial Breast Irradiation (PBI): a Prospective Randomized Trial — NCT02276885.
• Registry record last updated 2025-12-30; status last verified 2025-12.
• Results first posted 2024-12-31.
• 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.

21. Record Summary

The registry describes a randomized, unmasked, parallel-group trial comparing prone partial breast irradiation at 6 Gy for five consecutive days with 8 Gy for three treatments over five days, every other day. It records enrollment of 284 participants and lists breast cancer as the condition.

The primary endpoint is the percentage with grade 2 or 3 fibrosis at 60 months. The posted percentages are 18.3% for the 6 Gy group and 12.3% for the 8 Gy group. The unadjusted comparison has a p-value of 0.172, and the risk-difference confidence interval includes zero. The registry lists recurrence outcomes but posts no analyses for them.

The record lists the study as active, not recruiting, with primary completion dated 2023-12-07. Its original statistical plan, analysis population, and missing-data procedures are not reported in the registry record.