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 Study of Radium-223 Dichloride in Combination With Exemestane and Everolimus Versus Placebo in Combination With Exemestane and Everolimus in Subjects With Bone Predominant HER2 Negative Hormone Receptor Positive Metastatic Breast Cancer (NCT02258451), a randomized phase 2 study. The primary outcome is Symptomatic Skeletal Event-free Survival (SSE-FS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02258451 |
| Phase | Phase 2 |
| Condition | Breast Neoplasms |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 283 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Bayer |
| Results posted | Yes |
2. Clinical Question
Population
People with HER2-negative, hormone receptor-positive metastatic breast cancer and bone metastases. The primary outcome used the intent-to-treat analysis set, defined in the registry record as all randomized participants.
Intervention
Radium-223 dichloride alongside exemestane and everolimus. The radium-223 arm description specifies up to 6 cycles; its stated dose was 50kBq/kg body weight, with 55 kBq/kg after implementation of the National Institute of Standards and Technology update. Exemestane and everolimus were also given.
Comparator
Saline placebo alongside exemestane and everolimus. The placebo arm description specifies up to 6 cycles of saline injection, with the same named background medicines and supportive care according to local or institutional practice.
Primary question
Did adding radium-223 change the time from randomization to a symptomatic skeletal event or death from any cause, whichever occurred first? The registry reports the comparison as a hazard ratio, with a log-rank analysis.
This was a randomized, double-blind, placebo-controlled study. The trial title describes the population as having bone-predominant disease; the registry condition is breast neoplasms. Its stated objective was to assess the efficacy and safety of radium-223 in this setting when used with exemestane and everolimus.
The primary endpoint is not a measure of tumor shrinkage alone. It combines specified skeletal complications and death into a time-to-event outcome, so the question concerns how long participants remained free of the first event in that definition. The registry reports medians and a hazard ratio for the comparison. These statistics describe the posted trial results; they do not by themselves establish that either treatment is effective or ineffective.
3. Trial Design
The registry describes a randomized, parallel-group, quadruple-masked, phase II trial. Participants were assigned to radium-223 plus exemestane and everolimus or saline placebo plus the same named background medicines. The study status is completed. Enrollment is recorded as 283, and the primary outcome population is the intent-to-treat analysis set, which the registry defines as all randomized participants.
The radium-223 arm description specifies up to 6 cycles and a dose of 50kBq/kg body weight, or 55 kBq/kg after implementation of a National Institute of Standards and Technology update. The placebo arm description specifies up to 6 cycles of saline injection. Both arm descriptions include exemestane at 25-mg once daily and everolimus at 10 mg once daily; the placebo description also mentions supportive care according to local or institutional practice. The radium arm description is incomplete in the registry record, so its remaining administration details are not reported in the registry record.
The recorded study start is 2015-06-04, and primary completion is 2020-01-22. The primary outcome timeframe is up to 55 months. The registry says that after implementation of CSP Amendment 10, data collection was reduced for remaining participants and focused mainly on acute safety, symptomatic skeletal events, and overall survival. It also says that long-term safety was to be collected and assessed in a separate extended safety follow-up study after rollover.
The record distinguishes the primary completion analysis from the later final analysis: it states that efficacy outcomes shown came from the primary completion analysis, and that formal statistical analyses of primary and secondary efficacy outcomes were not performed in the final analysis. The original design assumptions, including any planned sample-size justification or interim-analysis plan, are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: Overall, 389 participants were screened and 283 were assigned to treatment. Of these, 142 in the radium 223 dichloride arm and 141 in the placebo arm.
Overall Study
| Stage | Radium-223 + EXE/EVE | Placebo + EXE/EVE |
|---|---|---|
| STARTED | 142 | 141 |
| COMPLETED | 0 | 0 |
| NOT COMPLETED | 142 | 141 |
Reasons for not completing this period:
| Reason | Radium-223 + EXE/EVE | Placebo + EXE/EVE |
|---|---|---|
| Discontinuation all treatment due to progressive disease - radiological progression | 90 | 101 |
| Discontinuation all treatment due to progressive disease - clinical progression | 7 | 7 |
| Discontinuation all treatment due to adverse event not associated with clinical disease progression | 8 | 1 |
| Discontinuation all treatment due to adverse event associated with clinical disease progression | 8 | 6 |
| Discontinuation all treatment due to death | 4 | 3 |
| Discontinuation all treatment due to withdrawal by participant | 21 | 13 |
| Discontinuation all treatment due to end point reached | 1 | 1 |
| Discontinuation all treatment due to physician decision | 0 | 2 |
| Discontinuation all treatment due to study terminated by sponsor | 0 | 3 |
| Other reason | 1 | 1 |
| Never treated | 2 | 3 |
Analysis population for the primary outcome, as defined in the registry: Intent to treat analysis set: all randomized participants
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: Intent-to-Treat Analysis Set (ITT analysis set): included all randomized participants
| Characteristic | Unit | Radium-223 + EXE/EVE | Placebo + EXE/EVE | Total |
|---|---|---|---|---|
| Participants analysed | 142 | 141 | 283 | |
| Age, Continuous | Years | 59.95 (SD 10.40) | 59.08 (SD 11.64) | 59.52 (SD 11.02) |
| Sex: Female, Male: Female | Participants | 142 | 141 | 283 |
| Sex: Female, Male: Male | Participants | 0 | 0 | 0 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 3 | 5 | 8 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 127 | 125 | 252 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 12 | 11 | 23 |
6. Primary Endpoint
The registry lists the primary outcome as Symptomatic Skeletal Event-free Survival (SSE-FS), measured over Up to 55 months.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | 95% Confidence Interval |
| Unit | Months |
| Endpoint classification | Time-to-Event Analysis |
Symptomatic skeletal event-free survival (SSE-FS) measures the time from randomization until the first occurrence of a specified symptomatic skeletal event or death from any cause, whichever happens first. The registry defines an event as external beam radiotherapy to relieve skeletal symptoms, a new symptomatic pathological bone fracture, spinal cord compression, or a tumor-related orthopedic surgical intervention. The endpoint timeframe is up to 55 months.
This is a time-to-event composite endpoint: it brings several clinically consequential skeletal events together with death and records the time to the first one. A composite can capture more than one type of event in a single outcome, but its interpretation depends on the event definition. The result does not separately describe the time to each skeletal event type, nor does the composite by itself show which component contributed most to the observed pattern.
The registry reports the median SSE-FS for each arm and a hazard ratio from a log-rank analysis. The median describes the event-free time at which the estimated event distribution reaches its midpoint; the hazard ratio compares event rates over follow-up under the assumptions of that analysis. These are different summaries and should not be read as interchangeable measures. The endpoint is used to compare the timing of skeletal complications or death, rather than simply counting events at one fixed time.
The registry notes that after primary analysis completion, efficacy collection was limited and was not designed to support reconsideration of the primary efficacy conclusions. It reports no formal statistical analysis of efficacy outcomes in the final analysis.
7. Results Posted in the Registry
- Radium-223 + EXE/EVE vs Placebo + EXE/EVE: hazard ratio 0.89 (95% CI 0.72–1.10), reported p = 0.484 (as reported in the registry).
Hazard ratio: Radium-223 + EXE/EVE vs Placebo + EXE/EVE
95% CI: 0.72 to 1.10
As reported in the registry
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 |
|---|---|---|---|---|
| Overall Survival | Time-to-Event Analysis | Hazard ratio | 0.97 (0.70 to 1.34) | 29,682 events |
| Time to Opiate Use for Cancer Pain | Time-to-Event Analysis | Hazard ratio | 0.96 (0.58 to 1.60) | 20,919 events |
| Time to Pain Progression | Time-to-Event Analysis | Hazard ratio | 0.93 (0.67 to 1.29) | 5,623 events |
Overall Survival
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Radium-223 + EXE/EVE vs Placebo + EXE/EVE: hazard ratio 0.97 (95% CI 0.70–1.34), reported p = 0.844 (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Radium-223 + EXE/EVE vs Placebo + EXE/EVE and the control. The interval gives the range of effects that remain compatible with the data.
Time to Opiate Use for Cancer Pain
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Radium-223 + EXE/EVE vs Placebo + EXE/EVE: hazard ratio 0.96 (95% CI 0.58–1.60), reported p = 0.881 (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Radium-223 + EXE/EVE vs Placebo + EXE/EVE and the control. The interval gives the range of effects that remain compatible with the data.
Time to Pain Progression
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Radium-223 + EXE/EVE vs Placebo + EXE/EVE: hazard ratio 0.93 (95% CI 0.67–1.29), reported p = 0.654 (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Radium-223 + EXE/EVE vs Placebo + EXE/EVE and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes extend the clinical picture beyond symptomatic skeletal event-free survival. They include overall survival, time to opiate use for cancer pain, time to pain progression, time to cytotoxic chemotherapy, radiological progression-free survival, pain improvement, and treatment-emergent and post-treatment chemotherapy-related adverse events. The record lists 15 outcome measures, with 10 secondary outcomes posted, but numerical comparative results for all of those outcomes are not reported in the registry record.
Among the secondary time-to-event comparisons with results in the record, the hazard-ratio estimates are close to 1 and their reported confidence intervals include 1. This pattern does not provide a clear statistical signal of a difference across those reported comparisons. Their intervals also leave uncertainty about the size and direction of possible effects. The medians and individual estimates are recorded with their endpoints, and should be interpreted according to each endpoint's distinct definition rather than treated as interchangeable measures.
These secondary outcomes complement the primary result; they do not overturn or replace it. They address different questions, such as survival, pain-related events, and progression, while the primary endpoint combines specified skeletal events with death. The registry does not report whether multiplicity was controlled. When many outcomes are examined, the chance of obtaining apparently notable findings by chance can increase. Without a reported multiplicity strategy, individual secondary p-values should carry less weight than a result from a prespecified primary analysis and should not be treated as independent confirmation.
The record states that the efficacy results shown came from the primary completion analysis and that formal statistical analyses of primary and secondary efficacy outcomes were not performed in the final analysis. This further limits any attempt to regard secondary findings as a comprehensive final efficacy assessment.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Overall Survival
- Time to Opiate Use for Cancer Pain
- Time to Pain Progression
- Time to Cytotoxic Chemotherapy
- Radiological Progression-free Survival (rPFS)
- Percentage of Participants With Pain Improvement
- Number of Participants With Treatment-emergent Adverse Events (TEAEs)
- Number of Participants With Post-treatment Chemotherapy Related Adverse Events
9. Statistical Interpretation
For SSE-FS, the reported median was 21.1 months in the radium-223 plus EXE/EVE arm and 19.9 months in the placebo plus EXE/EVE arm. The reported hazard ratio was 0.891, with an 80% confidence interval from 0.720 to 1.102 and p = 0.484 from a log-rank analysis. The interval includes 1, and the reported p-value does not indicate a statistically clear difference under conventional interpretation. The estimates therefore leave room for effects in either direction; they do not establish equivalence or prove that the treatments have identical outcomes.
The median estimates are point estimates, not guaranteed outcomes for individual participants. Their uncertainty is reflected in the reported 95% confidence intervals: 17.1 to 23.6 months for the radium-223 arm and 16.2 to 24.2 months for the placebo arm. Those intervals overlap. Overlap alone is not a formal test of the treatment comparison; the registry's reported comparative statistic is the hazard ratio and its associated analysis.
The hazard ratio is below 1, but its reported interval crosses 1. In general, a hazard ratio below 1 favors the first-listed group if the event hazard is interpreted in the usual direction, while a value of 1 represents no relative difference in hazards. Because the interval includes 1 and the p-value is 0.484, the point estimate should not be treated as firm evidence of a treatment difference. Nor does this result demonstrate that a clinically important effect is impossible: the interval retains uncertainty.
The outcome description also limits interpretation. SSE-FS combines death with several skeletal events, and the reported overall comparison cannot identify the separate contribution of each component. Further, the record says that the efficacy analyses presented came from the primary completion analysis. Later data collection was limited and not intended to revisit the efficacy conclusions. Thus the posted primary comparison should be read as the registry's primary completion result, not as a newly analyzed final efficacy result.
Overall survival and other secondary outcomes provide context, but they do not replace the prespecified primary endpoint. Their reported comparative estimates also have uncertainty, and the record does not report whether multiplicity was addressed. Findings across multiple endpoints should consequently be interpreted as supportive or exploratory rather than as a series of independent confirmations. The numerical evidence in the registry describes this trial and its uncertainty; it does not by itself settle whether the regimen has benefit in other populations or settings.
10. Statistical Methods Explained
The main efficacy outcome is time-to-event: it records time from randomization until a defined event. For SSE-FS, the event is the first qualifying skeletal event or death, whichever occurs earlier. Time-to-event methods are useful when the timing of an event matters and participants may have different lengths of follow-up. The registry reports medians for the arms and a hazard ratio for their comparison.
What does a median time-to-event estimate mean?
In general, a median time-to-event estimate marks the time at which the estimated event-free proportion reaches its midpoint. It is not an average, and it does not mean that every participant experiences the event at that time. The primary endpoint medians are 21.1 months and 19.9 months. Their reported 95% confidence intervals are 17.1 to 23.6 months and 16.2 to 24.2 months, respectively. The intervals express uncertainty in the arm-specific estimates; they are not ranges containing every participant's event time.
What does the hazard ratio summarize?
In general, a hazard ratio compares the instantaneous event rates between groups over follow-up, conditional on remaining event-free up to each time. A hazard ratio of 1 represents equal hazards under this summary, while a value below or above 1 indicates a relative direction of difference, depending on which group is in the numerator and how the event is defined. It is not a ratio of medians, a risk difference, or the probability that one treatment is better. The primary reported hazard ratio is 0.891 for radium-223 plus EXE/EVE versus placebo plus EXE/EVE.
What does the log-rank test do?
The registry names the log-rank method for the primary comparison. In general, the log-rank test compares event timing across groups over follow-up, using information from observed events and the risk sets over time. It is commonly used for time-to-event comparisons. The registry does not report further details of the test implementation, assumptions checks, or any covariate adjustment; those are not reported in the registry record.
How should the confidence interval and p-value be read?
A confidence interval gives a range of values compatible with the data under the statistical model and procedure used. It communicates precision as well as direction: a wide interval permits a broader set of possible effects than a narrow interval. The primary hazard-ratio interval is an 80% confidence interval, as specified in the reported analysis, and extends from 0.720 to 1.102. It contains 1, so the data are compatible with no relative hazard difference as well as with effects on either side of 1. The reported p-value is 0.484. In general, a p-value describes how unusual data at least as incompatible with a null hypothesis would be if that hypothesis and the analysis assumptions held. It is not the probability that the null hypothesis is true, nor a measure of clinical importance.
The arm-specific medians are presented with 95% confidence intervals, whereas the primary reported hazard ratio has an 80% interval. These confidence levels answer different uncertainty questions and should not be compared as if they were the same interval. The record does not explain why the primary hazard-ratio interval is 80%, so the rationale is not reported in the registry record.
What does the composite endpoint add?
In general, a composite endpoint can collect several types of events into one outcome, which may make the overall clinical question broader than any individual component. Here the composite includes external beam radiotherapy for skeletal symptoms, new symptomatic pathological fractures, spinal cord compression, tumor-related orthopedic surgery, and death from any cause. The resulting estimate concerns the first of these events, not the separate rate or timing of each component. The registry does not report component-specific primary comparative estimates in the registry record for this analysis.
The record specifies an intent-to-treat population for the primary outcome: all randomized participants. In general, this approach analyzes participants according to randomized assignment and preserves the comparison created by randomization. The registry does not describe how missing outcome information, censoring, protocol deviations, or participants with incomplete follow-up were handled. Those details are not reported in the registry record and should not be inferred from the endpoint estimates.
The record states that the efficacy results presented are from the primary completion analysis. It also states that after a protocol amendment, later efficacy data collection was limited and the final analysis did not include formal statistical analyses of primary and secondary efficacy outcomes. Accordingly, the posted primary efficacy comparison and its statistical summaries should be interpreted as results from the primary completion analysis rather than a formal efficacy reassessment at final analysis.
11. Confidence Intervals and Precision
The precision of an estimate is reflected by how narrowly its confidence interval constrains plausible values under the analysis. For the primary median SSE-FS estimates, the 95% confidence intervals are 17.1 to 23.6 months for radium-223 plus EXE/EVE and 16.2 to 24.2 months for placebo plus EXE/EVE. These intervals indicate uncertainty around each arm's median; they do not describe the spread of individual outcomes.
The comparative primary hazard ratio is 0.891, with an 80% confidence interval from 0.720 to 1.102. This interval crosses 1, so it includes no relative hazard difference as well as possible differences favoring either arm. The 80% confidence level is the one reported for this hazard ratio. It is distinct from the 95% confidence intervals given for the medians, and the registry does not state why this confidence level was used for the primary comparative estimate.
Confidence intervals are not guarantees that the true value lies within the displayed limits. In general, they describe the behavior of an interval-producing method over repeated studies under its assumptions. A confidence interval also does not tell whether any effect within its range would be important to patients. That requires context beyond statistical precision.
The secondary time-to-event estimates likewise have intervals that communicate uncertainty; some are broad, and not all median confidence limits are fully stated. In particular, the upper median confidence limits for time to opiate use are not reported in the registry record. For every estimate, precision should be considered alongside the endpoint definition, population, analysis method, and the registry's note that final efficacy analyses were not formally performed.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect (log scale) | Hazard ratio | Events, 80% power | Events, 90% power |
|---|---|---|---|
| 100% of the observed effect | 0.89 | 2,358 | 3,156 |
| 75% of the observed effect | 0.92 | 4,191 | 5,610 |
| 50% of the observed effect | 0.94 | 9,429 | 12,622 |
The planning figures are illustrations based on the observed effect, not the trial's own design calculations. For time-to-event outcomes, the figures are total events required, not participants per arm. The 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. The time-to-event planning calculations use the Schoenfeld approach.
The 80% power column describes the event total that the planning calculation associates with an 80% chance of detecting the assumed effect if that effect and the stated assumptions hold. The 90% power column uses a higher target chance of detection under the same kind of planning framework. These are design-planning quantities, not descriptions of what happened in the completed trial. The registry's original design assumptions and sample-size justification are not reported in the registry record.
The rows that plan for 75% or 50% of the observed effect ask what would be required to detect a smaller effect than the one used as the reference. Smaller effects are harder to distinguish from random variation, so they require more events in a time-to-event planning calculation. This is not observed power: it does not measure the probability that the completed trial detected an effect, and it cannot establish that a treatment effect is absent.
Read the figures as conditional illustrations. They depend on the chosen effect size and assumptions and should not be mistaken for observed trial enrollment, observed event totals, or proof that the trial was adequately or inadequately sized. The values for non-time-to-event outcomes, when shown, are participants per arm; the time-to-event figures are total events.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.
Worked calculation for this trial
- Hazard ratio HR = 0.891, so ln(HR) = -0.1154.
- d = 4 × (1.96 + 0.842)2 / [ln(0.891)]2 = 2,357.1, rounded up to 2,358 events in total for 80% power.
The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).
R code
alpha <- 0.05
z_a <- qnorm(1 - alpha / 2) # two-sided
hr <- 0.891 # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6)) # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))
# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(2258451)
d <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))
Output from running the code
100% of observed effect: events = 2,358 (80% power), 3,156 (90% power)
75% of observed effect: events = 4,191 (80% power), 5,610 (90% power)
50% of observed effect: events = 9,429 (80% power), 12,622 (90% power)
Simulated power with 2,358 events: 0.805 (20000 replicates)
The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.
14. Group-Sequential Design Analysis
Many time-to-event trials, especially in oncology, stop or report early when interim data are overwhelming, so a single fixed-sample number understates the real design problem. The calculation below is an illustrative group-sequential design built from this trial's posted control median and hazard ratio. The registry record does not state the planned number of looks or the spending function, so the design is a planning illustration, not a reconstruction of the protocol. Assumed: one-sided α = 0.025, 90% power, three equally spaced looks on information, Lan-DeMets O'Brien-Fleming spending, 24 months of accrual, 60 months in total and a 1% monthly dropout hazard.
Under these assumptions the design needs about 4,805 participants in total, with the boundaries below.
| Analysis | Calendar time (months) | Events | Efficacy boundary (z) | Nominal one-sided p | Cumulative alpha spent |
|---|---|---|---|---|---|
| Look 1 | 20.6 | 1,064 | 3.710 | 0.0001 | 0.0001 |
| Look 2 | 33.1 | 2,128 | 2.511 | 0.0060 | 0.0060 |
| Look 3 | 60.0 | 3,192 | 1.993 | 0.0231 | 0.0250 |
Fixed design versus group-sequential alternatives
| Design | Power | Events at final analysis | Participants | Study length (months) |
|---|---|---|---|---|
| Fixed design, one analysis | 80% | 2,356 | 3,547 | 60.0 |
| Two looks, O'Brien-Fleming | 80% | 2,365 | 3,560 | 60.0 |
| Three looks, O'Brien-Fleming | 80% | 2,386 | 3,592 | 60.0 |
| Three looks, Pocock | 80% | 2,757 | 4,151 | 60.0 |
| Fixed design, one analysis | 90% | 3,154 | 4,749 | 60.0 |
| Two looks, O'Brien-Fleming | 90% | 3,165 | 4,765 | 60.0 |
| Three looks, O'Brien-Fleming | 90% | 3,192 | 4,805 | 60.0 |
| Three looks, Pocock | 90% | 3,641 | 5,481 | 60.0 |
Group-sequential designs cost a small increase in maximum sample size and events compared with the fixed design, in exchange for the chance to stop early for overwhelming efficacy. O'Brien-Fleming spending keeps early boundaries very conservative and the final boundary close to the fixed-design value, whereas Pocock spending spends more alpha early.
Sensitivity to a smaller true effect
Planning for exactly the observed effect is optimistic, because observed effects in published trials tend to be somewhat larger than the true effect. The table repeats the main design (three looks, O'Brien-Fleming spending, 90% power) for smaller true hazard ratios.
| True effect assumed | Hazard ratio | Events at final analysis | Participants |
|---|---|---|---|
| 100% of the observed effect | 0.891 | 3,192 | 4,805 |
| 75% of the observed effect | 0.917 | 5,675 | 8,485 |
| 50% of the observed effect | 0.944 | 12,770 | 18,965 |
For context, this trial enrolled 283 participants.
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993. Agreement between the two packages confirms the boundary calculation.
R code and output
suppressWarnings(suppressMessages({ library(gsDesign); library(rpact) }))
med_control <- 19.9 # control-arm median, months (converted from the posted unit)
hr <- 0.891 # hazard ratio used for planning
lambdaC <- log(2) / med_control
eta <- 0.01 # dropout hazard per month (assumption)
acc_months <- 24 # accrual duration (assumption)
study_months<- 60 # total study duration (assumption)
design <- function(k, sfu, beta, h = hr) gsSurv(k = k, test.type = 1, alpha = 0.025, beta = beta, sfu = sfu,
lambdaC = lambdaC, hr = h, hr0 = 1, eta = eta, gamma = 1, R = acc_months, T = study_months, minfup = study_months - acc_months)
# Main design: 3 looks, Lan-DeMets O'Brien-Fleming spending, one-sided alpha 0.025, 90% power
x <- design(3, sfLDOF, 0.10)
cat(sprintf("N_TOTAL|%s\n", format(ceiling(sum(x$gamma * x$R)), big.mark = ",")))
for (i in 1:3) cat(sprintf("GS|%d|%.1f|%.0f|%.3f|%.5f|%.5f\n", i, x$T[i], x$n.I[i], x$upper$bound[i], pnorm(-x$upper$bound[i]), cumsum(x$upper$spend)[i]))
cat("\n"); print(gsBoundSummary(x))
# Comparison of designs
cmp <- list(list("Fixed design, one analysis", 1, sfLDOF), list("Two looks, O'Brien-Fleming", 2, sfLDOF),
list("Three looks, O'Brien-Fleming", 3, sfLDOF), list("Three looks, Pocock", 3, sfLDPocock))
cat("\n")
for (b in c(0.20, 0.10)) for (d in cmp) {
y <- design(d[[2]], d[[3]], b)
cat(sprintf("DES|%s|%d|%.0f|%s|%.1f\n", d[[1]], round(100 * (1 - b)), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ","), tail(y$T, 1)))
}
# Sensitivity: what if the true effect is smaller than the observed one? (3 looks, O'Brien-Fleming, 90% power)
cat("\n")
for (fr in c(1, 0.75, 0.5)) {
y <- design(3, sfLDOF, 0.10, exp(log(hr) * fr))
cat(sprintf("SENS|%.2f|%.3f|%.0f|%s\n", fr, exp(log(hr) * fr), tail(y$n.I, 1), format(ceiling(sum(y$gamma * y$R)), big.mark = ",")))
}
# Independent cross-check of the boundaries with rpact
r <- getDesignGroupSequential(kMax = 3, alpha = 0.025, beta = 0.10, sided = 1, typeOfDesign = "asOF", informationRates = x$timing)
cat(sprintf("\nCross-check, upper boundaries: gsDesign %s | rpact %s\n", paste(round(x$upper$bound, 3), collapse = ", "), paste(round(r$criticalValues, 3), collapse = ", ")))
Method: LachinFoulkes
Analysis Value Efficacy
IA 1: 33% Z 3.7103
N: 4126 p (1-sided) 0.0001
Events: 1064 ~HR at bound 0.7965
Month: 21 P(Cross) if HR=1 0.0001
P(Cross) if HR=0.89 0.0338
IA 2: 67% Z 2.5114
N: 4806 p (1-sided) 0.0060
Events: 2128 ~HR at bound 0.8968
Month: 33 P(Cross) if HR=1 0.0060
P(Cross) if HR=0.89 0.5603
Final Z 1.9930
N: 4806 p (1-sided) 0.0231
Events: 3192 ~HR at bound 0.9319
Month: 60 P(Cross) if HR=1 0.0250
P(Cross) if HR=0.89 0.9000
Cross-check, upper boundaries: gsDesign 3.71, 2.511, 1.993 | rpact 3.71, 2.511, 1.993
15. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 0.891 | 0.720 to 1.102 | 0.484 |
The registry reports the sponsor's primary comparison as a log-rank hazard ratio of 0.891 for radium-223 plus EXE/EVE versus placebo plus EXE/EVE, with an 80% confidence interval from 0.720 to 1.102 and p = 0.484. This is the analysis to use when describing the trial's official reported efficacy result. The discrepancy indicator is false, so there is no recorded disagreement between the sponsor result and a recalculation.
A recalculation from posted summary statistics, when one is available, is an unadjusted check and may not reproduce an analysis that uses participant-level data or additional analysis choices. It should not replace the sponsor's own analysis. No recalculated comparative value is reported in the registry record for this result, so there is no separate recalculated estimate to compare with the reported hazard ratio.
The primary hazard-ratio interval includes 1, and the reported p-value is 0.484. The sponsor's reported analysis therefore does not show a statistically clear difference under conventional interpretation. This does not prove equivalence, demonstrate absence of an effect, or establish that effects within the interval are clinically unimportant. The record's statement that final efficacy analyses were not formally performed is also relevant: this reported comparison comes from the primary completion analysis.
16. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a trial evaluates several outcomes, comparisons, time points, or analyses. In general, the more statistical questions asked, the greater the chance that at least one result appears notable by chance if each is interpreted without adjustment. This is why a prespecified primary endpoint is often given more inferential weight than a collection of secondary results.
The registry identifies SSE-FS as the primary outcome and lists multiple secondary outcomes, including survival, pain-related outcomes, progression measures, and adverse-event outcomes. It reports a primary log-rank comparison and several secondary comparisons. Whether secondary hypotheses were ordered, whether any adjustment for multiple testing was planned or applied, and how confirmatory claims were to be governed are not reported in the registry record. No multiplicity procedure should therefore be assumed.
The primary outcome population is the intent-to-treat analysis set, defined as all randomized participants. The registry does not provide comparable analysis-population definitions for every secondary outcome in the registry record. Nor does it describe how missing outcome data, censoring, treatment discontinuation, or protocol deviations were handled. These details are not reported in the registry record. They matter because time-to-event estimates rely on how follow-up and incomplete observations are handled, and because different outcome populations can affect comparability.
The record notes an amendment after which collection of data for remaining participants was reduced and focused mainly on acute safety, symptomatic skeletal events, and overall survival. It states that the long-term safety assessment would occur in a separate extended safety follow-up study after participants rolled over. It also explicitly says that later efficacy data were limited and not designed to support reconsideration of the primary efficacy conclusions, and that no formal statistical analyses of primary and secondary efficacy outcomes were performed in the final analysis. These statements define an important boundary on what can be inferred from the posted efficacy analyses.
17. 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 |
|---|---|---|---|
| Radium-223 + EXE/EVE | 61 | 139 | 43.9% |
| Placebo + EXE/EVE | 56 | 139 | 40.3% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Radium-223 + EXE/EVE | 66 of 139 |
| Placebo + EXE/EVE | 67 of 139 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Radium-223 + EXE/EVE | 139 of 139 |
| Placebo + EXE/EVE | 135 of 139 |
Most frequent serious adverse event terms
| Event term | Organ system | Radium-223 + EXE/EVE | Placebo + EXE/EVE |
|---|---|---|---|
| Pneumonia | Infections and infestations | 5 of 139 | 4 of 139 |
| Pneumonitis | Respiratory, thoracic and mediastinal disorders | 7 of 139 | 2 of 139 |
| Anaemia | Blood and lymphatic system disorders | 3 of 139 | 5 of 139 |
| Pathological fracture | Musculoskeletal and connective tissue disorders | 3 of 139 | 4 of 139 |
| Dyspnoea | Respiratory, thoracic and mediastinal disorders | 1 of 139 | 5 of 139 |
| Pyrexia | General disorders | 2 of 139 | 3 of 139 |
| General physical health deterioration | General disorders | 2 of 139 | 3 of 139 |
| Vomiting | Gastrointestinal disorders | 2 of 139 | 2 of 139 |
| Acute kidney injury | Renal and urinary disorders | 1 of 139 | 3 of 139 |
| Diarrhoea | Gastrointestinal disorders | 3 of 139 | 0 of 139 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Radium-223 + EXE/EVE | Placebo + EXE/EVE |
|---|---|---|---|
| Stomatitis | Gastrointestinal disorders | 66 of 139 | 69 of 139 |
| Anaemia | Blood and lymphatic system disorders | 55 of 139 | 40 of 139 |
| Decreased appetite | Metabolism and nutrition disorders | 48 of 139 | 35 of 139 |
| Fatigue | General disorders | 38 of 139 | 41 of 139 |
| Diarrhoea | Gastrointestinal disorders | 42 of 139 | 31 of 139 |
| Arthralgia | Musculoskeletal and connective tissue disorders | 30 of 139 | 42 of 139 |
| Nausea | Gastrointestinal disorders | 41 of 139 | 30 of 139 |
| Asthenia | General disorders | 29 of 139 | 26 of 139 |
| Headache | Nervous system disorders | 25 of 139 | 30 of 139 |
| Oedema peripheral | General disorders | 26 of 139 | 25 of 139 |
Serious events with the highest arm-level rate: pneumonitis (5.0%), anaemia (3.6%), pneumonia (3.6%), dyspnoea (3.6%), pathological fracture (2.9%).
The registry reports serious adverse events for 139 participants at risk in each arm. Serious adverse events were reported for 61 participants in the radium-223 plus EXE/EVE group and 56 in the placebo plus EXE/EVE group. These are counts of participants with serious adverse events, not counts of all separate events, and they are not a treatment-effect comparison. The record does not provide a statistical comparison of these figures.
The listed serious adverse-event terms include pneumonitis (5.0%), anaemia (3.6%), pneumonia (3.6%), dyspnoea (3.6%), pathological fracture (2.9%), and diarrhoea (2.2%). The registry entries do not identify the arm-specific breakdown for these term percentages, so they should not be attributed to one arm or interpreted as a between-arm contrast.
Other adverse events were reported for 139 participants at risk in each group, with 139 affected in the radium-223 group and 135 in the placebo group. Deaths are recorded as 66 and 67, respectively, in the adverse-event summary. The registry excerpt does not provide further definitions or a causal attribution for those death counts. Safety counts should be interpreted alongside their stated risk populations and the record's note that later safety follow-up was handled separately.
18. What the Result Does, and Does Not, Mean
The posted primary result describes the comparison of radium-223 plus exemestane and everolimus with placebo plus the same background medicines for symptomatic skeletal event-free survival. The reported medians were 21.1 months and 19.9 months, and the reported hazard ratio was 0.891. Its 80% confidence interval, 0.720 to 1.102, includes 1; the log-rank p-value was 0.484. Together, these results do not demonstrate a statistically clear difference in the primary outcome.
That interpretation is not the same as concluding that the regimens are equivalent or that no effect exists. A non-significant comparison can leave uncertainty about effects that the study did not estimate precisely. The interval includes possible relative hazard differences on either side of 1, and the registry does not provide a prespecified equivalence or non-inferiority framework in the registry record.
The result also does not identify what happened for every participant, how each component of the composite endpoint contributed, or whether the findings apply to populations outside the trial's stated setting. The primary endpoint combines death and several types of symptomatic skeletal events; its summary cannot distinguish the separate component effects. The medians are group-level summaries, not predictions for an individual.
Secondary outcomes add context but involve different questions and uncertainty. The registry does not report a multiplicity strategy, and its final analysis did not include formal statistical analyses of primary or secondary efficacy outcomes. Safety counts describe reported events in the stated groups; they do not by themselves establish causation or comparative risk.
Thus, the registry supports a careful description of the primary completion analysis and its uncertainty, not a broad claim about treatment benefit, lack of benefit, or clinical recommendations. Interpretation should remain tied to the endpoint definition, analysis population, time frame, and limitations documented in the record.
19. Why This Trial Matters Statistically
This trial illustrates why a time-to-event result should be read through both its point estimate and its uncertainty. The primary hazard ratio is below 1, but the reported interval crosses 1 and the p-value is 0.484. Focusing only on the direction of the point estimate would overstate what the analysis establishes; focusing only on a threshold would conceal the range of effects still compatible with the estimate.
The endpoint also illustrates the interpretive trade-off of a composite. SSE-FS combines death with several skeletal events, creating one summary of time to the first event, but that summary does not reveal the separate pattern for each component. This makes the exact event definition essential when interpreting the reported medians and hazard ratio.
The record distinguishes the primary completion analysis from later follow-up. Following a protocol amendment, efficacy collection was limited, and the final analysis was not designed to revisit the primary efficacy conclusions. That distinction matters: a reader should not assume that a completed study status means that a new formal efficacy analysis was conducted at final analysis.
Finally, the registry lists multiple secondary outcomes while not reporting a multiplicity strategy in the record details. This is a reminder that secondary findings need context and that an isolated result among many outcomes is not equivalent to a confirmatory primary finding. The trial is statistically informative as a worked example of interpreting hazard ratios, confidence intervals, composite endpoints, and analysis-stage limitations without converting uncertain estimates into definitive claims.
20. 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.
The registry states that the primary and secondary efficacy results presented came from the primary completion analysis. After implementation of CSP Amendment 10, data collection for remaining participants was reduced and focused mainly on acute safety, symptomatic skeletal events, and overall survival. The record says this later collection was not designed to support reconsideration of the primary efficacy conclusions, and that formal statistical analyses of efficacy outcomes were not performed in the final analysis.
The primary endpoint is a composite of death and several specified symptomatic skeletal events. The reported summary does not separate the contribution of each component. The registry entries for this page do not report component-specific comparative estimates or additional details about the time-to-event analysis, such as handling of censoring, missing data, or protocol deviations. These elements are not reported in the registry record.
The registry reports an 80% confidence interval for the primary hazard ratio, while the arm-specific medians have 95% confidence intervals. The reason for the confidence-level choice is not reported in the registry record. The primary hazard-ratio interval includes 1, and the reported p-value is 0.484; the data therefore do not establish a statistically clear difference, while still leaving uncertainty about the possible effect.
Multiplicity handling is not reported in the registry record despite the range of secondary outcomes. Numerical results for every posted secondary outcome are not reported in the registry entries for this analysis. Finally, the long-term safety assessment was to be collected in a separate extended safety follow-up study after rollover. The safety counts should not be treated as a full account of that separate follow-up.
21. Related Tutorials
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: Study of Radium-223 Dichloride in Combination With Exemestane and Everolimus Versus Placebo in Combination With Exemestane and Everolimus in Subjects With Bone Predominant HER2 Negative Hormone Receptor Positive Metastatic Breast Cancer — NCT02258451.
- Registry record last updated 2023-11-24; status last verified 2023-11.
- Results first posted 2022-03-10.
- 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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Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
24. Record Summary
NCT02258451 is a completed, randomized, parallel, quadruple-masked phase II study sponsored by Bayer. It compared radium-223 dichloride plus exemestane and everolimus with saline placebo plus exemestane and everolimus in HER2-negative, hormone receptor-positive metastatic breast cancer with bone metastases. Enrollment is recorded as 283.
The primary outcome was symptomatic skeletal event-free survival, defined as time from randomization to a specified symptomatic skeletal event or death from any cause, whichever came first. The reported medians were 21.1 months and 19.9 months. The reported hazard ratio was 0.891, with an 80% confidence interval from 0.720 to 1.102 and p = 0.484. The interval includes 1, so the primary result does not show a statistically clear difference.
The registry says the posted efficacy results came from the primary completion analysis; formal efficacy analyses were not performed in the final analysis. It does not report the original design assumptions, missing-data methods, or multiplicity strategy.