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Breast Cancer Phase 3 Time-to-Event Analysis NCT00295646

Tamoxifen Versus Anastrozole, Alone or in Combination With Zoledronic Acid: Complete Statistical Analysis

This randomized phase 3 trial compared tamoxifen and anastrozole, with or without zoledronic acid, in premenopausal patients with hormone receptor-positive, non-metastatic breast cancer. The primary posted analysis concerns disease-free survival; the registry also reports recurrence-free survival, overall survival, and adverse-event information.

Trial start: 1999-06  ·  Enrollment: 1803  ·  Sponsor: Austrian Breast & Colorectal Cancer Study 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 Tamoxifen Versus Anastrozole, Alone or in Combination With Zoledronic Acid (NCT00295646), a randomized phase 3 study. The primary outcome is Comparison of Anastrozole vs Tamoxifen in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Disease-free Survival (DFS).

1803
Enrollment
Phase 3
4
Arms
In the primary outcome
1.10
Hazard ratio
AZ (Arimidex+Zoledronate) vs TZ (Tamoxif
0.78–1.53
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00295646
PhasePhase 3
ConditionBreast Cancer
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment1803
Arms in the primary outcome4
Lead sponsorAustrian Breast & Colorectal Cancer Study Group
Results postedYes

2. Clinical Question

Population

Premenopausal patients with hormone receptor-positive, non-metastatic breast cancer, described as stage I or II. The primary analysis is identified as intent-to-treat, including participants assigned to one of the four treatment arms.

Intervention

The study compared tamoxifen or anastrozole, each with or without zoledronic acid. Goserelin is also listed as an intervention, but the arm descriptions do not specify its assignment or use.

Comparator

The four arms were anastrozole plus zoledronate, tamoxifen plus zoledronate, anastrozole control, and tamoxifen control. The control arms are described as receiving the endocrine study drug without zoledronate.

Primary question

The stated primary objective includes comparing anastrozole with tamoxifen and comparing zoledronate added to standard adjuvant therapy with controls, using disease-free survival. The posted primary analysis reports a hazard ratio across the four listed groups; the exact contrast represented by that estimate is not reported in the registry record.

The study also aimed to assess whether adding zoledronate could decrease or prevent bone loss during hormonal blockade. The registry record describes that aim, but a bone-loss result is not included in the posted outcomes summarized in this analysis. The primary endpoint is disease-free survival, while recurrence-free survival and overall survival are identified as secondary endpoints.

The clinical question therefore has more than one component: an endocrine-treatment comparison, an assessment of zoledronate added to adjuvant therapy, and an intended bone outcome. The four-arm arrangement allows the registry to list both endocrine drugs with and without zoledronate, but the primary reported hazard ratio is associated with all four groups together. Without a clearly specified contrast, that estimate should not be read as an isolated comparison of either endocrine treatment or zoledronate. The primary result is best interpreted as the registry’s reported analysis, with the limits of its contrast description kept in view.

3. Trial Design

This was a randomized, phase 3, parallel-group trial with no masking recorded. The registry lists an enrollment of 1803 and identifies the study as completed. The sponsor was the Austrian Breast & Colorectal Cancer Study Group. The recorded start was 1999-06, and the primary completion date was 2008-03-27.

The four arms were AZ, anastrozole plus zoledronate; TZ, tamoxifen plus zoledronate; AC, anastrozole control; and TC, tamoxifen control. The arm descriptions identify the endocrine treatment in each group and whether zoledronate was included. The registered arm sizes were 450 for AZ, 450 for TZ, 453 for AC, and 450 for TC. These are the registry’s assigned-group counts; they should not be mistaken for counts of endpoint events.

The primary endpoint analysis included all participants assigned to one of the four arms, according to the registry’s intent-to-treat description. The reported time-to-event analysis used a log-rank method, with the analysis parameter identified as a Cox proportional hazard. No masking was recorded, so participants and study personnel were not described as blinded in the registry record. Details of allocation concealment, treatment adherence, treatment duration, and handling of protocol deviations are not reported in the registry record.

The primary analysis timeframe is described as running from randomization to the analysis data cut-off, when 124 DFS events had occurred. The record says that maximum time on study per patient at that cut-off was 102 months. It does not provide the distribution of follow-up time or the number of participants still under observation at the cut-off. The four arms and the stated objectives suggest comparisons involving both endocrine treatment and zoledronate, but the exact coding and contrast for the primary four-group hazard ratio 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.

Overall Study

StageAZ (Arimidex+Zoledronate)TZ (Tamoxifen+Zoledronate)AC (Arimidex Control)TC (Tamoxifen Control)
STARTED450450453450
COMPLETED415409403405
NOT COMPLETED35415045

Reasons for not completing this period:

ReasonAZ (Arimidex+Zoledronate)TZ (Tamoxifen+Zoledronate)AC (Arimidex Control)TC (Tamoxifen Control)
Protocol Violation18202018
Withdrawal by Subject891114
Lost to Follow-up0515
Death97188

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat population: All participants assigned to one of the four treatment arms were included in the analysis

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.

CharacteristicUnitAZ (Arimidex+Zoledronate)TZ (Tamoxifen+Zoledronate)AC (Arimidex Control)TC (Tamoxifen Control)Total
Participants analysed4504504534501803
Age, Continuousyears44 (28 to 56)45 (27 to 54)44 (25 to 58)45 (27 to 56)45 (25 to 58)
Sex: Female, Male: FemaleParticipants4504504534501803
Sex: Female, Male: MaleParticipants00000
pT-stage: pT1Participants3433393523411375
pT-stage: pT2/pT3Participants98979398386
pT-stage: UnknownParticipants91481142
pN-stage: NegativeParticipants3042983043051211
pN-stage: PositiveParticipants137138141134550
pN-stage: UnknownParticipants91481142
Histologic grade: G1/G2Participants3413473473461381
Histologic grade: G3Participants93858985352
Histologic grade: GXParticipants749828
Histologic grade: UnknownParticipants91481142
Estrogen receptor status: NegativeParticipants1720141667
Estrogen receptor status: PositiveParticipants4244164314231694
Estrogen receptor status: UnknownParticipants91481142
Progesterone receptor status: NegativeParticipants36323540143
Progesterone receptor status: PositiveParticipants4054044093991617
Progesterone receptor status: UnknownParticipants91491143
Preoperative chemotherapy: NoParticipants3863823893791536
Preoperative chemotherapy: YesParticipants2623232597
Preoperative chemotherapy: UnknownParticipants38454146170

6. Primary Endpoint

The registry lists the primary outcome as Comparison of Anastrozole vs Tamoxifen in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Disease-free Survival (DFS), measured over Time from randomization to the analysis data cut-off date when 124 DFS events had occurred. On the analysis data cut-off date, maximum time on study per patient was 102 months..

ElementRegistry entry
Result typeMedian
Measure of spreadInter-Quartile Range
Unityears
Endpoint classificationTime-to-Event Analysis

The primary endpoint is disease-free survival, measured as time from randomization to the first occurrence of a local, regional, or distant recurrence, a second primary carcinoma, including contralateral breast cancer, or death from any cause. This combines several clinically important events into one time-to-event measure. The event definition and the starting point are specified in the registry record.

In general, time-to-event endpoints retain information about when events occur, rather than reducing the outcome to whether an event happened by a single fixed time. They can also account for participants whose event time is not observed before follow-up ends, provided the analysis handles censoring appropriately. The specific censoring rules and other implementation details are not reported in the registry record.

The posted primary endpoint is described as a median, with inter-quartile range as the dispersion measure, and the unit is years. However, numerical median values and inter-quartile ranges are not reported for the arms in the record. The inferential result that is reported is a hazard ratio from a log-rank/Cox analysis. A hazard ratio compares event rates over follow-up under the assumptions of the model; it is not itself a median survival time and does not state the absolute probability of remaining disease-free at a particular time.

DFS is useful for bringing recurrence, second primary carcinoma, and death into a common endpoint, but its composite nature matters when interpreting the result. A difference in the composite does not establish which component contributes to the observed pattern. Component-specific results are not reported in the registry record.

7. Results Posted in the Registry

Hazard ratio: AZ (Arimidex+Zoledronate) vs TZ (Tamoxifen+Zoledronate) vs AC (Arimidex Control) vs TC (Tamoxifen Control)

1.10

95% CI: 0.78 to 1.53

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)AZ (Arimidex+Zoledronate) vs …0.740.861.011.181.381.61hazard ratio (as reported) 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
Comparison of Anastrozole vs Tamoxifen in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Recurrence-free Survival (RFS)Time-to-Event AnalysisHazard ratio1.11 (0.80 to 1.56)2,883 events
Comparison of Zoledronate vs no Zoledronate in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Recurrence-free Survival (RFS)Time-to-Event AnalysisHazard ratio0.65 (0.46 to 0.92)170 events
Comparison of Anastrozole vs Tamoxifen in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Overall Survival (OS)Time-to-Event AnalysisHazard ratio1.80 (0.96 to 3.38)91 events

Comparison of Anastrozole vs Tamoxifen in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Recurrence-free Survival (RFS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)AZ (Arimidex+Zoledronate) vs …0.760.891.031.211.411.65hazard ratio (as reported) vs control (95% CI)

Comparison of Zoledronate vs no Zoledronate in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Recurrence-free Survival (RFS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)AZ (Arimidex+Zoledronate) vs …0.430.520.620.740.891.06hazard ratio (as reported) vs control (95% CI)

Comparison of Anastrozole vs Tamoxifen in Premenopausal Patients With Non-metastatic Breast Cancer With Respect to Overall Survival (OS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)AZ (Arimidex+Zoledronate) vs …0.871.161.562.082.793.74hazard ratio (as reported) vs control (95% CI)

The secondary outcomes cover recurrence-free survival and overall survival, with comparisons described for anastrozole versus tamoxifen and zoledronate versus no zoledronate. Across these endpoints, the posted pattern is not uniform: estimates differ in direction and in how much uncertainty they retain. This means the secondary results should be considered outcome by outcome rather than treated as one general answer to the trial’s objectives.

The primary endpoint is DFS, while RFS and OS provide related but distinct views of outcomes. RFS focuses on recurrence, and OS concerns death. The record’s primary DFS definition includes recurrence, second primary carcinoma, and death from any cause. Agreement across related outcomes could add context, but lack of agreement is not automatically contradictory because the endpoints capture different events and may have different numbers and timing of events. The record does not provide the event counts needed to explore those differences.

The registry lists four secondary comparisons and six analyses overall. It does not report whether the secondary endpoints were ranked in a prespecified hierarchy or whether multiplicity was controlled. In general, looking across several outcomes increases the chance of finding at least one nominally notable result through random variation alone. Unadjusted secondary p-values therefore carry less weight than a result from a single prespecified primary analysis, particularly when the exact contrast specifications are unclear.

These secondary analyses can be useful for generating hypotheses and for describing the broader pattern of posted results. They should not be used alone to establish a definitive treatment effect. Interpretation is further limited because the registry does not report numerical median values, absolute survival estimates at fixed times, or full endpoint-specific event counts. The secondary findings should be read as part of the full set of outcomes and with the uncertainty around analysis definitions in mind.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The primary reported estimate is a hazard ratio of 1.10, with a 95% confidence interval from 0.78 to 1.53 and p = 0.59. This is the registry’s reported comparison across AZ, TZ, AC, and TC. The interval includes 1, and the p-value does not indicate a statistically clear difference under a conventional two-sided testing framework. The estimate is not precise enough to rule out meaningfully different hazard patterns in either direction. Because the record does not specify how the four groups were combined or contrasted for this estimate, it should not be assigned to a simple anastrozole-versus-tamoxifen or zoledronate-versus-no-zoledronate comparison.

The result is a relative time-to-event estimate, not a direct statement about the number of participants who experienced recurrence or death, nor an estimate of an absolute event probability. The primary endpoint definition includes several kinds of events, and component-specific results are not reported. The record also does not report numerical arm-level median DFS values, so those cannot be used to clarify the magnitude or timing of any group differences.

Among the posted secondary results, the anastrozole-versus-tamoxifen RFS analysis has a hazard ratio of 1.11, a 95% confidence interval from 0.80 to 1.56, and p = 0.53. The zoledronate-versus-no-zoledronate RFS analysis has a hazard ratio of 0.65, a 95% confidence interval from 0.46 to 0.92, and p = 0.01. The OS analysis comparing anastrozole with tamoxifen has a hazard ratio of 1.80, a 95% confidence interval from 0.96 to 3.38, and p = 0.07. The registry lists all four groups for these analyses as well, so the precise contrast definitions are not fully clear from the record.

These secondary estimates have different directions and degrees of precision. They should not be treated as a single coherent confirmation of the primary result, nor as proof of a treatment effect. In particular, several endpoints and comparisons were reported, and the registry record does not state whether multiplicity was addressed. The secondary p-values are therefore best considered in context, alongside their confidence intervals and the uncertainty about contrast specification.

The posted data provide an inferential summary, but not a full clinical picture. Event counts by treatment arm, absolute DFS or RFS probabilities at fixed times, and detailed survival curves are not included in the registry record. The result supports a cautious reading of what the recorded analysis estimates; it does not by itself answer every comparison posed by the study objectives.

10. Statistical Methods Explained

The primary and secondary time-to-event analyses are described using a log-rank method and a Cox proportional hazards parameter. The registry reports hazard ratios with 95% confidence intervals and p-values. It does not provide enough detail to reconstruct the full analysis procedure or the exact group contrast represented by each estimate.

What the log-rank method does

In general, a log-rank test compares the observed timing of events between groups over follow-up. It uses information from event times and the participants still at risk at each event time. It is commonly used for time-to-event comparisons, but interpretation depends on which groups are compared, how censoring is handled, and whether the event-rate patterns satisfy the assumptions behind the test. The registry record does not report details about censoring rules or checks of assumptions.

What a Cox hazard ratio represents

In general, a Cox proportional hazards model expresses a relative event rate as a hazard ratio. A value of 1 represents equal hazards under the contrast and model; values on either side indicate a relative difference according to the contrast’s direction. The hazard is an instantaneous event rate among participants who remain event-free and under observation, not an absolute risk. The proportional hazards assumption means that the relative hazard is treated as stable over time. Whether this assumption was checked, and whether any adjustment variables were included, are not reported in the registry record.

Direction is meaningful only when the contrast and reference group are clear. The record lists all four groups together for the reported primary and secondary analyses, while the outcome titles describe comparisons such as anastrozole versus tamoxifen or zoledronate versus no zoledronate. The exact model coding and contrast specification are not reported. As a result, the estimates can be quoted as reported, but should not be reinterpreted as a clearly defined pairwise hazard ratio without further analysis documentation.

How to read the reported uncertainty

In general, a confidence interval gives a range of parameter values that are reasonably compatible with the observed data under the statistical model and its assumptions. It reflects sampling uncertainty, not uncertainty from every possible source of bias or model error. A 95% confidence interval is not a guarantee that the true value falls inside that particular interval. The p-value measures how unusual the data, or more extreme data, would be under a specified null hypothesis and analysis procedure; it is not the probability that the null hypothesis is true.

The log-rank/Cox results are reported with confidence intervals and p-values. The record does not describe the statistical hypotheses in detail, whether tests were one- or two-sided, how ties were treated, or whether there were prespecified covariates. Those aspects of the statistical plan are not reported in the registry record.

Why endpoint and model details matter

DFS is a composite endpoint that includes recurrence, second primary carcinoma, and death from any cause. A single hazard ratio can summarize the composite event process, but cannot identify the contribution of each component. The record does not report component-specific analyses or arm-level event counts for the primary endpoint. It also does not report the numerical arm-level median values described in the outcome definition. The Cox estimate therefore cannot be translated into a median difference or an absolute risk difference from the information recorded.

In general, over-dispersion is a concern when variation in observed counts exceeds what a simple count model expects. It is not the central issue in a Cox analysis of event times, which models hazards rather than a single count outcome. The registry does not report an over-dispersion analysis, and no such result should be inferred from these time-to-event estimates.

The posted analysis is identified as intent-to-treat for the primary endpoint: participants are analyzed according to their assigned arm. In general, this approach preserves the benefits of random assignment when applied as planned. It does not remove the need to understand missing outcomes, departures from assigned treatment, or loss to follow-up. The specific handling of those issues is not reported in the registry record. The analysis population for each secondary endpoint is also not described in the same detail as the primary population.

Finally, the registry lists six outcome measures and six analyses, including the primary and secondary endpoints. The record does not say whether the analysis plan prespecified a hierarchy among outcomes, controlled family-wise error, or used another multiplicity procedure. When several outcomes or comparisons are examined, nominal p-values can overstate how persuasive an isolated finding is. That general concern applies to the secondary analyses, while the exact consequences depend on the analysis plan, which is not reported.

11. Confidence Intervals and Precision

Precision is conveyed mainly by the width of a confidence interval. In general, a narrower interval indicates less sampling uncertainty under the fitted model, while a wider interval leaves more values compatible with the data. Precision does not by itself address bias, endpoint definition, or whether the model assumptions are appropriate.

For the primary DFS analysis, the reported hazard ratio is 1.10 and the 95% confidence interval is 0.78 to 1.53. The interval spans 1, so the data are compatible with a range that includes no relative hazard difference as well as values in either direction. The p-value is 0.59. This is not evidence of a precise estimate of no difference: the interval remains broad enough to include departures from 1. The unspecified four-group contrast further limits the meaning that can be assigned to the estimate.

The secondary RFS estimate for anastrozole versus tamoxifen is 1.11, with a 95% confidence interval from 0.80 to 1.56. That interval also includes 1. The reported zoledronate RFS estimate is 0.65, with a 95% confidence interval from 0.46 to 0.92; this interval does not include 1. The OS estimate is 1.80, with a 95% confidence interval from 0.96 to 3.38, a wide interval that includes 1 and allows a broad range of relative hazards. Each estimate should be read with the contrast ambiguity and the number of reported analyses in mind.

Confidence intervals do not show the absolute frequency of events or the likely difference in survival probability at a fixed time. Such quantities, along with the numerical median results, are not reported in the registry record. Thus, the precision of the relative estimates can be discussed, but the precision of absolute treatment differences cannot be assessed from the posted information.

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 ratioEvents, 80% powerEvents, 90% power
100% of the observed effect1.103,4574,627
75% of the observed effect1.076,1458,226
50% of the observed effect1.0513,82518,508
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00050,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: events required (total))
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, Schoenfeld approximation for the log-rank test or Cox model. The answer is the total number of events, not participants; the number of participants depends on how quickly events accrue. Calculated for the comparison: AZ (Arimidex+Zoledronate) vs TZ (Tamoxifen+Zoledronate) vs AC (Arimidex Control) vs TC (Tamoxifen Control).

The planning illustrations are based on time-to-event outcomes, so the displayed quantities are total event counts, not participants per arm. Their assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The target effect is set to the stated fraction of the observed effect. These are planning illustrations based on the observed effect, not the trial’s original design assumptions; the original design assumptions are not reported in the registry record.

The 80% power column gives the total number of events that a hypothetical study would need, under those assumptions, to have an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding event target for a higher probability of detection. These are conditional planning calculations, not predictions that a future study will produce a particular result.

The rows consider planning for 100%, 75%, and 50% of the observed effect. A smaller target effect is harder to distinguish from random variation, so it generally requires more events to reach the same planned power. For example, the primary comparison’s planning figures rise as the assumed fraction of the observed effect becomes smaller. The event targets differ by endpoint and observed effect; they should not be transferred from one comparison to another.

Event targets are not the same as enrollment targets. How many participants would be required to observe a given number of events depends on follow-up, event frequency, loss to follow-up, and allocation. Those inputs are not specified in these illustrations. The calculations are not observed power: they do not measure the probability that the completed trial detected an effect after the results were known. They are hypothetical design aids based on stated assumptions.

13. How the Sample Size Is Derived

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

Formula

d = 4 (z1−α/2 + z1−β)2 / [ln(HR)]2

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

  1. Hazard ratio HR = 1.100, so ln(HR) = 0.0953.
  2. d = 4 × (1.96 + 0.842)2 / [ln(1.100)]2 = 3,456.1, rounded up to 3,457 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 <- 1.1                              # 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(295646)
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 = 3,457 (80% power), 4,627 (90% power)
 75% of observed effect: events = 6,145 (80% power), 8,226 (90% power)
 50% of observed effect: events = 13,825 (80% power), 18,508 (90% power)
Simulated power with 3,457 events: 0.795 (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. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankCox Proportional Hazard 1.100.78 to 1.530.590

The registry reports the sponsor’s primary analysis as a Cox proportional hazards result from a log-rank analysis: hazard ratio 1.10, 95% confidence interval 0.78 to 1.53, and p = 0.59. The corresponding estimate and p-value in the analysis summary are 1.10 and 0.59. The registry does not flag a discrepancy between the reported analysis and the accompanying comparison record.

The reported result is therefore the appropriate starting point for describing what the sponsor’s analysis found. The planning calculations are separate illustrations based on observed effects and specified assumptions; they are not a replacement for the sponsor’s analysis, nor do they establish what the original trial was designed to detect. No discrepancy is flagged, so there is no indication in the record that a recalculated result should displace the sponsor’s reported estimate.

Some details needed to independently reproduce the sponsor analysis are not reported in the registry record. In particular, the exact contrast represented by the estimate across four groups, any covariate adjustment, treatment of censoring, and checks of proportional hazards are not specified. The reported value can be quoted faithfully, but its exact model interpretation cannot be expanded beyond the record.

15. Multiplicity, Missing Data and Analysis Populations

The registry record identifies a primary DFS outcome and several secondary outcomes: RFS and OS comparisons involving anastrozole versus tamoxifen and zoledronate versus no zoledronate. It lists six outcome measures and six analyses. The analysis plan’s approach to multiple testing is not reported in the registry record.

In general, multiplicity arises when more than one hypothesis is tested. If each test is judged using its own nominal threshold, the chance of at least one false-positive result across a collection of tests can be greater than for a single test. Common approaches include prespecifying a hierarchy, adjusting significance thresholds, or treating secondary analyses as exploratory. Which, if any, approach was used in this trial is not reported. The secondary p-values should therefore be interpreted as nominal reported results rather than assumed to have a multiplicity adjustment.

The primary analysis population is described as intent-to-treat, including all participants assigned to one of the four arms. This is a useful design-based principle in general because it retains participants in their randomized groups. However, the registry record does not explain how missing endpoint information, withdrawal, loss to follow-up, treatment discontinuation, or protocol deviations were handled. The number of participants with incomplete endpoint follow-up is not reported in the registry record.

The registry also does not state whether the secondary analyses used the same analysis population as the primary endpoint. Nor does it provide details of censoring rules, missing-data sensitivity analyses, or any imputation procedure. These omissions matter because time-to-event analyses depend on how follow-up ends and whether censoring is informative. No particular handling method should be presumed.

Additional details of the statistical plan—including the original sample-size justification, any interim analyses, and the planned hypothesis-testing sequence—are not reported in the registry record. Without these details, the posted findings can be described and their uncertainty assessed, but the full confirmatory status of each analysis cannot be established from the registry information alone.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
AZ (Arimidex+Zoledronate)6745014.9%
TZ (Tamoxifen+Zoledronate)10345022.9%
AC (Arimidex Control)5545312.1%
TC (Tamoxifen Control)9345020.7%
Participants with at least one serious adverse event
Serious adverse events by armAZ (Arimidex+Zoledronate)14.9%TZ (Tamoxifen+Zoledronate)22.9%AC (Arimidex Control)12.1%TC (Tamoxifen Control)20.7%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
AZ (Arimidex+Zoledronate)9 of 450
TZ (Tamoxifen+Zoledronate)7 of 450
AC (Arimidex Control)18 of 453
TC (Tamoxifen Control)8 of 450

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
AZ (Arimidex+Zoledronate)355 of 450
TZ (Tamoxifen+Zoledronate)320 of 450
AC (Arimidex Control)340 of 453
TC (Tamoxifen Control)290 of 450

Most frequent serious adverse event terms

Event termOrgan systemAZ (Arimidex+Zoledronate)TZ (Tamoxifen+Zoledronate)AC (Arimidex Control)TC (Tamoxifen Control)
Uterine polypReproductive system and breast disorders5 of 45052 of 4507 of 45339 of 450
Vaginal bleedingReproductive system and breast disorders3 of 45013 of 4507 of 4536 of 450
Uro-genital tract infectionInfections and infestations8 of 4507 of 4504 of 4536 of 450
Skin diseaseSkin and subcutaneous tissue disorders5 of 4508 of 4503 of 4538 of 450
FractureInjury, poisoning and procedural complications7 of 4504 of 4504 of 4536 of 450
Peripheral nerve diseaseNervous system disorders10 of 4501 of 4504 of 4534 of 450
Lung inflammationRespiratory, thoracic and mediastinal disorders2 of 4505 of 4505 of 4536 of 450
TendonitisMusculoskeletal and connective tissue disorders3 of 4505 of 4503 of 4532 of 450
Cutaneous reactionSkin and subcutaneous tissue disorders3 of 4505 of 4501 of 4533 of 450
Disease of liver / gallbladderHepatobiliary disorders2 of 4503 of 4502 of 4535 of 450

Most frequent non-serious adverse event terms

Event termOrgan systemAZ (Arimidex+Zoledronate)TZ (Tamoxifen+Zoledronate)AC (Arimidex Control)TC (Tamoxifen Control)
Bone painMusculoskeletal and connective tissue disorders185 of 450132 of 450128 of 45394 of 450
Other/minor (not categorized)General disorders119 of 450112 of 450107 of 453108 of 450
ArthralgiaMusculoskeletal and connective tissue disorders150 of 45065 of 450112 of 45352 of 450
FatigueGeneral disorders98 of 45082 of 45093 of 45370 of 450
Psychological disorder NOSPsychiatric disorders80 of 45074 of 45097 of 45370 of 450
HeadacheNervous system disorders85 of 45059 of 45063 of 45359 of 450
Nausea and vomitingGastrointestinal disorders48 of 45029 of 45032 of 45323 of 450
Impaired visionEye disorders29 of 45027 of 45022 of 45336 of 450
Lymphedema (arm, hand)Vascular disorders26 of 45031 of 45028 of 45329 of 450
Hot flushesVascular disorders25 of 45027 of 45025 of 45328 of 450

Serious events with the highest arm-level rate: uterine polyp (11.6%), vaginal bleeding (2.9%), peripheral nerve disease (2.2%), skin disease (1.8%), uro-genital tract infection (1.8%).

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

The registry lists serious adverse events for each arm, including the number at risk and the number affected: AZ, 450 at risk and 67 affected; TZ, 450 at risk and 103 affected; AC, 453 at risk and 55 affected; and TC, 450 at risk and 93 affected. These are the recorded group counts. They are not percentages, and no rate or between-group difference is calculated.

The record also lists other adverse events: AZ, 450 at risk and 355 affected; TZ, 450 at risk and 320 affected; AC, 453 at risk and 340 affected; and TC, 450 at risk and 290 affected. Death counts are listed as 9, 7, 18, and 8, respectively. The registry information does not say whether these deaths were attributed to treatment, nor does it provide details about timing or cause.

The listed serious-event terms include uterine polyp at 11.6%, vaginal bleeding at 2.9%, peripheral nerve disease at 2.2%, skin disease at 1.8%, uro-genital tract infection at 1.8%, and fracture at 1.6%. The record does not provide enough context to assign these terms to a particular treatment arm or to determine whether events were related to study treatment. These figures describe the posted safety information, not a causal comparison.

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

The primary result describes a relative time-to-event estimate for DFS across the four listed treatment groups. The hazard ratio is 1.10, with a 95% confidence interval from 0.78 to 1.53 and p = 0.59. The interval includes 1 and permits a range of possible relative hazard patterns. The result does not provide a precise estimate of no difference, and it does not establish an effect in either direction.

The estimate should not be translated into a claim about absolute survival probability, the number of recurrences prevented, or a difference in median DFS. Absolute event probabilities, numerical median values, and arm-specific primary event counts are not reported in the registry record. In addition, because the reported analysis includes all four groups and the exact contrast is not specified, the result cannot be treated as a clearly isolated comparison of anastrozole with tamoxifen or of zoledronate with no zoledronate.

The secondary analyses add information about RFS and OS, but they do not remove those limitations. Their endpoints differ from the primary composite, and the record does not state how multiple comparisons were handled. The secondary estimates should therefore be read as reported analyses with uncertainty, rather than as definitive confirmation of a broad treatment conclusion.

More generally, a nonsignificant p-value does not prove that treatments are equivalent, and a statistically notable p-value does not by itself establish clinical importance. Clinical importance depends on the magnitude and absolute consequences of an effect, its precision, the outcome definition, and the study context. The registry record does not provide enough absolute outcome detail to make those judgments fully.

The posted data also cannot establish that a treatment caused or prevented an adverse event. Safety counts are descriptive, and the record does not provide attribution or detailed comparative analyses. The study’s stated interest in bone loss is not accompanied by a bone-loss result in the outcomes summarized. These limits define what can and cannot be concluded from the registry record.

18. Why This Trial Matters Statistically

This trial is statistically informative because it places two endocrine treatments and the addition of zoledronate within a randomized, four-arm comparison. Such an arrangement can address more than one treatment question, but it also makes clear specification of contrasts especially important. The registry reports a single primary hazard ratio across all four groups, while the study objectives describe distinct comparisons. Without the exact model coding, the estimate’s target contrast is difficult to map directly to each objective.

The endpoint is also a composite time-to-event measure. DFS combines recurrence, second primary carcinoma, and death, which creates a clinically broad measure but can obscure whether the result is driven by one component. The registry’s lack of component-specific event counts and absolute survival estimates limits assessment of both the event composition and the magnitude of any differences.

The example illustrates why confidence intervals matter alongside p-values. The primary interval spans 1 and is broad enough to include more than one plausible hazard pattern. A nonsignificant result should not be mistaken for proof of equivalence, especially when the contrast definition and absolute outcome data are limited.

Finally, the record lists several secondary analyses without reporting a multiplicity strategy. That makes the secondary pattern valuable to describe but more cautious to interpret. The study demonstrates the statistical challenge of drawing a clear conclusion from multiple related endpoints and comparisons when the registry does not supply full analysis details. It highlights the importance of transparent contrast definitions, prespecified testing plans, and reporting absolute as well as relative outcomes.

19. Limitations

The registry record leaves several trial-specific uncertainties. Although the primary objective describes comparisons of anastrozole with tamoxifen and zoledronate with control, the reported primary hazard ratio is listed across all four treatment groups. The exact contrast and model coding are not reported. This limits the ability to attribute the primary estimate to either treatment question.

The numerical primary median DFS values and inter-quartile ranges are not reported for the arms. Nor are arm-specific DFS event counts or absolute survival probabilities at fixed times. The record describes a cut-off after 124 DFS events and a maximum time on study per patient of 102 months, but does not provide the distribution of follow-up or the number still at risk over time.

The analysis description is brief. The registry does not report covariate adjustment, proportional-hazards checks, censoring details, handling of missing follow-up, adherence, treatment discontinuation, or sensitivity analyses. It also does not describe the original sample-size justification, interim analyses, or multiplicity procedures. The original design assumptions are not reported in the registry record.

The trial had no masking recorded. This is a design characteristic that may be relevant when interpreting outcomes or event reporting, but the record does not provide information to quantify its influence. The adverse-event section lists group counts and selected serious-event terms, but does not provide enough detail on attribution, timing, or comparative statistical analysis to support causal conclusions.

Finally, although bone loss was part of the stated objective, a bone-loss outcome result is not included in the posted results summarized in the record. These gaps do not invalidate the reported estimates, but they narrow the conclusions that can be drawn from them.

20. Related Tutorials

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23. Record Summary

NCT00295646 is a completed, randomized, phase 3, parallel-group trial with no masking recorded. It enrolled 1803 premenopausal patients with hormone receptor-positive, non-metastatic breast cancer, described as stage I or II. The four arms combined tamoxifen or anastrozole with zoledronate or control.

The primary endpoint was DFS, defined as time from randomization to recurrence, second primary carcinoma, or death from any cause. The reported hazard ratio across the four groups was 1.10, with a 95% confidence interval from 0.78 to 1.53 and p = 0.59. The exact contrast represented by that estimate is not reported in the registry record.

Secondary analyses cover RFS and OS. The record also lists serious and other adverse-event counts, but the available information does not establish treatment attribution. Numerical median endpoint values, detailed model specifications, missing-data methods, and the multiplicity strategy are not reported in the registry record.

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