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Adenocarcinoma of the Prostate Phase 3 Time-to-Event Analysis NCT00110214

Docetaxel and Prednisone With or Without Bevacizumab in Treating Patients With Prostate Cancer That Did Not Respond to Hormone Therapy: Complete Statistical Analysis

This randomized phase III trial compared docetaxel and prednisone with docetaxel, prednisone, and bevacizumab in men with hormone-refractory prostate cancer. The primary outcome was overall survival; the registry also reports progression-free survival, PSA decline, and toxicity outcomes.

Trial start: 2005-04  ·  Enrollment: 1050  ·  Sponsor: National Cancer Institute (NCI)
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 Docetaxel and Prednisone With or Without Bevacizumab in Treating Patients With Prostate Cancer That Did Not Respond to Hormone Therapy (NCT00110214), a randomized phase 3 study. The primary outcome is Overall Survival.

1050
Enrollment
Phase 3
2
Arms
In the primary outcome
0.91
Hazard ratio
Docetaxel + Placebo vs Docetaxel + Bevac
0.70–1.05
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00110214
PhasePhase 3
ConditionAdenocarcinoma of the Prostate, Hormone-resistant Prostate Cancer, Recurrent Prostate Cancer
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment1050
Arms in the primary outcome2
Lead sponsorNational Cancer Institute (NCI)
Results postedYes

2. Clinical Question

Population

Men with prostate cancer that did not respond to hormone therapy were eligible for this study. The registry describes conditions including adenocarcinoma of the prostate, hormone-resistant prostate cancer, recurrent prostate cancer, and stage IV prostate cancer. It does not report a more detailed eligibility description in the outcomes record.

Intervention

Participants in the experimental arm received docetaxel and prednisone, with bevacizumab added. Docetaxel was given intravenously on day 1, and prednisone was taken orally on days 1-21. Bevacizumab was given intravenously on day 1.

Comparator

The comparison arm received docetaxel and prednisone with an intravenous placebo instead of bevacizumab. The study was randomized, double-blinded, and parallel-group, so the planned comparison was between these two treatment regimens.

Primary question

The primary question was whether overall survival differed between the regimens. Overall survival was measured from randomization until death from any cause. The registry reports median survival estimates and a sponsor-reported hazard ratio. Those results describe the observed trial comparison; they do not, by themselves, establish why any difference occurred or how it applies to people outside the study.

3. Trial Design

This was a randomized, double-blinded, placebo-controlled, parallel-group phase III trial sponsored by the National Cancer Institute (NCI). The registry reports enrollment of 1050. Participants were assigned to docetaxel and prednisone with either bevacizumab or placebo. The stated aim was to compare the regimens in patients with prostate cancer that did not respond to hormone therapy.

In the placebo arm, participants received docetaxel intravenously over 1 hour and placebo intravenously over 30-90 minutes on day 1, plus oral prednisone once daily on days 1-21. In the bevacizumab arm, docetaxel and prednisone were administered as in the placebo arm, with bevacizumab intravenously over 30-90 minutes on day 1. The registry lists laboratory biomarker analysis as an intervention, but does not give further details about it in the outcome information.

The registry gives a start date of 2005-04, a primary completion date of 2010-03, and a completed status. Overall survival and the listed secondary outcomes have a timeframe of the duration of study, up to 5 years; grade 3 or higher toxicity was assessed during treatment, up to 2 years. The observed group sizes differ slightly across outcomes: the overall survival and PSA results list 526.0 and 524.0 participants, while the toxicity results list 505.0 and 504.0. The reason for these outcome-specific denominators is not reported in the registry record.

The registry does not report the original statistical design assumptions, the planned enrollment rationale, or the intended analysis populations in the posted results. The sample-size illustrations are based on observed effects and should not be read as the trial’s original design calculations.

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

StageDocetaxel + PlaceboDocetaxel + Bevacizumab
STARTED526524
COMPLETED1721
NOT COMPLETED509503

Reasons for not completing this period:

ReasonDocetaxel + PlaceboDocetaxel + Bevacizumab
Never started treatment2120
Disease progression or death260151
Adverse Event115192
Refused further treatment5265
Other (not specified)6175

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.

CharacteristicUnitDocetaxel + PlaceboDocetaxel + BevacizumabTotal
Participants analysed5265241050
Age, Continuousyears69.3 (62.4 to 75.6)68.8 (63.0 to 74.4)69.0 (62.7 to 75.2)
Age, Customized: < 65 yearsparticipants174179353
Age, Customized: >=65 yearsparticipants352345697
Sex: Female, Male: FemaleParticipants000
Sex: Female, Male: MaleParticipants5265241050
Region of Enrollment: United Statesparticipants5265241050
24-month predicted survival probability: <10%participants9594189
24-month predicted survival probability: 10-29.9%participants184183367
24-month predicted survival probability: >=30%participants247247494
Prior history of arterial events: Yesparticipants423779
Prior history of arterial events: Noparticipants484487971

6. Primary Endpoint

The registry lists the primary outcome as Overall Survival, measured over Duration of study (up to 5 years).

ElementRegistry entry
Result typeMedian
Measure of spread95% Confidence Interval
Unitmonths
Endpoint classificationTime-to-Event Analysis

Overall survival (OS) was the primary endpoint. It was measured from the date of randomization to death due to any cause, with estimates calculated using the Kaplan-Meier method. A median survival is the time by which the estimated survival probability has reached one half; it summarizes the timing of deaths in the study population without requiring every participant to have died by the end of follow-up.

Overall survival is used in clinical trials because it captures a direct outcome—death from any cause—and does not require decisions about which signs or test results count as disease progression. Measuring from randomization also gives the comparison a common starting point for the assigned groups. The endpoint description does not indicate that deaths from particular causes were treated differently.

Median estimates are only one way to describe survival. The registry also reports a hazard ratio from a log-rank analysis. In general, a hazard ratio compares the instantaneous event rates over follow-up, subject to the assumptions of the analysis; it is not a direct comparison of median survival times. The posted record gives the median estimates, their 95% confidence intervals, and the sponsor-reported hazard ratio and p-value. It does not provide further detail on censoring or on whether the relative hazard changed over time.

7. Results Posted in the Registry

Hazard ratio: Docetaxel + Placebo vs Docetaxel + Bevacizumab

0.91

95% CI: 0.70 to 1.05

As reported in the registry

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Docetaxel + Placebo vs Doceta…0.680.740.820.900.991.08hazard 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
Proportion of Participants Who Experienced at Least a 50% Post-therapy PSA (Prostate-Specific Antigen) DeclineBinary EndpointRisk difference+11.5 pts (5.7 to 17.3)275 per arm
Progression-free Survival (PFS)Time-to-Event AnalysisHazard ratio0.80 (0.71 to 0.91)631 events
Proportion of Participants Who Experience (Maximum) Grade 3 or Higher ToxicitiesBinary EndpointRisk difference+19.2 pts (13.4 to 24.9)96 per arm

Proportion of Participants Who Experienced at Least a 50% Post-therapy PSA (Prostate-Specific Antigen) Decline

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Docetaxel + Bevacizumab-1.382.626.63111519risk difference (percentage points) vs control (95% CI)

Progression-free Survival (PFS)

Treatment effect versus the control arm
Forest plot of hazard ratio (as reported) vs control (95% CI)Docetaxel + Placebo vs Doceta…0.690.750.810.880.951.03hazard ratio (as reported) vs control (95% CI)

Proportion of Participants Who Experience (Maximum) Grade 3 or Higher Toxicities

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Docetaxel + Bevacizumab-1.993.789.56152127risk difference (percentage points) vs control (95% CI)

Across the secondary outcomes, the posted estimates show a pattern that is not captured by the primary endpoint alone: measures of PSA response and progression-free survival favor the bevacizumab-containing regimen in their reported comparisons, while the grade 3 or higher toxicity measure is higher in that arm. These outcomes address different dimensions of the trial and should not be collapsed into a single overall treatment effect.

Progression-free survival is the secondary measure most directly related to the time-to-event analysis used for overall survival, but it is not the same endpoint. PSA decline is a response measure, and toxicity describes harms recorded during treatment. A favorable result on a secondary efficacy measure does not override the OS result; conversely, the OS result does not make the other outcomes irrelevant. The primary and secondary findings need to be considered as distinct pieces of evidence.

Secondary outcomes generally carry less confirmatory weight when many endpoints are tested without a reported plan to control the chance of false-positive findings. The registry does not report a multiplicity strategy or a hierarchy for interpreting the secondary endpoints. The PSA p-value is described as unadjusted, and the registry does not report an adjustment for the set of secondary outcomes. This means a small p-value should not be read as if it had been evaluated in isolation under a prespecified, fully documented confirmatory framework.

The registry lists three secondary outcomes, but does not provide enough information to determine whether all planned outcomes, analyses, or timepoints are represented in the posted results. The appropriate summary is therefore the overall direction of the recorded endpoint estimates, coupled with caution about their multiplicity and the missing details of the analysis plan.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The median overall survival was 21.5 months in the docetaxel-plus-placebo arm and 22.6 months in the docetaxel-plus-bevacizumab arm. The corresponding 95% confidence intervals were 20.0 to 23.0 months and 21.1 to 24.5 months. The sponsor-reported hazard ratio was 0.91, with a 95% confidence interval from 0.7 to 1.05 and p = 0.181. The interval includes 1, and the p-value does not indicate a statistically significant difference at conventional thresholds. The result is therefore compatible with a range of relative effects; it is not evidence that the regimens are equivalent.

For the secondary outcomes, the posted point estimates show a higher proportion with at least a 50% post-therapy PSA decline in the bevacizumab arm, and longer median progression-free survival in that arm. The reported progression-free survival hazard ratio was 0.80, with a 95% confidence interval from 0.71 to 0.91 and p < 0.001. Grade 3 or higher toxicity was also more frequent in the bevacizumab arm in the posted outcome figures. These outcomes are relevant context but do not replace the primary overall-survival comparison.

The pattern across outcomes is not a single uniform measure of benefit or harm. PSA decline is a laboratory response measure, progression-free survival concerns time to progression or death as defined by the trial, and overall survival concerns death from any cause. Toxicity measures a different aspect of the treatment experience. The registry’s outcome descriptions do not provide detailed definitions of progression or the rules for evaluating PSA response, so those operational details are not reported in the registry record.

Secondary comparisons require caution because the registry does not report whether or how the analysis accounted for multiple outcomes. Testing many endpoints can increase the chance that at least one result appears noteworthy by chance. The PSA comparison is explicitly accompanied by an unadjusted p-value, and no reported multiplicity adjustment is described for the posted secondary results. Thus, the secondary findings are best viewed as supportive descriptions rather than as a substitute for the primary endpoint result.

These results describe the groups and outcomes recorded in this trial. They do not establish the biological mechanism behind the observed differences, and the record does not report enough detail to assess all aspects of follow-up, missingness, or analysis conduct. Interpretation should keep the distinction between a point estimate and its uncertainty in view.

10. Statistical Methods Explained

The overall-survival and progression-free survival outcomes are time-to-event measures. Such outcomes account for both whether an event occurred and the time until it occurred, while allowing follow-up to end before an event is observed for some participants. The registry says OS was estimated by the Kaplan-Meier method. In general, Kaplan-Meier estimation uses the observed event and follow-up information to estimate the probability of remaining event-free over time. The registry does not give details about censoring rules or the handling of missing follow-up.

What does a median survival describe?

A median time-to-event estimate is the point at which the estimated event-free proportion has reached one half. It is a useful summary of the middle of the estimated survival distribution, but it does not describe the entire curve. Groups can have similar medians while differing at other points in follow-up, or can have different medians without the same difference persisting throughout follow-up. The registry’s outcome data give medians and confidence intervals, but do not include a fuller description of the survival curves in the record details.

How should a hazard ratio be read?

A hazard ratio summarizes the relative instantaneous event rate between groups over the observed follow-up under the model or test framework used. A value around 1 indicates similar estimated event rates; values on either side of 1 indicate relative differences according to the comparison’s group ordering. A hazard ratio is not a ratio of median times, nor does it directly state the percentage of participants who experienced an event. Its interpretation can also be less straightforward if the relative event rate changes over time. Whether that assumption was assessed is not reported in the registry record.

For OS, the registry reports a hazard ratio of 0.91 with a 95% confidence interval from 0.7 to 1.05 and p = 0.181, using a log-rank method. The interval spans 1, so the data are compatible with relative event rates on either side of 1 under this summary. For progression-free survival, the reported hazard ratio is 0.80, with a 95% confidence interval from 0.71 to 0.91 and p < 0.001. These values are the sponsor-reported analyses. They should not be reconstructed from the medians, because medians do not contain enough information to reproduce a time-to-event comparison.

What does the log-rank test contribute?

In general, a log-rank test compares the event experience of groups across follow-up, accounting for the timing of events and the risk sets at each event time. Its p-value describes how incompatible the observed group pattern is with the null hypothesis of no difference, under the test’s assumptions. A p-value is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The registry identifies the log-rank method for the reported OS and progression-free survival comparisons.

How are binary outcomes different?

PSA decline and grade 3 or higher toxicity are reported as percentages of participants. These outcomes classify participants according to whether they met a stated criterion during the defined timeframe, rather than describing time to an event. The registry’s PSA analysis reports a chi-squared test with p < 0.001. The additional risk-difference, risk-ratio, and odds-ratio values are unadjusted re-calculations from the posted summary statistics. In general, a risk difference compares proportions by subtraction, a risk ratio compares them as a ratio, and an odds ratio compares odds. These measures answer related but distinct questions, so their numerical scales should not be treated as interchangeable.

The toxicity outcome gives the percentages experiencing maximum grade 3 or higher toxicity. The outcome record does not list a reported sponsor analysis for that endpoint. Its posted comparison is therefore descriptive and accompanied by the unadjusted re-calculation, rather than a documented sponsor test. A general statistical reason to consider over-dispersion is that outcomes can vary more than a simple probability model anticipates, for example when observations are more heterogeneous than assumed. The registry does not report a model for over-dispersion or indicate that one was used.

Confidence intervals express uncertainty around estimates under the analysis method. A 95% confidence interval is generated by a procedure that, under its assumptions, would cover the target parameter in 95% of repeated applications. It is not a statement that there is a 95% probability that this particular interval contains the true value. The interval’s width indicates how precisely the estimate is determined by the data and method, while its position indicates which values are more or less compatible with the observations.

The registry labels the OS analysis type as non-inferiority or equivalence, but does not report the non-inferiority margin, equivalence bounds, or the corresponding decision criteria. Without those details, the reported hazard ratio and p-value do not establish non-inferiority or equivalence. The record’s posted numerical result can be described, but the full interpretation of the design label is not reported in the registry record.

11. Confidence Intervals and Precision

The OS median estimates are 21.5 months for docetaxel plus placebo and 22.6 months for docetaxel plus bevacizumab. Their 95% confidence intervals are 20.0 to 23.0 months and 21.1 to 24.5 months, respectively. These intervals convey uncertainty in each median estimate. Their overlap does not by itself determine whether the between-group comparison is statistically significant; that question is addressed by the reported comparison, which gives a hazard ratio of 0.91, a 95% confidence interval from 0.7 to 1.05, and p = 0.181.

The hazard-ratio interval includes 1, leaving uncertainty about the direction of the relative event-rate difference. The p-value is consistent with the interval’s failure to exclude 1. Neither the point estimate nor the p-value proves that there is no difference. A non-significant result can reflect a small underlying effect, limited precision, or both; the registry record does not identify which explanation applies.

For progression-free survival, the reported hazard ratio is 0.80, with a 95% confidence interval from 0.71 to 0.91. The interval does not include 1 and the reported p-value is < 0.001. The median estimates and their intervals are also reported for each arm. These results indicate a more precise relative estimate for progression-free survival than the OS comparison in the sense that the reported hazard-ratio interval does not span 1, but they do not answer the primary overall-survival question.

Confidence intervals do not account for every potential source of uncertainty. Their interpretation depends on the analysis method and available follow-up. The registry record does not report detailed missing-data handling, censoring rules, or assessment of model assumptions. Those omissions limit how fully the precision of the estimates can be evaluated.

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 effect0.913,5304,726
75% of the observed effect0.936,2768,401
50% of the observed effect0.9514,12018,902
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: Docetaxel + Placebo vs Docetaxel + Bevacizumab.

The planning illustrations translate an assumed effect into a target for a future study; they are not the number of participants or events observed in this trial. For time-to-event outcomes, the figures are total event targets. For the other outcomes, the figures are participants per arm. The distinction matters: an event target is not a group enrollment target, while a per-arm participant target applies separately to each study group.

The calculations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is set to the stated fraction of the observed effect. The survival illustrations use the Schoenfeld method. The 80% power column describes the event or participant target that would give the assumed design an 80% chance of detecting the specified effect at the stated significance level, if the assumptions hold. The 90% power column gives the corresponding target for 90% power. These are planning probabilities under the calculation’s assumptions, not guarantees about a future study.

Rows for 100%, 75%, and 50% of the observed effect show how the target changes when planning for effects smaller than the observed estimate. Smaller effects require more information to distinguish them from no difference, so the participant or event targets increase as the assumed effect becomes smaller. For a time-to-event outcome, that means more events are needed; for a binary outcome, it means more participants per arm.

The original trial’s sample-size justification, planned effect size, and design assumptions are not reported in the registry record. The planning illustrations are based on the observed effect and are not observed power. They should be read as sensitivity illustrations about study planning, not as a retrospective score of the trial’s success.

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 = 0.910, so ln(HR) = -0.0943.
  2. d = 4 × (1.96 + 0.842)2 / [ln(0.910)]2 = 3,529.8, rounded up to 3,530 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 <- 0.91                              # 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(110214)
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 = 3,530 (80% power), 4,726 (90% power)
 75% of observed effect: events = 6,276 (80% power), 8,401 (90% power)
 50% of observed effect: events = 14,120 (80% power), 18,902 (90% power)
Simulated power with 3,530 events: 0.801 (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 7,428 participants in total, with the boundaries below.

AnalysisCalendar time (months)EventsEfficacy boundary (z)Nominal one-sided pCumulative alpha spent
Look 120.91,5933.7100.00010.0001
Look 233.63,1872.5110.00600.0060
Look 360.04,7801.9930.02310.0250
01234z = 3.7121 mo1593 eventsz = 2.5134 mo3187 eventsz = 1.9960 mo4780 eventsUpper efficacy boundary (z)

Fixed design versus group-sequential alternatives

DesignPowerEvents at final analysisParticipantsStudy length (months)
Fixed design, one analysis80%3,5295,48460.0
Two looks, O'Brien-Fleming80%3,5425,50460.0
Three looks, O'Brien-Fleming80%3,5745,55460.0
Three looks, Pocock80%4,1306,41860.0
Fixed design, one analysis90%4,7247,34260.0
Two looks, O'Brien-Fleming90%4,7417,36760.0
Three looks, O'Brien-Fleming90%4,7807,42860.0
Three looks, Pocock90%5,4538,47460.0

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 assumedHazard ratioEvents at final analysisParticipants
100% of the observed effect0.9104,7807,428
75% of the observed effect0.9328,49913,130
50% of the observed effect0.95419,12429,376

For context, this trial enrolled 1,050 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 <- 21.5          # control-arm median, months (converted from the posted unit)
hr          <- 0.91          # 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: 6462         p (1-sided)   0.0001
 Events: 1594        ~HR at bound   0.8304
    Month: 21    P(Cross) if HR=1   0.0001
              P(Cross) if HR=0.91   0.0338
    IA 2: 67%                   Z   2.5114
      N: 7428         p (1-sided)   0.0060
 Events: 3187        ~HR at bound   0.9149
    Month: 34    P(Cross) if HR=1   0.0060
              P(Cross) if HR=0.91   0.5603
        Final                   Z   1.9930
      N: 7428         p (1-sided)   0.0231
 Events: 4781        ~HR at bound   0.9440
    Month: 60    P(Cross) if HR=1   0.0250
              P(Cross) if HR=0.91   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

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.910.7 to 1.050.181

For overall survival, the registry reports the sponsor’s log-rank analysis as a hazard ratio of 0.91, with a 95% confidence interval from 0.7 to 1.05 and p = 0.181. The same reported analysis is used for the time-to-event interpretation; no separate recalculated hazard ratio is presented. The registry’s comparison description and the reported analysis give the same estimate and inferential result, and no discrepancy is flagged.

This distinction matters because a hazard ratio depends on event timing and follow-up information that cannot be recovered from arm-level medians alone. A simple calculation from the posted medians would not reproduce the sponsor’s time-to-event analysis. The sponsor’s reported analysis therefore takes precedence for describing the OS comparison.

For PSA decline, the registry reports a chi-squared analysis with p < 0.001. The associated risk-difference, risk-ratio, and odds-ratio estimates are unadjusted re-calculations from the posted summary statistics, not additional sponsor-reported adjusted analyses. For progression-free survival, the registry reports a log-rank hazard ratio of 0.80, its 95% confidence interval, and p < 0.001. The posted toxicity outcome has no reported sponsor analysis. Readers should distinguish those reported tests from descriptive or recalculated comparisons, and should not treat them as if they came from one common adjusted model.

16. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study evaluates more than one endpoint, comparison, or analysis. Even if each test is conducted at a fixed significance level, repeated testing can raise the overall chance of at least one result crossing that threshold by chance. Strategies such as prioritizing a primary endpoint or adjusting for multiple comparisons can address this issue, but the registry does not report a multiplicity procedure or a complete testing hierarchy for this trial.

The registry identifies overall survival as the primary outcome and lists PSA decline, progression-free survival, and grade 3 or higher toxicity as secondary outcomes. It reports a p-value for the primary survival comparison, a p-value for the PSA analysis, and a p-value for progression-free survival. It does not report a sponsor analysis for the toxicity outcome. The record does not explain whether the secondary outcomes were prespecified in this order, whether additional analyses were conducted, or whether any p-values were adjusted.

The outcome populations and analysis populations are also not fully described. The registry reports arm-specific denominators for the posted outcomes, but does not state whether analyses followed an intention-to-treat approach, whether participants were excluded from particular analyses, or why denominators differ between outcomes. Missing outcome data, losses to follow-up, censoring rules, and imputation procedures are not reported in the registry record.

The registry’s OS analysis is labeled non-inferiority or equivalence, but it does not provide the non-inferiority margin, equivalence bounds, or the prespecified decision rule. A non-significant p-value alone cannot demonstrate equivalence or non-inferiority. Those conclusions require the appropriate margin-based criteria and a documented analysis plan.

These gaps do not invalidate the numerical results, but they constrain what can be concluded about confirmatory status, selection of analyses, and robustness to missing data. The observed estimates should be interpreted alongside the stated limits of what the registry record documents.

17. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Docetaxel + Placebo23750546.9%
Docetaxel + Bevacizumab17850435.3%
Participants with at least one serious adverse event
Serious adverse events by armDocetaxel + Placebo46.9%Docetaxel + Bevacizumab35.3%% of participants with at least one serious adverse event

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
Docetaxel + Placebo420 of 505
Docetaxel + Bevacizumab363 of 504

Most frequent serious adverse event terms

Event termOrgan systemDocetaxel + PlaceboDocetaxel + Bevacizumab
Neutrophils/granulocytes (ANC/AGC)Investigations67 of 50546 of 504
FeverGeneral disorders43 of 50532 of 504
Leukocytes (total WBC)Investigations39 of 50525 of 504
InfectionInfections and infestations35 of 50527 of 504
Fatigue (asthenia, lethargy, malaise)General disorders39 of 50522 of 504
Hemorrhage, GIGastrointestinal disorders38 of 50518 of 504
Thrombosis/thrombus/embolismVascular disorders17 of 50528 of 504
Febrile neutropeniaBlood and lymphatic system disorders25 of 50519 of 504
PainNervous system disorders25 of 50519 of 504
DehydrationMetabolism and nutrition disorders27 of 50514 of 504

Most frequent non-serious adverse event terms

Event termOrgan systemDocetaxel + PlaceboDocetaxel + Bevacizumab
HypertensionVascular disorders156 of 50582 of 504
Neutrophils/granulocytes (ANC/AGC)Investigations110 of 50597 of 504
Hemorrhage pulmonary/upper respiratoryRespiratory, thoracic and mediastinal disorders153 of 50554 of 504
ProteinuriaRenal and urinary disorders89 of 50570 of 504
Fatigue (asthenia, lethargy, malaise)General disorders90 of 50551 of 504
FeverGeneral disorders77 of 50550 of 504
Rash/desquamationSkin and subcutaneous tissue disorders69 of 50556 of 504
Leukocytes (total WBC)Investigations56 of 50550 of 504
Glucose serum-high (hyperglycemia)Metabolism and nutrition disorders48 of 50540 of 504
PainNervous system disorders44 of 50534 of 504

Serious events with the highest arm-level rate: neutrophils/granulocytes (anc/agc) (13.3%), fever (8.5%), fatigue (asthenia, lethargy, malaise) (7.7%), leukocytes (total wbc) (7.7%), hemorrhage, gi (7.5%).

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 reports serious adverse event figures separately from the broader grade 3 or higher toxicity outcome. For serious adverse events, the listed at-risk counts are 505 in the docetaxel-plus-placebo arm and 504 in the docetaxel-plus-bevacizumab arm. The numbers reported as affected are 237 and 178, respectively. The record also gives other adverse-event affected counts of 420 and 363, with the same arm-specific at-risk counts. These are counts, not percentages; no rate or between-group difference is calculated.

The listed serious adverse-event terms include neutrophils/granulocytes (ANC/AGC), 13.3%; fever, 8.5%; fatigue (asthenia, lethargy, malaise), 7.7%; leukocytes (total WBC), 7.7%; hemorrhage, GI, 7.5%; and infection, 6.9%. The registry does not identify these listed percentages as arm-specific in the registry record for the outcome, so they should not be assigned to either arm. The deaths field is not reported in the registry record.

Serious adverse events and maximum grade 3 or higher toxicities are different summaries. The latter is a secondary outcome assessed during treatment, up to 2 years, and the posted proportions are 56.2% and 75.4% for the placebo and bevacizumab arms, respectively. The serious-event counts alone do not establish causation or capture the full balance of risks and benefits.

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

The registry’s primary result is a comparison of overall survival between docetaxel and prednisone with placebo and the same regimen with bevacizumab. The median estimates are 21.5 months and 22.6 months. The sponsor-reported hazard ratio is 0.91, with a 95% confidence interval from 0.7 to 1.05 and p = 0.181. These data do not show a statistically significant OS difference in the reported analysis, but they also do not prove that the regimens are equivalent or that no difference exists.

The secondary results provide additional, but distinct, information. PSA response and progression-free survival estimates favor the bevacizumab arm in the registry’s reported comparisons, while the grade 3 or higher toxicity proportion is greater in that arm. The available record does not report a multiplicity adjustment, full analysis populations, or all operational details of the outcomes. These factors limit the strength of conclusions drawn from secondary comparisons.

The results apply to the study’s enrolled population and the regimens as described in the registry. They do not establish how results would differ for other populations, treatment settings, or treatment schedules. The record does not provide a detailed eligibility protocol, subgroup results, or the original sample-size assumptions. It also does not report the non-inferiority margin despite labeling the primary analysis as non-inferiority or equivalence.

Statistical significance is not the same as clinical importance, and an estimate’s uncertainty should be considered along with its point value. The OS confidence interval includes relative effects on either side of 1, while the progression-free survival interval does not. Neither pattern alone resolves all questions about the overall clinical value of the regimen. The registry reports outcomes; it does not provide medical advice or determine an individual treatment choice.

19. Why This Trial Matters Statistically

This trial illustrates why a primary endpoint should remain central when several outcomes are reported. The overall-survival comparison is the primary question, and its reported hazard ratio interval includes 1. The more favorable point estimates for PSA response and progression-free survival are informative, but they answer different questions and do not replace the primary survival result.

It also demonstrates the value of separating time-to-event measures from binary outcomes. Survival analyses use event timing and follow-up, while PSA response and toxicity proportions classify participants according to whether an outcome occurred. Each requires a different summary and interpretation. A median, hazard ratio, percentage, and risk difference cannot be treated as interchangeable descriptions of the same effect.

Precision and analysis transparency matter alongside the estimates themselves. Confidence intervals show the range of values compatible with the analysis, while the registry’s limited reporting of multiplicity, missing data, analysis populations, and non-inferiority criteria restricts how fully the results can be assessed. The sample-size illustrations also clarify that planning targets depend on the effect size investigators aim to detect; smaller effects require more events or participants under the stated assumptions.

Together, these statistical features make the record useful for learning how endpoint choice, uncertainty, multiple comparisons, and safety outcomes shape interpretation. They also show why a single p-value should not carry the full weight of a trial’s conclusions.

20. Limitations

The registry’s posted results do not include detailed eligibility criteria, baseline characteristics, or subgroup estimates. It is therefore not possible from this record to assess how the enrolled groups were distributed across important prognostic characteristics or whether results differed across subgroups.

The record does not describe missing-data handling, censoring rules, follow-up completeness, or the analysis populations used for each endpoint. The outcome-specific denominators differ, but the reasons are not reported. This limits assessment of whether the reported estimates reflect all randomized participants or a subset defined by outcome availability.

The OS analysis is labeled non-inferiority or equivalence, yet the registry does not state the margin, decision criteria, or design assumptions required to interpret that label. The original sample-size rationale and interim analysis plan are also not reported in the registry record. The planning illustrations based on observed effects do not fill those gaps.

For secondary outcomes, the registry does not report an adjustment for multiple comparisons or a complete hierarchy of planned tests. It also gives limited operational detail about the definition of progression, PSA response assessment, and toxicity ascertainment. The serious adverse-event terms are not identified by arm in the posted information, and the deaths field is not reported in the registry record.

These reporting limits do not change the numerical results that are posted, but they reduce the ability to evaluate robustness, potential bias, and the confirmatory status of secondary findings. Conclusions should remain tied to the outcomes and statistical details the registry records.

21. Related Tutorials

22. Related Statistical Calculators

23. Sources

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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

NCT00110214 is a completed randomized, double-blinded, placebo-controlled phase III trial sponsored by the National Cancer Institute (NCI). It compared docetaxel and prednisone with placebo against docetaxel and prednisone with bevacizumab in men with prostate cancer that did not respond to hormone therapy. The registry reports enrollment of 1050.

Overall survival was the primary endpoint. The median estimates were 21.5 months and 22.6 months, with a sponsor-reported hazard ratio of 0.91, 95% confidence interval 0.7 to 1.05, and p = 0.181. Secondary outcomes included PSA decline, progression-free survival, and grade 3 or higher toxicity. The registry reports favorable point estimates for PSA decline and progression-free survival in the bevacizumab arm and a higher grade 3 or higher toxicity proportion in that arm.

The registry does not report key details including the original statistical design assumptions, multiplicity plan, analysis populations, and missing-data procedures. Those omissions should be considered when weighing the posted estimates.

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