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Cardiovascular Disease Phase 3 Event-Rate Endpoint NCT01975376

The Evaluation of Bococizumab (PF-04950615;RN316) in Reducing the Occurrence of Major Cardiovascular Events in High Risk Subjects: Complete Statistical Analysis

This analysis examines the registry results for bococizumab versus placebo on first major cardiovascular events in high-risk participants receiving background lipid-lowering therapy. It explains the primary event-rate comparison, the sponsor’s time-to-event analysis, and the limits of the posted results.

Trial start: 2013-10-29  ·  Enrollment: 16784  ·  Sponsor: Pfizer
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 The Evaluation of Bococizumab (PF-04950615;RN316) in Reducing the Occurrence of Major Cardiovascular Events in High Risk Subjects (NCT01975376), a randomized phase 3 study. The primary outcome is Event Rate Per 100 Participant-Years For First Occurrence of Major Cardiovascular (CV) Event.

16784
Enrollment
Phase 3
2
Arms
In the primary outcome
1.00
Rate ratio
Bococizumab (PF-04950615)
0.80–1.24
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01975376
PhasePhase 3
ConditionCardiovascular Disease
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment16784
Arms in the primary outcome2
Lead sponsorPfizer
Results postedYes

2. Clinical Question

Population

High-risk subjects with cardiovascular disease who were receiving background lipid-lowering therapy and had LDL-C >= 70 mg/dL (1.8 mmol/L) or non-HDL-C >= 100 mg/dL (2.6 mmol/L). The primary outcome description refers to a full analysis set of randomized participants, with exclusions described in part; the full population definition is not reported in the registry record.

Intervention

Bococizumab (PF-04950615), 150 mg administered subcutaneously every 2 weeks.

Comparator

Placebo administered subcutaneously every 2 weeks.

Primary question

What was the event rate per 100 participant-years for the first adjudicated major cardiovascular event in each randomized group, and how did the rate comparison and its uncertainty describe the difference between groups?

The registry describes a randomized, placebo-controlled comparison in high-risk subjects on background lipid-lowering therapy. The primary outcome combined cardiovascular death, non-fatal myocardial infarction, non-fatal stroke, and hospitalization for unstable angina requiring urgent revascularization. The comparison concerns the rate of first events over follow-up, rather than a simple count that ignores how long participants were observed.

The posted primary rates were 3.02 events per 100 participant-years for placebo and 3.01 for bococizumab. The recalculated rate ratio was 0.997, with a 95% confidence interval from 0.804 to 1.236. Those figures describe the observed rates and the uncertainty in their relative comparison; they do not, by themselves, establish a cause for any difference. The record does not report the reason the study was terminated.

3. Trial Design

This was a phase 3, randomized, quadruple-masked, parallel-group study with placebo control. The registry lists an enrollment of 16784. The primary outcome analysis lists 8390 participants in the placebo group and 8394 in the bococizumab group. The study evaluated bococizumab, identified also as PF-04950615 and RN316, among high-risk subjects receiving background lipid-lowering therapy.

The intervention was bococizumab 150 mg by subcutaneous administration every 2 weeks; the comparator was placebo by the same route and schedule. Eligibility in the brief description included LDL-C >= 70 mg/dL (1.8 mmol/L) or non-HDL-C >= 100 mg/dL (2.6 mmol/L). The primary endpoint was the first adjudicated and confirmed major cardiovascular event, with follow-up described as from baseline until that event and a maximum duration of up to 3.4 years.

The registry lists a start date of 2013-10-29, a primary completion date of 2017-03-22, and status as terminated. The reason for termination and the date or circumstances of termination are not reported in the registry record. The registry’s title and summary describe the study’s aim, but its original sample-size justification, planned number of events, and trial-specific statistical design assumptions are not reported in the registry record.

Randomization supports a comparison of the assigned groups, while masking is intended to limit influence from knowledge of assignment. The registry identifies the masking level as quadruple but does not specify in the posted information which participant, investigator, or other roles were masked. Details of implementation, allocation concealment, and any departures from assigned treatment 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

StagePlaceboBococizumab (PF-04950615)
STARTED83908394
Treated83748386
COMPLETED81648177
NOT COMPLETED226217

Reasons for not completing this period:

ReasonPlaceboBococizumab (PF-04950615)
Adverse Event55
Death6572
Lost to Follow-up7066
Withdrew consent6862
Other24
Randomized, Not Treated168

Analysis population for the primary outcome, as defined in the registry: Full analysis set (FAS): all participants who were randomized, excluding who attempted to be randomized more than once into a bococizumab CV outcomes trial (B1481022/B1481038) or attempted to be randomized in more than 1 CV outcomes trial and all participants enrolled at study Site 3027 where a quality-related event was identified.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: Full analysis set (FAS): all participants who were randomized, excluding who attempted to be randomized more than once into a bococizumab cardiovascular (CV) outcomes trial (B1481022/B1481038) or attempted to be randomized in more than 1 CV outcomes trial and all participants enrolled at study Site 3027 where a quality-related event was identified.

CharacteristicUnitPlaceboBococizumab (PF-04950615)Total
Participants analysed8390839416784
Age, ContinuousYears63.3 (SD 9.2)63.3 (SD 9.1)63.3 (SD 9.1)
Sex: Female, Male: FemaleParticipants222322074430
Sex: Female, Male: MaleParticipants6167618712354
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants175817463504
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants6631664213273
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants167
Race (NIH/OMB): American Indian or Alaska NativeParticipants000
Race (NIH/OMB): AsianParticipants354369723
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants392412804
Race (NIH/OMB): WhiteParticipants7315728014595
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants329333662

6. Primary Endpoint

The registry lists the primary outcome as Event Rate Per 100 Participant-Years For First Occurrence of Major Cardiovascular (CV) Event, measured over From baseline until the date of first adjudicated and confirmed occurrence of major CV event (maximum duration: up to 3.4 years).

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
UnitEvents Per 100 Participant-Years
Endpoint classificationEvent-Rate Endpoint

The primary endpoint is the event rate per 100 participant-years for the first occurrence of a major cardiovascular event. The composite includes cardiovascular death, non-fatal myocardial infarction, non-fatal stroke, and hospitalization for unstable angina requiring urgent revascularization. The event was described as adjudicated by an Adjudication Committee, and the outcome timeframe extends from baseline to the first adjudicated and confirmed event, with a maximum duration of up to 3.4 years.

An event rate uses the number of events in relation to participant-time at risk. This is useful when participants contribute different amounts of observed follow-up: the rate expresses event occurrence relative to exposure time rather than treating every participant as though follow-up were identical. The registry states that its rate was calculated as events per 100 participant-years at risk.

The endpoint focuses on the first event in the composite for each participant, not every recurrence. Combining several clinically defined event types produces a broader outcome than any one component alone, but the components may differ in nature and frequency. The posted primary result is therefore an overall comparison of the composite rate. It does not establish that every component had the same pattern, and component-specific results must be interpreted separately where reported.

The registry’s primary outcome population is described as a full analysis set, with exclusions for certain attempted duplicate randomizations and participants enrolled at a specified site. That description is truncated in the registry record, so the complete population criteria are not reported there.

7. Results Posted in the Registry

Rate ratio: Bococizumab (PF-04950615)

1.00

95% CI: 0.80 to 1.24

Recalculated from the posted summary statistics

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Bococizumab (PF-04950615)0.780.860.951.051.161.28rate ratio 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
Event Rate Per 100 Participant-Years For First Occurrence of Composite Endpoint of Cardiovascular Death, Non-Fatal Myocardial Infraction, or Non-Fatal StrokeEvent-Rate EndpointRate ratio1.04 (0.82 to 1.31)117,287 per arm
Event Rate Per 100 Participant-Years For First Occurrence of Composite Endpoint of All-Cause Death, Non-Fatal Myocardial Infraction, Non-Fatal Stroke, or Hospitalization for Unstable Angina Needing Urgent RevascularizationEvent-Rate EndpointRate ratio0.99 (0.81 to 1.21)1,792,942 per arm
Event Rate Per 100 Participant-Years For First Occurrence of Composite Endpoint of All-Cause Death, Non-Fatal Myocardial Infarction, or Non-Fatal StrokeEvent-Rate EndpointRate ratio1.03 (0.83 to 1.27)217,877 per arm

Event Rate Per 100 Participant-Years For First Occurrence of Composite Endpoint of Cardiovascular Death, Non-Fatal Myocardial Infraction, or Non-Fatal Stroke

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Bococizumab (PF-04950615)0.790.880.991.101.221.36rate ratio vs control (95% CI)

Event Rate Per 100 Participant-Years For First Occurrence of Composite Endpoint of All-Cause Death, Non-Fatal Myocardial Infraction, Non-Fatal Stroke, or Hospitalization for Unstable Angina Needing Urgent Revascularization

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Bococizumab (PF-04950615)0.790.860.951.041.141.25rate ratio vs control (95% CI)

Event Rate Per 100 Participant-Years For First Occurrence of Composite Endpoint of All-Cause Death, Non-Fatal Myocardial Infarction, or Non-Fatal Stroke

Treatment effect versus the control arm
Forest plot of rate ratio vs control (95% CI)Bococizumab (PF-04950615)0.800.880.981.081.191.32rate ratio vs control (95% CI)

The posted secondary outcomes cover additional composites and individual cardiovascular event categories, expressed as event rates per 100 participant-years. The comparisons reported for the available secondary outcomes do not suggest a consistent separation between groups: some estimates are below 1 and some above 1, and their confidence intervals include 1. This broad pattern is compatible with the primary comparison, whose rate ratio is also close to 1 with an interval including equal rates.

The secondary results do not change the meaning of the primary result. They provide additional views of event combinations and components, but differences in endpoint definition can change event frequency and precision. A composite that includes additional events is not identical to the primary composite, and an individual component may be less frequent than a broader composite. Estimates should therefore be interpreted according to the specific outcome they measure.

The registry lists 26 secondary outcomes as posted and 27 outcome measures overall. It also lists 34 analyses. Multiple outcomes and analyses create multiple opportunities to observe estimates that appear separated by chance. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for these secondary analyses. Unadjusted secondary p-values, where reported, consequently carry less weight than a result interpreted under a fully specified multiplicity plan.

The secondary pattern is best treated as descriptive and supportive context, rather than as a set of independent confirmatory tests. The registry does not report enough detail to determine whether all secondary analyses were prespecified, how missing outcomes were handled, or how the multiplicity of comparisons was addressed. Those omissions limit how strongly the secondary results can be used to make claims beyond the primary endpoint.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted primary event rates were 3.02 events per 100 participant-years for placebo and 3.01 for bococizumab. The recalculated rate ratio was 0.997, with a 95% confidence interval of 0.804 to 1.236. A rate ratio of 1 represents equal rates; the interval includes that value and also includes values on either side. The estimate is therefore close to equality, while the interval allows for a range of relative rate differences.

The unadjusted recalculated p-value was 0.976. This is consistent with the uncertainty expressed by the interval: the posted summary statistics do not provide evidence of a clear separation in primary event rates. It is not a probability that either treatment assignment is effective or ineffective, and it does not quantify the probability that the null hypothesis is true.

The sponsor’s own posted analysis is a log-rank comparison reported as a hazard ratio of 0.99, with a 95% confidence interval from 0.80 to 1.22. This is a time-to-event measure rather than the rate ratio recalculated from the posted event rates. Both estimates are near 1, and both intervals include 1. The two estimates are not identical because they describe the comparison using different statistical summaries and methods.

The primary result should be read as a comparison of the observed first-event rates during the recorded follow-up, alongside substantial uncertainty about the relative rate. It is not a comparison of risk at one fixed follow-up time, nor does the event rate identify how many participants had an event without regard to time at risk. The posted values do not explain why the study was terminated or whether termination affected follow-up or the analysis.

The registry describes a full analysis set, but the population definition is incomplete in the posted outcome record. The reported arm sizes and rates are useful for understanding the analysis, yet readers cannot fully assess the handling of exclusions, missing observations, or adherence from the information recorded. These issues do not alter the arithmetic of the posted comparison, but they limit interpretation of how closely the reported analysis follows the original trial plan.

The recalculation is unadjusted and uses posted summary rates and confidence limits. The registry also reports a sponsor analysis using a log-rank method. Since the discrepancy indicator is false, there is no recorded conflict between the recalculation and sponsor analysis requiring one result to supersede the other. The distinctions in estimand and method remain important: the recalculated rate ratio and sponsor-reported hazard ratio should not be treated as interchangeable quantities.

Overall, the primary data describe similar observed event rates and a relative comparison with a confidence interval that includes equal rates. The result is informative about the estimate and its precision in this trial record, but it does not settle questions beyond the recorded endpoint, population, and follow-up.

10. Statistical Methods Explained

What does an event rate represent?

General explanation: An event rate relates events to the amount of time participants were observed and at risk. The registry reports the primary measure as events per 100 participant-years and says it is calculated from event counts and participant-time at risk. This exposure-based measure can accommodate differing observation times. It is distinct from a proportion of participants with an event by a fixed date, and the registry does not give a fixed-time risk estimate as the primary result.

The primary outcome concerns the first occurrence of a composite event. In this setting, the rate comparison concerns first events, not repeated events per participant. The record describes event adjudication and confirmation, but does not report additional detail about the adjudication process or the handling of events that could not be confirmed.

How should the rate ratio be read?

General explanation: A rate ratio compares the event rate in one group with the rate in the reference group. A ratio of 1 indicates equal rates; a value below 1 indicates a lower estimated rate in the numerator group, and a value above 1 indicates a higher estimated rate. The recalculated primary rate ratio is 0.997, comparing bococizumab with placebo. Its 95% confidence interval is 0.804 to 1.236, so it includes the equal-rate value of 1.

The confidence interval describes a range of values reasonably compatible with the data under the statistical model and its assumptions. It is not a range containing a known fixed percentage of individual outcomes, and it is not a guarantee that the true value lies inside it. Its width is one indication of precision: a wider interval permits a broader set of relative effects than a narrower interval.

Why is a Poisson model relevant?

General explanation: Poisson methods are commonly used to model event counts relative to exposure time. They rely on assumptions about how event counts vary around their expected rates. Over-dispersion means that observed variability is greater than the model expects; if it is present but not accounted for, standard errors and confidence intervals may not reflect the actual uncertainty. The recalculation is marked as Poisson-based, but whether over-dispersion was assessed, and what model diagnostics were used, are not reported in the registry record.

The recalculated comparison uses the posted arm rates and their confidence intervals to form a rate ratio and confidence interval. It is labeled unadjusted: it does not incorporate covariate adjustment or other modeling detail not present in the posted summary statistics. The associated unadjusted p-value is 0.976. A p-value measures how incompatible the data are with a specified null model under the method’s assumptions; it is not an effect size, a measure of clinical importance, or the probability that the null model is true.

How does the sponsor analysis differ?

The sponsor’s reported analysis uses a log-rank method and reports a hazard ratio of 0.99, with a 95% confidence interval from 0.80 to 1.22. General explanation: A hazard ratio compares event rates at a given point in time among participants who have not yet experienced the event, subject to the time-to-event model and its assumptions. It is not identical to an overall event-rate ratio. A log-rank test compares the pattern of event timing between groups over follow-up. The registry does not report additional details about the sponsor model, its assumptions, or any adjustment for covariates.

Both the recalculated rate ratio and sponsor-reported hazard ratio are relative measures. They answer related but not identical questions. Differences between them can arise from their distinct definitions and analysis methods; no cause for any numerical difference should be inferred from the posted summary alone.

What does “unadjusted” imply for the comparison?

General explanation: An unadjusted comparison uses the group-level outcome information without correcting the estimate for other measured characteristics. Randomization is intended to balance characteristics across groups on average, but an unadjusted summary does not show whether any particular prognostic factors were included in a model. The registry does not report covariate-adjustment details for the recalculation, and its own analysis is identified as log rank rather than as a covariate-adjusted model.

The registry labels the sponsor result as a superiority analysis. That label describes the analysis type, not a conclusion that superiority was established. The estimate and interval must be interpreted on their own terms. The confidence interval includes the null value of 1, while the sponsor’s exact p-value is not repeated because the posted value has more than three decimal places.

What is not established by these methods?

The registry lists 27 outcome measures and 34 analyses, but a complete statistical analysis plan, multiplicity procedure, interim analysis plan, missing-data method, and full analysis-population definition are not reported in the registry record. The available methods therefore support an explanation of the posted calculations, but not a reconstruction of every planned analysis decision. General methodological considerations should not be mistaken for confirmation that a particular procedure was used in this trial.

11. Confidence Intervals and Precision

The primary event rate was 3.02 events per 100 participant-years in the placebo group, with a 95% confidence interval from 2.59 to 3.51. In the bococizumab group, it was 3.01, with a 95% confidence interval from 2.58 to 3.5. The recalculated rate ratio was 0.997, with a 95% confidence interval from 0.804 to 1.236.

General explanation: A confidence interval communicates uncertainty around an estimate. Its endpoints indicate the range of values compatible with the observed data under the method’s assumptions and confidence procedure. It does not mean that the same percentage of individual participants had outcomes within that range. The interval for the primary rate ratio includes 1, the value corresponding to equal rates, and also allows relative-rate values below and above 1.

The interval is not narrow enough to identify a single precise relative rate. The point estimate is near 1, but the confidence limits permit a range of differences in either direction. The arm-specific rate intervals also overlap substantially, though overlap between separate arm intervals is not itself the formal test of the rate comparison. The direct comparison is better represented by the rate ratio and its interval.

The sponsor’s time-to-event analysis reported a hazard ratio of 0.99, with a 95% confidence interval from 0.80 to 1.22. This interval also includes 1. Because the hazard ratio and rate ratio are different measures, their intervals should be interpreted within their respective analyses rather than combined as if they were one estimate.

Confidence intervals reflect sampling uncertainty under the analysis method; they do not capture every possible source of uncertainty, including unreported analysis decisions, missing data, or limitations in the registry description.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect13,920,23218,635,241
75% of the observed effect24,736,80733,115,565
50% of the observed effect55,634,72074,479,105
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10,000,00020,000,00050,000,000100,000,000200,000,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, Poisson model with equal follow-up (from the outcome time frame: 3.40 years per participant). Real event counts are usually over-dispersed, so a negative binomial model would need more participants than shown; treat these figures as a lower bound. Calculated for the comparison: Bococizumab (PF-04950615).

The planning figures are illustrations based on the observed effect, not the trial’s original design calculations. For this event-rate endpoint, the figures are participants per arm. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is set at 100%, 75%, or 50% of the observed effect. These are planning scenarios, not observed trial outcomes.

The 80% power column means the number of participants per arm estimated to give an 80% chance of detecting the specified effect if that effect were the true one and the planning assumptions held. The 90% power column describes the corresponding participant count for a 90% chance. Power is a design property under an assumed effect and statistical model; it is not the probability that the observed result is correct.

The observed primary rate ratio is close to 1, so planning around the full observed effect produces very large participant requirements: 13,920,232 participants per arm for 80% power and 18,635,241 participants per arm for 90% power. Planning for 75% of the observed effect gives 24,736,807 participants per arm for 80% power and 33,115,565 participants per arm for 90% power. Planning for 50% of the observed effect gives 55,634,720 participants per arm for 80% power and 74,479,105 participants per arm for 90% power.

Smaller effects require more participants to distinguish them from no difference with the same target power. These illustrations use the observed effect as their anchor, so they should not be read as a recommended design or as evidence that the original study had those assumptions. The registry’s original sample-size justification and design assumptions are not reported in the registry record. This is not observed power.

For clarity, the planning description says that time-to-event illustrations give total event counts using the Schoenfeld approach, whereas other illustrations give participants per arm. The primary result is an event-rate analysis, so its planning figures are participants per arm, not total events.

13. How the Sample Size Is Derived

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

Formula

n = (z1−α/2 + z1−β)2 (1/λ0 + 1/λ1) / ( T · [ln(λ1/λ0)]2 )

n is the number of participants in each arm, λ0 and λ1 are event rates per patient-year, and T is follow-up per participant in years. This assumes Poisson counts and equal follow-up.

Worked calculation for this trial

  1. Control rate λ0 = 0.0302; treatment rate λ1 = 0.0301 events per patient-year; follow-up T = 3.40 years.
  2. n = (1.96 + 0.842)2 × (1/0.0302 + 1/0.0301) / (3.40 × [ln(0.997)]2) = 13,920,231.8, rounded up to 13,920,232 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
lambda0 <- 0.0302                      # control rate, events per patient-year
lambda1 <- 0.0301                      # treatment rate
tt      <- 3.4                       # follow-up per participant, years
n_per_arm <- function(power, frac = 1) {
  l1 <- lambda0 * (lambda1 / lambda0)^frac   # smaller effect = fraction of the observed log rate ratio
  ceiling(round((z_a + qnorm(power))^2 * (1 / lambda0 + 1 / l1) / (tt * log(l1 / lambda0)^2), 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Simulation 1: Poisson counts. Simulation 2: over-dispersed counts (variance = 1.5 x mean), analysed with the matching variance.
set.seed(1975376)
n    <- n_per_arm(0.80)
reps <- 20000
m0 <- lambda0 * n * tt; m1 <- lambda1 * n * tt
x0 <- rpois(reps, m0); x1 <- rpois(reps, m1)
z  <- log(x1 / x0) / sqrt(1 / x0 + 1 / x1)
cat(sprintf("Simulated power, Poisson counts, n = %s per arm: %.3f\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE)))
phi <- 1.5
y0 <- rnbinom(reps, mu = m0, size = m0 / (phi - 1)); y1 <- rnbinom(reps, mu = m1, size = m1 / (phi - 1))
z2 <- log(y1 / y0) / sqrt(phi * (1 / y0 + 1 / y1))
cat(sprintf("Simulated power, over-dispersed counts (phi = 1.5), same n: %.3f\n", mean(abs(z2) > z_a, na.rm = TRUE)))

Output from running the code

100% of observed effect: n per arm = 13,920,232 (80% power), 18,635,241 (90% power)
 75% of observed effect: n per arm = 24,736,807 (80% power), 33,115,565 (90% power)
 50% of observed effect: n per arm = 55,634,720 (80% power), 74,479,105 (90% power)
Simulated power, Poisson counts, n = 13,920,232 per arm: 0.796
Simulated power, over-dispersed counts (phi = 1.5), same n: 0.627

The first simulation draws Poisson counts and should land close to the target power. The second allows extra variability (variance 1.5 times the mean, a purely illustrative value), which lowers the power at the same sample size, so rate trials usually need more participants than the Poisson formula suggests.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.990.80 to 1.220.931

The sponsor’s posted result is a log-rank analysis with a hazard ratio of 0.99 and a 95% confidence interval from 0.80 to 1.22. The recalculation from the posted event rates gives a rate ratio of 0.997 and a 95% confidence interval from 0.804 to 1.236. Both estimates are near 1, and both intervals include 1.

These are related but distinct summaries. The sponsor’s hazard ratio comes from a time-to-event analysis, while the recalculated rate ratio compares the posted event rates per participant-time. The reported values need not match exactly because the measures and statistical methods differ. The sponsor’s analysis is the registry’s reported trial analysis; the recalculation is an unadjusted analysis derived from the posted summary statistics.

The record does not indicate a discrepancy between these results. The sponsor’s p-value is reported in the registry with more than three decimal places and is not reproduced. Details of any covariate adjustment, model diagnostics, or additional assumptions for the sponsor’s analysis are not reported in the registry record. Interpretation should therefore distinguish the sponsor’s analysis from the summary-statistic recalculation rather than treating one as a direct replication of the other.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 27 outcome measures and 34 analyses, including a primary endpoint and multiple secondary outcomes. It does not report a multiplicity-adjustment method, a hierarchy for testing endpoints, or a distinction between confirmatory and exploratory secondary analyses. Without those details, the overall chance of false-positive findings across multiple analyses cannot be assessed from the record. Individual unadjusted secondary results should not be interpreted as though they were protected by a reported family-wise testing plan.

The registry does not report whether interim analyses were planned or conducted, whether any stopping boundaries were specified, or how such analyses might have affected the reported estimates. The study status is listed as terminated, but the reason for termination and its relationship to the conduct or analysis are not reported in the registry record.

The primary outcome description identifies a full analysis set and lists certain exclusions, including attempted duplicate randomizations and participants enrolled at a specified site. The population definition is truncated, so the complete analysis-population criteria are not reported in the registry record. Details of the handling of participants who discontinued, crossed over, had incomplete follow-up, or had missing endpoint information are also not reported.

The registry does not report a missing-data strategy, sensitivity analyses for missing outcomes, or the extent of missingness. It also does not provide enough information to establish whether the primary analysis followed an intention-to-treat principle in its complete operational form. The randomized group counts and reported outcome data remain interpretable as posted, but the record does not permit a full audit of population handling or robustness to missing data.

The original statistical analysis plan, trial-specific sample-size justification, and details of model checks are not reported. These gaps matter because they prevent a reader from comparing the posted analyses against a complete prespecified plan and from assessing whether decisions were made before or after outcome data were examined.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo986837411.8%
Bococizumab (PF-04950615)1060838612.6%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo11.8%Bococizumab (PF-04950615)12.6%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo65 of 8374
Bococizumab (PF-04950615)72 of 8386

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

ArmParticipants affected of at risk
Placebo1570 of 8374
Bococizumab (PF-04950615)2015 of 8386

Most frequent serious adverse event terms

Event termOrgan systemPlaceboBococizumab (PF-04950615)
Angina unstableCardiac disorders84 of 837465 of 8386
Angina pectorisCardiac disorders52 of 837473 of 8386
Non-cardiac chest painGeneral disorders47 of 837445 of 8386
PneumoniaInfections and infestations39 of 837434 of 8386
Acute myocardial infarctionCardiac disorders29 of 837440 of 8386
Myocardial infarctionCardiac disorders32 of 837435 of 8386
Coronary artery diseaseCardiac disorders31 of 837430 of 8386
Atrial fibrillationCardiac disorders32 of 837427 of 8386
Cardiac failure congestiveCardiac disorders32 of 837424 of 8386
Ischaemic strokeNervous system disorders28 of 837420 of 8386

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboBococizumab (PF-04950615)
Injection site reactionGeneral disorders88 of 8374588 of 8386
HypertensionVascular disorders303 of 8374270 of 8386
NasopharyngitisInfections and infestations289 of 8374283 of 8386
Back painMusculoskeletal and connective tissue disorders203 of 8374217 of 8386
Type 2 diabetes mellitusMetabolism and nutrition disorders195 of 8374217 of 8386
ArthralgiaMusculoskeletal and connective tissue disorders197 of 8374208 of 8386
Upper respiratory tract infectionInfections and infestations193 of 8374183 of 8386
MyalgiaMusculoskeletal and connective tissue disorders160 of 8374170 of 8386
HeadacheNervous system disorders136 of 8374171 of 8386
DiarrhoeaGastrointestinal disorders133 of 8374169 of 8386

Serious events with the highest arm-level rate: angina unstable (1.0%), angina pectoris (0.9%), non-cardiac chest pain (0.6%), acute myocardial infarction (0.5%), pneumonia (0.5%).

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 events among 8374 participants at risk in the placebo group and 8386 in the bococizumab group. Serious adverse events affected 986 participants in the placebo group and 1060 in the bococizumab group. Other adverse events affected 1570 and 2015 participants, respectively. The record lists 65 deaths in the placebo group and 72 in the bococizumab group.

These figures are counts of participants with reported events, not event rates per participant-year, and the at-risk denominators differ from the primary outcome analysis populations. They should not be compared directly with the primary event rates. The registry lists selected serious adverse event terms, including unstable angina at 1.0%, angina pectoris at 0.9%, and non-cardiac chest pain at 0.6%.

Counts alone do not establish that an event was caused by the assigned intervention, and the registry excerpt does not provide a full assessment of timing, exposure, severity breakdown, or causal attribution. The listed figures describe the posted safety data; they do not by themselves establish comparative safety.

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

The primary result describes the rates of first adjudicated major cardiovascular events observed in the randomized groups during the recorded follow-up. The placebo rate was 3.02 events per 100 participant-years and the bococizumab rate was 3.01. The recalculated rate ratio was 0.997, with a 95% confidence interval from 0.804 to 1.236. The sponsor’s time-to-event analysis reported a hazard ratio of 0.99, with a 95% confidence interval from 0.80 to 1.22.

These estimates are close to 1, and both intervals include 1. The posted results therefore describe little estimated separation in the primary comparison, while retaining uncertainty across a range of relative values. The interpretation is limited to the defined composite endpoint, the analyzed population, and the observed follow-up in this study record.

The results do not establish that every component of the composite behaved in the same way. Nor do they provide a fixed-time probability of an event, a measure of recurrent events, or an explanation for the study’s termination. The registry does not report a complete account of missing data, analysis-population criteria, interim analyses, or multiplicity procedures, which constrains interpretation beyond the posted summaries.

General explanation: A trial estimate is not a guarantee that the same result will occur in another population or setting. Confidence intervals express statistical uncertainty under a model; they do not encompass every uncertainty about study conduct, outcome definition, or generalizability. The registry results should be understood as the recorded comparison rather than as a universal statement about outcomes.

No medical recommendation follows from these statistics. The data identify what the registry reports for the comparison and how precisely the relative effect is estimated; they do not, on their own, resolve decisions for individual patients or establish the cause of observed outcomes.

18. Why This Trial Matters Statistically

This trial offers a useful example of why the choice of statistical measure matters. The primary endpoint is an event rate per participant-time, while the sponsor’s analysis reports a hazard ratio from a log-rank method. Both summarize group differences in event experience, but they do not estimate exactly the same quantity. Reporting them distinctly avoids treating a rate ratio and a hazard ratio as interchangeable.

The primary estimate is close to 1, and its confidence interval includes 1 while spanning a range on both sides. This illustrates why a point estimate alone is insufficient: the interval communicates the degree of uncertainty around the estimated relative rate. The arm-specific rates are also close, but the direct comparison and its interval are the more appropriate basis for judging the relative estimate.

The registry also illustrates the limits of interpreting a collection of secondary analyses. Multiple endpoint definitions and analyses can produce a broad set of estimates; without a reported multiplicity plan, individual secondary results are less suitable for confirmatory conclusions. The count of posted outcomes and analyses makes transparency about prespecification and adjustment especially relevant.

Finally, the planning illustrations demonstrate that sample-size calculations depend on the effect assumed for planning. When the estimated effect is close to no difference, detecting a smaller departure from equality requires a large planned sample under the stated assumptions. Such illustrations are not evidence about the power achieved by the completed trial and cannot replace its original design rationale, which is not reported in the registry record.

19. Limitations

Several trial-specific limitations follow from the registry information. The study is listed as terminated, but the reason for termination, its timing, and any effect on follow-up or analysis are not reported in the registry record. The listed primary completion date is 2017-03-22, but the record does not explain the relationship between that date and termination.

The primary analysis population description is incomplete. It identifies a full analysis set and mentions exclusions, but the full criteria are truncated. The registry therefore does not permit a complete assessment of which randomized participants contributed to the primary result or how the analysis population was defined in practice.

Methodological details are also limited. The registry does not report the original sample-size rationale, a complete statistical analysis plan, multiplicity handling, interim analysis procedures, missing-data methods, or details of model diagnostics. These are not claims that the trial omitted such procedures; they are details not reported in the registry record.

The primary outcome is a composite of cardiovascular death, non-fatal myocardial infarction, non-fatal stroke, and hospitalization for unstable angina requiring urgent revascularization. An overall composite rate cannot show whether each component had the same direction or magnitude. Secondary outcomes offer related definitions, but the multiplicity approach is not reported, limiting their confirmatory interpretation.

The posted rate comparison is a recalculation from summary statistics and is unadjusted. The sponsor’s own reported analysis uses a log-rank method and gives a hazard ratio. Both can be informative, but their different estimands and methods mean that neither should be presented as an exact replication of the other. Additional participant-level information and the complete analysis plan are not reported in the registry record.

20. Related Tutorials

21. Related Statistical Calculators

22. 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.

23. Record Summary

The registry describes a phase 3, randomized, quadruple-masked, parallel-group, placebo-controlled study of bococizumab in high-risk subjects receiving background lipid-lowering therapy. Enrollment is listed as 16784, and study status is terminated. The primary endpoint is the event rate per 100 participant-years for first major cardiovascular events, comprising cardiovascular death, non-fatal myocardial infarction, non-fatal stroke, and hospitalization for unstable angina requiring urgent revascularization.

Posted primary rates were 3.02 for placebo and 3.01 for bococizumab events per 100 participant-years. The recalculated rate ratio was 0.997, with a 95% confidence interval from 0.804 to 1.236. The sponsor-reported log-rank hazard ratio was 0.99, with a 95% confidence interval from 0.80 to 1.22. The registry does not report the reason for termination or several details needed to reconstruct the full statistical plan and analysis population.

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