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Hyperlipidemia Phase 3 Continuous Endpoint NCT01763827

Monoclonal Antibody Against PCSK9 to Reduce Elevated LDL-C in Subjects Currently Not Receiving Drug Therapy for Easing Lipid Levels-2: Complete Statistical Analysis

A randomized, masked phase 3 trial compared evolocumab given every two weeks or monthly with placebo and ezetimibe in adults with elevated LDL-C and a 10-year Framingham risk score of 10% or less. The statistical analysis focuses on the change in LDL-C after 12 weeks, the precision of the posted estimates, and the limits of what the registry results establish.

Trial start: 2013-01-21  ·  Enrollment: 615  ·  Sponsor: Amgen
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 Monoclonal Antibody Against PCSK9 to Reduce Elevated LDL-C in Subjects Currently Not Receiving Drug Therapy for Easing Lipid Levels-2 (NCT01763827), a randomized phase 3 study. The primary outcome is Percent Change From Baseline in Low-density Lipoprotein Cholesterol (LDL-C) at Week 12.

615
Enrollment
Phase 3
6
Arms
In the primary outcome
-1.44
Mean difference
Placebo QM
-5.89–3.01
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01763827
PhasePhase 3
ConditionHyperlipidemia
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment615
Arms in the primary outcome6
Lead sponsorAmgen
Results postedYes

2. Clinical Question

Population

Adults with elevated LDL-C and a 10-year Framingham risk score of 10% or less who were not currently receiving drug therapy for easing lipid levels. The registry record describes the condition as hyperlipidemia.

Intervention

Evolocumab administered by subcutaneous injection either once every two weeks or once every month, with placebo tablets. The listed doses were 140 mg for the every-two-weeks schedule and 420 mg for the monthly schedule.

Comparator

Placebo injections and placebo tablets, or ezetimibe 10 mg taken orally once a day with placebo injections. The injection schedule was matched to the relevant evolocumab schedule.

Primary question

What was the percent change from baseline in LDL-C at Week 12 in the randomized groups, and how did evolocumab compare with placebo and ezetimibe? The primary objective covered evolocumab given every two weeks and monthly over 12 weeks.

3. Trial Design

This was a randomized, quadruple-masked, parallel-group phase 3 study described as double-blind, placebo- and ezetimibe-controlled, and multicenter. The registry record lists enrollment of 615 participants and a completed status. The sponsor was Amgen. The primary objective was to evaluate the effect of evolocumab monotherapy on LDL-C over 12 weeks in adults with a 10-year Framingham risk score of 10% or less.

Six groups received different combinations of injections and tablets. The evolocumab groups received 140 mg subcutaneously every two weeks or 420 mg subcutaneously monthly, along with placebo tablets. The placebo groups received placebo injections on the corresponding schedule and placebo tablets. The ezetimibe groups received placebo injections and ezetimibe 10 mg orally once a day. Treatment was described as lasting up to 12 weeks.

These schedules allowed comparisons with placebo and an active lipid-lowering comparator while keeping the injection schedule aligned across relevant groups. The posted primary results use the full analysis set and report least-squares means for percent change in LDL-C from baseline to Week 12. The registry record does not report the detailed eligibility criteria, the definition of the full analysis set, or the original sample-size justification. Further protocol details about allocation procedures and the masking process are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Participants received subcutaneous placebo corresponding to the once monthly dose volume during a 6 week screening period. Participants who completed the screening period and met final eligibility criteria were randomized 1:1:1:1:2:2 into 6 treatment groups. Randomization was stratified by LDL-C concentration (\< 130 mg/dL or ≥ 30 mg/dL).

Overall Study

StagePlacebo Q2WPlacebo QMEzetimibe (Q2W)Ezetimibe (QM)Evolocumab Q2WEvolocumab QM
STARTED77787777153153
Received at Least 1 Dose of Study Drug76787777153153
COMPLETED74777376147151
NOT COMPLETED314162

Reasons for not completing this period:

ReasonPlacebo Q2WPlacebo QMEzetimibe (Q2W)Ezetimibe (QM)Evolocumab Q2WEvolocumab QM
Withdrawal by Subject100020
Decision by sponsor203021
Lost to Follow-up011121

Analysis population for the primary outcome, as defined in the registry: Full analysis set

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.

Only the first 6 of 7 groups are shown.

CharacteristicUnitPlacebo Q2WPlacebo QMEzetimibe (Q2W)Ezetimibe (QM)Evolocumab Q2WEvolocumab QM
Participants analysed77787777153153
Age, Continuousyears54.4 (SD 10.3)52.6 (SD 10.7)53.9 (SD 11.3)53.0 (SD 12.7)52.5 (SD 13.7)52.9 (SD 12.1)
Sex: Female, Male: FemaleParticipants49475352104101
Sex: Female, Male: MaleParticipants283124254952
Race/Ethnicity, Customized: American Indian or Alaska Nativeparticipants000102
Race/Ethnicity, Customized: Asianparticipants987101212
Race/Ethnicity, Customized: Black or African Americanparticipants466699
Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islanderparticipants010000
Race/Ethnicity, Customized: Whiteparticipants64636360132129
Race/Ethnicity, Customized: Otherparticipants000000
Race/Ethnicity, Customized: Mixed Raceparticipants001001
Race/Ethnicity, Customized: Hispanic or Latinoparticipants689111421
Race/Ethnicity, Customized: Not Hispanic or Latinoparticipants71706866139132
Stratification Factor: Low-density Lipoprotein Cholesterol (LDL-C): < 130 mg/dLparticipants232422224545
Stratification Factor: Low-density Lipoprotein Cholesterol (LDL-C): ≥ 130 mg/dLparticipants54545555108108
LDL-C Concentrationmg/dL139.5 (SD 21.3)144.3 (SD 23.9)143.3 (SD 23.8)143.5 (SD 23.1)141.7 (SD 22.3)144.4 (SD 23.3)
Non-High-Density Lipoprotein Cholesterol (Non-HDL-C) Concentrationmg/dL167.4 (SD 25.8)172.8 (SD 31.0)168.8 (SD 28.9)169.4 (SD 27.3)166.5 (SD 25.6)170.4 (SD 26.6)
Apolipoprotein B Concentrationmg/dL103.7 (SD 16.8)107.3 (SD 19.9)107.2 (SD 19.7)106.2 (SD 17.8)104.5 (SD 17.2)108.3 (SD 17.9)
Total Cholesterol/High-density Lipoprotein Cholesterol Ratioratio4.148 (SD 1.311)4.444 (SD 1.465)4.055 (SD 1.082)4.335 (SD 1.118)4.170 (SD 1.170)4.175 (SD 1.071)
Apolipoprotein B/Apolipoprotein A-1 Ratioratio0.671 (SD 0.193)0.713 (SD 0.194)0.691 (SD 0.187)0.712 (SD 0.173)0.687 (SD 0.169)0.707 (SD 0.170)
Lipoprotein(a)nmol/L21.0 (inter quartile range 62.9)21.5 (inter quartile range 84.0)28.0 (inter quartile range 79.1)28.0 (inter quartile range 65.7)20.0 (inter quartile range 61.5)28.0 (inter quartile range 86.9)
Triglyceridesmg/dL113.5 (inter quartile range 74.7)118.0 (inter quartile range 83.4)112.5 (inter quartile range 64.9)116.5 (inter quartile range 52.4)112.0 (inter quartile range 62.6)119.0 (inter quartile range 59.1)
Very Low-density Lipoprotein Cholesterol (VLDL-C) Concentrationmg/dL22.5 (inter quartile range 13.2)23.8 (inter quartile range 15.4)22.5 (inter quartile range 12.4)23.5 (inter quartile range 10.5)22.5 (inter quartile range 11.5)23.5 (inter quartile range 11.8)
High-density Lipoprotein Cholesterol (HDL-C) Concentrationmg/dL57.0 (inter quartile range 23.6)54.0 (inter quartile range 17.8)58.5 (inter quartile range 16.8)53.5 (inter quartile range 18.5)53.0 (inter quartile range 18.0)56.5 (inter quartile range 18.0)

6. Primary Endpoint

The registry lists the primary outcome as Percent Change From Baseline in Low-density Lipoprotein Cholesterol (LDL-C) at Week 12, measured over Baseline and Week 12.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
Unitpercent change
Endpoint classificationContinuous Endpoint

The primary endpoint is percent change from baseline in low-density lipoprotein cholesterol (LDL-C) at Week 12. It describes the relative change in a laboratory measure between the starting assessment and the Week 12 assessment, rather than a change in symptoms or clinical events. A negative percent change represents a decrease from baseline; a value near zero represents little change in that measure.

LDL-C is used as a lipid outcome because the trial’s stated objective was to assess lipid lowering. Reporting percent change allows the result to express the change relative to participants’ baseline levels, while the accompanying group estimates show the pattern across randomized treatment groups. The registry record also reports secondary LDL-C outcomes in mg/dL, including change at Week 12 and change averaged over Weeks 10 and 12.

The primary endpoint is a biomarker measure. On its own, it does not establish whether participants experienced fewer cardiovascular events, lived longer, or had better quality of life. Those outcomes are not reported in the registry record. The primary endpoint’s timeframe is limited to baseline and Week 12, so it describes the short-term laboratory response recorded for this study.

7. Results Posted in the Registry

Mean difference: Placebo QM

-1.44

95% CI: -5.89 to 3.01

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-65.7-50.7-35.6-20.5-5.49.7Placebo Q2W (n=76)Placebo QM (n=78)Ezetimibe (Q2W) (n=77)Ezetimibe (QM) (n=77)Evolocumab Q2W (n=153)Evolocumab QM (n=153)percent change (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Placebo QMEzetimibe (Q2W)Ezetimibe (QM)Evolocumab Q2WEvolocumab QM-66-51-37-22-6.758.15mean difference 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
Change From Baseline in LDL-C at the Mean of Weeks 10 and 12Continuous EndpointMean difference-1.20 (-7.30 to 4.90)4,063 per arm
Change From Baseline in LDL-C at Week 12Continuous EndpointMean difference-2.00 (-8.79 to 4.79)1,813 per arm
Percentage of Participants Who Achieved LDL-C < 70 mg/dL at Week 12Binary EndpointRisk difference-1.3 pts (-3.9 to 1.2)n/a

Change From Baseline in LDL-C at the Mean of Weeks 10 and 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Placebo QMEzetimibe (Q2W)-34-25-17-8.76-0.507.75mean difference vs control (95% CI)

Change From Baseline in LDL-C at Week 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Placebo QMEzetimibe (Q2W)-35-27-18-9.42-0.837.75mean difference vs control (95% CI)

Percentage of Participants Who Achieved LDL-C < 70 mg/dL at Week 12

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Placebo QMEzetimibe (Q2W)-4.47-2.74-1.010.722.454.18risk difference (percentage points) vs control (95% CI)

The secondary outcomes extend the primary LDL-C question by examining LDL-C at other time points, attainment of an LDL-C threshold, and changes in other lipid measures, including non-HDL-C and apolipoprotein B. Across the posted secondary LDL-C summaries, the general pattern is that the evolocumab groups have larger decreases than placebo groups, while ezetimibe estimates also show decreases. The binary threshold outcome similarly distinguishes the evolocumab groups from placebo in the sponsor’s reported comparisons.

These outcomes provide context around the primary endpoint: the registry reports LDL-C change both at Week 12 and averaged across Weeks 10 and 12, as well as a threshold measure. This can help readers see whether the broad pattern is present across related LDL-C definitions. The secondary endpoints are still distinct outcomes, with different scales and estimands, so they should not be collapsed into a single overall effect.

The registry record lists 20 secondary outcomes as posted, but the detailed results represented in the registry record are incomplete. Detailed estimates for the listed non-HDL-C and apolipoprotein B outcomes are not reported in the registry record. The overall pattern in the posted LDL-C results should therefore not be extended to every secondary endpoint.

Unadjusted secondary results carry less inferential weight when many outcomes and comparisons are examined. Testing multiple hypotheses increases the chance that some results appear statistically notable by chance, unless the analysis plan controls that risk. Whether a multiplicity adjustment was used for the secondary analyses is not reported in the registry record. Secondary findings are best read as supporting context rather than as independent confirmation of a single primary conclusion.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted least-squares mean percent changes at Week 12 were -57.04 for evolocumab every two weeks and -56.12 for evolocumab monthly. The corresponding placebo group estimates were 0.1 for placebo every two weeks and -1.34 for placebo monthly. The ezetimibe group estimates were -17.75 with the every-two-weeks injection schedule and -18.57 with the monthly injection schedule. These are group estimates, not individual participant outcomes.

The sponsor’s reported repeated measures analyses found a treatment difference of -57.14 for evolocumab every two weeks versus placebo every two weeks, with a 95% confidence interval from -61.14 to -53.14 and p < 0.001. For evolocumab monthly versus placebo monthly, the reported difference was -54.78, with a 95% confidence interval from -58.46 to -51.10 and p < 0.001. The sponsor also reported differences comparing each evolocumab schedule with its corresponding ezetimibe schedule; those estimates and intervals are included with the posted results.

The unadjusted recalculations compare arm-level summaries using the placebo every-two-weeks group as the reference for the primary outcome. For example, the recalculated mean difference for evolocumab every two weeks versus that placebo group is -57.14, with a 95% interval from -61.21 to -53.07 and an unadjusted p < 0.001. These recalculations are not the same analysis as the sponsor’s repeated measures model. The registry record flags a discrepancy, so the sponsor’s own analysis takes precedence when interpreting the official reported comparisons.

The intervals for the sponsor’s placebo comparisons do not include zero, and the reported p-values are below 0.001. This indicates that the posted model-based estimates are inconsistent with a zero treatment difference under the model’s assumptions. It does not by itself establish the size or importance of a difference for an individual, or show an effect on clinical outcomes. The registry record does not report a minimally important difference for this endpoint.

Across the posted LDL-C results, the group estimates for evolocumab are more negative than those for placebo or ezetimibe. That is a description of the laboratory outcome and the contrasts analyzed, not medical advice. Interpretation also depends on the analysis model, the precision of the estimates, the multiple outcomes assessed, and the limitations of a 12-week endpoint.

10. Statistical Methods Explained

The primary outcome is continuous: each participant’s LDL-C change can take a range of values rather than being only an event/no-event result. The posted arm summaries are least-squares means, accompanied by standard errors. A least-squares mean is a model-based group estimate; it can differ from a simple arithmetic average when the analysis accounts for features of the model. The registry record does not report enough detail to reconstruct every feature of the model.

What does the sponsor’s model estimate?

The sponsor reports use a repeated measures linear effects model and label the contrasts as least-squares mean treatment differences. Repeated-measures models are generally used when outcomes are observed at multiple time points, so that measurements from the same participant are treated as related rather than independent. A linear model estimates group differences while accounting for the specified model structure. The registry record does not report the complete model specification, covariance structure, covariates, or handling of missing measurements; those details are not reported in the registry record.

A treatment difference is the model’s estimated contrast between two groups. Its sign depends on the order of subtraction used in the reported comparison. For the sponsor’s listed contrasts, negative values indicate a lower percent change estimate in the evolocumab group than in its named comparator. This direction should be read alongside the endpoint definition and the group estimates, rather than interpreted without the contrast labels.

What is a standard error?

A standard error describes the statistical uncertainty in an estimated group mean. It reflects how much the estimate would tend to vary across repeated samples under the analysis assumptions. It is not the spread of individual participant values. The posted primary group estimates have standard errors, including 1.23 for evolocumab every two weeks and 1.12 for evolocumab monthly. The registry record labels the reported arm dispersion as standard error.

How do the recalculations differ?

The recalculated contrasts are simple, unadjusted comparisons from the posted summary statistics. For these calculations, the arm-level standard errors are used to approximate standard deviations, as indicated by the recalculation method. That approximation does not reproduce the sponsor’s repeated measures analysis, and it does not account for any model features that are not captured in the posted arm summaries. Consequently, a recalculated estimate or interval can differ from the sponsor’s estimate or interval. The record flags a discrepancy, so the sponsor’s analysis takes precedence.

The recalculated results are useful as a transparent, approximate check on the direction and scale of contrasts that can be derived from the posted summaries. They should not be treated as a replacement for the prespecified or sponsor-reported analysis. Some comparisons also address different questions: the recalculated primary contrasts use placebo every two weeks as the reference, whereas the sponsor reports comparisons of each evolocumab schedule with its matched placebo and matched ezetimibe schedule.

What do p-values tell the reader?

A p-value describes how compatible the observed data are with a specified null hypothesis, under the statistical model and its assumptions. A small 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 sponsor’s reported primary comparisons have p < 0.001. The recalculated comparisons are explicitly unadjusted; they do not incorporate an adjustment for the number of outcomes or comparisons.

For a binary outcome such as reaching LDL-C < 70 mg/dL, the registry reports percentages and confidence intervals. A percentage gives the observed or estimated proportion meeting the threshold, while a confidence interval describes uncertainty around that proportion. Continuous and binary endpoints answer different questions and should not be treated as interchangeable.

11. Confidence Intervals and Precision

Confidence intervals express uncertainty about an estimated quantity under the analysis assumptions. A 95% confidence interval is produced by a procedure that, under repeated sampling and the same assumptions, would cover the underlying quantity in 95% of such intervals. It is not a statement that there is a 95% probability that a particular fixed treatment effect lies inside the interval.

For the sponsor’s primary comparison of evolocumab every two weeks with placebo every two weeks, the reported estimate is -57.14, with a 95% confidence interval from -61.14 to -53.14. For the monthly evolocumab versus monthly placebo comparison, the reported estimate is -54.78, with a 95% confidence interval from -58.46 to -51.10. Both intervals lie below zero. Their widths indicate uncertainty around the model-based estimates; they do not describe the range of individual participant responses.

The recalculated intervals are approximate and unadjusted. For the every-two-weeks evolocumab versus placebo comparison, the recalculated interval is -61.21 to -53.07. Its difference from the sponsor interval reflects that the recalculation uses posted summaries rather than the sponsor’s repeated measures model. Because the registry record flags a discrepancy, the sponsor’s reported analysis takes precedence.

Precision is influenced by the amount and variability of the data and by the analysis model. Standard errors are reported for the continuous arm estimates, and 95% intervals are reported for the binary threshold outcome. The registry record does not report all details needed to assess the model’s assumptions or missing-data uncertainty. Confidence intervals also do not account automatically for the many outcomes and comparisons unless an appropriate multiplicity procedure is used; such a procedure is not reported in the registry record.

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 effect1,5022,010
75% of the observed effect2,6693,573
50% of the observed effect6,0058,039
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1,0002,0005,00010,00020,00040%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, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Placebo QM.

The planning figures are illustrative calculations based on observed effects, not the trial’s original design assumptions. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. For continuous comparisons, the figures are participants per arm; they are not total participants across both arms and are not total event counts. The event-total convention for time-to-event outcomes does not apply to these continuous outcomes.

The 80% power column gives the number of participants per arm estimated to provide an 80% chance of detecting the specified effect under the calculation assumptions, if that effect is truly present. The 90% power column gives the corresponding estimate for a 90% chance. These are planning concepts, not guarantees about a future study’s result. Smaller effects require more participants to detect with the same assumed power and significance level, which is why the illustrations using smaller fractions of the observed effect call for larger sample sizes.

Some estimates are extremely small when based on the large observed contrasts, while comparisons with effects close to zero can yield very large planning requirements. Such outputs are sensitive to the observed effect and the assumptions used, and should not be read as recommendations or as the original enrollment calculation. The registry record does not report the trial’s own sample-size justification or original design assumptions. These figures are not observed power: they are hypothetical planning illustrations, not a retrospective measure of the probability that this completed trial detected an effect.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

  1. Observed difference Δ = -1.440; pooled standard deviation σ = 14.082.
  2. n = 2 × (1.96 + 0.842)2 × 14.0822 / -1.4402 = 1,501.1, rounded up to 1,502 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
delta <- -1.44                      # observed difference in means
sigma <- 14.0816602452679                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1763827)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 1,502 (80% power), 2,010 (90% power)
 75% of observed effect: n per arm = 2,669 (80% power), 3,573 (90% power)
 50% of observed effect: n per arm = 6,005 (80% power), 8,039 (90% power)
power.t.test: 1502.1 
Simulated power at n = 1,502 per arm: 0.799 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Repeated measures linear effects modelLS Mean Treatment Difference -57.14-61.14 to -53.14< 0.001
Repeated measures linear effects modelLS Mean Treatment Difference -54.78-58.46 to -51.10< 0.001
Repeated measures linear effects modelLS Mean Treatment Difference -39.29-43.28 to -35.31< 0.001
Repeated measures linear effects modelLS Mean Treatment Difference -37.55-41.24 to -33.86< 0.001
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The registry includes sponsor-reported contrasts from a repeated measures linear effects model, alongside unadjusted recalculations based on arm-level summaries. The two sets of numbers are not interchangeable. The sponsor’s contrasts use a model-based analysis; the recalculations approximate unadjusted differences using the posted estimates and standard errors.

For the primary outcome, the sponsor reported the every-two-weeks evolocumab versus placebo contrast as -57.14, with a 95% confidence interval from -61.14 to -53.14 and p < 0.001. The recalculated contrast for the same named comparison is also -57.14, but its approximate interval is -61.21 to -53.07. The sponsor reported -54.78 for monthly evolocumab versus monthly placebo, while the recalculated comparison against placebo every two weeks is -56.22. Those latter contrasts use different reference groups and should not be treated as direct disagreement about the same comparison.

The registry record flags a discrepancy. Accordingly, the sponsor’s own analysis takes precedence for the trial’s reported inferential results. Recalculations can still help readers understand what follows from the posted summary statistics, but they cannot reproduce unreported modeling choices or replace the official analysis. The full details of the sponsor model are not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 22 outcome measures and 88 analyses. Looking across many outcomes and comparisons raises a multiplicity question: when many hypotheses are tested, the chance of at least one apparently unusual result can increase. A prespecified testing hierarchy or a statistical adjustment can address this issue, but the registry record does not report whether such a strategy was used, how it was defined, or which comparisons it covered.

The primary outcome is identified as percent change from baseline in LDL-C at Week 12, and the primary analysis population is described as the full analysis set. The definition of that population, including the criteria for inclusion in the analysis, is not reported in the registry record. The posted results also include multiple schedules and comparator groups. The complete prespecified ordering of tests and any adjustment for these comparisons are not reported in the registry record.

Missing-data methods matter because participants may have measurements absent at one or more time points. The sponsor reports a repeated measures linear effects model, but the specific assumptions about missing measurements, the method used to handle them, and any sensitivity analyses are not reported in the registry record. The numbers of participants with missing primary outcome measurements and the reasons for missingness are not reported in the registry record.

The registry record does not report whether interim analyses were conducted, whether any stopping rules were used, or how the final analysis was affected by them. These details should not be inferred from the completed status or from the posted p-values. Without the full analysis plan and missing-data details, readers can describe the posted estimates and their reported uncertainty but cannot fully audit the prespecified inferential strategy.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo Q2W0760.0%
Placebo QM1781.3%
Ezetimibe (Q2W)0770.0%
Ezetimibe (QM)1771.3%
Evolocumab Q2W31532.0%
Evolocumab QM11530.7%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo Q2W0.0%Placebo QM1.3%Ezetimibe (Q2W)0.0%Ezetimibe (QM)1.3%Evolocumab Q2W2.0%Evolocumab QM0.7%% 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 5% reporting threshold.

ArmParticipants affected of at risk
Placebo Q2W9 of 76
Placebo QM4 of 78
Ezetimibe (Q2W)10 of 77
Ezetimibe (QM)4 of 77
Evolocumab Q2W12 of 153
Evolocumab QM12 of 153

Most frequent serious adverse event terms

Event termOrgan systemPlacebo Q2WPlacebo QMEzetimibe (Q2W)Ezetimibe (QM)Evolocumab Q2WEvolocumab QM
Pancreatitis acuteGastrointestinal disorders0 of 760 of 780 of 770 of 770 of 1531 of 153
Upper limb fractureInjury, poisoning and procedural complications0 of 760 of 780 of 770 of 771 of 1530 of 153
Hepatic enzyme increasedInvestigations0 of 760 of 780 of 770 of 771 of 1530 of 153
Bladder cancerNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 761 of 780 of 770 of 770 of 1530 of 153
Breast cancerNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 760 of 780 of 771 of 770 of 1530 of 153
Renal cancerNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 760 of 780 of 770 of 771 of 1530 of 153
Pleural effusionRespiratory, thoracic and mediastinal disorders0 of 760 of 780 of 770 of 771 of 1530 of 153

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo Q2WPlacebo QMEzetimibe (Q2W)Ezetimibe (QM)Evolocumab Q2WEvolocumab QM
HeadacheNervous system disorders3 of 761 of 784 of 771 of 775 of 1535 of 153
DiarrhoeaGastrointestinal disorders5 of 761 of 782 of 771 of 774 of 1535 of 153
NasopharyngitisInfections and infestations1 of 762 of 784 of 772 of 773 of 1533 of 153

Serious events with the highest arm-level rate: breast cancer (1.3%), bladder cancer (1.3%), pancreatitis acute (0.7%), upper limb fracture (0.7%), hepatic enzyme increased (0.7%).

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.

Serious adverse event counts are reported for each group with the number at risk as the denominator. The posted counts are 0 of 76 for placebo every two weeks, 1 of 78 for placebo monthly, 0 of 77 for ezetimibe with the every-two-weeks injection schedule, 1 of 77 for ezetimibe with the monthly schedule, 3 of 153 for evolocumab every two weeks, and 1 of 153 for evolocumab monthly. These are participant counts during the study, not rates adjusted for exposure time.

The registry also lists serious adverse event terms with percentages: breast cancer, 1.3%; bladder cancer, 1.3%; pancreatitis acute, 0.7%; upper limb fracture, 0.7%; hepatic enzyme increased, 0.7%; and renal cancer, 0.7%. The posted details do not identify the treatment group for each term, so those percentages should not be attributed to a particular group. Death counts are not reported in the registry record.

These figures describe serious adverse events recorded during a study lasting up to 12 weeks. The counts alone do not establish whether an event was caused by treatment, and differences in counts do not by themselves demonstrate a safety difference. The registry record does not provide event narratives or a causal assessment for these terms.

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

The posted results describe a short-term change in a laboratory measure among randomized groups. The sponsor’s model-based estimates show substantially more negative percent changes in LDL-C for the evolocumab groups than for the matched placebo groups, with reported p-values below 0.001 for those comparisons. The active-comparator contrasts and the secondary LDL-C outcomes add context, but they do not change what the primary endpoint measures.

A statistical difference is not the same as a demonstrated difference in clinical outcomes. LDL-C change is a biomarker endpoint; the registry record does not report cardiovascular events, mortality results, or quality-of-life results. Nor does the reported group mean indicate what any particular participant experienced. Individual responses can vary, and the arm-level summaries do not show the full distribution of outcomes.

The findings apply to the population and treatment period described in the record: adults with a 10-year Framingham risk score of 10% or less, treated for up to 12 weeks under the listed schedules. The registry record does not establish how the estimates would apply to populations outside that description, to longer treatment periods, or to different treatment regimens.

The record supports a statistical description of the reported LDL-C estimates and contrasts, with the sponsor’s model-based results taking precedence over the approximate recalculations. It does not, by itself, answer broader questions about long-term benefits, harms, or treatment choices. Those questions require evidence beyond the posted short-term endpoint and should not be inferred from a p-value or a laboratory change alone.

18. Why This Trial Matters Statistically

This trial presents a useful statistical comparison because it includes placebo and ezetimibe controls and evaluates two evolocumab schedules. The parallel randomized design makes it possible to compare assigned groups, while masking is intended to reduce the influence of treatment knowledge on study conduct and outcome assessment. The registry describes the study as quadruple-masked and multicenter.

The results also illustrate why the estimand and comparator matter. A contrast against placebo answers a different question from a contrast against ezetimibe. Similarly, a comparison using the every-two-weeks placebo group is not automatically interchangeable with one using the monthly placebo group. Reading the labels alongside each estimate prevents unlike contrasts from being treated as if they were the same statistical question.

The record is also a practical example of the distinction between model-based sponsor results and recalculations from summary data. The model-based analyses use repeated measurements, while the recalculations are unadjusted approximations. Even when a point estimate agrees, intervals may differ because the methods and available information differ. Where the registry flags a discrepancy, the sponsor’s reported analysis takes precedence.

Finally, this study highlights the separation between a precise short-term biomarker result and a broader claim about clinical outcomes. Confidence intervals and p-values characterize uncertainty within a stated analysis; they do not supply missing long-term outcomes or resolve multiplicity and missing-data questions. Those boundaries are important when interpreting any randomized trial’s posted results.

19. Limitations

The primary endpoint is limited to percent change in LDL-C at Week 12. Although the record lists secondary LDL-C outcomes and other lipid measures, the posted details do not contain detailed results for every listed secondary endpoint. Non-HDL-C and apolipoprotein B result estimates are not reported in the registry record. Long-term clinical outcomes are also not reported in the registry record.

The primary arm estimates are least-squares means with standard errors, but the full model specification is not reported. Important details, including model covariates, covariance assumptions, missing-data handling, and sensitivity analyses, are not reported in the registry record. The definition of the full analysis set is also not reported. These omissions limit independent reconstruction of the sponsor’s analysis.

The recalculated contrasts are approximate, unadjusted comparisons derived from arm summaries. They do not replace the repeated measures model, and the registry flags a discrepancy. The sponsor’s analysis takes precedence. The recalculations also do not account for any multiplicity strategy that might have been used in the trial; whether such a strategy was used is not reported in the registry record.

The study’s treatment period was up to 12 weeks, and the recorded population had a 10-year Framingham risk score of 10% or less. Generalizability beyond the described population and timeframe cannot be assessed from these results alone. The registry record does not report the trial’s original sample-size justification, detailed eligibility criteria, or the reasons for missing outcomes. Serious adverse event counts are available, but the posted details do not give event-level narratives or identify the treatment group for each listed serious-event term.

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23. Record Summary

NCT01763827 is a completed randomized, quadruple-masked, parallel-group phase 3 study sponsored by Amgen. It enrolled 615 adults with hyperlipidemia and a 10-year Framingham risk score of 10% or less. Participants received evolocumab every two weeks or monthly, placebo, or ezetimibe with placebo injections for up to 12 weeks.

The primary outcome was percent change from baseline in LDL-C at Week 12, analyzed in the full analysis set. The sponsor reported repeated measures model comparisons, including evolocumab versus matched placebo, with p < 0.001. Approximate unadjusted recalculations are also available, but the registry flags a discrepancy; the sponsor’s analysis takes precedence.

The record does not report the full analysis plan, missing-data methods, multiplicity strategy, or original sample-size justification. Its primary endpoint is a short-term laboratory measure, and longer-term clinical outcomes are not reported in the registry record.

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