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Heterozygous Familial Hypercholesterolemia Phase 3 Continuous Endpoint NCT02326220

Study of Alirocumab (REGN727/SAR236553) in Patients With Heterozygous Familial Hypercholesterolemia (HeFH) Undergoing Low-density Lipoprotein (LDL) Apheresis Therapy: Complete Statistical Analysis

A randomized, placebo-controlled phase 3 trial evaluated alirocumab in people with heterozygous familial hypercholesterolemia receiving LDL apheresis. The primary question was whether treatment changed the standardized rate of apheresis treatments during the blinded period.

Trial start: 2015-03-31  ·  Enrollment: 62  ·  Sponsor: Regeneron Pharmaceuticals
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 Study of Alirocumab (REGN727/SAR236553) in Patients With Heterozygous Familial Hypercholesterolemia (HeFH) Undergoing Low-density Lipoprotein (LDL) Apheresis Therapy (NCT02326220), a randomized phase 3 study. The primary outcome is Change in Standardized Rate of Apheresis Treatments From Week 7 to Week 18.

62
Enrollment
Phase 3
2
Arms
In the primary outcome
-0.68
Mean difference
Alirocumab 150 mg Q2W (Double Blind Peri
-0.79–-0.57
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02326220
PhasePhase 3
ConditionHeterozygous Familial Hypercholesterolemia
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment62
Arms in the primary outcome2
Lead sponsorRegeneron Pharmaceuticals
Results postedYes

2. Clinical Question

Population

Participants had heterozygous familial hypercholesterolemia (HeFH) and were undergoing weekly or bi-weekly low-density lipoprotein (LDL) apheresis therapy. The primary analysis population was the intent-to-treat population: all randomized participants, analyzed according to the group assigned at randomization. The registry record describes normalization of apheresis frequency using each participant’s established schedule at screening.

Intervention

During the double-blind period, participants assigned to alirocumab received 150 mg by subcutaneous injection every 2 weeks, up to Week 16. The record also describes an open-label period in which alirocumab 150 mg every 2 weeks began at Week 18 and continued up to Week 76.

Comparator

The blinded comparison group received placebo by subcutaneous injection every 2 weeks, up to Week 16. The randomized comparison was between the placebo group and the alirocumab group during the double-blind period.

Primary question

Did alirocumab change the standardized rate of LDL apheresis treatments from Week 7 to Week 18, before the open-label treatment period? The rate was standardized against the number of treatments planned for each participant’s baseline apheresis schedule. The clinical question therefore concerns treatment frequency relative to an established schedule, rather than a direct measurement of LDL cholesterol concentration. The registry record also lists lipid measures and a later standardized apheresis-rate outcome as secondary questions.

3. Trial Design

This was a phase 3, randomized, parallel-group study sponsored by Regeneron Pharmaceuticals. The registry record gives enrollment as 62. Participants were assigned to placebo or alirocumab 150 mg every 2 weeks during the double-blind period. The record describes quadruple masking. It does not specify the identities of every role covered by that masking in the registry record.

The placebo and alirocumab groups were followed during the double-blind period, with injections scheduled every 2 weeks up to Week 16. The primary outcome window extended from Week 7 to Week 18 and was described as occurring before open-label treatment. The record separately describes open-label alirocumab 150 mg every 2 weeks beginning at Week 18 and continuing up to Week 76. These are different treatment periods, so the open-label group should not be treated as a third randomized comparison group.

The primary population was intent-to-treat: randomized participants were analyzed according to their assigned group. The posted primary outcome summaries include 21 participants in the placebo group and 41 in the blinded alirocumab group. The study’s original allocation rationale and sample-size justification are not reported in the registry record. The enrollment total alone does not establish how the trial’s design assumptions were selected.

The record identifies multiple secondary outcomes, including lipid measures at Week 6 and a standardized apheresis rate from Week 15 to Week 18. It reports 23 outcome measures and 7 analyses. The registry record does not describe whether all outcomes were included in a prespecified testing hierarchy, or whether the analyses were adjusted for testing multiple outcomes.

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: Randomization was stratified according to the frequency of the apheresis procedure (every 7 or 14 days) and lipoprotein (a) (Lp \[a\]) levels (normal or elevated). Assignment to treatment arms was done using an Interactive Voice/Web Response System in 1:2 ratio to placebo or alirocumab 150 mg Q2W.

Double-blind Treatment Period

StagePlacebo Q2W (Double Blind Period)Alirocumab 150 mg Q2W (Double Blind Period)Alirocumab 150 Q2W (Open Label Treatment Period)
STARTED21410
COMPLETED20370
NOT COMPLETED140

Reasons for not completing this period:

ReasonPlacebo Q2W (Double Blind Period)Alirocumab 150 mg Q2W (Double Blind Period)Alirocumab 150 Q2W (Open Label Treatment Period)
Adverse Event120
Protocol Violation010
Withdrawal by Subject010

Open-label Treatment Period

StagePlacebo Q2W (Double Blind Period)Alirocumab 150 mg Q2W (Double Blind Period)Alirocumab 150 Q2W (Open Label Treatment Period)
STARTED0029
COMPLETED0027
NOT COMPLETED002

Reasons for not completing this period:

ReasonPlacebo Q2W (Double Blind Period)Alirocumab 150 mg Q2W (Double Blind Period)Alirocumab 150 Q2W (Open Label Treatment Period)
Withdrawal by Subject001
Lost to Follow-up001

Analysis population for the primary outcome, as defined in the registry: Primary intent-to-treat (ITT) population defined as all randomized participants and were analyzed according to the treatment group allocated by randomization.

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: Analysis was performed on randomized population.

CharacteristicUnitPlacebo Q2W (Double Blind Period)Alirocumab 150 mg Q2W (Double Blind Period)Total
Participants analysed214162
Age, Continuousyears57 (SD 10.5)59.5 (SD 9.2)58.7 (SD 9.7)
Sex: Female, Male: FemaleParticipants111526
Sex: Female, Male: MaleParticipants102636
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants000
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants214162
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants000
Race (NIH/OMB): American Indian or Alaska NativeParticipants000
Race (NIH/OMB): AsianParticipants000
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants022
Race (NIH/OMB): WhiteParticipants213960
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants000
Frequency in which participants are undergoing LDL apheresis: Every weekTreatments91827
Frequency in which participants are undergoing LDL apheresis: Every 2 weeksTreatments122335
Calculated low-density lipoprotein cholesterol (LDL-C)mg/dL191.6 (SD 68.9)175.1 (SD 54.6)180.7 (SD 59.7)
Measured LDL-Cmg/dL195.0 (SD 66.9)174.0 (SD 51.4)181.1 (SD 57.4)
Non-high-density lipoprotein cholesterol (HDL-C)mg/dL224.5 (SD 68.0)210.3 (SD 62.8)215.1 (SD 64.4)
Total-cholesterol (Total-C)mg/dL272.3 (SD 73.6)256.9 (SD 60.6)262.1 (SD 65.1)
High-density lipoprotein cholesterol (HDL-C)mg/dL47.8 (SD 17.3)46.6 (SD 16.2)47.0 (SD 16.4)
Triglycerides (TGs)mg/dL164.4 (SD 61.4)176.0 (SD 87.2)172.1 (SD 79.0)
Lipoprotein a [Lp(a)]mg/dL45.7 (SD 49.5)43.0 (SD 54.5)43.9 (SD 52.4)
Apolipoprotein B (Apo-B)mg/dL145.8 (SD 34.0)135.2 (SD 36.4)138.8 (SD 35.7)
Apolipoprotein A1 (Apo-A1)mg/dL145.8 (SD 32.5)140.1 (SD 25.5)142.1 (SD 27.9)

6. Primary Endpoint

The registry lists the primary outcome as Change in Standardized Rate of Apheresis Treatments From Week 7 to Week 18, measured over Week 7 to Week 18 (before start of open-label treatment).

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
UnitTreatments
Endpoint classificationContinuous Endpoint

The primary endpoint was the change in standardized rate of apheresis treatments from Week 7 to Week 18, before the start of open-label treatment. The registry record defines the participant-level rate using the actual number of apheresis treatments received during that period relative to the number planned for the participant’s baseline schedule. The planned schedule was represented by 6 treatments for the every-2-week stratum and 12 for the weekly stratum.

Standardization is useful when participants follow different treatment schedules: it expresses treatment frequency in relation to the schedule each participant was expected to follow. The outcome is therefore not simply a raw count of procedures, and its interpretation depends on the baseline schedule used as the reference. A lower standardized rate means fewer actual treatments relative to the planned number during the specified period; the outcome itself does not measure LDL concentration or directly establish why treatment frequency changed.

The endpoint was chosen to address the study’s stated objective of evaluating apheresis-treatment frequency. The registry record does not report a separate explanation for choosing this endpoint over other clinical or laboratory measures, or further detail about how deviations from planned schedules were handled.

7. Results Posted in the Registry

Mean difference: Alirocumab 150 mg Q2W (Double Blind Period)

-0.68

95% CI: -0.79 to -0.57

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-0.00.20.40.60.81.0Placebo Q2W (Double Blind Per… (n=21)Alirocumab 150 mg Q2W (Double… (n=41)Treatments (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Alirocumab 150 mg Q2W (Double…-0.85-0.67-0.49-0.30-0.120.06mean 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
Percent Change From Baseline in Calculated LDL-C (Pre-apheresis) at Week 6Continuous EndpointMean difference-55.30 (-62.87 to -47.73)2 per arm
Change in Standardized Rate of Apheresis Treatments From Week 15 to Week 18Continuous EndpointMean difference-0.61 (-0.78 to -0.44)5 per arm
Percent Change From Baseline in Apolipoprotein B (Apo B) (Pre-apheresis) to Week 6Continuous EndpointMean difference-44.00 (-51.18 to -36.82)2 per arm

Percent Change From Baseline in Calculated LDL-C (Pre-apheresis) at Week 6

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Alirocumab 150 mg Q2W (Double…-68-53-39-24-9.565.03mean difference vs control (95% CI)

Change in Standardized Rate of Apheresis Treatments From Week 15 to Week 18

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Alirocumab 150 mg Q2W (Double…-0.84-0.66-0.48-0.30-0.120.06mean difference vs control (95% CI)

Percent Change From Baseline in Apolipoprotein B (Apo B) (Pre-apheresis) to Week 6

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Alirocumab 150 mg Q2W (Double…-55-43-32-20-7.784.09mean difference vs control (95% CI)

The secondary outcomes broadly point in a direction consistent with the primary group summaries. At Week 6, the posted lipid estimates for calculated LDL-C and Apo B are lower in the alirocumab group than in the placebo group. The Week 15 to Week 18 standardized apheresis-rate comparison also has a lower posted estimate in the alirocumab group. These measures relate to the primary question but are not interchangeable: the lipid outcomes concern laboratory measures at an earlier time, while the primary outcome concerns standardized treatment frequency over a specified interval.

The registry lists a range of additional lipid outcomes, including non-HDL-C, total cholesterol, and Apo A1, as well as thresholds for reductions in calculated LDL-C. Numerical results for those outcomes are not reported in the registry record. The record lists 22 secondary outcomes, but only a subset has numerical summaries in the analysis details available in the registry record. The direction of unreported outcomes should not be inferred from the outcomes with numerical summaries.

For the secondary analyses with reported model results, the registry gives p-values below < 0.001. Those results indicate evidence of group separation under the reported analyses, but the registry does not report a multiplicity adjustment or a testing hierarchy. When many outcomes are examined, the chance of at least one apparently significant result can increase unless the analysis plan accounts for multiple testing. Therefore, unadjusted secondary findings generally carry less confirmatory weight than a clearly designated primary outcome.

The secondary results can support a coherent description of what was measured during the trial, but they should be interpreted as additional evidence rather than independent confirmation of the primary result. Their different scales, time points, and analysis methods mean that consistency in direction is informative but does not make the outcomes equivalent. The registry record does not report enough detail to determine whether all planned secondary comparisons were analyzed or how the choice of reported secondary analyses was made.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary outcome, the posted group means were 0.806 for placebo and 0.128 for alirocumab. These are mean standardized rates during the Week 7 to Week 18 window. The unadjusted recalculation gives a mean difference of -0.678 for alirocumab relative to placebo, with p < 0.001. The negative direction reflects the lower posted mean in the alirocumab group. This is a descriptive comparison of group summaries, not a claim about an individual participant’s experience.

The registry’s reported primary analysis used ANCOVA and reported a Hodges–Lehmann estimate of median difference of 0.750, with a 95% confidence interval from 0.667 to 0.833 and p < 0.001. This reported estimate is not the same statistical summary as the unadjusted mean difference. Its positive direction should not be read as contradicting the lower alirocumab mean: the registry reports a median-difference estimate, while the recalculation is framed as the alirocumab mean minus the placebo mean. The registry result is the sponsor’s own analysis and is the relevant reported primary analysis.

The record also reports a lower standardized apheresis rate in the alirocumab group in the later Week 15 to Week 18 outcome. Lipid outcomes at Week 6 show lower posted group estimates for calculated LDL-C and Apo B in the alirocumab group than in the placebo group. These secondary findings are directionally consistent with the primary group summaries, but they answer different questions and have different timeframes. They should not be treated as substitutes for the primary endpoint.

The reported p-values indicate that the analyzed groups were separated under the statistical tests recorded for these outcomes. They do not quantify the probability that a treatment effect is true, and they do not by themselves convey clinical importance, study conduct, or the reliability of every aspect of the analysis. The record’s primary endpoint is a standardized treatment-frequency measure; interpretation should stay focused on that measure and its defined period.

The findings apply to the randomized study population and the specific blinded comparison described in the record. The record does not establish how the result would generalize beyond participants with HeFH undergoing the stated apheresis schedules. Nor does a comparison during the blinded period determine what would occur under different treatment schedules, in other populations, or over other time horizons.

10. Statistical Methods Explained

The registry record’s primary analysis is described as ANCOVA, with a Hodges–Lehmann estimate of median difference. The recalculated comparison is an unadjusted difference between group means. These methods summarize the randomized groups in different ways, so their estimates need not match numerically or share the same direction convention. The reported primary analysis should be interpreted using the statistic and direction as described by the registry, rather than treating the recalculation as a replacement.

What does a mean difference describe?

A mean difference subtracts one group’s average from another’s. The recalculation defines the comparison as alirocumab relative to placebo, so the posted group means yield a negative estimate when the alirocumab mean is lower. This summary is easy to relate to the displayed group averages, but it does not account for covariates in the way an adjusted model may. It is also sensitive to the distribution of the outcome: a small number of unusual values can influence a mean.

The outcome is a continuous standardized rate, and the group summaries include standard deviations. A standard deviation describes spread among participant values within a group; it is not the uncertainty of the group mean. The standard error, by contrast, describes the estimated sampling uncertainty of a statistic. For some secondary outcomes, the record reports least-squares means with standard errors, which are model-based summaries rather than raw group means with standard deviations.

What does ANCOVA contribute?

ANCOVA is a regression approach that compares groups while accounting for covariates included in the model. The registry record identifies ANCOVA for the primary analysis, but it does not report the covariates, model specification, or handling of all model assumptions. Those details are not reported in the registry record. The presence of ANCOVA alone does not reveal which participant characteristics were included or the extent to which the estimate was adjusted.

The reported primary parameter is a Hodges–Lehmann estimate of median difference. In general, this is a location-shift summary based on pairwise differences between observations, rather than a subtraction of the two group means. A median-based summary can be less influenced by extreme observations than a mean, but it answers a different statistical question. The registry gives a confidence interval and p-value for this estimate, allowing the reported analysis to be read on its own terms.

Why distinguish reported and recalculated results?

The recalculated primary comparison is an unadjusted calculation from posted summary statistics. It is useful as a transparent check of the group means, but it is not the trial’s complete analysis plan or a reconstruction of the ANCOVA. The two estimates differ in both the summary statistic and analysis approach. Since the registry record does not mark a discrepancy, no conflict is asserted; nevertheless, the sponsor’s reported primary analysis remains the trial’s own inferential result, while the recalculation is a supplementary descriptive comparison.

For outcomes summarized by least-squares means, the recalculation uses posted estimates and uncertainty summaries. In the LDL-C and Apo B comparisons, the record identifies the spread as a standard error, not a standard deviation. The recalculated pooled spread is therefore approximate, rather than a direct pooled estimate from participant-level data. This matters because standard errors describe uncertainty in estimated means, while standard deviations describe participant-to-participant variability. A recalculation built from standard errors should not be presented as if it had access to raw observations.

What role do p-values play?

A p-value describes how incompatible the observed data are with a specified null hypothesis under the assumptions of the test. A small p-value is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. For the primary outcome, both the registry analysis and the unadjusted recalculation report small p-values, but the registry analysis is the sponsor’s prespecified-style analysis as recorded; the detailed protocol plan is not reported in the registry record. The registry’s report of an analysis does not, by itself, establish the exact timing or prespecification of every decision.

As a general statistical point, continuous outcomes can be affected by skewness, outliers, and unequal variability. Model assumptions and diagnostic checks help determine whether an analysis is suitable. The registry record does not report diagnostic plots, residual checks, or sensitivity analyses for this endpoint, so those aspects cannot be evaluated from the record. This is not evidence that such checks were or were not performed.

As a general statistical point, over-dispersion is more often discussed for count outcomes when observed variability exceeds what a simple count model expects. Apheresis frequency is conceptually related to a count, but the primary endpoint is reported as a standardized continuous rate with means and standard deviations. The record does not describe a count model or an over-dispersion adjustment. It would therefore be inappropriate to assume that a particular count-model method was used.

11. Confidence Intervals and Precision

A confidence interval expresses a range of values compatible with the observed data under the assumptions of the analysis. It conveys uncertainty around an estimate, not a guarantee that the true value lies within that particular interval. Narrower intervals indicate greater statistical precision under the same analysis framework, while wider intervals indicate more uncertainty.

For the primary reported analysis, the estimated median difference was 0.750, with a 95% confidence interval from 0.667 to 0.833. The interval lies on the positive side of zero, and the reported p-value is p < 0.001. The statistic is the registry’s Hodges–Lehmann median-difference estimate from ANCOVA, not the unadjusted mean difference. The direction and scale should therefore be interpreted according to that reported statistic.

The recalculated mean difference is -0.678, with p < 0.001. Its direction follows the alirocumab-minus-placebo convention and the lower posted alirocumab mean. The recalculation’s confidence limits are not repeated because the recorded values have more than 3 decimal places. The sponsor’s reported interval and the recalculated estimate should not be combined into one interval or treated as estimates of precisely the same parameter.

The size of a confidence interval depends on the variability of the outcome, the amount of information in the groups, and the analysis method. The registry’s interval reflects its reported model and statistic; the unadjusted recalculation reflects a different calculation. Neither interval captures every source of uncertainty, such as uncertainty about generalizing to people outside the trial population or uncertainty about unreported model choices.

For the reported LDL-C and Apo B comparisons, the confidence intervals also exclude zero and the registry reports p-values below < 0.001. These intervals concern secondary outcomes and do not resolve the limitations of multiple testing or unreported analysis details. Statistical precision for an estimate is not the same as certainty about clinical meaning.

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 effect23
75% of the observed effect45
50% of the observed effect710
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect25102040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: Alirocumab 150 mg Q2W (Double Blind Period).

The planning figures are participants per arm, not a total sample size or a count of events. They are illustrations based on the observed treatment effect, not the original trial’s sample-size calculation. For the primary outcome, the planning illustration gives 2 participants per arm for 80% power and 3 participants per arm for 90% power when planning for 100% of the observed effect. Planning for 75% of the observed effect gives 4 participants per arm for 80% power and 5 participants per arm for 90% power. Planning for 50% of the observed effect gives 7 participants per arm for 80% power and 10 participants per arm for 90% power.

The stated assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. In plain terms, the 80% power column describes an illustrative design with an 80% chance of detecting the assumed effect under those planning assumptions if that effect were present. The 90% column describes the corresponding design using a higher target chance of detection. Achieving a higher target generally requires more participants for the same effect.

Smaller effects require more participants to detect with the same target power. These calculations are not observed power: they are planning illustrations based on the effect observed in this trial, not a retrospective measure of whether the trial was adequately powered. The original design assumptions and sample-size justification are not reported in the registry record. The calculated illustrations should not be used to infer what the investigators planned before enrollment.

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 = -0.678; pooled standard deviation σ = 0.226.
  2. n = 2 × (1.96 + 0.842)2 × 0.2262 / -0.6782 = 1.7, rounded up to 2 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 <- -0.678                      # observed difference in means
sigma <- 0.226280799008665                     # 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(2326220)
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 = 2 (80% power), 3 (90% power)
 75% of observed effect: n per arm = 4 (80% power), 5 (90% power)
 50% of observed effect: n per arm = 7 (80% power), 10 (90% power)
power.t.test: 3.1 
Simulated power at n = 2 per arm: 0.387 (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.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
ANCOVAH-L estimate of median difference 0.7500.667 to 0.833< 0.001

The registry’s own primary analysis reports an ANCOVA result as a Hodges–Lehmann estimate of median difference: 0.750, with a 95% confidence interval from 0.667 to 0.833 and p < 0.001. The separate recalculation is an unadjusted mean difference of -0.678, with p < 0.001. The two estimates are not like-for-like: one is a median-difference estimate from the reported analysis, and the other compares posted means without the reported ANCOVA model.

The direction also uses different conventions. The recalculation is expressed as alirocumab minus placebo, giving a negative value because the alirocumab mean is lower. The registry’s positive median-difference estimate is reported in its own analysis and does not mean that the alirocumab group had the higher posted mean. The registry does not give a direction convention in the result description that would justify relabeling the sponsor estimate as the same contrast used in the recalculation.

Because the sponsor’s result is the trial’s reported analysis, it takes precedence as the primary inferential result. The recalculation is a check based on posted summary statistics and is useful for understanding the group means; it does not replace the reported model or recover its covariate adjustment. The record does not flag a discrepancy between the analyses.

15. Multiplicity, Missing Data and Analysis Populations

The registry record identifies a primary outcome and multiple secondary outcomes, but it does not report a multiplicity-control procedure, a hierarchy for testing outcomes, or a familywise error strategy. This information is important because testing many outcomes can raise the chance of obtaining one or more small p-values by chance, even when each individual test uses a conventional significance threshold. Without a reported adjustment or hierarchy, secondary p-values should be read as nominal evidence rather than as proof that every secondary finding is independently confirmatory.

The record gives an intent-to-treat definition for the primary population: all randomized participants are analyzed according to their assigned treatment group. This approach preserves the randomized comparison in the analysis definition. The record does not report details about missing outcome values, exclusions from particular analyses, imputation, or sensitivity analyses. Those details are not reported in the registry record, so the effect of missing data on the estimates cannot be assessed from the listed summaries.

The registry describes the primary method as ANCOVA but does not provide the model covariates or other specification details. It also does not report the full statistical analysis plan, interim-analysis procedures, or the timing of decisions about outcomes. These details are not reported in the registry record. Their absence from the record should not be read as evidence that no such plans or procedures existed.

For the secondary lipid outcomes, the record reports least-squares means and standard errors, but does not provide enough information to reconstruct each model or assess its assumptions. The primary endpoint’s reported median-difference analysis likewise cannot be fully reproduced from the group summaries alone. Participant-level data and additional analysis documentation would be needed to examine missingness, model fit, and alternative analytic choices.

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 Q2W (Double Blind Period)2219.5%
Alirocumab 150 Q2W (Double Blind Period)4419.8%
Alirocumab 150 Q2W (Open Label Treatment Period)1293.4%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo Q2W (Double Blind Per…9.5%Alirocumab 150 Q2W (Double Bl…9.8%Alirocumab 150 Q2W (Open Labe…3.4%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo Q2W (Double Blind Period)0 of 21
Alirocumab 150 Q2W (Double Blind Period)0 of 41
Alirocumab 150 Q2W (Open Label Treatment Period)0 of 29

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 Q2W (Double Blind Period)10 of 21
Alirocumab 150 Q2W (Double Blind Period)22 of 41
Alirocumab 150 Q2W (Open Label Treatment Period)2 of 29

Most frequent serious adverse event terms

Event termOrgan systemPlacebo Q2W (Double Blind Period)Alirocumab 150 Q2W (Double Blind Period)Alirocumab 150 Q2W (Open Label Treatment Period)
Acute myocardial infarctionCardiac disorders0 of 212 of 410 of 29
Angina pectorisCardiac disorders1 of 210 of 410 of 29
Angina unstableCardiac disorders0 of 211 of 410 of 29
Aortic valve stenosisCardiac disorders0 of 211 of 410 of 29
Cardiac failure congestiveCardiac disorders0 of 211 of 410 of 29
Myocardial ischaemiaCardiac disorders0 of 210 of 411 of 29
Sinus bradycardiaCardiac disorders1 of 210 of 410 of 29
PneumoniaInfections and infestations0 of 211 of 410 of 29
SepsisInfections and infestations0 of 211 of 410 of 29
Muscle ruptureInjury, poisoning and procedural complications0 of 211 of 410 of 29

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo Q2W (Double Blind Period)Alirocumab 150 Q2W (Double Blind Period)Alirocumab 150 Q2W (Open Label Treatment Period)
FatigueGeneral disorders2 of 216 of 410 of 29
NasopharyngitisInfections and infestations2 of 214 of 411 of 29
Upper respiratory tract infectionInfections and infestations4 of 213 of 410 of 29
MyalgiaMusculoskeletal and connective tissue disorders1 of 215 of 410 of 29
NauseaGastrointestinal disorders3 of 212 of 410 of 29
ArthralgiaMusculoskeletal and connective tissue disorders2 of 213 of 410 of 29
HeadacheNervous system disorders2 of 213 of 410 of 29
DiarrhoeaGastrointestinal disorders0 of 214 of 410 of 29
Back painMusculoskeletal and connective tissue disorders2 of 212 of 410 of 29
AnaemiaBlood and lymphatic system disorders0 of 211 of 412 of 29

Serious events with the highest arm-level rate: acute myocardial infarction (4.9%), angina pectoris (4.8%), sinus bradycardia (4.8%), shunt thrombosis (4.8%), myocardial ischaemia (3.4%).

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

The registry lists serious adverse events and other adverse events separately for the double-blind placebo group, the double-blind alirocumab group, and an open-label alirocumab group. Serious adverse events affected 2 participants in the placebo group, 4 in the blinded alirocumab group, and 1 in the open-label group. The corresponding at-risk counts are 21, 41, and 29. These are group-specific counts, not a randomized comparison across all three periods: the open-label group belongs to a different treatment period.

Other adverse events affected 10 participants in the placebo group, 22 in the blinded alirocumab group, and 2 in the open-label group. The record reports 0 deaths in each group. These counts alone do not describe event severity beyond the serious-versus-other distinction, timing, duration, or relationship to treatment. Nor do they establish that an event was caused by the assigned treatment.

The registry lists several serious-event terms with percentages, including acute myocardial infarction, angina pectoris, sinus bradycardia, shunt thrombosis, myocardial ischaemia, and peripheral artery restenosis. The denominators and event-level details for those percentages are not described in the summary. Small group counts and the separate open-label period limit direct comparisons. The safety figures should be read as descriptive registry counts, not as a complete assessment of comparative safety.

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

The primary result describes a difference in standardized apheresis-treatment frequency between the randomized groups during the Week 7 to Week 18 window. The registry’s reported analysis estimates a median difference of 0.750, with a 95% confidence interval from 0.667 to 0.833 and p < 0.001. The posted means are lower in the alirocumab group than in the placebo group. The recalculated mean difference of -0.678 expresses that mean comparison with alirocumab minus placebo.

This result does not mean that every participant changed apheresis frequency by the same amount. Group-level summaries do not show the distribution of individual responses, the number of people who changed their schedule, or why any schedule changed. The endpoint is standardized against each participant’s planned schedule, so it should not be interpreted as a raw treatment count or as a direct measure of cholesterol concentration.

The outcome also does not establish that alirocumab has a particular effect in people who do not receive LDL apheresis, or in people with conditions other than HeFH. The result pertains to the randomized population and the recorded treatment period. The open-label phase is described separately and is not the blinded randomized comparison underlying the primary endpoint.

A small p-value is not proof of clinical importance, and a confidence interval does not remove uncertainty about the study’s analysis choices, missing data, or generalizability. The registry record does not report enough detail to evaluate all of those issues. The results should be read as evidence about the measured endpoint under this trial’s conditions, rather than as a broad conclusion about treatment for every person with HeFH.

18. Why This Trial Matters Statistically

This trial is statistically notable for asking a treatment-frequency question in a population already receiving apheresis, rather than relying only on a laboratory measure. The primary endpoint standardizes actual apheresis treatments against each participant’s established schedule. That definition makes the baseline schedule central to interpretation and helps distinguish this outcome from a simple count of procedures.

The randomized, blinded, placebo-controlled parallel-group design provides a direct comparison during the double-blind period. The primary intent-to-treat population is defined according to randomized assignment, which keeps the analysis aligned with the randomized groups. The registry’s reported ANCOVA analysis and the unadjusted mean recalculation illustrate why the choice of estimand and model matters: two valid summaries can answer related but different statistical questions and use different directional conventions.

The trial also illustrates the need to keep primary and secondary evidence distinct. Lipid outcomes and a later apheresis-rate measure can add context, but they differ in measurement, timing, and analysis. Without reported multiplicity procedures, secondary p-values warrant more caution than the designated primary result. Similarly, planning illustrations derived from the observed effect are not a substitute for the trial’s original design assumptions.

Finally, safety summaries require attention to period and group. The open-label data are not a third randomized arm, and descriptive event counts should not be interpreted as randomized treatment effects. These distinctions make the registry record useful for statistical learning: design, endpoint definition, analysis method, and reporting context all shape what a numerical result can support.

19. Limitations

The endpoint depends on a participant’s established apheresis schedule, and the registry record does not describe how changes to that schedule, missed procedures, or deviations from plans were handled. It gives the normalization definition but not enough detail to independently evaluate the underlying participant-level counts or their distribution.

The record reports the primary analysis method and estimate but does not specify the ANCOVA covariates, model diagnostics, or sensitivity analyses. The recalculation from summary statistics is unadjusted and does not reproduce the sponsor’s model. For some secondary endpoints, standard errors are used in the posted summaries; recalculations based on these are approximate rather than calculations from raw participant-level observations.

Details about missing data, exclusions in individual analyses, and imputation are not reported in the registry record. Neither is a multiplicity strategy for the many outcomes listed. These omissions limit assessment of how robust the secondary findings are and how missing observations may affect the estimates.

The record describes a blinded randomized period and a later open-label period. The open-label results do not provide a concurrent placebo comparison and should not be combined with the blinded comparison as if all groups were randomized in the same way. The reported adverse-event counts are descriptive and do not include all event-level information needed to judge timing, treatment relationship, or exposure-adjusted risk.

Generalizability is also bounded by the population and treatment setting recorded: participants had HeFH and were receiving weekly or bi-weekly LDL apheresis. The registry record does not provide information that would support extending the findings to other populations or treatment contexts.

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23. Record Summary

NCT02326220 records a completed, randomized, double-blind, placebo-controlled, parallel-group phase 3 study of alirocumab in participants with HeFH undergoing LDL apheresis. The record lists enrollment of 62 and describes blinded treatment with alirocumab 150 mg every 2 weeks or placebo. The primary endpoint was the standardized rate of apheresis treatments from Week 7 to Week 18.

The sponsor’s reported primary analysis used ANCOVA and gave a Hodges–Lehmann median-difference estimate of 0.750, with a 95% confidence interval from 0.667 to 0.833 and p < 0.001. The unadjusted recalculation of the posted means is -0.678, with p < 0.001; it is a different statistical summary and does not replace the reported analysis. The record also describes secondary lipid and apheresis outcomes, a later open-label period, and adverse-event counts. Details of multiplicity handling, missing-data methods, and the original sample-size justification are not reported in the registry record.

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