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Hypercholesterolemia Phase 3 Continuous Endpoint NCT01730040

Study of the Efficacy and Safety of Alirocumab (REGN727/SAR236553) in Combination With Other Lipid-modifying Treatment (LMT) (ODYSSEY OPTIONS I): Complete Statistical Analysis

This page examines the registry results for ODYSSEY OPTIONS I, a randomized study comparing alirocumab added to atorvastatin with several active lipid-modifying strategies. It focuses on the Week 24 change in calculated LDL-C, the sponsor’s analyses, and the limits of the posted results.

Trial start: 2012-10  ·  Enrollment: 355  ·  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 the Efficacy and Safety of Alirocumab (REGN727/SAR236553) in Combination With Other Lipid-modifying Treatment (LMT) (ODYSSEY OPTIONS I) (NCT01730040), a randomized phase 3 study. The primary outcome is Percent Change From Baseline in Calculated LDL-C at Week 24 - Intent-to-treat (ITT) Analysis.

355
Enrollment
Phase 3
7
Arms
In the primary outcome
-15.50
Mean difference
Ezetimibe 10 mg + Atorvastatin 20 mg
-28.39–-2.61
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01730040
PhasePhase 3
ConditionHypercholesterolemia
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment355
Arms in the primary outcome7
Lead sponsorRegeneron Pharmaceuticals
Results postedYes

2. Clinical Question

Population

The study enrolled patients at high cardiovascular risk with nonfamilial hypercholesterolemia or heterozygous familial hypercholesterolemia who were not controlled on atorvastatin. The registry describes two baseline atorvastatin-dose groups: some participants were receiving atorvastatin 20 mg and others atorvastatin 40 mg. The primary analysis population was defined more narrowly than everyone enrolled: it included randomized participants with a baseline calculated LDL-C value and at least one post-baseline value, whether on or off treatment.

Intervention

Alirocumab was added to ongoing atorvastatin. The study included a 20 mg atorvastatin group and a 40 mg atorvastatin group. The intervention descriptions state that alirocumab began at 75 mg by subcutaneous injection every two weeks, with an option to increase up to 150 mg. The treatment period described for the relevant arms was 24 weeks.

Comparator

The active comparison depended on baseline atorvastatin dose. For participants receiving atorvastatin 20 mg, the listed alternatives were ezetimibe 10 mg plus atorvastatin 20 mg and atorvastatin 40 mg. For participants receiving atorvastatin 40 mg, alternatives included ezetimibe 10 mg plus atorvastatin 40 mg, atorvastatin 80 mg, and rosuvastatin 40 mg. The trial therefore compared several treatment strategies rather than a single intervention against one common active control.

Primary question

The primary endpoint was percent change from baseline in calculated LDL-C at Week 24, assessed in the intent-to-treat analysis. The statistical question was how the adjusted mean change in the alirocumab groups compared with the changes in the specified active-comparator groups. This is a question about a laboratory measure over the trial period; it is not a question about cardiovascular events or longer-term clinical outcomes.

3. Trial Design

ODYSSEY OPTIONS I was a Phase 3, randomized, double-blind, active-comparator, parallel-group study. The registry records quadruple masking. Enrollment was 355, and the study status is completed. The recorded start was 2012-10 and primary completion was 2014-04. The study concerned patients at high cardiovascular risk with nonfamilial hypercholesterolemia or heterozygous familial hypercholesterolemia who were not controlled on atorvastatin.

The design used two baseline atorvastatin-dose pathways. Participants who were receiving atorvastatin 20 mg at baseline were assigned to continue that dose with alirocumab, add ezetimibe 10 mg, or increase atorvastatin to 40 mg. Participants receiving atorvastatin 40 mg at baseline were assigned to alirocumab plus atorvastatin 40 mg, ezetimibe 10 mg plus atorvastatin 40 mg, atorvastatin 80 mg, or a switch to rosuvastatin 40 mg. Placebo preparations were included in the arm descriptions to support masking. The alirocumab arms used an initial dose of 75 mg every two weeks, with an option to increase up to 150 mg.

The primary measure was followed from baseline to Week 24. The registry also lists Week 12 and Week 24 LDL-C analyses and other lipid outcomes. Its analysis descriptions distinguish intent-to-treat from on-treatment analyses. These labels matter: the intent-to-treat primary analysis included eligible post-baseline values whether they were collected on or off treatment, while on-treatment analyses focused on data collected while participants were receiving treatment.

The registry record does not report the original sample-size justification, the trial’s planned power, or a complete statistical analysis plan. The planning illustrations elsewhere on this page are recalculations from observed estimates, not the study’s own design calculations.

4. Participant Flow and Accounting

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

Before assignment: Randomization was stratified according to prior history of myocardial infarction or ischemic stroke, and intensity of statin treatment (atorvastatin 20 or 40 mg). Assignment to treatment arms was done centrally using an Interactive Voice/Web Response System in a 1:1:1:1:1:1:1 ratio after confirmation of selection criteria.

Only the first 6 of 7 groups are shown.

Overall Study

StageAtorvastatin 40 mgEzetimibe 10 mg + Atorvastatin 20 mgAlirocumab 75 mg/up to 150 mg + Atorvastatin 20 mgAtorvastatin 80 mgRosuvastatin 40 mgEzetimibe 10 mg + Atorvastatin 40 mg
STARTED575557474547
Treated575557474546
COMPLETED444046393940
NOT COMPLETED131511867

Reasons for not completing this period:

ReasonAtorvastatin 40 mgEzetimibe 10 mg + Atorvastatin 20 mgAlirocumab 75 mg/up to 150 mg + Atorvastatin 20 mgAtorvastatin 80 mgRosuvastatin 40 mgEzetimibe 10 mg + Atorvastatin 40 mg
Randomized but not treated000001
Subject moved001000
Physician Decision000001
Other than specified785554
Adverse Event435311
Poor compliance to protocol240000

Analysis population for the primary outcome, as defined in the registry: ITT population: all randomized participants with one baseline and at least one post-baseline calculated LDL-C value on- or off-treatment.

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 8 groups are shown.

CharacteristicUnitAtorvastatin 40 mgEzetimibe 10 mg + Atorvastatin 20 mgAlirocumab 75 mg/up to 150 mg + Atorvastatin 20 mgAtorvastatin 80 mgRosuvastatin 40 mgEzetimibe 10 mg + Atorvastatin 40 mg
Participants analysed575557474547
Age, Continuousyears63 (SD 9.91)65.7 (SD 8.96)62.2 (SD 10.03)63.2 (SD 10.89)57.5 (SD 9.96)63.9 (SD 10.33)
Sex: Female, Male: FemaleParticipants222424141311
Sex: Female, Male: MaleParticipants353133333236
Low density lipoprotein cholesterol (LDL-C) in mg/dLmg/dL100.3 (SD 29.8)100.4 (SD 29.5)103.9 (SD 34.9)108.6 (SD 37.5)109.8 (SD 39.0)98.9 (SD 29.2)
LDL-C in mmol/Lmmol/L2.957 (SD 0.773)2.599 (SD 0.765)2.692 (SD 0.905)2.813 (SD 0.97)2.844 (SD 1.011)2.562 (SD 0.756)

6. Primary Endpoint

The registry lists the primary outcome as Percent Change From Baseline in Calculated LDL-C at Week 24 - Intent-to-treat (ITT) Analysis, measured over From Baseline to Week 24.

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

The primary endpoint measures percent change from baseline in calculated low-density lipoprotein cholesterol (LDL-C) at Week 24. It is a continuous laboratory outcome: a value describes the change in the measured quantity relative to its baseline level, rather than whether a participant experienced a clinical event. The registry says calculated LDL-C values were obtained using the Friedewald formula.

The reported arm results are adjusted least-squares means from a mixed model for repeated measures, with standard errors. The primary analysis population included randomized participants with a baseline value and at least one post-baseline calculated LDL-C value, on or off treatment. The model used available post-baseline observations from Week 4 to Week 24, regardless of treatment status. The registry describes this approach as accounting for missing data.

In general, a continuous biomarker endpoint can show the average direction and magnitude of change across treatment groups, while retaining more information than a simple category such as improved or not improved. Here, comparing adjusted mean changes addresses whether the observed average LDL-C trajectory differed between the assigned strategies during the measured period. It does not, by itself, establish effects on cardiovascular events, longer-term outcomes, or every participant’s individual response. Those outcomes and conclusions require evidence beyond this endpoint.

7. Results Posted in the Registry

Mean difference: Ezetimibe 10 mg + Atorvastatin 20 mg

-15.50

95% CI: -28.39 to -2.61

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-69.1-53.1-37.2-21.2-5.310.7Atorvastatin 40 mg (n=53)Ezetimibe 10 mg + Atorvastati… (n=53)Alirocumab 75 mg/up to 150 mg… (n=55)Atorvastatin 80 mg (n=47)Rosuvastatin 40 mg (n=45)Ezetimibe 10 mg + Atorvastati… (n=46)Alirocumab 75 mg/up to 150 mg… (n=46)percent change (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ezetimibe 10 mg + Atorvastati…Alirocumab 75 mg/up to 150 mg…Atorvastatin 80 mgRosuvastatin 40 mgEzetimibe 10 mg + Atorvastati…Alirocumab 75 mg/up to 150 mg…-67-50-33-161.2018mean 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 at Week 24 - On-Treatment AnalysisContinuous EndpointMean difference-17.60 (-30.49 to -4.71)57 per arm
Percent Change From Baseline in Calculated LDL-C at Week 12 - ITT AnalysisContinuous EndpointMean difference-14.10 (-24.91 to -3.29)64 per arm
Percent Change From Baseline in Calculated LDL-C at Week 12 - On-Treatment AnalysisContinuous EndpointMean difference-17.90 (-26.49 to -9.31)25 per arm

Percent Change From Baseline in Calculated LDL-C at Week 24 - On-Treatment Analysis

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ezetimibe 10 mg + Atorvastati…Alirocumab 75 mg/up to 150 mg…-60-47-34-21-8.384.41mean difference vs control (95% CI)

Percent Change From Baseline in Calculated LDL-C at Week 12 - ITT Analysis

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ezetimibe 10 mg + Atorvastati…Alirocumab 75 mg/up to 150 mg…-55-43-31-19-7.694.05mean difference vs control (95% CI)

Percent Change From Baseline in Calculated LDL-C at Week 12 - On-Treatment Analysis

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ezetimibe 10 mg + Atorvastati…Alirocumab 75 mg/up to 150 mg…-57-45-33-20-8.074.25mean difference vs control (95% CI)

The secondary results broadly follow the same pattern as the primary endpoint: the posted LDL-C summaries show more negative mean changes in the alirocumab combination arms than in the corresponding active-comparator arms. This pattern appears across the Week 12 and Week 24 LDL-C summaries and across intent-to-treat and on-treatment presentations. The magnitude differs by time point and analysis population, so the endpoints should not be treated as interchangeable replications of one estimate.

These secondary analyses complement the primary result by showing whether the direction of the LDL-C pattern is also visible at another visit or under a different treatment-status definition. They do not replace the primary Week 24 intent-to-treat analysis. In particular, the on-treatment analyses use a different set of observations from analyses that include data whether or not participants remained on treatment, and therefore address a related but distinct summary.

The registry lists additional outcomes involving apolipoprotein B, non-HDL cholesterol, and total cholesterol. Numerical results for those outcomes are not reported in the registry record in the material, so no quantitative conclusion about their observed changes can be drawn from this page.

Secondary results generally carry less inferential weight than the prespecified primary endpoint, especially when many endpoints, time points, and treatment comparisons are considered. In general, multiple testing can increase the chance of a nominally striking result arising by chance if the analysis does not control multiplicity. The record does not report a complete multiplicity strategy. Accordingly, secondary p-values and patterns should be treated as supportive context rather than as independent confirmation or as a basis for 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 primary results show negative adjusted mean percent changes in calculated LDL-C across all seven reported arms. The values ranged from -4.8 for atorvastatin 80 mg to -54.0 for alirocumab 75 mg/up to 150 mg plus atorvastatin 40 mg. In the lower-baseline-dose pathway, the corresponding values were -5.0 for atorvastatin 40 mg, -20.5 for ezetimibe 10 mg plus atorvastatin 20 mg, and -44.1 for alirocumab 75 mg/up to 150 mg plus atorvastatin 20 mg. In the higher-baseline-dose pathway, the other values were -21.4 for rosuvastatin 40 mg and -22.6 for ezetimibe 10 mg plus atorvastatin 40 mg. These are adjusted group means, not individual participant results.

The sponsor’s mixed-model comparisons are the principal inferential results to read. For the atorvastatin 20 mg pathway, the reported LS mean difference between alirocumab plus atorvastatin 20 mg and atorvastatin 40 mg was -39.1, with a 99% confidence interval from -55.9 to -22.2 and p < 0.001. The comparison with ezetimibe plus atorvastatin 20 mg was -23.6, with a 99% confidence interval from -40.7 to -6.5 and p < 0.001.

For the atorvastatin 40 mg pathway, the sponsor reported LS mean differences of -49.2 versus atorvastatin 80 mg, -32.6 versus rosuvastatin 40 mg, and -31.4 versus ezetimibe plus atorvastatin 40 mg. Their respective 99% confidence intervals were -65 to -33.5, -48.4 to -16.9, and -47.4 to -15.4; each reported p-value was below < 0.001. The negative estimates indicate a more negative adjusted mean change in the alirocumab arm on the registry’s reported scale. These results describe the biomarker comparisons during the study, not clinical benefit or harm.

The recalculated comparisons on this page are simple, unadjusted comparisons derived from posted arm summaries. They can help readers see the approximate contrast between group means, but they do not reproduce the sponsor’s repeated-measures model or its covariate and missing-data handling. Because the record flags a discrepancy, the sponsor’s own analysis takes precedence. The recalculated estimates and intervals should therefore be treated as supplementary summaries rather than replacements for the reported inferential analyses.

Statistical significance does not settle questions about the size, clinical importance, or persistence of an effect. The endpoint is calculated LDL-C over the stated period, and the results do not include cardiovascular event outcomes. Interpretation should also keep the multiple comparisons and unreported analysis-plan details in view.

10. Statistical Methods Explained

The registry describes an adjusted analysis of a repeated continuous measure. Understanding the result means distinguishing the model-based primary analysis from the simpler recalculations based on arm summaries, and distinguishing the intent-to-treat analysis from the on-treatment analyses.

What does the primary model estimate?

The primary endpoint is percent change from baseline in calculated LDL-C at Week 24. The registry reports least-squares means (LS means) and standard errors from a mixed-effect model with repeated measures, commonly abbreviated MMRM. An LS mean is a model-adjusted group mean. It is not necessarily the same as the raw arithmetic average of the observed values, because it comes from a statistical model that uses the repeated measurements and the specified model structure.

Repeated-measures models are used when participants can contribute measurements at more than one time point. In general, such models can represent the pattern of change over time and use available observations without requiring every participant to have a complete set of measurements. The registry says the primary model used all available post-baseline calculated LDL-C data from Week 4 to Week 24, on or off treatment, and was used to account for missing data. The model specification beyond that description, including its covariance structure and other detailed settings, is not reported in the registry record.

What does intent-to-treat mean?

The primary analysis population is defined as randomized participants with one baseline and at least one post-baseline calculated LDL-C value, whether collected on or off treatment. That definition is the registry’s operational description of the intent-to-treat population for this endpoint. It does not say that every randomized participant contributed a primary outcome measurement: the stated eligibility requirement includes at least one post-baseline value. The number of participants contributing to each arm’s reported analysis is shown with the results. In general, an intent-to-treat approach aims to preserve the comparison created by random assignment, while the record’s particular population definition and available-data rules determine who contributes to the model.

The secondary outcome list also distinguishes intent-to-treat and on-treatment analyses. An on-treatment analysis uses observations associated with treatment exposure under the record’s definitions. Such an analysis can answer a related but different question from an analysis that includes values collected after treatment has stopped. The registry does not give full operational definitions for every on-treatment rule in the material.

Why use calculated LDL-C?

The endpoint is a calculated laboratory measure. The registry states that calculated LDL-C values were obtained using the Friedewald formula. In general, a calculated measure depends on the formula and its input measurements, so it should be understood as the specified calculated outcome rather than a direct measurement of every component. The record does not describe additional details about the calculation or its handling in circumstances where a calculation might be unavailable.

How do the recalculations differ?

The recalculated comparisons use the posted arm means and standard errors to form simple, unadjusted estimates. The posted summaries give standard errors rather than participant-level data or standard deviations. The recalculation therefore uses an approximate standard deviation, as indicated with those comparisons. It is not a recreation of the sponsor’s MMRM, and it does not account for the repeated time points in the same way. The displayed p-values and intervals for those comparisons are unadjusted recalculations, not the sponsor’s model-based results.

In general, an unadjusted comparison of summary means can be useful as a transparent check on the direction and rough scale of a contrast. It is less suited to replacing an analysis that uses repeated observations, model adjustment, and the trial’s defined analysis population. Here the registry marks a discrepancy between the recalculation and the reported result. Accordingly, the sponsor’s analysis is the one to prioritize for inference.

What can the planning illustrations tell us?

The sample-size illustrations use an observed contrast as a planning input and show hypothetical participant requirements under stated assumptions. They are not a reconstruction of the trial’s original design. In general, planning calculations depend on the anticipated effect, variability, allocation, significance threshold, and target power; changing an assumption changes the resulting requirement. The original sample-size justification and planned power are not reported in the registry record.

Finally, multiple treatment comparisons and multiple endpoints raise the general issue of multiplicity: when many hypotheses are tested, the chance of at least one apparently strong result can increase if no adjustment is made. The registry’s record does not report a complete multiplicity strategy, so the posted p-values should not be treated as evidence that all comparisons had a specified family-wise error control. The model’s detailed assumptions and diagnostic checks are also not reported in the registry record.

11. Confidence Intervals and Precision

A confidence interval expresses uncertainty around an estimated contrast. In general, it gives a range of values that are more or less compatible with the data and model under the interval’s stated confidence procedure. A narrower interval indicates greater statistical precision; a wider interval indicates more uncertainty about the exact size of the contrast. An interval does not describe the range of individual participant responses.

The sponsor’s primary comparisons are reported with 99% confidence intervals. For the comparison of alirocumab plus atorvastatin 20 mg with atorvastatin 40 mg, the estimate was -39.1 and the interval ran from -55.9 to -22.2. For the comparison with ezetimibe plus atorvastatin 20 mg, the estimate was -23.6 and the interval ran from -40.7 to -6.5. In the higher-dose pathway, the reported contrasts were -49.2 versus atorvastatin 80 mg, -32.6 versus rosuvastatin 40 mg, and -31.4 versus ezetimibe plus atorvastatin 40 mg; the corresponding 99% intervals are displayed with the reported analyses.

These intervals communicate uncertainty in the model-based average contrasts, not certainty about every person’s result. Their reported bounds are below zero, and the corresponding sponsor p-values are reported in the results. That statistical pattern does not by itself establish clinical importance or address outcomes beyond calculated LDL-C during the study period.

The recalculated intervals are based on arm-level summaries and approximate variability, not the sponsor’s repeated-measures model. Their assumptions and inferential basis therefore differ. Because the registry flags a discrepancy, the sponsor’s own intervals take precedence. The confidence level for the recalculated intervals is not stated in the displayed details, so they should not be confused with the sponsor’s explicitly reported 99% intervals.

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 effect75101
75% of the observed effect134179
50% of the observed effect300402
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect501002005001,00040%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. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Ezetimibe 10 mg + Atorvastatin 20 mg.

The sample-size table and curve are planning illustrations based on observed treatment contrasts, not the trial’s original design calculations. For these continuous outcomes, the displayed figures are participants per arm, not total participants or total events. The registry record’s original sample-size assumptions and justification are not reported.

The illustrations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They consider detecting 100%, 75%, or 50% of the observed effect. The 80% power column means the hypothetical per-arm sample size under those assumptions for an 80% chance of detecting the specified effect if that effect and the planning assumptions were correct. The 90% power column gives the corresponding requirement for a 90% chance. These are planning targets, not descriptions of what happened in the completed trial.

The direction of the relationship is important when reading the table or curve: smaller effects require more participants to detect with the same target power, because a smaller contrast is harder to distinguish from random variation. The very large planning figures for a near-zero observed contrast should be read as a consequence of using that observed contrast as the planning input, not as a recommendation or as evidence about the original trial design. The illustrations are not observed power; observed power is not a substitute for reading the estimated effect and its uncertainty.

These calculations also simplify the trial into a two-arm comparison. They do not reproduce the MMRM analysis, the multiple treatment groups, the full pattern of repeated measurements, or the sponsor’s analysis procedures. Their purpose is to illustrate how sample-size requirements change with the assumed effect size under the stated planning assumptions.

13. How the Sample Size Is Derived

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

Formula

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 = -15.500; pooled standard deviation σ = 33.854.
  2. n = 2 × (1.96 + 0.842)2 × 33.8542 / -15.5002 = 74.9, rounded up to 75 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 <- -15.5                      # observed difference in means
sigma <- 33.8544679473773                     # 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(1730040)
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 = 75 (80% power), 101 (90% power)
 75% of observed effect: n per arm = 134 (80% power), 179 (90% power)
 50% of observed effect: n per arm = 300 (80% power), 402 (90% power)
power.t.test: 75.9 
Simulated power at n = 75 per arm: 0.795 (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
Mixed Models AnalysisLS Mean Difference -39.1-55.9 to -22.2< 0.001
Mixed Models AnalysisLS Mean Difference -23.6-40.7 to -6.5= 0.0004
Mixed Models AnalysisLS Mean Difference -49.2-65 to -33.5< 0.001
Mixed Models AnalysisLS Mean Difference -32.6-48.4 to -16.9< 0.001
Mixed Models AnalysisLS Mean Difference -31.4-47.4 to -15.4< 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 sponsor’s reported analyses use mixed models and report LS mean differences, 99% confidence intervals, and p-values. These are the principal results for the primary endpoint. They are not identical in method to the recalculated comparisons, which use arm-level means and standard errors to make simple unadjusted estimates.

For example, the recalculated contrast for alirocumab plus atorvastatin 20 mg versus atorvastatin 40 mg is -39.1, while the sponsor reports an LS mean difference of -39.1. The matching point estimate does not make the analyses interchangeable: the recalculated interval is -51.71 to -26.49, whereas the sponsor reports a 99% interval from -55.9 to -22.2. The model, information used, and inferential procedure differ. Other comparisons also show differences between recalculated and sponsor estimates.

The record explicitly flags a discrepancy. In that situation, the sponsor’s own analysis takes precedence over the simple recalculations. Readers should use the sponsor’s model-based contrasts for the trial’s reported inference, and regard the recalculations as supplementary checks on the broad direction and scale of the arm-level comparisons. The registry record does not report enough detail to reproduce the sponsor’s complete model specification independently.

15. Multiplicity, Missing Data and Analysis Populations

The trial compares several assigned strategies across two baseline atorvastatin-dose pathways and reports multiple outcomes at different time points, including intent-to-treat and on-treatment analyses. In general, testing many comparisons can increase the probability of observing at least one small p-value even when there is no corresponding effect. Prespecified testing hierarchies or multiplicity adjustments can address this issue, but the registry record does not report a complete multiplicity plan or explain how the reported p-values should be interpreted across all comparisons.

The primary endpoint and its analysis population are described: percent change from baseline in calculated LDL-C at Week 24, in the intent-to-treat population defined as randomized participants with baseline and at least one post-baseline value. The stated model used available observations from Week 4 through Week 24, on or off treatment, and was intended to account for missing data. This description helps readers understand which measurements entered the analysis, but it does not fully specify how the model handled every missingness pattern or what assumptions underlie that handling.

In general, a model that uses available repeated measurements still depends on assumptions about the relationship between observed and missing values. The registry record does not report sensitivity analyses for departures from those assumptions. It also does not report a detailed protocol for missing values, the full model specification, or the original sample-size justification. Those omissions limit independent reconstruction of the analysis and assessment of how robust the estimates are to alternative analytical choices.

The results also distinguish on-treatment from intent-to-treat analyses for secondary outcomes. Such analyses can answer different questions because they may include different observations. Their labels should therefore be read alongside their analysis-population definitions rather than as merely alternate names for the same estimate. The registry record does not report complete operational details for all analysis populations or the planned status of each analysis.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Atorvastatin 40 mg2573.5%
Ezetimibe 10 mg + Atorvastatin 20 mg5559.1%
Alirocumab 75 mg/up to 150 mg + Atorvastatin 20 mg3575.3%
Atorvastatin 80 mg4478.5%
Rosuvastatin 40 mg2454.4%
Ezetimibe 10 mg + Atorvastatin 40 mg2464.3%
Alirocumab 75 mg/up to 150 mg + Atorvastatin 40 mg1472.1%
Participants with at least one serious adverse event
Serious adverse events by armAtorvastatin 40 mg3.5%Ezetimibe 10 mg + Atorvastati…9.1%Alirocumab 75 mg/up to 150 mg…5.3%Atorvastatin 80 mg8.5%Rosuvastatin 40 mg4.4%Ezetimibe 10 mg + Atorvastati…4.3%Alirocumab 75 mg/up to 150 mg…2.1%% 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
Atorvastatin 40 mg17 of 57
Ezetimibe 10 mg + Atorvastatin 20 mg24 of 55
Alirocumab 75 mg/up to 150 mg + Atorvastatin 20 mg15 of 57
Atorvastatin 80 mg18 of 47
Rosuvastatin 40 mg23 of 45
Ezetimibe 10 mg + Atorvastatin 40 mg12 of 46

Most frequent serious adverse event terms

Event termOrgan systemAtorvastatin 40 mgEzetimibe 10 mg + Atorvastatin 20 mgAlirocumab 75 mg/up to 150 mg + Atorvastatin 20 mgAtorvastatin 80 mgRosuvastatin 40 mgEzetimibe 10 mg + Atorvastatin 40 mg
PneumoniaInfections and infestations0 of 571 of 550 of 571 of 470 of 451 of 46
Angina unstableCardiac disorders0 of 570 of 552 of 570 of 470 of 450 of 46
Atrioventricular block completeCardiac disorders0 of 570 of 550 of 571 of 470 of 450 of 46
Cardiac arrestCardiac disorders0 of 571 of 550 of 570 of 470 of 450 of 46
Coronary artery diseaseCardiac disorders0 of 570 of 550 of 570 of 470 of 451 of 46
Chest painGeneral disorders0 of 571 of 550 of 570 of 470 of 450 of 46
Non-Cardiac chest painGeneral disorders0 of 570 of 550 of 570 of 471 of 450 of 46
Cholecystitis acuteHepatobiliary disorders0 of 571 of 550 of 570 of 470 of 450 of 46
DiverticulitisInfections and infestations1 of 570 of 550 of 570 of 470 of 450 of 46
SeromaInjury, poisoning and procedural complications1 of 570 of 550 of 570 of 470 of 450 of 46

Most frequent non-serious adverse event terms

Event termOrgan systemAtorvastatin 40 mgEzetimibe 10 mg + Atorvastatin 20 mgAlirocumab 75 mg/up to 150 mg + Atorvastatin 20 mgAtorvastatin 80 mgRosuvastatin 40 mgEzetimibe 10 mg + Atorvastatin 40 mg
Upper respiratory tract infectionInfections and infestations2 of 574 of 552 of 572 of 473 of 455 of 46
Urinary tract infectionInfections and infestations3 of 575 of 551 of 574 of 471 of 453 of 46
NauseaGastrointestinal disorders3 of 573 of 551 of 575 of 473 of 451 of 46
DiarrhoeaGastrointestinal disorders4 of 571 of 551 of 571 of 473 of 452 of 46
NasopharyngitisInfections and infestations1 of 573 of 551 of 573 of 474 of 450 of 46
Back painMusculoskeletal and connective tissue disorders2 of 573 of 553 of 572 of 472 of 450 of 46
Accidental overdoseInjury, poisoning and procedural complications2 of 572 of 550 of 572 of 473 of 450 of 46
ArthralgiaMusculoskeletal and connective tissue disorders1 of 573 of 552 of 571 of 471 of 451 of 46
HypertensionVascular disorders0 of 571 of 552 of 571 of 470 of 455 of 46
Muscle spasmsMusculoskeletal and connective tissue disorders0 of 571 of 554 of 571 of 471 of 450 of 46

Serious events with the highest arm-level rate: angina unstable (3.5%), non-cardiac chest pain (2.2%), intraductal proliferative breast lesion (2.2%), coronary artery disease (2.2%), pneumonia (2.2%).

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 by arm, with the number of participants at risk and the number affected. For serious adverse events, the listed affected counts range from 1 to 5 across the groups; the denominators at risk range from 45 to 57. These are counts, not a basis for a direct causal comparison between treatments. The “other” adverse-event counts are also shown by group, with affected counts ranging from 12 to 24 and at-risk counts from 45 to 57.

These figures should be read as descriptive summaries over the registry’s adverse-event reporting period, not as proof that an event was caused by a study treatment. The posted summary does not give event-level timing, severity detail beyond the serious-event classification, or a statistical comparison that would support a comparative safety conclusion. The death counts are not reported in the registry record.

The registry also lists serious-event terms with percentages, including unstable angina, non-cardiac chest pain, intraductal proliferative breast lesion, coronary artery disease, pneumonia, and complete atrioventricular block. These terms are presented in the record without enough group-specific context to interpret them as comparative rates. The safety table should be used to locate the reported counts and terms, while recognizing that it does not settle treatment attribution or comparative risk.

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

The posted primary results describe differences in adjusted mean change in calculated LDL-C over the study period. The alirocumab combination arms had more negative Week 24 adjusted mean changes than the corresponding active-comparator arms, and the sponsor’s model-based comparisons report contrasts with 99% confidence intervals and p-values. Those are findings about the measured biomarker and the statistical model used for the registry analysis.

They do not establish whether the observed differences are clinically important, how long they persist after the study period, or whether they translate into fewer cardiovascular events. Cardiovascular events are not the primary endpoint. The results also do not imply that every participant experienced a change equal to the group mean. Individual responses can vary, and the registry summaries do not provide participant-level trajectories.

The trial’s active-comparator design helps frame the question as a comparison among treatment strategies for patients described in the record, rather than as a comparison with no treatment. But the findings should remain within the recorded population, endpoint, analysis, and follow-up context. They do not automatically generalize to populations or treatment situations not described in the registry.

The reported estimates should also be interpreted with the limits of the analysis record in mind. The primary model is described but not fully specified, and the complete multiplicity plan and original sample-size justification are not reported. The simple recalculations are not a substitute for the sponsor’s mixed-model analyses; the record flags a discrepancy, so the sponsor’s results take precedence. Secondary outcomes add context but are not all numerically, and multiple secondary tests carry less weight when their multiplicity handling is unreported.

In short, the page summarizes a randomized comparison of short-term lipid-measure changes. It does not provide medical advice, establish an individual treatment choice, or answer broader clinical questions that were not measured in the posted results.

18. Why This Trial Matters Statistically

This study is statistically informative because it compares several active treatment strategies within two baseline atorvastatin-dose pathways, rather than relying on one comparator for every participant. That structure makes it important to keep the treatment pathways straight: a comparison with atorvastatin 40 mg in the lower-dose pathway is not the same contrast as a comparison with atorvastatin 80 mg, rosuvastatin 40 mg, or ezetimibe plus atorvastatin 40 mg in the higher-dose pathway.

The primary endpoint is a repeated continuous measure, and the sponsor used a mixed model for repeated measures. This illustrates why model-based results should be distinguished from simple differences between posted arm means. The model uses the repeated observations as described by the registry, whereas the recalculations are approximate and unadjusted. The record’s discrepancy flag makes that distinction especially relevant: a calculation that happens to match a point estimate does not reproduce the sponsor’s uncertainty estimate or analysis.

The study also provides a useful example of reading an endpoint alongside its population definition. The primary intent-to-treat analysis includes participants with baseline and at least one post-baseline value, whether on or off treatment. Secondary summaries include on-treatment analyses, which use a different analysis basis. Recognizing this prevents readers from treating every estimate as if it summarized the same participants and observations.

Finally, the record shows why statistical interpretation includes more than p-values. Confidence intervals communicate uncertainty about the average contrasts, while missing multiplicity details and unreported design assumptions limit what can be reconstructed. These features are common challenges in reading registry results and make transparent separation of primary, secondary, sponsor-reported, and recalculated findings essential.

19. Limitations

The registry record describes the primary model and analysis population but does not report a complete statistical analysis plan, full model specification, or detailed missing-data sensitivity analyses. That makes it difficult to independently reproduce the sponsor’s repeated-measures results or assess how results might change under alternative assumptions about missing observations.

The record does not report the original sample-size justification or planned power. The planning table and curve on this page are recalculations based on observed effects and stated illustrative assumptions; they cannot be used to infer what the trial was designed to detect. Some recalculated requirements are highly sensitive to the size of the observed contrast, especially where that contrast is near zero.

There are several arms, multiple active comparisons, and secondary outcomes at different time points and under different analysis populations. The registry record does not report a complete multiplicity strategy. This limits the interpretation of nominal p-values across the full set of analyses. The sponsor’s results should remain primary for the comparisons because the record flags a discrepancy with the recalculations.

The primary endpoint is a calculated biomarker measured through Week 24, not a cardiovascular event endpoint. The record therefore cannot answer whether the observed laboratory differences correspond to differences in clinical events or persist beyond the stated period. The registry also does not report numerical findings for some listed secondary lipid outcomes in the material. Finally, adverse-event summaries are presented as counts and terms; they do not by themselves establish causation or comparative safety.

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

ODYSSEY OPTIONS I was a completed, randomized, double-blind, active-comparator, parallel-group Phase 3 study with quadruple masking and enrollment of 355. It examined alirocumab added to atorvastatin against several active lipid-modifying strategies in patients at high cardiovascular risk with nonfamilial hypercholesterolemia or heterozygous familial hypercholesterolemia.

The primary endpoint was percent change from baseline in calculated LDL-C at Week 24, analyzed in a defined intent-to-treat population with a mixed model for repeated measures. The sponsor reported model-based comparisons with 99% confidence intervals. The record flags a discrepancy with the simple unadjusted recalculations, so the sponsor’s analyses take precedence. The registry record does not report the original sample-size justification, complete multiplicity strategy, or full model specification.

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