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 Effects on Lipoprotein Metabolism From PCSK9 Inhibition Utilizing a Monoclonal Antibody (NCT02189837), a randomized phase 3 study. The primary outcome is Percent Change From Baseline in Low-density Lipoprotein (LDL) Apolipoprotein B-100 Fractional Catabolic Rate (FCR).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02189837 |
| Phase | Phase 3 |
| Condition | Primary Hyperlipidemia and Mixed Dyslipidemia |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 89 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Amgen |
| Results posted | Yes |
2. Clinical Question
Population
The study concerned participants with primary hyperlipidemia and mixed dyslipidemia. The primary endpoint analysis included randomized and dosed participants who completed both baseline and Day 50 measurements. The registry record does not report further eligibility details or participant characteristics in the results presented.
Intervention
Participants received evolocumab, atorvastatin, or both. Evolocumab was given as a 420 mg subcutaneous injection once every 2 weeks on days 1, 15, 29 and 43. Atorvastatin was given as 80 mg orally once a day. Treatment was described for up to 8 weeks.
Comparator
The placebo group received placebo injections on the same schedule as evolocumab and placebo tablets once a day. The design also permits comparisons between atorvastatin alone and the combination, as well as between placebo and evolocumab alone.
Primary question
The primary question was whether the treatment groups differed in percent change from baseline in LDL apolipoprotein B-100 fractional catabolic rate at Day 50. This rate describes how rapidly LDL-associated apolipoprotein B-100 is replaced, transferred, or lost over time. It is a kinetic measure rather than a direct clinical outcome.
The trial also assessed LDL-C and other lipoprotein kinetic outcomes. These additional measures help characterize changes in lipid concentrations and in the production or removal of lipoproteins. They are distinct outcomes and should not be treated as interchangeable evidence. The registry record does not report a clinical-event question, such as whether treatment changed the occurrence of cardiovascular events.
3. Trial Design
The registry record describes a randomized, placebo-controlled, parallel-group phase 3 trial sponsored by Amgen. Its official title describes a double-blind, single-site study, while the registry’s masking classification is triple. Both descriptions indicate that masking was used, but the precise roles masked are not reported in the registry record. The record lists an enrollment of 89 and a completed status.
Four groups received placebo, atorvastatin, evolocumab, or evolocumab with atorvastatin. The placebo group received placebo injections every 2 weeks on days 1, 15, 29 and 43, plus daily placebo tablets. The atorvastatin group received placebo injections and 80 mg atorvastatin daily. The evolocumab group received 420 mg evolocumab on the injection schedule and placebo tablets. The combination group received both active treatments. The described treatment period was up to 8 weeks.
The primary endpoint compared baseline with Day 50. Its analysis population was the Efficacy Analysis Set: randomized and dosed participants who completed baseline and Day 50 measurements. The arm counts for this endpoint are 20 for placebo, 22 for atorvastatin, 20 for evolocumab, and 19 for the combination. These are endpoint analysis counts, not the total enrollment.
The registry gives a start date of 2014-07-08 and a primary completion date of 2015-02-13. The original sample-size justification, the trial’s prespecified statistical analysis plan, any interim analyses, and details of randomization or allocation concealment are not reported in the registry record. The listed sample-size figures are planning illustrations based on observed effects, not the trial’s original design assumptions.
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 who met eligibility criteria underwent an initial 4 week run-in period of dietary stabilization before randomization. Randomization was stratified based on screening low-density lipoprotein (LDL-C) concentration (\< 130 mg/dL vs ≥ 130 mg/dL)
Overall Study
| Stage | Placebo | Atorvastatin | Evolocumab | Evolocumab and Atorvastatin |
|---|---|---|---|---|
| STARTED | 22 | 23 | 23 | 21 |
| Received Treatment | 21 | 22 | 22 | 20 |
| COMPLETED | 20 | 22 | 20 | 19 |
| NOT COMPLETED | 2 | 1 | 3 | 2 |
Reasons for not completing this period:
| Reason | Placebo | Atorvastatin | Evolocumab | Evolocumab and Atorvastatin |
|---|---|---|---|---|
| Withdrawal by Subject | 2 | 1 | 3 | 1 |
| Sponsor Decision | 0 | 0 | 0 | 1 |
Analysis population for the primary outcome, as defined in the registry: Efficacy Analysis Set including all randomized and dosed participants who completed baseline and Day 50 measurements.
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: The full analysis set includes all randomized participants who received any study drug.
| Characteristic | Unit | Placebo | Atorvastatin | Evolocumab | Evolocumab and Atorvastatin | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 21 | 22 | 22 | 20 | 85 | |
| Age, Continuous | years | 33.9 (SD 12.7) | 30.4 (SD 7.4) | 33.5 (SD 11.6) | 31.0 (SD 9.8) | 32.2 (SD 10.5) |
| Sex: Female, Male: Female | Participants | 0 | 0 | 0 | 0 | 0 |
| Sex: Female, Male: Male | Participants | 21 | 22 | 22 | 20 | 85 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | participants | 0 | 0 | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Asian | participants | 1 | 2 | 1 | 3 | 7 |
| Race/Ethnicity, Customized: Black or African American | participants | 0 | 0 | 0 | 3 | 3 |
| Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islander | participants | 0 | 0 | 0 | 0 | 0 |
| Race/Ethnicity, Customized: White | participants | 19 | 20 | 20 | 14 | 73 |
| Race/Ethnicity, Customized: Other | participants | 1 | 0 | 1 | 0 | 2 |
| Race/Ethnicity, Customized: Mixed Race | participants | 0 | 0 | 0 | 0 | 0 |
| Screening LDL-C Level: < 130 mg/dL | participants | 9 | 9 | 9 | 8 | 35 |
| Screening LDL-C Level: ≥ 130 mg/dL | participants | 12 | 13 | 13 | 12 | 50 |
| LDL-C Concentration | mg/dL | 118.1 (SD 18.1) | 123.2 (SD 21.3) | 118.2 (SD 18.4) | 116.5 (SD 23.7) | 119.1 (SD 20.2) |
6. Primary Endpoint
The registry lists the primary outcome as Percent Change From Baseline in Low-density Lipoprotein (LDL) Apolipoprotein B-100 Fractional Catabolic Rate (FCR), measured over Baseline (5 days prior to Day 1) and Day 50; plasma samples for fasting lipids were obtained at 0, 5, 10, 20, 30, 40, and 60 min, as well as at 1.5, 2, 2.5, 3, 4, 5, 6, 8, and 10 hours, and 2, 3, 4 and 5 days after D3-leucine administration..
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | percent change |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was percent change from baseline in LDL apolipoprotein B-100 fractional catabolic rate at Day 50. Apolipoprotein B-100 is a protein associated with LDL particles. Fractional catabolic rate describes the percentage of this protein in LDL that is replaced, transferred, or lost per unit of time. It therefore measures aspects of particle turnover, rather than simply measuring the concentration of LDL cholesterol in a blood sample.
To estimate the rate, the study used the stable isotope tracer D3-leucine over 5 consecutive days at baseline and Day 50. LDL particles were isolated from plasma, and isotopic enrichment was measured using gas chromatography-mass spectrometry. Mathematical modelling of the protein enrichment data was then used to estimate protein catabolism. The registry describes fasting lipid sampling at multiple time points after tracer administration.
General explanation: kinetic endpoints are used when investigators want to characterize the processes contributing to a measured concentration, including production and removal. A change in fractional catabolic rate does not by itself establish a change in clinical outcomes. It also depends on the measurement and modelling procedures used. The registry record does not report further validation details or a clinically meaningful threshold for interpreting a change in this endpoint.
7. Results Posted in the Registry
- Atorvastatin: mean 74.13 versus -5.07 on control; difference 79.20 (95% CI 8.64 to 149.76), standardized effect d = 0.68; z-test p = 0.028.
- Evolocumab: mean 83.70 versus -5.07 on control; difference 88.77 (95% CI 16.54 to 161.00), standardized effect d = 0.76; z-test p = 0.016.
- Evolocumab and Atorvastatin: mean 310.48 versus -5.07 on control; difference 315.55 (95% CI 242.45 to 388.65), standardized effect d = 2.71; z-test p = <0.001.
Mean difference: Atorvastatin
95% CI: 8.64 to 149.76
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percent Change From Baseline in LDL-C at Day 50 | Continuous Endpoint | Mean difference | -44.60 (-52.85 to -36.35) | 2 per arm |
| Percent Change From Baseline in LDL Apolipoprotein B-100 Production Rate (PR) | Continuous Endpoint | Mean difference | 0.53 (-19.50 to 20.56) | 61,153 per arm |
| Percent Change From Baseline in Lipoprotein (a) Fractional Catabolic Rate (FCR) | Continuous Endpoint | Mean difference | 18.03 (-7.04 to 43.10) | 66 per arm |
Percent Change From Baseline in LDL-C at Day 50
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Atorvastatin: mean -45.25 versus -0.65 on control; difference -44.60 (95% CI -52.85 to -36.35), standardized effect d = -3.32; z-test p = <0.001.
- Evolocumab: mean -57.79 versus -0.65 on control; difference -57.14 (95% CI -65.79 to -48.49), standardized effect d = -4.26; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Atorvastatin than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Evolocumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percent Change From Baseline in LDL Apolipoprotein B-100 Production Rate (PR)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Atorvastatin: mean -3.27 versus -3.80 on control; difference 0.53 (95% CI -19.50 to 20.56), standardized effect d = 0.02; z-test p = 0.959.
- Evolocumab: mean -20.45 versus -3.80 on control; difference -16.65 (95% CI -37.16 to 3.86), standardized effect d = -0.50; z-test p = 0.112.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Atorvastatin and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Evolocumab and the control. The interval gives the range of effects that remain compatible with the data.
Percent Change From Baseline in Lipoprotein (a) Fractional Catabolic Rate (FCR)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Atorvastatin: mean 25.52 versus 7.49 on control; difference 18.03 (95% CI -7.04 to 43.10), standardized effect d = 0.49; z-test p = 0.159.
- Evolocumab: mean 5.37 versus 7.49 on control; difference -2.12 (95% CI -28.44 to 24.20), standardized effect d = -0.06; z-test p = 0.875.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Atorvastatin and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Evolocumab and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes cover several related but distinct aspects of lipoprotein metabolism: LDL-C concentration, LDL apolipoprotein B-100 production rate, and lipoprotein(a) production and fractional catabolic rate. Taken together, the pattern is not uniform across these measures or across treatment contrasts. Some sponsor-reported contrasts are more clearly separated from zero than others, while some estimates remain imprecise. This variation means the secondary results add detail about different biological processes rather than forming a single, consistent confirmation of the primary endpoint.
The LDL-C outcome provides a concentration measure, while production and catabolic-rate outcomes address processes that can contribute to concentrations. The primary endpoint concerns LDL apolipoprotein B-100 fractional catabolic rate, so the secondary kinetic endpoints are related in topic but do not measure the same quantity. A difference in one measure does not automatically predict the direction or size of a difference in another.
General explanation: secondary outcomes are often useful for understanding a trial’s broader pattern, but they commonly involve multiple outcomes and contrasts. Unless a prespecified hierarchy or multiplicity adjustment is reported, individual p-values should be treated cautiously. The registry record does not report such an adjustment or hierarchy. The secondary analyses therefore carry less confirmatory weight than the primary analysis, and their results should be interpreted as supporting context rather than independent proof of a broad treatment effect.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percent Change From Baseline in LDL-C at Day 50
- Percent Change From Baseline in LDL Apolipoprotein B-100 Production Rate (PR)
- Percent Change From Baseline in Lipoprotein (a) Fractional Catabolic Rate (FCR)
- Percent Change From Baseline in Lipoprotein(a) Production Rate (PR)
9. Statistical Interpretation
The primary endpoint arm estimates are least-squares means for percent change from baseline. The posted means were -5.07 for placebo, 74.13 for atorvastatin, 83.7 for evolocumab, and 310.5 for evolocumab with atorvastatin. These estimates describe the analyzed groups at Day 50; they are not individual participant values. The reported spread is a standard error, which reflects uncertainty in an estimated mean rather than the full range of participant responses.
The sponsor’s ANCOVA results include a placebo-versus-evolocumab least-squares mean treatment difference of 88.76, with a 95% confidence interval from 15.73 to 161.80 and p = 0.018. The comparison between atorvastatin and the combination is 236.35, with a 95% confidence interval from 164.02 to 308.69 and p < 0.001. The reported overall treatment effect is 147.59, with a 95% confidence interval from 44.80 to 250.38 and p = 0.005. These are the sponsor’s adjusted analyses and take precedence over simple re-calculations.
The registry also allows simple, unadjusted comparisons reconstructed from arm-level summary statistics. Those calculations compare each active arm with placebo. They estimate mean differences of 79.2 for atorvastatin, 88.77 for evolocumab, and 315.6 for the combination, with unadjusted p-values of 0.028, 0.016, and <0.001, respectively. The calculations are not the same as the sponsor’s ANCOVA contrasts, and the combination comparison in particular uses a different comparator from the sponsor’s atorvastatin-versus-combination analysis. Because a discrepancy is flagged, the sponsor’s own analysis takes precedence.
General explanation: a p-value evaluates how compatible the observed data are with a specified null hypothesis under a statistical model. It does not measure the size or clinical importance of an effect. A confidence interval gives a range of values compatible with the analysis and its assumptions. The sponsor’s confidence intervals for its reported comparisons do not include zero, but this statistical feature alone does not establish clinical benefit or describe all uncertainty in the trial.
The results concern a short-term mechanistic endpoint in participants with dyslipidemia. They do not establish longer-term effects or clinical outcomes. The record does not report a threshold for clinical importance, and it does not provide the full model specification needed to assess all features of the sponsor’s adjustment.
10. Statistical Methods Explained
What do the least-squares means represent?
The primary outcome is continuous, and the registry reports least-squares means for each treatment group. General explanation: a least-squares mean is a model-based estimate of a group mean. In an analysis of covariance, or ANCOVA, the estimate can account for specified covariates. The covariates included in the sponsor’s model are not reported in the registry record, so the adjusted means cannot be independently reconstructed from the information available. The reported spread is standard error, which describes uncertainty around an estimated mean, not the variability of individual measurements.
What is ANCOVA doing?
General explanation: ANCOVA models an outcome using treatment group and one or more covariates. When baseline outcome is included, the treatment contrast can account for baseline differences and may improve precision. ANCOVA reports an adjusted treatment contrast, often alongside a confidence interval and p-value. The registry labels the posted analyses as ANCOVA and gives least-squares mean treatment differences. It does not report the model formula, covariates, missing-data method, or whether any assumptions were checked.
How do the re-calculations differ?
The simple re-calculations use the posted arm-level means and standard errors to estimate unadjusted differences. The pooled standard deviations are approximate, as indicated in the calculations, and the resulting comparisons are not ANCOVA-adjusted. They are useful as a transparent check on the direction and broad scale of contrasts, but they do not replace the sponsor’s model-based analysis. Because the registry flags a discrepancy, the sponsor’s own analysis takes precedence. In addition, the re-calculated comparisons use placebo as the reference for each active group, whereas some sponsor-reported comparisons use a different reference group.
General explanation: adjustment can change an estimate or its precision when covariates are related to the outcome. Small differences between adjusted and unadjusted estimates are not necessarily errors; they can arise because the analyses answer the question using different models and information. A discrepancy should therefore be described rather than resolved by selecting whichever estimate appears preferable.
How should the confidence intervals and p-values be read?
General explanation: a confidence interval expresses the uncertainty around an estimate under the model and sampling assumptions. A wider interval indicates less precision; a narrower interval indicates greater precision, though it does not address bias or model misspecification. A p-value is not the probability that a hypothesis is true, nor does it measure the probability that a finding will replicate. The registry reports 95% confidence intervals for the sponsor’s analyses. The simple re-calculations also include intervals, but these are based on approximate unadjusted methods.
General explanation: repeated testing of multiple outcomes or contrasts creates a multiplicity issue. If many hypotheses are examined without an adjustment or a prespecified testing hierarchy, the chance of at least one apparently notable result can increase. The registry record lists 5 outcome measures and 15 analyses, but a multiplicity adjustment or formal testing hierarchy is not reported. Results for secondary outcomes should therefore be viewed as exploratory unless the analysis plan establishes otherwise.
Why might over-dispersion matter?
General explanation: over-dispersion occurs when observed variability is greater than a model assumes. It is especially relevant for count outcomes, where a simple Poisson model assumes that the mean and variance are equal. Excess variability can make standard errors too small and intervals too narrow if it is ignored. The primary endpoint is continuous, not a count, so over-dispersion is not the central issue for its analysis. More generally, the suitability of any model depends on its assumptions and on how well they fit the data. The registry does not report diagnostic checks for the continuous-outcome models.
The posted arm-level standard errors also do not reveal the distribution of individual responses. General explanation: a mean and its standard error can summarize an estimated group value while concealing skewness, outliers, or heterogeneous responses. The registry record does not provide participant-level data or distributional plots in the registry record reported for the endpoint. Consequently, the adequacy of distributional assumptions cannot be assessed from these summary statistics alone.
The primary analysis set requires completion of both baseline and Day 50 measurements. This is a defined analysis population, but it may differ from an analysis that includes every randomized participant. The registry record does not report a detailed account of missing measurements, reasons for non-completion, imputation, or sensitivity analyses. No conclusion about the impact of missing data can be drawn from the endpoint counts alone.
11. Confidence Intervals and Precision
The sponsor’s primary ANCOVA comparisons are reported with 95% confidence intervals. For placebo versus evolocumab, the estimated treatment difference is 88.76 and the interval runs from 15.73 to 161.80. For atorvastatin versus the combination, the estimate is 236.35 and the interval runs from 164.02 to 308.69. The overall treatment effect is 147.59, with an interval from 44.80 to 250.38. The intervals indicate uncertainty around the model-based estimates; they should be interpreted in the context of the specific contrast and analysis population.
The unadjusted re-calculated intervals are wider in several comparisons and are based on approximate pooled variability derived from posted standard errors. For example, the placebo comparison intervals are 8.637 to 149.8 for atorvastatin, 16.54 to 161.0 for evolocumab, and 242.5 to 388.6 for the combination. These are not substitutes for the sponsor’s adjusted intervals, and the combination re-calculation does not use the same comparator as the sponsor’s reported combination contrast. The discrepancy flag is a reason to prioritize the sponsor analysis for interpretation.
General explanation: interval width reflects statistical precision conditional on the model, available sample, and assumptions. It does not capture every source of uncertainty, such as selection from incomplete outcome data or an incorrectly specified model. Standard errors and confidence intervals also do not show the full distribution of participant-level outcomes. The registry does not report a clinically meaningful threshold against which to judge whether the interval is narrow enough for a practical decision.
The endpoint analysis counts are 19 to 22 across the four groups. These modest group counts mean that estimates should be read with attention to their intervals rather than as exact treatment effects. The registry’s reported 95% intervals are informative about sampling uncertainty, but the missing details of the analysis plan and model prevent a complete assessment of precision.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 34 | 46 |
| 75% of the observed effect | 61 | 81 |
| 50% of the observed effect | 136 | 182 |
The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design. They give participants per arm for 80% power and participants per arm for 90% power. They are not total enrollment targets, and they do not represent the number of participants who actually completed an endpoint. The sample-size assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect.
The 80% power column describes a hypothetical design that would have an 80% chance of detecting the selected effect under the listed assumptions, if that effect and the assumptions were correct. The 90% power column describes a higher chance of detection for the same hypothetical effect, generally requiring more participants. The table includes scenarios planning for 100%, 75%, and 50% of the observed effect. Smaller effects need more participants to detect under otherwise identical assumptions.
For continuous outcomes, the figures are participants per arm; they are not total events. The special rule for time-to-event outcomes does not apply to this continuous primary endpoint. The figures are based on summary statistics and approximate variability, so they should be treated as illustrations rather than as a definitive design recommendation. The original sample-size justification and assumptions are not reported in the registry record. These are planning scenarios, not observed power.
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 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
- Observed difference Δ = 79.200; pooled standard deviation σ = 116.526.
- n = 2 × (1.96 + 0.842)2 × 116.5262 / 79.2002 = 34.0, rounded up to 34 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 <- 79.2 # observed difference in means
sigma <- 116.526048075098 # 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(2189837)
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 = 34 (80% power), 46 (90% power)
75% of observed effect: n per arm = 61 (80% power), 81 (90% power)
50% of observed effect: n per arm = 136 (80% power), 182 (90% power)
power.t.test: 35
Simulated power at n = 34 per arm: 0.782 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| ANCOVA | LS Mean Treatment Difference 88.76 | 15.73 to 161.80 | 0.018 |
| ANCOVA | LS Mean Treatment Difference 236.35 | 164.02 to 308.69 | < 0.001 |
| ANCOVA | Treatment Effect 147.59 | 44.80 to 250.38 | 0.005 |
The sponsor reported ANCOVA analyses for selected contrasts. For the primary endpoint, these include placebo versus evolocumab, atorvastatin versus evolocumab with atorvastatin, and an overall treatment effect across the four groups. These model-based estimates are not identical to the simple unadjusted re-calculations, which compare each active group with placebo using posted arm summaries.
The distinction is important for the combination group: the re-calculation compares the combination with placebo, while the sponsor-reported pairwise ANCOVA contrast compares the combination with atorvastatin. They therefore address different contrasts. Even where the groups align, an adjusted model and an unadjusted summary-statistic calculation can produce different estimates and intervals.
The registry flags a discrepancy between the sponsor’s reported analyses and the re-calculations. The sponsor’s own analysis takes precedence. The re-calculations remain a secondary, approximate check and should not be used to overwrite or reinterpret the ANCOVA results. The full model specification and the reason for any numerical differences are not reported in the registry record, so their source cannot be established from the posted information.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists 5 outcome measures and 15 analyses. Multiple outcomes and treatment contrasts create opportunities to test a number of hypotheses. General explanation: when many tests are performed, at least one small p-value can occur by chance even if no corresponding effect exists. A prespecified hierarchy or multiplicity adjustment can help control the interpretation of repeated testing. The registry record does not report whether the analyses used either approach, so the family-wise interpretation of the p-values is uncertain.
The primary endpoint is identified, and the sponsor reports an overall treatment effect as well as pairwise contrasts. However, the registry record does not report a complete testing sequence, whether pairwise comparisons were gated by the overall test, or whether the reported p-values were adjusted. The secondary results should accordingly be read with caution and should not be treated as if every contrast had been a single prespecified primary hypothesis.
The primary endpoint population consists of randomized and dosed participants who completed baseline and Day 50 measurements. This completion requirement differs from an analysis that includes every randomized participant regardless of outcome availability. The endpoint counts vary across outcomes and groups, but the registry record does not report all reasons for missingness, how missing data were handled, or whether sensitivity analyses were conducted.
The original sample-size justification, interim-analysis plan, and full statistical analysis plan are not reported in the registry record. The record also does not provide enough detail to assess covariate selection, model diagnostics, or the handling of protocol deviations. These omissions do not establish that the methods were inadequate; they limit independent appraisal of how prespecified and robust the analyses were.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo | 0 | 21 | 0.0% |
| Atorvastatin | 0 | 22 | 0.0% |
| Evolocumab | 0 | 22 | 0.0% |
| Evolocumab and Atorvastatin | 1 | 20 | 5.0% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo | 5 of 21 |
| Atorvastatin | 12 of 22 |
| Evolocumab | 14 of 22 |
| Evolocumab and Atorvastatin | 10 of 20 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | Atorvastatin | Evolocumab | Evolocumab and Atorvastatin |
|---|---|---|---|---|---|
| Liver injury | Hepatobiliary disorders | 0 of 21 | 0 of 22 | 0 of 22 | 1 of 20 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | Atorvastatin | Evolocumab | Evolocumab and Atorvastatin |
|---|---|---|---|---|---|
| Headache | Nervous system disorders | 2 of 21 | 5 of 22 | 8 of 22 | 7 of 20 |
| Nausea | Gastrointestinal disorders | 1 of 21 | 3 of 22 | 2 of 22 | 2 of 20 |
| Nasopharyngitis | Infections and infestations | 1 of 21 | 1 of 22 | 2 of 22 | 0 of 20 |
| Myalgia | Musculoskeletal and connective tissue disorders | 1 of 21 | 1 of 22 | 0 of 22 | 2 of 20 |
| Abdominal pain | Gastrointestinal disorders | 0 of 21 | 2 of 22 | 0 of 22 | 1 of 20 |
| Pharyngitis | Infections and infestations | 0 of 21 | 2 of 22 | 1 of 22 | 0 of 20 |
| Upper respiratory tract infection | Infections and infestations | 0 of 21 | 2 of 22 | 0 of 22 | 1 of 20 |
| Blood creatine phosphokinase increased | Investigations | 0 of 21 | 2 of 22 | 0 of 22 | 1 of 20 |
| Neck pain | Musculoskeletal and connective tissue disorders | 0 of 21 | 2 of 22 | 1 of 22 | 0 of 20 |
| Influenza like illness | General disorders | 0 of 21 | 0 of 22 | 2 of 22 | 0 of 20 |
Serious events with the highest arm-level rate: liver injury (5.0%).
The serious adverse event counts are reported separately from the primary efficacy analysis. The groups at risk were 21 for placebo, 22 for atorvastatin, 22 for evolocumab, and 20 for evolocumab with atorvastatin. Serious adverse events affected 0 participants in the placebo group, 0 in the atorvastatin group, 0 in the evolocumab group, and 1 in the combination group.
The record lists liver injury among the top serious adverse event terms at 5.0%. This listing does not, by itself, establish causation or describe the full clinical context. The registry record does not report death counts in the safety results presented. Other adverse events affected 5 participants in the placebo group, 12 in the atorvastatin group, 14 in the evolocumab group, and 10 in the combination group; these are not the serious-event counts.
General explanation: adverse-event counts describe events recorded during a study and need to be interpreted in light of the number observed, follow-up period, definitions, and ascertainment procedures. A small study and a short treatment period provide limited information about uncommon or longer-term events. The registry record does not provide detailed event narratives or enough context to make causal judgments from these counts alone.
17. What the Result Does, and Does Not, Mean
The posted results describe changes in a laboratory-based lipoprotein kinetic endpoint over the study’s short treatment period. The sponsor’s ANCOVA reports differences for placebo versus evolocumab and for atorvastatin versus the combination, as well as an overall treatment effect. The reported confidence intervals indicate uncertainty around those estimates under the sponsor’s model. The record also includes secondary outcomes that assess LDL-C and other lipoprotein production or removal measures.
These findings do not establish whether any treatment changes symptoms, cardiovascular events, survival, or other patient-important outcomes. The registry record does not report such outcomes as trial endpoints in the registry record presented. Nor does it report a clinically meaningful threshold for the primary kinetic measure. Statistical separation from zero is not the same as evidence that a difference is clinically important.
The results also cannot establish longer-term effects. Treatment was described for up to 8 weeks, and the primary endpoint was assessed at Day 50. The study’s single-site setting, endpoint-specific analysis population, and limited group counts constrain how broadly the estimates can be generalized. No information in the record presented establishes how the results apply to populations with different characteristics.
General explanation: a randomized comparison can help estimate differences between assigned groups, but the interpretation still depends on follow-up, adherence, missing data, the analysis model, and outcome selection. The registry record does not report enough detail to fully assess each of those factors. Accordingly, the findings should be understood as short-term statistical results for the measured endpoints, not as a complete evaluation of benefits and harms.
18. Why This Trial Matters Statistically
This trial is statistically interesting because it compares a treatment aimed at lipoprotein metabolism alone, a statin alone, their combination, and placebo while measuring a kinetic endpoint. The primary outcome is not only a concentration measurement; it estimates a rate of LDL-associated apolipoprotein turnover using tracer measurements and mathematical modelling. That distinction makes the endpoint informative about mechanism while also making it dependent on specialized measurement and analysis.
The results illustrate why the choice of contrast matters. A re-calculated combination-versus-placebo difference is not the same question as the sponsor’s combination-versus-atorvastatin ANCOVA comparison. Likewise, adjusted model estimates should not be silently replaced with unadjusted estimates from arm summaries. Reporting both requires clear attention to comparator, population, and model.
The trial also shows the value of reading estimates with their uncertainty. A point estimate alone can look definitive, while its interval and the analysis population provide essential context. In addition, multiple secondary outcomes can illuminate different parts of a biological pathway but do not automatically provide multiple independent confirmations of the primary result.
These are general statistical lessons from the design and posted analyses. The record’s limited detail on multiplicity, missing data, and model specification means that a reader should distinguish what is directly reported from what cannot be independently evaluated.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
This was a single-site study, as described in its official title. The registry record does not give further information about the site or the characteristics of the participants, limiting assessment of how representative the analyzed group may be. Although enrollment is listed as 89, endpoint counts differ across outcomes, and the primary analysis requires completion of both baseline and Day 50 measurements. The record does not explain all differences in analysis counts or report reasons for missing measurements.
The primary endpoint is a specialized kinetic measure based on stable isotope tracer administration, serial plasma sampling, laboratory isolation, mass spectrometry, and mathematical modelling. The registry describes these procedures but does not provide enough detail to independently evaluate model diagnostics, reproducibility, or the impact of measurement assumptions. No clinically meaningful threshold is reported.
The described treatment period was up to 8 weeks, and the primary endpoint was measured at Day 50. This limits the results to the short-term outcomes posted. The registry record does not report clinical-event outcomes in the registry record presented. It also does not report the original sample-size justification, full statistical analysis plan, multiplicity procedures, interim analyses, detailed missing-data methods, or all ANCOVA covariates.
Finally, the sponsor’s adjusted analyses and simple re-calculations differ, and the discrepancy is explicitly flagged. The sponsor analysis takes precedence, but the record does not explain the source of the discrepancy. This makes it especially important not to conflate adjusted and unadjusted estimates or comparisons that use different reference groups.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Effects on Lipoprotein Metabolism From PCSK9 Inhibition Utilizing a Monoclonal Antibody — NCT02189837.
- Registry record last updated 2018-10-03; status last verified 2018-09.
- Results first posted 2016-08-31.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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23. Record Summary
NCT02189837 is a completed randomized, placebo-controlled phase 3 trial sponsored by Amgen, with an enrollment of 89. It compared placebo, atorvastatin, evolocumab, and evolocumab with atorvastatin in participants with primary hyperlipidemia and mixed dyslipidemia. The primary outcome was percent change from baseline in LDL apolipoprotein B-100 fractional catabolic rate at Day 50.
The sponsor reported ANCOVA comparisons and an overall treatment effect for the primary endpoint. Simple unadjusted re-calculations are also available, but the registry flags a discrepancy, so the sponsor’s own analysis takes precedence. Secondary outcomes address LDL-C and other lipoprotein kinetic measures. The safety results include one serious adverse event in the combination group, with none reported in the other groups; death counts are not reported in the registry record.
The record does not report the original sample-size justification, a full statistical analysis plan, multiplicity procedures, or detailed missing-data methods. The results describe short-term endpoint estimates and should not be read as evidence about unreported clinical outcomes.