Safety and Immunogenicity Study of the Hepatitis B Virus (HBV) Vaccine, HEPLISAV Compared to Engerix-B Vaccine: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Immunogenicity Study of the Hepatitis B Virus (HBV) Vaccine, HEPLISAV Compared to Engerix-B Vaccine (NCT01005407), a randomized phase 3 study. The primary outcome is Percentage of Subjects Who Have a Seroprotective Immune Response.

2. Clinical Question

The registry record describes a comparison of HEPLISAV with Engerix-B among healthy adults aged 40 to 70. Its primary question concerns the percentage of participants who reach a seroprotective immune response after vaccination. The response is defined by an anti-HBsAg antibody level of at least 10 mIU/mL, measured 8 weeks after the last active dose. The record identifies Week 12 and Week 32 as the endpoint time points.

The posted percentages are 90.1 for HEPLISAV and placebo and 70.5 for Engerix-B. The registry record does not separately map those displayed percentages to Week 12 or Week 32. The trial also names safety and lot-to-lot consistency among its purposes, but the posted primary result addressed is the immune-response endpoint.

3. Trial Design

This was a Phase 3, randomized, parallel-group study with quadruple masking. The official title describes it as observer-blinded and multi-center. The registry record lists an enrollment of 2452 and a status of completed. The study started in 2010-02, and primary completion was in 2011-01. Those record dates describe the study timeline; they do not provide the duration of follow-up for each outcome.

The two groups in the primary comparison were HEPLISAV and placebo and Engerix-B. The listed HEPLISAV intervention was 0.5 mL, containing 20 mcg HBsAg and 3000 mcg 1018; the Engerix-B description lists 1.0 mL. The endpoint population description refers to subjects who received all 3 study injections as randomized and within the study visit windows. The injection schedule itself is not reported in the registry record.

Random assignment is intended to reduce systematic differences between treatment groups at the start of a trial. Masking can help limit influences on care, outcome assessment, or reporting, though the registry record does not specify which roles were included in the quadruple masking. The parallel-group structure means the groups were followed as separate treatment groups rather than participants crossing between treatments.

The record gives group counts for the primary outcome of 1121.0 for HEPLISAV and placebo and 353.0 for Engerix-B. These are not the same counts as the safety denominators. The record does not explain the differences in analysis populations or provide a participant-flow account connecting enrollment to each endpoint population.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: Non-Inferiority per Protocol population:Randomized subjects who received 1 of 3 consistency lots of HEPLISAV or Engerix-B within the study visit windows, had all 3 study injections as randomized and within the study visit windows, no major protocol deviations, and anti-HBs levels obtained within study visit windows at baseline, Week 12, and Week 32

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: Safety Population: All participants who received at least 1 study injection and who had any post-baseline safety data

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Subjects Who Have a Seroprotective Immune Response, measured over at Week 12 and at Week 32.

The primary endpoint is the percentage of participants with a seroprotective immune response, defined as an anti-HBsAg antibody concentration of at least 10 mIU/mL. The registry record states that this response was assessed 8 weeks after the last active dose, with Week 12 and Week 32 named as the endpoint time points. A threshold-based endpoint turns a laboratory measurement into a binary outcome: each participant is classified as meeting or not meeting the stated antibody threshold at the assessment.

In general, a seroprotection threshold provides a consistent way to summarize immune response across participants and compare the proportions in randomized groups. It is not the same as comparing the full distribution of antibody concentrations, since values above the threshold are all counted as responses for this endpoint. The record does not report the antibody values’ distribution or additional thresholds.

The result is posted as a percentage for each group: 90.1 for HEPLISAV and placebo and 70.5 for Engerix-B. The endpoint population is described as non-inferiority per protocol. However, the non-inferiority margin is not reported in the registry record, and the displayed result does not identify which of the two named time points it represents. Those details matter when assessing a formal non-inferiority claim; the endpoint percentages alone do not establish that such a criterion was met.

7. Results Posted in the Registry

• Engerix-B: 70.5% (249/353) versus 90.1% (1010/1121) on control; risk difference -19.6 percentage points (95% CI -24.6 to -14.5), risk ratio 0.78 (0.73–0.84); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: a participant either meets the seroprotection threshold or does not. The group percentage is the proportion of participants classified as having a response. In general, binary outcomes can be summarized as proportions and compared using a risk difference, a risk ratio, or an odds ratio. Each expresses a different aspect of the contrast, so the measure and the order of groups need to be clear.

What does the risk difference express?

The posted risk difference is -0.196, comparing Engerix-B with HEPLISAV and placebo. It is an absolute difference on the proportion scale, rather than a relative measure. The negative direction means the Engerix-B proportion is lower in this contrast. The accompanying interval runs from -0.246 to -0.145. In general, a confidence interval communicates uncertainty about the estimated contrast: a narrower interval indicates greater precision, while a wider one indicates more uncertainty. The interval does not cross zero, but statistical compatibility with a nonzero difference is not the same as clinical importance or proof of a causal mechanism.

How should the p-value be read?

The unadjusted p-value is <0.001. In general, a p-value describes how unusual data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the statistical model assumptions held. It is not the probability that the null hypothesis is true, nor is it a measure of the size or importance of the effect. This result comes from an unadjusted recalculation based on posted summary statistics. The registry record does not report the sponsor’s detailed testing procedures or a formal multiplicity strategy.

What does randomization contribute?

In general, random allocation aims to make treatment groups comparable with respect to both measured and unmeasured characteristics at the start of a trial. That supports interpretation of group contrasts, provided that follow-up, outcome ascertainment, and analysis preserve the benefits of randomization. The registry record identifies randomized allocation, but does not provide enough participant-flow or missing-data detail to assess those issues fully. The endpoint population is per protocol, with criteria that select participants according to treatment and protocol adherence; it is not simply described as all randomized participants.

What does masking contribute?

The record lists quadruple masking and describes the study as observer-blinded. In general, masking can reduce the possibility that knowledge of treatment assignment influences participant reporting, clinical decisions, outcome assessment, or analysis. The record does not specify which four roles were masked or how masking was maintained, so those details are not reported in the registry record.

What would a non-inferiority analysis require?

In general, a non-inferiority analysis asks whether the new intervention’s outcome is no worse than the comparator by more than a prespecified margin. The margin defines the largest difference that would still count as acceptable for the study’s objective. The endpoint population is labeled non-inferiority per protocol, but the margin, formal decision rule, and sponsor analysis are not reported in the registry record. The observed contrast and its recalculated interval should not be used to infer those missing design and analysis details.

Why can over-dispersion matter for other outcomes?

General explanation: over-dispersion occurs when observed variability in data exceeds what a chosen statistical model expects. It can make standard errors too small and uncertainty look understated if the model does not account for the extra variability. The primary endpoint is a binary percentage, and the registry record does not report an over-dispersion analysis. This concept may be relevant to other data types, but it should not be assumed to have been a feature of this endpoint’s analysis.

The registry record lists two outcome measures, one posted secondary outcome, and zero analyses. It names the percentage of participants with local and systemic reactions to injections as a secondary outcome. The statistical methods used for that outcome, for the primary sponsor analysis, and for any lot-to-lot comparisons are not reported in the registry record.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an estimated effect. For the primary comparison, the recalculated risk difference is -0.196, with an interval from -0.246 to -0.145. The interval lies on the negative side of zero, matching the direction of the point estimate: the response proportion is lower for Engerix-B than for HEPLISAV and placebo in this contrast.

In general, a confidence interval is a range generated by a method designed to have a stated long-run coverage rate under its assumptions. It reflects sampling uncertainty, not every possible source of uncertainty. It does not account automatically for missing data, deviations from the analysis plan, measurement problems, or choices among multiple outcomes. Those features require information about the study’s methods, much of which is not reported in the registry record.

The interval provides more information than the point estimate alone because it shows a range of contrasts that remain compatible with the data under the recalculation method. The registry record does not give confidence intervals for the two group percentages themselves. The interval also does not settle whether the contrast is important in practice: that judgment requires a relevant clinical context and, for a non-inferiority conclusion, the prespecified margin and formal analysis.

These uncertainty estimates are unadjusted recalculations from posted summary statistics. The record does not report the sponsor’s full analysis or clarify the mapping of the displayed result to Week 12 or Week 32. Accordingly, precision can be described for the displayed contrast, but not independently confirmed for each stated time point or for every analysis population.

11. 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.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design assumptions. The original sample-size justification and design assumptions are not reported in the registry record. These figures are participants per arm, not total event counts. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect.

The rows describe planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. Within each row, the 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions. The 90% power column gives the corresponding number for a 90% chance. These are design calculations, not statements about what happened in this trial.

The listed values increase as the assumed effect becomes smaller: for 100% of the observed effect, the figures are 64 participants per arm for 80% power and 85 for 90% power; for 75%, they are 103 and 138; for 50%, they are 206 and 275. In general, smaller effects are harder to distinguish from random variation, so detecting them at the same power typically requires more participants.

This is not observed power. It is an illustration of how sample-size requirements change across assumed effects and power targets, using the stated calculation assumptions. The curve visualizes that planning relationship; it does not report a separate trial result.

12. 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 z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.901; treatment proportion p₁ = 0.705; average p̄ = 0.803.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5623 = 1.1021.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5450 = 0.4587.
4. n = (1.1021 + 0.4587)² / (-0.1956)² = 63.7, rounded up to 64 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
p0 <- 0.900981266726137                          # control proportion
p1 <- 0.705382436260623                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1005407)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 64 (80% power), 85 (90% power)
 75% of observed effect: n per arm = 103 (80% power), 138 (90% power)
 50% of observed effect: n per arm = 206 (80% power), 275 (90% power)
power.prop.test: 63.7 
Simulated power at n = 64 per arm: 0.811 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record names the primary immune-response outcome and a secondary outcome for local and systemic reactions to injections. It lists two outcome measures, one posted secondary outcome, and zero analyses. The record does not report a multiplicity adjustment, a hierarchy among outcomes, or a strategy for repeated testing across the stated Week 12 and Week 32 time points.

In general, testing multiple outcomes or time points can increase the chance of at least one apparently unusual result when all comparisons are considered together. A prespecified testing plan can control how results are interpreted across those comparisons. Without such a plan in the registry record, the displayed unadjusted p-value should be read as pertaining to the recalculated contrast, not as evidence that all possible testing has been accounted for.

The registry describes the primary endpoint population as non-inferiority per protocol. It includes randomized subjects who received one of the three consistency lots of HEPLISAV or Engerix-B within study visit windows, had all 3 study injections as randomized and within those windows, and had no major protocol deviations. The remaining antibody-measurement criterion is truncated in the registry description, so its full wording is not reported in the registry record.

The record does not report how missing antibody measurements were handled, how many measurements were missing, whether participants were excluded for missingness, or whether imputation was used. It also does not provide a complete analysis-population flow or a posted intention-to-treat analysis. These omissions make it difficult to assess how the per-protocol selection and missing outcomes may affect the result.

In general, missing-data handling matters when the probability of an unavailable measurement is related to treatment or outcome. The direction and size of any resulting bias depend on information not present in the registry record. No particular missing-data mechanism or analysis should be inferred.

14. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: prostate cancer (0.6%), osteoarthritis (0.5%), anaemia (0.2%), acute myocardial infarction (0.2%), angina unstable (0.2%).

The registry lists serious adverse event figures for HEPLISAV and/or Placebo and Engerix-B(1). For the first group, 78 affected participants are listed among 1968 at risk; for the second, 23 are listed among 481 at risk. For other adverse events, the corresponding entries are 80 among 1968 at risk and 25 among 481 at risk. These are safety counts and denominators, not the primary immune-response population counts.

The record also lists serious-event terms with percentages: Prostate cancer, 0.6%; Osteoarthritis, 0.5%; Anaemia, 0.2%; Acute myocardial infarction, 0.2%; Angina unstable, 0.2%; and Cardiac failure, 0.2%. These entries describe listed event terms; they do not establish that the vaccine caused an event. The registry record does not report the exposure duration or a detailed event-assessment method, so the figures should not be interpreted as rates over a known follow-up period.

Death counts are not reported in the registry record. As with any adverse-event summary, counts alone do not establish comparative risk or causation.

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

The posted result describes a higher seroprotective-response percentage in the HEPLISAV and placebo group than in the Engerix-B group: 90.1 compared with 70.5. The recalculated risk difference is -0.196 for Engerix-B relative to HEPLISAV and placebo, with an interval from -0.246 to -0.145 and an unadjusted p-value of <0.001. These statistics describe the observed binary endpoint and its uncertainty under the recalculation method.

They do not establish that either vaccine is appropriate for an individual, and they are not medical advice. They also do not prove a mechanism or establish effects on outcomes beyond the measured antibody threshold. The endpoint classifies participants by whether their anti-HBsAg antibody level reached at least 10 mIU/mL; it does not summarize the full antibody-value distribution or other clinical outcomes.

The study’s stated objective included non-inferiority, but the non-inferiority margin and sponsor’s formal analysis are not reported in the registry record. The displayed contrast alone therefore does not establish whether a prespecified non-inferiority criterion was met. The endpoint population is per protocol, and the registry record does not provide a complete missing-data account or a full participant-flow description.

Nor should the primary result be read as a complete account of safety or lot-to-lot consistency. The record lists safety counts and selected serious-event terms, but these summaries do not establish causality. Although lot-to-lot consistency is named as a study purpose, results for that objective are not reported in the registry record. The record also names Week 12 and Week 32 but does not map the displayed percentages and contrast to one of those time points.

16. Why This Trial Matters Statistically

This trial illustrates why the definition of an endpoint matters. A laboratory measurement is converted into a binary seroprotection classification using a stated threshold, then summarized as a percentage. That makes the result readily interpretable as the share of participants meeting the criterion, while leaving unanswered how antibody levels are distributed above or below the threshold.

It also demonstrates why the contrast scale and group order matter. The risk difference is negative because it is expressed as Engerix-B relative to HEPLISAV and placebo; the group percentages make the direction clear. A confidence interval adds information about uncertainty, while the p-value addresses compatibility with a null contrast under the calculation’s assumptions. Neither measure alone determines clinical importance.

The non-inferiority label creates an additional statistical question: a formal conclusion depends on a prespecified margin and analysis procedures. Those details are not reported in the registry record. The posted result is a useful description of the response proportions, but it should not be treated as a substitute for the trial’s full analysis.

Finally, the record brings attention to analysis-population and reporting limits. The primary population is per protocol, while the safety denominators differ from the primary outcome group counts. Missing-data handling, full population flow, and the time-point mapping of the displayed result are not reported. Recognizing these distinctions helps keep an observed endpoint comparison separate from broader claims about the study.

17. 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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

Several trial-specific details needed for a fuller interpretation are not reported in the registry record. The record identifies Week 12 and Week 32, but does not state which time point corresponds to the displayed group percentages and risk difference. It labels the endpoint population non-inferiority per protocol, but the non-inferiority margin and formal decision procedure are not reported.

The per-protocol description is incomplete: its final antibody-measurement criterion is truncated. The record does not provide a full participant-flow account, a corresponding intention-to-treat result, missing measurement counts, or methods for handling missing antibody values. The primary outcome group counts differ from the safety denominators, but the record does not explain the population differences.

The comparison and interval are unadjusted recalculations from posted summary statistics. The sponsor’s full analysis methods and results are not reported in the registry record. The registry lists zero analyses, and it does not report a multiplicity strategy for outcomes or the two named time points. It also does not report the original sample-size justification, detailed injection schedule, duration of safety follow-up, or which roles were included in quadruple masking.

Although the study purpose includes lot-to-lot consistency and safety, the available primary result does not report the consistency analysis. The safety summary provides affected counts and selected event terms, but no death counts or detailed assessment information. These limitations constrain interpretation to the posted endpoint and summaries rather than the full trial analysis.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Safety and Immunogenicity Study of the Hepatitis B Virus (HBV) Vaccine, HEPLISAV Compared to Engerix-B Vaccine — NCT01005407.
• Registry record last updated 2019-03-20; status last verified 2019-03.
• Results first posted 2018-01-11.
• 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.

21. Record Summary

NCT01005407 is a completed Phase 3 randomized, parallel-group, quadruple-masked study comparing HEPLISAV with Engerix-B in healthy adults aged 40 to 70. The registry lists enrollment of 2452, a start in 2010-02, and primary completion in 2011-01.

The primary endpoint is the percentage of participants reaching an anti-HBsAg antibody level of at least 10 mIU/mL, assessed 8 weeks after the last active dose, with Week 12 and Week 32 named in the record. Posted percentages are 90.1 for HEPLISAV and placebo and 70.5 for Engerix-B. The recalculated risk difference is -0.196, with an interval from -0.246 to -0.145 and an unadjusted p-value of <0.001.

The endpoint population is described as non-inferiority per protocol. The margin, full sponsor analysis, missing-data methods, and mapping of the displayed result to the stated time points are not reported in the registry record.