Influenza Vaccine Dose-Response in Infants and Toddlers: Immunogenicity and Reactogenicity: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Influenza Vaccine Dose-Response in Infants and Toddlers: Immunogenicity and Reactogenicity (NCT00710866), a randomized phase 3 study. The primary outcome is Seroprotection Rate Infants (6-11 Months)-A/Brisbane/59/07(H1N1).

2. Clinical Question

3. Trial Design

This was a phase 3, randomized, triple-masked, parallel-group trial. The registry record lists an enrollment of 262 and a completed status. It identifies influenza as the condition and the British Columbia Centre for Disease Control as the sponsor. The recorded study dates are 2008-08 for study start and 2009-03 for primary completion.

Participants were assigned to one of two schedules of the same named vaccine: two 0.5mL doses or two 0.25mL doses, each given at months 0 and 1. A parallel design means participants were assigned to a group and the groups were compared; the record does not describe participants switching between schedules. Randomization indicates assignment by chance, while triple masking indicates that the record classifies the trial as masked at three levels. The identities of those masked are not reported in the registry record.

The posted primary outcome is limited to infants aged 6–11 months and the A/Brisbane/59/07(H1N1) strain. It counts participants meeting the stated seroprotection threshold 27–46 days after the second dose, using the per-protocol population. The two arm counts for this endpoint are 41 of 57 in the 0.5mL group and 34 of 63 in the 0.25mL group.

The registry record lists eight outcome measures and no analyses. It does not report the original sample-size justification, detailed procedures for allocation concealment, the identities covered by masking, or a complete protocol description. Those details should not be inferred from the design labels or enrollment figure.

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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Per Protocol

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.

6. Primary Endpoint

The registry lists the primary outcome as Seroprotection Rate Infants (6-11 Months)-A/Brisbane/59/07(H1N1), measured over 27-46 days after the second dose.

The primary endpoint is the number of infants with seroprotection against A/Brisbane/59/07(H1N1), assessed 27–46 days after the second vaccine dose. Seroprotection is defined in the registry record as HI titers >40. The reported population is per protocol, and the age group for this endpoint is infants aged 6–11 months.

Hemagglutination-inhibition (HI) titers are an antibody measure. In general, applying a prespecified threshold converts an antibody measurement into a binary endpoint: each participant either meets the criterion or does not. A count of participants meeting the threshold can therefore be compared between the two schedules. This endpoint describes the proportion-level response through counts and arm denominators, rather than displaying each participant’s antibody measurement or the distribution of all titers.

A threshold-based endpoint is useful for communicating how often participants reach a stated antibody criterion. It does not, by itself, describe the full range of antibody responses, establish how long a response persists, or measure clinical influenza outcomes. The registry’s broader study purpose mentions antibody response and reaction rates, but the posted primary result is this specific seroprotection count for one strain and age group.

7. Results Posted in the Registry

• 0.25mL VAXIGRIP®: 54.0% (34/63) versus 71.9% (41/57) on control; risk difference -18.0 percentage points (95% CI -34.9 to -1.0), risk ratio 0.75 (0.57–0.99); unadjusted two-proportion z-test p = 0.042.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary: a participant either met the HI-titer criterion or did not. The record presents counts of participants meeting the criterion and the number assessed in each group. For this type of outcome, a comparison can be expressed using an absolute difference, a ratio of probabilities, or a ratio of odds. Each measure retains the same underlying participant outcomes but emphasizes a different scale.

What does the risk difference express?

The risk difference is the probability of the endpoint in one group minus the probability in the reference group, with the comparison direction stated as 0.25mL relative to 0.5mL. Here, the reported estimate is -0.180. A negative value indicates a lower observed endpoint probability in the 0.25mL group for that direction of comparison. The confidence interval, -0.349 to -0.01, describes a range of values compatible with the data under the method used to construct it. In general, an absolute difference is useful because it preserves the scale of the probability contrast rather than expressing it as a relative change.

How do risk ratios and odds ratios differ?

A risk ratio compares the endpoint probabilities between groups. The reported estimate is 0.750, with an interval from 0.567 to 0.993. An odds ratio instead compares the odds of meeting the endpoint, and its reported estimate is 0.458, with an interval from 0.214 to 0.979. The two ratios need not have the same numerical value: odds and probabilities are different quantities. General statistical guidance is to identify which measure is being reported and which group is in the numerator before interpreting its direction or magnitude.

What does the p-value say?

The unadjusted p-value is 0.042. In general, a p-value describes how incompatible the observed data, or data more extreme under a specified test, are with a null hypothesis under that test’s assumptions. It is not the probability that the null hypothesis is true, and it is not a measure of the size or practical importance of an effect. The registry record does not report the test specification or a broader analysis plan, so the p-value should be read as the unadjusted result posted for this comparison.

What does a confidence interval contribute?

In general, a confidence interval conveys uncertainty around an estimate. A narrower interval indicates greater precision on that measure’s scale, while a wider interval indicates greater uncertainty. Its interpretation depends on the statistical method and assumptions used. The primary comparison has a risk-difference interval from -0.349 to -0.01. The endpoints provide a range for the estimated contrast, not a range of participant outcomes and not a guarantee that the underlying value lies within the interval.

The endpoint uses a threshold rather than the full set of antibody measurements. This turns the outcome into a count that can be analyzed with binary-outcome methods, but it discards information about how far an individual titer is above or below the threshold. In general, changing a threshold can change which observations count as events; the threshold reported for this endpoint is HI titers >40.

The comparison is based on the per-protocol population. In general, a per-protocol analysis concerns participants who meet protocol-defined criteria, but the criteria and participant-flow details are not reported in the registry record. The arm denominators for this endpoint are 57 and 63, whereas overall enrollment is 262. The record does not provide enough detail to explain the difference between the enrolled population and the endpoint analysis population, so it should not be attributed to any particular reason.

These methods describe the posted comparison and general statistical concepts. The registry record does not report enough information to reconstruct a full analysis, including the exact interval method, the prespecified analysis plan, or whether other planned comparisons were conducted.

10. Confidence Intervals and Precision

The risk-difference estimate is -0.180, with a confidence interval from -0.349 to -0.01. The interval is entirely below zero, but its limits span a range of possible contrasts rather than specifying a single exact value. The upper endpoint is near zero, so the estimate’s direction is more precisely constrained than its magnitude is. The interval should be considered alongside the group counts, 41 of 57 and 34 of 63, which show the number of participants and the denominator contributing to this endpoint.

The reported risk-ratio interval is 0.567 to 0.993 around an estimate of 0.750. The odds-ratio interval is 0.214 to 0.979 around an estimate of 0.458. For ratio measures, 1 represents equal values between groups; both posted intervals reach close to that reference. The scales differ, however, and the risk difference remains the direct absolute contrast.

In general, a confidence interval reflects both the estimate and sampling uncertainty under its statistical assumptions. It is not a prediction interval for individual participants, and it does not account automatically for design features, missing outcomes, or multiple testing. The registry record does not identify the interval-construction method or report a multiplicity procedure. The modest endpoint denominators are relevant context when judging precision, but the record does not establish what caused those denominators or how they were determined.

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 planning figures are participants per arm, not total events. The entries give planning illustrations for detecting 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For 80% power, the listed participants per arm are 113, 196, and 427, respectively. For 90% power, they are 150, 261, and 571, respectively.

In plain language, the 80% power column gives the number planned per group under the stated assumptions for an 80% chance of detecting the selected effect if that effect were the true one. The 90% column uses a higher target chance of detection and consequently lists more participants per group for each effect scenario. These are planning illustrations calculated from the observed effect, not the trial’s original design targets. Smaller effects require more participants to detect under otherwise comparable assumptions.

The stated 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 share of the observed effect. These assumptions describe the planning calculation; the original trial’s sample-size justification and design assumptions are not reported in the registry record. This is not observed power: the figures do not measure the probability that the completed trial detected an effect, nor do they revise the uncertainty in the posted 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 = 0.719; treatment proportion p₁ = 0.540; average p̄ = 0.629.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6830 = 1.3386.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6711 = 0.5648.
4. n = (1.3386 + 0.5648)² / (-0.1796)² = 112.3, rounded up to 113 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 <- 0.719298245614035                          # control proportion
p1 <- 0.53968253968254                          # 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(710866)
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 = 113 (80% power), 150 (90% power)
 75% of observed effect: n per arm = 196 (80% power), 261 (90% power)
 50% of observed effect: n per arm = 427 (80% power), 571 (90% power)
power.prop.test: 112.3 
Simulated power at n = 113 per arm: 0.799 (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 lists eight outcome measures and no analyses. It posts the primary seroprotection result, but reports no secondary outcome analyses. The broader study description refers to antibody response and reaction rates, but the available record does not supply a complete set of results for those outcomes. Their absence from the posted analyses should not be interpreted as evidence that an outcome was measured and found to have no effect.

Multiplicity arises when several outcomes, comparisons, or analyses are considered. In general, testing multiple hypotheses can increase the chance of obtaining at least one apparently notable result by chance. Statistical plans may address this through prespecified primary outcomes, adjustments, or other strategies. The registry record does not report whether multiplicity was planned or addressed, and the posted p-value is unadjusted. No adjustment should be assumed.

The primary outcome specifies a per-protocol population. The record does not describe the criteria for inclusion in that population, participant flow, missing endpoint data, or methods for handling missing data. The posted arm denominators for the primary endpoint are 57 and 63; overall enrollment is 262. Without further participant-flow information, the reasons for the difference cannot be determined.

The registry record also does not report whether interim analyses were performed, what statistical model or test was prespecified, or whether the posted analysis differed from an original plan. These omissions limit assessment of how the result fits into the trial’s full analysis strategy. They do not change the arithmetic meaning of the reported counts and estimates, but they constrain interpretation of the evidence as a complete trial report.

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 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: pneumonia (0.8%).

The serious-event counts are reported against the numbers at risk: 0 of 124 in the 0.5mL group and 1 of 128 in the 0.25mL group. The registry record lists pneumonia at 0.8% among the top serious-event terms. It does not specify a group assignment for that term in the information. Deaths are not reported in the registry record.

In general, a serious adverse-event count describes events classified as serious under the trial’s reporting definitions; it does not by itself establish that an event was caused by the intervention. The record does not provide event narratives, severity criteria, timing, or an assessment of relatedness. The counts are therefore descriptive and should not be treated as a complete account of safety.

The record also lists other adverse-event counts of 108 among 124 at risk in the 0.5mL group and 107 among 126 at risk in the 0.25mL group. These are distinct from the serious-event figures. The available record does not provide enough detail to characterize the events, their duration, or their relationship to vaccination. The figures are not a substitute for the complete safety results across all participants and outcomes.

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

The posted data show that, among infants in the per-protocol primary analysis, 41 of 57 in the 0.5mL group and 34 of 63 in the 0.25mL group met the stated HI-titer criterion for A/Brisbane/59/07(H1N1) 27–46 days after dose two. The reported risk difference for the 0.25mL group relative to the 0.5mL group is -0.180, with a confidence interval from -0.349 to -0.01, and an unadjusted p-value of 0.042.

This finding concerns one binary antibody endpoint, one strain, one age group, one assessment window, and the per-protocol analysis population. It does not describe every antibody measure or every outcome that may have been considered. The record lists eight outcome measures but no analyses, and it does not post secondary analyses. It also does not report the trial’s full statistical plan or missing-data procedures.

In general, meeting an antibody threshold is not identical to a clinical outcome. The posted endpoint does not establish how long the measured response persisted, whether participants later developed influenza, or how the two schedules compare on outcomes not reported in the registry record. The event counts and estimates describe the observed analysis; they do not establish the cause of any individual participant’s result or support a broader conclusion beyond the information recorded.

The confidence interval communicates uncertainty around the risk-difference estimate. Although its reported limits lie below zero, it spans a range of values, and the upper limit is close to zero. The p-value is unadjusted, and multiplicity handling is not reported. These considerations are part of interpreting the statistical evidence, not grounds for treating the estimate as an exact or universally applicable effect.

16. Why This Trial Matters Statistically

This trial presents a useful statistical example of how a binary immunogenicity endpoint can be interpreted across two randomized groups. The endpoint is based on a clear threshold: HI titers >40. Reporting the participant counts and denominators makes the underlying event information visible alongside the relative and absolute comparison measures.

The trial also illustrates why effect measures should be read on their own scales. The risk difference gives an absolute contrast, whereas the risk ratio and odds ratio express relative comparisons using different quantities. Presenting several measures can aid interpretation, but none removes the uncertainty reflected in the confidence intervals. The reported risk-difference interval, -0.349 to -0.01, helps show the range around the estimate rather than implying a single exact contrast.

Another important statistical issue is the distinction between enrollment and the analysis population. Overall enrollment is 262, while the primary per-protocol endpoint is reported with denominators of 57 and 63. The registry record does not explain the participant flow or analysis-population criteria. This makes clear why population labels and denominators matter when interpreting a trial result.

Finally, the record shows how limited reporting can constrain interpretation even when a primary estimate is available. It lists eight outcome measures but no analyses, and does not describe multiplicity procedures, missing-data handling, or the original sample-size rationale. The planning illustrations are based on the observed effect and stated assumptions; they are not a substitute for an original design justification. Statistical interpretation therefore depends not only on an estimate, but also on knowing its population, endpoint, precision, and analysis context.

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.

The primary result is confined to infants aged 6–11 months in the per-protocol population and to seroprotection for A/Brisbane/59/07(H1N1) at 27–46 days after the second dose. It does not summarize results for the full age range described in the study purpose or for other strains. The record does not report additional analyzed endpoints that would show whether the pattern was similar across outcomes.

There is a substantial difference between overall enrollment of 262 and the primary endpoint denominators of 57 and 63. The record does not give participant-flow details or the per-protocol criteria, so the reason for the analyzed population size cannot be established. Missing-data methods and the amount of missing endpoint information are not reported.

The record gives an unadjusted p-value and does not describe multiplicity control, the exact test or confidence-interval method, or the prespecified statistical analysis plan. It also does not report the original sample-size justification or whether interim analyses were conducted. The planning figures are explicitly based on the observed effect and should not be mistaken for original design targets.

Safety reporting is limited in the available record: it lists serious-event counts and a top serious-event term, but not event narratives, timing, relatedness, or group assignment for the pneumonia term. Deaths are not reported. These limitations do not invalidate the posted counts, but they narrow what can be concluded from the record alone.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Influenza Vaccine Dose-Response in Infants and Toddlers: Immunogenicity and Reactogenicity — NCT00710866.
• Registry record last updated 2011-08-04; status last verified 2011-07.
• Results first posted 2011-08-04.
• 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

The registry record identifies NCT00710866 as a completed phase 3, randomized, triple-masked, parallel-group trial sponsored by the British Columbia Centre for Disease Control. It lists enrollment of 262, a study start of 2008-08, and primary completion of 2009-03. The study compared two 0.5mL doses of VAXIGRIP® with two 0.25mL doses, given at months 0 and 1.

The primary posted result concerns seroprotection against A/Brisbane/59/07(H1N1) among infants aged 6–11 months, 27–46 days after the second dose, in the per-protocol population. The counts are 41 of 57 for 0.5mL and 34 of 63 for 0.25mL; the reported risk difference is -0.180, with a confidence interval from -0.349 to -0.01 and an unadjusted p-value of 0.042. The record lists eight outcome measures and no analyses.