Influenza Vaccination for Flu Prevention in Patients With Plasma Cell Disorders: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Influenza Vaccination for Flu Prevention in Patients With Plasma Cell Disorders (NCT04080531), a randomized phase 4 study. The primary outcome is Seroprotection Based on Hemagglutination Antibody Inhibition (HAI).

2. Clinical Question

3. Trial Design

This was a phase IV, randomized, parallel-group trial with no masking reported. The registry lists Emory University as the sponsor, enrollment of 165, and a completed status. The recorded start date is 2019-10-18, and the primary completion date is 2021-05-11. These registry entries describe the study record; they do not establish how participants were recruited or whether all enrolled participants contributed data to the primary endpoint.

Both arms received trivalent influenza vaccine and pneumococcal 13-valent conjugate vaccine. The schedules recorded for Arm I were influenza vaccine at weeks 1, 9, and 17 and pneumococcal vaccine at week 5. Arm II received influenza vaccine at week 1 and pneumococcal vaccine at week 5. Both descriptions qualify treatment administration on the absence of disease progression or unacceptable toxicity. The registry does not report additional details about adherence to these schedules or treatment received after a participant did not meet that condition.

The primary outcome is a participant count for HAI-based seroprotection, assessed at week 21. The registry lists one outcome measure and no posted analysis entries. Although the record identifies the primary endpoint and gives counts for both arms, it does not report the analysis population definition, handling of missing endpoint measurements, or a detailed statistical analysis plan. Those omissions limit interpretation of how the endpoint counts were assembled and how the arm comparison was intended to be analyzed.

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

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 Based on Hemagglutination Antibody Inhibition (HAI), measured over 21 weeks.

The primary endpoint is seroprotection based on hemagglutination antibody inhibition, abbreviated HAI. The registry describes HAI measured in blood at week 21 for all variants and reports the outcome as a count of participants. In this binary outcome, each participant is classified according to whether the seroprotection criterion was met; the posted result is the number meeting it in each arm, rather than an average antibody measurement.

HAI is used as an antibody-based measure of immune response to influenza. In general, a seroprotection endpoint can provide a defined way to compare immune responses between groups at a specified assessment time. It is a surrogate or laboratory endpoint: it measures the stated antibody response, not the occurrence of influenza infection, hospitalization, or death. The registry’s background describes those clinical outcomes as motivations for studying vaccination, but the posted primary endpoint is HAI-based seroprotection.

The counts at week 21 were 32 in Arm I and 22 in Arm II. The registry says the assessment covered all variants, but does not report variant-specific counts or further detail about how results across variants were combined for the participant-level endpoint. The endpoint definition therefore supports interpretation of the recorded overall participant counts, while leaving those operational details not reported in the registry record.

7. Results Posted in the Registry

• Arm II (Trivalent Influenza Vaccine, Prevnar): 25.9% (22/85) versus 40.0% (32/80) on control; risk difference -14.1 percentage points (95% CI -28.3 to 0.1), risk ratio 0.65 (0.41–1.01); unadjusted two-proportion z-test p = 0.053.

8. Statistical Interpretation

9. Statistical Methods Explained

The result is a comparison of a binary outcome: each participant either met the HAI-based seroprotection definition or did not. For a binary endpoint, the most direct summaries are the number meeting the definition and the proportion within each arm. The registry provides the counts and arm denominators, as well as a risk-difference comparison. The arm counts are 32 of 80 in Arm I and 22 of 85 in Arm II. No extra totals or derived percentages are needed to understand the reported comparison.

What does a risk difference express?

A risk difference subtracts one group’s event proportion from the other group’s event proportion. It is expressed on the proportion scale and retains the direction of the comparison: a negative value means the proportion in the group named first in the contrast is lower than the reference group’s proportion. In this record, the comparison is Arm II relative to Arm I, and the estimated risk difference is -0.141. This is an unadjusted comparison of the posted binary endpoint counts; it does not account for other participant characteristics in an adjusted model.

The risk difference is one possible effect measure. A risk ratio instead compares proportions as a ratio, and an odds ratio compares event odds. The registry also lists ratio measures, but the risk difference is useful for describing an absolute contrast on the probability scale. These measures can summarize the same data in different ways and need not have the same numerical interpretation. None removes uncertainty about the estimate or resolves limitations in endpoint reporting.

What does the confidence interval add?

A confidence interval describes the uncertainty around an estimated effect under the method’s assumptions. In general, a confidence interval is not a guarantee that the true effect lies within its particular limits, and its interpretation depends on the sampling procedure and model. The risk-difference interval in the registry spans values on both sides of zero, with an upper endpoint of 0.001. Because zero represents no risk difference, the interval does not exclude a null contrast. The interval also includes values consistent with a lower observed proportion in Arm II. Its breadth means the point estimate should not be treated as a precise description of the underlying contrast.

How should the p-value be read?

The unadjusted p-value is 0.053. In general, a p-value evaluates the compatibility of the observed data with a specified null hypothesis under a statistical model. It is not the probability that the null hypothesis is correct, and it does not quantify the likelihood that a result will replicate. The p-value is unadjusted, and the registry does not report whether another test, model, or threshold was specified in a protocol or analysis plan. It should therefore be read alongside the effect estimate and confidence interval, not as a stand-alone decision rule.

The registry lists zero posted analysis entries. It still contains arm-level endpoint counts and a comparison derived from those summaries. A detailed sponsor analysis, adjustment strategy, and model specification are not reported in the registry record. The record does not state whether randomization strata, baseline covariates, or other design features were used in analysis. No such methods should be inferred from the fact that allocation was randomized.

Why can binary outcomes be difficult to interpret?

A count is easy to read, but its precision depends in part on how many participants contribute usable endpoint information and how common the outcome is. Small changes in event counts can move the estimated group contrast, especially when the endpoint is not frequent. A confidence interval helps express that sampling uncertainty. General statistical practice also considers whether outcome classifications are comparable across groups and whether missing measurements could alter the observed pattern. The registry does not report enough detail to assess those issues fully for this endpoint.

The outcome description refers to HAI in blood at week 21 for all variants. It does not report separate outcomes by variant, the threshold used to define seroprotection, or details on combining measurements into the participant-level result. Thus the statistical interpretation should remain tied to the recorded overall seroprotection counts, rather than extending to unreported variant-specific responses or clinical outcomes.

10. Confidence Intervals and Precision

The registry’s risk-difference estimate is -0.141, with a confidence interval from -0.283 to 0.001. The interval includes zero, meaning that the range of effects compatible with the data under the interval method includes no difference between the arms. It also extends into negative values, consistent with a lower seroprotection proportion in Arm II under the comparison’s direction. The interval is not a statement that all values within it are equally likely, nor does it guarantee that the true effect lies within those limits.

The interval is wide enough to encompass materially different interpretations of the size of the contrast. The point estimate alone can appear more definite than the evidence warrants; the interval makes the uncertainty visible. The unadjusted p-value of 0.053 is consistent with the interval’s inclusion of zero under commonly used two-sided inference, but the interval is more informative about the range of effect sizes compatible with the data than a threshold-focused reading of the p-value.

Precision is limited by the amount of endpoint information and by reporting gaps. The registry gives arm denominators and endpoint counts, but the analysis population definition and missing-data handling are not reported. It also does not report an adjusted estimate. These omissions prevent a fuller assessment of whether all randomized participants were represented and how analytic choices might affect uncertainty. The interval should therefore be interpreted as uncertainty around the posted unadjusted comparison, not as a complete account of every source of uncertainty.

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. They are illustrations based on the observed effect and are not the original trial’s design calculation. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the arms, and a normal approximation. The original trial’s own sample-size assumptions and justification are not reported in the registry record.

The figures are organized around planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each assumed effect, the 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting that effect under the stated assumptions, if the assumed effect and model are appropriate. The 90% power column gives the corresponding planning number for a 90% chance. For the 100% effect illustration, the figures are 173 participants per arm for 80% power and 231 for 90% power. For 75% of the observed effect, they are 317 and 423 participants per arm. For 50% of the observed effect, they are 729 and 976 participants per arm.

Smaller effects are harder to distinguish from random variation, so the planning illustrations require more participants per arm as the assumed effect becomes smaller. The curve can be read as the same general relationship across effect sizes: planning for a smaller effect calls for a larger sample under the listed assumptions. These are planning illustrations, not observed power. They should not be treated as a retrospective measure of how informative the completed trial was, and they do not establish the sample size needed for a future study unless its design and target effect match the stated assumptions.

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 = 0.400; treatment proportion p₁ = 0.259; average p̄ = 0.329.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6647 = 1.3027.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6571 = 0.5531.
4. n = (1.3027 + 0.5531)² / (-0.1412)² = 172.8, rounded up to 173 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 <- 0.4                          # control proportion
p1 <- 0.258823529411765                          # 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(4080531)
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 = 173 (80% power), 231 (90% power)
 75% of observed effect: n per arm = 317 (80% power), 423 (90% power)
 50% of observed effect: n per arm = 729 (80% power), 976 (90% power)
power.prop.test: 172.8 
Simulated power at n = 173 per arm: 0.804 (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 lists one outcome measure and no posted secondary outcome measures. It reports zero analysis entries. The primary endpoint description refers to HAI-based seroprotection for all variants, but variant-specific results are not reported. The record does not explain whether assessments across variants involved separate statistical tests, a combined endpoint, or another approach. A multiplicity adjustment or strategy for handling multiple comparisons is not reported in the registry record.

Without a complete list of planned outcomes and analyses, it is not possible to determine whether the reported unadjusted p-value represents the only planned inferential test. If several outcomes, variants, time points, or analytic choices are examined, the chance of a nominally notable finding can increase unless the analysis plan accounts for multiplicity. This is a general statistical concern, not evidence that unreported analyses occurred in this trial.

Missing-data handling is also not reported. The registry gives endpoint counts and arm denominators, but does not say whether participants without a week-21 blood assessment were excluded, counted as not seroprotected, handled through imputation, or addressed by another method. It does not provide reasons for missing endpoint data or describe follow-up completeness. These details matter because a group comparison can be affected if the availability of measurements differs between arms or relates to the outcome.

The analysis population is not specified. The record does not state whether the primary comparison followed an intention-to-treat principle, included only participants who received scheduled vaccinations, or used another population definition. Randomized allocation is reported, but the analysis population cannot be inferred from that design fact alone. The registry also does not report a prespecified adjustment set or a detailed statistical analysis plan. Consequently, the posted result is best understood as an unadjusted comparison of recorded counts, with important analysis and missingness decisions not reported.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

The registry’s adverse-event fields list serious adverse events as zero in Arm I and zero in Arm II, with the respective risk sets recorded as 80 and 85. Other adverse events are also recorded as zero in both arms, with the same risk sets. These are the counts reported in those fields; they do not establish that no symptoms or events of any kind occurred outside the registry’s defined and reported categories.

Deaths are listed separately: 3 in Arm I and 1 in Arm II. The registry record does not provide cause, timing, relationship to vaccination, or further context for these deaths. The numbers should not be interpreted as showing that treatment caused or prevented deaths. No serious adverse-event terms are listed in the record.

Safety summaries depend on how events were defined, collected, and attributed, as well as the period of observation. Those details are not reported, so the recorded counts alone do not provide a complete safety assessment or support causal comparisons.

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

The result answers a narrow question: how many participants in each randomized arm were recorded as having HAI-based seroprotection at week 21? The counts were 32 in Arm I and 22 in Arm II. The unadjusted risk-difference estimate favored a higher observed proportion in Arm I, while its confidence interval included zero. The data therefore do not give a highly precise estimate of the difference between the schedules on this endpoint.

The primary endpoint is an antibody-based measure, not a clinical outcome. The registry’s stated motivation includes prevention of influenza and possible effects on complications or plasma cell disorder status, but those outcomes are not reported as secondary measures. The seroprotection counts do not establish whether influenza infections, hospitalizations, deaths, or disease progression differed between arms. Nor do they establish that the observed antibody response translates into a particular level of clinical protection.

The trial was randomized and unmasked, but the record does not report enough analysis detail to assess all aspects of the comparison. In particular, the analysis population and handling of missing week-21 measurements are not specified. The endpoint description also does not give variant-specific results or the seroprotection threshold. These omissions limit what can be concluded from the posted counts and comparison.

Accordingly, the result is descriptive evidence about the measured week-21 endpoint in the recorded trial arms. It is not a treatment recommendation, proof of benefit or lack of benefit, or a basis for inferring effects on outcomes that were not posted. The uncertainty interval, outcome definition, and reporting gaps are central to interpreting the estimate.

16. Why This Trial Matters Statistically

This trial illustrates why a randomized comparison should be read through both its effect estimate and its uncertainty. The arm counts alone identify the observed endpoint pattern, while the risk difference expresses the contrast on an absolute scale. The confidence interval and unadjusted p-value show that the observed pattern is not estimated with enough precision to exclude a null difference using the reported interval.

It also demonstrates the distinction between an immune-response endpoint and a clinical endpoint. HAI-based seroprotection provides a measurable laboratory outcome at a defined time, but it is not the same as documenting influenza infection or a complication. Keeping that distinction explicit prevents the result from being interpreted beyond what was measured.

Finally, the record highlights the importance of reporting the analysis population, missing-data approach, multiplicity strategy, and endpoint definition. These elements help readers assess whether a reported estimate answers the intended question and how robust it may be to analytic choices. Their absence does not invalidate the counts, but it narrows the conclusions that can be drawn from them.

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 record provides limited detail about the primary endpoint’s operational definition. It identifies HAI measurement in blood at week 21 for all variants, but does not report the seroprotection threshold, assay procedures, or how variant-specific measurements were combined into the participant count. Variant-specific counts are not reported, so the overall result cannot be used to compare responses across variants.

The analysis population and missing-data approach are not reported. Although the record gives denominators and event counts for the arms, it does not explain whether those denominators represent all randomized participants with available measurements or another analysis set. It also does not report follow-up completeness, missing outcome counts, or reasons for unavailable measurements. These details are needed to assess potential bias from incomplete endpoint data.

The registry lists no posted analysis entries and does not report a statistical analysis plan, adjustment strategy, or multiplicity procedure. It is therefore not possible to determine from the record which analyses were prespecified or whether additional comparisons were conducted. The reported comparison is unadjusted, and no covariate-adjusted estimate is reported.

The study is unmasked, and the registry does not describe procedures that might reduce measurement or assessment bias. It also does not provide detailed safety-event definitions, collection methods, or context for the deaths recorded in the adverse-event fields. These limits apply to interpretation of the registry record and do not establish that the trial lacked procedures not entered in the record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Influenza Vaccination for Flu Prevention in Patients With Plasma Cell Disorders — NCT04080531.
• Registry record last updated 2025-02-28; status last verified 2025-02.
• Results first posted 2025-02-28.
• 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

NCT04080531 is a completed phase IV randomized, unmasked, parallel-group trial sponsored by Emory University. It enrolled 165 participants and studied influenza-vaccination schedules in patients with plasma cell disorders. Arm I received trivalent influenza vaccine at weeks 1, 9, and 17; Arm II received it at week 1. Both arms were scheduled to receive pneumococcal 13-valent conjugate vaccine at week 5, subject to the stated condition.

The primary endpoint was HAI-based seroprotection in blood at week 21 for all variants. The recorded counts were 32 in Arm I and 22 in Arm II. The unadjusted risk difference for Arm II relative to Arm I was -0.141, with a confidence interval from -0.283 to 0.001 and p = 0.053. The registry does not report secondary outcomes, a detailed analysis plan, the analysis population, or missing-data handling.