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 ProQuad Dose Selection Study (V221-011)(COMPLETED) (NCT00986232), a randomized phase 2 study. The primary outcome is Number of Participants With Varicella Glycoprotein Enzyme-Linked Immunosorbent Assay (gpELISA) Antibody Titer ≥ 5 gpELISA Units.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00986232 |
| Phase | Phase 2 |
| Condition | Measles, Mumps, Rubella |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 1551 |
| Arms in the primary outcome | 7 |
| Lead sponsor | Merck Sharp & Dohme LLC |
| Results posted | Yes |
2. Clinical Question
Population
Healthy children enrolled in a study of vaccines for measles, mumps, rubella, and varicella. The primary endpoint population was per protocol: participants had blood samples within predefined day ranges before and after randomization, were seronegative to varicella at baseline, and followed protocol procedures. The registry record does not report the age range or further eligibility details.
Intervention
Three ProQuad dose groups were compared: low, middle, and high dose. Posted outcome groups distinguish results after one injection and after two injections for the ProQuad doses. The record describes ProQuad as a live measles, mumps, rubella, and varicella vaccine.
Comparator
The comparator was concomitant M-M-R II and process-upgrade varicella vaccine (PUVV), administered as separate injections. The posted primary comparison uses ProQuad low dose after one injection as its reference group and also reports contrasts for other groups, including M-M-R II + PUVV.
Primary question
At 6 weeks postvaccination, how many participants in the per-protocol population with baseline varicella titer below 1.25 gpELISA units had a varicella gpELISA antibody titer of at least 5 gpELISA units? The registry record reports group counts and unadjusted comparisons of this threshold response. This is an antibody-response question, not a direct measure of clinical illness or duration of protection.
3. Trial Design
The registry record describes NCT00986232, titled ProQuad Dose Selection Study (V221-011)(COMPLETED). It is a Phase 2, randomized, double-masked, parallel-group study. The stated enrollment is 1551, and the study status is completed. The record lists a start date of 1999-04 and primary completion of 2000-04.
The study compared three different ProQuad doses with concomitant M-M-R II and PUVV vaccines. The arm descriptions identify low-, middle-, and high-dose ProQuad and the combined M-M-R II + PUVV comparator. Posted outcome group labels also distinguish one-injection and two-injection ProQuad results. The registry record does not explain the relationship between the injection-specific outcome groups and the original allocation in enough detail to infer additional design features.
The primary endpoint was a count of participants with a varicella gpELISA antibody titer at or above 5 gpELISA units, measured 6 weeks postvaccination. Its specified population was per protocol and restricted to participants seronegative to varicella at baseline. This is not necessarily the same population as all enrolled or randomized participants; the record does not provide a complete participant-flow account alongside these endpoint results.
Measles, mumps, and rubella antibody thresholds and several geometric mean titer outcomes are listed as secondary outcomes, along with serious vaccine-related clinical adverse experiences. The registry record lists no reported analyses in its analysis field. It does not report the original statistical plan, the allocation ratio, the masking procedures, or the rationale for the planned enrollment. Those details should not be inferred from the posted endpoint comparisons.
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
| Stage | ProQuad™ (Low Dose) | ProQuad™ (Middle Dose) | ProQuad™ (High Dose) | M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) |
|---|---|---|---|---|
| STARTED | 387 | 393 | 381 | 390 |
| Vaccination Visit 1 | 387 | 393 | 381 | 390 |
| Vaccination Visit 2 | 360 | 365 | 360 | 0 |
| COMPLETED | 336 | 343 | 346 | 370 |
| NOT COMPLETED | 51 | 50 | 35 | 20 |
Reasons for not completing this period:
| Reason | ProQuad™ (Low Dose) | ProQuad™ (Middle Dose) | ProQuad™ (High Dose) | M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) |
|---|---|---|---|---|
| Adverse Event | 1 | 2 | 3 | 0 |
| Lost to Follow-up | 19 | 12 | 12 | 7 |
| Protocol Violation | 2 | 3 | 0 | 1 |
| Withdrawal by Subject | 13 | 16 | 12 | 3 |
| Missed one or more bleeds | 13 | 10 | 6 | 7 |
| Incomplete safety follow-up | 3 | 7 | 2 | 2 |
Analysis population for the primary outcome, as defined in the registry: The per-protocol analysis set included participants who had pre- and post-randomization blood samples within predefined day ranges, were seronegative to varicella at baseline, and followed protocol procedures.
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.
| Characteristic | Unit | ProQuad™ (Low Dose) | ProQuad™ (Middle Dose) | ProQuad™ (High Dose) | M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 387 | 393 | 381 | 390 | 1551 | |
| Age, Continuous | Months | 12.9 (SD 1.5) | 12.9 (SD 1.5) | 12.9 (SD 1.5) | 13.0 (SD 1.7) | 12.9 (SD 1.5) |
| Sex: Female, Male: Female | Participants | 186 | 181 | 192 | 161 | 720 |
| Sex: Female, Male: Male | Participants | 201 | 212 | 189 | 229 | 831 |
| Race/Ethnicity, Customized: African American | participants | 65 | 55 | 64 | 54 | 238 |
| Race/Ethnicity, Customized: Asian/Pacific | participants | 19 | 11 | 19 | 13 | 62 |
| Race/Ethnicity, Customized: Caucasian | participants | 241 | 267 | 251 | 262 | 1021 |
| Race/Ethnicity, Customized: Hispanic | participants | 34 | 44 | 22 | 25 | 125 |
| Race/Ethnicity, Customized: Native American | participants | 1 | 1 | 1 | 0 | 3 |
| Race/Ethnicity, Customized: Other | participants | 27 | 15 | 24 | 36 | 102 |
6. Primary Endpoint
The registry lists the primary outcome as Number of Participants With Varicella Glycoprotein Enzyme-Linked Immunosorbent Assay (gpELISA) Antibody Titer ≥ 5 gpELISA Units, measured over 6 weeks postvaccination.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint counts participants whose varicella antibody response reached a specified laboratory threshold: a varicella gpELISA titer of at least 5 gpELISA units at 6 weeks postvaccination. The endpoint description limits this assessment to participants with a baseline titer below 1.25 gpELISA units. The primary population is further described as per protocol, requiring samples within predefined day ranges, baseline seronegativity, and adherence to protocol procedures.
A threshold endpoint converts a continuous laboratory measurement into a count of participants above or below a defined cut point. That can make group response frequencies straightforward to compare, but it also discards information about how far individual titers lie above or below the threshold. A participant just below the cut point is classified differently from one just above it, even if their measurements are close. These are general properties of threshold outcomes, not additional claims about individual participants in this study.
The endpoint measures an antibody response, not varicella illness, transmission, duration of immunity, or a clinical benefit. The registry record does not report a link between this threshold and any later clinical outcome. Interpretation should therefore remain specific to the laboratory response, the stated six-week assessment, and the per-protocol population.
7. Results Posted in the Registry
- ProQuad™ (Low Dose) After 2 Injections: 99.7% (299/300) versus 63.9% (198/310) on control; risk difference 35.8 percentage points (95% CI 30.4 to 41.2), risk ratio 1.56 (1.43–1.70); unadjusted two-proportion z-test p = <0.001.
- ProQuad™ (Middle Dose) After 1 Injection: 80.8% (253/313) versus 63.9% (198/310) on control; risk difference 17.0 percentage points (95% CI 10.1 to 23.9), risk ratio 1.27 (1.15–1.40); unadjusted two-proportion z-test p = <0.001.
- ProQuad™ (Middle Dose) After 2 Injections: 100.0% (303/303) versus 63.9% (198/310) on control; risk difference 36.1 percentage points (95% CI 30.8 to 41.5), risk ratio 1.57 (1.44–1.70); unadjusted two-proportion z-test p = <0.001.
- ProQuad™ (High Dose) After 1 Injection: 88.6% (272/307) versus 63.9% (198/310) on control; risk difference 24.7 percentage points (95% CI 18.3 to 31.1), risk ratio 1.39 (1.26–1.52); unadjusted two-proportion z-test p = <0.001.
Risk difference: ProQuad™ (Low Dose) After 2 Injections
95% CI: 30.4 to 41.2 percentage points
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 |
|---|---|---|---|---|
| Number of Participants With Postvaccination Measles Enzyme-Linked Immunosorbent Assay (ELISA) Antibody Titer ≥ 207.5 mIU/mL | Binary Endpoint | Risk difference | +0.3 pts (-1.1 to 1.7) | 14,800 per arm |
| Number of Participants With Postvaccination Mumps ELISA Antibody Titer ≥ 2.0 Ab Units/mL | Binary Endpoint | Risk difference | +0.3 pts (-0.3 to 0.9) | n/a |
Number of Participants With Postvaccination Measles Enzyme-Linked Immunosorbent Assay (ELISA) Antibody Titer ≥ 207.5 mIU/mL
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- ProQuad™ (Low Dose) After 2 Injections: 99.4% (311/313) versus 99.1% (321/324) on control; risk difference 0.3 percentage points (95% CI -1.1 to 1.7), risk ratio 1.00 (0.99–1.02); unadjusted two-proportion z-test p = 0.682.
- ProQuad™ (Middle Dose) After 1 Injection: 98.8% (338/342) versus 99.1% (321/324) on control; risk difference -0.2 percentage points (95% CI -1.8 to 1.3), risk ratio 1.00 (0.98–1.01); unadjusted two-proportion z-test p = 0.758.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between ProQuad™ (Low Dose) After 2 Injections 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 ProQuad™ (Middle Dose) After 1 Injection and the control. The interval gives the range of effects that remain compatible with the data.
Number of Participants With Postvaccination Mumps ELISA Antibody Titer ≥ 2.0 Ab Units/mL
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- ProQuad™ (Low Dose) After 2 Injections: 100.0% (322/322) versus 99.7% (333/334) on control; risk difference 0.3 percentage points (95% CI -0.3 to 0.9), risk ratio 1.00 (1.00–1.01); unadjusted two-proportion z-test p = 0.326.
- ProQuad™ (Middle Dose) After 1 Injection: 99.1% (344/347) versus 99.7% (333/334) on control; risk difference -0.6 percentage points (95% CI -1.7 to 0.6), risk ratio 0.99 (0.98–1.01); unadjusted two-proportion z-test p = 0.335.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between ProQuad™ (Low Dose) After 2 Injections 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 ProQuad™ (Middle Dose) After 1 Injection and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists eight secondary outcomes, including antibody threshold responses for measles, mumps, and rubella, geometric mean titer outcomes, and serious vaccine-related clinical adverse experiences. Detailed arm counts and unadjusted comparison summaries are posted for two antibody-threshold outcomes: measles and mumps. Full numerical results for every listed secondary outcome are not reported in the registry record.
Across the posted measles and mumps threshold comparisons, response counts are close to the respective group denominators. The reported risk-difference intervals for the comparisons with estimates do not establish a clear group separation: the bounds span zero, and the listed p-values are not small by conventional significance thresholds. This pattern contrasts with the positive primary varicella risk-difference intervals. That comparison is descriptive, not proof that the vaccines differ in a broader immunologic or clinical sense. Different antibodies, thresholds, and analysis populations can yield different patterns.
Secondary outcomes can help characterize responses beyond the primary endpoint, but they generally carry less confirmatory weight when many outcomes and comparisons are considered without a reported multiplicity adjustment. The registry record does not report a hierarchy of secondary hypotheses or a testing procedure that controls the chance of false-positive findings across them. The secondary results should therefore be treated as supportive or exploratory descriptions rather than as independent confirmation of the primary finding.
Geometric mean titer results and the complete serious vaccine-related clinical adverse experience outcome are not available in the posted numerical summaries. Their inclusion in the outcome list does not establish what those results were. This limits conclusions about consistency across all antibody measures and about the complete safety outcome set.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Number of Participants With Postvaccination Measles Enzyme-Linked Immunosorbent Assay (ELISA) Antibody Titer ≥ 207.5 mIU/mL
- Number of Participants With Postvaccination Mumps ELISA Antibody Titer ≥ 2.0 Ab Units/mL
- Number of Participants With Postvaccination Rubella ELISA Antibody Titer ≥ 10 IU/mL
- Number of Participants With Serious Vaccine-Related Clinical Adverse Experiences (CAEs)
- Antibody Response to Varicella at 6 Weeks Postvaccination in Participants With Baseline Titer < 1.25 gpELISA Units - Geometric Mean Titer (GMT)
- Antibody Response to Measles at 6 Weeks Postvaccination in Participants Initially Seronegative to Measles at Baseline - Geometric Mean Titer (GMT)
- Antibody Response to Mumps at 6 Weeks Postvaccination in Participants Initially Seronegative to Mumps at Baseline - Geometric Mean Titer (GMT)
- Antibody Response to Rubella at 6 Weeks Postvaccination in Participants Initially Seronegative to Rubella at Baseline - Geometric Mean Titer (GMT)
9. Statistical Interpretation
For the primary response, the posted counts are 198.0 of 310.0 in ProQuad low dose after one injection and 299.0 of 300.0 in ProQuad low dose after two injections. The unadjusted risk difference is 0.358, with interval bounds of 0.304 and 0.412, and the unadjusted p-value is <0.001. This contrast describes a larger observed proportion meeting the antibody threshold in the two-injection group than in the low-dose one-injection reference group. It is a group-level comparison; it does not indicate that every participant had the same response.
Other posted primary contrasts likewise show positive risk differences relative to the reference group. The comparison for ProQuad middle dose after one injection is 0.170, with interval bounds of 0.101 and 0.239; the middle-dose two-injection contrast is 0.361, with bounds of 0.308 and 0.415. The high-dose one-injection contrast is 0.247, with bounds of 0.183 and 0.311, and the high-dose two-injection contrast is 0.352, with bounds of 0.297 and 0.406. M-M-R II + PUVV after one injection has a posted risk difference of 0.292, with bounds of 0.232 and 0.353. Each of these comparisons has an unadjusted p-value of <0.001.
These numerical summaries support a description of differences in the specified antibody response, not a conclusion about clinical efficacy or safety. The comparisons are unadjusted, and the record does not report a multiplicity procedure. Thus the p-values do not account for the several groups and outcomes examined. The primary population is per protocol rather than a stated all-randomized analysis, and the record does not report detailed missing-data handling or a participant-flow explanation for the endpoint denominators.
Precision is also relevant: the risk-difference intervals for the primary comparisons do not span zero, but their widths indicate that the exact magnitude is uncertain. The registry record does not state the confidence level attached to the interval bounds. The findings should be read as evidence about the posted group response counts at the stated assessment time, with the analysis-population and multiplicity limitations kept in view.
10. Statistical Methods Explained
What does a risk difference describe?
A risk difference compares the proportion with the defined response in one group against the proportion in a reference group. Positive values mean the response proportion is higher in the named comparison group on the posted scale; negative values mean it is lower. The primary results express the contrast for meeting the antibody threshold. This is an unadjusted group comparison, not an estimate adjusted for baseline characteristics or other variables. The registry record does not report an adjusted model for these results.
How should the p-values be read?
A p-value describes how incompatible the observed data are with a specified no-difference model, under the assumptions of the statistical test. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The primary comparison p-values are identified as unadjusted. They do not account for the set of multiple group contrasts or secondary outcomes. A small unadjusted p-value therefore does not, by itself, resolve the multiplicity issue or the limitations of the analysis population.
What do interval bounds add?
An interval gives a range of values compatible with the observed data under the method used to calculate it. A narrower interval indicates greater statistical precision, while a wider interval indicates less precision. Whether an interval contains zero is informative for a risk difference: zero represents no difference in response proportions. The posted primary interval bounds are positive. The confidence level and exact interval method are not reported in the registry record, so they should not be assigned a confidence percentage or a more specific interpretation than the record supports.
General statistical interpretation: intervals and p-values address sampling uncertainty under a model; they do not account automatically for bias from missing outcomes, departures from protocol, selective reporting, or an analysis population that differs from the intended population.
What are risk ratios and odds ratios?
The comparison summaries also include risk ratios for several primary contrasts and odds ratios for some contrasts. A risk ratio compares response proportions as a ratio, whereas a risk difference compares them by subtraction. An odds ratio compares odds, which are not the same as probabilities. These measures express the same group data on different scales and can therefore look numerically different. Their interpretation depends on the outcome frequency and the chosen measure. They should not be treated as interchangeable, nor should an odds ratio be described as a risk ratio.
The registry record posts interval bounds for these measures in some comparisons, but not uniformly for every contrast. The main interpretation above uses the risk differences because they directly state the absolute group contrast on the posted scale. No further transformation or calculation is needed to understand the posted estimates.
What does the per-protocol population mean?
The primary endpoint population is defined by protocol-related conditions: timing of blood samples, baseline varicella seronegativity, and following protocol procedures. A per-protocol analysis can describe response among participants meeting those conditions, but it may not preserve all the advantages of randomized assignment if inclusion depends on events after randomization. The registry record does not report enough information to assess exclusions, missing samples, or how the listed denominators arose. The primary results should therefore be described as applying to the specified per-protocol population, not automatically to every randomized participant.
The record identifies randomization and double masking but does not report the randomization method, masking implementation, or detailed statistical plan. It also lists no reported analyses in the analysis field. The comparison summaries can be interpreted as posted unadjusted contrasts, but they do not establish what analyses were prespecified or how the sponsor handled all outcomes in its original analysis.
Why do threshold responses lose information?
General statistical explanation: dichotomizing a continuous measurement creates an easily interpreted response count but compresses the underlying data. It cannot show the distribution of antibody titers within the response and nonresponse categories. Two groups can have similar threshold counts while differing in values within those categories, or can have different counts because many measurements lie near the cut point. The registry lists geometric mean titer outcomes among secondary measures, but complete results for those outcomes are not included in the endpoint details.
Finally, an unadjusted comparison is not necessarily a poor analysis; it is simply a limited one. Its interpretation is clearest when the comparison, outcome, population, and timing are specified, as they are for the posted primary result. Stronger claims about robustness, causal effects in a broader population, or confirmatory testing would require information that is not reported in the registry record.
11. Confidence Intervals and Precision
The primary risk-difference intervals provide information about the range of effect sizes compatible with the posted counts under the calculation method. For ProQuad low dose after two injections versus low dose after one injection, the estimate is 0.358, and the interval bounds are 0.304 and 0.412. The interval does not include zero, so the posted contrast is not centered on a no-difference value. The other posted primary risk-difference intervals also have positive lower bounds. Their estimates and bounds are given with the comparisons, and the widths vary across contrasts.
Precision is not the same as certainty that an estimate is exactly correct. An interval reflects sampling uncertainty under its statistical assumptions; it does not capture every potential source of error. In particular, it cannot resolve questions about selection into the per-protocol population, missing data, unreported analytic choices, or multiple comparisons. The registry record does not state the confidence level or method used for the interval bounds. They should therefore be read as the posted uncertainty intervals without attaching an unreported confidence percentage.
Group counts help explain why precision can differ: the primary outcome denominators vary by comparison, and the observed response counts also vary. No additional precision measure needs to be inferred from these counts. The posted estimates and interval bounds are the appropriate basis for describing statistical uncertainty. They do not establish whether a difference is important outside the laboratory outcome being measured.
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 | 18 | 23 |
| 75% of the observed effect | 38 | 50 |
| 50% of the observed effect | 96 | 128 |
The sample-size table gives planning illustrations based on the observed effect, rather than the original trial design. The figures are participants per arm for 80% power and participants per arm for 90% power. They are not total sample sizes. The assumptions listed are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. Smaller effects need more participants to detect under these assumptions.
The 80% power column represents the planned chance of detecting the specified effect if that effect is true, under the assumed statistical model and significance level. The 90% column applies the same idea with a higher target chance of detection, which generally requires a larger planned group size. These are design calculations, not a measure of how likely the completed study was to detect its actual result. This is not observed power.
For the binary antibody outcomes, the figures are participants per arm. The general sample-size note distinguishes time-to-event calculations, which would report a total number of events, but the endpoint is not time-to-event. The registry record does not report the trial's original sample-size justification or original design assumptions. These planning illustrations therefore should not be mistaken for the enrollment target or for a reconstruction of the trial's design.
The curve, when read alongside the table, represents how the planned group size changes as the effect assumed for planning changes. A smaller assumed effect requires more participants; the relationship is a planning aid, not a prediction of future results. Results based on a large observed contrast can yield small illustrative group sizes, but those calculations inherit uncertainty and possible exaggeration in the observed effect. They should be used cautiously when planning a new study.
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, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.639; treatment proportion p1 = 0.997; average p̄ = 0.818.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5460 = 1.0702.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4838 = 0.4072.
- n = (1.0702 + 0.4072)2 / (0.3580)2 = 17.0, rounded up to 18 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 <- 0.638709677419355 # control proportion
p1 <- 0.996666666666667 # 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(986232)
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 = 18 (80% power), 23 (90% power)
75% of observed effect: n per arm = 38 (80% power), 50 (90% power)
50% of observed effect: n per arm = 96 (80% power), 128 (90% power)
power.prop.test: 17
Simulated power at n = 18 per arm: 0.922 (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.
14. Multiplicity, Missing Data and Analysis Populations
The registry record lists multiple arms, several primary contrasts, and eight secondary outcomes. It does not report a multiplicity adjustment, a prespecified testing hierarchy, or an explicit plan for controlling the chance of false-positive results across the full set of comparisons. The primary comparison p-values are unadjusted. Each p-value describes its own contrast and should not be read as if it accounts for the other comparisons.
There is also limited information about missing data. The primary population definition requires appropriately timed pre- and post-randomization blood samples, baseline varicella seronegativity, and adherence to protocol procedures. The record does not report the number excluded for each reason, the amount or pattern of missing endpoint data, or an imputation or sensitivity-analysis method. The per-protocol denominator should not be assumed to include every randomized participant.
The record identifies the trial as randomized, double masked, and parallel group, but does not report the allocation procedure or detailed statistical methods. It lists no reported analyses in its analysis field. This absence does not prove that no analysis was done; it means the registry record does not provide those analyses as a reported plan. The original sample-size justification, interim analyses, and detailed analysis plan are not reported in the registry record.
These gaps affect how securely the reported results can be placed in a confirmatory framework. The posted response counts and unadjusted comparisons remain interpretable as summaries of the stated outcomes and populations. They do not resolve the potential effects of selection, missingness, or multiple testing. A reader should distinguish what the endpoint summaries show from what cannot be evaluated because the registry record does not report it.
15. 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 |
|---|---|---|---|
| ProQuad (Low Dose) After Injection 1 | 2 | 378 | 0.5% |
| ProQuad (Middle Dose) After Injection 1 | 3 | 387 | 0.8% |
| ProQuad (High Dose) After Injection 1 | 1 | 377 | 0.3% |
| M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) | 1 | 381 | 0.3% |
| ProQuad (Low Dose) After Injection 2 | 1 | 353 | 0.3% |
| ProQuad (Middle Dose) After Injection 2 | 0 | 361 | 0.0% |
| ProQuad (High Dose) After Injection 2 | 2 | 358 | 0.6% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 1% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| ProQuad (Low Dose) After Injection 1 | 286 of 378 |
| ProQuad (Middle Dose) After Injection 1 | 286 of 387 |
| ProQuad (High Dose) After Injection 1 | 289 of 377 |
| M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) | 297 of 381 |
| ProQuad (Low Dose) After Injection 2 | 253 of 353 |
| ProQuad (Middle Dose) After Injection 2 | 258 of 361 |
Most frequent serious adverse event terms
| Event term | Organ system | ProQuad (Low Dose) After Injection 1 | ProQuad (Middle Dose) After Injection 1 | ProQuad (High Dose) After Injection 1 | M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) | ProQuad (Low Dose) After Injection 2 | ProQuad (Middle Dose) After Injection 2 |
|---|---|---|---|---|---|---|---|
| Asthma | Respiratory, thoracic and mediastinal disorders | 1 of 378 | 1 of 387 | 1 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Seizure, febrile | Nervous system disorders | 0 of 378 | 1 of 387 | 0 of 377 | 1 of 381 | 0 of 353 | 0 of 361 |
| Laryngotracheobronchitis | Respiratory, thoracic and mediastinal disorders | 1 of 378 | 0 of 387 | 0 of 377 | 0 of 381 | 1 of 353 | 0 of 361 |
| Bacteremia | Infections and infestations | 0 of 378 | 1 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Fever | General disorders | 0 of 378 | 1 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Acidosis | Metabolism and nutrition disorders | 0 of 378 | 1 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Respiratory distress, newborn | Respiratory, thoracic and mediastinal disorders | 1 of 378 | 0 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Diarrhea | Gastrointestinal disorders | 0 of 378 | 0 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Dehydration | Metabolism and nutrition disorders | 0 of 378 | 0 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
| Otitis media | Ear and labyrinth disorders | 0 of 378 | 0 of 387 | 0 of 377 | 0 of 381 | 0 of 353 | 0 of 361 |
Most frequent non-serious adverse event terms
| Event term | Organ system | ProQuad (Low Dose) After Injection 1 | ProQuad (Middle Dose) After Injection 1 | ProQuad (High Dose) After Injection 1 | M-M-R™ II + PUVV (Process Upgrade Varicella Vaccine) | ProQuad (Low Dose) After Injection 2 | ProQuad (Middle Dose) After Injection 2 |
|---|---|---|---|---|---|---|---|
| Fever | General disorders | 116 of 378 | 128 of 387 | 145 of 377 | 136 of 381 | 81 of 353 | 98 of 361 |
| Infection, Respiratory, Upper | Infections and infestations | 60 of 378 | 58 of 387 | 67 of 377 | 64 of 381 | 82 of 353 | 110 of 361 |
| Pain/Tenderness/Soreness (ProQuad Injection-site) | Skin and subcutaneous tissue disorders | 84 of 378 | 70 of 387 | 78 of 377 | 0 of 0 | 57 of 353 | 52 of 361 |
| Irritability | Psychiatric disorders | 52 of 378 | 49 of 387 | 51 of 377 | 42 of 381 | 29 of 353 | 28 of 361 |
| Otitis Media | Ear and labyrinth disorders | 34 of 378 | 37 of 387 | 34 of 377 | 42 of 381 | 53 of 353 | 48 of 361 |
| Erythema (ProQuad Injection-site) | Skin and subcutaneous tissue disorders | 48 of 378 | 43 of 387 | 32 of 377 | 0 of 0 | 36 of 353 | 46 of 361 |
| Rhinorrhea | Respiratory, thoracic and mediastinal disorders | 28 of 378 | 34 of 387 | 38 of 377 | 41 of 381 | 28 of 353 | 29 of 361 |
| Diarrhea | Gastrointestinal disorders | 34 of 378 | 23 of 387 | 31 of 377 | 31 of 381 | 19 of 353 | 26 of 361 |
| Cough | Respiratory, thoracic and mediastinal disorders | 21 of 378 | 20 of 387 | 20 of 377 | 25 of 381 | 26 of 353 | 33 of 361 |
| Swelling (ProQuad Injection-site) | Skin and subcutaneous tissue disorders | 29 of 378 | 23 of 387 | 30 of 377 | 0 of 0 | 31 of 353 | 22 of 361 |
Serious events with the highest arm-level rate: dehydration (0.6%), laryngotracheobronchitis (0.3%), fever (0.3%), diarrhea (0.3%), otitis media (0.3%).
The safety summaries report serious adverse experiences by group, with the number at risk and the number affected. The group counts for serious adverse experiences are 2 among 378 for low-dose ProQuad after injection 1, 3 among 387 for middle-dose ProQuad after injection 1, 1 among 377 for high-dose ProQuad after injection 1, and 1 among 381 for M-M-R II + PUVV. For the second-injection ProQuad groups, the corresponding counts are 1 among 353, 0 among 361, and 2 among 358 for low, middle, and high dose.
These are descriptive group counts. They do not by themselves establish that an event was caused by vaccination. The listed secondary outcome specifically refers to serious vaccine-related clinical adverse experiences, but the relationship between that outcome and each safety summary row is not explained in the registry record. Death results are not reported in the registry record. The record also lists serious-event terms, including dehydration at 0.6% and laryngotracheobronchitis, fever, diarrhea, otitis media, and asthma at 0.3% each. These summaries do not establish comparative safety or rule out uncommon events.
16. What the Result Does, and Does Not, Mean
The central statistical result is a higher observed proportion meeting the specified varicella antibody threshold in several posted groups than in the ProQuad low-dose-after-one-injection reference group. The primary comparison for low-dose ProQuad after two injections has a positive risk difference, interval bounds above zero, and an unadjusted p-value of <0.001. The other posted primary contrasts also have positive risk differences and unadjusted p-values of <0.001. These statements describe laboratory response counts at 6 weeks postvaccination in the specified per-protocol population.
The result does not show that every participant responded, nor does it tell how long antibody levels persisted. It does not directly measure infection, disease severity, transmission, or clinical protection. A threshold response is a laboratory endpoint, and the registry record does not report evidence connecting this specific endpoint to later clinical outcomes. The posted comparisons also do not establish that one vaccination regimen is preferable for an individual or a population.
The analysis is limited to the groups, time point, endpoint definition, and population recorded. Unadjusted comparisons across multiple groups and outcomes require caution, and the record does not provide a multiplicity procedure. The per-protocol definition raises a separate question about how participants excluded from that population may differ from those included; the registry record does not provide enough flow or missing-data detail to assess that issue.
Accordingly, the results are best understood as evidence of differences in the measured antibody response under the posted comparisons. They are not a complete account of efficacy, durability, or safety. Broader conclusions would require clinical outcome evidence and analytic details not reported in the registry record.
17. Why This Trial Matters Statistically
This study illustrates how a dose-selection question can be framed with an objective laboratory threshold and compared across randomized groups. The primary endpoint is a count of participants reaching a defined antibody titer, so the results can be expressed as response proportions and risk differences. Those measures make the size and direction of a group contrast easier to interpret than a p-value alone.
It also illustrates why the analysis population matters. The primary endpoint is reported for a per-protocol population with baseline seronegativity and specified blood-sample timing. That restriction describes a clinically and analytically specific subset, but it is not interchangeable with an all-randomized comparison. Without participant-flow details, readers cannot fully assess how selection into that subset might affect interpretation.
The pattern across outcomes underscores that different antibody measures answer different questions. The primary varicella threshold comparisons have positive contrasts, while the posted measles and mumps threshold comparisons do not show a similarly clear separation in their unadjusted summaries. This does not create a contradiction: outcomes have different thresholds, biological targets, and statistical behavior. It does show why the endpoint and its population must be stated precisely.
Finally, this record is a useful example of the difference between statistical evidence and broader clinical meaning. An interval and p-value can describe uncertainty around an antibody-response contrast, but they cannot supply unreported information about clinical protection, durability, multiplicity, or missing data. Keeping those distinctions explicit makes the registry results more useful and less prone to overinterpretation.
18. 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.
Several limitations are specific to the information available for this study. The primary endpoint concerns a threshold antibody response measured 6 weeks postvaccination, so it does not describe later persistence or clinical disease outcomes. The record does not report a clinical correlate for the threshold or explain how it should be interpreted beyond the laboratory measurement.
The primary analysis is per protocol and requires baseline varicella seronegativity, appropriately timed blood samples, and following protocol procedures. The registry record does not provide participant flow by arm or explain all differences between the endpoint denominators and the stated enrollment. Without those details, the effect of exclusions and missing samples cannot be assessed.
The trial compares different ProQuad doses and injection-specific outcome groups, but the registry record does not provide enough detail to reconstruct the relation between every outcome group and the original allocation. The original sample-size rationale, allocation procedure, and full statistical analysis plan are not reported. Nor is a multiplicity strategy given, despite multiple groups and secondary outcomes.
Only a subset of the listed secondary outcomes has numerical arm and comparison summaries in the outcome details. Geometric mean titer results and complete results for the listed serious vaccine-related clinical adverse experience outcome are not reported in the registry record. Safety counts are descriptive and do not establish causation. These gaps constrain conclusions about consistency across all outcomes and about the full safety profile.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: ProQuad Dose Selection Study (V221-011)(COMPLETED) — NCT00986232.
- Registry record last updated 2015-04-10; status last verified 2015-03.
- Results first posted 2010-02-15.
- 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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22. Record Summary
NCT00986232 is a completed Phase 2 randomized, double-masked, parallel-group study of three ProQuad doses compared with concomitant M-M-R II and PUVV. The registry record states enrollment of 1551, a start date of 1999-04, and primary completion of 2000-04.
The primary outcome is the number of per-protocol participants meeting a varicella gpELISA antibody threshold at 6 weeks postvaccination. Posted primary comparisons show positive unadjusted risk differences relative to the ProQuad low-dose-after-one-injection group. Secondary outcomes include additional antibody measures and serious vaccine-related clinical adverse experiences, but complete numerical results are not reported for all listed outcomes.
The record does not report the original statistical plan, multiplicity handling, detailed missing-data methods, or full participant flow. The findings therefore describe the posted antibody response summaries and should not be extended to clinical protection, durability, or comparative safety.