Study Using Xolair in Rush Multi Oral Immunotherapy in Multi Food Allergic Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study Using Xolair in Rush Multi Oral Immunotherapy in Multi Food Allergic Patients (NCT02643862), a randomized phase 1, phase 2 study. The primary outcome is Desensitization Measured by Proportion of Food Allergic (FA) Participants Who Pass a DBPCFC to 2,000 mg Protein for Each of 2 Allergens at Week 36.

2. Clinical Question

3. Trial Design

This was a randomized, double-blind, parallel-group pilot study at a single center, listed in Phase 1 and Phase 2. The registry identifies Stanford University as the sponsor and records the study as completed. The start date is 2015-03-18 and the primary completion date is 2016-08-20.

The randomized comparison assigned participants to Xolair or matching placebo, with a stated 3:1 ratio. The registry describes 36 participants receiving Xolair and 12 receiving placebo. Both randomized groups received oral immunotherapy for their specific food allergies. The summary describes Xolair or placebo administration over 16 weeks and limits the oral immunotherapy allergens to up to 5 in the relevant investigational application.

A further 12 controls are described as receiving neither oral immunotherapy nor Xolair. The summary explicitly says those controls were not randomized. Consequently, they are distinct from the placebo arm and are not the comparator used for the posted primary comparison. The registry enrollment field states 48, while the summary describes 48 randomized participants as well as 12 nonrandomized controls. How those enrollment descriptions are reconciled is not reported in the registry record.

The primary endpoint was assessed at week 36 and concerned passing a double-blind, placebo-controlled food challenge to 2,000 mg protein for each of 2 allergens. One secondary outcome is listed, assessing passing a challenge to 4,000 mg for each of 2 allergens at week 36. The registry lists 2 outcome measures but no posted analyses. Further details of allocation concealment, the precise randomization procedure, and the statistical analysis plan are not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: this is an ITT population

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 Desensitization Measured by Proportion of Food Allergic (FA) Participants Who Pass a DBPCFC to 2,000 mg Protein for Each of 2 Allergens at Week 36, measured over 36 weeks.

The primary endpoint is the number and proportion of food-allergic participants who passed a double-blind, placebo-controlled food challenge (DBPCFC) to 2,000 mg protein for each of 2 allergens at week 36. The registry identifies the endpoint population as intention-to-treat. The posted results are 30/36 (83.3%) for Xolair and 4/12 (33.3%) for placebo.

This is a binary endpoint: each participant is counted according to whether the specified challenge criterion was passed. Using a common challenge criterion and assessment time makes it possible to describe the randomized groups on the same outcome. A food challenge is the operational measure used in this trial to assess desensitization; the endpoint is therefore tied to the challenge dose, the allergens evaluated, and the week-36 assessment. It does not directly express a continuous level of response, nor does it describe outcomes at other doses or times.

The registry also lists a secondary outcome at a higher challenge dose, but that is a separate measure and should not be substituted for the primary endpoint. Details such as how participants with an unavailable challenge result were handled are not reported in the registry record. The posted counts are the central evidence for interpreting the primary endpoint; the outcome definition alone does not establish whether the observed group difference was caused by the intervention.

7. Results Posted in the Registry

• Xolair: 83.3% (30/36) versus 33.3% (4/12) on control; risk difference 50.0 percentage points (95% CI 20.7 to 79.3), risk ratio 2.50 (1.11–5.64); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a binary endpoint count?

For this primary outcome, each participant contributes to one of two categories: passing or not passing the specified challenge. The registry reports the number passing and the group denominator. The proportion is a compact description of how common a pass result was in each randomized arm. It does not capture gradations among participants who did not pass, nor does it measure response outside the challenge conditions specified by the endpoint.

Comparing proportions can be expressed on several scales. The risk difference is the contrast between the two proportions, expressed on the probability scale. Here the reported risk difference is 0.5. A value of zero would represent no difference in the proportions under that measure. The relative risk compares the proportions as a ratio and is reported as 2.5. The odds ratio compares odds rather than proportions and is reported as 10.0. Because these measures use different scales, a large odds ratio should not be read as the same quantity as a large difference in percentage points. The risk difference often gives a direct description of absolute separation, while ratio measures describe relative separation.

What does the p-value address?

The registry gives an unadjusted p-value of <0.001 for the primary comparison. In general, a p-value describes how incompatible the observed data, or data more extreme, would be with a specified null model, if that model and its assumptions were true. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The specific test, its assumptions, and any covariate adjustments are not reported in the registry record, so the p-value cannot be fully reconstructed from the posted information alone.

The word unadjusted matters because it signals that the reported value is not presented as a multiplicity-adjusted result. If several outcomes or comparisons are examined, the chance of at least one small p-value can increase. The registry lists a primary outcome and a secondary outcome, but does not report a multiplicity procedure or a complete analysis plan. Therefore, the p-value should be read as the unadjusted value reported for this comparison, not as an all-purpose statement covering every possible analysis.

How should confidence intervals be understood?

A confidence interval gives a range of values reasonably compatible with the data under the statistical procedure used. In repeated use of the same procedure under its assumptions, intervals constructed in this way would cover the fixed parameter at the stated rate. For the risk difference, the reported interval is 0.207 to 0.793. The interval communicates both the direction and the uncertainty of the estimate: it lies above zero, yet includes a range of possible magnitudes. It is not a prediction interval for individual participants and does not account automatically for biases or design features omitted from the analysis.

Different measures have different reference values. For a risk difference, zero represents no difference. For a relative risk or odds ratio, one represents no relative contrast. The reported interval for the relative risk is 1.108 to 5.639, and that for the odds ratio is 2.262 to 44.2. All are estimates from the posted comparison, and their width reflects uncertainty under the methods used. The registry does not identify the interval-construction procedure.

Why does the trial design affect interpretation?

Random assignment is intended to make the randomized groups comparable on average at baseline, while blinding and a matching placebo can reduce some influences of knowing treatment assignment. These are general features of trial design; the registry record identifies randomization and double masking, but does not report all implementation details. The comparison is between the Xolair and placebo arms, with oral immunotherapy described for both. It is not a comparison of Xolair plus oral immunotherapy against no oral immunotherapy.

The 12 separate controls were not randomized and received neither oral immunotherapy nor Xolair. Their presence does not alter the two-arm randomized comparison reported for the primary endpoint. Combining them with the randomized placebo arm would answer a different question and would not preserve the stated comparison.

What does the intention-to-treat description establish?

The primary outcome description identifies an intention-to-treat population. In general, an intention-to-treat approach analyzes participants according to randomized assignment, which helps preserve the comparability created by randomization. The registry does not report the operational details of this analysis, including how unavailable outcomes, protocol deviations, or withdrawals were handled. Thus the population label should not be taken as evidence that every randomized participant had an observed endpoint or that a particular missing-data method was used.

The registry records no posted analysis count. It also does not report a detailed statistical analysis plan, interim analyses, model specifications, or the original trial sample-size justification. These absences limit the ability to verify analytic choices and to determine whether the reported comparison was prespecified in precisely the form presented. General statistical interpretation can explain the measures, but cannot fill in those unreported design and analysis details.

10. Confidence Intervals and Precision

The main absolute-effect estimate is a risk difference of 0.5, with a 95% confidence interval from 0.207 to 0.793. The interval lies above zero, so the estimated direction of the difference is positive under the reported analysis. Its breadth also shows meaningful uncertainty about the size of the contrast. A single point estimate should not be read as if it were known exactly.

The ratio estimates show uncertainty as well. The relative risk is 2.5, with a 95% confidence interval from 1.108 to 5.639. The odds ratio is 10.0, with a 95% confidence interval from 2.262 to 44.2. Each interval remains on the side of its no-contrast value, but spans a range of magnitudes. These intervals refer to different effect measures and should be interpreted on their respective scales.

Precision depends in part on the amount of outcome information in the groups. The placebo arm has 12 participants, compared with 36 in the Xolair arm. Smaller groups generally yield less precise estimates, particularly when the outcome is binary, because the estimate depends on a limited number of pass and non-pass outcomes. The interval reflects sampling uncertainty under its calculation method, not uncertainty from every possible source. It does not account automatically for missing outcomes, measurement limitations, selective reporting, or departures from the analysis assumptions.

The interval-construction method and treatment of missing observations are not reported in the registry record. The confidence intervals therefore communicate the reported statistical precision, not a complete assessment of the reliability or generalizability of the result.

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 participants or total events. They illustrate sample sizes under stated assumptions using the observed effect as a reference point. The assumed significance level is two-sided 0.05, allocation is equal between the two arms, and the calculation uses a normal approximation. The effect to detect is set to a stated fraction of the observed effect. The registry's own original design assumptions and sample-size justification are not reported in the registry record.

For planning at 100% of the observed effect, the figures are 15 participants per arm for 80% power and 19 participants per arm for 90% power. At 75% of the observed effect, they are 27 per arm for 80% power and 36 per arm for 90% power. At 50% of the observed effect, they are 62 per arm for 80% power and 82 per arm for 90% power.

Power is the probability, under a specified assumed effect and statistical model, of rejecting the null hypothesis at the stated significance level. The 80% and 90% columns therefore describe planning targets under those assumptions: the higher target requires more participants for the same assumed effect. The displayed values are illustrations based on the observed effect, not observed power for this completed trial. Smaller effects require more participants to detect with a given power target, as the figures for the smaller fractions illustrate.

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 = 0.333; treatment proportion p₁ = 0.833; average p̄ = 0.583.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6972 = 1.3665.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6009 = 0.5058.
4. n = (1.3665 + 0.5058)² / (0.5000)² = 14.0, rounded up to 15 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 <- 0.333333333333333                          # control proportion
p1 <- 0.833333333333333                          # 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(2643862)
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 = 15 (80% power), 19 (90% power)
 75% of observed effect: n per arm = 27 (80% power), 36 (90% power)
 50% of observed effect: n per arm = 62 (80% power), 82 (90% power)
power.prop.test: 14 
Simulated power at n = 15 per arm: 0.827 (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 primary outcome and one secondary outcome. The primary measure concerns passing a challenge to 2,000 mg protein for each of 2 allergens at week 36; the secondary measure concerns a challenge to 4,000 mg for each of 2 allergens at week 36. The registry reports no posted analyses. It does not describe a multiplicity adjustment, a hierarchy for testing outcomes, or how any comparisons beyond the primary one were intended to be interpreted.

Multiplicity is the issue that arises when several hypotheses, outcomes, time points, or subgroups are tested. Even when each test uses a conventional threshold, conducting multiple tests can increase the chance of at least one apparently unusual result by chance. This is a general statistical consideration, not evidence that a particular adjustment was or was not used in an analysis. The primary p-value is labeled unadjusted, and the registry record does not report a correction procedure.

The primary endpoint description identifies an intention-to-treat population. In general, this means participants are analyzed according to the groups to which they were randomized. The record does not say whether every randomized participant had a measured week-36 challenge outcome, how missing endpoint data were treated, or whether any participants were excluded from the reported counts. It also does not report the number of missing outcomes or reasons for missingness. No missing-data method should therefore be inferred from the intention-to-treat label alone.

Details of analysis populations for the secondary outcome are not reported in the registry record. Likewise, the statistical analysis plan, prespecified subgroup analyses, interim analyses, and rules for handling protocol deviations are not reported. These omissions limit assessment of whether the posted analysis followed a prespecified plan and how robust conclusions would be across alternative analytic choices.

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 0% reporting threshold.

Most frequent non-serious adverse event terms

The posted serious adverse event figures show 0 serious adverse events among 36 participants at risk in the Xolair group and 0 among 12 participants at risk in the placebo group. Deaths are recorded as 0 in each group. These figures describe the counts in the registry record; they do not establish that no serious events could occur or provide a precise estimate of rare risks.

For other adverse events, the registry records 33 participants affected among 36 at risk in the Xolair arm and 12 among 12 at risk in the placebo arm. The categories are labeled “other” adverse events in the record. They should not be assumed to indicate a particular severity level, relationship to treatment, or clinical consequence. Those details are not reported in the registry record.

Adverse-event counts are interpreted in relation to the number at risk and the period of observation, but the registry figures do not provide event-level descriptions, timing, duration, or attribution. The absence of a serious-event count in these groups is not proof of absence of risk. These safety figures are descriptive and should be read separately from the efficacy endpoint.

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

The primary result describes a higher observed proportion passing the specified challenge in the Xolair arm than in the placebo arm at week 36: 30/36 (83.3%) compared with 4/12 (33.3%). The reported risk difference is 0.5, with a 95% confidence interval from 0.207 to 0.793, and the unadjusted p-value is <0.001. This is evidence of a difference in the posted randomized-arm outcome under the analysis represented by those statistics.

The result applies to the defined challenge: 2,000 mg protein for each of 2 allergens, assessed at week 36. It does not indicate how participants would perform at every dose, with every food allergen, or at other times. The separately listed secondary outcome uses a different challenge dose and should be regarded as a distinct endpoint. The result also does not establish whether the observed performance persisted after the assessment point.

Both randomized groups received oral immunotherapy, according to the trial summary. Thus, the comparison is Xolair plus oral immunotherapy versus placebo plus oral immunotherapy, not Xolair versus no treatment or oral immunotherapy versus no oral immunotherapy. The separate 12 controls received neither oral immunotherapy nor Xolair and were not randomized. They are not the comparator for the posted primary estimate.

The confidence interval indicates uncertainty about the magnitude of the group contrast, and the placebo group is comparatively small. The registry record does not report missing-data handling, detailed analysis methods, multiplicity adjustment, or a complete statistical plan. These gaps limit how fully the result can be independently assessed. The counts should not be interpreted as a guarantee of an individual participant's outcome, as proof of lasting benefit, or as evidence beyond the population and endpoint studied.

16. Why This Trial Matters Statistically

This trial illustrates why the structure of a comparison matters. The randomized, double-blind, placebo-controlled arms provide a direct contrast between Xolair and placebo while both groups receive oral immunotherapy. Separating that contrast from the nonrandomized controls is essential: the controls received neither intervention and answer a different descriptive question.

The endpoint also shows how a binary outcome can communicate an intuitively clear event while leaving important detail outside the measure. Passing a specified challenge at week 36 is straightforward to count, and the result can be expressed as a difference in proportions or as a ratio. But the conclusion remains bound to the specified protein dose, the 2 allergens, and the assessment time. Those details define the claim that the statistics support.

The reported risk difference and its interval make both the direction and uncertainty visible. The point estimate is distinct from its precision, and the ratio measures use different scales. A small p-value does not replace an effect estimate or confidence interval, nor does it answer questions about the clinical meaning, persistence, or generalizability of the endpoint.

Finally, the registry record is a reminder that summary results may not include all details needed to reproduce or audit an analysis. The endpoint is identified as intention-to-treat, but missing-data procedures and the statistical plan are not reported. The sample-size figures are planning illustrations based on the observed effect rather than the trial's original design rationale. Keeping these distinctions clear prevents planning calculations, analysis assumptions, and posted outcome counts from being mistaken for one another.

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.

This was a pilot study, and the randomized placebo arm included 12 participants. The limited group size means the reported estimates have appreciable uncertainty, as reflected in the confidence intervals. The study was described as single-center, which may constrain how readily its findings can be generalized to other settings or populations.

The registry enrollment field states 48, while the brief summary describes 48 participants randomized to the two arms plus 12 controls outside the randomization. The record does not reconcile those enrollment descriptions. The primary randomized comparison itself is reported with 36 participants in the Xolair arm and 12 in the placebo arm.

The posted primary outcome is tied to passing a challenge at week 36, at a specified protein dose for each of 2 allergens. It does not supply evidence about other challenge doses, longer-term outcomes, or results for every allergen. The listed secondary outcome has a different challenge dose, and its result is not included in the registry entries available for this analysis.

The registry does not report the detailed statistical analysis plan, the exact test underlying the unadjusted p-value, missing-data handling, or multiplicity procedures. The primary population is labeled intention-to-treat, but that label does not clarify how unavailable outcomes were handled. The record also provides no posted analysis count. These limitations make it difficult to assess the full analysis process or determine the influence of incomplete data and alternative analytic decisions.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Study Using Xolair in Rush Multi Oral Immunotherapy in Multi Food Allergic Patients — NCT02643862.
• Registry record last updated 2018-01-12; status last verified 2017-12.
• Results first posted 2017-10-25.
• 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

NCT02643862 is a completed randomized, double-blind, parallel-group pilot study listed in Phase 1 and Phase 2 and sponsored by Stanford University. The registry describes 36 participants receiving Xolair and 12 receiving placebo, with oral immunotherapy in both randomized arms; 12 additional controls are described as nonrandomized and receiving neither treatment.

The primary outcome is passing a double-blind, placebo-controlled food challenge to 2,000 mg protein for each of 2 allergens at week 36. The posted counts are 30/36 (83.3%) for Xolair and 4/12 (33.3%) for placebo. The reported risk difference is 0.5 (95% confidence interval 0.207 to 0.793), with unadjusted p < 0.001. The registry lists one secondary outcome and reports no posted analyses. Detailed missing-data and multiplicity methods are not reported in the registry record.