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Celiac Disease NA Continuous Endpoint NCT00931892

Serum Markers in Gluten Challenge: Complete Statistical Analysis

This analysis examines a randomized, unmasked gluten-challenge pilot study in people with celiac disease in remission. It focuses on changes in duodenal biopsy crypt depth to villous height ratio and on what the posted results can establish statistically.

Trial start: 2009-04  ·  Enrollment: 21  ·  Sponsor: Beth Israel Deaconess Medical Center
Scope of this record

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 Serum Markers in Gluten Challenge (NCT00931892), a randomized na study. The primary outcome is Crypt Depth to Villous Height Ratio.

21
Enrollment
NA
6
Arms
In the primary outcome
2.28
Mean difference
Baseline (Day -14) High Gluten Group
-1.90–6.46
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00931892
PhaseNA
ConditionCeliac Disease
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment21
Arms in the primary outcome6
Lead sponsorBeth Israel Deaconess Medical Center
Results postedYes

2. Clinical Question

Population

Participants had biopsy-proven celiac disease and were in remission while following a gluten-free diet. The registry record reports 21 enrolled participants. The primary-outcome description notes that 17 had evaluable pathology biopsies on Day 3 and 19 had evaluable pathology biopsies on Day 14.

Intervention

Participants were assigned to a gluten challenge. The low-gluten group was to consume 3g of gluten per day; the high-gluten group was to consume 10g of gluten per day.

Comparator

The two randomized parallel groups received different daily gluten amounts. The primary outcome summaries also report baseline measurements for each group, allowing the posted results to describe values at baseline and after challenge.

Primary question

The study aimed to evaluate non-invasive markers of celiac disease activity during gluten challenge. Its posted primary outcome was crypt depth to villous height ratio in duodenal biopsy samples, measured at screening, Day 3, and Day 14. The record also lists secondary aims concerning disease mechanisms and metabolic changes with gluten exposure.

The clinical question is exploratory: whether measures of intestinal histology and other markers change during a short gluten challenge, and whether the observed patterns differ between the two dose groups. The registry record identifies this as a pilot study. It does not report a prespecified hypothesis about a particular between-group difference, a target effect size, or the original statistical decision criteria. The outcome summaries should therefore be read as descriptive and exploratory, rather than as a definitive test of a treatment strategy.

3. Trial Design

This was a randomized, unmasked, parallel-group study, listed as completed, with 21 participants enrolled. The registry record gives a start of 2009-04 and primary completion of 2011-08. It describes two dietary-supplement arms: a low-gluten group assigned 3g per day and a high-gluten group assigned 10g per day. The record does not report the randomization procedure, allocation concealment, or whether any additional procedures were used to reduce bias.

Participants were described as having biopsy-proven celiac disease, being in remission, and following a gluten-free diet before gluten challenge. The primary outcome was measured at screening (Day -7 to -14), Day 3, and Day 14. The arm summaries list baseline as Day -14, followed by Day 3 and Day 14. For the primary outcome, the recorded group counts are 10 in each group at baseline, 8 in the low-gluten group and 9 in the high-gluten group on Day 3, and 10 and 9 respectively on Day 14. The record specifically states that 17 participants had evaluable pathology biopsies on Day 3 and 19 on Day 14.

The registry lists eight outcome measures and 14 analyses. It names several secondary outcomes, including intraepithelial lymphocyte counts, intestinal permeability, immune activation, protein expression in intestinal biopsies, and symptom questionnaires. Not all of these outcomes have posted numerical summaries in the record used for this analysis. The original protocol’s planned sample size, analysis populations, missing-data procedures, and complete statistical analysis plan are not reported in the registry record. The reported design details therefore support describing the randomized comparison and the collected measurements, but not reconstructing every intended analytic decision.

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.

Before assignment: 21 patients were enrolled in the study. 1 patient was found to be negative for DQ2 and DQ8, therefore did not have Celiac disease. This patient was excluded from the study. Therefore, for the study we had a total of 20 participants.

Completed Gluten Challenge

StageLow Gluten GroupHigh Gluten Group
STARTED1010
COMPLETED1010
NOT COMPLETED00

Completed Endoscopies

StageLow Gluten GroupHigh Gluten Group
STARTED1010
First Endoscopy1010
Second Endoscopy1010
Third Endoscopy109
COMPLETED109
NOT COMPLETED01

Reasons for not completing this period:

ReasonLow Gluten GroupHigh Gluten Group
Patient did not complete third endoscopy due to discomfort01

Analysis population for the primary outcome, as defined in the registry: Subjects with biopsy proven celiac disease in remission were enrolled. For Day 3, 17 subjects had evaluable pathology biopsies. On Day 14, 19 participants had evaluable pathology biopsies.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: Subjects with biopsy proven coelic dieasese in remission were enrolled.

CharacteristicUnitLow Gluten GroupHigh Gluten GroupTotal
Participants analysed101020
Age, Categorical: <=18 yearsParticipants000
Age, Categorical: Between 18 and 65 yearsParticipants101020
Age, Categorical: >=65 yearsParticipants000
Age, Continuousyears48.8 (SD 13.0)38.8 (SD 13.1)43.3 (SD 13.7)
Sex: Female, Male: FemaleParticipants10919
Sex: Female, Male: MaleParticipants011
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants000
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants101020
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants000
Race (NIH/OMB): American Indian or Alaska NativeParticipants000
Race (NIH/OMB): AsianParticipants101
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants000
Race (NIH/OMB): WhiteParticipants91019
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants000
Region of Enrollment: United Statesparticipants101020
Age at Celiac Diagnosisyears45.4 (SD 13.9)31.0 (SD 11.7)35.7 (SD 14.4)
Months since Celiac Disease diagnosismonths42.3 (SD 21.3)92.5 (SD 49.1)62.3 (SD 87.1)
Laboratory Characteristics: HLA DQ2Participants4610
Laboratory Characteristics: HLA DQ8Participants336
Laboratory Characteristics: HLA DQ2 + DQ 8Participants112
Laboratory Characteristics: HLA A1 * 05 aloneParticipants202
Villous height to crypt depth ratiounitless2.05 (SD 0.80)4.33 (SD 6.69)2.21 (SD 0.8)
Mean number of Intraepithelial lymphocytesunitless37.10 (SD 13.66)28.4 (SD 13.3)32.59 (SD 15.1)
Baseline tissue transglutaminase (tTG)units13.76 (SD 8.30)8.27 (SD 5.70)11.00 (SD 7.50)
Baseline Deamidated gliadin peptide (DGP)units6.70 (SD 2.59)14.04 (SD 26.49)10.90 (SD 19.60)
Baseline Celiac Dietary Adherence test (CDAT)scores on a scale11.33 (SD 3.2)11.40 (SD 2.9)11.37 (SD 2.9)

6. Primary Endpoint

The registry lists the primary outcome as Crypt Depth to Villous Height Ratio, measured over Screening (Day -7 to -14), Day 3, Day 14.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitratio
Endpoint classificationContinuous Endpoint

The primary endpoint is the crypt depth to villous height ratio, a continuous measure derived from duodenal biopsy histology. The registry description says that biopsy fragments were evaluated by measuring the height of adjacent villi and the depth of proliferative crypt zones. It also describes the Vh:Cd ratio, the average of individual biopsy ratios for an endoscopy, and says that a normal Vh:Cd ratio was regarded as 3:1 or greater. Because the endpoint title calls the measure crypt depth to villous height ratio while the methods description refers to villous height to crypt depth, readers should note that the endpoint label and the descriptive notation are not expressed in the same order.

Histology is used to characterize intestinal tissue structure, so a biopsy-based measure can offer information distinct from symptoms or circulating markers. The study measured the endpoint at screening and during the gluten challenge, allowing the record to describe group means at the listed time points. The record reports means and standard deviations, rather than individual observations or a model-based estimate of change over time. It also notes that evaluations were considered discrepant when Vh:Cd differed by more than 0.5 and reports excellent concordance for the 165 biopsy fragments deemed optimal for evaluation. This describes the assessment process, but does not itself establish the precision of the group comparisons.

7. Results Posted in the Registry

Mean difference: Baseline (Day -14) High Gluten Group

2.28

95% CI: -1.90 to 6.46

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-0.61.33.35.37.39.3Baseline (Day -14) Low Gluten… (n=10)Baseline (Day -14) High Glute… (n=10)Day 3 Low Gluten Group (n=8)Day 3 High Gluten Group (n=9)Day 14 Low Gluten Group (n=10)Day 14 High Gluten Group (n=9)ratio (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Baseline (Day -14) High Glute…Day 14 Low Gluten Group-2.56-0.631.313.255.197.12mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Count of Intraepithelial Lymphocytes Per 100 Enterocytes in Duodenal Biopsy SamplesContinuous EndpointMean difference-8.17 (-21.12 to 4.78)52 per arm
Symptomatic Response to Gluten Exposure Determined by Celiac Symptom Index QuestionnaireContinuous EndpointMean difference-0.06 (-5.42 to 5.30)163,262 per arm
Symptomatic Response to Gluten Exposure Determined by Gastrointestinal Symptom Rating ScaleContinuous EndpointMean difference8.59 (0.16 to 17.02)20 per arm

Count of Intraepithelial Lymphocytes Per 100 Enterocytes in Duodenal Biopsy Samples

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Baseline (Day -14) High Glute…Day 14 Low Gluten Dose Group-25-14-4.136.141627mean difference vs control (95% CI)

Symptomatic Response to Gluten Exposure Determined by Celiac Symptom Index Questionnaire

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Day 0 Low Gluten Dose GroupDay 0 High Gluten Dose Group-12-7.98-4.34-0.712.926.56mean difference vs control (95% CI)

Symptomatic Response to Gluten Exposure Determined by Gastrointestinal Symptom Rating Scale

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Day 3 Low Gluten Dose GroupDay 3 High Gluten Dose Group-6.16-1.183.808.781419mean difference vs control (95% CI)

The secondary outcomes cover several types of measurement: biopsy-based cell counts and protein assessments, intestinal permeability, immune activation, and symptom scores. The posted numerical summaries show that observed values and group patterns vary by outcome and measurement time. Across these domains, the results do not form a single uniform pattern that independently confirms the primary histology result. Some summaries describe differences between groups or time points, while others are less distinct; the registry record does not provide complete numerical results for every listed secondary outcome.

Secondary outcomes can help characterize a pilot study by showing which measures were collected and how their observed values behaved during the challenge. They may also help identify endpoints for later research. They should not be treated as independent confirmation of the primary result, particularly when many outcomes and time points are examined and the record does not report a multiplicity strategy.

The posted secondary comparisons are unadjusted. When many statistical tests are conducted, the chance of observing at least one apparently unusual result by chance can increase. Without a reported plan identifying a primary comparison hierarchy or controlling multiplicity, isolated secondary p-values carry less weight than a prespecified primary analysis. The registry record does not report whether any secondary findings were confirmatory, how they were selected for reporting, or how the full set of analyses was interpreted by the investigators.

Accordingly, the secondary findings are best read as exploratory context around the primary endpoint, not as evidence that resolves its uncertainty. They broaden the description of measured biological and symptom outcomes, but do not remove the limitations arising from small group counts, missing observations, and incomplete analytic detail.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

The posted primary-outcome means vary across time and between the randomized groups, but the summaries are based on small numbers of evaluable biopsies and substantial variability is evident in some groups. At baseline, the low-gluten group mean was 2.05 (standard deviation 0.8) and the high-gluten group mean was 4.33 (standard deviation 6.69). At Day 3, the corresponding means were 1.19 (0.67) and 2.02 (0.99). At Day 14, they were 0.98 (0.85) and 1.26 (1.08). These summaries describe the observed data; they do not by themselves establish a causal effect or a reliable dose-response pattern.

The posted sponsor analysis reports a two-sided t-test with p = 0.670 across the six primary-outcome group summaries. Its reported analysis does not include an estimate or confidence interval. The separate recalculated comparisons are simple, unadjusted comparisons based on posted summary statistics. For the baseline high-gluten group compared with baseline low-gluten group, the recalculated mean difference is 2.28, with a 95% confidence interval from -1.896 to 6.456 and an unadjusted p-value of 0.285. For the Day 14 low-gluten group compared with baseline low-gluten group, the recalculated mean difference is -1.07, with a 95% confidence interval from -1.793 to -0.346 and an unadjusted p-value of 0.004.

Those recalculations should not be treated as equivalent to the sponsor’s analysis. The comparisons use a different contrast and do not account for the longitudinal structure or any adjustment that may have been used in the sponsor analysis. Because the registry record flags a discrepancy, the sponsor’s own analysis takes precedence when describing the sponsor-reported result. The recalculated contrasts are useful as transparent, unadjusted descriptions of selected group means, but they do not replace the reported analysis.

The Day 14 comparison of a follow-up low-gluten group mean with a baseline low-gluten group mean is also not the randomized between-group comparison at Day 14. It compares measurements from different time points and should not be interpreted as an isolated causal effect of gluten dose. A direct randomized comparison at the same follow-up time is not included in the recalculated comparisons listed for the primary endpoint. The registry record does not report enough detail to establish how the reported p-value was derived or how time and repeated observations were handled.

Overall, the record offers descriptive evidence about observed histology values during the challenge, along with a sponsor-reported non-significant omnibus result. The small group counts, missing evaluable biopsies at some time points, wide variation, and difference between the reported and recalculated analyses limit the strength of any conclusion about the pattern or magnitude of change.

10. Statistical Methods Explained

The registry reports a continuous primary outcome summarized by mean and standard deviation. A mean describes the arithmetic center of the observations, while a standard deviation describes how dispersed individual values are around that center. Neither statistic shows the full shape of the data. In a small pilot study, a few unusually high or low observations can influence a mean and its uncertainty, particularly when variability differs greatly between groups.

What does a mean difference represent?

A mean difference is the mean in one group minus the mean in a reference group, following the contrast’s stated direction. Positive and negative values indicate opposite directions of difference, but their practical meaning depends on how the endpoint is defined and which group is subtracted from which. The recalculated primary comparisons use baseline low-gluten participants as the reference: one compares baseline high-gluten with baseline low-gluten, and another compares Day 14 low-gluten with baseline low-gluten. These are not the same contrast, and the latter combines a change in time with a difference in group summary.

The recalculations are unadjusted calculations from posted summary statistics. They use group means, standard deviations, and counts to estimate a simple difference and its uncertainty. They do not represent a reconstruction of the sponsor’s statistical model. In particular, the record does not report whether the sponsor used an analysis that accounted for repeated measurements, baseline values, or other factors. Repeated observations from the same participant are generally related rather than independent; an analysis that models that relationship can answer a different question from a comparison treating summary groups independently.

How should a p-value be read?

A p-value describes how compatible the observed data are with a specified statistical model and a null hypothesis, assuming the model and hypothesis apply. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect. A small unadjusted p-value does not automatically mean that a result is robust, especially when many endpoints, time points, or comparisons are examined. A larger p-value does not prove that groups are identical; it may also reflect imprecision or limited information.

The sponsor’s primary result is reported as a two-sided t-test with p = 0.670 across six group summaries. The registry gives no estimate or confidence interval for that analysis. The recalculated pairwise p-values address selected comparisons rather than the same overall test, so the values should not be read as conflicting answers to an identical question. The discrepancy flag further indicates that the sponsor-reported analysis takes precedence over the simple recalculation.

What do confidence intervals add?

A confidence interval expresses uncertainty around an estimated effect under the method’s assumptions. Its width reflects both the observed variability and the amount of information. An interval spanning values on either side of zero is compatible with a range of possible differences, including no difference, under the stated comparison. An interval that does not span zero indicates that the corresponding unadjusted test would be statistically distinguishable from zero under the same assumptions, but it does not resolve bias, multiplicity, missingness, or clinical relevance.

The primary recalculated intervals are based on the selected unadjusted contrasts, not on the sponsor’s overall reported test. Their interpretation is therefore conditional on the simple comparison used. The record does not report an adjusted interval for the sponsor’s analysis or its confidence level.

Why does over-dispersion matter?

In general, over-dispersion means observed variation exceeds what a statistical model expects. Greater variation reduces the precision of estimates and can make a given mean difference harder to distinguish from random variation. The primary baseline high-gluten group has a standard deviation of 6.69, compared with 0.8 for the baseline low-gluten group, illustrating markedly different observed spreads in those summaries. A pooled-variance calculation assumes a common underlying variance for the compared groups; that assumption may be questionable when the observed spreads differ substantially. The recalculated comparisons should therefore be viewed as simple illustrations, not as a substitute for a prespecified analysis suited to the data.

Finally, the registry record does not report the original statistical analysis plan, missing-data method, treatment of multiple testing, or whether analyses were based on intention-to-treat or evaluable participants. Without those details, the reported statistics can be described, but their full analytic context cannot be confirmed.

11. Confidence Intervals and Precision

The recalculated confidence intervals show how uncertain the selected mean differences are under the simple unadjusted comparison. For baseline high-gluten versus baseline low-gluten, the estimated mean difference is 2.28 and the interval extends from -1.896 to 6.456. The interval is broad and includes zero, so the summary statistics are compatible with a range of possible differences, including no difference, under this calculation.

For Day 14 low-gluten versus baseline low-gluten, the recalculated mean difference is -1.07, with an interval from -1.793 to -0.346. That interval does not include zero under the unadjusted calculation. It nevertheless compares different time points, and does not isolate the randomized contrast between gluten-dose groups at the same follow-up visit. The interval cannot correct for a mismatch between the comparison and the question of interest.

Confidence intervals are not guarantees that the true effect lies within their limits, and their coverage depends on the statistical method and assumptions. Here, the estimates are based on small group counts, and standard deviations vary considerably between some groups. The primary outcome description also reports fewer evaluable biopsies on Day 3 than at baseline, with a different count again on Day 14. These factors limit precision and may affect how representative the analyzed observations are.

The sponsor’s reported primary analysis provides p = 0.670 but no estimate or confidence interval in the registry record. Its precision and the range of effects compatible with that analysis therefore cannot be evaluated from the reported result alone. The recalculated intervals add uncertainty estimates for selected contrasts, but they are not intervals from the sponsor’s own analysis and should not be presented as such.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect6992
75% of the observed effect122164
50% of the observed effect275368
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect501002005001,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: Baseline (Day -14) High Gluten Group.

The sample-size figures are planning illustrations based on the observed effects in selected comparisons, not the trial’s original design justification. For these continuous outcomes, the entries are participants per arm. The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect. The original trial’s own sample-size assumptions are not reported in the registry record.

The 80% power column gives the estimated participants per arm under those assumptions for a design intended to have an 80% chance of detecting the specified effect if that effect were present. The 90% power column gives the corresponding per-arm planning figure for a 90% chance. These are design targets, not guarantees, and they depend on the assumptions about variability, allocation, analysis, and the effect size being planned for.

The rows for 100%, 75%, and 50% of the observed effect illustrate how planning changes if the target effect is smaller than the observed estimate. Smaller effects need more participants to detect with the same nominal power, which is why the participant requirements increase in the smaller-effect rows. Estimates based on an observed pilot effect can be unstable, particularly when group counts are small, so they are best treated as illustrations rather than reliable forecasts.

These figures are not observed power. Observed power is not a useful substitute for interpreting the estimate, confidence interval, and data quality after a study has been conducted. The planning values do not imply that the pilot had adequate or inadequate power for its original aims, because its original sample-size justification is not reported in the registry record.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

  1. Observed difference Δ = 2.280; pooled standard deviation σ = 4.764.
  2. n = 2 × (1.96 + 0.842)2 × 4.7642 / 2.2802 = 68.5, rounded up to 69 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
delta <- 2.28                      # observed difference in means
sigma <- 4.76424705488706                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(931892)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 69 (80% power), 92 (90% power)
 75% of observed effect: n per arm = 122 (80% power), 164 (90% power)
 50% of observed effect: n per arm = 275 (80% power), 368 (90% power)
power.t.test: 69.5 
Simulated power at n = 69 per arm: 0.800 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
t-test, 2 sidednot reported0.670
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The registry reports a sponsor analysis for the primary outcome using a two-sided t-test across the six group summaries, with p = 0.670. It does not report an estimate, confidence interval, or further detail about that test. The recalculated results are different in scope: they compare selected pairs using simple unadjusted calculations from posted means, standard deviations, and counts.

For example, the recalculated baseline contrast compares the high-gluten group with the low-gluten group, whereas the other primary recalculation compares the Day 14 low-gluten summary with the baseline low-gluten summary. Neither is the same as the sponsor’s reported test across the six groups. Their p-values and intervals therefore cannot be used to overwrite or directly contradict the sponsor’s result.

The discrepancy flag means the sponsor’s own analysis takes precedence when reporting the trial’s stated analysis. The recalculations remain useful as transparent descriptions of particular differences implied by the posted summaries, but they are not a reproduction of the sponsor’s test. The registry record does not explain the discrepancy, identify the sponsor’s full statistical model, or state how repeated measurements were handled. Those omissions limit any further reconciliation.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists eight outcome measures and 14 analyses, including repeated assessments at multiple time points and several secondary measures. Testing many outcomes or contrasts creates a multiplicity concern: even when none of the underlying effects is real, some tests may appear notable by chance. A prespecified statistical plan can address this by identifying the primary comparison, defining an order of testing, or adjusting inference across tests. The registry record does not report whether such a plan or adjustment was used.

The primary sponsor result is reported across six group summaries, while the recalculated comparisons focus on selected contrasts. The record does not explain how those contrasts were selected or whether they were prespecified. The unadjusted p-values for secondary results should therefore be considered exploratory. Their apparent statistical strength should not be interpreted as if each were the sole planned test.

Missingness also matters. The primary-outcome description reports 17 participants with evaluable pathology biopsies on Day 3 and 19 on Day 14. The arm-level counts differ by time point, and some secondary outcome summaries also have counts below the group’s baseline count. The registry record does not report why observations were unavailable, whether missingness was related to symptoms or study procedures, or how missing values were handled in the sponsor’s analysis.

The record does not identify whether the analysis population was intention-to-treat, per-protocol, or based on available observations. It also does not report a method for handling repeated measures, a model specification, or whether analysis assumptions were checked. These gaps prevent a full assessment of bias from missing data or the consequences of analytic choices. They do not establish that the analysis was inappropriate; they mean that the relevant safeguards and assumptions are not reported in the registry record.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Low Gluten Group0100.0%
High Gluten Group0100.0%

Deaths

ArmDeaths (participants affected of at risk)
Low Gluten Group0 of 10
High Gluten Group0 of 10

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Low Gluten Group1 of 10
High Gluten Group0 of 10

Most frequent non-serious adverse event terms

Event termOrgan systemLow Gluten GroupHigh Gluten Group
Nausea and vomitingGastrointestinal disorders1 of 100 of 10
Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The posted serious adverse event summaries report 0 serious adverse events among 10 participants at risk in the low-gluten group and 0 among 10 participants at risk in the high-gluten group. The record also reports 0 deaths in each group. These figures describe the reported serious adverse events for the groups and period represented in the registry.

The record lists 1 other, non-serious adverse event among 10 participants at risk in the low-gluten group and 0 among 10 at risk in the high-gluten group. It does not provide serious adverse event terms, and the list of top serious terms is empty. These counts should not be taken to mean that no symptoms or other effects occurred; the registry distinguishes serious events from other adverse events, and the study also measured symptom responses as outcomes.

Small participant counts provide limited information about uncommon events. The absence of reported serious events in these summaries does not establish that the challenge is free of risk, nor does it support a broad safety conclusion. The registry record does not report additional detail about event timing, duration, severity for non-serious events, or attribution to the study intervention.

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

The registry record describes a pilot investigation of histology and other markers during gluten challenge in participants with biopsy-proven celiac disease in remission. It reports group means and standard deviations for the primary biopsy outcome, a sponsor-reported two-sided test, selected unadjusted recalculations, and several secondary outcome summaries. Together, these data provide a limited account of what was observed in this study.

The sponsor’s primary result is p = 0.670 across the six group summaries. That result does not establish that the groups or time points are equivalent; the registry provides no estimate or confidence interval for the sponsor analysis. The recalculated comparisons offer additional estimates for specific contrasts, but they are not the sponsor’s analysis and one compares different time points rather than the randomized groups at the same visit. The discrepancy flag means the sponsor’s own analysis takes precedence.

Neither a p-value nor a confidence interval alone answers whether an observed difference is clinically important. The registry record does not provide a threshold for a meaningful change in the primary ratio or an interpretation tying the observed estimates to clinical consequences. The title and descriptive methods also use different ratio orderings, which should be kept in mind when interpreting direction.

This pilot study does not, on the information in the registry record, establish the performance of a non-invasive marker, a definitive dose-response relationship, or a general conclusion about gluten challenge. Small group counts, missing evaluable biopsies, variability, multiple outcomes, and incomplete reporting of the analysis plan all constrain inference. Its results are most appropriately understood as exploratory observations that may inform further study, rather than as a stand-alone basis for clinical decisions.

18. Why This Trial Matters Statistically

This study illustrates several recurring statistical issues in small clinical studies. First, a randomized design does not by itself ensure that every reported comparison retains the advantages of randomization. The clearest randomized contrast is between assigned groups measured at the same time point; comparing a follow-up mean in one group with a baseline mean can mix time and group differences.

Second, small pilot samples can yield unstable estimates. The group means are accompanied by variable standard deviations, and the primary outcome has fewer evaluable observations at some follow-up points than at baseline. Confidence intervals help display this uncertainty, while p-values alone do not show the range of effects compatible with the data.

Third, registry reporting needs to make the analysis question clear. The sponsor reports a test across six group summaries, while the recalculations address selected contrasts. Because the record flags a discrepancy and does not supply the full analytic details, the reported sponsor analysis and the transparent recalculations must be kept distinct.

Finally, multiple endpoints and repeated time points require careful interpretation. Without a reported multiplicity plan, secondary results are appropriately treated as exploratory. This trial therefore demonstrates why design, estimand, missing observations, and analysis reporting matter alongside the numerical result. The values are informative as a pilot record, but their statistical meaning depends on knowing exactly which groups and time points are being compared.

19. Limitations

The small enrollment and the outcome-specific counts constrain precision. Although 21 participants were enrolled, the primary endpoint summaries include 10 participants per group at baseline, 8 and 9 at Day 3, and 10 and 9 at Day 14. The registry record does not explain the unavailable pathology observations or describe how their absence was handled in the sponsor analysis. If evaluability is related to participant characteristics or study experience, summaries among observed participants may not fully represent all randomized participants.

The study was unmasked. The record does not report procedures to limit the potential for assessment bias, though it describes evaluation of biopsy fragments and excellent concordance for 165 fragments considered optimal. It also does not report details of the randomization process or allocation concealment.

The primary endpoint’s title and descriptive ratio notation are not aligned: the title says crypt depth to villous height ratio, while the description specifies Vh:Cd, or villous height to crypt depth. The record’s statement that normal Vh:Cd was 3:1 or greater may be difficult to reconcile with the endpoint title without clarification. This ambiguity affects interpretation of direction and makes careful reference to the exact reported measure important.

Other limitations include the lack of a reported original sample-size justification, full statistical analysis plan, missing-data approach, analysis population, or multiplicity method. The sponsor-reported primary test has no accompanying estimate or interval. The recalculated comparisons are unadjusted and do not reproduce that test. These reporting limitations are specific obstacles to interpreting the statistical findings, not proof that procedures were absent from the study.

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23. Record Summary

NCT00931892, “Serum Markers in Gluten Challenge,” is a completed randomized, unmasked, parallel pilot study sponsored by Beth Israel Deaconess Medical Center. It enrolled 21 participants with biopsy-proven celiac disease in remission. The groups were assigned 3g or 10g of gluten per day.

The primary outcome was crypt depth to villous height ratio in duodenal biopsy samples, assessed at screening, Day 3, and Day 14. The registry reports group means and standard deviations, a sponsor two-sided t-test result of p = 0.670 across six summaries, and selected recalculated comparisons. Because a discrepancy is flagged, the sponsor’s own analysis takes precedence over those simple unadjusted recalculations.

The record also lists secondary biopsy, permeability, immune, protein-expression, and symptom outcomes, along with adverse event counts. The original sample-size justification, full analysis plan, missing-data approach, and multiplicity strategy are not reported in the registry record. The findings are therefore best read as exploratory pilot data with limited precision and incomplete analytic context.

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