Efficacy of Eluxadoline in the Treatment of Irritable Bowel Syndrome With Diarrhea in Patients With Inadequate Control of Symptoms With Prior Loperamide Use: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy of Eluxadoline in the Treatment of Irritable Bowel Syndrome With Diarrhea in Patients With Inadequate Control of Symptoms With Prior Loperamide Use (NCT02959983), a randomized phase 4 study. The primary outcome is Percentage of Participants Who Were Composite Responders Based on Improvements From Baseline in Daily Worst Abdominal Pain And Daily Stool Consistency Scores.

2. Clinical Question

3. Trial Design

This was a Phase 4, multicenter, multinational, prospective, randomized, placebo-controlled, double-blinded, parallel-group study. The registry describes masking as quadruple. The trial was sponsored by Allergan and is recorded as completed. Its listed start date is 2016-10-25, and its primary completion date is 2018-01-22. Registry enrollment is 346.

The study compared eluxadoline with matching placebo. Eluxadoline was given as 100 mg oral tablets twice daily with food for 12 weeks; the matching placebo was also taken twice daily with food for 12 weeks. The target population was patients with IBS-D who reported that loperamide use in the prior 12 months had failed to control their symptoms.

The primary outcome was the percentage of participants meeting a composite responder definition based on daily worst abdominal pain and stool consistency scores. The measurement period was Baseline, Weeks 1 to 12. The posted primary-outcome population is the Intent-to-Treat population, defined as all randomized patients. The posted arm results were 22.7% for eluxadoline and 10.3% for placebo. The registry also lists three secondary outcome measures: stool consistency responders, pain responders, and monthly composite responders.

The registry record does not report the original sample-size justification, the planned statistical analysis details beyond the posted analysis, or whether interim analyses were planned or conducted. Those design features should not be inferred from the observed enrollment or posted results.

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: A total of 660 participants were screened; 346 participants were randomized; 344 participants received at least 1 dose of study drug which comprises the safety population. Randomization and treatment assignment were based on a randomization scheme prepared by Allergan Biostatistics prior to the start of the study.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The Intent-to-Treat population includes all randomized patients.

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: The Intent-to-Treat population includes all randomized patients.

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Were Composite Responders Based on Improvements From Baseline in Daily Worst Abdominal Pain And Daily Stool Consistency Scores, measured over Baseline, Weeks 1 to 12.

The primary endpoint was the percentage of participants who met a daily composite response definition based on worst abdominal pain and stool consistency. To qualify, a participant had to meet both daily criteria on at least 50% of days with diary entry during the outcome period. The pain criterion required the worst abdominal pain score to improve by >=40% from Baseline. The stool criterion required a Bristol Stool Score below 5, or no bowel movement when accompanied by the required pain improvement.

Participants recorded worst abdominal pain over the prior 24 hours on a 0-to-10 scale, ranging from no pain to worst imaginable pain. Stool consistency was recorded using the Bristol Stool Score, which ranges from 1 for hard stool to 7 for watery stool. The composite therefore combines an abdominal-pain measure with a stool measure rather than counting improvement in either symptom alone.

A responder endpoint can make a result easier to interpret as the proportion of participants meeting a prespecified clinical pattern of improvement. It also simplifies continuous or daily measurements into a yes-or-no classification for each participant. That simplification has a trade-off: people close to a response threshold may be classified differently despite similar underlying symptom patterns. The registry record describes the composite definition, but does not report additional justification for choosing this endpoint or its thresholds.

7. Results Posted in the Registry

• Eluxadoline: 22.7% (39/172) versus 10.3% (18/174) on control; risk difference 12.3 percentage points (95% CI 4.6 to 20.1), risk ratio 2.19 (1.31–3.68); unadjusted two-proportion z-test p = 0.002.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the primary endpoint count?

The outcome is a binary percentage: each participant is classified as meeting or not meeting the composite responder definition. The registry defines response using daily worst abdominal pain and stool consistency measurements, requiring both criteria on at least 50% of days with diary entry. The pain response threshold is an improvement of >=40% compared with Baseline. The stool requirement is a Bristol Stool Score below 5, or no bowel movement when accompanied by the pain improvement.

Turning daily records into a participant-level responder outcome is one way to make a complex symptom pattern easier to summarize. The resulting percentage is interpretable as the proportion meeting the defined threshold, but it does not retain every detail from the daily records. Two participants with different symptom trajectories could receive the same responder classification, and small changes around a threshold can alter classification.

What does the chi-squared test assess?

The registry-reported analysis is a chi-squared test of superiority comparing the outcome groups. In general, a chi-squared test assesses whether the observed counts across categories differ from what would be expected if there were no association between assigned group and response status. Here, the categories are responder and non-responder, and the groups are eluxadoline and placebo.

The registry reports p = 0.002 for this analysis. A p-value is calculated under a null hypothesis and statistical model; it summarizes how incompatible the observed data are with that null model. It is not an effect-size measure and does not express the probability that the treatment is effective. The registry record does not report further details of the sponsor's analysis method, such as any covariate adjustment or handling of missing observations.

What is the unadjusted recalculation?

The simple recalculation uses posted arm-level response counts and denominators to estimate the unadjusted difference in response proportions. It gives a risk difference of 0.123 and a 95% confidence interval from 0.046 to 0.201, with p = 0.002. “Unadjusted” means that the calculation compares the posted group summaries without accounting for other participant characteristics or applying a model-based adjustment. It is an additional summary, not a replacement for the registry-reported analysis.

Risk difference is an absolute measure: it represents the difference between the two response proportions on the proportion scale. Relative measures answer a different question by expressing the relationship between proportions as a ratio. The recalculation also reports a risk ratio of 2.192 with a 95% confidence interval from 1.307 to 3.676, and an odds ratio of 2.541 with a 95% confidence interval from 1.388 to 4.652. These measures are not interchangeable. In particular, an odds ratio is a ratio of odds, not a ratio of probabilities.

Why do confidence intervals matter?

A confidence interval conveys uncertainty around an estimated effect. In general, a 95% confidence interval is produced by a procedure designed to cover the true effect in 95% of repeated samples under its assumptions. It does not mean there is a 95% probability that the particular interval contains the true effect. The interval's width reflects both the observed data and the calculation method. For the risk difference, the interval extends from 0.046 to 0.201; the interval does not include zero. This is consistent with the recalculated test result, but it remains an unadjusted estimate based on posted summary statistics.

Precision is scale-specific. A confidence interval for a risk difference describes uncertainty in an absolute difference, whereas intervals for a risk ratio or odds ratio describe uncertainty on relative scales. The registry itself reports the chi-squared p-value but does not provide a confidence interval for the primary comparison in the posted result. The intervals above belong to the simple recalculations.

Why can binary outcomes be over-dispersed?

General statistical explanation: a basic binomial model assumes that participants' outcomes are independent and that each participant in a group has the same underlying response probability. If outcomes vary more than that model expects—for example, because participant characteristics or response tendencies differ—there may be over-dispersion. Over-dispersion means the actual variability exceeds the model's assumed variability and can make conventional standard errors too small if it is ignored.

The registry record does not report a specific over-dispersion assessment or correction for the primary endpoint. The endpoint is a binary participant-level response, and the posted analysis is identified as chi-squared; it would be inappropriate to assume that an over-dispersion adjustment was applied. General concerns about model assumptions are not evidence that they were violated in this trial.

What can the posted analysis establish?

The posted percentages and tests describe the randomized comparison for the defined composite endpoint. Randomization is intended to support a fair comparison between assigned groups, while masking can reduce certain sources of bias in care and outcome assessment. The registry identifies randomized allocation and quadruple masking, but does not describe the exact roles masked or the details of allocation concealment. Statistical results should therefore be interpreted alongside the reported design and the information the registry does not provide.

The p-value and confidence intervals do not address every issue relevant to interpretation. They do not describe the clinical importance of the threshold, the distribution of daily symptom experience, the consequences of missing diary entries, or whether multiple analyses affected interpretation. The registry lists secondary outcomes and analyses, but does not report a multiplicity adjustment or a complete analysis plan. These uncertainties limit what can be concluded from the primary result alone.

10. Confidence Intervals and Precision

The posted arm percentages are 22.7% for eluxadoline and 10.3% for placebo. On the absolute scale, the simple unadjusted recalculation estimates a risk difference of 0.123. Its 95% confidence interval ranges from 0.046 to 0.201. The interval gives a sense of the precision of that recalculated estimate: it includes a range of positive absolute differences rather than a single exact value.

The interval is calculated from posted summary statistics and is not reported as the sponsor's own confidence interval. The registry-reported chi-squared analysis gives p = 0.002; the simple recalculation gives p = 0.002. Those values come from different presentations of the comparison and should be kept distinct. The registry record does not flag a discrepancy.

The recalculated relative measures are a risk ratio of 2.192, with a 95% confidence interval from 1.307 to 3.676, and an odds ratio of 2.541, with a 95% confidence interval from 1.388 to 4.652. Their intervals express uncertainty on relative scales, so their magnitudes should not be read as absolute percentage-point changes. The risk-difference interval is more directly connected to the absolute difference between the reported proportions.

Confidence intervals are not guarantees about the range of effects in every setting, nor do they capture uncertainty arising from unreported design or analysis choices. They depend on the assumptions and method used for their calculation. The registry record does not provide its own primary-outcome confidence interval, or details sufficient to evaluate every assumption behind the sponsor's analysis. The recalculated intervals therefore offer an additional statistical perspective, not a complete account of uncertainty.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are based on a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect. These are planning illustrations, not the trial's original design assumptions, which are not reported in the registry record.

For planning at 100% of the observed effect, the figures are 142 participants per arm for 80% power and 189 participants per arm for 90% power. At 75% of the observed effect, they are 233 participants per arm for 80% power and 311 participants per arm for 90% power. At 50% of the observed effect, they are 479 participants per arm for 80% power and 641 participants per arm for 90% power.

In general, 80% power means that, if the assumed effect and planning assumptions were correct, the design would have an 80% chance of rejecting the null hypothesis at the stated significance level. The 90% column applies the same idea with a higher target probability. A higher power target generally requires a larger planned sample under otherwise unchanged assumptions. The listed illustrations also show that smaller effects need more participants to detect than larger effects.

These figures are not observed power. They are forward-looking planning calculations based on the observed effect, not evidence about the probability that this completed trial detected an effect. The original sample-size justification and assumptions are not reported in the registry record.

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 = 0.103; treatment proportion p₁ = 0.227; average p̄ = 0.165.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5251 = 1.0291.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5178 = 0.4358.
4. n = (1.0291 + 0.4358)² / (0.1233)² = 141.2, rounded up to 142 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 <- 0.103448275862069                          # control proportion
p1 <- 0.226744186046512                          # 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(2959983)
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 = 142 (80% power), 189 (90% power)
 75% of observed effect: n per arm = 233 (80% power), 311 (90% power)
 50% of observed effect: n per arm = 479 (80% power), 641 (90% power)
power.prop.test: 141.2 
Simulated power at n = 142 per arm: 0.812 (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. Analyses Reported by the Sponsor

The registry reports the sponsor's primary comparison as a chi-squared superiority analysis with p = 0.002. The simple recalculation from the posted summary statistics gives a risk difference of 0.123, a 95% confidence interval from 0.046 to 0.201, and p = 0.002. The recalculation is unadjusted and should be understood as an additional analysis of the posted arm-level data, not as a reproduction of every possible feature of the sponsor's analysis.

The values are close but not identical. A small difference can arise when analyses use different statistical procedures, conventions, or underlying data details; the registry record does not specify which, if any, explains the difference in this case. The record does not flag a discrepancy. The sponsor's reported result and the unadjusted recalculation should therefore be described separately, with the registry-reported chi-squared p-value identified as the trial's posted analysis and the recalculated estimate identified as a supplementary summary.

The registry does not provide a sponsor-reported confidence interval for the primary comparison in the posted result. The confidence interval for the risk difference, along with the relative-measure intervals, belongs to the simple recalculation. Neither set of summaries addresses unreported choices such as missing-data handling or multiplicity adjustment.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary composite responder endpoint and three secondary outcomes: percentage of stool consistency responders, percentage of pain responders, and percentage of monthly composite responders. It also records 4 outcome measures and 12 analyses. When a study examines several outcomes or performs several analyses, the chance of at least one nominally significant result can increase if each test is interpreted separately without accounting for multiplicity. Statistical approaches to multiplicity can control or describe that issue, but the registry record does not report whether a multiplicity procedure was planned or used.

The primary outcome is identified, which helps distinguish the main question from secondary questions. However, the full statistical analysis plan, ordering of secondary analyses, and any hierarchy among them are not reported in the registry record. The primary p-value should not be treated as evidence that every secondary outcome was positive, and no secondary-outcome results are available in the registry record described for this analysis.

The primary analysis population is described as the Intent-to-Treat population, including all randomized patients. The posted outcome denominators are 172 for eluxadoline and 174 for placebo. The registry record does not report how missing diary entries, participants with incomplete follow-up, or other missing endpoint information were handled. That omission matters because the composite definition depends on daily diary entries and the proportion of days meeting response criteria. Different missing-data rules can affect who is classed as a responder and the uncertainty of the comparison.

The registry record also does not report whether the primary analysis included covariate adjustment, how protocol deviations were treated, or whether sensitivity analyses were conducted. These should not be inferred from the posted chi-squared test. Without such information, it is not possible to assess how robust the result is to alternative missing-data assumptions or analysis choices.

The stated population is all randomized patients, but the record does not detail any exclusions between randomization and the posted primary outcome results. The distinction between an intended analysis population and the observations contributing to a specific analysis can matter in practice. The available information identifies the intended population but does not fully document its implementation.

15. 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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: pancreatic mass (0.6%), cellulitis (0.6%), pneumonia (0.6%), cardiac failure congestive (0.6%), uterine leiomyoma (0.6%).

The registry reports serious adverse events for an at-risk group of 171 participants in the eluxadoline arm, with 1 participant affected, and an at-risk group of 173 in the placebo arm, with 3 affected. Other adverse events are reported for the same at-risk denominators: 10 affected in the eluxadoline group and 5 in the placebo group. Deaths are recorded as 0 in both groups.

The registry also lists serious-event terms with percentages of 0.6%: pancreatic mass, cellulitis, pneumonia, cardiac failure congestive, uterine leiomyoma, and dysmenorrhea. The posted listing does not establish in the registry record whether each term occurred in a particular arm, nor does the listed percentage by itself describe severity, duration, or causal relationship.

These are descriptive safety counts. They should not be interpreted as proof that an event was caused by, or unrelated to, study treatment. The counts do not by themselves provide a complete comparison of safety risks, and the record does not give additional detail about event timing, seriousness criteria, or adjudication. Safety interpretation should remain separate from the primary efficacy comparison.

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

The posted result concerns a specific population: patients with IBS-D who reported inadequate control of symptoms with prior loperamide. In that trial, the primary composite responder percentage was 22.7% with eluxadoline and 10.3% with placebo. The registry's own chi-squared superiority analysis reported p = 0.002. The simple unadjusted recalculation estimates a risk difference of 0.123, with a 95% confidence interval from 0.046 to 0.201.

These statistics describe the group comparison under the study's composite definition. They do not mean that every participant receiving eluxadoline met the response criteria, or that no placebo participant did. The endpoint requires a specified combination of pain and stool consistency findings over diary days, so it does not describe every aspect of IBS-D symptoms, daily experience, or response outside that definition.

The result does not establish the effect in populations unlike the trial's stated group, or under treatment conditions different from those recorded. The study compared eluxadoline 100 mg twice daily with matching placebo for 12 weeks. The registry record does not provide results that would support conclusions about other doses, longer treatment, or other comparators.

A statistically significant result is not, by itself, a measure of clinical importance. The p-value does not give the probability that the null hypothesis is true, and the confidence interval does not account for every source of uncertainty, including unreported missing-data procedures or multiplicity handling. The posted efficacy result should also not be read as a full safety conclusion. The adverse-event counts are descriptive and do not establish causation.

In short, the registry reports a difference between randomized groups on the defined primary composite outcome, with the sponsor's analysis indicating statistical evidence of superiority. The result remains bounded by the endpoint definition, trial population, duration, and analysis details that are and are not reported in the registry record.

17. Why This Trial Matters Statistically

This trial raises several useful statistical issues for clinical researchers. First, its endpoint combines repeated daily symptom measurements into a binary participant-level responder outcome. That makes the comparison readily expressible as percentages, but means that interpretation depends on the response thresholds, diary completeness, and the rule for combining pain and stool consistency.

Second, the result can be expressed on both absolute and relative scales. The posted arm percentages are 22.7% and 10.3%; the unadjusted recalculation gives a risk difference of 0.123 and a risk ratio of 2.192. The absolute scale describes the estimated separation in response proportions, while the relative scale describes their ratio. Both are useful, but they answer different questions and should not be conflated.

Third, the registry-reported chi-squared p-value and the recalculated estimates illustrate the distinction between a trial's reported analysis and a simple analysis of posted summary data. A recalculation can add an effect estimate and confidence interval, but it cannot recover unreported model choices or missing-data rules. Keeping those sources distinct makes interpretation more transparent.

Finally, the registry lists multiple secondary outcomes and analyses, while information about multiplicity procedures and missing diary data is not reported. Those details are important for judging how confidently one can interpret a single primary result in the context of a broader analysis program. The sample-size illustrations also show why planning depends on the effect size researchers consider important, rather than relying only on the observed effect.

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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The registry record does not report how incomplete daily diaries were handled, even though response classification depends on diary entries and the percentage of qualifying days. It also does not provide the full statistical analysis plan, details of any covariate adjustment, or sensitivity analyses for missing data. These gaps limit assessment of how robust the primary comparison is to alternative analysis decisions.

The record lists secondary outcomes and 12 analyses but does not report a multiplicity strategy or the analysis hierarchy. It therefore does not establish how the primary result was positioned relative to other analyses or whether adjustments were made when interpreting multiple tests.

The endpoint reduces daily symptom information to a responder classification based on thresholds. The posted percentages do not show the distribution of pain scores, stool scores, diary completion, or changes among participants who did not meet the composite definition. A participant near a threshold may be classified differently from one just beyond it, even when their symptom patterns are similar.

The population was specifically patients with IBS-D who reported inadequate control with prior loperamide. The registry record does not provide enough information to assess how representative that group was of other people with IBS-D. The intervention and comparator were given for 12 weeks, so the result does not describe longer-term outcomes.

The safety information is limited to the posted at-risk groups, affected counts, deaths, and listed serious-event terms. Further detail about timing, duration, severity, causal attribution, and event handling is not reported in the registry record. Finally, the original sample-size justification and planned design assumptions are not reported, so the planning illustrations should not be mistaken for the trial's original design rationale.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Efficacy of Eluxadoline in the Treatment of Irritable Bowel Syndrome With Diarrhea in Patients With Inadequate Control of Symptoms With Prior Loperamide Use — NCT02959983.
• Registry record last updated 2019-02-15; status last verified 2019-01.
• Results first posted 2019-02-15.
• 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.

22. Record Summary

The registry record describes NCT02959983, a completed Phase 4 randomized, quadruple-masked, parallel-group trial sponsored by Allergan. It compared eluxadoline 100 mg twice daily with matching placebo for 12 weeks in patients with IBS-D who reported inadequate symptom control with prior loperamide use. Registry enrollment is 346.

The primary endpoint was the percentage meeting a composite daily abdominal-pain and stool-consistency responder definition during Baseline, Weeks 1 to 12. The posted results were 22.7% for eluxadoline and 10.3% for placebo. The registry-reported chi-squared superiority analysis gave p = 0.002. A simple unadjusted recalculation gives a risk difference of 0.123, with a 95% confidence interval from 0.046 to 0.201.

The registry lists three secondary outcome measures. Details of the original sample-size justification, missing-data handling, and multiplicity procedures are not reported in the registry record.