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Liver Cirrhosis, Biliary Phase 2 Continuous Endpoint NCT00570765

Study of INT-747 as Monotherapy in Participants With Primary Biliary Cirrhosis (PBC): Complete Statistical Analysis

A randomized, double-blind phase 2 trial compared two doses of obeticholic acid with placebo over the double-blind treatment phase in participants with primary biliary cirrhosis. The primary analysis concerns mean percent change in serum alkaline phosphatase from baseline to Day 85, with secondary laboratory outcomes and serious adverse events also described.

Trial start: 2008-01-17  ·  Enrollment: 60  ·  Sponsor: Intercept Pharmaceuticals
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 Study of INT-747 as Monotherapy in Participants With Primary Biliary Cirrhosis (PBC) (NCT00570765), a randomized phase 2 study. The primary outcome is DB Phase: Mean Percent Change In Serum Alkaline Phosphatase (ALP) From Baseline To Day 85.

60
Enrollment
Phase 2
3
Arms
In the primary outcome
-44.90
Mean difference
DB OCA 10 mg
-57.29–-32.51
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00570765
PhasePhase 2
ConditionLiver Cirrhosis, Biliary
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment60
Arms in the primary outcome3
Lead sponsorIntercept Pharmaceuticals
Results postedYes

2. Clinical Question

Population

Participants with primary biliary cirrhosis were enrolled. The primary endpoint population is described as the intention-to-treat population: participants randomized to receive investigational product, regardless of their actual treatment status.

Intervention

Obeticholic acid (OCA) was studied as monotherapy. In the double-blind phase, the posted arms received OCA 10 mg, OCA 50 mg, or matching placebo for 3 months.

Comparator

The comparator was matching placebo during the double-blind phase. Each OCA dose was compared with the placebo group for the primary endpoint.

Primary question

The primary hypothesis was that OCA would reduce alkaline phosphatase levels over a 12-week treatment period compared with placebo. The endpoint reports mean percent change in serum ALP from baseline to Day 85; baseline was the mean of the pretreatment Screening and Day 0 evaluations.

The registry record describes a randomized, double-blind, parallel-group phase 2 study with enrollment of 60 participants. The primary outcome is a laboratory measure, not a clinical event or a direct measure of how participants felt or functioned. Its comparison therefore addresses whether the groups' ALP changes differed during the posted treatment period. The record also lists other laboratory outcomes, including GGT, ALT, and conjugated bilirubin, as well as longer-term ALP and GGT outcomes in an open-label extension. The extension was offered to eligible participants after the 3-month double-blind phase, so those later observations address a different treatment setting from the randomized placebo-controlled comparison.

3. Trial Design

This was a phase 2, randomized, double-blind, parallel-group study of OCA monotherapy in participants with primary biliary cirrhosis. The registry record lists 60 participants enrolled and describes three double-blind arms: OCA 10 mg, OCA 50 mg, and matching placebo. The arm descriptions specify treatment for 3 months during the double-blind phase. The record's primary hypothesis refers to a 12-week treatment period, and the primary endpoint is measured from baseline to Day 85.

Randomization is intended to create comparable groups at the start of a trial, while masking is intended to limit the influence of treatment knowledge on participant care, assessment, and reporting. Those design features support a placebo-controlled comparison, but they do not by themselves establish that every possible source of bias was prevented. Details of the randomization procedure, concealment, and which parties were masked beyond the double-blind designation are not reported in the registry record.

The primary endpoint population is the intention-to-treat population, defined in the record as participants randomized to receive investigational product regardless of actual treatment status. The number contributing to each posted outcome is not identical across the endpoints; the registry record lists the endpoint-specific counts. Reasons for differences between those counts, and the handling of missing outcome values, are not reported in the registry record.

After completion of the 3-month double-blind phase, eligible participants were offered the opportunity to enter an open-label long-term safety extension for up to 96 months, beginning at 10 mg OCA. Doses up to 50 mg daily were evaluated. Because that extension was open-label and had no placebo arm described in the record, its results should be distinguished from the randomized double-blind comparison. The detailed trial protocol and original statistical 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.

Before assignment: Screening interim allowed for pre-randomization eligibility assessment of 1 to 4 weeks. Other than 3-month (pre-Screening) washout for ursodeoxycholic acid and other medications, no washout or run-in period was defined between Screening and Randomization. During LTSE, OCA dosing (milligrams \[mg\]) remained oral once daily.

DB Phase

StageDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboLTSE OCA Total
STARTED2016240
Received at Least 1 Dose of Study Drug2016230
Safety Population2016230
COMPLETED169230
NOT COMPLETED4710

Reasons for not completing this period:

ReasonDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboLTSE OCA Total
Withdrawal by Subject1000
Protocol Violation0100
Adverse Event3600
Did Not Receive Study Drug0010

LTSE Phase

StageDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboLTSE OCA Total
STARTED00028
Received at Least 1 Dose of Study Drug00028
Safety Population00028
COMPLETED00016
NOT COMPLETED00012

Reasons for not completing this period:

ReasonDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboLTSE OCA Total
Withdrawal by Subject0001
Adverse Event0007
Physician Decision0004

Analysis population for the primary outcome, as defined in the registry: Intention-to-treat (ITT): participants randomized to receive investigational product regardless of their actual treatment status.

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: Safety Population: all randomized participants who received at least 1 dose of investigational product based on the treatment group assignment and had at least 1 post-treatment safety assessment.

CharacteristicUnitDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboTotal
Participants analysed20162359
Age, Categorical: <=18 yearsParticipants0000
Age, Categorical: Between 18 and 65 yearsParticipants16151849
Age, Categorical: >=65 yearsParticipants41510
Age, Continuousyears54.8 (SD 10.9)54.1 (SD 7.3)55.3 (SD 10.0)54.8 (SD 9.5)
Sex: Female, Male: FemaleParticipants14162050
Sex: Female, Male: MaleParticipants6039
Region of Enrollment: Franceparticipants2114
Region of Enrollment: United Statesparticipants45817
Region of Enrollment: Canadaparticipants3249
Region of Enrollment: Spainparticipants0112
Region of Enrollment: Germanyparticipants4138
Region of Enrollment: United Kingdomparticipants76619

6. Primary Endpoint

The registry lists the primary outcome as DB Phase: Mean Percent Change In Serum Alkaline Phosphatase (ALP) From Baseline To Day 85, measured over Baseline, Day 85.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
UnitPercent change
Endpoint classificationContinuous Endpoint

The primary endpoint is mean percent change in serum alkaline phosphatase (ALP) from baseline to Day 85. ALP is a blood laboratory measure relevant to the study's stated focus on primary biliary cirrhosis. The endpoint describes change over the treatment period as a percentage of baseline, then summarizes that change as a group mean. A negative mean percent change represents a decline from baseline on this measure; it is not, by itself, a measure of symptoms, quality of life, disease progression, or a clinical event.

Baseline was defined as the mean of the pretreatment Screening and Day 0 evaluations. The primary endpoint record identifies the analysis population as intention-to-treat: randomized participants were included regardless of actual treatment status. The endpoint is useful for comparing average laboratory changes between randomized groups at a specified follow-up time. Using a common baseline and follow-up time gives the groups a shared frame for the comparison, although the interpretation still depends on the completeness and conduct of the measurements and analysis.

For this endpoint, the posted mean percent changes were -44.5 for OCA 10 mg, -37.6 for OCA 50 mg, and 0.4 for placebo. The standard deviations were 24.4, 21.0, and 15.3, respectively. These group summaries describe the observed laboratory results in the posted analyses. A mean change does not imply that every participant changed by that amount; the standard deviations convey variation among observations around the group mean. The endpoint's clinical meaning and its relationship to longer-term outcomes are not established by these summaries alone.

7. Results Posted in the Registry

Mean difference: DB OCA 10 mg

-44.90

95% CI: -57.29 to -32.51

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-61.4-46.5-31.7-16.8-2.012.8DB OCA 10 mg (n=20)DB OCA 50 mg (n=16)DB OCA Placebo (n=23)Percent change (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)DB OCA 10 mgDB OCA 50 mg-62-49-35-22-8.714.58mean 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
DB Phase: Mean Percent Change In Gamma-glutamyl Transferase (GGT) From Baseline To Day 85Continuous EndpointMean difference-70.00 (-82.25 to -57.75)2 per arm
DB Phase: Mean Percent Change In Alanine Transaminase (ALT) From Baseline To Day 85Continuous EndpointMean difference-33.00 (-55.96 to -10.04)21 per arm
DB Phase: Mean Percent Change In Conjugated Bilirubin From Baseline To Day 85Continuous EndpointMean difference-29.60 (-72.23 to 13.03)85 per arm

DB Phase: Mean Percent Change In Gamma-glutamyl Transferase (GGT) From Baseline To Day 85

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)DB OCA 10 mgDB OCA 50 mg-89-70-51-32-136.58mean difference vs control (95% CI)

DB Phase: Mean Percent Change In Alanine Transaminase (ALT) From Baseline To Day 85

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)DB OCA 10 mgDB OCA 50 mg-60-47-34-21-8.514.48mean difference vs control (95% CI)

DB Phase: Mean Percent Change In Conjugated Bilirubin From Baseline To Day 85

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)DB OCA 10 mgDB OCA 50 mg-79-59-39-200.0720mean difference vs control (95% CI)

The posted secondary outcomes extend the laboratory picture beyond ALP to GGT, ALT, and conjugated bilirubin during the double-blind phase, and to longer-term ALP and GGT summaries during the open-label extension. In broad terms, the double-blind GGT and ALT summaries show decreases in the OCA arms relative to the placebo summaries, while the conjugated bilirubin results are more variable and do not show the same clear separation in the recalculated comparisons. The primary ALP finding is therefore accompanied by directionally similar patterns in some other enzymes, but not a uniform pattern across every measured laboratory outcome.

That overall pattern should be treated as supportive context rather than as a set of independent confirmations. The measures are related laboratory outcomes, and many outcomes and comparisons are listed. The record reports a global rank-based test for GGT and ALT, but does not report a test for the conjugated bilirubin outcome. Detailed results and the associated uncertainties belong to each endpoint's posted analysis; the broad pattern alone cannot establish that all outcomes changed consistently or that changes were clinically meaningful.

The long-term extension is open-label and was offered to eligible participants after the double-blind phase. It has no placebo comparison described in the record, so its later measurements cannot be interpreted like randomized between-group contrasts. Follow-up duration and participation may differ, and the registry record does not report a detailed account of those factors.

Unadjusted secondary results carry less weight than a prespecified primary comparison because examining many outcomes increases the chance of chance findings. Whether the trial used a formal multiplicity adjustment, a sequence of testing, or a prespecified priority among secondary outcomes is not reported in the registry record. Secondary endpoints can help characterize consistency and generate questions, but they do not replace a clear primary analysis or independently establish a treatment effect.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The primary endpoint results show a mean percent change in ALP of -44.5 in the OCA 10 mg arm, -37.6 in the OCA 50 mg arm, and 0.4 in the placebo arm. The posted, simple unadjusted recalculation gives mean differences versus placebo of -44.9 for OCA 10 mg, with a 95% confidence interval from -57.29 to -32.51, and -38.0 for OCA 50 mg, with a 95% confidence interval from -50.04 to -25.96. Both intervals lie below zero, so the recalculated mean contrasts are compatible with lower average percent change in the OCA groups than in placebo under the assumptions used for those calculations.

The corresponding unadjusted recalculated p-values are <0.001 for each dose comparison. These are pairwise calculations from posted summary statistics, not the sponsor's reported analysis. The registry record reports a Wilcoxon (Mann-Whitney) test across the three groups, with p < 0.001. That reported test is an overall rank-based comparison and does not provide a separate estimated mean difference or confidence interval for either dose versus placebo. The two kinds of results answer related, but not identical, statistical questions.

Both OCA arms had negative mean ALP changes, while the placebo mean was close to zero and slightly positive. The 10 mg arm's mean change was more negative than the 50 mg arm's mean change, but the posted results do not establish a dose-response relationship or a statistically tested difference between the two OCA doses. The principal recalculated comparisons are each against placebo. No dose-to-dose estimate or confidence interval is reported in the registry record.

These results concern a laboratory endpoint over the double-blind phase. They do not, on their own, show the magnitude of an effect on symptoms, complications, long-term disease course, or survival. Nor do small p-values resolve how clinically important a difference is. The confidence intervals convey uncertainty about the mean contrasts under the simple unadjusted calculation; they do not account for unreported design or analysis choices. The registry record does not report a prespecified hierarchy across outcomes or the full analysis plan, so the primary endpoint carries a different interpretive status from multiple secondary comparisons.

The endpoint-specific counts were 20 for OCA 10 mg, 16 for OCA 50 mg, and 23 for placebo. These are the posted analysis counts, not a description of why observations may be absent from a particular analysis. The reasons and any missing-data procedures are not reported in the registry record. That limits assessment of whether the available outcome summaries fully represent the intended analysis population.

10. Statistical Methods Explained

The posted primary outcome is continuous: each participant has a percent change in ALP, and the arm summaries report the mean and standard deviation. A mean is the arithmetic average of the observed values. A standard deviation describes how spread out those values are around the mean; it is not the uncertainty interval for the mean itself. The confidence interval for a between-group mean difference instead reflects uncertainty in the estimated contrast, given the calculation's assumptions and the observed group summaries.

What does the randomized comparison estimate?

The OCA-versus-placebo comparison is a contrast between group means at the endpoint. The recalculated difference is expressed as the OCA mean minus the placebo mean: -44.9 for OCA 10 mg and -38.0 for OCA 50 mg. Because these are percent-change values, a negative contrast indicates that the OCA arm's average percent change was lower than the placebo arm's average. It does not represent an individual participant's response, and it is not a comparison of the OCA doses with each other.

Randomization supports a causal interpretation when it is properly implemented and when follow-up and analysis preserve the intended comparison. The registry record identifies the study as randomized and double-blind, but further implementation details are not reported in the registry record. Statistical calculations cannot verify those design features or remedy bias from incomplete follow-up.

Why distinguish the reported test from the recalculation?

The registry record reports a Wilcoxon (Mann-Whitney) analysis across all three primary-outcome groups, with p < 0.001. This rank-based method compares the distributions of observations through their ranks; it does not directly test the displayed difference between two arithmetic means. In contrast, the recalculated estimates use the posted means, standard deviations, and group sizes to form unadjusted pairwise mean contrasts and confidence intervals. A rank-based test and a mean-based contrast can lead to related conclusions about group separation, but they summarize the data differently and need not yield identical inferences.

The recalculated pairwise p-values are unadjusted and are not substitutes for a complete prespecified analysis. The registry record does not report the detailed statistical plan, including whether the sponsor used additional adjustments, covariates, or a testing sequence. The sponsor's reported global p-value should therefore be read as the registry's reported analysis, while the recalculated contrasts offer a transparent, summary-statistic-based view of each dose against placebo.

What does a confidence interval express?

A confidence interval gives a range of values that are reasonably compatible with the data under the statistical model and procedure used. For OCA 10 mg, the recalculated 95% interval for the mean difference is -57.29 to -32.51; for OCA 50 mg, it is -50.04 to -25.96. These intervals summarize uncertainty around the pairwise estimates. They do not mean that the true value has a 95% probability of lying in the particular interval, and they do not include uncertainty from every possible source, such as unreported choices in trial conduct or analysis.

Both intervals exclude zero, the value corresponding to no mean difference under this contrast. That is consistent with the small unadjusted pairwise p-values. Statistical compatibility with a nonzero mean difference is distinct from the question of whether the size of that difference matters clinically; the registry record does not specify a threshold for clinical importance.

Why can rank-based methods be used?

Rank-based methods compare the ordering of observations rather than relying directly on the numerical distances between them. As a general statistical explanation, this can be useful when a distribution is skewed or contains influential extreme observations, although the registry record does not state why this method was selected. The reported global Wilcoxon result is not a pairwise mean estimate and does not identify which particular group contrast drives the overall result.

Mean-based recalculations have a different target and rely on the posted means and standard deviations. Their confidence intervals reflect uncertainty in the mean contrast under the calculation used. When outcome distributions are notably non-normal or contain influential observations, a mean-based summary may not fully describe the pattern that a rank-based procedure detects. Distributional details are not reported in the registry record, so the two approaches should be treated as complementary summaries rather than interchangeable tests.

What is the role of standard deviation?

The primary arm standard deviations are 24.4, 21.0, and 15.3 for OCA 10 mg, OCA 50 mg, and placebo. As a general statistical concept, more variability usually makes an estimate less precise when group sizes are otherwise similar. A standard deviation describes participant-level variation, whereas a standard error describes uncertainty in an estimated quantity. The recalculation uses the posted group sizes and standard deviations; it does not replace the sponsor's analysis.

In general, over-dispersion means that observed variability is greater than a model assumes. If a model understates variability, its standard errors can be too small and its intervals too narrow. The registry record does not report a model-based dispersion assessment for the primary endpoint, so no claim about over-dispersion in this trial can be made.

What can be inferred from p-values?

A p-value measures how unusual results at least as incompatible with a null hypothesis would be if that hypothesis and the analysis assumptions were correct. It is not the probability that the null hypothesis is true, and it does not measure effect size or clinical importance. The reported global p-value and the recalculated pairwise p-values must be interpreted in relation to their different tests and the number of outcomes and comparisons considered.

The secondary outcomes include several laboratory measures, and the record lists 15 outcome measures overall. Testing multiple outcomes can increase the chance of apparently notable results arising by chance if no multiplicity strategy is used. Whether any adjustment or gatekeeping approach was prespecified is not reported in the registry record. That missing information supports a cautious interpretation of secondary findings.

11. Confidence Intervals and Precision

Precision concerns how tightly the data locate an estimated effect, not whether an effect is important. For the primary endpoint, the recalculated mean difference for OCA 10 mg versus placebo is -44.9, with a 95% confidence interval from -57.29 to -32.51. For OCA 50 mg versus placebo, the estimate is -38.0, with a 95% confidence interval from -50.04 to -25.96. Each interval is entirely below zero, indicating that the summary-statistic recalculations are inconsistent with a zero mean difference at the corresponding unadjusted 95% interval level.

The intervals also show a range of effect sizes compatible with the calculation. They are not guarantees that the true effect falls inside these particular bounds, and they do not incorporate every possible source of uncertainty. In particular, they do not address bias from missing outcomes, protocol deviations, measurement issues, or choices in the unreported full analysis plan. The primary outcome is defined for an intention-to-treat population, but the registry record does not describe how missing measurements or other deviations were handled.

Each interval is for a comparison against placebo. The intervals overlap, but overlap is not a formal test of whether the two OCA doses differ. The registry record does not report a direct OCA 10 mg versus OCA 50 mg comparison. The mean values alone should not be used to claim that one dose is superior to the other.

The sponsor-reported Wilcoxon analysis has a p-value but no corresponding effect estimate or confidence interval in the registry record. Its statistical significance therefore does not give a direct measure of the size or precision of a pairwise mean difference. Taken together, the reported global test and recalculated intervals provide different information: one is a rank-based test across three groups, and the others quantify uncertainty around unadjusted pairwise mean contrasts. Neither establishes the clinical importance of the laboratory changes.

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 effect45
75% of the observed effect68
50% of the observed effect1317
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect510205040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
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: DB OCA 10 mg.

The sample-size display is a planning illustration based on the observed effect, not the trial's original design calculation. For these continuous outcomes, the values are participants per arm, not total events. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the target effect is the stated fraction of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for an 80% chance of detecting the specified effect under those assumptions if that effect were the true effect. The 90% power column gives the corresponding illustration for a 90% chance. These are design-planning probabilities conditional on the assumed effect and model; they are not probabilities that the trial's conclusion is correct.

Rows representing 100%, 75%, and 50% of the observed effect let readers consider how the planning figures change when the target effect is smaller than the observed estimate. Smaller effects generally require more participants to distinguish them from no difference with the same target power and significance level. The display's values are especially sensitive to the observed effect used as their starting point; an effect estimated from a modest study can be an uncertain basis for planning a future study.

These figures are not observed power. Observed power calculated after a trial using its estimated effect largely restates the p-value and does not measure the probability that the result is true. The planning illustration is most useful as a conditional comparison of hypothetical designs, not as a retrospective evaluation of whether the completed study was adequately designed.

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 = -44.900; pooled standard deviation σ = 20.038.
  2. n = 2 × (1.96 + 0.842)2 × 20.0382 / -44.9002 = 3.1, rounded up to 4 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 <- -44.9                      # observed difference in means
sigma <- 20.0376596656907                     # 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(570765)
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 = 4 (80% power), 5 (90% power)
 75% of observed effect: n per arm = 6 (80% power), 8 (90% power)
 50% of observed effect: n per arm = 13 (80% power), 17 (90% power)
power.t.test: 4.3 
Simulated power at n = 4 per arm: 0.752 (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.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Wilcoxon (Mann-Whitney)not reported< 0.001

The registry record reports a Wilcoxon (Mann-Whitney) analysis across the three primary endpoint groups, with p < 0.001. It does not report a sponsor-estimated pairwise mean difference or confidence interval for each OCA dose versus placebo. The recalculated estimates instead use posted group means, standard deviations, and counts to produce simple unadjusted pairwise mean contrasts. They are not a reconstruction of the sponsor's full analysis.

The reported global rank-based test addresses whether the group distributions differ overall; the recalculated contrasts address differences in arithmetic means for each dose versus placebo. A global test does not by itself identify which pairwise comparison accounts for the overall result. The two recalculated mean differences and intervals add an estimate of direction and magnitude for the placebo comparisons, but their p-values are unadjusted and rely on the summary-statistic approach.

The registry record indicates no discrepancy between the sponsor's analysis and the recalculation. Even so, the sponsor's reported analysis remains the trial's own analysis, and the recalculation should be read as an additional, limited summary-statistic comparison. The detailed statistical plan, including any covariate adjustment or multiplicity procedure, is not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists 15 outcome measures and reports several secondary laboratory outcomes in addition to the primary ALP endpoint. Multiple statistical tests create a multiplicity issue: as a general statistical concept, the chance of at least one false-positive result can rise when many hypotheses are tested without a suitable strategy. A prespecified testing hierarchy, adjustment procedure, or clear distinction between confirmatory and exploratory outcomes can help frame that risk. Such details are not reported in the registry record.

The reported global Wilcoxon test for the primary endpoint and some secondary endpoints is different from the unadjusted pairwise mean recalculations. The recalculated p-values are not adjusted for multiple comparisons. The registry record does not say whether the sponsor's own analysis controlled family-wise error or used another multiplicity approach. Accordingly, the primary endpoint result is best kept distinct from the many secondary comparisons, and secondary findings should be viewed cautiously rather than treated as confirmatory evidence.

The primary endpoint population is defined as intention-to-treat, including participants randomized to receive investigational product regardless of actual treatment status. The registry record does not provide details of the analysis population for every secondary endpoint beyond their posted group counts, nor does it explain discrepancies in outcome-specific counts. It also does not report reasons for missing measurements, the extent of missingness by group, or methods such as imputation or sensitivity analyses.

These omissions matter because missing outcomes can affect both the estimate and its uncertainty, particularly if missingness is related to participants' outcomes or treatment experience. The registry record also does not report how protocol deviations, treatment discontinuation, or outlying values were handled. Without these details, the posted summaries can be described, but the robustness of the results to alternative missing-data or analysis choices cannot be assessed from 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
DB OCA 10 mg0200.0%
DB OCA 50 mg0160.0%
DB OCA Placebo1234.3%
LTSE OCA Total92832.1%
Participants with at least one serious adverse event
Serious adverse events by armDB OCA 10 mg0.0%DB OCA 50 mg0.0%DB OCA Placebo4.3%LTSE OCA Total32.1%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 4.99% reporting threshold.

ArmParticipants affected of at risk
DB OCA 10 mg18 of 20
DB OCA 50 mg15 of 16
DB OCA Placebo19 of 23
LTSE OCA Total28 of 28

Most frequent serious adverse event terms

Event termOrgan systemDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboLTSE OCA Total
Abdominal painGastrointestinal disorders0 of 200 of 160 of 232 of 28
RashSkin and subcutaneous tissue disorders0 of 200 of 161 of 230 of 28
Peripheral ischaemiaVascular disorders0 of 200 of 160 of 231 of 28
Lung neoplasmNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 200 of 160 of 231 of 28
Uterine prolapseReproductive system and breast disorders0 of 140 of 160 of 201 of 23
CystoceleReproductive system and breast disorders0 of 140 of 160 of 201 of 23
Pelvic fractureInjury, poisoning and procedural complications0 of 200 of 160 of 231 of 28
Hip fractureInjury, poisoning and procedural complications0 of 200 of 160 of 231 of 28
BradycardiaCardiac disorders0 of 200 of 160 of 231 of 28
Atrial flutterCardiac disorders0 of 200 of 160 of 231 of 28

Most frequent non-serious adverse event terms

Event termOrgan systemDB OCA 10 mgDB OCA 50 mgDB OCA PlaceboLTSE OCA Total
PruritusSkin and subcutaneous tissue disorders14 of 2015 of 167 of 2325 of 28
HeadacheNervous system disorders4 of 202 of 165 of 238 of 28
NauseaGastrointestinal disorders0 of 204 of 164 of 2311 of 28
FatigueGeneral disorders0 of 201 of 163 of 2314 of 28
ArthralgiaMusculoskeletal and connective tissue disorders0 of 200 of 162 of 2313 of 28
Back painMusculoskeletal and connective tissue disorders0 of 200 of 164 of 237 of 28
DiarrhoeaGastrointestinal disorders0 of 202 of 161 of 238 of 28
ConstipationGastrointestinal disorders0 of 202 of 160 of 239 of 28
Upper respiratory tract infectionInfections and infestations2 of 200 of 160 of 239 of 28
Abdominal painGastrointestinal disorders1 of 202 of 161 of 236 of 28

Serious events with the highest arm-level rate: abdominal pain (7.1%), rash (4.3%), uterine prolapse (4.3%), cystocele (4.3%), peripheral ischaemia (3.6%).

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.

During the double-blind phase, the registry record reports 0 participants with serious adverse events among 20 at risk in the OCA 10 mg arm, 0 among 16 at risk in the OCA 50 mg arm, and 1 among 23 at risk in the placebo arm. These are counts of participants with at least one serious adverse event as represented in the registry record, not counts of every event. The record also reports other adverse events in 18 of 20, 15 of 16, and 19 of 23 participants in those respective arms.

The open-label extension lists 9 participants with serious adverse events among 28 at risk, and other adverse events in 28 of 28. Those observations come from an extension in which eligible participants were offered open-label OCA, not from the randomized placebo-controlled comparison. The registry record does not provide deaths counts for these groups, so deaths are not reported in the registry record.

Serious adverse event counts should be interpreted with group sizes, follow-up, event definitions, and the trial's ability to detect uncommon harms in mind. The record lists serious event terms and percentages, including abdominal pain, rash, uterine prolapse, cystocele, peripheral ischaemia, and lung neoplasm, but the displayed list should not be treated as a causal attribution. The registry record does not provide enough detail to assess comparative risk or determine whether an event was caused by treatment.

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

The posted primary results show that mean percent change in ALP was negative in both OCA groups and close to zero in the placebo group over the double-blind phase. The unadjusted recalculated mean contrasts are negative for both doses, with confidence intervals that exclude zero. The registry's reported three-group rank-based test also has a small p-value. Together, these are statistical descriptions of the posted laboratory data, not a complete account of treatment benefit or harm.

ALP is a laboratory endpoint. A change in this measure does not, by itself, establish a change in symptoms, daily functioning, complications, or long-term outcomes. The registry record does not report a threshold for a clinically important difference or establish how the measured changes relate to those outcomes. Therefore, the size and statistical detectability of the mean differences should not be equated with demonstrated clinical importance.

The primary comparisons are each against placebo; they do not establish that one OCA dose is better than the other. The difference between their observed mean changes is not a reported direct test. The results also apply to the defined trial setting and follow-up, and cannot automatically be extended to other populations, treatment durations, or clinical circumstances.

The study's randomized, double-blind design provides a stronger basis for comparing the double-blind groups than an uncontrolled observational comparison would, but interpretation still depends on implementation, outcome completeness, and analysis choices. Those details are not fully reported in the registry record. The open-label extension offers longer-term observations, but it lacks a placebo comparison described in the record and should not be used as if it preserved the randomized contrast.

Safety summaries likewise describe reported events, not proof of either safety or harm. Small group counts and the absence of a complete account of event attribution and follow-up limit what can be concluded about comparative risks. The registry record supports a careful account of the posted ALP and safety data, while leaving broader clinical questions unresolved.

18. Why This Trial Matters Statistically

Statistically, this trial illustrates why an endpoint's summary and its inferential analysis should not be conflated. The primary outcome is reported as group means and standard deviations, while the registry's reported test is a Wilcoxon (Mann-Whitney) comparison across three groups. The additional unadjusted recalculations express pairwise mean differences and confidence intervals. Each provides a different view: the mean contrasts quantify average separation from placebo, while the rank-based test evaluates group separation through ranks.

The results also show why uncertainty should accompany an effect estimate. The intervals for both dose-versus-placebo mean contrasts lie below zero, but their range remains important for judging how precisely the effects are estimated. A p-value alone does not communicate that range or the size of a difference. Conversely, an interval for a laboratory measure does not establish clinical importance.

The study has several outcome measures and multiple comparisons. Without a reported multiplicity strategy, the primary result and secondary signals should not be given equal confirmatory weight. Distinguishing a prespecified primary question from exploratory patterns is central to responsible interpretation, especially when several biomarkers are examined.

Finally, the registry record separates a randomized, double-blind treatment phase from an open-label extension. Statistical comparisons from the randomized period and descriptive observations from the extension have different evidential roles. Recognizing that distinction prevents longer follow-up from being mistaken for a controlled comparison. The record also shows the limits of registry summaries: without details of missing-data handling, the full analysis plan, and the original sample-size rationale, precision and robustness can be discussed only within the boundaries of the posted information.

19. Limitations

Several limitations specific to this trial follow from the registry record. The enrollment is 60, while the primary endpoint analyses list 20 participants in the OCA 10 mg arm, 16 in the OCA 50 mg arm, and 23 in the placebo arm. The record does not explain the difference between the enrollment figure and those outcome counts, or whether any participants lacked Day 85 measurements. This prevents a full assessment of outcome completeness.

The reported primary analysis is a global Wilcoxon (Mann-Whitney) test, while the pairwise mean contrasts and confidence intervals are recalculated from posted summary statistics. Those unadjusted estimates are not the sponsor's reported pairwise estimates, and the record does not provide the sponsor's detailed model or complete statistical plan. No direct comparison between OCA doses is reported. The multiplicity strategy is also not reported, despite several outcomes and comparisons.

The original sample-size justification, interim analyses, and detailed randomization and masking procedures are not reported in the registry record. This means the planning illustration based on observed effects cannot be used to infer the original design rationale. Missing-data methods, sensitivity analyses, and handling of protocol deviations are also not reported, limiting assessment of robustness.

Finally, the extension was open-label, offered to eligible participants, and had no placebo group described. Its data cannot establish a randomized long-term comparison. The posted endpoint is a laboratory change, and the registry record does not report a clinical-importance threshold linking that change to patient-centered or long-term outcomes. Safety counts are descriptive, with deaths not reported in the registry record and limited information on event attribution.

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23. Record Summary

The registry record describes NCT00570765, a completed phase 2 randomized, double-blind, parallel-group study of OCA monotherapy in participants with primary biliary cirrhosis. Enrollment was 60. The double-blind phase compared OCA 10 mg, OCA 50 mg, and matching placebo for 3 months.

The primary endpoint was mean percent change in serum ALP from baseline to Day 85 in the intention-to-treat population. Mean changes were -44.5, -37.6, and 0.4 for the 10 mg, 50 mg, and placebo groups, respectively. The registry reported a three-group Wilcoxon test with p < 0.001. Unadjusted recalculated mean differences versus placebo were -44.9 and -38.0, with 95% confidence intervals of -57.29 to -32.51 and -50.04 to -25.96.

Secondary outcomes included other laboratory measures and open-label extension observations. Original sample-size assumptions, missing-data methods, and a detailed multiplicity strategy are not reported in the registry record. The open-label extension should be distinguished from the randomized comparison.

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