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Chronic HCV Infection Phase 2 Binary Endpoint NCT01938430

Ledipasvir/Sofosbuvir Fixed-Dose Combination + Ribavirin in Subjects With Chronic HCV With Advanced Liver Disease or Post-Liver Transplant: Complete Statistical Analysis

This analysis examines a randomized, open-label Phase 2 study of ledipasvir/sofosbuvir plus ribavirin in people with chronic genotype 1 or 4 HCV and advanced liver disease or a prior liver transplant. It focuses on SVR12, the posted secondary outcomes, and the limits of interpreting comparisons across the study’s clinical groups.

Trial start: 2013-09  ·  Enrollment: 339  ·  Sponsor: Gilead Sciences
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 Ledipasvir/Sofosbuvir Fixed-Dose Combination + Ribavirin in Subjects With Chronic HCV With Advanced Liver Disease or Post-Liver Transplant (NCT01938430), a randomized phase 2 study. The primary outcome is Percentage of Participants With Sustained Virologic Response (SVR) 12 Weeks After Discontinuation of Therapy (SVR12).

339
Enrollment
Phase 2
14
Arms
In the primary outcome
+2.2 pts
Risk difference
Cohort A, Group 1 (24 wk): CPT Class B (
-14.8 to 19.2 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01938430
PhasePhase 2
ConditionChronic HCV Infection
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment339
Arms in the primary outcome14
Lead sponsorGilead Sciences
Results postedYes

2. Clinical Question

Population

Participants had chronic genotype 1 or 4 HCV infection and either decompensated cirrhosis without a prior liver transplant or a prior liver transplant, with or without cirrhosis. The registry describes these as Cohort A and Cohort B, respectively. The primary analysis population included randomized participants who received at least one dose; Cohort A participants who received a liver transplant before the lower bound of the Posttreatment Week 12 visit were excluded from that analysis.

Intervention

All listed groups received ledipasvir/sofosbuvir fixed-dose combination plus ribavirin. Treatment duration was 12 or 24 weeks. Ribavirin dosing varied by clinical group and was adjusted according to tolerability in several groups.

Comparator

Participants within groups were randomized 1:1 to 12 or 24 weeks. There was no untreated or placebo group: both assignments received the combination regimen. The posted comparisons also use the Cohort A, Group 1, 12-week arm as a reference, but comparisons with other clinical groups are not randomized comparisons of duration alone.

Primary question

What percentage of participants had sustained virologic response 12 weeks after stopping treatment, defined as HCV RNA below the lower limit of quantitation at that visit? The posted results describe SVR12 by clinical group and treatment duration. The registry record does not report a sponsor-conducted comparative analysis.

3. Trial Design

This was a Phase 2, multicenter, open-label, randomized, parallel-group study. The registry lists enrollment of 339 and a completed status. The study start is recorded as 2013-09 and primary completion as 2015-01. Masking was none, so treatment assignment was not blinded.

The study evaluated ledipasvir/sofosbuvir fixed-dose combination plus ribavirin in people with chronic genotype 1 or 4 HCV infection and advanced liver disease or a prior liver transplant. Cohort A comprised participants with decompensated cirrhosis and no prior liver transplant. Cohort B comprised post-liver-transplant participants, with or without cirrhosis. Group assignment within cohorts reflected liver impairment and clinical status, including Child-Pugh-Turcotte class, fibrosis, or fibrosing cholestatic hepatitis.

Within these groups, participants were randomized 1:1 to 12 or 24 weeks of treatment. Thus, the randomized treatment-duration contrast is most directly interpretable within a group. A comparison across different groups can also reflect differences in transplant status, liver impairment, and the criteria defining those groups. The study did not include a no-treatment or placebo arm.

The primary endpoint was the percentage with SVR12 after treatment discontinuation. The primary analysis set was defined as randomized participants who received at least one dose, with an additional exclusion for specified Cohort A participants who underwent liver transplantation before the lower bound of the Posttreatment Week 12 visit. Although the registry record identifies the population and endpoint, the sponsor’s detailed statistical analysis plan and original sample-size assumptions 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: * Cohort A: decompensated cirrhosis (advanced liver disease), no prior liver transplant; * Cohort B: post-liver transplant, with or without cirrhosis; * Group assignment within cohorts was based on severity of liver impairment at screening (or presence of disease for FCH groups); * Randomization was 1:1 within groups to 12 or 24 weeks of treatment.

Only the first 6 of 14 groups are shown.

Overall Study

StageCohort A, Group 1 (12 wk): CPT Class B (7-9)Cohort A, Group 1 (24 wk): CPT Class B (7-9)Cohort A, Group 2 (12 wk): CPT Class C (10-12)Cohort A, Group 2 (24 wk): CPT Class C (10-12)Cohort B, Group 3 (12 wk): F0-F3 FibrosisCohort B, Group 3 (24 wk): F0-F3 Fibrosis
STARTED302923265556
COMPLETED262618245555
NOT COMPLETED435201

Reasons for not completing this period:

ReasonCohort A, Group 1 (12 wk): CPT Class B (7-9)Cohort A, Group 1 (24 wk): CPT Class B (7-9)Cohort A, Group 2 (12 wk): CPT Class C (10-12)Cohort A, Group 2 (24 wk): CPT Class C (10-12)Cohort B, Group 3 (12 wk): F0-F3 FibrosisCohort B, Group 3 (24 wk): F0-F3 Fibrosis
Randomized but Not Treated000000
Adverse Event000000
Death122100
Investigator's Discretion001000
Lack of Efficacy311100
Lost to Follow-up001001
Withdrew Consent000000

Analysis population for the primary outcome, as defined in the registry: Full Analysis Set: participants who were randomized and received at least one dose of study drug. Participants in Cohort A who received a liver transplant prior to the lower bound of the Posttreatment Week 12 visit were not included in the analysis.

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 Analysis Set: participants who were enrolled and received at least one dose of study drug

Only the first 6 of 15 groups are shown.

CharacteristicUnitCohort A, Group 1 (12 wk): CPT Class B (7-9)Cohort A, Group 1 (24 wk): CPT Class B (7-9)Cohort A, Group 2 (12 wk): CPT Class C (10-12)Cohort A, Group 2 (24 wk): CPT Class C (10-12)Cohort B, Group 3 (12 wk): F0-F3 FibrosisCohort B, Group 3 (24 wk): F0-F3 Fibrosis
Participants analysed302923265556
Age, Continuousyears57 (SD 9.1)58 (SD 6.5)57 (SD 6.2)59 (SD 4.6)59 (SD 6.6)58 (SD 6.4)
Sex: Female, Male: FemaleParticipants811981010
Sex: Female, Male: MaleParticipants221814184546
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants432446
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants262621225150
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants000000
Race/Ethnicity, Customized: Black or African Americanparticipants132144
Race/Ethnicity, Customized: Whiteparticipants292621245049
Race/Ethnicity, Customized: Asianparticipants000000
Race/Ethnicity, Customized: American Indian/Alaska Nativeparticipants000011
Race/Ethnicity, Customized: Otherparticipants000102
Region of Enrollment: United Statesparticipants302923265556
Hepatitis C Virus (HCV) RNAlog10 IU/mL5.9 (SD 0.68)5.8 (SD 0.82)5.6 (SD 0.62)5.8 (SD 0.71)6.5 (SD 0.62)6.4 (SD 0.93)
HCV RNA Category: < 800 IU/mLparticipants141114151010
HCV RNA Category: ≥ 800 IU/mLparticipants16189114546
HCV Genotype: Genotype 1aparticipants192215184040
HCV Genotype: Genotype 1bparticipants107681416
HCV Genotype: Genotype 4participants102010
IL28b Status: CCparticipants45671110
IL28b Status: CTparticipants201813153327
IL28b Status: TTparticipants66441119

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With Sustained Virologic Response (SVR) 12 Weeks After Discontinuation of Therapy (SVR12), measured over Posttreatment Week 12.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint was the percentage of participants with sustained virologic response 12 weeks after discontinuing treatment. SVR12 was defined as HCV RNA below the lower limit of quantitation, stated as 15 IU/mL, at Posttreatment Week 12. The endpoint therefore records whether each participant met the specified virologic threshold at a defined follow-up visit; it is reported as a proportion rather than a continuous measurement.

As a general statistical explanation, a fixed-time binary endpoint can be summarized by counting participants who meet the definition and relating that count to the analysis population. This produces an interpretable percentage, but the estimate’s precision depends on how many participants contribute and how many meet the definition. It also depends on the endpoint definition and handling of participants without an evaluable result. The registry record specifies the Full Analysis Set and the Cohort A transplant exclusion, but further details about missing endpoint data and their treatment are not reported in the registry record.

SVR12 is used as a study outcome because it assesses whether the virologic threshold is met after treatment has ended, rather than only during dosing. It is not a direct measure of every aspect of liver status or other clinical outcomes. The registry also lists SVR at other posttreatment visits and virologic measures during treatment, but those do not replace the primary endpoint’s specific timing and definition.

7. Results Posted in the Registry

Risk difference: Cohort A, Group 1 (24 wk): CPT Class B (7-9)

+2.2

95% CI: -14.8 to 19.2 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals63.471.379.287.195.1103Cohort A, Group 1 (12 wk): CP… (n=30)Cohort A, Group 1 (24 wk): CP… (n=27)Cohort A, Group 2 (12 wk): CP… (n=22)Cohort A, Group 2 (24 wk): CP… (n=23)Cohort B, Group 3 (12 wk): F0… (n=55)Cohort B, Group 3 (24 wk): F0… (n=56)Cohort B, Group 4 (12 wk): CP… (n=26)Cohort B, Group 4 (24 wk): CP… (n=25)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Cohort A, Group 1 (24 wk): CP…Cohort A, Group 2 (12 wk): CP…Cohort A, Group 2 (24 wk): CP…Cohort B, Group 3 (12 wk): F0…Cohort B, Group 3 (24 wk): F0…Cohort B, Group 4 (12 wk): CP…Cohort B, Group 4 (24 wk): CP…Cohort B, Group 5 (12 wk): CP…-24-14-3.347.031728risk difference (percentage points) 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
Percentage of Participants With Virologic FailureBinary EndpointRisk difference-6.3 pts (-19.2 to 6.6)252 per arm
Percentage of Participants With HCV RNA < LLOQ at Week 1Binary EndpointRisk difference+0.2 pts (-12.6 to 13.1)187,780 per arm
Percentage of Participants With HCV RNA < LLOQ at Week 2Binary EndpointRisk difference+4.7 pts (-20.2 to 29.6)1,681 per arm

Percentage of Participants With Virologic Failure

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Cohort A, Group 1 (24 wk): CP…Cohort A, Group 2 (12 wk): CP…-21-15-8.66-2.254.1611risk difference (percentage points) vs control (95% CI)

Percentage of Participants With HCV RNA < LLOQ at Week 1

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Cohort A, Group 1 (24 wk): CP…Cohort A, Group 2 (12 wk): CP…-15-7.230.989.191726risk difference (percentage points) vs control (95% CI)

Percentage of Participants With HCV RNA < LLOQ at Week 2

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Cohort A, Group 1 (24 wk): CP…Cohort A, Group 2 (12 wk): CP…-28-16-3.369.052134risk difference (percentage points) vs control (95% CI)

The secondary outcomes cover several stages of virologic response: early HCV RNA measurements during treatment, posttreatment SVR assessments, virologic failure, and posttransplant response. This range adds context to the primary endpoint by describing whether the posted pattern is confined to SVR12 or is also represented in outcomes measured at other times. The outcomes remain distinct because their definitions and assessment times differ.

Across the secondary results, values vary among clinical groups and treatment durations. The group-specific patterns should be read in light of the different clinical profiles and analysis population sizes, rather than pooled mentally into a single overall result. In particular, early RNA measurements describe response during treatment, whereas SVR outcomes assess response after treatment has stopped. Virologic failure is a separate outcome and does not simply reverse the SVR12 measure.

The secondary endpoints can complement the primary result, but they do not replace it. A secondary pattern that appears consistent with the primary measure may add descriptive context; it does not independently confirm the primary finding. Conversely, a difference in a secondary measure need not contradict SVR12 because timing and outcome definitions differ.

Unadjusted secondary comparisons carry less weight because multiple outcomes and arm contrasts create opportunities for chance findings. The registry record does not report a multiplicity strategy or sponsor-conducted analyses for these outcomes. The recalculated comparisons therefore should be treated as exploratory descriptions, not as a collection of independent confirmatory tests. The posted secondary outcomes are best interpreted alongside the primary endpoint, clinical-group structure, and uncertainty in the small groups, without elevating an isolated unadjusted result.

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

9. Statistical Interpretation

Clinical Biostats interpretation

SVR12 percentages vary across the listed clinical groups and treatment durations. For example, the posted values range from 60.0% in Cohort B, Group 6 (12 weeks; CPT Class C) to 100.0% in both Cohort B, Group 7 FCH groups. These groups have different clinical profiles, and the FCH groups include very small analysis populations. The percentages should therefore be read as group-specific descriptions, not as a single estimate for every person represented by the study’s broad eligibility description.

The randomized assignment was between 12 and 24 weeks within groups. The posted recalculated comparisons primarily contrast the reference arm, Cohort A, Group 1 (12 weeks), with other arms. For the same Cohort A, Group 1 clinical group, the recalculated risk difference for 24 weeks versus the 12-week reference was 0.022, with a 95% confidence interval from -0.148 to 0.192 and an unadjusted p-value of 0.799. This interval includes no difference and also allows values in either direction. It is wide, so the estimate does not precisely distinguish the duration groups.

Comparisons against arms from other cohorts or severity groups combine treatment-duration differences with clinical-group differences. For instance, the reference arm and Cohort B, Group 3 have different transplant and fibrosis characteristics. Such a comparison is not equivalent to a randomized comparison of 12 versus 24 weeks in the same group. Randomization within the study groups does not make every cross-group comparison randomized.

The registry record reports no sponsor-conducted analyses for the primary endpoint. The numerical comparisons are recalculated, unadjusted contrasts from the posted arm summaries. They are useful for describing the observed data, but they are not a substitute for the sponsor’s own analysis; the registry record does not report one. No multiplicity adjustment is represented in these unadjusted results, so isolated p-values should not carry the same weight as a prespecified, fully reported analysis.

Small analysis populations, especially in some post-transplant clinical groups, make percentages sensitive to individual outcomes and limit precision. The arm-level registry results also do not include confidence intervals for each percentage. In combination, these features support a cautious reading: the results describe the observed SVR12 proportions in distinct study groups, while neither cross-group contrasts nor unadjusted statistical tests alone establish a general treatment-duration effect.

10. Statistical Methods Explained

The primary outcome is binary at the participant level: each participant either met the SVR12 definition or did not. The registry reports percentages by arm. The Full Analysis Set includes randomized participants who received at least one dose of study drug, subject to the stated Cohort A transplant exclusion. The displayed arm sizes and percentages describe that reported endpoint population; they should not be assumed to represent every person enrolled or randomized.

What does a percentage describe?

As a general explanation, a percentage is a sample estimate of the proportion meeting an outcome definition in the population represented by the analysis. A high observed percentage can coexist with substantial uncertainty when the analysis population is small. That is especially relevant when interpreting the post-transplant CPT Class C and FCH groups, whose posted analysis populations are small. An observed percentage is not, by itself, proof that the underlying proportion is known precisely.

The trial design randomized treatment duration within groups. That design supports a direct comparison of the two durations within the same group, subject to the study’s analysis methods and limitations. The posted recalculated comparisons instead use Cohort A, Group 1 (12 weeks) as the reference for multiple arms. Contrasts with arms from different clinical groups can reflect group composition as well as treatment duration. The clinical groups were defined by transplant status and liver disease characteristics, so those broader contrasts should not be interpreted as if the arms differed only in treatment duration.

How should the risk difference be read?

The recalculated comparison is expressed as a risk difference: the observed proportion in one arm minus the observed proportion in the reference arm, with the direction determined by the comparison. A value of zero represents no difference in the observed proportions. The reported 95% confidence interval describes a range of values compatible with the data under the calculation’s assumptions. If it includes zero, the data are compatible with no difference as well as with differences in either direction. The unadjusted p-value evaluates a no-difference reference under the particular calculation; it does not measure the probability that the null hypothesis is true, nor does it measure clinical importance.

These contrasts are labeled recalculated because they are simple, unadjusted calculations from the posted arm summaries. They are not presented as the trial’s own adjusted or prespecified inferential analyses. The registry record lists zero reported analyses for the primary outcome. The sponsor’s detailed statistical model, covariate adjustments, and analysis plan are not reported in the registry record. No discrepancy between the posted results and these recalculations is flagged.

Why do analysis populations and endpoint timing matter?

The primary outcome is evaluated at Posttreatment Week 12, so the endpoint concerns a specific follow-up time after treatment cessation. The Full Analysis Set definition and Cohort A transplant exclusion determine whose outcomes enter the primary result. The record does not state detailed rules for participants who missed the assessment, had an unavailable HCV RNA result, or otherwise lacked a classifiable endpoint. Such missing-data rules can affect a binary outcome estimate, particularly when the analysis population is not large.

The registry lists secondary measures at other posttreatment visits, measures of virologic failure, posttransplant virologic response, and HCV RNA below the lower limit of quantitation during treatment. These outcomes differ in timing and meaning. They provide additional descriptions, but they are not interchangeable with SVR12, and multiple tests across outcomes and arms can produce chance findings even when no true difference exists.

What does an unadjusted result leave out?

An unadjusted comparison uses the observed arm summaries without accounting for other factors or the multiple comparisons made. As a general statistical point, a prespecified analysis may use a different model or account for planned comparisons; whether this study did so cannot be determined because the detailed plan and sponsor analyses are not reported in the registry record. The recalculated estimates therefore help readers understand the posted proportions and their uncertainty, but should not be treated as a complete reconstruction of the trial’s intended analysis.

11. Confidence Intervals and Precision

A confidence interval communicates uncertainty around an estimate. In general, a narrower interval indicates greater precision, while a wider interval leaves more uncertainty about the size and direction of the underlying difference. A 95% confidence interval is a statistical procedure’s range of values compatible with the observed data and its assumptions; it is not a guarantee that the true value lies within the interval.

For the recalculated comparison of Cohort A, Group 1 at 24 weeks against the 12-week reference, the risk difference was 0.022 and the 95% confidence interval was -0.148 to 0.192. Because the interval includes zero and extends in both directions, it does not rule out either no difference or a difference favoring either arm. The unadjusted p-value was 0.799. That value should be interpreted alongside the interval and the study context, not as a standalone judgment.

Precision is particularly limited in smaller clinical groups. The FCH and post-transplant CPT Class C groups have few participants in their endpoint populations, so a small change in the observed outcomes could materially change the percentage. The registry does not provide confidence intervals around the individual arm percentages, which limits direct assessment of their precision. The recalculated comparison intervals also remain broad in several contrasts.

As a general principle, confidence intervals do not resolve design limitations. They quantify uncertainty for the specific comparison calculated, but cannot make cross-group comparisons equivalent to within-group randomization, account for unreported missing-data methods, or address multiplicity unless the analysis does so. The intervals should therefore be read as one part of the evidence, together with the small group sizes, clinical-group definitions, and absence of reported sponsor analyses.

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 effect3,4104,564
75% of the observed effect6,1808,273
50% of the observed effect14,17018,970
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00050,00040%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, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Cohort A, Group 1 (24 wk): CPT Class B (7-9).

The planning figures describe participants per arm for the binary-outcome comparisons. They are not total event counts. They are calculated as planning illustrations from the observed effect, rather than from the trial’s original design assumptions. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set at 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 participants per arm for a future study to have an 80% chance of detecting the specified effect under those assumptions, if that effect and the other assumptions hold. The 90% power column describes the corresponding planning target for a 90% chance. These are design calculations, not guarantees about what a future study will find. They do not say how likely the observed result was to occur under the actual trial design.

Rows describing 100%, 75%, or 50% of the observed effect illustrate how the planning target changes when the effect to detect is smaller than the observed estimate. Smaller effects need more participants to detect, all else equal. In some comparisons the observed effect is close to zero, which produces extremely large planning figures; this illustrates how poorly a near-zero estimate can anchor a future study’s target. Such estimates can also be unstable when they come from small groups.

These figures are not observed power. They are hypothetical planning calculations based on observed summary estimates, not a retrospective measure of how informative the completed study was. The confidence intervals and analysis populations are more useful for judging the precision of the posted results. Any interpretation of the planning values should also account for the fact that the recalculated contrasts are unadjusted and, across different clinical groups, may not represent randomized contrasts of duration alone.

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 = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

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 = 0.867; treatment proportion p1 = 0.889; average p̄ = 0.878.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4632 = 0.9079.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4629 = 0.3896.
  4. n = (0.9079 + 0.3896)2 / (0.0222)2 = 3,409.2, rounded up to 3,410 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 <- 0.866666666666667                          # control proportion
p1 <- 0.888888888888889                          # 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(1938430)
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 = 3,410 (80% power), 4,564 (90% power)
 75% of observed effect: n per arm = 6,180 (80% power), 8,273 (90% power)
 50% of observed effect: n per arm = 14,170 (80% power), 18,970 (90% power)
power.prop.test: 3409.2 
Simulated power at n = 3,410 per arm: 0.801 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The study includes a primary endpoint and numerous secondary outcome measures. When many outcomes or arm comparisons are examined, the chance of at least one apparently notable result arising by chance increases. A multiplicity strategy can address this issue by defining which tests are confirmatory, adjusting significance thresholds, or otherwise controlling interpretation. Whether the trial used such a strategy is not reported in the registry record.

The registry record lists zero reported analyses for the primary outcome and does not provide sponsor-reported inferential analyses for the listed secondary measures. The displayed recalculated comparisons are unadjusted. Their p-values therefore should not be treated as if they were adjusted for multiple comparisons or as definitive evidence on their own. The detailed statistical analysis plan, including any hierarchy among endpoints or multiplicity procedure, is not reported in the registry record.

The primary population is described as randomized participants who received at least one dose, with a specified exclusion for some Cohort A participants who received a transplant before the lower bound of the Posttreatment Week 12 visit. The registry record does not report detailed missing-data rules for participants lacking a Week 12 HCV RNA result, nor whether missing results were counted as not meeting SVR12, excluded, or handled by another method. It also does not report sensitivity analyses assessing the effect of missing outcomes.

These omissions matter because endpoint classification and analysis population can affect the estimated percentage, while multiplicity affects how much confidence to place in isolated comparisons. The available descriptions permit a clear account of the stated endpoint and analysis population, but not a full reconstruction of the prespecified analysis or its handling of missing data. This limits confirmatory interpretation of the recalculated results.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Cohort A, Group 1 (12 wk): CPT Class B (7-9)33010.0%
Cohort A, Group 1 (24 wk): CPT Class B (7-9)102934.5%
Cohort A, Group 2 (12 wk): CPT Class C (10-12)62326.1%
Cohort A, Group 2 (24 wk): CPT Class C (10-12)112642.3%
Cohort B, Group 3 (12 wk): F0-F3 Fibrosis65510.9%
Cohort B, Group 3 (24 wk): F0-F3 Fibrosis125621.4%
Cohort B, Group 4 (12 wk): CPT Class A (5-6)32611.5%
Cohort B, Group 4 (24 wk): CPT Class A (5-6)42516.0%
Cohort B, Group 5 (12 wk): CPT Class B (7-9)52619.2%
Cohort B, Group 5 (24 wk): CPT Class B (7-9)112642.3%
Cohort B, Group 6 (12 wk): CPT Class C (10-12)1520.0%
Cohort B, Group 6 (24 wk): CPT Class C (10-12)3475.0%
Cohort B, Group 7 (12 wk): FCH1425.0%
Cohort B, Group 7 (24 wk): FCH1250.0%
Participants with at least one serious adverse event
Serious adverse events by armCohort A, Group 1 (12 wk): CP…10.0%Cohort A, Group 1 (24 wk): CP…34.5%Cohort A, Group 2 (12 wk): CP…26.1%Cohort A, Group 2 (24 wk): CP…42.3%Cohort B, Group 3 (12 wk): F0…10.9%Cohort B, Group 3 (24 wk): F0…21.4%Cohort B, Group 4 (12 wk): CP…11.5%Cohort B, Group 4 (24 wk): CP…16.0%% 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 5% reporting threshold.

ArmParticipants affected of at risk
Cohort A, Group 1 (12 wk): CPT Class B (7-9)26 of 30
Cohort A, Group 1 (24 wk): CPT Class B (7-9)28 of 29
Cohort A, Group 2 (12 wk): CPT Class C (10-12)22 of 23
Cohort A, Group 2 (24 wk): CPT Class C (10-12)26 of 26
Cohort B, Group 3 (12 wk): F0-F3 Fibrosis54 of 55
Cohort B, Group 3 (24 wk): F0-F3 Fibrosis54 of 56

Most frequent serious adverse event terms

Event termOrgan systemCohort A, Group 1 (12 wk): CPT Class B (7-9)Cohort A, Group 1 (24 wk): CPT Class B (7-9)Cohort A, Group 2 (12 wk): CPT Class C (10-12)Cohort A, Group 2 (24 wk): CPT Class C (10-12)Cohort B, Group 3 (12 wk): F0-F3 FibrosisCohort B, Group 3 (24 wk): F0-F3 Fibrosis
Hepatic encephalopathyNervous system disorders3 of 300 of 292 of 232 of 260 of 550 of 56
Renal failure acuteRenal and urinary disorders0 of 301 of 290 of 232 of 261 of 552 of 56
Gastric varices haemorrhageGastrointestinal disorders0 of 304 of 290 of 230 of 260 of 550 of 56
AnaemiaBlood and lymphatic system disorders1 of 300 of 290 of 230 of 261 of 551 of 56
Abdominal painGastrointestinal disorders0 of 300 of 291 of 232 of 260 of 550 of 56
Peritonitis bacterialInfections and infestations0 of 300 of 290 of 233 of 260 of 550 of 56
SepsisInfections and infestations1 of 302 of 290 of 230 of 260 of 550 of 56
AscitesGastrointestinal disorders0 of 301 of 291 of 230 of 260 of 550 of 56
DiarrhoeaGastrointestinal disorders0 of 300 of 290 of 230 of 260 of 552 of 56
MelaenaGastrointestinal disorders0 of 301 of 290 of 231 of 260 of 550 of 56

Most frequent non-serious adverse event terms

Event termOrgan systemCohort A, Group 1 (12 wk): CPT Class B (7-9)Cohort A, Group 1 (24 wk): CPT Class B (7-9)Cohort A, Group 2 (12 wk): CPT Class C (10-12)Cohort A, Group 2 (24 wk): CPT Class C (10-12)Cohort B, Group 3 (12 wk): F0-F3 FibrosisCohort B, Group 3 (24 wk): F0-F3 Fibrosis
FatigueGeneral disorders17 of 3015 of 2913 of 2312 of 2634 of 5531 of 56
NauseaGastrointestinal disorders8 of 3011 of 299 of 2313 of 2610 of 5521 of 56
HeadacheNervous system disorders11 of 3012 of 297 of 235 of 2617 of 5519 of 56
AnaemiaBlood and lymphatic system disorders3 of 307 of 294 of 2311 of 2624 of 5518 of 56
DiarrhoeaGastrointestinal disorders5 of 307 of 298 of 238 of 269 of 5515 of 56
InsomniaPsychiatric disorders9 of 307 of 294 of 238 of 268 of 5511 of 56
DizzinessNervous system disorders4 of 306 of 293 of 237 of 266 of 5510 of 56
DyspnoeaRespiratory, thoracic and mediastinal disorders2 of 304 of 293 of 234 of 2613 of 556 of 56
CoughRespiratory, thoracic and mediastinal disorders4 of 306 of 294 of 234 of 264 of 555 of 56
IrritabilityPsychiatric disorders4 of 303 of 292 of 233 of 265 of 559 of 56

Serious events with the highest arm-level rate: dyspnoea (50.0%), cardiac failure (25.0%), cardiac failure congestive (25.0%), nausea (25.0%), generalised oedema (25.0%).

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 registry lists serious adverse events and other adverse events by treatment group, with the number at risk and the number affected. These are descriptive counts for the listed groups. They should be read separately from SVR12: the endpoint populations, follow-up definitions, and event definitions are not interchangeable. The registry does not provide a comparative statistical analysis of the adverse-event figures.

Among the serious adverse event terms listed, dyspnoea is reported at 50.0%; cardiac failure, cardiac failure congestive, nausea, generalised oedema, and pyrexia are each listed at 25.0%. The registry record does not report the denominator or further detail needed to interpret those term-specific percentages in context. Serious adverse event counts vary across groups, which also differ in clinical composition and size.

Deaths are not reported in the registry record. These adverse-event summaries do not establish whether an event was caused by treatment, and the posted figures alone do not support a direct comparison of risk between the different clinical groups.

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

The results describe SVR12 percentages among the study’s analysis groups after 12 or 24 weeks of ledipasvir/sofosbuvir plus ribavirin. They show that the observed percentages differed across groups defined by transplant status and liver disease characteristics, and that some smaller groups have very limited precision. These are findings about the participants represented in the posted outcome data under the registry’s stated endpoint definition.

The results do not show a comparison against no treatment or placebo, because every listed group received the combination regimen. Nor do the cross-group recalculated comparisons isolate treatment duration: clinical group, transplant status, liver impairment, and treatment duration can all differ across those arms. The randomized duration assignment within groups is the more relevant design feature for a duration comparison, but the registry record does not report the sponsor’s own comparative analysis.

The posted percentages do not establish that the same results would occur in a different population, nor do they describe every clinical outcome. SVR12 is a virologic endpoint at a specified follow-up visit, not a complete measure of liver health, adverse effects, or long-term outcomes. The registry’s adverse-event information is descriptive and does not establish causation.

Unadjusted recalculations and p-values are not a substitute for a prespecified analysis, especially when several outcomes and comparisons are available. Small group sizes, broad confidence intervals, unavailable arm-level confidence intervals, and unreported missing-data and multiplicity procedures further constrain interpretation. The appropriate statistical reading is therefore descriptive and cautious: the registry records the observed results, but the information does not support broad causal claims from cross-group differences or a complete assessment of uncertainty.

17. Why This Trial Matters Statistically

This study illustrates a common challenge in clinical trial interpretation: randomization can be present while not every comparison in the results is randomized in the same way. Participants were assigned to 12 or 24 weeks within clinically defined groups, but the posted recalculated comparisons use one reference arm across a range of cohorts and severity groups. Recognizing that distinction prevents a cross-group contrast from being mistaken for a clean duration effect.

It also demonstrates why percentages need context. A percentage from a small group can look definitive when stated alone, even though few participants contribute and the estimate may be imprecise. The posted SVR12 values for the smallest groups show why group size and uncertainty matter alongside the point estimate. Arm-level confidence intervals are not reported, and the registry does not include sponsor-conducted analyses for the primary endpoint.

The record also makes endpoint structure important: SVR12 is a defined posttreatment virologic measure, while early HCV RNA measures and other posttreatment outcomes answer different questions. Multiple secondary outcomes can provide a broader description, but unadjusted results across many comparisons should not be treated as independent confirmation.

For biostatisticians and clinical researchers, the case reinforces a practical lesson: begin with the trial’s allocation structure, analysis population, and endpoint definition before interpreting contrasts. Then assess precision and the completeness of the analysis record. These steps help separate what the registry directly documents from what remains uncertain.

18. Limitations

The registry’s primary analysis population excludes Cohort A participants who received a liver transplant before the lower bound of the Posttreatment Week 12 visit. This is a specific eligibility rule for the endpoint analysis, and the registry record does not report additional detail about the consequences of that exclusion or whether sensitivity analyses were performed.

Analysis populations vary considerably across the clinical groups, with especially small groups among post-transplant CPT Class C and FCH participants. Percentages from these groups are therefore sensitive to a small number of outcomes, and broad inferences from their observed values are limited. The registry does not provide confidence intervals for each arm percentage.

The design’s clinical stratification is another interpretive limitation: the groups differ by transplant status, fibrosis, or Child-Pugh-Turcotte class. Comparisons between groups are not equivalent to randomized comparisons of treatment duration alone. The registry also lacks reported sponsor analyses, the detailed statistical analysis plan, original sample-size assumptions, multiplicity procedures, and specific rules for handling missing endpoint values. These items are not reported in the registry record.

Finally, the trial was open-label and had no placebo or untreated arm. The posted results can describe outcomes under the treatment regimen and compare randomized durations within groups, but they cannot provide a randomized comparison with no treatment. The registry’s adverse-event summaries are descriptive and do not by themselves establish treatment attribution.

19. Related Tutorials

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22. Record Summary

This completed Phase 2, multicenter, open-label, randomized parallel-group study enrolled 339 participants with chronic genotype 1 or 4 HCV and advanced liver disease or a prior liver transplant. Participants within clinical groups were assigned 1:1 to 12 or 24 weeks of ledipasvir/sofosbuvir plus ribavirin.

The primary endpoint was SVR12, defined as HCV RNA below the lower limit of quantitation at Posttreatment Week 12. The registry reports group-specific percentages, but no sponsor-conducted primary analyses. Recalculated comparisons are unadjusted, and cross-group contrasts should not be treated as randomized duration comparisons.

Small clinical groups, unreported missing-data and multiplicity procedures, and limited precision constrain interpretation. The results are best read as descriptive observations within the registry’s defined analysis populations.

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