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Chronic Hepatitis C Virus Phase 3 Binary Endpoint NCT01768286

Safety and Efficacy of Ledipasvir/Sofosbuvir Fixed-Dose Combination ± Ribavirin in Treatment-Experienced Subjects With Genotype 1 HCV Infection: Complete Statistical Analysis

This analysis examines a randomized, open-label phase 3 trial of ledipasvir/sofosbuvir, with or without ribavirin, given for 12 or 24 weeks to treatment-experienced participants with chronic genotype 1 HCV infection. It focuses on sustained virologic response 12 weeks after treatment and the precision, interpretation, and limitations of the posted results.

Trial start: 2013-01  ·  Enrollment: 441  ·  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 Safety and Efficacy of Ledipasvir/Sofosbuvir Fixed-Dose Combination ± Ribavirin in Treatment-Experienced Subjects With Genotype 1 HCV Infection (NCT01768286), a randomized phase 3 study. The primary outcome is Percentage of Participants With Sustained Virologic Response (SVR) 12 Weeks After Discontinuation of Therapy (SVR12).

441
Enrollment
Phase 3
4
Arms
In the primary outcome
+2.8 pts
Risk difference
LDV/SOF+RBV 12 Weeks
-2.9 to 8.6 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01768286
PhasePhase 3
ConditionChronic Hepatitis C Virus
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment441
Arms in the primary outcome4
Lead sponsorGilead Sciences
Results postedYes

2. Clinical Question

Population

Treatment-experienced participants with chronic genotype 1 hepatitis C virus infection. The primary endpoint population was the Full Analysis Set: participants who were randomized and received at least one dose of study drug.

Intervention

Ledipasvir/sofosbuvir fixed-dose combination, administered for 12 or 24 weeks, either alone or with ribavirin.

Comparator

The registry lists four treatment groups: ledipasvir/sofosbuvir for 12 weeks, the same combination plus ribavirin for 12 weeks, ledipasvir/sofosbuvir for 24 weeks, and the same combination plus ribavirin for 24 weeks. The recalculated comparisons use ledipasvir/sofosbuvir for 12 weeks as the reference group.

Primary question

What percentage of participants in each group had a sustained virologic response 12 weeks after stopping study treatment? The registry also reports comparisons of each other group with the 12-week ledipasvir/sofosbuvir group. The study was intended to investigate safety, tolerability, and antiviral efficacy across treatment duration and use of ribavirin; the posted endpoint results address response, not every aspect of that broader purpose.

The central statistical distinction is between response within each treatment group and differences between groups. A high response percentage in a group describes what was observed there. It does not, by itself, establish that the group had a higher response than another group. Comparisons need to account for the uncertainty around both groups’ results, and the registry’s sponsor analyses and the simple recalculations have different roles in interpreting that uncertainty.

3. Trial Design

This was a phase 3, multicenter, randomized, open-label study with a parallel-group design. The registry reports enrollment of 441 and a completed status. The study start is recorded as 2013-01 and primary completion as 2013-11. Gilead Sciences is listed as the sponsor.

Participants were assigned to one of four regimens: ledipasvir/sofosbuvir fixed-dose combination for 12 weeks; that combination plus ribavirin for 12 weeks; the combination for 24 weeks; or the combination plus ribavirin for 24 weeks. The posted primary endpoint group sizes were 109, 111, 109, and 111, respectively. These are the group-specific figures; they should not be added to construct a different analysis population.

Randomization supports a comparative design, while the parallel structure means each group followed its assigned regimen rather than switching between regimens as part of the stated design. The study was unmasked: the registry lists masking as none. Open-label conduct can matter when outcomes involve judgment or participant reporting, although the primary endpoint is a laboratory-defined virologic response. The registry record does not report further details about allocation procedures, concealment, stratification, or the rationale for the selected treatment durations.

The primary endpoint was assessed after treatment ended, at posttreatment week 12. The Full Analysis Set included participants who were randomized and received at least one dose of study drug. The trial’s original sample-size assumptions and statistical design calculations are not reported in the registry record. Planning illustrations based on observed effects are separate from those original design decisions.

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: 551 participants were screened.

Overall Study

StageLDV/SOF 12 WeeksLDV/SOF+RBV 12 WeeksLDV/SOF 24 WeeksLDV/SOF+RBV 24 Weeks
STARTED109111110111
COMPLETED102107108110
NOT COMPLETED7421

Reasons for not completing this period:

ReasonLDV/SOF 12 WeeksLDV/SOF+RBV 12 WeeksLDV/SOF 24 WeeksLDV/SOF+RBV 24 Weeks
Randomized But Not Treated0010
Lack of Efficacy7401
Withdrew Consent0010

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.

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 were randomized and received at least one dose of study drug. Participants failed a previous HCV treatment regimen consisting of pegylated interferon alfa-2a (Pegasys) or pegylated interferon alfa-2b (Pegintron) plus ribavirin (RBV), with or without a protease inhibitor (PI).

CharacteristicUnitLDV/SOF 12 WeeksLDV/SOF+RBV 12 WeeksLDV/SOF 24 WeeksLDV/SOF+RBV 24 WeeksTotal
Participants analysed109111109111440
Age, Continuousyears56 (SD 6.9)57 (SD 8.0)56 (SD 8.3)55 (SD 7.8)56 (SD 7.8)
Sex: Female, Male: FemaleParticipants35403543153
Sex: Female, Male: MaleParticipants74717468287
Race/Ethnicity, Customized: Black or African Americanparticipants2416172077
Race/Ethnicity, Customized: Whiteparticipants84949189358
Race/Ethnicity, Customized: Asianparticipants10001
Race/Ethnicity, Customized: Hawaiian or Pacific Islanderparticipants01012
Race/Ethnicity, Customized: Otherparticipants00112
Race/Ethnicity, Customized: Hispanic/Latinoparticipants712111141
Race/Ethnicity, Customized: Not Hispanic or Latinoparticipants100999899396
Race/Ethnicity, Customized: Not Disclosedparticipants20013
HCV RNAlog10 IU/mL6.5 (SD 0.44)6.4 (SD 0.54)6.4 (SD 0.57)6.5 (SD 0.60)6.5 (SD 0.54)
HCV RNA Category: < 800,000 IU/mLparticipants613161550
HCV RNA Category: ≥ 800,000 IU/mLparticipants103989396390
HCV Genotype: Genotype 1aparticipants86888588347
HCV Genotype: Genotype 1bparticipants2323242393
IL28b Status: CCparticipants1011161855
IL28b Status: CTparticipants70776868283
IL28b Status: TTparticipants29232525102
Prior HCV Treatment: PEG-IFN-alfa-2a or PEG-IFN-alfa-2b+RBVparticipants43475859207
Prior HCV Treatment: PI+PEG-IFN-alfa-2a or PEG-IFN-alfa-2b+RBVparticipants66645051231
Prior HCV Treatment: IFN-alfa-2b+RBVparticipants00112

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 is the percentage of participants with sustained virologic response 12 weeks after discontinuation of therapy, abbreviated SVR12. The registry defines this response as HCV RNA below the lower limit of quantitation, or LLOQ, 12 weeks following the last dose of study drug. It identifies the LLOQ as 25 IU/mL. The endpoint is therefore a binary classification for each participant at a specified posttreatment assessment: the participant either met the stated viral RNA criterion or did not.

A posttreatment response endpoint is used to assess whether the virologic response is maintained after treatment has stopped, rather than only measuring viral RNA while treatment is being taken. That general statistical interpretation explains why timing and the threshold definition matter. It does not, on its own, say anything about symptoms, long-term health outcomes, or outcomes beyond those assessed in the trial.

The registry reports percentages for each randomized treatment group and sponsor-reported binomial tests. The Full Analysis Set is defined as randomized participants who received at least one dose of study drug. The registry record does not report a confidence interval for each group’s primary percentage in the listed endpoint results. Thus the group percentages describe the posted response proportions, while the simple pairwise recalculations add estimates of between-group differences and their uncertainty.

7. Results Posted in the Registry

Risk difference: LDV/SOF+RBV 12 Weeks

+2.8

95% CI: -2.9 to 8.6 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals86.189.192.195.198.1101LDV/SOF 12 Weeks (n=109)LDV/SOF+RBV 12 Weeks (n=111)LDV/SOF 24 Weeks (n=109)LDV/SOF+RBV 24 Weeks (n=111)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)LDV/SOF+RBV 12 WeeksLDV/SOF 24 WeeksLDV/SOF+RBV 24 Weeks-4.01-0.912.205.318.4112risk 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 HCV RNA < LLOQ at Week 1Binary EndpointRisk difference+6.7 pts (-5.3 to 18.8)727 per arm
Percentage of Participants With HCV RNA < LLOQ at Week 2Binary EndpointRisk difference+1.2 pts (-8.9 to 11.3)15,099 per arm
Percentage of Participants With HCV RNA < LLOQ at Week 4Binary EndpointRisk difference-0.9 pts (-2.7 to 0.9)n/a

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)LDV/SOF+RBV 12 WeeksLDV/SOF 24 Weeks-21-12-3.644.811322risk 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)LDV/SOF+RBV 12 WeeksLDV/SOF 24 Weeks-12-6.99-1.983.038.0413risk difference (percentage points) vs control (95% CI)

Percentage of Participants With HCV RNA < LLOQ at Week 4

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)LDV/SOF+RBV 12 WeeksLDV/SOF 24 Weeks-2.99-2.16-1.33-0.500.331.16risk difference (percentage points) vs control (95% CI)

The registry names secondary outcomes that include SVR at 4 and 24 weeks after treatment, HCV RNA below LLOQ at several treatment weeks, and change from baseline in HCV RNA. The numerical secondary results described in the registry record include HCV RNA below LLOQ at week 1, week 2, and week 4. These are early on-treatment measures and address a different time point and aspect of response than SVR12, which is assessed after treatment has ended.

Across the early viral RNA outcomes, the overall pattern is that the percentages vary by assessment week and are generally high by week 4. The group percentages at weeks 1 and 2 are less uniformly close together than those at week 4. This broad pattern supplies context about early viral response, but it cannot establish whether differences in early response predict or explain the primary posttreatment outcome. The registry record does not report a formal analysis connecting these secondary outcomes to SVR12.

For the reported early outcomes, the simple recalculated comparisons are unadjusted. Secondary outcomes often involve multiple endpoints, assessment times, and group contrasts. If many hypotheses are tested, the chance of at least one apparently notable result can increase. General statistical principle: multiplicity procedures or a prespecified hierarchy can help control that risk, but the registry record does not report such a procedure for these outcomes. Therefore unadjusted secondary p-values, where shown, carry less weight than a clearly specified primary analysis and should be treated as exploratory rather than definitive.

The registry lists additional secondary outcomes, but not every listed outcome has numerical results described in the record. Results for those outcomes are not reported in the registry record. Their absence from the available numerical results cannot be treated as evidence of either a favorable or unfavorable finding. The secondary outcomes add breadth to the study’s assessment, but they do not replace the primary endpoint or resolve the discrepancy between the sponsor analyses and the simple recalculations.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For SVR12, the posted percentages were 93.6% with ledipasvir/sofosbuvir for 12 weeks, 96.4% with that regimen plus ribavirin for 12 weeks, 99.1% with ledipasvir/sofosbuvir for 24 weeks, and 99.1% with the 24-week regimen plus ribavirin. These figures describe the results in each treatment group. They do not, on their own, establish the size or certainty of a treatment-group difference.

The simple unadjusted recalculations compare each alternative group with ledipasvir/sofosbuvir for 12 weeks. For the 12-week ribavirin comparison, the estimated risk difference is 0.028, with a confidence interval from -0.029 to 0.086 and an unadjusted p-value of 0.338. The interval includes no difference and also allows for differences in either direction. For the ledipasvir/sofosbuvir 24-week comparison, the risk difference is 0.055, with an interval from 0.006 to 0.104 and an unadjusted p-value of 0.031. For the 24-week regimen plus ribavirin, the difference is 0.055, with an interval from 0.006 to 0.104 and an unadjusted p-value of 0.029.

These are unadjusted recalculations from posted summary statistics, not a substitute for the sponsor’s analysis. The registry marks a discrepancy between the recalculations and sponsor results; accordingly, the sponsor’s own analysis takes precedence. The sponsor reported binomial tests for each treatment group, each with p < 0.001. The registry record does not state the null hypothesis or comparison for those tests, so these values should not be treated as direct evidence for a particular pairwise contrast.

Overall, the observed group percentages are high, and the recalculated comparisons suggest little evidence of a clear difference for the 12-week ribavirin comparison, while the two 24-week comparisons have intervals above zero in these simple analyses. That description is limited to the recalculations and their stated uncertainty. The discrepancy, unadjusted nature of the comparisons, and absence of a reported multiplicity procedure mean the recalculated p-values should not be read as definitive sponsor conclusions.

10. Statistical Methods Explained

Several statistical ideas help distinguish the observed response percentages from evidence about differences among treatment groups. The primary outcome is binary: each participant’s SVR12 status is determined using the stated HCV RNA threshold and assessment time. A group percentage expresses the proportion meeting that definition. Comparing percentages across groups is a separate question from testing whether the percentage in any one group differs from a hypothesized benchmark.

What does a risk difference describe?

A risk difference is the response proportion in one group minus the response proportion in the reference group. It is expressed on the proportion scale, so zero corresponds to no difference between the two group proportions. A positive estimate means the first named group’s observed proportion is higher; a negative estimate means it is lower. The recalculated risk differences for this primary outcome are 0.028 for the 12-week ribavirin group, 0.055 for ledipasvir/sofosbuvir for 24 weeks, and 0.055 for the 24-week regimen with ribavirin, each compared with ledipasvir/sofosbuvir for 12 weeks.

Those estimates are unadjusted comparisons derived from the posted group summaries. They do not account for any covariates or other features beyond the simple comparison described. The registry record does not report whether the sponsor used an adjusted analysis for these group contrasts, and it does not identify a sponsor pairwise comparison matching each recalculation.

How should the confidence intervals be read?

A confidence interval describes the range of effect values reasonably compatible with the observed data under the method used. It communicates uncertainty around an estimate; it is not a guarantee that the true value lies in the interval, nor does it measure the probability that the estimate is correct. For the recalculated primary comparisons, an interval that crosses zero is compatible with no difference as well as with differences in either direction. An interval entirely above zero is compatible with a positive difference under the calculation used. Neither pattern resolves the discrepancy with the sponsor’s analysis or the issue of multiple comparisons.

What do the p-values represent?

A p-value measures how surprising data at least as incompatible with a specified null hypothesis would be, if that null hypothesis and the model assumptions held. It does not measure the size or clinical importance of an effect, and it is not the probability that the null hypothesis is true. The recalculated p-values are labelled unadjusted. The sponsor’s posted primary analyses are described as binomial tests with p < 0.001 in every group. Because the registry record does not specify the tests’ null hypothesis, the sponsor p-values cannot be assumed to be tests of the recalculated pairwise risk differences.

The endpoint percentages and the recalculated comparisons also have different denominators in some comparisons because the posted group sizes differ. Each comparison uses the reported group-specific summary. It would be inappropriate to infer additional participant outcomes or analysis details by reconstructing counts from rounded percentages.

Why does the analysis method matter?

A binomial test is a method for evaluating a binary outcome against a stated reference probability or hypothesis. The registry identifies the sponsor’s method but does not provide the reference value or more detailed test specification. By contrast, the posted recalculated comparisons use a risk difference and an unadjusted confidence interval and p-value. These approaches answer different questions unless their hypotheses and estimands match, and that match is not documented in the registry record.

General statistical principle: when outcomes are binary, the observed proportion is subject to sampling uncertainty. The amount of uncertainty depends in part on the number of observations and on how close the probability is to the extremes of the scale. Near a boundary, differences in proportions and relative measures can behave differently, and standard approximations warrant particular care. The recalculations are simple, unadjusted illustrations; their details should not be confused with the sponsor’s full analysis plan, which is not reported in the registry record.

Finally, randomization is a design feature that supports fair group comparisons, but it does not eliminate sampling uncertainty, missing-data concerns, or multiplicity. Interpretation still depends on the endpoint definition, the population analyzed, the analysis method, and the completeness of reporting. Those details are not all available for this trial in the registry record.

11. Confidence Intervals and Precision

The posted primary group percentages are 93.6%, 96.4%, 99.1%, and 99.1%. They are descriptive estimates from the four groups, not exact population values. The registry record does not report confidence intervals around those individual percentages in the listed primary results, so their precision cannot be judged from the percentages alone.

The recalculated pairwise risk differences have intervals of -0.029 to 0.086 for the 12-week regimen with ribavirin, 0.006 to 0.104 for ledipasvir/sofosbuvir for 24 weeks, and 0.006 to 0.104 for the 24-week regimen with ribavirin. These ranges show that the estimates are uncertain. The first includes zero; the latter two are entirely above zero in the unadjusted recalculations. Their proximity to the boundary and their breadth matter: a point estimate alone gives an incomplete account of the evidence.

A confidence interval is not a measure of clinical importance. The registry record does not report a threshold for a clinically important difference, so statistical compatibility with a positive difference should not be translated into a claim about clinical value. Also, the reported recalculated intervals do not resolve the discrepancy with sponsor analyses. The sponsor’s own analysis takes precedence for interpretation when the registry flags that discrepancy.

Precision is also affected by the fact that response percentages are close to the upper end of the percentage scale. General statistical principle: when an outcome is near a boundary, there may be less room for observed increases, and estimates can be sensitive to a small number of outcome changes. This context makes interval-based interpretation especially important. It does not justify extrapolating to unobserved participants or outcomes.

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 effect9401,258
75% of the observed effect1,7832,386
50% of the observed effect4,2605,703
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00010,00040%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: LDV/SOF+RBV 12 Weeks.

The planning estimates are participants per arm, not totals across the two comparison groups. They are planning illustrations computed from the observed effect, not the trial’s own original design assumptions. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect.

The 80% power column describes the number of participants per arm estimated to give an 80% chance of detecting the specified effect under those planning assumptions, if the assumed effect and model are appropriate. The 90% power column gives the corresponding planning estimate for a 90% chance. Greater planned power generally requires more participants for the same effect. Smaller target effects require more participants because they are harder to distinguish from random variation.

For the primary comparison of ledipasvir/sofosbuvir plus ribavirin for 12 weeks against ledipasvir/sofosbuvir for 12 weeks, the estimates are 940 participants per arm for 80% power and 1,258 for 90% power when planning for 100% of the observed effect. Planning for 75% of that effect gives 1,783 and 2,386 participants per arm; planning for 50% gives 4,260 and 5,703. For the 24-week comparisons, the corresponding estimates are listed separately for each contrast and effect assumption in the planning display.

These figures are planning illustrations, not observed power. They do not show that the completed study had a particular probability of success, and they are not a retrospective justification for its enrollment. The original trial’s design assumptions, including its own sample-size justification, are not reported in the registry record.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = [ 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 = 0.936; treatment proportion p1 = 0.964; average p̄ = 0.950.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.3086 = 0.6048.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.3080 = 0.2592.
  4. n = (0.6048 + 0.2592)2 / (0.0282)2 = 939.8, rounded up to 940 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 <- 0.935779816513762                          # control proportion
p1 <- 0.963963963963964                          # 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(1768286)
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 = 940 (80% power), 1,258 (90% power)
 75% of observed effect: n per arm = 1,783 (80% power), 2,386 (90% power)
 50% of observed effect: n per arm = 4,260 (80% power), 5,703 (90% power)
power.prop.test: 939.8 
Simulated power at n = 940 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.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Binomial testnot reported< 0.001
Binomial testnot reported< 0.001
Binomial testnot reported< 0.001
Binomial testnot reported< 0.001
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The sponsor-reported primary analyses use binomial tests. The registry lists p < 0.001 for each of the four treatment groups. It does not provide a test statistic, confidence interval, reference probability, or a clear description of the null hypothesis for these tests. The listed results therefore should be reported as sponsor analyses for each group, without recasting them as direct tests of differences between groups.

The simple recalculations answer a different, explicitly pairwise question: how the observed response proportion in each of three groups compares with the ledipasvir/sofosbuvir 12-week reference group. They report risk differences, confidence intervals, and unadjusted p-values. The registry marks a discrepancy between these recalculations and sponsor results. Under that circumstance, the sponsor’s own analysis takes precedence; the recalculations remain secondary illustrations based on posted summary statistics, not corrections to or replacements for the sponsor analysis.

The available information does not establish why the results differ. The registry record does not report enough detail to reconcile the test hypotheses, analysis specifications, or any other source of discrepancy. It is therefore most accurate to keep the two kinds of results distinct: describe the sponsor’s binomial-test findings as reported, and label the pairwise risk-difference results as simple unadjusted recalculations. Neither should be assigned a hypothesis or interpretation not documented in the record.

15. Multiplicity, Missing Data and Analysis Populations

The primary endpoint is identified, but the registry record does not report a full statistical analysis plan, a testing hierarchy, or a multiplicity adjustment. It also does not state whether interim analyses were planned or conducted. These details matter because several treatment groups and secondary outcomes create opportunities for multiple statistical tests. Without a reported strategy, unadjusted p-values should not be interpreted as if they were protected from multiplicity.

The primary analysis population is specified as the Full Analysis Set: participants who were randomized and received at least one dose of study drug. The registry record does not describe how missing SVR12 assessments were handled, how participants with unavailable measurements were classified, or whether sensitivity analyses were performed. These omissions limit assessment of how missing outcome data might affect the reported group percentages.

The record also does not report a detailed account of protocol deviations, withdrawals, adherence, or reasons for missing assessments. Such information can help readers judge whether the analyzed participants and observed outcomes remain comparable across randomized groups. The record’s Full Analysis Set definition is useful, but it does not by itself answer these questions.

The study was open-label, and the primary endpoint is laboratory-defined. The objective threshold reduces reliance on subjective judgment in classifying the primary outcome, but open-label design does not eliminate all possible influences on study conduct or outcome availability. The registry record does not provide enough detail to evaluate those influences fully.

Finally, the record identifies sponsor binomial tests but does not state their null hypotheses or provide the broader analysis specifications. It also flags a discrepancy with recalculations. Taken together, the missing analysis-plan details, multiplicity information, and missing-data methods prevent a complete independent reconstruction of the inferential approach. They do not establish that the analyses were inappropriate; they limit what can be concluded from the registry record alone.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
LDV/SOF 12 Weeks01090.0%
LDV/SOF+RBV 12 Weeks01110.0%
LDV/SOF 24 Weeks61095.5%
LDV/SOF+RBV 24 Weeks31112.7%
Participants with at least one serious adverse event
Serious adverse events by armLDV/SOF 12 Weeks0.0%LDV/SOF+RBV 12 Weeks0.0%LDV/SOF 24 Weeks5.5%LDV/SOF+RBV 24 Weeks2.7%% 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
LDV/SOF 12 Weeks73 of 109
LDV/SOF+RBV 12 Weeks96 of 111
LDV/SOF 24 Weeks87 of 109
LDV/SOF+RBV 24 Weeks100 of 111

Most frequent serious adverse event terms

Event termOrgan systemLDV/SOF 12 WeeksLDV/SOF+RBV 12 WeeksLDV/SOF 24 WeeksLDV/SOF+RBV 24 Weeks
Angina unstableCardiac disorders0 of 1090 of 1111 of 1090 of 111
Upper gastrointestinal haemorrhageGastrointestinal disorders0 of 1090 of 1111 of 1090 of 111
Non-cardiac chest painGeneral disorders0 of 1090 of 1111 of 1090 of 111
Cholecystitis acuteHepatobiliary disorders0 of 1090 of 1110 of 1091 of 111
Wound infectionInfections and infestations0 of 1090 of 1110 of 1091 of 111
Intervertebral disc protrusionMusculoskeletal and connective tissue disorders0 of 1090 of 1111 of 1090 of 111
SpondylolisthesisMusculoskeletal and connective tissue disorders0 of 1090 of 1111 of 1090 of 111
ConvulsionNervous system disorders0 of 1090 of 1111 of 1090 of 111
Hepatic encephalopathyNervous system disorders0 of 1090 of 1111 of 1090 of 111
Vaginal prolapseReproductive system and breast disorders0 of 1090 of 1110 of 1091 of 111

Most frequent non-serious adverse event terms

Event termOrgan systemLDV/SOF 12 WeeksLDV/SOF+RBV 12 WeeksLDV/SOF 24 WeeksLDV/SOF+RBV 24 Weeks
FatigueGeneral disorders23 of 10945 of 11126 of 10950 of 111
HeadacheNervous system disorders28 of 10926 of 11125 of 10935 of 111
NauseaGastrointestinal disorders13 of 10920 of 1117 of 10925 of 111
InsomniaPsychiatric disorders10 of 10918 of 1114 of 10919 of 111
ArthralgiaMusculoskeletal and connective tissue disorders7 of 10913 of 1117 of 10917 of 111
CoughRespiratory, thoracic and mediastinal disorders5 of 10916 of 1115 of 10916 of 111
DiarrhoeaGastrointestinal disorders7 of 1095 of 1119 of 10917 of 111
RashSkin and subcutaneous tissue disorders2 of 10911 of 1116 of 10916 of 111
IrritabilityGeneral disorders2 of 10913 of 1114 of 10912 of 111
DizzinessNervous system disorders3 of 1098 of 1117 of 10912 of 111

Serious events with the highest arm-level rate: angina unstable (0.9%), upper gastrointestinal haemorrhage (0.9%), non-cardiac chest pain (0.9%), intervertebral disc protrusion (0.9%), spondylolisthesis (0.9%).

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 reports serious adverse events for each treatment group. There were no serious adverse events reported in the 12-week groups; the 24-week ledipasvir/sofosbuvir group had 6 affected participants, and the 24-week group with ribavirin had 3. The corresponding groups at risk were 109, 111, 109, and 111. These are group-level counts and denominators as recorded; they describe serious-event reporting, not a causal comparison between regimens.

The registry also reports other adverse events affecting 73 participants in the 12-week ledipasvir/sofosbuvir group, 96 in the 12-week group with ribavirin, 87 in the 24-week ledipasvir/sofosbuvir group, and 100 in the 24-week group with ribavirin. These figures are distinct from the serious adverse event counts and should not be combined with them. The registry lists several serious-event terms at 0.9% each, including unstable angina, upper gastrointestinal haemorrhage, non-cardiac chest pain, intervertebral disc protrusion, spondylolisthesis, and convulsion.

Deaths are not reported in the registry record. The summary does not provide enough information about event timing, exposure, relatedness, or statistical comparisons to assess differences in safety between groups. Counts should be read as descriptive reporting, not as proof that a regimen caused or prevented an event.

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

The posted primary results describe the proportions of participants meeting the registry’s SVR12 definition in each of four randomized treatment groups. They show high response percentages in all groups, ranging from 93.6% to 99.1%. The registry’s sponsor-reported binomial tests are listed as p < 0.001 for every group, but the record does not state the null hypothesis for those tests. They should not be presented as tests that one regimen outperformed another.

The simple recalculations estimate pairwise risk differences against ledipasvir/sofosbuvir for 12 weeks. Two recalculated intervals lie above zero, while one crosses zero. These comparisons are unadjusted, and the registry marks a discrepancy between them and the sponsor’s analysis. The sponsor’s own analysis therefore takes precedence. The recalculations can help illustrate uncertainty in simple group contrasts, but they do not replace the sponsor results or establish a definitive comparative conclusion.

These results do not show that any treatment works or does not work in a broader clinical sense. They concern a specified endpoint, population, and follow-up time in this trial. They do not establish effects in people outside the study population, long-term outcomes beyond those measured, or differences in outcomes not reported in the registry record. The record also does not provide a clinical-importance threshold for interpreting the size of the recalculated differences.

Statistical significance and clinical importance are different concepts. A p-value does not quantify the importance of an effect, and a confidence interval does not by itself identify which effect sizes matter to patients or clinicians. Interpretation should keep the endpoint definition, analysis population, uncertainty, discrepancy, and missing reporting details in view rather than relying on the response percentages alone.

18. Why This Trial Matters Statistically

This trial is statistically informative because it places treatment duration and use of ribavirin into a randomized, parallel-group comparison. The four-group structure lets readers examine the posted SVR12 percentages across regimens rather than relying on a single treatment arm. The primary endpoint is also defined with a specific posttreatment time point and laboratory threshold, allowing its meaning to be distinguished from an on-treatment viral RNA measurement.

The record illustrates why group-level response rates and between-group contrasts must not be conflated. The sponsor reported binomial tests for each group, while the simple recalculations compare each alternative group with the 12-week ledipasvir/sofosbuvir group. Those analyses need not answer the same statistical question. The recorded discrepancy makes transparent labeling especially important: sponsor results remain primary for interpretation, and recalculated estimates are useful only as unadjusted illustrations.

It also demonstrates the role of uncertainty intervals. Point estimates alone can make small differences appear conclusive, but intervals show how much uncertainty accompanies them. In this setting, the recalculated intervals differ in whether they include zero, while the record’s incomplete multiplicity and analysis-plan reporting limits the weight that should be placed on unadjusted comparisons.

Finally, the trial highlights the difference between planning calculations and the study’s original design. Planning estimates based on observed effects can illustrate how sample requirements change when targeting smaller effects, but they are not evidence of observed power and do not reveal the assumptions used when the trial was designed. Keeping these statistical distinctions clear helps prevent overinterpretation of the posted data.

19. Limitations

The registry record gives a focused description of the primary endpoint and group results but does not report participant characteristics in detail. It therefore does not allow assessment of how results varied across baseline subgroups or how representative the enrolled population was beyond the stated treatment-experienced, chronic genotype 1 HCV population.

The study was open-label. Although the primary endpoint uses a laboratory threshold, the record does not provide details sufficient to assess whether knowledge of assigned treatment affected follow-up, adherence, reporting, or availability of endpoint measurements. Information on allocation concealment and other randomization procedures is also not reported in the registry record.

The sponsor’s primary analyses are described as binomial tests, but the record does not state the null hypothesis or provide detailed test specifications. It also flags a discrepancy with the simple recalculations. This prevents a direct reconciliation of the sponsor’s reported results with pairwise estimates. The recalculated confidence intervals and p-values are unadjusted, and the record does not report a multiplicity strategy.

Missing-data handling, sensitivity analyses, interim analyses, and the trial’s original sample-size justification are not reported in the registry record. The posted group percentages consequently cannot answer how alternative missing-outcome assumptions would affect the results. The primary endpoint results also do not supply confidence intervals for the individual group percentages.

For safety, the registry provides adverse-event counts and selected serious-event terms, but not a full account of timing, duration, relatedness, or a comparative analysis. Deaths are not reported in the registry record. These limitations do not negate the posted findings; they define the questions the registry record can and cannot address.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT01768286 is a completed, randomized, open-label, parallel-group phase 3 study sponsored by Gilead Sciences. It evaluated ledipasvir/sofosbuvir, with or without ribavirin, administered for 12 or 24 weeks in treatment-experienced participants with chronic genotype 1 HCV infection. The registry reports enrollment of 441.

The primary endpoint was SVR12, defined by HCV RNA below the LLOQ 12 weeks after the last dose. The four posted group percentages range from 93.6% to 99.1%. Sponsor-reported binomial tests are listed as p < 0.001 for each group, but their null hypothesis is not specified. Simple unadjusted recalculations compare three groups with the 12-week ledipasvir/sofosbuvir group; the registry flags a discrepancy, so the sponsor’s analysis takes precedence.

The record also includes early viral RNA outcomes and descriptive adverse-event counts. Details about multiplicity, missing-data handling, the original sample-size rationale, and several analysis specifications are not reported in the registry record.

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