LIVE-C-Free: Early and Late Treatment of Hepatitis C With Sofosbuvir/Ledipasvir in Liver Transplant Recipients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for LIVE-C-Free: Early and Late Treatment of Hepatitis C With Sofosbuvir/Ledipasvir in Liver Transplant Recipients (NCT02631772), a randomized phase 4 study. The primary outcome is Treatment Efficacy.

2. Clinical Question

3. Trial Design

The registry record identifies LIVE-C-Free as a Phase 4, randomized, open-label, parallel-group study of sofosbuvir/ledipasvir treatment in liver transplant recipients with hepatitis C. The study is listed as completed. The record gives a start date of 2016-06-01 and a primary completion date of 2018-05-30. Enrollment is listed as 32.

The posted primary outcome compares two arms in the late cohort. Late Cohort, Arm 1 received ledipasvir and sofosbuvir without ribavirin for 12 weeks; Late Cohort, Arm 2 received ledipasvir and sofosbuvir with ribavirin for 12 weeks. Each arm has 16 participants in the posted outcome data. The registry record describes the study as multicenter, prospective, randomized, and open-label. Further details about how randomization was carried out, including the allocation method and any stratification, are not reported in the registry record. Masking is listed as none.

The endpoint timeframe is described as 12 weeks, and the endpoint definition specifies SVR12 12 weeks after completion of the antiviral regimen. The registry record lists two secondary outcomes: number of participants with virologic failure and hemoglobin levels. It lists three outcome measures in total, while the posted record indicates that no analyses are listed. The original sample-size justification, the planned statistical analysis, and any interim analysis details are not reported in the registry record. The sample-size illustrations associated with the observed comparison are not the trial's original design calculations.

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.

Overall Study

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.

6. Primary Endpoint

The registry lists the primary outcome as Treatment Efficacy, measured over 12 Weeks.

The primary endpoint is treatment efficacy, defined in the registry record as the percentage of participants achieving sustained virologic response 12 weeks after completing the antiviral regimen. In this context, the endpoint records whether each participant achieved the specified virologic response at the stated follow-up time. The posted values are percentages of participants, rather than a continuous measurement such as a laboratory value.

SVR12 is used as a treatment-response endpoint in this trial because the registry record identifies it as the primary measure of antiviral treatment efficacy. It allows the outcomes of the two assigned regimens to be described on the same binary basis: each participant either met the endpoint definition or did not. A percentage then expresses how common endpoint achievement was within each arm. This endpoint alone does not describe every aspect of treatment experience, including virologic failure details, hemoglobin levels, or adverse events; the registry record lists some of these as secondary outcomes or safety information.

The posted results give 88.0% for Late Cohort, Arm 1 and 75.0% for Late Cohort, Arm 2. The associated participant counts are 14 of 16 and 12 of 16, respectively. The registry record does not report further operational details of endpoint assessment, such as how missing or indeterminate endpoint results were handled.

7. Results Posted in the Registry

• Late Cohort, Arm 2: 75.0% (12/16) versus 87.5% (14/16) on control; risk difference -12.5 percentage points (95% CI -39.2 to 14.2), risk ratio 0.86 (0.61–1.20); unadjusted two-proportion z-test p = 0.365.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary: for each participant, SVR12 was either achieved or not achieved according to the registry definition. A binary outcome can be summarized as the number meeting the definition and the percentage within each arm. The posted results give 14 of 16 participants and 88.0% for Late Cohort, Arm 1, and 12 of 16 participants and 75.0% for Late Cohort, Arm 2. Reporting the counts alongside percentages is useful because it makes the small arm sizes visible and clarifies how the percentages arise.

The arm comparison is expressed as a risk difference. In general, a risk difference subtracts the proportion with an outcome in one group from the proportion in another. For this result, the comparison is Arm 2 relative to Arm 1, giving an estimate of -0.125. A value below zero means the observed proportion with SVR12 was lower in Arm 2 than in Arm 1; it is not itself a measure of statistical certainty. The confidence interval describes uncertainty in the estimated difference, while the p-value summarizes how compatible the observed data are with a specified null comparison under the analysis used. Neither quantity answers every clinical or design question.

The posted confidence interval for the risk difference extends from -0.392 to 0.142. In general, a confidence interval gives a range of values consistent with the data and the method used to construct it, at the stated confidence level. It is not a guarantee that the true effect lies within that particular interval, and it is not a range of individual participant outcomes. Because the interval contains zero, the posted data do not rule out no difference under this interval-based comparison. Its width also shows that the comparison is imprecise.

The unadjusted p-value is 0.365. In general, a p-value is calculated under a null hypothesis and the assumptions of a statistical test; it is not the probability that the null hypothesis is true. The registry record does not report the original statistical analysis plan or enough detail to identify every analysis decision. Therefore, the posted unadjusted value should not be treated as a complete account of all planned or possible analyses. No adjusted comparison is listed in the record.

General statistical context: binary-outcome analyses can use different methods, and methods may behave differently when sample sizes or event counts are small. The registry record does not name the method used for the posted risk difference, confidence interval, or p-value. No specific alternative test should be assumed. Likewise, a randomized design does not by itself answer whether the posted analysis followed an intention-to-treat population, a per-protocol population, or another analysis population; that information is not reported in the registry record.

The sample-size illustrations use the observed effect as their starting point, then consider smaller fractions of that effect. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The figures are participants per arm for this binary comparison, not total events. They are planning illustrations and not evidence about the study's original sample-size planning. In general, power describes the chance that a planned analysis will detect an effect of a specified size under a set of assumptions if that effect is present. It is not a measure of whether the observed result is correct or whether treatment is effective.

General statistical context: when outcomes are binary, uncertainty depends on the numbers of participants and outcomes as well as the comparison being estimated. With only 16 participants in each arm, the percentage estimates are based on limited information, which is consistent with the broad interval for the risk difference. Larger studies can often provide more precise estimates, though the degree of precision also depends on the observed event proportions and the analysis method. The posted record does not report a sample-size justification or whether the trial was designed to have a particular power for the primary endpoint.

The registry record lists two secondary outcomes, virologic failure and hemoglobin levels, and three outcome measures overall. It does not list analyses for these outcomes in the record presented. It also does not report whether any multiplicity adjustment was planned, how missing endpoint values were treated, or which analysis population was prespecified. These omissions limit reconstruction of the full inferential plan; they should not be filled in by assuming common practice.

10. Confidence Intervals and Precision

The point estimate for the risk difference is -0.125, and its 95% confidence interval runs from -0.392 to 0.142. This interval is the main precision statement for the posted comparison. It spans negative and positive values, so the estimated difference is uncertain in both direction and magnitude. It is compatible with a lower SVR12 proportion in the ribavirin arm, little or no difference, or a higher proportion in that arm, within the limits represented by the interval.

The interval is broad, and the arm sizes are 16 participants each. The observed percentages, 88.0% and 75.0%, are therefore estimates based on a small number of participant outcomes. Small changes in the observed counts could materially change the percentages. The confidence interval communicates this uncertainty more directly than the point estimate by itself.

The unadjusted p-value is 0.365. It should not be read as the probability that the regimens are the same or as proof of equivalence. The registry record does not report a prespecified equivalence or noninferiority margin, and no such conclusion can be drawn from the p-value alone. A nonsignificant comparison can reflect imprecision as well as a small underlying difference.

In general, a confidence interval reflects sampling uncertainty under its calculation method and assumptions. It does not account automatically for every concern, such as missing data, deviations from assigned treatment, or selective outcome reporting. The registry record does not report sufficient analysis details to evaluate those issues fully. The most defensible reading is that the posted comparison estimates an arm difference but leaves substantial uncertainty about its size and direction.

11. Planning a Similar Trial: Sample Size

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

The planning figures describe participants per arm for 80% power and participants per arm for 90% power. They are not total event counts. The registry record's stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect being targeted is set to the stated fraction of the observed effect.

In plain terms, the 80% power column gives the number of participants per arm indicated by the planning calculation for an analysis with an 80% chance of detecting the specified effect, if that effect is present and the planning assumptions hold. The 90% power column uses a higher target chance of detection and therefore calls for more participants per arm for the same effect. The calculations list 152 participants per arm for 80% power and 203 for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, the corresponding figures are 254 and 339 participants per arm. For 50% of the observed effect, they are 529 and 708 participants per arm.

Smaller effects are harder to distinguish from random variation, so the planning figures rise as the targeted effect becomes smaller. These calculations are illustrations based on the observed comparison, not a reconstruction of the trial's original design. The original design assumptions and sample-size justification are not reported in the registry record. This is not observed power: it does not measure the probability that the completed trial found a real effect, and it does not alter the uncertainty in the posted result.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.875; treatment proportion p₁ = 0.750; average p̄ = 0.812.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5520 = 1.0819.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5449 = 0.4586.
4. n = (1.0819 + 0.4586)² / (-0.1250)² = 151.9, rounded up to 152 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 <- 0.875                          # control proportion
p1 <- 0.75                          # 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(2631772)
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 = 152 (80% power), 203 (90% power)
 75% of observed effect: n per arm = 254 (80% power), 339 (90% power)
 50% of observed effect: n per arm = 529 (80% power), 708 (90% power)
power.prop.test: 151.9 
Simulated power at n = 152 per arm: 0.812 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists the primary outcome as treatment efficacy and also lists two secondary outcomes: number of participants with virologic failure and hemoglobin levels. Three outcome measures are reported overall. The record does not describe whether the study tested multiple hypotheses for these outcomes, whether a hierarchy of tests was planned, or whether a multiplicity adjustment was specified. It is therefore not possible to determine from the registry record how the risk of false-positive findings across multiple analyses was addressed.

The record indicates no analyses listed, while the primary outcome comparison is posted. The original statistical analysis plan, including any rules for choosing analysis populations or handling outcome data, is not reported in the registry record. No details are reported about whether the efficacy comparison included all randomized participants, participants who completed treatment, or another population. The available results identify 16 participants in each arm for the primary endpoint but do not explain whether these are all randomized participants or how any deviations were handled.

Missing outcome data can affect both the percentages and the comparison between groups. The registry record does not report whether any primary endpoint results were missing, how missing or indeterminate SVR12 status was classified, or whether a sensitivity analysis was conducted. No assumptions about missing outcomes should be inferred from the posted percentages alone.

The same caution applies to the secondary outcomes. Their names appear in the registry record, but detailed analysis methods and results are not included in the registry record for interpretation. Without the planned analysis approach and missing-data rules, it is not possible to assess the full analysis strategy or establish whether the posted comparison reflects the intended analysis population.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: anemia (12.5%), acute kidney injury (6.2%), hyperkalemia (6.2%), diarrhea (6.2%), pulmonary hypertension (6.2%).

The posted safety figures give counts at risk and counts with serious adverse events, other adverse events, and deaths for each arm. In Late Cohort, Arm 1, 4 of 16 participants had a serious adverse event, 11 of 16 had another adverse event, and 1 death was recorded. In Late Cohort, Arm 2, 12 of 16 participants had a serious adverse event, 16 of 16 had another adverse event, and 0 deaths were recorded.

These are descriptive counts from the registry record. The record lists anemia at 12.5% as a leading serious adverse event term, and acute kidney injury, hyperkalemia, diarrhea, pulmonary hypertension, and fractured hip at 6.2% each. These terms and percentages do not establish that an event was caused by treatment, nor do the summary figures provide enough context to judge severity, timing, duration, or relationship to the assigned regimen. The registry record does not report further detail about event definitions or attribution in the registry record for interpretation.

Because the arms are small, the counts should not be interpreted as precise comparative risks. Safety summaries also answer a different question from the primary SVR12 endpoint and should be considered separately.

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

The posted efficacy results describe SVR12 in two late-cohort arms: 88.0% in the arm receiving sofosbuvir/ledipasvir without ribavirin and 75.0% in the arm receiving sofosbuvir/ledipasvir with ribavirin. The risk-difference estimate is -0.125 for the ribavirin arm relative to the non-ribavirin arm. The 95% confidence interval, from -0.392 to 0.142, is broad and includes values on either side of zero. The unadjusted p-value is 0.365.

These figures show the observed outcomes among the participants represented in the posted results. They do not establish a reliable difference between the regimens, and they do not show that the regimens are equivalent. The interval leaves considerable uncertainty about the direction and size of any difference. The small arm sizes make it especially important to distinguish the observed percentages from conclusions about a broader population.

The registry record identifies the study as randomized and open-label, but the randomization procedure and detailed analysis plan are not reported. The registry entries do not establish how missing data were handled or which analysis population was used. Such details matter when judging how well a posted comparison reflects the effect of assignment to treatment.

The primary endpoint also does not capture every outcome relevant to the study. The record lists virologic failure and hemoglobin levels as secondary outcomes and posts safety counts, but the posted efficacy comparison should not be treated as a complete account of safety or all treatment outcomes. The reported adverse-event counts are descriptive and do not by themselves establish causation or comparative risk.

The most limited conclusion is that SVR12 was observed in 14 of 16 participants in one late-cohort arm and 12 of 16 in the other, with substantial statistical uncertainty around the arm comparison. The record does not support a broader claim about effectiveness or safety beyond these posted data.

16. Why This Trial Matters Statistically

This trial raises a clinically relevant statistical comparison: whether the late-cohort outcomes differ between a sofosbuvir/ledipasvir regimen without ribavirin and the same named regimen with ribavirin. The registry record describes its broader questions as whether a ribavirin-free regimen is possible and whether pre-emptive treatment is a potential option to prevent long-term allograft damage. The posted primary result addressed in this comparison is SVR12, not every broader question named in the study summary.

Statistically, the record illustrates why an observed difference and the uncertainty around it must be read together. The arm percentages differ in the posted sample, but the risk-difference confidence interval is wide and crosses zero. The point estimate alone would conceal how little precision is available. The p-value also cannot resolve the uncertainty or establish equivalence.

The trial's randomized design is relevant to comparative interpretation, but the reported sample is small, with 16 participants per arm. This makes the estimate sensitive to individual outcomes and limits precision. Planning illustrations based on the observed effect show that substantially larger per-arm sample sizes would be required to target smaller effects under the stated assumptions. Those illustrations are not the original design rationale and are not evidence about what the trial was powered to detect.

The record also demonstrates the need to distinguish an efficacy endpoint from safety summaries and to account for incomplete reporting. Analysis populations, missing-data handling, multiplicity plans, and the original sample-size justification are not reported in the registry record. These gaps limit what can be inferred from a posted result even when the primary outcome and arm counts are available.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The posted primary comparison is based on 16 participants in each arm, limiting precision. The confidence interval for the risk difference extends from -0.392 to 0.142, so the estimated difference is uncertain in both direction and magnitude. The results come from the late cohort; the posted primary arm data do not provide a comparison with an early cohort.

The registry record describes randomization and open-label treatment but does not report the method used to generate or implement allocation, or whether any stratification was used. It also does not report the original statistical analysis plan, the sample-size justification, or any interim analysis details. The planning illustrations based on the observed comparison cannot fill in those missing design details.

Important analysis details are not reported in the registry record, including the analysis population, the handling of missing or indeterminate SVR12 outcomes, and any sensitivity analyses. The record also does not describe whether multiplicity was addressed across primary and secondary outcomes. These absences limit assessment of the robustness and prespecification of the posted comparison.

The safety summaries provide counts and a short list of serious adverse event terms, but the record does not report further details in the registry record for interpretation about event timing, duration, attribution, or individual participant histories. The counts therefore support description, not conclusions about causation. More broadly, these posted data are specific to the participants and outcomes recorded and do not establish results outside this study comparison.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: LIVE-C-Free: Early and Late Treatment of Hepatitis C With Sofosbuvir/Ledipasvir in Liver Transplant Recipients — NCT02631772.
• Registry record last updated 2019-05-07; status last verified 2019-04.
• Results first posted 2019-05-07.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

LIVE-C-Free is listed as a completed, Phase 4, randomized, open-label, parallel-group study of sofosbuvir/ledipasvir treatment for hepatitis C in liver transplant recipients. Enrollment is 32. The posted primary outcome is treatment efficacy, defined as the percentage achieving SVR12 12 weeks after completing the antiviral regimen.

In the late cohort, 14 of 16 participants in the arm without ribavirin achieved SVR12, reported as 88.0%; 12 of 16 in the arm with ribavirin achieved SVR12, reported as 75.0%. The risk difference for Arm 2 relative to Arm 1 is -0.125, with a 95% confidence interval from -0.392 to 0.142 and an unadjusted p-value of 0.365. The estimate is imprecise, and the interval includes values in both directions.

The registry record lists virologic failure and hemoglobin levels as secondary outcomes and posts safety counts. Details of the original statistical plan, missing-data handling, analysis populations, multiplicity approach, and sample-size justification are not reported in the registry record.