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Hepatitis C, Chronic Phase 2 Binary Endpoint NCT01353911

Grazoprevir (MK-5172) Administered With Peginterferon and Ribavirin in Treatment-Naïve Participants With Chronic Hepatitis C (MK-5172-003): Complete Statistical Analysis

This randomized phase 2 study evaluated grazoprevir with peginterferon and ribavirin in treatment-naïve participants with chronic hepatitis C. The primary result is the percentage achieving complete early viral response after 12 weeks, alongside secondary virologic outcomes and reported adverse events.

Trial start: 2011-06-27  ·  Enrollment: 368  ·  Sponsor: Merck Sharp & Dohme LLC
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 Grazoprevir (MK-5172) Administered With Peginterferon and Ribavirin in Treatment-Naïve Participants With Chronic Hepatitis C (MK-5172-003) (NCT01353911), a randomized phase 2 study. The primary outcome is Percentage of Participants Achieving Complete Early Viral Response (cEVR).

368
Enrollment
Phase 2
8
Arms
In the primary outcome
-14.1 pts
Risk difference
Grazoprevir 100 mg
-26.3 to -2.0 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01353911
PhasePhase 2
ConditionHepatitis C, Chronic
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment368
Arms in the primary outcome8
Lead sponsorMerck Sharp & Dohme LLC
Results postedYes

2. Clinical Question

Population

Treatment-naïve participants with chronic hepatitis C were enrolled. The main dose groups were described as non-cirrhotic; an open-label grazoprevir group included participants with cirrhosis. The primary outcome population was the FAS: randomized or enrolled participants who received at least one dose of study treatment. Missing primary-outcome data were counted as failures.

Intervention

Participants in the non-cirrhotic dose groups received grazoprevir at different doses with peginterferon alfa-2b and ribavirin. The planned grazoprevir combination period was 12 weeks, followed by peginterferon and ribavirin for 12 or 36 weeks according to response-guided therapy. Some participants assigned to higher-dose groups were unblinded after an interim analysis and transitioned to 100 mg grazoprevir.

Comparator

The active-control group received boceprevir with peginterferon alfa-2b and ribavirin. It began with a 4 week lead-in of peginterferon and ribavirin, followed by boceprevir combination treatment and then additional peginterferon and ribavirin according to response-guided therapy. The posted primary comparison also uses the open-label grazoprevir 100 mg group, which is described as a cirrhotic group rather than the non-cirrhotic population of the other dose groups.

Primary question

What percentage of participants had undetectable HCV RNA at Week 12, defined as complete early viral response, after treatment with grazoprevir or boceprevir in combination with peginterferon and ribavirin? The record also reports later viral-response outcomes, including sustained virologic response, and safety summaries.

The study is a dose-ranging evaluation, not a single comparison of one grazoprevir regimen against one otherwise identical regimen. The listed groups differ in grazoprevir dose, treatment sequence, cirrhosis status, or whether treatment was open-label. Those differences matter when interpreting the arm percentages: they do not all represent exchangeable groups in a simple head-to-head comparison. Random assignment is recorded, but the registry record does not report detailed allocation procedures or the original statistical plan.

3. Trial Design

This completed phase 2 trial is recorded as randomized, double-masked, and parallel-group. Enrollment was 368. Its stated purpose was to evaluate the safety, tolerability, and antiviral activity of grazoprevir with peginterferon alfa-2b and ribavirin in treatment-naïve participants with chronic hepatitis C. Boceprevir with the same background medicines served as an active control.

The main grazoprevir groups received different doses for 12 weeks alongside peginterferon and ribavirin, followed by additional peginterferon and ribavirin. The further treatment duration depended on response-guided therapy. The boceprevir regimen used a 4 week lead-in with peginterferon and ribavirin, then boceprevir combination treatment, followed by further peginterferon and ribavirin according to response-guided therapy. A separate open-label grazoprevir 100 mg group was described for participants with cirrhosis; the other main dose groups were described as non-cirrhotic.

The registry record says that an interim analysis led to unblinding participants assigned to the 400 mg and 800 mg grazoprevir groups, who then transitioned to 100 mg grazoprevir and remained in the study. Outcomes for those transitioned participants are listed separately. Details of the interim analysis, its timing, and its decision criteria are not reported in the registry record.

The primary endpoint was assessed after 12 weeks of treatment. Follow-up outcomes include rapid viral response after 4 weeks and sustained virologic response after treatment ended. The SVR12 timeframe is 12 weeks after the end of all treatment, up to 60 weeks; the SVR24 timeframe is 24 weeks after the end of all treatment, up to 72 weeks. The registry record does not report the original sample-size justification, detailed randomization methods, or complete analysis plan. The presence of both double-masked design information and an open-label treatment group should be kept in view when considering how masking applied across the full study.

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: 368 participants enrolled on study. 36 cirrhotic participants received open-label (OL) grazoprevir + peginterferon (Peg-IFN) + ribavirin (RBV), and 332 non-cirrhotic participants were randomized to receive 100, 200, 400, or 800 mg grazoprevir + Peg-IFN + RBV. 43 in the 400 mg group and 36 in the 800 mg group were down-dosed to 100 mg grazoprevir.

Only the first 6 of 8 groups are shown.

Overall Study

StageOL Grazoprevir 100 mgGrazoprevir 100 mgGrazoprevir 200 mgGrazoprevir 400 mgGrazoprevir 800 mgGrazoprevir 400 mg/100 mg
STARTED366668242943
COMPLETED285759222336
NOT COMPLETED899267

Reasons for not completing this period:

ReasonOL Grazoprevir 100 mgGrazoprevir 100 mgGrazoprevir 200 mgGrazoprevir 400 mgGrazoprevir 800 mgGrazoprevir 400 mg/100 mg
Lost to Follow-up264044
Withdrawal by Subject234223
Status Not Recorded401000

Analysis population for the primary outcome, as defined in the registry: FAS; all randomized/enrolled participants who received ≥1 dose of study treatment. A Missing = Failure approach was used for missing data. Results for participants who received grazoprevir 400 or 800 mg and were then down-dosed to receive grazoprevir 100 mg are reported separately from participants who completed the 400 mg and 800 mg regimens.

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: Full Analysis Set (FAS); all randomized/enrolled participants who received ≥1 dose of study treatment. Results for participants who received grazoprevir 400 or 800 mg and were then down-dosed to receive grazoprevir 100 mg are reported separately from participants who completed the 400 mg and 800 mg regimens.

Only the first 6 of 9 groups are shown.

CharacteristicUnitOL Grazoprevir 100 mgGrazoprevir 100 mgGrazoprevir 200 mgGrazoprevir 400 mgGrazoprevir 800 mgGrazoprevir 400 mg/100 mg
Participants analysed366668242943
Age, Continuousyears54.4 (SD 6.9)46.4 (SD 11.3)48.3 (SD 10.6)44.6 (SD 12.5)50.4 (SD 13.4)48.3 (SD 11.4)
Sex: Female, Male: FemaleParticipants142532121515
Sex: Female, Male: MaleParticipants224136121428

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Achieving Complete Early Viral Response (cEVR), measured over After 12 weeks of treatment with grazoprevir/boceprevir.

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants achieving complete early viral response, or cEVR, after 12 weeks of treatment with grazoprevir or boceprevir. The registry definition is undetectable HCV RNA, with the target not detected, at Week 12. Blood samples were assessed with the Roche COBAS Taqman HCV Test, version 2.0. The assay description gives a lower limit of quantification of 25 IU/mL and a limit of detection of 9.3 IU/mL in plasma.

As a general explanation, a virologic endpoint records whether a specified viral measurement meets a defined threshold at a particular assessment time. It can provide a direct, consistently defined measure of early antiviral activity, but it is not the same as a later sustained-response outcome. The study also reports SVR12 and SVR24, which assess response after treatment has ended.

The endpoint is presented as a percentage with a 95% confidence interval calculated using the Clopper-Pearson method. The primary population is described as participants who were randomized or enrolled and received at least one dose. The registry specifies a missing-equals-failure approach: participants with missing data for this outcome were treated as not achieving cEVR. That rule affects how the reported percentages should be understood, because the endpoint incorporates both observed responses and the stated handling of missing assessments.

7. Results Posted in the Registry

Risk difference: Grazoprevir 100 mg

-14.1

95% CI: -26.3 to -2.0 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals53.763.573.283.092.8103OL Grazoprevir 100 mg (n=36)Grazoprevir 100 mg (n=66)Grazoprevir 200 mg (n=68)Grazoprevir 400 mg (n=24)Grazoprevir 800 mg (n=29)Grazoprevir 400 mg/100 mg (n=43)Grazoprevir 800 mg/100 mg (n=36)Boceprevir 800 mg (n=66)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Grazoprevir 100 mgGrazoprevir 200 mgGrazoprevir 400 mgGrazoprevir 800 mgGrazoprevir 400 mg/100 mgGrazoprevir 800 mg/100 mgBoceprevir 800 mg-42-31-20-9.551.2112risk 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 Achieving Rapid Viral Response (RVR)Binary EndpointRisk difference+18.7 pts (2.5 to 34.9)67 per arm
Percentage of Participants Achieving Sustained Virologic Response 12 Weeks After the End of Study Therapy (SVR12)Binary EndpointRisk difference+17.2 pts (0.8 to 33.6)82 per arm
Percentage of Participants Achieving Sustained Virologic Response 24 Weeks After the End of Study Therapy (SVR24)Binary EndpointRisk difference+14.1 pts (-2.7 to 31.0)128 per arm

Percentage of Participants Achieving Rapid Viral Response (RVR)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Grazoprevir 100 mgGrazoprevir 200 mg-2.815.3313223038risk difference (percentage points) vs control (95% CI)

Percentage of Participants Achieving Sustained Virologic Response 12 Weeks After the End of Study Therapy (SVR12)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Grazoprevir 100 mgGrazoprevir 200 mg-2.815.3313223038risk difference (percentage points) vs control (95% CI)

Percentage of Participants Achieving Sustained Virologic Response 24 Weeks After the End of Study Therapy (SVR24)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Grazoprevir 100 mgGrazoprevir 200 mg-5.793.2612213039risk difference (percentage points) vs control (95% CI)

The secondary outcomes add response information at an early on-treatment assessment and after treatment has ended. Across the posted arm summaries, rapid viral response and the sustained-response outcomes generally show higher percentages in the main grazoprevir groups than in the open-label cirrhotic reference group, while the boceprevir percentages are lower than several grazoprevir arm percentages. There is no single uniform ordering across every dose, transitioned group, and time point. The posted secondary comparison analyses are limited to selected contrasts, so the overall pattern is descriptive rather than a complete inferential ranking of all groups.

These endpoints complement cEVR by looking at response at different times. Rapid viral response is assessed after 4 weeks, while SVR12 and SVR24 assess sustained response after treatment ends. Agreement across outcomes can add context, but one endpoint does not validate another automatically. Differences in assessment timing and the specific endpoint definition matter. The secondary results do not overcome the primary analysis limitations involving the open-label cirrhotic reference group, treatment transitions, missing-data handling, or the absence of a reported multiplicity strategy.

The registry lists median time to first achievement of undetectable HCV RNA and the percentage with undetectable HCV RNA at Week 72 as secondary outcomes, but results for those outcomes are not reported in the registry record. Results for the other posted secondary endpoints should be interpreted as exploratory unless a prespecified testing hierarchy or multiplicity plan is established; that plan is not reported in the registry record.

As a general statistical explanation, testing multiple outcomes and comparisons without controlling the overall error rate makes isolated nominal p-values less persuasive. Secondary findings can identify patterns for further study, but they carry less weight than a clearly prespecified primary analysis when the analysis hierarchy and multiplicity handling are unavailable. No adjusted secondary analyses are reported in the registry record.

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

9. Statistical Interpretation

Clinical Biostats interpretation

Complete early viral response was reported in 94.4% of the open-label grazoprevir 100 mg group, compared with 80.3% in the non-cirrhotic grazoprevir 100 mg group, 85.3% with 200 mg, 87.5% with 400 mg, and 75.9% with 800 mg. The separately reported groups transitioned from 400 mg to 100 mg and from 800 mg to 100 mg had response percentages of 86.0% and 86.1%. The boceprevir group had a reported response of 69.7%.

These percentages are descriptive arm results, and the open-label reference group differs in cirrhosis status from the main non-cirrhotic dose groups. Consequently, comparisons with that group should not be read as uncomplicated randomized contrasts between otherwise similar populations. The reported arm estimates also have varying precision, particularly in groups with smaller enrollment.

The posted recalculated, unadjusted comparisons use the open-label grazoprevir group as the reference. For the 800 mg grazoprevir group, the recalculated p-value is 0.031; for the boceprevir group it is 0.004. Their recalculated risk-difference confidence intervals exclude no difference. The other listed primary comparisons have recalculated p-values of 0.054, 0.165, 0.34, 0.218, and 0.233, and their risk-difference intervals include no difference. These are unadjusted calculations based on posted summary statistics, not sponsor-reported comparative analyses. The registry record does not report sponsor comparative analyses for these results, so the recalculations should not be mistaken for the trial's prespecified inferential analysis.

General statistical interpretation: a confidence interval that includes no difference indicates that the interval is compatible with no difference as well as with effects in either direction. A p-value does not measure the size or clinical importance of an effect. Neither a nominal p-value nor an interval alone resolves the limitations created by different populations, treatment changes, multiple comparisons, or unreported analysis details.

The secondary results show additional response assessments during and after treatment, but they do not remove these interpretive constraints. The study's dose-ranging structure, the interim transition of participants in two dose groups, and the mix of cirrhotic and non-cirrhotic groups make simple dose-response conclusions especially uncertain. The record supports describing the observed percentages and their uncertainty; it does not support a broad conclusion that any regimen is effective or ineffective.

10. Statistical Methods Explained

What does a percentage endpoint represent?

The primary outcome is a binary response summarized as a percentage: each participant either met the cEVR definition at Week 12 or did not. The registry defines a response as HCV RNA target not detected. The percentage therefore describes the share meeting that definition in each reported group, subject to the stated population and missing-data rule. It does not report the amount by which viral RNA changed for each participant.

As a general explanation, binary outcomes are often reported as proportions because they are easy to interpret in clinical terms. Comparisons can then be expressed as a risk difference, a risk ratio, or an odds ratio. These measures answer related but different questions. A risk difference compares proportions by subtraction, a risk ratio compares them by division, and an odds ratio compares the odds of the event. The recalculated comparisons available for this trial focus on risk differences. No need arises to infer one measure from another to read the arm percentages.

How should the confidence intervals be read?

The registry reports 95% confidence intervals for the arm percentages and states that the primary intervals used the Clopper-Pearson method. As a general explanation, a confidence interval conveys uncertainty around an estimate under the assumptions of its statistical method. A wider interval indicates less precision; a narrower interval indicates more precision. The interval is not a guarantee that the true value lies within its bounds, nor does it describe the range of individual participant outcomes.

The recalculated risk-difference intervals are unadjusted intervals based on posted summary statistics. Their interpretation is distinct from the intervals reported around each arm percentage. An interval around a difference addresses uncertainty in the contrast; separate intervals around two arm percentages do not, by themselves, provide the same calculation. Comparative analyses adjusted for covariates or trial design features are not reported in the registry record.

What does the missing-data rule do?

For the primary endpoint, the stated approach treats missing data as failure. In general, this is a conservative classification relative to counting missing outcomes as responses, but it can still affect comparisons if missingness differs between groups or relates to participants' underlying response. The registry record does not report the number of missing primary assessments in each group or provide alternative analyses under other missing-data assumptions. Therefore, the sensitivity of the result to missing-data handling cannot be evaluated from the posted record.

What is the role of unadjusted recalculation?

The displayed comparisons are recalculated from the posted summary statistics and are unadjusted. They are not a substitute for the sponsor's analysis plan or a published model-based analysis. The registry record lists no reported analyses for these comparisons. The discrepancy indicator is false, but that does not establish that the calculations reproduce every planned analysis; it only means a discrepancy is not flagged in the available record. No adjustment for multiple comparisons is reported for the posted recalculations.

General explanation: adjustment can matter when many outcomes or contrasts are examined because the chance of obtaining at least one apparently notable result can increase as testing expands. Without a reported multiplicity strategy, nominal p-values for multiple comparisons should be interpreted cautiously. The record does not report the planned hierarchy, if any, among dose groups or endpoints.

Why does the study structure matter?

The primary reference group is open-label grazoprevir 100 mg and is described as cirrhotic, whereas the principal dose groups are described as non-cirrhotic. The listed percentages therefore compare groups with different stated population characteristics. In addition, participants assigned to 400 mg and 800 mg who transitioned to 100 mg after an interim analysis are reported separately from the original dose-group results. These features limit a straightforward interpretation of all arm comparisons as estimates of a single dose effect.

As a general explanation, randomization supports comparability of assigned groups when the planned randomization and analysis are maintained, but changes after randomization and subgroup differences can complicate interpretation. Detailed allocation procedures, the interim analysis methods, and statistical treatment of treatment transitions are not reported in the registry record. Any causal or dose-response claim would require more complete information than the arm-level summaries alone provide.

The endpoint results should thus be read as registry-reported group summaries with confidence intervals, alongside unadjusted recalculated comparisons. They give useful information about the range and precision of observed responses, but not a complete account of the trial's inferential methods.

11. Confidence Intervals and Precision

The primary arm estimates have 95% confidence intervals, and their widths vary across groups. For example, the open-label grazoprevir 100 mg group is reported as 94.4% with an interval from 81.3% to 99.9%, while the 800 mg grazoprevir group is 75.9% with an interval from 56.5% to 89.7%. The 400 mg group is 87.5%, with an interval from 67.6% to 97.3%. These intervals show that the estimates are not equally precise across arms.

As a general explanation, confidence intervals tend to be wider when an estimate is based on less information. Differences in group size and the observed response pattern can both affect precision. The intervals quantify sampling uncertainty under the chosen method; they do not account for every source of uncertainty, such as differences in population characteristics, treatment transitions, missing outcomes, or unreported analysis decisions.

The primary comparison intervals also vary. The recalculated intervals for the 800 mg grazoprevir and boceprevir contrasts exclude no difference, while the other listed primary risk-difference intervals include no difference. This distinction concerns compatibility with a zero risk difference under the recalculation method, not certainty about the true effect or clinical importance.

Precision should be considered alongside the design. The open-label control group is described as cirrhotic, whereas the principal grazoprevir dose groups are non-cirrhotic. The high-dose groups that transitioned to 100 mg are presented separately. These features mean that narrow statistical uncertainty would not, by itself, remove concerns about comparability or interpretation. The registry record does not report adjusted comparative intervals or additional analyses that address those issues.

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 effect86114
75% of the observed effect134179
50% of the observed effect259346
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10020050040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, 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: Grazoprevir 100 mg.

The planning figures are participants per arm, not total participants and not total events. They are illustrations based on the observed effect, rather than the trial's original design assumptions. The stated calculation 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 to the stated fraction of the observed effect. The original trial's sample-size justification and design assumptions are not reported in the registry record.

The 80% power column gives the estimated participants per arm for a planning scenario designed to have an 80% chance of detecting the assumed effect under the calculation assumptions, if that effect and the assumptions were correct. The 90% power column expresses the corresponding planning estimate for a 90% chance. These percentages describe target power for a hypothetical future design; they are not probabilities that the observed trial result is true.

Rows for 100% of the observed effect use the full observed contrast as the planning target. Rows for 75% and 50% of the observed effect use smaller target effects. Smaller effects need more participants to detect, all else being equal, which is why the displayed planning estimates rise as the assumed fraction declines. For example, the 100 mg grazoprevir comparison has 86 participants per arm for 80% power at 100% of the observed effect, and 259 participants per arm for 80% power at 50% of the observed effect.

These calculations are planning illustrations and are not observed power. They are especially sensitive to the observed effect, which can be uncertain in a dose-ranging study with modest group sizes and differing populations. The figures do not establish that the original trial was designed around these assumptions or that it had adequate power for each endpoint or comparison.

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 = 0.944; treatment proportion p1 = 0.803; average p̄ = 0.874.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4697 = 0.9206.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4590 = 0.3863.
  4. n = (0.9206 + 0.3863)2 / (-0.1414)2 = 85.4, rounded up to 86 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 <- 0.944444444444444                          # control proportion
p1 <- 0.803030303030303                          # 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(1353911)
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 = 86 (80% power), 114 (90% power)
 75% of observed effect: n per arm = 134 (80% power), 179 (90% power)
 50% of observed effect: n per arm = 259 (80% power), 346 (90% power)
power.prop.test: 85.4 
Simulated power at n = 86 per arm: 0.825 (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 registry record identifies a primary endpoint and several secondary outcomes, but it does not report a complete statistical analysis plan, a testing hierarchy, or a multiplicity adjustment. The recalculated comparisons are unadjusted. Accordingly, the listed p-values should not be treated as if they account for examining multiple doses, endpoints, and contrasts. This is particularly relevant when interpreting nominally small p-values among a collection of comparisons.

As a general explanation, multiplicity arises when more than one statistical hypothesis is tested. Without a stated method to control the chance of false-positive findings across tests, the evidential strength of an isolated result is reduced. The record does not report whether the sponsor used a gatekeeping procedure, selected contrasts in advance, or applied another multiplicity method.

The primary endpoint specifies a missing-equals-failure rule for the FAS population, defined as participants who were randomized or enrolled and received at least one dose of study treatment. This is a clearly stated handling rule, but the registry record does not report the missing-outcome counts by group or sensitivity analyses using alternative assumptions. It is therefore not possible to assess whether missingness differed by group or how much the chosen rule influenced the comparisons.

The record also reports an interim analysis that prompted unblinding and transitions from the 400 mg and 800 mg groups to 100 mg grazoprevir. The details of that interim analysis, including its timing, stopping or decision criteria, and statistical consequences, are not reported in the registry record. The original sample-size justification, any interim monitoring plan, and the statistical treatment of participants after transition are likewise not reported.

These gaps do not negate the posted arm summaries, but they limit reconstruction of the trial's confirmatory inference. The unadjusted recalculations can describe the contrasts implied by the posted summary statistics; they cannot replace information about prespecification, missingness, multiplicity, or interim decision-making.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Cirr: OL Grazoprevir 100 mg3368.3%
Non-cirr: Grazoprevir 100 mg6669.1%
Non-cirr: Grazoprevir 200 mg96813.2%
Non-cirr: Grazoprevir 400 mg2248.3%
Non-cirr: Grazoprevir 800 mg2296.9%
Non-cirr: Grazoprevir 400 mg/100 mg54311.6%
Non-cirr: Grazoprevir 800 mg/100 mg43611.1%
Non-cirr: Boceprevir 800 mg5667.6%
Participants with at least one serious adverse event
Serious adverse events by armCirr: OL Grazoprevir 100 mg8.3%Non-cirr: Grazoprevir 100 mg9.1%Non-cirr: Grazoprevir 200 mg13.2%Non-cirr: Grazoprevir 400 mg8.3%Non-cirr: Grazoprevir 800 mg6.9%Non-cirr: Grazoprevir 400 mg/…11.6%Non-cirr: Grazoprevir 800 mg/…11.1%Non-cirr: Boceprevir 800 mg7.6%% 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
Cirr: OL Grazoprevir 100 mg34 of 36
Non-cirr: Grazoprevir 100 mg64 of 66
Non-cirr: Grazoprevir 200 mg65 of 68
Non-cirr: Grazoprevir 400 mg23 of 24
Non-cirr: Grazoprevir 800 mg27 of 29
Non-cirr: Grazoprevir 400 mg/100 mg42 of 43

Most frequent serious adverse event terms

Event termOrgan systemCirr: OL Grazoprevir 100 mgNon-cirr: Grazoprevir 100 mgNon-cirr: Grazoprevir 200 mgNon-cirr: Grazoprevir 400 mgNon-cirr: Grazoprevir 800 mgNon-cirr: Grazoprevir 400 mg/100 mg
AnaemiaBlood and lymphatic system disorders1 of 360 of 661 of 680 of 240 of 290 of 43
DehydrationMetabolism and nutrition disorders0 of 360 of 660 of 682 of 240 of 290 of 43
Normochromic normocytic anaemiaBlood and lymphatic system disorders0 of 361 of 660 of 680 of 240 of 290 of 43
HyperparathyroidismEndocrine disorders0 of 360 of 661 of 680 of 240 of 290 of 43
Abdominal painGastrointestinal disorders1 of 360 of 660 of 680 of 240 of 290 of 43
DiarrhoeaGastrointestinal disorders1 of 360 of 660 of 680 of 240 of 290 of 43
Intestinal obstructionGastrointestinal disorders0 of 361 of 660 of 680 of 240 of 290 of 43
NauseaGastrointestinal disorders1 of 360 of 660 of 680 of 240 of 290 of 43
PancreatitisGastrointestinal disorders0 of 361 of 660 of 680 of 240 of 290 of 43
VomitingGastrointestinal disorders1 of 360 of 660 of 680 of 240 of 290 of 43

Most frequent non-serious adverse event terms

Event termOrgan systemCirr: OL Grazoprevir 100 mgNon-cirr: Grazoprevir 100 mgNon-cirr: Grazoprevir 200 mgNon-cirr: Grazoprevir 400 mgNon-cirr: Grazoprevir 800 mgNon-cirr: Grazoprevir 400 mg/100 mg
FatigueGeneral disorders18 of 3627 of 6631 of 6811 of 2416 of 2917 of 43
HeadacheNervous system disorders12 of 3628 of 6631 of 688 of 2412 of 2912 of 43
NauseaGastrointestinal disorders9 of 3625 of 6625 of 686 of 2416 of 2915 of 43
PyrexiaGeneral disorders9 of 3620 of 6624 of 6812 of 248 of 2912 of 43
ChillsGeneral disorders10 of 3620 of 6619 of 686 of 2410 of 2912 of 43
Influenza like illnessGeneral disorders9 of 3614 of 6620 of 687 of 245 of 2915 of 43
AlopeciaSkin and subcutaneous tissue disorders8 of 3617 of 6619 of 687 of 249 of 298 of 43
AnaemiaBlood and lymphatic system disorders13 of 3611 of 6617 of 682 of 247 of 295 of 43
PainGeneral disorders8 of 3612 of 6612 of 683 of 2411 of 298 of 43
Decreased appetiteMetabolism and nutrition disorders4 of 3616 of 6611 of 684 of 249 of 2910 of 43

Serious events with the highest arm-level rate: dehydration (8.3%), schizoaffective disorder (3.4%), intermittent claudication (3.4%), peripheral vascular disorder (3.4%), anaemia (2.8%).

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 safety summary gives the number at risk and the number affected by serious adverse events and other adverse events for each listed group. Serious adverse events were reported for 3 participants in the cirrhotic open-label grazoprevir 100 mg group, 6 in the non-cirrhotic grazoprevir 100 mg group, 9 in the 200 mg group, 2 in the 400 mg group, and 2 in the 800 mg group. The transitioned 400 mg/100 mg and 800 mg/100 mg groups had 5 and 4 participants affected, respectively; the boceprevir group had 5.

The summary also lists other adverse events, with affected counts ranging from 23 to 65 across the non-cirrhotic dose and boceprevir groups, and 34 in the cirrhotic open-label group. These are group counts, not a measure of comparative risk adjusted for follow-up or population differences. The registry record does not report death counts in this safety summary.

Several serious-event terms are listed with percentages, including dehydration at 8.3%, schizoaffective disorder at 3.4%, intermittent claudication at 3.4%, peripheral vascular disorder at 3.4%, anaemia at 2.8%, and abdominal pain at 2.8%. The record does not report the denominator details for those term percentages. The summaries do not establish whether an event was caused by a particular treatment, and they should be read as reported safety counts rather than causal comparisons.

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

The registry results describe early viral response and later virologic outcomes among participants assigned to the listed treatment groups. They provide arm-level percentages and confidence intervals, along with safety counts. These data can be used to understand what the record reports and how uncertain some estimates are.

They do not establish that one regimen works better in a clinically meaningful sense. The posted primary comparisons are unadjusted recalculations from summary statistics, rather than sponsor-reported comparative analyses. Several features also complicate direct comparison: the open-label reference group is described as cirrhotic while the main dose groups are non-cirrhotic; participants in two dose groups transitioned to 100 mg after an interim analysis; and the registry record does not report the full analysis plan or multiplicity handling.

A nominal p-value is not a measure of treatment benefit, and a confidence interval is not a statement about what will happen to an individual participant. Statistical uncertainty is only one part of interpretation. Clinical importance, safety, the appropriateness of the comparator, and the trial's analysis methods would also need consideration, and the posted registry entries do not resolve all of those questions.

The record also does not report the original sample-size justification, the detailed interim analysis methods, or results for every listed secondary outcome. The planning estimates derived from observed effects are not observed power and should not be read as evidence about the design quality of this completed trial. The results are best treated as registry-reported evidence from a phase 2 dose-ranging study, with limits on how broadly or causally its between-group patterns can be interpreted.

17. Why This Trial Matters Statistically

This trial illustrates several statistical issues that commonly arise in dose-ranging clinical studies. Multiple dose groups can reveal variation in observed responses, but a set of arm percentages is not by itself proof of a dose-response relationship. Sampling uncertainty, group comparability, and the analysis plan all affect how the pattern should be read.

The study also makes the distinction between an endpoint estimate and a comparative analysis important. Each arm's response percentage describes that group. A risk difference compares a group with a reference, but the recalculated contrasts are unadjusted and the registry record does not report sponsor comparative analyses. That difference in analytic status matters when readers encounter p-values alongside descriptive results.

The use of an open-label cirrhotic reference group alongside non-cirrhotic dose groups highlights a comparability concern that can be missed when attention is limited to numerical contrasts. The interim transition from two higher-dose groups to 100 mg also shows why treatment changes and the handling of participants after those changes need clear reporting. The registry gives the basic transition description but not the detailed analysis methods.

Finally, the record pairs a defined missing-equals-failure primary outcome with incomplete reporting of missing counts, multiplicity procedures, and the original sample-size plan. Those details are essential to distinguishing a descriptive result from a confirmatory conclusion. The example is statistically useful because it shows why confidence intervals, endpoint definitions, population descriptions, and analysis transparency should be considered together.

18. Limitations

Several trial-specific features constrain interpretation. The principal grazoprevir dose groups are described as non-cirrhotic, whereas the open-label 100 mg reference group is described as cirrhotic. The displayed comparisons therefore involve groups with differing stated clinical characteristics. The record does not report adjusted analyses to account for that difference.

Participants assigned to 400 mg or 800 mg grazoprevir were unblinded and transitioned to 100 mg after an interim analysis, with transitioned participants reported separately. The record does not explain the interim analysis criteria, timing, or the analytical handling of these changes beyond the separate reporting. The planned response-guided treatment durations also mean that treatment exposure after the initial combination period could vary according to response.

The primary outcome uses missing equals failure, but group-specific missing-data counts and sensitivity analyses are not reported in the registry record. The registry record also does not report a detailed statistical analysis plan, the original sample-size justification, a multiplicity strategy, or sponsor-reported comparative analyses. Results for median time to first undetectable HCV RNA and undetectable HCV RNA at Week 72 are not reported in the registry record.

These limitations do not make the arm summaries unusable; they restrict the strength and scope of comparisons that can be drawn from them. In particular, the unadjusted recalculations should not be interpreted as a complete account of the trial's planned statistical inference.

19. Related Tutorials

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Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

22. Record Summary

NCT01353911 is a completed randomized, double-masked, parallel-group phase 2 study of grazoprevir with peginterferon alfa-2b and ribavirin in treatment-naïve participants with chronic hepatitis C. Enrollment was 368. Boceprevir with peginterferon and ribavirin served as an active control, and an open-label grazoprevir group was listed for participants with cirrhosis.

The primary outcome was complete early viral response after 12 weeks, defined as undetectable HCV RNA with target not detected. The record reports arm percentages with 95% confidence intervals and specifies missing equals failure for the primary population. Secondary outcomes include rapid viral response and sustained response after treatment. Results for some listed secondary outcomes are not reported in the registry record.

The posted summaries support descriptive interpretation, but comparative conclusions are limited by differences in the stated populations, interim treatment transitions, unadjusted recalculations, and unreported details of the analysis plan and multiplicity handling.

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