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HIV Phase 3 Binary Endpoint NCT01095796

Study to Evaluate the Safety and Efficacy of Stribild Versus Atripla in Human Immunodeficiency Virus, Type 1 (HIV-1) Infected, Antiretroviral Treatment-Naive Adults: Complete Statistical Analysis

A randomized, double-blind Phase 3 trial compared Stribild with Atripla in antiretroviral treatment-naive adults with HIV-1. The primary result was the percentage with HIV-1 RNA below 50 copies/mL at Week 48, with further virologic outcomes recorded at later time points.

Trial start: 2010-03  ·  Enrollment: 707  ·  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 Study to Evaluate the Safety and Efficacy of Stribild Versus Atripla in Human Immunodeficiency Virus, Type 1 (HIV-1) Infected, Antiretroviral Treatment-Naive Adults (NCT01095796), a randomized phase 3 study. The primary outcome is The Percentage of Participants With Virologic Success Using the Food and Drug Administration (FDA)-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 Ribonucleic Acid (RNA) < 50 Copies/mL at Week 48.

707
Enrollment
Phase 3
2
Arms
In the primary outcome
-3.6 pts
Risk difference
Atripla
-8.7 to 1.6 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01095796
PhasePhase 3
ConditionHIV, HIV Infections
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment707
Arms in the primary outcome2
Lead sponsorGilead Sciences
Results postedYes

2. Clinical Question

Population

Adults with HIV-1 infection who had not previously received antiretroviral treatment. The primary analysis population included participants randomized into the study who received at least one dose of study drug. The registry record reports 707 enrolled participants.

Intervention

Stribild, a single-tablet regimen containing elvitegravir, cobicistat, emtricitabine, and tenofovir disoproxil fumarate. Participants assigned to this group also received placebo to match Atripla.

Comparator

Atripla, containing efavirenz, emtricitabine, and tenofovir disoproxil fumarate. Participants assigned to this group also received placebo to match Stribild, supporting the double-blind design.

Primary question

At Week 48, what percentage of participants in each group achieved HIV-1 RNA below 50 copies/mL under the FDA-defined Snapshot analysis, and how precisely did the observed group difference estimate the contrast between the regimens?

The clinical question is framed around virologic success at a specified follow-up time, rather than around a continuous change in viral load or a time-to-event endpoint. The outcome is binary at the participant level: each participant is classified according to whether the specified HIV-1 RNA threshold was achieved under the stated analysis approach. The registry identifies the endpoint as a percentage of participants and names the Intent-to-treat Analysis Set as the population for the primary outcome.

This comparison was randomized and quadruple-masked according to the registry record. The treatment groups were designed to appear alike through the use of matching placebos. The registry describes the study as a Phase 3 parallel-group trial. These design features identify the intended comparison, but the registry record does not report additional details about the allocation procedure, masking roles, or the protocol's rationale for selecting this endpoint.

3. Trial Design

The registry record describes a randomized, quadruple-masked, parallel-group Phase 3 study of Stribild and Atripla in antiretroviral treatment-naive adults with HIV-1 infection. The study status is completed. The registry lists a start of 2010-03 and a primary completion of 2011-08, and reports enrollment of 707 participants.

The two groups received different active regimens, with matching placebos used in each group: Stribild plus placebo to match Atripla, or Atripla plus placebo to match Stribild. This double-dummy arrangement is stated in the arm descriptions and is consistent with the study title's double-blind description. The registry separately labels masking as quadruple; it does not identify the masked roles in the record summarized for this analysis.

The primary endpoint was assessed at Week 48 using the FDA-defined Snapshot analysis. The named analysis population included randomized participants who received at least one dose of study drug. The outcome was the percentage with HIV-1 RNA below 50 copies/mL. The registry also lists secondary virologic outcomes at Week 96, Week 144, and Week 192, along with outcomes involving confirmed virologic response, CD4 cell-count change, and HIV-1 RNA below 50 copies/mL at Week 48.

The record does not report the original sample-size justification, the assumptions used in the trial's design, an interim-analysis plan, or further details of the statistical analysis plan. It also does not report the randomization sequence or allocation-concealment procedures. Those details should not be inferred from the fact that the study was randomized and masked. The design establishes the broad comparison and analysis framework, while the registry record leaves some operational and statistical details unspecified.

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: 917 participants were screened.

Overall Study

StageStribildAtripla
STARTED353354
COMPLETED5865
NOT COMPLETED295289

Reasons for not completing this period:

ReasonStribildAtripla
Randomized but Not Treated52
Adverse Event919
Death32
Pregnancy20
Lack of Efficacy53
Investigator's Discretion72
Withdrew Consent1622
Lost to Follow-up2729
Participant Noncompliance510
Protocol Violation10
Participant Transferred to Another Study215200

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) Analysis Set: participants who were randomized into the study and received at least 1 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 medication.

CharacteristicUnitStribildAtriplaTotal
Participants analysed348352700
Age, Continuousyears38 (SD 10.4)38 (SD 10.6)38 (SD 10.5)
Sex: Female, Male: FemaleParticipants413677
Sex: Female, Male: MaleParticipants307316623
Race/Ethnicity, Customized: American Indian or Alaska Nativeparticipants246
Race/Ethnicity, Customized: Asianparticipants61016
Race/Ethnicity, Customized: Black or African Heritageparticipants10691197
Race/Ethnicity, Customized: Native Hawaiian or Pacific Islanderparticipants415
Race/Ethnicity, Customized: Whiteparticipants214227441
Race/Ethnicity, Customized: Otherparticipants161935
Region of Enrollment: United Statesparticipants348352700
HIV Disease Status: Asymptomaticparticipants290295585
HIV Disease Status: Symptomatic HIV Infectionsparticipants303363
HIV Disease Status: AIDSparticipants282452
Hepatitis B Virus (HBV) Infection Status: Negativeparticipants343343686
Hepatitis B Virus (HBV) Infection Status: Positiveparticipants5914
Hepatitis C Virus (HCV) Infection Status: Negativeparticipants331337668
Hepatitis C Virus (HCV) Infection Status: Positiveparticipants171532
HIV-1 RNA Category (copies/mL): ≤ 100,000participants230236466
HIV-1 RNA Category (copies/mL): > 100,000participants118116234
CD4 Cell Count (/µL): ≤ 50participants7613
CD4 Cell Count (/µL): 51 to ≤ 200participants364581
CD4 Cell Count (/µL): 201 to ≤ 350participants11296208
CD4 Cell Count (/µL): 351 to ≤ 500participants113136249
CD4 Cell Count (/µL): > 500participants8069149

6. Primary Endpoint

The registry lists the primary outcome as The Percentage of Participants With Virologic Success Using the Food and Drug Administration (FDA)-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 Ribonucleic Acid (RNA) < 50 Copies/mL at Week 48, measured over Week 48.

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

The primary endpoint measures the percentage of participants who achieved HIV-1 RNA below 50 copies/mL at Week 48 under the FDA-defined Snapshot analysis. It is a binary response outcome: each participant contributes to the response rate according to whether the threshold was met within the endpoint's defined assessment. The registry identifies the unit as a percentage of participants and names the Intent-to-treat Analysis Set, defined as randomized participants who received at least one dose of study drug.

A threshold-based virologic endpoint provides a direct way to summarize how many participants meet a prespecified level of viral suppression at a particular follow-up point. It translates individual measurements into a group response proportion, which can be compared between randomized groups. The Snapshot label identifies the analysis approach, but the registry record does not include the detailed rules for handling every possible visit or outcome status. Those rules are therefore not described beyond the named FDA-defined approach.

The endpoint is not the same as a measure of average change in HIV-1 RNA, nor does it by itself describe the timing of response or how long a response was maintained. The trial lists other outcomes that address different questions, including confirmed response over time and CD4 cell-count change. Interpretation of the primary endpoint should remain tied to its Week 48 time point, threshold, analysis approach, and specified population. The registry record does not report a separate clinical rationale for choosing this threshold or time point.

7. Results Posted in the Registry

Risk difference: Atripla

-3.6

95% CI: -8.7 to 1.6 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals78.881.484.086.689.291.8Stribild (n=348)Atripla (n=352)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Atripla-9.53-7.14-4.75-2.360.032.42risk 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
The Percentage of Participants With Virologic Success Using the FDA-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 RNA < 50 Copies/mL at Week 96Binary EndpointRisk difference-2.7 pts (-8.2 to 2.9)3,146 per arm
The Percentage of Participants With Virologic Success Using the FDA-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 RNA < 50 Copies/mL at Week 144Binary EndpointRisk difference-4.9 pts (-11.0 to 1.3)1,137 per arm
The Percentage of Participants With Virologic Success Using the FDA-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 RNA < 50 Copies/mL at Week 192Binary EndpointRisk difference+2.0 pts (-11.7 to 15.8)6,759 per arm

The Percentage of Participants With Virologic Success Using the FDA-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 RNA < 50 Copies/mL at Week 96

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Atripla-9.13-6.54-3.96-1.371.223.81risk difference (percentage points) vs control (95% CI)

The Percentage of Participants With Virologic Success Using the FDA-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 RNA < 50 Copies/mL at Week 144

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Atripla-12-9.17-6.32-3.46-0.612.25risk difference (percentage points) vs control (95% CI)

The Percentage of Participants With Virologic Success Using the FDA-Defined Snapshot Analysis as Determined by the Achievement of HIV-1 RNA < 50 Copies/mL at Week 192

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Atripla-14-7.53-1.165.211218risk difference (percentage points) vs control (95% CI)

The registry lists six secondary outcomes, covering virologic response at later follow-up, confirmed and maintained response, CD4 cell-count change, and a Week 48 virologic response definition. Numerical group summaries are posted for the FDA-defined Snapshot virologic outcome at Week 96, Week 144, and Week 192. Numerical results for the other listed secondary outcomes are not reported in the registry record.

Across the posted later Snapshot outcomes, the point estimates do not all have the same direction. At the earlier reported follow-up points, the response percentages are numerically higher for Stribild; at the latest reported follow-up point, the ordering is reversed. This is a broad description of the pattern, not a claim that the groups differ at those time points. The later comparisons' recalculated confidence intervals include zero, so they do not exclude no difference under those calculations. The Week 192 analysis also uses smaller reported group sizes than the primary analysis, which is relevant to the uncertainty of that result.

The secondary outcomes relate to the primary result by examining virologic response at other times or under other definitions, and by measuring other aspects of response. They do not replace the primary Week 48 endpoint. Differences in follow-up time, outcome definition, and analysis population can change what each result means, even when outcomes concern the same underlying disease.

As a general statistical explanation, examining multiple outcomes increases the opportunities to observe apparently notable results by chance. Unless a multiplicity strategy is specified and accounted for, secondary p-values and comparisons should be treated as exploratory rather than as independent confirmatory evidence. The registry record does not report a multiplicity adjustment or an inferential plan for the secondary outcomes. The posted secondary estimates are therefore best interpreted as supportive descriptive information, with appropriate caution about multiple comparisons and uncertainty.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 48, the posted response percentages were 87.6 for Stribild and 84.1 for Atripla. The simple unadjusted recalculation gives an Atripla-minus-Stribild risk difference of -0.035, with a 95% confidence interval from -0.087 to 0.016 and an unadjusted p-value of 0.177. The negative direction means the recalculated response proportion was lower in the Atripla group than in the Stribild group. The interval includes zero, so the data are compatible with no group difference as well as with differences in either direction within the interval.

The sponsor's reported analysis presents the difference in the opposite order: Stribild minus Atripla. It reports a difference in response rates of 3.6, with a 95.2% confidence interval from -1.6 to 8.8. The opposing signs of the reported and recalculated estimates reflect the reversed group order; their direction is not evidence of a disagreement. The sponsor's analysis is the trial's reported analysis and should be distinguished from the simple recalculation based on posted group summaries.

The central statistical point is not that one group can be declared superior from the response percentages alone. The uncertainty interval includes the no-difference value, and the unadjusted p-value is 0.177. These figures describe the strength and precision of evidence for a difference under the respective calculations; they do not establish that the regimens are identical. A finding of no statistically detectable difference is not proof of equivalence. The registry labels the sponsor analysis as a non-inferiority or equivalence type, but the non-inferiority margin and the complete decision rules are not reported in the registry record, so the margin-based conclusion cannot be reconstructed from these numbers alone.

The outcome is specific to Week 48 and the FDA-defined Snapshot approach. It does not by itself describe responses at later times, changes in CD4 cell count, tolerability, or other clinical outcomes. Later virologic summaries are listed separately, and their interpretation depends on their own time points and populations. The primary result should therefore be read as a comparison of response proportions at the stated endpoint, not as a comprehensive assessment of every benefit or risk associated with either regimen.

The enrolled total and the endpoint analysis-group sizes represent different reported quantities. The registry reports 707 enrolled participants, while the primary response summaries are based on the named analysis set in the two groups. The registry record does not explain any difference between these totals, so the enrollment count should not be substituted for the endpoint denominators or used to infer why participants were not included in a particular analysis.

10. Statistical Methods Explained

The primary endpoint is a binary response: a participant either meets the HIV-1 RNA threshold under the Week 48 Snapshot definition or does not. A group percentage summarizes the proportion classified as responders. Comparing two such percentages focuses on the difference in response probability between the randomized groups. The posted arm results give percentages, while the recalculation uses the underlying responder counts and analysis-set denominators recorded for the groups.

What does a risk difference express?

As a general statistical explanation, a risk difference subtracts one group's response proportion from the other group's response proportion. It is expressed on the proportion scale, so zero represents equal response proportions, a positive value indicates a higher proportion in the first group as ordered, and a negative value indicates a lower proportion. The recalculated contrast is Atripla minus Stribild; the sponsor's reported contrast is Stribild minus Atripla. Reversing the order reverses the sign but does not change the underlying comparison.

The recalculated risk difference is an unadjusted comparison of the posted group summaries. It does not include covariate adjustment or recreate an analysis method that is not specified in the registry record. The record labels the sponsor analysis as a non-inferiority or equivalence type, but does not report its statistical method, test statistic, or margin. The sponsor's result therefore remains a distinct reported analysis rather than a method that can be fully reproduced from the available description.

How should a confidence interval be read?

As a general explanation, a confidence interval expresses the range of values that are reasonably compatible with the observed data under the calculation's assumptions. It communicates uncertainty about an estimated group contrast; it is not a range containing a fixed percentage of individual participant outcomes. For a difference, an interval that includes zero means the data do not exclude equal response proportions at the corresponding confidence level. It does not show that the groups are identical, nor does it rule out potentially meaningful differences within the interval.

The recalculated interval and the sponsor's reported interval use different displayed scales and group order. The recalculated estimate and bounds are given as proportions; the sponsor reports a difference in response rates and a 95.2% interval. The registry record does not provide enough detail to identify every computational choice behind the sponsor result. Comparisons between the intervals should therefore account for their presentation and analysis origin, rather than treating them as outputs from one identical procedure.

What does the p-value add?

As a general statistical explanation, a p-value measures how unusual data at least as incompatible with a specified null model would be if that model were true, under the test's assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The recalculated unadjusted p-value is 0.177. The sponsor's p-value is not reported in the registry record. The recalculated value should not be mistaken for the sponsor's inferential result or for a multiplicity-adjusted test.

The registry gives the sponsor's analysis type but not its method or margin. For a non-inferiority question, the interpretation ordinarily depends on comparing an appropriate confidence bound with a prespecified margin. That is a general description of the statistical framework, not a claim about the trial's undocumented margin or decision rule. Since the margin is not reported in the registry record, the reported interval alone cannot establish which margin was used or independently verify a margin-based conclusion.

Why can binary outcomes be uncertain?

As a general explanation, a response percentage is estimated from a finite number of participants. Uncertainty depends on both the observed response proportion and the amount of information in the analysis. A confidence interval communicates that sampling uncertainty. A difference can have a modest point estimate yet still have an interval spanning a wider range of possible contrasts. The observed percentages should consequently be read together with their uncertainty estimates, not as exact population response rates.

Randomization supports a comparison between assigned groups, while masking can limit some forms of differential assessment or behavior. These design features do not remove sampling uncertainty, missing-outcome concerns, or the need to follow the specified analysis rules. The registry record identifies the study as randomized and quadruple-masked and describes the primary analysis population, but it does not report enough detail to assess every implementation feature or sensitivity analysis.

Finally, outcome time points and analytic populations matter. A Week 48 Snapshot response is not interchangeable with a response at Week 96 or Week 144, or with a measure requiring response to be maintained over time. The registry lists such distinct secondary outcomes. Each addresses a related but nonidentical question and should be interpreted according to its own definition and available results.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data estimate the group contrast, not whether a treatment is effective or whether two groups are identical. For the primary recalculation, the Atripla-minus-Stribild risk difference is -0.035, with a 95% confidence interval from -0.087 to 0.016. The interval crosses zero. It therefore includes equal response proportions as well as values on either side of zero, indicating that the direction and magnitude of the underlying difference are not estimated with enough precision to exclude all of those possibilities.

The sponsor reports a Stribild-minus-Atripla difference in response rates of 3.6, with a 95.2% confidence interval from -1.6 to 8.8. This interval also includes zero. The different direction of subtraction and the reported interval level should be kept in view when comparing the sponsor estimate with the recalculation. The sponsor's own result is the trial's reported analysis; the recalculation is an unadjusted estimate from the posted summary statistics.

As a general explanation, an interval gives a range of estimates compatible with the observed data under the procedure's assumptions. A wider interval reflects less precision than a narrower interval on the same scale and for the same confidence level. An interval spanning zero is not proof of no effect. It means the data do not exclude zero under that interval calculation, while also allowing nonzero values within the bounds.

The registry record does not report a clinical threshold for a meaningful difference or the non-inferiority margin. Consequently, precision can be described statistically, but the bounds cannot be classified against an unreported clinical or protocol threshold. The reported endpoint estimates should be understood as specific to the Week 48 Snapshot outcome and its analysis population. They do not describe precision for other outcomes or follow-up times.

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 effect1,5092,019
75% of the observed effect2,6123,495
50% of the observed effect5,7157,651
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1,0002,0005,00010,00020,00040%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: Atripla.

The planning figures are participants per arm, not total participants across both arms. They are planning illustrations calculated from the observed effect, not the original trial's sample-size justification; the trial's own design assumptions are not reported in the registry record. The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect.

The 80% power column describes the planned number of participants per arm under those assumptions for a design with an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding planning target for a 90% chance. These are prospective design concepts, not measures of how likely the completed trial was to find a result or evidence that a particular effect is present. This is not observed power.

For the primary endpoint, planning for 100% of the observed effect gives 1,509 participants per arm for 80% power and 2,019 participants per arm for 90% power. Planning for 75% of the observed effect gives 2,612 participants per arm for 80% power and 3,495 participants per arm for 90% power. Planning for 50% of the observed effect gives 5,715 participants per arm for 80% power and 7,651 participants per arm for 90% power. These are illustrations under the stated assumptions and should not be read as the trial's planned enrollment target.

The pattern reflects a general planning principle: smaller effects are harder to distinguish from random variation, so detecting them at the same power generally requires more participants. The illustration is sensitive to the observed effect used as its starting point. Because that effect is itself estimated with uncertainty, these figures are not guarantees that a future study will detect the same contrast. Any sample-size curve should be read as a representation of these planning assumptions and effect choices, not as a description of the completed trial's observed power.

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 = 0.876; treatment proportion p1 = 0.841; average p̄ = 0.859.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4927 = 0.9656.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4920 = 0.4141.
  4. n = (0.9656 + 0.4141)2 / (-0.0355)2 = 1,508.1, rounded up to 1,509 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 <- 0.876436781609195                          # control proportion
p1 <- 0.840909090909091                          # 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(1095796)
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 = 1,509 (80% power), 2,019 (90% power)
 75% of observed effect: n per arm = 2,612 (80% power), 3,495 (90% power)
 50% of observed effect: n per arm = 5,715 (80% power), 7,651 (90% power)
power.prop.test: 1508.1 
Simulated power at n = 1,509 per arm: 0.801 (20000 replicates)

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

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
not statedDifference in response rates 3.6-1.6 to 8.8not reported

The sponsor's reported analysis gives a difference in response rates of 3.6, with a 95.2% confidence interval from -1.6 to 8.8. The registry identifies the comparison as a non-inferiority or equivalence type. It does not report a p-value for that analysis, its detailed statistical method, or the non-inferiority margin.

The simple recalculation uses the posted response counts and group sizes and orders the comparison as Atripla minus Stribild. Its estimate is -0.035, with a 95% confidence interval from -0.087 to 0.016 and an unadjusted p-value of 0.177. The reversed signs are consistent with the reversed group order: the sponsor's contrast is Stribild minus Atripla, while the recalculation is Atripla minus Stribild. The registry reports no discrepancy between the sponsor result and the recalculation.

These analyses should not be treated as interchangeable. The sponsor's analysis is the reported trial analysis and is the relevant source for the registry's non-inferiority or equivalence classification. The recalculation is a simple, unadjusted estimate based on posted summary statistics and does not reproduce an undocumented analysis plan. Because the margin and full method are not reported in the registry record, the sponsor's margin-based decision cannot be independently checked from the available information. The recalculated p-value is not a substitute for the sponsor's analysis.

15. Multiplicity, Missing Data and Analysis Populations

The primary endpoint is clearly identified as a Week 48 FDA-defined Snapshot response in the Intent-to-treat Analysis Set. The registry also lists multiple secondary outcomes across different time points and measures. However, the multiplicity strategy for handling multiple endpoints, time points, or comparisons is not reported in the registry record. It is therefore not possible to determine from this record whether a hierarchy, adjustment procedure, or other prespecified approach was used to control the overall chance of false-positive findings.

As a general statistical explanation, testing many outcomes can increase the chance that at least one result appears notable by chance alone. A prespecified multiplicity plan can clarify which outcomes are confirmatory and how evidence is evaluated across tests. In the absence of a reported plan, the secondary results should be interpreted cautiously and should not be treated as though each comparison were the only test conducted. The unadjusted p-value for the primary recalculation is also not a multiplicity-adjusted result.

The primary analysis population is described as participants randomized into the study who received at least one dose of study drug. That definition supplies a clear broad population description, but the record does not report all analysis-population details, such as whether additional populations were used for the sponsor's non-inferiority analysis. Nor does it provide the number or reasons for participants excluded from each outcome analysis beyond the group sizes listed for those results.

The Snapshot method is named, but detailed missing-data rules and sensitivity analyses are not reported in the registry record. In general, missing outcome data can affect a response proportion because the treatment of participants without an observed qualifying result can influence the numerator, denominator, or classification. The registry record does not support an account of the specific handling rules beyond the FDA-defined Snapshot label. The original sample-size justification, interim analyses, and full statistical analysis plan are also not reported. These omissions limit independent reconstruction of the trial's inferential procedures; they do not by themselves establish that the procedures were inadequate.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Stribild6934819.8%
Atripla5035214.2%
Participants with at least one serious adverse event
Serious adverse events by armStribild19.8%Atripla14.2%% 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
Stribild313 of 348
Atripla326 of 352

Most frequent serious adverse event terms

Event termOrgan systemStribildAtripla
PneumoniaInfections and infestations9 of 3482 of 352
AppendicitisInfections and infestations4 of 3483 of 352
CellulitisInfections and infestations6 of 3480 of 352
BronchitisInfections and infestations1 of 3483 of 352
AsthmaRespiratory, thoracic and mediastinal disorders3 of 3481 of 352
Abdominal painGastrointestinal disorders1 of 3482 of 352
PyrexiaGeneral disorders1 of 3482 of 352
GastroenteritisInfections and infestations2 of 3481 of 352
NeurosyphilisInfections and infestations1 of 3482 of 352
Viral infectionInfections and infestations3 of 3480 of 352

Most frequent non-serious adverse event terms

Event termOrgan systemStribildAtripla
DiarrhoeaGastrointestinal disorders93 of 34891 of 352
Upper respiratory tract infectionInfections and infestations92 of 34878 of 352
Abnormal dreamsPsychiatric disorders56 of 348101 of 352
NauseaGastrointestinal disorders80 of 34859 of 352
DizzinessNervous system disorders29 of 34894 of 352
DepressionPsychiatric disorders56 of 34859 of 352
FatigueGeneral disorders53 of 34861 of 352
InsomniaPsychiatric disorders47 of 34863 of 352
HeadacheNervous system disorders62 of 34845 of 352
RashSkin and subcutaneous tissue disorders35 of 34853 of 352

Serious events with the highest arm-level rate: pneumonia (2.6%), cellulitis (1.7%), appendicitis (1.1%), viral infection (0.9%), asthma (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 safety summary reports serious adverse events in 69 of 348 participants at risk in the Stribild group and 50 of 352 at risk in the Atripla group. These are counts of participants with serious adverse events and the corresponding reported at-risk group sizes. The summary also reports other adverse events for 313 of 348 participants at risk with Stribild and 326 of 352 at risk with Atripla. The two categories should be kept distinct: serious adverse events are not interchangeable with the broader other-adverse-event counts.

The listed serious-event terms include Pneumonia at 2.6%, Cellulitis at 1.7%, Appendicitis at 1.1%, and Viral infection, Asthma, and Bronchitis at 0.9% each. The registry record does not specify an arm for these listed terms in the summary, so they should not be attributed to either group based on this information. Death counts are not reported in the registry record.

These figures are descriptive safety counts. They do not, on their own, establish whether an event was caused by a study regimen, how long participants were exposed, or how event severity and timing compared. The registry record summarized for this analysis does not report those details or a statistical comparison of safety outcomes. Safety interpretation should therefore remain limited to the reported event counts and terms rather than treating them as a complete assessment of comparative risk.

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

The primary result describes the proportion of participants in each randomized group who met the Week 48 HIV-1 RNA threshold under the FDA-defined Snapshot analysis. The posted percentages were 87.6 for Stribild and 84.1 for Atripla. The estimates describe the trial's analysis population and endpoint definition; they are not exact predictions for every patient or every clinical setting.

The recalculated contrast and its confidence interval express uncertainty around the group difference. Because the interval includes zero, the recalculation does not exclude equal response proportions. It also permits differences in either direction within its bounds. This is not proof that the regimens are equivalent, and it does not show that no clinically meaningful difference exists. The registry classifies the sponsor analysis as non-inferiority or equivalence type, but the margin needed to interpret that framework is not reported in the registry record.

The result does not answer every question about virologic control. It is tied to Week 48, the threshold of HIV-1 RNA below 50 copies/mL, the Snapshot approach, and the named analysis population. It does not by itself describe response durability, CD4 cell-count changes, all adverse events, or outcomes at later follow-up. Those are separate questions and require their own outcome definitions and data.

Nor should the primary result be read as a treatment recommendation. The statistics describe what was observed in this randomized study and how uncertain the estimated comparison is. They do not establish how an individual would respond, address circumstances not represented in the study population, or replace clinical judgment. The registry record does not provide enough detail to infer how the trial's results apply to populations beyond the described antiretroviral treatment-naive adults with HIV-1.

Finally, non-significance and equivalence are different concepts. A confidence interval that includes zero indicates that the calculated data do not rule out no difference, but a formal equivalence or non-inferiority conclusion depends on prespecified margins and analysis rules. Those details are not reported in the registry record. The sponsor's stated analysis type should therefore be reported as such, while the limitations on independent verification remain clear.

18. Why This Trial Matters Statistically

This trial illustrates how a binary clinical endpoint and an uncertainty interval answer different parts of a research question. The response percentages describe the observed groups, while the risk difference puts their contrast on a common scale. The confidence interval shows that the estimated difference is uncertain and includes zero. Reading all three elements together is more informative than treating a small numerical separation between percentages as a definitive conclusion.

It also demonstrates why the direction and definition of a comparison must be stated explicitly. The sponsor reports Stribild minus Atripla, while the simple recalculation is Atripla minus Stribild. The estimates therefore have opposite signs, even though they describe the same two-group contrast in reversed order. Clear labeling prevents a sign change from being mistaken for conflicting findings.

The registry identifies a sponsor analysis as non-inferiority or equivalence type, but does not report the margin or detailed method. This highlights a broader statistical point: a study label alone cannot establish how a formal conclusion was reached. The estimand, contrast direction, interval, margin, analysis population, and missing-data rules all matter. Where key details are absent, interpretation should distinguish what the record reports from what cannot be independently evaluated.

Finally, the later outcomes show why endpoint time points should not be collapsed into one general claim. Virologic response at Week 48 and response at later follow-up are separate measurements, and the latest reported comparison has smaller group sizes. Multiplicity is also relevant when several endpoints and time points are considered. Statistical interpretation requires attention to the full analysis context, not merely a favorable-looking point estimate or a single p-value.

19. Limitations

The registry record gives limited detail about how the primary analysis was implemented. It names the FDA-defined Snapshot approach but does not report the detailed outcome-classification and missing-data rules. It also does not provide sensitivity analyses that would show how conclusions might change under alternative assumptions about missing outcomes.

The sponsor analysis is labeled non-inferiority or equivalence type, but its method, prespecified margin, and p-value are not reported in the registry record. The simple recalculation is unadjusted and cannot reproduce an analysis plan that is not described. The absence of a reported multiplicity strategy also makes it difficult to determine how the secondary endpoints were positioned as confirmatory or exploratory.

Numerical results are available for only some of the listed secondary outcomes in the record summarized for this analysis. Results for the other listed secondary endpoints are not reported in the registry record. The later Week 192 Snapshot result has substantially smaller reported analysis-group sizes than the primary endpoint; the registry record does not explain the reason for those group sizes. That limits interpretation of the later comparison and its precision.

The safety summary supplies event counts and selected serious-event terms but does not give the full context needed to assess timing, exposure, attribution, or a formal comparative safety analysis. Death counts are not reported in the registry record. The record also does not report the original sample-size justification, interim-analysis plan, or detailed randomization and allocation-concealment procedures. These limitations concern what can be assessed from the registry record; they should not be turned into assumptions about procedures that may have been documented elsewhere.

20. Related Tutorials

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23. Record Summary

NCT01095796 is a completed Phase 3 randomized, quadruple-masked, parallel-group study comparing Stribild with Atripla in antiretroviral treatment-naive adults with HIV-1 infection. The registry reports enrollment of 707 participants, a start of 2010-03, and primary completion of 2011-08. Matching placebos were used in the arm descriptions.

The primary outcome was the percentage with HIV-1 RNA below 50 copies/mL at Week 48 under the FDA-defined Snapshot analysis. The posted response percentages were 87.6 for Stribild and 84.1 for Atripla. The sponsor reports a difference in response rates of 3.6, with a 95.2% confidence interval from -1.6 to 8.8, and classifies the analysis as non-inferiority or equivalence type. A simple unadjusted recalculation gives an Atripla-minus-Stribild risk difference of -0.035, with a 95% confidence interval from -0.087 to 0.016.

The registry lists further virologic and other secondary outcomes, but numerical results are not reported for every listed outcome. The non-inferiority margin, detailed missing-data rules, multiplicity plan, and original sample-size justification are not reported in the registry record.

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