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HIV Infections Phase 4 Binary Endpoint NCT00207142

Induction-Maintenance With Atazanavir in HIV Naïve Patients (The INDUMA Study): Complete Statistical Analysis

The INDUMA study compared switching to atazanavir without ritonavir with continuing atazanavir plus ritonavir after an induction phase in treatment-naive participants with HIV. The primary outcome was the percentage meeting a virologic success definition through Week 48 of maintenance.

Trial start: 2005-11  ·  Enrollment: 252  ·  Sponsor: Bristol-Myers Squibb
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 Induction-Maintenance With Atazanavir in HIV Naïve Patients (The INDUMA Study) (NCT00207142), a randomized phase 4 study. The primary outcome is Percentage of Participants With HIV-1 RNA <50 Copies/mL (c/mL) Through Week 48 of the Maintenance Phase.

252
Enrollment
Phase 4
2
Arms
In the primary outcome
-2.9 pts
Risk difference
Continuation Regimen
-15.5 to 9.8 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00207142
PhasePhase 4
ConditionHIV Infections
AllocationRandomized
Design modelParallel
MaskingNone (open label)
Enrollment252
Arms in the primary outcome2
Lead sponsorBristol-Myers Squibb
Results postedYes

2. Clinical Question

Population

The primary outcome concerns the as-randomized population: participants assigned to a regimen at randomization. The study enrolled treatment-naive participants with HIV infection. Its stated primary question focused on participants who had an initially undetectable viral load following an induction phase with a regimen containing atazanavir and ritonavir. The endpoint denominator, however, included all randomized participants.

Intervention

After induction, the switch regimen was atazanavir 400 mg once daily with two nucleoside reverse transcriptase inhibitors (NRTIs). The NRTI backbone was to continue from the previous phase; the specific NRTIs are listed as to be determined in the registry record.

Comparator

The continuation regimen was atazanavir 300 mg plus ritonavir 100 mg once daily, with two NRTIs. The study therefore contrasts an unboosted atazanavir maintenance regimen with a ritonavir-boosted regimen, while continuing the NRTI backbone.

Primary question

Among randomized participants, what proportion met the registry's definition of success through Week 48 of maintenance, based on HIV-1 RNA below 50 copies/mL and the absence of treatment failure or missing Week 48 viral-load data? The comparison is between switching to atazanavir alone and remaining on atazanavir plus ritonavir after induction. The registry record reports arm percentages and a sponsor analysis, while a simple unadjusted comparison can also be expressed as a risk difference. Neither estimate alone establishes that the regimens are equivalent or that one is preferable; that interpretation depends on the prespecified analysis and its criteria, which are not fully reported in the registry record.

3. Trial Design

INDUMA was a Phase IV, randomized, open-label, multicenter, parallel-group trial. It enrolled 252 participants and is recorded as completed. The registry lists a start of 2005-11 and primary completion in 2007-08. The interventions were atazanavir with two NRTIs and atazanavir plus ritonavir with two NRTIs.

The study had an induction phase followed by maintenance. The stated primary question concerned participants who had an initially undetectable viral load after induction with a regimen containing atazanavir and ritonavir. During maintenance, the switch group received atazanavir 400 mg once daily with two NRTIs; the continuation group received atazanavir 300 mg and ritonavir 100 mg once daily with two NRTIs. The named NRTI drugs are not specified in the registry record.

The primary outcome was assessed in the as-randomized population, defined in the registry as referring to the regimen assigned at randomization. The primary denominator included all randomized participants. The posted primary arm sizes were 87 for the Switch Regimen and 85 for the Continuation Regimen. The registry also describes a rescue regimen and reports some outcomes for nonrandomized participants, so not every result applies to the randomized comparison.

Open-label treatment means the study was not masked. The registry record does not report the method used to generate the random allocation sequence, allocation concealment procedures, the detailed multicenter structure, or the trial's original sample-size justification. The protocol's full statistical plan, including any planned interim analyses, is not reported in the registry record. The trial design can therefore be described from its posted characteristics and outcome definitions, but details beyond those details should not be inferred.

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: 288 subjects were enrolled, of which 36 did not start Induction Phase Therapy (22 did not meet study criteria, 6 withdrew consent, 4 lost to follow-up, 3 had missing information, and 1 for investigator's decision).

Induction Phase

StageInduction TreatmentMaintenance Treatment: Switch RegimenMaintenance Treatment: Continuation RegimenRescue Treatment
STARTED252000
COMPLETED222000
NOT COMPLETED30000

Reasons for not completing this period:

ReasonInduction TreatmentMaintenance Treatment: Switch RegimenMaintenance Treatment: Continuation RegimenRescue Treatment
Adverse Event9000
Death1000
Lack of Efficacy1000
Lost to Follow-up5000
Physician Decision2000
Poor/noncompliance2000
Pregnancy1000
Subject no longer meets study criteria3000
Withdrawal by Subject4000
Incarceration1000
Missing lab data1000

Maintenance Phase/Rescue Phase

StageInduction TreatmentMaintenance Treatment: Switch RegimenMaintenance Treatment: Continuation RegimenRescue Treatment
STARTED0878550
COMPLETED0787241
NOT COMPLETED09139

Reasons for not completing this period:

ReasonInduction TreatmentMaintenance Treatment: Switch RegimenMaintenance Treatment: Continuation RegimenRescue Treatment
Adverse Event0141
Lost to Follow-up0112
RTV intake impossible0010
Poor/noncompliance0323
Pregnancy0220
Subject no longer meets study criteria0010
Withdrawal by Subject0221
Death0001
Lack of Efficacy0001

Analysis population for the primary outcome, as defined in the registry: As-randomized population (as-randomized refers to the treatment regimen assigned at randomization).

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.

CharacteristicUnitRandomized Subjects: Switch RegimenRandomized Subjects: Continuation RegimenNonrandomized SubjectsTotal
Participants analysed878580252
Age, Customizedyears35 (21 to 66)35 (19 to 70)36 (20 to 71)36 (19 to 71)
Sex: Female, Male: FemaleParticipants22241662
Sex: Female, Male: MaleParticipants656164190
Race/Ethnicity, Customized: WhiteParticipants737066209
Race/Ethnicity, Customized: BlackParticipants14141139
Race/Ethnicity, Customized: OtherParticipants0134
Region of Enrollment: Europeparticipants686860196
Region of Enrollment: Russian Federationparticipants19172056
Hepatitis B or C: Hepatitis B/C positiveParticipants16202359
Hepatitis B or C: Hepatitis B/C negativeParticipants716557193
Baseline CD4cells/mm3255 (50 to 660)265 (64 to 490)227 (2 to 876)245 (2 to 876)
Baseline HIV-1 RNAlog10c/mL4.85 (3.51 to 5.88)4.86 (3.58 to 5.88)5.46 (3.74 to 5.88)4.95 (3.51 to 5.88)

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With HIV-1 RNA <50 Copies/mL (c/mL) Through Week 48 of the Maintenance Phase, measured over From the end of Induction Phase (Week 26 to Week 30 of Induction Phase treatment) through Week 48 of Maintenance Phase.

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

The primary endpoint is the percentage of participants with HIV-1 RNA below 50 copies/mL through Week 48 of the maintenance phase. The timeframe begins at the end of induction, defined as Week 26 to Week 30 of induction treatment, and continues through Week 48 of maintenance. This endpoint is a binary success measure: each participant is classified as a success or not a success according to the registry definition.

Participants counted as successes unless they experienced treatment failure or had a missing Week 48 HIV-1 RNA result. Treatment failure included virologic rebound, defined as two consecutive on-treatment HIV-1 RNA results at or above 50 copies/mL, or a last HIV-1 RNA result at or above 50 copies/mL followed by discontinuation. Discontinuation before Week 48 also counted as failure. The denominator included all randomized participants.

A threshold-based endpoint offers a clinically interpretable way to describe whether participants met a specified virologic target over a defined period. Counting discontinuations and missing Week 48 results as failures also makes the success definition explicit for those cases rather than silently omitting them from the denominator. At the same time, this composite rule combines different reasons for not being classified as a success. The percentage therefore summarizes the endpoint definition as a whole; it does not separately identify the frequency or cause of each component. The registry's rationale for choosing this threshold, rather than another viral-load outcome, is not reported in the registry record.

7. Results Posted in the Registry

Risk difference: Continuation Regimen

-2.9

95% CI: -15.5 to 9.8 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals63.168.072.977.882.787.6Switch Regimen (n=87)Continuation Regimen (n=85)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Continuation Regimen-18-12-5.800.065.9212risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Percentage of Participants With HIV-1 RNA <400 c/mL Through Week 48 of the Maintenance PhaseBinary EndpointRisk difference-5.0 pts (-16.1 to 6.0)846 per arm
Change From End of Induction Phase in CD4 Cell Count at Week 48 of Maintenance PhaseContinuous EndpointMean difference-8.00 (-53.70 to 37.70)4,706 per arm
Change From Baseline in CD4 Cell Count at Week 24 of Induction PhaseContinuous EndpointMean difference31.00 (-10.22 to 72.22)259 per arm

Percentage of Participants With HIV-1 RNA <400 c/mL Through Week 48 of the Maintenance Phase

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Continuation Regimen-18-13-7.59-2.472.647.76risk difference (percentage points) vs control (95% CI)

Change From End of Induction Phase in CD4 Cell Count at Week 48 of Maintenance Phase

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Continuation Regimen-61-40-192.602445mean difference vs control (95% CI)

Change From Baseline in CD4 Cell Count at Week 24 of Induction Phase

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Nonrandomized Subjects-172.3121416079mean difference vs control (95% CI)

The registry posts a range of secondary outcomes covering another viral-load threshold, treatment failure over time, and changes in CD4 cell count and HIV-1 RNA at different study phases. The available numerical results include the Week 48 maintenance outcome using the 400 copies/mL threshold and CD4 cell-count changes. The registry record lists additional secondary outcomes, but not every listed outcome has a numerical result in the posted material summarized for this analysis.

Across the posted secondary comparisons with numerical estimates, the confidence intervals are broad and include no between-group difference. They therefore do not provide a precise, consistent basis for a separate claim about the comparative effects of the randomized maintenance regimens. The findings are best read alongside the primary result as additional, less definitive descriptions rather than as independent confirmation of a particular treatment conclusion. Some outcomes concern induction or nonrandomized participants, and those results do not answer the same randomized maintenance question as the primary endpoint.

Secondary results generally carry less weight than the primary result because they are often numerous, may be exploratory, and can be subject to multiplicity: when many hypotheses are tested, chance findings become more likely unless the analysis accounts for that testing. The registry record does not report a multiplicity adjustment or a hierarchy for interpreting the secondary outcomes. Unadjusted p-values, where posted, should therefore be treated cautiously and should not be isolated as confirmatory evidence. The secondary outcomes may add context about the study's measured domains, but they do not remove the uncertainty in the primary comparison or supply the missing non-inferiority margin.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, the posted percentages are 78.0 for the Switch Regimen and 75.0 for the Continuation Regimen. The registry's reported analysis gives a difference in proportions of 2.9, with a 95% confidence interval from -9.8 to 15.5. The registry labels this analysis as a non-inferiority or equivalence analysis, but the margin and the conclusion drawn by the sponsor are not reported in the registry record. The interval includes values on both sides of zero, so the estimate is compatible with a range of between-group differences rather than a single precise effect.

A separate simple, unadjusted re-calculation from the posted event counts gives a risk difference of -0.029 for continuation relative to switch, with a 95% confidence interval from -0.155 to 0.098. The corresponding counts are 64 of 85 in the continuation arm and 68 of 87 in the switch arm. These re-calculated results use the displayed counts and an unadjusted comparison; they are not a replacement for the sponsor's analysis. Because the registry's reported analysis is expressed as a difference in proportions and the recalculation is defined as continuation relative to switch, the sign and scale should be read with the group ordering in mind. The sponsor's own analysis takes precedence when describing the trial's reported analysis.

The estimate should not be read as evidence of equivalence merely because the reported analysis is labeled non-inferiority or equivalence. A formal non-inferiority interpretation requires a prespecified margin and a comparison of the confidence interval with that margin. The margin is not reported in the registry record. Nor should a non-significant unadjusted p-value be treated as proof that the regimens have identical outcomes. The posted unadjusted p-value is 0.656, but a failure to reject a null hypothesis is not evidence that any clinically meaningful difference has been ruled out.

The endpoint also applies a conservative classification to participants with missing Week 48 viral-load results and those who discontinued before Week 48. This rule is part of the outcome definition, not a general guarantee that all forms of missing information are handled without bias. The registry does not report the amount or pattern of missing data, reasons for discontinuation, or sensitivity analyses for alternative missing-data assumptions. Those details would help assess how dependent the result is on the endpoint's classification rule.

Overall, the posted estimates describe the observed randomized comparison under the registry's endpoint definition. They do not establish that either regimen is clinically superior, equivalent, or non-inferior. Such conclusions would require the full prespecified analysis context, including the non-inferiority margin and analysis-population details, which are not reported in the registry record.

10. Statistical Methods Explained

The primary outcome is a proportion: the number of participants meeting the endpoint definition relative to the randomized arm denominator. For this endpoint, the posted percentages are 78.0 in the switch arm and 75.0 in the continuation arm. The underlying posted counts are 68 of 87 and 64 of 85, respectively. A proportion is useful for a binary outcome because it communicates how often the defined event or success occurred in each group.

What a risk difference describes

A risk difference subtracts one group's proportion from the other's. It is expressed as an absolute difference on the proportion scale, not as a ratio. The recalculated comparison is defined as continuation relative to switch and is -0.029, with a 95% confidence interval from -0.155 to 0.098. This is a simple unadjusted calculation from the posted event counts. The confidence interval communicates uncertainty about the estimated difference; it is not a range that guarantees where the true effect lies.

Other measures, such as a risk ratio or odds ratio, compare groups on a relative scale. They answer a different question from the risk difference and can have different numerical behavior. The registry record includes recalculated relative measures, but an absolute difference is often more directly tied to the observed percentage-point contrast. No adjusted analysis is reported in the registry record, so the recalculated comparison should not be described as adjusted for participant characteristics or other factors.

How to read a confidence interval

A confidence interval is a range of estimates compatible with the data under the statistical method and its assumptions. A narrower interval indicates greater precision; a wider interval indicates less precision. The primary recalculated interval spans values below and above zero. That means it does not isolate a single direction of difference at the conventional two-sided 0.05 level. It also does not establish equivalence: an interval can include zero and still include differences that matter for a non-inferiority or equivalence question. That judgment requires a prespecified margin, which is not reported in the registry record.

What the sponsor reported

The registry lists a normal-approximation analysis of the difference in proportions, with a 95% confidence interval. It reports an estimate of 2.9 and interval limits of -9.8 and 15.5. No p-value is listed for that analysis. The registry labels it as non-inferiority or equivalence, but does not post the margin needed to assess that claim. The recalculated risk difference is not the same reported analysis; it is a straightforward unadjusted calculation based on the posted counts. The sponsor's own analysis takes precedence when describing what the trial reported.

Why outcome definitions matter

The primary outcome does not count only the Week 48 viral-load threshold. It also counts treatment failure and missing Week 48 viral-load results against success. The registry defines rebound using consecutive results or a final result followed by discontinuation, and also classifies discontinuation before Week 48 as failure. This makes the endpoint a composite decision rule that combines virologic and follow-up events. A reader should interpret the percentages as success under that entire rule rather than as a simple snapshot of viral load among participants with an observed Week 48 result.

Binary outcomes can be summarized using the event count and denominator, a proportion, and a between-group contrast with uncertainty. Those measures are related but not interchangeable. A percentage describes one arm; a risk difference compares arms; and a confidence interval describes precision around an estimate. General statistical interpretation also depends on the sampling and analysis assumptions. The registry does not report enough detail to assess every assumption of the sponsor's full analysis or to reconstruct its non-inferiority decision.

Why an unadjusted test is not the whole analysis

The posted recalculated p-value is 0.656. In general, a p-value measures how incompatible the observed data are with a specified null hypothesis under the model used. It is not the probability that the null hypothesis is true, and it does not show that the groups are equivalent. It also does not convey the range of plausible effect sizes as directly as a confidence interval. The registry does not report whether the sponsor used additional covariate adjustment, stratification, or other model features in its own analysis; these details are not reported in the registry record.

The trial's randomized allocation supports a comparison of the assigned regimens, but the registry record alone does not establish that every analysis detail was prespecified or that all relevant sensitivity analyses were performed. General statistical practice distinguishes a primary, prespecified endpoint from exploratory or secondary analyses because the evidential weight depends partly on how many questions were examined and how they were selected. For the posted primary result, the safest reading is descriptive: the arm percentages and reported interval characterize the observed comparison under the stated endpoint definition, while formal non-inferiority or equivalence cannot be assessed without the missing margin and fuller analysis plan.

11. Confidence Intervals and Precision

The primary sponsor-reported 95% confidence interval for the difference in proportions runs from -9.8 to 15.5, with an estimate of 2.9. This interval is broad enough to include values on either side of zero. The unadjusted recalculated risk difference, defined as continuation relative to switch, is -0.029, and its 95% confidence interval runs from -0.155 to 0.098. These intervals are not identical analyses: the first is the registry's reported result, while the second is a simple recalculation from the posted event counts.

In general, a confidence interval describes the precision of an estimate under the chosen method and assumptions. It is not a statement that every value inside the interval is equally likely, nor is it a guarantee about the true effect. A broad interval indicates that the estimate is uncertain enough to remain compatible with a range of effects. Here, the primary interval does not narrowly constrain the difference to values close to zero. It also extends in directions that could be relevant to a non-inferiority or equivalence question, depending on the chosen margin.

The registry record labels the sponsor's analysis as non-inferiority or equivalence but does not report the margin. Without that margin, the interval cannot be judged against the criterion required for such a conclusion. The arm percentages alone also do not convey precision: similar-looking point estimates can be accompanied by intervals that leave substantial uncertainty. The sample sizes and outcome counts are relevant to that precision, but the registry does not report the full planning rationale or all analysis details.

Accordingly, the posted result supports a description of the observed success proportions, not a definitive claim that the regimens are equivalent or that any meaningful difference has been excluded.

12. Planning a Similar Trial: Sample Size

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

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect3,4104,564
75% of the observed effect5,9978,028
50% of the observed effect13,34517,865
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00050,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Continuation Regimen.

The planning figures are illustrations based on the observed effect, not the trial's original design calculation. They list participants per arm for the binary outcomes and continuous outcomes discussed in the planning material. For time-to-event outcomes, the stated convention is a total number of events; the primary endpoint is not a time-to-event outcome, so its planning figures are participants per arm.

The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The trial's own original sample-size assumptions and justification are not reported in the registry record.

The 80% power column describes the planning number of participants per arm under which the stated assumptions would give an 80% chance of detecting the selected effect if that effect were the true effect and the model assumptions held. The 90% power column gives the corresponding planning number for a 90% chance. These are design calculations, not a measure of how much power the completed trial had after its results were observed.

The planning rows consider 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. A smaller effect is harder to distinguish from random variation, so the planning calculation requires more participants per arm. The figures are hypothetical planning illustrations and should not be read as evidence that the trial was adequately or inadequately powered. This is not observed power; it is a forward-looking calculation based on specified assumptions and an effect size drawn from the observed result.

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 = 0.782; treatment proportion p1 = 0.753; average p̄ = 0.767.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5976 = 1.1713.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5973 = 0.5027.
  4. n = (1.1713 + 0.5027)2 / (-0.0287)2 = 3,409.5, rounded up to 3,410 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.781609195402299                          # control proportion
p1 <- 0.752941176470588                          # 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(207142)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 3,410 (80% power), 4,564 (90% power)
 75% of observed effect: n per arm = 5,997 (80% power), 8,028 (90% power)
 50% of observed effect: n per arm = 13,345 (80% power), 17,865 (90% power)
power.prop.test: 3409.5 
Simulated power at n = 3,410 per arm: 0.802 (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
Normal approximationDifference in proportions 2.9-9.8 to 15.5not reported

The registry's sponsor-reported primary analysis uses a normal approximation for a difference in proportions. It reports an estimate of 2.9 with a 95% confidence interval from -9.8 to 15.5 and is labeled as a non-inferiority or equivalence analysis. The registry does not list a p-value for this analysis, and the non-inferiority or equivalence margin is not reported in the registry record.

The recalculated result is a simple, unadjusted risk difference based on the posted event counts. With continuation defined relative to switch, it is -0.029, with a 95% confidence interval from -0.155 to 0.098. These are not interchangeable labels for one exact analysis: the sponsor analysis and the recalculation can differ in group order, scale, and analytical details. The sponsor's estimate is reported in the registry's stated difference-in-proportions format; the recalculation follows the stated continuation-relative-to-switch convention.

The sponsor's own analysis takes precedence when describing the trial's reported result. The recalculation is useful as a transparent check based on the posted counts, but it does not establish what methods the sponsor used beyond the method named in the registry. Since the margin and fuller analysis plan are unavailable, the label alone is not enough to verify a formal non-inferiority or equivalence conclusion.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 17 outcome measures and 5 analyses. The posted record includes a primary endpoint alongside multiple secondary questions involving viral-load thresholds, treatment failure, and changes in laboratory measures across study phases. Examining several outcomes creates a multiplicity concern: even when none of the underlying effects is present, repeated testing can produce apparently notable results by chance.

Whether the investigators addressed multiplicity through a testing hierarchy, adjusted significance thresholds, or another procedure is not reported in the registry record. The registry also does not report a complete statistical analysis plan, so it is not possible to determine from the record which secondary analyses were confirmatory, how their results were intended to be interpreted, or whether planned analyses differed from those posted. Secondary findings should consequently be treated as less definitive than a prespecified primary analysis.

Missingness is partly addressed within the primary endpoint definition: participants with a missing Week 48 HIV-1 RNA result are not counted as successes. Discontinuation before Week 48 and specified virologic rebound events also count as treatment failure. This is an explicit classification rule, but the registry record does not report the number of missing Week 48 results, their reasons, or their distribution by treatment group. It does not describe sensitivity analyses under alternative assumptions about missing outcomes.

The primary analysis population is described as as-randomized, and the denominator includes all randomized participants. The registry does not report detailed analysis-population conventions for every secondary outcome, such as how participants with unavailable measurements were handled. Nor does it provide enough information to assess whether the sponsor performed additional analyses in other populations. These omissions limit assessment of robustness and make it important to distinguish the posted primary endpoint definition from unreported analysis details.

Finally, the record labels the primary analysis as non-inferiority or equivalence, but the margin is not reported. A multiplicity strategy, missing-data approach, and population definition are each important to interpreting such a claim. The record allows a careful description of the posted endpoint and estimates, but not a complete audit of the analysis plan or its confirmatory status.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Switch Regimen7878.0%
Continuation Regimen5855.9%
Non-Randomized Participants118013.8%
Participants with at least one serious adverse event
Serious adverse events by armSwitch Regimen8.0%Continuation Regimen5.9%Non-Randomized Participants13.8%% 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
Switch Regimen72 of 87
Continuation Regimen75 of 85
Non-Randomized Participants52 of 80

Most frequent serious adverse event terms

Event termOrgan systemSwitch RegimenContinuation RegimenNon-Randomized Participants
PNEUMONIAInfections and infestations1 of 871 of 852 of 80
INGUINAL HERNIAGastrointestinal disorders2 of 870 of 850 of 80
PANCREATITIS ACUTEGastrointestinal disorders0 of 870 of 852 of 80
ANAEMIABlood and lymphatic system disorders1 of 870 of 851 of 80
ANXIETYPsychiatric disorders0 of 870 of 851 of 80
DRUG DEPENDENCEPsychiatric disorders1 of 870 of 850 of 80
SUICIDE ATTEMPTPsychiatric disorders0 of 870 of 851 of 80
CHOLELITHIASISHepatobiliary disorders0 of 870 of 851 of 80
VOMITINGGastrointestinal disorders1 of 870 of 850 of 80
DIARRHOEAGastrointestinal disorders0 of 870 of 851 of 80

Most frequent non-serious adverse event terms

Event termOrgan systemSwitch RegimenContinuation RegimenNon-Randomized Participants
BLOOD BILIRUBIN INCREASEDInvestigations32 of 8733 of 8517 of 80
OCULAR ICTERUSEye disorders15 of 8718 of 856 of 80
NAUSEAGastrointestinal disorders10 of 8713 of 8512 of 80
DIARRHOEAGastrointestinal disorders14 of 8714 of 855 of 80
HEADACHENervous system disorders11 of 8713 of 858 of 80
ASTHENIAGeneral disorders7 of 8710 of 858 of 80
ALANINE AMINOTRANSFERASE INCREASEDInvestigations8 of 878 of 857 of 80
NASOPHARYNGITISInfections and infestations5 of 877 of 857 of 80
ABDOMINAL PAINGastrointestinal disorders7 of 879 of 852 of 80
ASPARTATE AMINOTRANSFERASE INCREASEDInvestigations7 of 873 of 857 of 80

Serious events with the highest arm-level rate: pancreatitis acute (2.5%), pneumonia (2.5%), inguinal hernia (2.3%), anxiety (1.2%), suicide attempt (1.2%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry reports serious adverse events for the randomized groups and for non-randomized participants. In the Switch Regimen group, 7 of 87 participants were affected; in the Continuation Regimen group, 5 of 85 were affected. Among non-randomized participants, 11 of 80 were affected. These figures describe the numbers at risk and the numbers affected in the registry's safety listing; they should not be interpreted as proof that treatment caused an event or that one regimen is safer.

The listed serious-event terms include acute pancreatitis and pneumonia, each reported as 2.5%, inguinal hernia at 2.3%, and anxiety, suicide attempt, and cholelithiasis, each at 1.2%. The registry also reports other adverse events for 72 of 87 switch participants, 75 of 85 continuation participants, and 52 of 80 non-randomized participants. These broad counts are distinct from the serious adverse event counts.

The registry record does not report deaths for these groups. It also does not provide enough detail to assess event timing, duration, severity beyond the serious-event classification, or how investigators judged relationship to treatment. Safety counts are descriptive and must be interpreted in the context of follow-up and ascertainment, which are not fully reported in the registry record.

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

The posted primary outcome describes success under a specific definition: participants had to avoid treatment failure and have a Week 48 HIV-1 RNA result, with the virologic threshold set below 50 copies/mL. The reported arm percentages are 78.0 for switching to atazanavir without ritonavir and 75.0 for continuing atazanavir with ritonavir. The sponsor's reported difference is 2.9, with a 95% confidence interval from -9.8 to 15.5. The unadjusted recalculation uses a different stated group-order convention and should be kept distinct from the sponsor result.

These findings do not, by themselves, establish that the regimens are equivalent, non-inferior, or superior. A non-inferiority or equivalence conclusion requires a prespecified margin and an analysis demonstrating that the confidence interval meets the relevant criterion. The margin is not reported in the registry record. The interval's inclusion of zero is also not proof that the groups are the same; it reflects uncertainty that is compatible with a range of differences.

The result applies to the trial's setting and to the endpoint and analysis population described in the registry. It should not be extended automatically to different populations, regimens, treatment durations, or outcome definitions. The registry describes treatment-naive participants, induction with atazanavir and ritonavir, and maintenance with the assigned regimen plus NRTIs. The specific NRTI backbone is not reported.

The endpoint combines virologic rebound, discontinuation, and missing Week 48 results in its failure rule. It therefore does not isolate a single biological outcome, and the percentages do not explain why participants failed to meet the success definition. The registry does not provide the full missing-data profile, sensitivity analyses, or complete statistical plan. The most defensible interpretation is a description of the posted randomized comparison with its stated uncertainty, not a treatment recommendation or a definitive claim of equivalence.

18. Why This Trial Matters Statistically

INDUMA illustrates why a point estimate alone is not enough to interpret a clinical trial comparison. The primary arm percentages are close in appearance, but the sponsor-reported 95% confidence interval extends across zero and over a range of possible differences. Statistical interpretation therefore depends on precision as well as the observed estimates.

The study is labeled as a non-inferiority or equivalence analysis, making the distinction between a conventional difference test and a margin-based conclusion especially important. A non-significant p-value cannot establish equivalence. The non-inferiority margin and full decision rule are not reported in the registry record, so the formal claim cannot be assessed from the posted information alone.

The endpoint definition also matters. Missing Week 48 data, discontinuation before Week 48, and specified rebound events are counted against success. That rule gives the outcome a practical treatment-failure interpretation, while combining different reasons for failure. A percentage based on this composite definition should not be mistaken for the percentage with a particular virologic measurement among only those with observed data.

The record further shows why reported analyses and transparent recalculations should be kept separate. A simple comparison from posted counts can help readers understand the scale and direction of an unadjusted contrast, but it cannot reproduce unreported elements of the sponsor's analysis. Finally, the multiple secondary outcomes highlight the need for a clear prespecified analysis hierarchy and cautious interpretation of unadjusted findings. These issues are central to reading evidence precisely, even when the displayed arm percentages appear similar.

19. Limitations

The registry record leaves important parts of the trial's statistical context unreported. It does not give the non-inferiority or equivalence margin, the original sample-size justification, a full statistical analysis plan, or details of any interim analyses. Without the margin, the sponsor's analysis label cannot be independently evaluated against a prespecified decision criterion.

The study was open-label, and the registry does not describe allocation concealment or the methods used to generate the random sequence. The primary outcome is based on an objective viral-load threshold, but the record does not detail outcome assessment procedures or whether all aspects of ascertainment were handled without knowledge of treatment assignment.

The NRTI backbone is not specified beyond two NRTIs, so the record does not identify the exact background regimens. The primary outcome's denominator includes all randomized participants and counts missing Week 48 results or discontinuations as failures, but the registry does not report the amount, timing, or reasons for missing data and discontinuation. Sensitivity analyses are not reported in the registry record.

The record lists numerous secondary outcomes, but a multiplicity strategy and a hierarchy for their interpretation are not reported. Some posted results concern nonrandomized participants or different trial phases, limiting their relevance to the randomized maintenance comparison. The secondary numerical findings are not a substitute for the primary analysis.

Finally, the posted safety figures are descriptive and do not include deaths in the registry record. Details about event timing, treatment relationship, or follow-up completeness are not reported. These limitations constrain what can be concluded from the registry entry, though they do not negate the descriptive value of the posted outcome counts and estimates.

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23. Record Summary

NCT00207142 is the completed Phase IV INDUMA randomized, open-label, multicenter, parallel-group trial. It enrolled 252 participants and compared switching to atazanavir with two NRTIs against continuing atazanavir plus ritonavir with two NRTIs after an induction phase.

The primary endpoint was the percentage meeting a Week 48 maintenance success definition based on HIV-1 RNA below 50 copies/mL, with treatment failure and missing Week 48 data counted against success. The registry reports arm percentages of 78.0 and 75.0 and a sponsor-reported difference of 2.9 with a 95% confidence interval from -9.8 to 15.5. The registry labels the analysis non-inferiority or equivalence, but the margin is not reported in the registry record.

The posted estimates describe the trial's defined outcomes and their uncertainty. They do not, on their own, establish superiority, non-inferiority, or equivalence. Important details of the original design assumptions, missing-data profile, and full statistical plan are not reported in the registry record.

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