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.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00207142 |
| Phase | Phase 4 |
| Condition | HIV Infections |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 252 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Bristol-Myers Squibb |
| Results posted | Yes |
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
| Stage | Induction Treatment | Maintenance Treatment: Switch Regimen | Maintenance Treatment: Continuation Regimen | Rescue Treatment |
|---|---|---|---|---|
| STARTED | 252 | 0 | 0 | 0 |
| COMPLETED | 222 | 0 | 0 | 0 |
| NOT COMPLETED | 30 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Induction Treatment | Maintenance Treatment: Switch Regimen | Maintenance Treatment: Continuation Regimen | Rescue Treatment |
|---|---|---|---|---|
| Adverse Event | 9 | 0 | 0 | 0 |
| Death | 1 | 0 | 0 | 0 |
| Lack of Efficacy | 1 | 0 | 0 | 0 |
| Lost to Follow-up | 5 | 0 | 0 | 0 |
| Physician Decision | 2 | 0 | 0 | 0 |
| Poor/noncompliance | 2 | 0 | 0 | 0 |
| Pregnancy | 1 | 0 | 0 | 0 |
| Subject no longer meets study criteria | 3 | 0 | 0 | 0 |
| Withdrawal by Subject | 4 | 0 | 0 | 0 |
| Incarceration | 1 | 0 | 0 | 0 |
| Missing lab data | 1 | 0 | 0 | 0 |
Maintenance Phase/Rescue Phase
| Stage | Induction Treatment | Maintenance Treatment: Switch Regimen | Maintenance Treatment: Continuation Regimen | Rescue Treatment |
|---|---|---|---|---|
| STARTED | 0 | 87 | 85 | 50 |
| COMPLETED | 0 | 78 | 72 | 41 |
| NOT COMPLETED | 0 | 9 | 13 | 9 |
Reasons for not completing this period:
| Reason | Induction Treatment | Maintenance Treatment: Switch Regimen | Maintenance Treatment: Continuation Regimen | Rescue Treatment |
|---|---|---|---|---|
| Adverse Event | 0 | 1 | 4 | 1 |
| Lost to Follow-up | 0 | 1 | 1 | 2 |
| RTV intake impossible | 0 | 0 | 1 | 0 |
| Poor/noncompliance | 0 | 3 | 2 | 3 |
| Pregnancy | 0 | 2 | 2 | 0 |
| Subject no longer meets study criteria | 0 | 0 | 1 | 0 |
| Withdrawal by Subject | 0 | 2 | 2 | 1 |
| Death | 0 | 0 | 0 | 1 |
| Lack of Efficacy | 0 | 0 | 0 | 1 |
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.
| Characteristic | Unit | Randomized Subjects: Switch Regimen | Randomized Subjects: Continuation Regimen | Nonrandomized Subjects | Total |
|---|---|---|---|---|---|
| Participants analysed | 87 | 85 | 80 | 252 | |
| Age, Customized | years | 35 (21 to 66) | 35 (19 to 70) | 36 (20 to 71) | 36 (19 to 71) |
| Sex: Female, Male: Female | Participants | 22 | 24 | 16 | 62 |
| Sex: Female, Male: Male | Participants | 65 | 61 | 64 | 190 |
| Race/Ethnicity, Customized: White | Participants | 73 | 70 | 66 | 209 |
| Race/Ethnicity, Customized: Black | Participants | 14 | 14 | 11 | 39 |
| Race/Ethnicity, Customized: Other | Participants | 0 | 1 | 3 | 4 |
| Region of Enrollment: Europe | participants | 68 | 68 | 60 | 196 |
| Region of Enrollment: Russian Federation | participants | 19 | 17 | 20 | 56 |
| Hepatitis B or C: Hepatitis B/C positive | Participants | 16 | 20 | 23 | 59 |
| Hepatitis B or C: Hepatitis B/C negative | Participants | 71 | 65 | 57 | 193 |
| Baseline CD4 | cells/mm3 | 255 (50 to 660) | 265 (64 to 490) | 227 (2 to 876) | 245 (2 to 876) |
| Baseline HIV-1 RNA | log10c/mL | 4.85 (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.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Percentage of participants |
| Endpoint classification | Binary 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
- Continuation Regimen: 75.3% (64/85) versus 78.2% (68/87) on control; risk difference -2.9 percentage points (95% CI -15.5 to 9.8), risk ratio 0.96 (0.82–1.14); unadjusted two-proportion z-test p = 0.656.
Risk difference: Continuation Regimen
95% CI: -15.5 to 9.8 percentage points
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percentage of Participants With HIV-1 RNA <400 c/mL Through Week 48 of the Maintenance Phase | Binary Endpoint | Risk 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 Phase | Continuous Endpoint | Mean difference | -8.00 (-53.70 to 37.70) | 4,706 per arm |
| Change From Baseline in CD4 Cell Count at Week 24 of Induction Phase | Continuous Endpoint | Mean difference | 31.00 (-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
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Continuation Regimen: 81.2% (69/85) versus 86.2% (75/87) on control; risk difference -5.0 percentage points (95% CI -16.1 to 6.0), risk ratio 0.94 (0.82–1.08); unadjusted two-proportion z-test p = 0.372.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Continuation Regimen and the control. The interval gives the range of effects that remain compatible with the data.
Change From End of Induction Phase in CD4 Cell Count at Week 48 of Maintenance Phase
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Continuation Regimen: mean 92.00 versus 100.00 on control; difference -8.00 (95% CI -53.70 to 37.70), standardized effect d = -0.06; z-test p = 0.732.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Continuation Regimen and the control. The interval gives the range of effects that remain compatible with the data.
Change From Baseline in CD4 Cell Count at Week 24 of Induction Phase
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Nonrandomized Subjects: mean 201.00 versus 170.00 on control; difference 31.00 (95% CI -10.22 to 72.22), standardized effect d = 0.25; z-test p = 0.140.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Nonrandomized Subjects and the control. The interval gives the range of effects that remain compatible with the data.
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):
- Percentage of Participants With HIV-1 RNA <400 c/mL Through Week 48 of the Maintenance Phase
- Kaplan-Meier Cumulative Proportion for Treatment Failure (HIV-1 RNA ≥50 c/mL) at Different Time Points Through Week 48 of the Maintenance Phase
- Kaplan-Meier Cumulative Proportion for Treatment Failure (HIV-1 RNA ≥400 c/mL) at Different Time Points Through Week 48 of the Maintenance Phase
- Change From End of Induction Phase in CD4 Cell Count at Week 48 of Maintenance Phase
- Change From Baseline in CD4 Cell Count at Week 24 of Induction Phase
- Change From Baseline in CD4 Cell Count at Week 48 of Rescue Phase
- Change From Baseline in HIV-1 RNA at Week 24 of the Induction Phase
- Change From Baseline in HIV-1 RNA at Week 48 of the Rescue Phase
9. Statistical 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 detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 3,410 | 4,564 |
| 75% of the observed effect | 5,997 | 8,028 |
| 50% of the observed effect | 13,345 | 17,865 |
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 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
- Control proportion p0 = 0.782; treatment proportion p1 = 0.753; average p̄ = 0.767.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5976 = 1.1713.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5973 = 0.5027.
- 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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Normal approximation | Difference in proportions 2.9 | -9.8 to 15.5 | not 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.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Switch Regimen | 7 | 87 | 8.0% |
| Continuation Regimen | 5 | 85 | 5.9% |
| Non-Randomized Participants | 11 | 80 | 13.8% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Switch Regimen | 72 of 87 |
| Continuation Regimen | 75 of 85 |
| Non-Randomized Participants | 52 of 80 |
Most frequent serious adverse event terms
| Event term | Organ system | Switch Regimen | Continuation Regimen | Non-Randomized Participants |
|---|---|---|---|---|
| PNEUMONIA | Infections and infestations | 1 of 87 | 1 of 85 | 2 of 80 |
| INGUINAL HERNIA | Gastrointestinal disorders | 2 of 87 | 0 of 85 | 0 of 80 |
| PANCREATITIS ACUTE | Gastrointestinal disorders | 0 of 87 | 0 of 85 | 2 of 80 |
| ANAEMIA | Blood and lymphatic system disorders | 1 of 87 | 0 of 85 | 1 of 80 |
| ANXIETY | Psychiatric disorders | 0 of 87 | 0 of 85 | 1 of 80 |
| DRUG DEPENDENCE | Psychiatric disorders | 1 of 87 | 0 of 85 | 0 of 80 |
| SUICIDE ATTEMPT | Psychiatric disorders | 0 of 87 | 0 of 85 | 1 of 80 |
| CHOLELITHIASIS | Hepatobiliary disorders | 0 of 87 | 0 of 85 | 1 of 80 |
| VOMITING | Gastrointestinal disorders | 1 of 87 | 0 of 85 | 0 of 80 |
| DIARRHOEA | Gastrointestinal disorders | 0 of 87 | 0 of 85 | 1 of 80 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Switch Regimen | Continuation Regimen | Non-Randomized Participants |
|---|---|---|---|---|
| BLOOD BILIRUBIN INCREASED | Investigations | 32 of 87 | 33 of 85 | 17 of 80 |
| OCULAR ICTERUS | Eye disorders | 15 of 87 | 18 of 85 | 6 of 80 |
| NAUSEA | Gastrointestinal disorders | 10 of 87 | 13 of 85 | 12 of 80 |
| DIARRHOEA | Gastrointestinal disorders | 14 of 87 | 14 of 85 | 5 of 80 |
| HEADACHE | Nervous system disorders | 11 of 87 | 13 of 85 | 8 of 80 |
| ASTHENIA | General disorders | 7 of 87 | 10 of 85 | 8 of 80 |
| ALANINE AMINOTRANSFERASE INCREASED | Investigations | 8 of 87 | 8 of 85 | 7 of 80 |
| NASOPHARYNGITIS | Infections and infestations | 5 of 87 | 7 of 85 | 7 of 80 |
| ABDOMINAL PAIN | Gastrointestinal disorders | 7 of 87 | 9 of 85 | 2 of 80 |
| ASPARTATE AMINOTRANSFERASE INCREASED | Investigations | 7 of 87 | 3 of 85 | 7 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%).
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 posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The 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.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Induction-Maintenance With Atazanavir in HIV Naïve Patients (The INDUMA Study) — NCT00207142.
- Registry record last updated 2010-01-12; status last verified 2010-01.
- Results first posted 2010-01-07.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
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.