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 An International Study to Evaluate Recombinant Interleukin-2 in HIV Positive Patients Taking Anti-retroviral Therapy (NCT00004978), a randomized phase 3 study. The primary outcome is New or Recurrent HIV Disease Progression Event Including Death.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00004978 |
| Phase | Phase 3 |
| Condition | HIV Infections |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 4150 |
| Arms in the primary outcome | 2 |
| Lead sponsor | National Institute of Allergy and Infectious Diseases (NIAID) |
| Results posted | Yes |
2. Clinical Question
Population
People with HIV-1 infection and CD4+ cell counts 300/mm^3 or greater were eligible, according to the official study title. The primary endpoint analysis is identified as an intention-to-treat population. The registry record does not provide further eligibility details in the registry record.
Intervention
Recombinant interleukin-2, or rIL-2, was given subcutaneously alongside the participant’s choice of combination anti-HIV medication. The study rationale describes rIL-2 as a naturally produced hormone involved in immune response and asks whether adding it to anti-HIV therapy changes longer-term HIV disease progression.
Comparator
The comparator arm received the participant’s anti-HIV medication of choice without rIL-2. The trial was randomized, open-label, and parallel-group, with no masking reported.
Primary question
From randomization through study end, did the proportion of participants experiencing a new or recurrent HIV disease progression event, including death, differ between the rIL-2 arm and the no-rIL-2 arm? The primary endpoint included death and specified serious HIV-related events. Follow-up had a median duration of 7.6 years.
This is a question about the effect of assignment to an add-on treatment strategy over extended follow-up, not only about short-term changes in laboratory measures. The registry describes immune-cell counts and plasma HIV RNA among secondary outcomes, but the primary endpoint concerns clinical disease progression or death. The posted results therefore speak to the recorded event outcome and its statistical uncertainty; they do not by themselves establish effects on every aspect of HIV disease, immune function, or quality of life.
3. Trial Design
NCT00004978 is a completed, randomized, phase III, international study of subcutaneous recombinant IL-2 in people with HIV-1 infection and CD4+ cell counts 300/mm^3 or greater. It used a parallel-group design and was open-label, with no masking. The registry lists 4150 participants enrolled and identifies the National Institute of Allergy and Infectious Diseases (NIAID) as sponsor. The study began in 2000-03, and primary completion was recorded in 2008-11.
One arm received rIL-2 with combination anti-HIV medication of choice; the other received anti-HIV medication of choice without rIL-2. The primary endpoint was assessed in the intention-to-treat population and covered the period from randomization through study end. The registry gives median follow-up of 7.6 years for this endpoint. The primary outcome was a participant-level event measure: whether a participant died or experienced at least one qualifying disease progression event.
Randomization supports comparison of assigned treatment groups, while the open-label design means participants and study personnel were not masked to assignment according to the registry record. The record does not report the method used to generate or conceal allocation, details of adherence to assigned treatment, or protocol-defined stopping rules. It also does not report the original sample-size justification, the planned statistical analysis in full, or interim analyses. These omissions limit what can be said about the study’s design decisions beyond the characteristics explicitly recorded.
The posted primary analysis includes event counts and an unadjusted comparison calculated from those counts, as well as the sponsor’s Cox regression result. These address related but not identical summaries: the event-count comparison contrasts the proportions with an event, whereas a Cox model is a time-to-event analysis. Interpretation should keep the analysis type in view rather than treating the estimates as interchangeable.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | rIL-2 | No rIL-2 |
|---|---|---|
| STARTED | 2090 | 2060 |
| COMPLETED | 1846 | 1790 |
| NOT COMPLETED | 244 | 270 |
Reasons for not completing this period:
| Reason | rIL-2 | No rIL-2 |
|---|---|---|
| Death | 107 | 116 |
| Lost to Follow-up | 101 | 108 |
| Withdrawal by Subject | 17 | 26 |
| site closure - not in analysis cohort | 19 | 20 |
Analysis population for the primary outcome, as defined in the registry: ITT
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 | rIL-2 | No rIL-2 | Total |
|---|---|---|---|---|
| Participants analysed | 2090 | 2060 | 4150 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 2071 | 2032 | 4103 |
| Age, Categorical: >=65 years | Participants | 19 | 28 | 47 |
| Age, Continuous | years | 40.8 (SD 8.8) | 40.9 (SD 9.1) | 40.8 (SD 9.0) |
| Sex: Female, Male: Female | Participants | 388 | 381 | 769 |
| Sex: Female, Male: Male | Participants | 1702 | 1679 | 3381 |
| Region of Enrollment: Argentina | participants | 276 | 278 | 554 |
| Region of Enrollment: Australia | participants | 107 | 98 | 205 |
| Region of Enrollment: Austria | participants | 16 | 18 | 34 |
| Region of Enrollment: Belgium | participants | 39 | 41 | 80 |
| Region of Enrollment: Brazil | participants | 48 | 50 | 98 |
| Region of Enrollment: Canada | participants | 74 | 67 | 141 |
| Region of Enrollment: Denmark | participants | 39 | 33 | 72 |
| Region of Enrollment: France | participants | 86 | 96 | 182 |
| Region of Enrollment: Germany | participants | 136 | 130 | 266 |
| Region of Enrollment: Ireland | participants | 3 | 1 | 4 |
| CD4+ cell count | cells/mm^3 | 465 (374 to 592) | 451 (370 to 578) | 458 (373 to 586) |
6. Primary Endpoint
The registry lists the primary outcome as New or Recurrent HIV Disease Progression Event Including Death, measured over from randomization through study end - median of 7.6 years follow-up.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint counts participants who died or experienced at least one specified HIV disease progression event from randomization through study end. Qualifying events included any CDC Category C 1993 AIDS-defining event, as well as a list of other serious conditions recorded in the endpoint description. The endpoint is reported as a number of participants, so it represents whether an individual had an event, not the total number of repeat events that may have occurred.
A combined endpoint of serious disease progression or death is used to capture clinically important outcomes over follow-up. Including death means that death is treated as an endpoint event rather than as an event-free outcome. This can be useful when the intervention question concerns the overall course of disease and mortality, but a composite can also combine outcomes that differ in type or severity. The registry record does not provide separate primary-endpoint results for each component.
The primary follow-up period runs from randomization through study end, with a median of 7.6 years. The posted participant counts show 159 participants with the endpoint in the rIL-2 arm and 165 in the no-rIL-2 arm. The sponsor’s reported analysis uses Cox regression and gives a hazard ratio with a confidence interval. These approaches describe different aspects of event experience: the count comparison records whether an event occurred over the specified period, while time-to-event analysis also uses event timing and follow-up information. The registry record does not provide further detail about event adjudication or the handling of incomplete follow-up.
7. Results Posted in the Registry
- No rIL-2: 8.1% (165/2040) versus 7.7% (159/2071) on control; risk difference 0.4 percentage points (95% CI -1.2 to 2.1), risk ratio 1.05 (0.85–1.30); unadjusted two-proportion z-test p = 0.625.
Risk difference: No rIL-2
95% CI: -1.2 to 2.1 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 |
|---|---|---|---|---|
| New or Recurrent Serious HIV Disease Progression Event Including Death | Binary Endpoint | Risk difference | +0.3 pts (-1.2 to 1.8) | 110,126 per arm |
| Number of Participants Who Died From Any Cause | Binary Endpoint | Risk difference | +0.5 pts (-0.9 to 1.9) | 29,828 per arm |
| Participants With a New Disease Progression Event or Death | Binary Endpoint | Risk difference | +0.6 pts (-1.0 to 2.2) | 30,800 per arm |
New or Recurrent Serious HIV Disease Progression Event Including Death
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- No rIL-2: 6.4% (130/2040) versus 6.1% (126/2071) on control; risk difference 0.3 percentage points (95% CI -1.2 to 1.8), risk ratio 1.05 (0.83–1.33); unadjusted two-proportion z-test p = 0.702.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between No rIL-2 and the control. The interval gives the range of effects that remain compatible with the data.
Number of Participants Who Died From Any Cause
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- No rIL-2: 5.7% (116/2040) versus 5.2% (107/2071) on control; risk difference 0.5 percentage points (95% CI -0.9 to 1.9), risk ratio 1.10 (0.85–1.42); unadjusted two-proportion z-test p = 0.462.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between No rIL-2 and the control. The interval gives the range of effects that remain compatible with the data.
Participants With a New Disease Progression Event or Death
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- No rIL-2: 8.0% (164/2040) versus 7.4% (154/2071) on control; risk difference 0.6 percentage points (95% CI -1.0 to 2.2), risk ratio 1.08 (0.88–1.34); unadjusted two-proportion z-test p = 0.469.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between No rIL-2 and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes add context to the primary endpoint by considering related clinical events, death, a broader combination of progression or death, and measures such as CD4 cell counts and plasma HIV RNA. In the event outcomes with posted comparisons, the recalculated risk differences are close to zero and the confidence intervals include no difference. The sponsor’s reported Cox estimates for those outcomes also have confidence intervals that include the no-difference value. This overall pattern is consistent with the primary result’s lack of a clearly resolved group separation.
That consistency should not be mistaken for independent confirmation. Secondary outcomes may overlap conceptually or in their event definitions, and the registry record does not report a prespecified hierarchy or multiplicity adjustment. When several outcomes are examined, the chance of at least one apparently unusual result can increase. Unadjusted secondary p-values therefore carry less weight than a single prespecified primary analysis, particularly when they are interpreted individually.
The registry identifies 9 secondary measures, including laboratory measures and treatment-related outcomes, but the details available for the event comparisons do not establish a consistent effect on all secondary domains. Results for an outcome should be interpreted in its own terms and with attention to its measurement and analysis. The registry record does not provide a complete account of how secondary analyses were selected, whether all planned analyses were posted, or how missing measurements were handled.
Secondary results can support interpretation by showing whether related outcomes point in a similar direction, but they cannot by themselves repair limitations in the primary analysis or establish a treatment effect. Here, the event-outcome pattern does not supply a strong contrasting signal to the primary result. Findings across multiple secondary measures remain exploratory unless the analysis plan and multiplicity approach establish otherwise; those details are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- New or Recurrent Serious HIV Disease Progression Event Including Death
- Number of Participants Who Died From Any Cause
- Participants With a New Disease Progression Event or Death
- Absolute CD4 Cell Counts Averaged Throughout Followup
- Plasma HIV RNA Levels
- Number of Participants With Changes in Anti-retroviral Treatment (ART)
- Grade 4 Signs and Symptoms
- Pattern of Use of Prophylaxis for Opportunistic Infections
9. Statistical Interpretation
For the primary endpoint, the posted counts are 159 participants in the rIL-2 arm and 165 in the no-rIL-2 arm. The corresponding posted event proportions are 0.077 and 0.081, respectively. The recalculated unadjusted risk difference is 0.004, with a 95% confidence interval from -0.012 to 0.021 and an unadjusted p-value of 0.625. The estimate is small, and the interval includes no difference. It also includes differences in either direction, so the count-based comparison does not establish a clear separation between the groups.
The sponsor’s Cox regression result for the primary endpoint is a hazard ratio of 0.94, with a 95% confidence interval from 0.75 to 1.16 and p = .55. This result likewise does not provide strong evidence of a between-group difference under conventional significance testing. The confidence interval includes the value corresponding to no difference in hazard and allows for effects in either direction. The hazard ratio and the unadjusted risk difference are not the same estimand: one is from a time-to-event model, while the other compares the proportions with an event over the recorded period.
For the other posted event outcomes, the recalculated risk differences are also close to zero and their confidence intervals include no difference. The sponsor’s Cox results for those outcomes have confidence intervals that also include the no-difference value. This broad pattern is compatible with the primary result, but the secondary outcomes should not be treated as independent confirmatory tests. Their multiplicity handling is not reported in the registry record, and unadjusted results are less persuasive when many outcomes are examined.
These findings describe the posted comparisons; they do not prove that the treatment strategies are equivalent. A non-significant result can arise when the data are compatible with no difference as well as with effects of potentially meaningful size. The confidence intervals are important for that reason: they show the range of estimates compatible with the data under the analysis, rather than establishing that the true effect is exactly the point estimate. The record does not identify a threshold for a clinically important difference, so the estimates cannot be classified against such a threshold from the registry information alone.
The trial’s randomized design supports an intention-to-treat comparison of assigned groups, but the registry record does not report enough detail about missing follow-up, treatment adherence, or analysis implementation to assess every possible source of bias. The posted analyses should therefore be read as evidence about the recorded outcomes and methods, with uncertainty retained. Neither a favorable interpretation nor a claim of no effect is justified by the p-values alone.
10. Statistical Methods Explained
Several statistical ideas help distinguish what the posted estimates say from what they cannot establish. The primary outcome is binary at the participant level: each participant is counted as having experienced the endpoint or not. A risk or event proportion describes the fraction of participants with an event during the stated follow-up period. The difference between the two proportions is an absolute comparison, expressed in the same scale as the proportions. A positive risk difference in the posted comparison means the no-rIL-2 proportion is higher than the rIL-2 proportion, based on the stated arm ordering.
What does the risk difference describe?
The recalculated unadjusted risk difference compares event proportions without adjustment for other variables. For the primary endpoint, the estimate is 0.004, with a 95% confidence interval from -0.012 to 0.021. The interval crosses zero, the value representing no difference in the risk-difference scale. This indicates that the data do not pinpoint the direction of the difference. The result should not be paraphrased as proof that the groups have identical risk: the interval allows values on both sides of zero.
The risk difference is an absolute measure. In contrast, a risk ratio compares proportions as a relative measure, and an odds ratio compares the odds of an event. Those measures answer related questions but use different scales. The record includes recalculated relative measures, but the primary sponsor analysis is a Cox regression hazard ratio. These estimates should not be mixed or translated into one another without assumptions and appropriate data.
Why is the Cox result different in form?
Cox regression is a time-to-event method. It uses information about when events occur and about how long participants are followed, rather than reducing all observations to only whether an event occurred. The sponsor reports a hazard ratio of 0.94 for the primary endpoint, with a 95% confidence interval from 0.75 to 1.16 and p = .55. A hazard ratio compares event rates over time under the model; it is not an absolute difference in the proportion experiencing an event. The registry record does not give the model’s covariate specifications or enough detail to assess its assumptions.
In general, a Cox model relies on a proportional-hazards assumption: the relative event rate between groups is treated as stable over time. If that assumption does not hold, a single hazard ratio may not adequately summarize changing effects. The registry record does not report a proportional-hazards assessment, so no claim about whether that assumption was met can be made. This is a general methodological consideration, not a reported finding about this trial.
What does a confidence interval add?
A confidence interval communicates statistical precision by showing a range of values compatible with the observed data under the chosen method. It is not a guarantee that the true effect lies within the interval, nor does it assign a probability to each value. For the primary risk difference, the interval includes zero and includes differences in either direction. For the sponsor’s hazard ratio, the interval includes 1.00, the no-difference value on the hazard-ratio scale. Both intervals therefore leave uncertainty about the direction and magnitude of the effect.
A p-value summarizes how inconsistent the observed data are with a specified null hypothesis under the statistical model. The primary recalculated unadjusted p-value is 0.625, and the sponsor’s reported p-value is .55. A p-value is not the probability that the null hypothesis is true, and it does not measure the importance of an effect. It should be interpreted alongside the estimate, its interval, and the design and analysis details.
Why can simple recalculations and the sponsor analysis differ?
The recalculated risk difference uses the posted event counts and group sizes as an unadjusted comparison. The sponsor’s analysis uses Cox regression and incorporates event timing. Different methods can produce different numerical estimates because they summarize different information and may use different modeling choices. The registry record does not report enough detail to reproduce the sponsor’s model fully. There is no flagged discrepancy between the posted and recalculated results, but the sponsor’s own analysis remains the relevant reported time-to-event analysis.
General statistical interpretation also depends on how outcome events and follow-up are measured. For time-to-event methods, participants who do not have an observed event may be censored when follow-up ends or is otherwise incomplete. Censoring is valid for standard interpretations only under assumptions about the relationship between censoring and event risk. The record does not describe censoring details or missing-data procedures, so these assumptions cannot be evaluated from the registry record.
Finally, interpretation across multiple outcomes requires attention to multiplicity. When many outcomes are tested, some results may appear noteworthy by chance. The registry record does not report a multiplicity adjustment or a hierarchy for confirmatory testing. The primary endpoint has a clearer role as the designated main outcome, while the secondary outcomes offer additional context and should be interpreted more cautiously when considered individually.
11. Confidence Intervals and Precision
Precision concerns how narrowly an analysis estimates the treatment-group contrast. For the primary unadjusted risk difference, the estimate is 0.004 and the 95% confidence interval runs from -0.012 to 0.021. The interval includes zero, so the observed data are compatible with a small difference in either direction. Its span also means that the point estimate alone gives an incomplete impression of uncertainty.
The sponsor’s primary Cox estimate is a hazard ratio of 0.94, with a 95% confidence interval from 0.75 to 1.16. The interval includes 1.00, the no-difference value for a hazard ratio. It allows for a lower or higher hazard relative to the model’s comparison direction, rather than identifying a single direction with precision. The registry record does not report a clinically important threshold against which to judge the interval.
In general, confidence intervals combine information about the estimate and its uncertainty under an analysis method. They are not a range of outcomes that individual participants might experience, and they do not mean that every value inside is equally plausible. A confidence interval is also not a substitute for understanding how the analysis was conducted, including follow-up, censoring, and model assumptions. The registry record does not report enough detail to assess all of those features.
Across the posted primary and secondary comparisons, the estimates do not show a sharply resolved separation between groups. That should be distinguished from proof of equivalence: equivalence requires a prespecified margin and an analysis designed to assess whether the uncertainty lies within that margin. Such a margin is not reported in the registry record. The available intervals therefore support a cautious reading focused on the range of effects that remains compatible with the analyses.
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 | 67,550 | 90,430 |
| 75% of the observed effect | 119,374 | 159,808 |
| 50% of the observed effect | 266,981 | 357,411 |
The planning figures are illustrative calculations based on the observed effect, not the trial’s original design assumptions. For the binary participant outcomes, they are expressed as participants per arm. The underlying 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 justification is not reported in the registry record.
The 80% power column describes the planned number of participants per arm for a hypothetical study designed to have an 80% chance of detecting the stated effect under those assumptions, if that effect were present. The 90% power column gives the corresponding planning target for a 90% chance. These are design calculations, not results about the probability that the completed study detected an effect. This is not observed power.
The rows for 100%, 75%, and 50% of the observed effect show how the planning requirement changes when the hypothetical effect to detect is smaller. Smaller effects need more participants because they are harder to distinguish from random variation. For example, the primary endpoint’s planning figures rise from 67,550 participants per arm for 80% power when planning for 100% of the observed effect, to 266,981 participants per arm when planning for 50% of that effect. The corresponding 90% figures are 90,430 and 357,411 participants per arm.
These illustrations should not be interpreted as a judgment that the completed trial was underpowered or that the assumed effects were clinically important. They are mechanically tied to the observed estimate, which is itself uncertain. If the observed effect is small, calculations based on fractions of it can produce very large planning targets. The registry record does not report that these assumptions were used to plan the actual trial.
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 = 0.077; treatment proportion p1 = 0.081; average p̄ = 0.079.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.3811 = 0.7469.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.3811 = 0.3207.
- n = (0.7469 + 0.3207)2 / (0.0041)2 = 67,549.9, rounded up to 67,550 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 <- 0.0767745050700145 # control proportion
p1 <- 0.0808823529411765 # 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(4978)
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 = 67,550 (80% power), 90,430 (90% power)
75% of observed effect: n per arm = 119,374 (80% power), 159,808 (90% power)
50% of observed effect: n per arm = 266,981 (80% power), 357,411 (90% power)
power.prop.test: 67549.9
Simulated power at n = 67,550 per arm: 0.805 (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 |
|---|---|---|---|
| Regression, Cox | Hazard Ratio (HR) 0.94 | 0.75 to 1.16 | 0.550 |
The sponsor’s reported primary analysis is Cox regression, with a hazard ratio of 0.94, a 95% confidence interval from 0.75 to 1.16, and p = .55. It is a time-to-event analysis and should be distinguished from the unadjusted recalculation based on event counts. The recalculated primary risk difference is 0.004, with a 95% confidence interval from -0.012 to 0.021 and unadjusted p-value 0.625.
These are not competing estimates of exactly the same quantity. The risk difference compares the proportions with an event over the recorded period; the Cox model uses event timing and follow-up. Both results are compatible with no clear between-group difference, and neither interval excludes its respective no-difference value. There is no reported discrepancy between the posted and recalculated results. The sponsor’s own analysis takes precedence as the registry’s reported time-to-event analysis, while the unadjusted recalculation is a simple check based on the posted summary counts.
The registry record does not provide enough model detail to independently reproduce or fully assess the Cox result. It does not specify covariate adjustment, model diagnostics, or censoring procedures. The hazard ratio should therefore be reported as the sponsor’s analysis, not treated as though it were derived from the unadjusted event proportions. The recalculation can help readers understand the crude event-count contrast, but it does not replace the sponsor’s analysis or resolve questions about model assumptions.
15. Multiplicity, Missing Data and Analysis Populations
The registry record does not report whether the trial used a formal multiplicity adjustment, a prespecified hierarchy among secondary outcomes, or a strategy for controlling the overall chance of false-positive findings. This matters because the record identifies 9 secondary measures. If many outcomes are tested and each is interpreted without adjustment, the likelihood that at least one result appears statistically notable by chance can increase. The posted secondary comparisons should therefore be read as supportive or exploratory evidence rather than as a set of independent confirmatory findings.
The primary endpoint is identified and analyzed in the intention-to-treat population. Intention-to-treat analysis generally compares participants according to randomized assignment, regardless of later adherence or treatment changes; this is a general explanation of the approach. The registry record does not provide details about the exact analysis implementation, such as how participants with missing outcome information were handled, whether follow-up was complete, or what assumptions were made for incomplete observation. Missing-data procedures are not reported in the registry record.
The record gives a Cox regression analysis for the primary endpoint, but the full statistical analysis plan is not reported. Details such as model covariates, diagnostic checks, censoring rules, and the handling of protocol deviations are not reported in the registry record. These omissions limit independent assessment of the time-to-event analysis and whether the reported estimate reflects all prespecified choices.
The original sample-size justification and any interim analyses are also not reported in the registry record. The planning illustrations associated with the posted effects are separate from those original design decisions. Without a protocol or analysis plan in the record, it is not possible to determine from the stated information whether outcomes, analysis choices, or stopping procedures were changed during the study. This uncertainty is a limitation of the available record, not evidence that such changes occurred.
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 |
|---|---|---|---|
| rIL-2 | 466 | 2071 | 22.5% |
| No rIL-2 | 383 | 2040 | 18.8% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0.5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| rIL-2 | 133 of 2071 |
| No rIL-2 | 92 of 2040 |
Most frequent serious adverse event terms
| Event term | Organ system | rIL-2 | No rIL-2 |
|---|---|---|---|
| Infections - pathogen unspecified | Infections and infestations | 47 of 2071 | 42 of 2040 |
| Coronary artery disorders | Cardiac disorders | 41 of 2071 | 46 of 2040 |
| Bacterial infectious disorders | Infections and infestations | 20 of 2071 | 17 of 2040 |
| Viral infectious disorders | Infections and infestations | 19 of 2071 | 18 of 2040 |
| Gastrointestinal signs and symptoms | Gastrointestinal disorders | 15 of 2071 | 13 of 2040 |
| Gastrointestinal neoplasms malignant and unspecified | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 20 of 2071 | 8 of 2040 |
| Suicidal and self-injurious behaviours NEC | Psychiatric disorders | 18 of 2071 | 10 of 2040 |
| Central nervous system vascular disorders | Nervous system disorders | 16 of 2071 | 11 of 2040 |
| General system disorders NEC | General disorders | 17 of 2071 | 6 of 2040 |
| Bone and joint injuries | Injury, poisoning and procedural complications | 15 of 2071 | 8 of 2040 |
Most frequent non-serious adverse event terms
| Event term | Organ system | rIL-2 | No rIL-2 |
|---|---|---|---|
| Myocardial infarction | Cardiac disorders | 14 of 2071 | 18 of 2040 |
| Acute myocardial infarction | Cardiac disorders | 16 of 2071 | 15 of 2040 |
| Pyrexia | General disorders | 18 of 2071 | 9 of 2040 |
| Diarrhoea | Gastrointestinal disorders | 16 of 2071 | 10 of 2040 |
| Coronary artery disease | Cardiac disorders | 12 of 2071 | 9 of 2040 |
| Depression | Psychiatric disorders | 14 of 2071 | 7 of 2040 |
| Suicide attempt | Psychiatric disorders | 11 of 2071 | 10 of 2040 |
| Anaemia | Blood and lymphatic system disorders | 9 of 2071 | 10 of 2040 |
| Appendicitis | Infections and infestations | 10 of 2071 | 8 of 2040 |
| Cerebrovascular accident | Nervous system disorders | 12 of 2071 | 4 of 2040 |
Serious events with the highest arm-level rate: infections - pathogen unspecified (2.3%), coronary artery disorders (2.3%), bacterial infectious disorders (1.0%), gastrointestinal neoplasms malignant and unspecified (1.0%), viral infectious disorders (0.9%).
The adverse-event record reports serious adverse events affecting 466 participants in the rIL-2 arm and 383 participants in the no-rIL-2 arm. It reports other adverse events affecting 133 participants in the rIL-2 arm and 92 participants in the no-rIL-2 arm. The at-risk counts are 2071 for rIL-2 and 2040 for no rIL-2. These are participant counts, not counts of every event episode, and they should not be interpreted as adjusted comparisons of safety.
The registry also lists serious-event terms with percentages, including infections - pathogen unspecified and coronary artery disorders at 2.3% each, and bacterial infectious disorders and gastrointestinal neoplasms malignant and unspecified at 1.0% each. These terms are listed among the top serious terms; the record does not provide arm-specific percentages for them in the registry record. Death-specific values in the adverse-event record are not reported in the registry record, although deaths are included in the primary and secondary efficacy outcomes.
Differences in raw adverse-event counts do not establish that one arm is safer or less safe. A fuller safety comparison would require context about exposure, event definitions, severity, duration, relatedness, follow-up completeness, and statistical analysis. Those details are not reported in the registry record. The figures describe what was posted, not a causal conclusion about the intervention.
17. What the Result Does, and Does Not, Mean
The registry results show that the posted primary event proportions were similar in scale between the assigned groups, and the sponsor’s time-to-event estimate did not provide a statistically clear separation. The unadjusted risk-difference interval includes zero, and the sponsor’s hazard-ratio interval includes the no-difference value. This supports a cautious summary: the analyses do not demonstrate a clear between-group difference in the primary endpoint.
That conclusion is not the same as proving that rIL-2 and no rIL-2 have identical effects. The intervals allow a range of possible effects, and the registry record does not provide a clinically important threshold to judge whether any of those effects would matter. Nor does a non-significant p-value establish that the intervention has no effect. It indicates that the data, under the analysis used, do not provide strong evidence against the tested no-difference hypothesis.
The result concerns the specified clinical endpoint and study population: people with HIV-1 infection and CD4+ cell counts 300/mm^3 or greater, as described in the official title. It does not establish effects for populations not described in the record, nor does it settle effects on every laboratory, clinical, or quality-of-life outcome. The posted study rationale discusses immune restoration, but the primary result is about disease progression events including death, not a general measure of immune recovery.
The trial was randomized and open-label, and the primary endpoint was analyzed in the intention-to-treat population. Those details are important to interpretation, but uncertainty remains about missing data, adherence, model assumptions, and outcome ascertainment because details are not reported in the registry record. The safest reading is bounded: describe the estimates and their uncertainty, avoid claims of equivalence or treatment success or failure, and distinguish the sponsor’s time-to-event analysis from unadjusted event-count calculations.
18. Why This Trial Matters Statistically
This trial is statistically instructive because it places a long-term clinical outcome at the center of a randomized comparison. The primary endpoint combines death with specified HIV disease progression events and follows participants from randomization through study end, with a median follow-up of 7.6 years. That design focus differs from judging an intervention only by short-term laboratory measures. It also highlights the importance of specifying which outcome is primary when a study examines several dimensions of disease.
The record offers both participant-level event counts and a sponsor-reported Cox regression result. Seeing these side by side illustrates why different statistical methods can yield estimates with different interpretations. A crude risk difference summarizes the contrast in event proportions; a hazard ratio summarizes a time-to-event comparison under model assumptions. Neither should be mistaken for the other, and each should be read with its own confidence interval.
The study also shows why uncertainty matters when a result is not statistically significant. A point estimate near no difference does not establish equivalence, while a confidence interval conveys the range of effects still compatible with the analysis. The registry does not provide an equivalence margin or a clinically important threshold, so statistical non-significance cannot be turned into a definitive claim about practical sameness.
Finally, the registry’s incomplete reporting of the original sample-size justification, missing-data procedures, multiplicity control, and full model specification illustrates a general challenge in reading trial records. Results can be described accurately while recognizing limits on independent evaluation. In this case, the broad consistency between the primary and posted event-related secondary results is useful context, but it does not replace a prespecified analysis plan or eliminate the need to consider uncertainty and reporting gaps.
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.
The registry record leaves several trial-specific questions unanswered. The original sample-size justification is not reported, so the planning illustrations based on observed effects cannot be used to determine the trial’s original power target or whether its enrollment plan was adequate for a particular clinically important difference. Interim analyses are not reported in the registry record. The statistical analysis plan, including any prespecified hierarchy across outcomes, is also not reported.
The primary outcome is a composite of death and a range of serious disease progression events. Separate primary results for the components are not reported, so the overall comparison cannot show whether one component drove the combined result. Event adjudication procedures are not reported in the registry record. The posted primary analysis uses intention-to-treat, but details about follow-up completeness, missing outcome data, censoring, adherence, and treatment changes are not reported.
The study was open-label, with no masking. The registry record does not describe how outcome assessment was protected from knowledge of assignment, or whether ascertainment could have been influenced by that knowledge. This is a consideration when interpreting reported clinical events, not evidence that ascertainment was biased. The model details and diagnostics for the Cox analyses are also not reported, limiting assessment of the assumptions behind the hazard ratios.
The available safety information gives participant counts and selected serious-event terms but does not provide enough detail for a comprehensive comparative safety assessment. Exposure-adjusted rates, event relatedness, and detailed arm-specific frequencies for the listed terms are not reported in the registry record. These limits mean the safety figures should be treated as descriptive counts rather than as a complete estimate of comparative risk.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: An International Study to Evaluate Recombinant Interleukin-2 in HIV Positive Patients Taking Anti-retroviral Therapy — NCT00004978.
- Registry record last updated 2021-11-05; status last verified 2012-10.
- Results first posted 2011-04-25.
- 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.
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23. Record Summary
NCT00004978 is a completed, randomized, open-label, phase III, international parallel-group study sponsored by the National Institute of Allergy and Infectious Diseases (NIAID). It compared subcutaneous rIL-2 added to combination anti-HIV medication with anti-HIV medication alone in people with HIV-1 infection and CD4+ cell counts 300/mm^3 or greater. Enrollment was 4150, and median follow-up for the primary outcome was 7.6 years.
The primary endpoint was a new or recurrent HIV disease progression event including death. The posted event counts and the sponsor’s Cox regression analysis do not show a statistically clear difference between groups; both analyses retain uncertainty about the effect’s direction and size. The registry record does not report the original sample-size justification, multiplicity handling, missing-data procedures, or full model details, which limits independent assessment beyond the posted results.