Secondary HIV Prevention and Adherence Among HIV-infected Drug Users: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Secondary HIV Prevention and Adherence Among HIV-infected Drug Users (NCT01741311), a randomized na study. The primary outcome is Number of Participants in Each Condition With Optimal ART Adherence.

2. Clinical Question

3. Trial Design

The registry identifies this as a randomized, parallel-group trial of two behavioral programs: 3H+ and HHRP+. Allocation is recorded as randomized, and masking is recorded as none. The phase is listed as not applicable. The sponsor is the University of Connecticut, the status is completed, the start is recorded as 2012-09, and primary completion is recorded as 2018-06. These administrative details describe the registry record; they do not establish how the study was conducted at every visit.

The comparison is between two active approaches rather than between an intervention and no treatment. The 3H+ description includes standard drug treatment care with HIV risk reduction sessions and a booster. The HHRP+ description specifies a longer sequence of manual-guided group sessions. The arm descriptions in the registry record are incomplete, so additional details about delivery, staffing, adherence to the intervention, or treatment received outside the described components are not reported in the registry record.

The registry summary describes a randomized controlled comparative effectiveness trial among 256 people, whereas the enrollment field reports 106. The record does not explain this difference, so neither figure can be used to infer the reason for the other. The outcome summaries list 52 participants for 3H+ and 54 for HHRP+. The registry does not explain the relationship between these outcome denominators, the enrollment field, and the summary’s stated target.

The primary outcome is reported at six months, although its timeframe says assessments occurred post-intervention, at three months, and at six months. Viral suppression has the same stated assessment schedule and is also reported at six months. The registry record does not report the original sample-size justification, randomization procedure, allocation concealment, or the planned analysis population.

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

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.

6. Primary Endpoint

The registry lists the primary outcome as Number of Participants in Each Condition With Optimal ART Adherence, measured over Assessed at post-intervention, 3-months, & 6-months. Reported in the table at 6-months..

The primary endpoint counts participants classified as having optimal antiretroviral therapy (ART) adherence. Adherence was assessed by self-report using a visual analogue scale (VAS), described as a continuous measure from 0 to 100%, with higher scores indicating better reported adherence. The registry defines optimal adherence as a VAS score >95%. The posted outcome is therefore a count above a threshold, not the average VAS score or a comparison of the full continuous adherence distributions.

The timeframe lists post-intervention, three-month, and six-month assessments, and specifies that the result is reported at six months. At that assessment, 27 of 52 participants in 3H+ and 29 of 54 in HHRP+ were counted as having optimal adherence. The comparison expresses the contrast in proportions meeting the threshold. This binary form can make the result easier to interpret as the number meeting a prespecified category, but it does not show how far scores were above or below the cutoff, nor does it preserve all variation in the underlying VAS scores.

The endpoint addresses reported medication-taking behavior, an important study outcome in a trial focused on adherence and HIV risk reduction. Because it is self-reported, its interpretation depends on participant reports; the registry record does not describe corroboration using medication records or another adherence measure. The endpoint does not by itself describe viral suppression, which is separately listed as a secondary outcome.

7. Results Posted in the Registry

• HHRP+ Group: 53.7% (29/54) versus 51.9% (27/52) on control; risk difference 1.8 percentage points (95% CI -17.2 to 20.8), risk ratio 1.03 (0.72–1.48); unadjusted two-proportion z-test p = 0.854.

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.

Viral Suppression

• 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:
  • Holistic Health Recovery Program (HHRP+): 63.0% (34/54) versus 86.5% (45/52) on control; risk difference -23.6 percentage points (95% CI -39.4 to -7.7), risk ratio 0.73 (0.58–0.92); unadjusted two-proportion z-test p = 0.005.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Holistic Health Recovery Program (HHRP+) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Viral suppression is the only posted secondary endpoint. Its estimated direction differs from the primary adherence comparison: the posted contrast favors a higher observed proportion in 3H+ than in HHRP+, whereas the primary contrast is slightly positive for HHRP+ relative to 3H+. The secondary comparison is unadjusted and has a reported p-value of 0.005. These are separate outcomes, measuring different aspects of the study question, so the secondary pattern does not resolve the primary adherence comparison.

Unadjusted secondary results carry less weight when several outcomes or comparisons may be considered, because repeated testing increases the chance of finding an apparently notable result by chance. This is a general statistical concern. The registry record does not report a multiplicity procedure, a hierarchy of outcomes, or a prespecified rule for drawing conclusions across endpoints. It is therefore not possible to determine from the record whether the secondary finding was part of a planned confirmatory testing strategy or how it was intended to be interpreted alongside other outcomes.

The record lists two outcome measures and one posted secondary endpoint, but reports no analyses in its analyses listing. There may be additional planned measures or analyses that are not documented in the registry record. The posted information also does not provide secondary outcomes at the other stated assessment times. Accordingly, the secondary evidence is limited to the reported six-month summary and should be treated as supportive and exploratory in interpretation, rather than as a replacement for the primary result or a definitive account of the overall intervention effects.

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

• Viral Suppression

9. Statistical Interpretation

10. Statistical Methods Explained

The posted comparisons concern binary outcomes: each participant is counted as either meeting the endpoint definition or not. For the primary endpoint, the classification is based on whether a self-reported VAS adherence score is >95%. For viral suppression, the registry posts counts of participants. The record does not provide a detailed statistical analysis plan or identify the method used for the sponsor’s original analyses.

What does a risk difference describe?

A risk difference subtracts the proportion in one group from the proportion in the other. In the primary comparison, the contrast is presented for HHRP+ relative to 3H+. A positive estimate means the reported proportion meeting the endpoint is higher in HHRP+; a negative estimate means it is lower. A value of zero represents equal proportions in the compared groups. This is an absolute contrast in proportions, not a relative increase and not a comparison of average VAS scores.

For the primary endpoint, the point estimate is positive, but its confidence interval includes zero and extends to negative and positive values. This indicates that the posted summary is compatible with a range of possible group differences, including little or no difference and differences in either direction. The unadjusted p-value is 0.854. A p-value describes how unusual data at least as incompatible with a specified null hypothesis would be under the test’s assumptions; it is not the probability that the null hypothesis is true, and it does not measure the size or importance of an effect.

Why use a confidence interval?

In general, a confidence interval communicates uncertainty around an estimate. Its width reflects precision: a wider interval permits a broader range of values than a narrower interval. The interval is not a list of effects known to be true, and its endpoints do not identify the exact effect in the population. The primary interval crossing zero means the result does not sharply distinguish the direction of the group contrast. The viral suppression interval, by contrast, lies below zero for the stated HHRP+ relative to 3H+ comparison. That pattern describes the posted estimate and uncertainty, not a guarantee that the same contrast would appear in another study.

What do the reported counts leave out?

Reducing a continuous VAS score to a threshold simplifies the endpoint to a count meeting the definition. In general, dichotomization can make a threshold-based outcome straightforward to communicate, but it discards information about scores within each category. Participants just above and well above the cutoff are treated alike for this endpoint. The registry does not post the underlying VAS distributions, so those cannot be recovered from the counts. Likewise, the group counts alone do not show individual changes over time or how many people changed classification between assessments.

Which analyses are documented?

The posted primary comparison includes an unadjusted risk difference, confidence interval, and p-value. A relative risk and odds ratio are also included in the registry’s comparison data, but the interpretation emphasizes the risk difference because it expresses an absolute contrast in proportions. The registry record lists no reported analyses and does not specify covariate adjustment, an analysis population, missing-data procedures, or the statistical test used for the posted p-values. Those methods are not reported in the registry record and should not be inferred from the numerical summaries alone.

General statistical reasoning also distinguishes an estimate from a test result. The estimate describes the direction and magnitude of the observed contrast; the interval conveys precision; and the p-value assesses compatibility with a null comparison under particular assumptions. None alone determines clinical importance. For this study, the registry does not state a threshold for a clinically meaningful difference, so the observed contrasts cannot be classified against such a threshold from the record.

For binary outcomes, the precision of a comparison depends in part on the amount of information in each group and on how common the outcome is. More information can generally narrow uncertainty, while sparse events can make estimates less stable. This is a general explanation; the registry record does not document a formal assessment of these issues or adjustments for them. It also does not report whether the posted denominators correspond to an intention-to-treat population or another analysis set.

Finally, the design is randomized and parallel, but randomization alone does not answer every analytic question. General interpretation requires attention to follow-up, outcome ascertainment, missing data, and the analysis population. These details are not reported in the registry record. The posted results therefore support a description of the recorded group outcomes and unadjusted contrasts, but not assumptions about how unreported aspects of the analysis were handled.

11. Confidence Intervals and Precision

Precision is conveyed by the confidence interval around each risk-difference estimate. For optimal ART adherence, the HHRP+ relative to 3H+ estimate is positive, but the interval spans negative and positive values, including zero. The corresponding unadjusted p-value is 0.854. The interval is broad enough that the posted result does not precisely determine either the direction or the size of the population contrast. It should not be interpreted as evidence that the groups are exactly alike.

For viral suppression, the reported HHRP+ relative to 3H+ estimate is negative, and the confidence interval remains below zero. Its unadjusted p-value is 0.005. This interval is more directionally informative than the primary endpoint interval, but it still represents uncertainty around an estimate from the posted comparison. It does not establish that the same magnitude would be observed in other settings or populations.

In general, a confidence interval describes uncertainty under the assumptions of the calculation. It is not a guarantee that the true effect lies within its endpoints, nor does it incorporate every possible source of bias. The registry does not report adjusted intervals or methods addressing missing outcomes. The widths should therefore be read as statistical precision for the posted comparisons, not as a complete measure of uncertainty about study conduct or generalizability.

The reported group counts are 52 and 54 for the primary outcome. These counts and the binary endpoint provide limited information about the continuous VAS measure, participant-level changes, and unreported assessment times. No numerical confidence bounds are posted for the group-level outcome values themselves, so additional precision claims about those values are not warranted from the registry record.

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.

The planning figures are participants per arm, not total participants and not total events. The assumptions stated for this planning illustration are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect. The original trial’s own sample-size justification and design assumptions are not reported in the registry record.

For each assumed effect, “participants per arm for 80% power” is the illustrative group size required for an 80% chance of detecting an effect of that size under the listed assumptions, if the assumptions and model hold. The 90% power column uses a higher chance of detection as its target, which generally requires more participants per arm for the same effect. These are planning illustrations computed from the observed effect, not observed power.

The scenarios use 100%, 75%, and 50% of the observed effect. For the primary adherence outcome, the corresponding 80% power figures are 12,338, 21,945, and 49,398 participants per arm; the 90% figures are 16,516, 29,377, and 66,129. For viral suppression, the corresponding 80% figures are 53, 86, and 176 participants per arm; the 90% figures are 70, 115, and 234. Within each outcome, the smaller assumed effect requires more participants per arm. The contrast between the two outcomes reflects their different observed effects and should not be taken as a statement about the trial’s original design.

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 z_1−α/2 = 1.960) and the desired power (z_1−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

1. Control proportion p₀ = 0.519; treatment proportion p₁ = 0.537; average p̄ = 0.528.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7060 = 1.3837.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.7059 = 0.5941.
4. n = (1.3837 + 0.5941)² / (0.0178)² = 12,337.1, rounded up to 12,338 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 <- 0.519230769230769                          # control proportion
p1 <- 0.537037037037037                          # 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(1741311)
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 = 12,338 (80% power), 16,516 (90% power)
 75% of observed effect: n per arm = 21,945 (80% power), 29,377 (90% power)
 50% of observed effect: n per arm = 49,398 (80% power), 66,129 (90% power)
power.prop.test: 12337.1 
Simulated power at n = 12,338 per arm: 0.800 (20000 replicates)

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

14. Multiplicity, Missing Data and Analysis Populations

The record identifies optimal ART adherence as the primary endpoint and lists viral suppression as a secondary endpoint. It does not report a multiplicity adjustment, an outcome hierarchy beyond these labels, or a prespecified strategy for interpreting multiple endpoints or time points. When more than one hypothesis is examined, general statistical reasoning indicates that the chance of at least one small p-value can increase. Adjustments or a clearly defined testing sequence can address that issue, but neither is documented in the registry record. The secondary comparison’s unadjusted p-value should therefore not be treated as if multiplicity had been handled.

The registry states that the outcomes were assessed post-intervention, at three months, and at six months, with the posted result at six months. Results for the other time points are not reported in the registry record. It is also not reported whether all assessments were planned for formal hypothesis testing, how repeated measurements were handled, or whether any additional outcomes were analyzed but not posted.

Missing-data handling is not reported in the registry record. The outcome summaries give group counts and denominators, but do not explain why the denominators take those values, whether participants lacked follow-up, or how incomplete measurements were treated. No imputation method, sensitivity analysis, or description of loss to follow-up is reported. As a result, the posted comparisons cannot establish how robust the findings are to missing outcome data.

The analysis population is also not reported in the registry record. It is not stated whether the comparison followed assignment regardless of intervention attendance, included only participants with outcome data, or used another definition. There is no reported adjusted analysis or account of protocol deviations. These omissions limit assessment of the extent to which the statistical comparison preserves the randomized design and make it important to interpret the estimates as posted summaries rather than as a fully documented analysis.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The serious-event summary lists 0 serious adverse events, 0 other serious events, and 0 deaths for 3H+, with 52 participants at risk in each of the two reported event categories. For HHRP+, it lists 0 serious adverse events, 0 other serious events, and 0 deaths, with 54 participants at risk in each category. No top serious-event terms are listed.

These figures describe what the registry record reports for the defined safety categories and risk groups. A zero count in a registry summary does not establish that an intervention has no safety risks, and it does not describe events outside the categories or reporting period covered by the record. The registry does not provide further detail on event definitions, collection procedures, severity grading, relatedness assessment, or the safety observation period. The figures should therefore be read as reported counts, not as a comprehensive safety evaluation or a comparison capable of excluding uncommon events.

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

The primary result describes how many participants met the registry’s self-reported optimal ART adherence threshold at the reported six-month assessment. The groups had similar observed counts relative to their reported denominators, and the unadjusted comparison is imprecise: its confidence interval crosses zero and its p-value is 0.854. This does not demonstrate equivalence, nor does it establish that the interventions have identical effects. It means the posted primary comparison does not precisely distinguish the groups.

The secondary viral suppression result has a different direction and a reported unadjusted p-value of 0.005. It is a secondary, unadjusted comparison, and the registry does not describe how multiple outcomes or time points were handled. It should not be treated as a confirmed overall benefit or as a reason to disregard the primary endpoint. The outcome-specific summaries address separate measures and should remain distinct in interpretation.

The randomized parallel design is relevant to comparing assigned groups, but the registry record does not report important analytic details, including missing-data handling, analysis population, or adjusted analyses. Nor does it provide the results for every scheduled assessment time. The posted summaries therefore do not establish whether the observed group contrasts would persist under other analysis choices or at other times.

These results do not show why the groups’ outcomes differed, if they did, and they do not establish effects on unreported outcomes. Optimal adherence is defined using a threshold applied to self-reported VAS scores, which does not capture all features of adherence. Viral suppression is a separate endpoint. No treatment recommendation or conclusion about an individual’s care follows from these group-level registry summaries.

The registry describes a study population in drug treatment with HIV-related risk behavior. Conclusions should be limited to that described context and to the reported endpoints. The registry does not provide enough information to determine how representative the analyzed participants were, how the interventions were implemented in practice, or whether the results apply to other populations or settings.

17. Why This Trial Matters Statistically

This trial illustrates why a primary endpoint and a secondary endpoint should be interpreted separately. The adherence outcome is a thresholded self-report measure, while viral suppression is a distinct outcome. Their posted contrasts point in different directions, emphasizing that an intervention comparison can look different depending on what is measured. A single endpoint should not be used as a proxy for every other outcome.

The primary comparison also illustrates the distinction between a point estimate and its precision. A small positive estimate alone does not establish a meaningful group difference; the interval and unadjusted p-value show that the data do not precisely determine the direction of the primary contrast. Conversely, an interval crossing zero does not prove equality. Clear interpretation requires considering the estimate, uncertainty, endpoint definition, and analysis context together.

The planning illustrations show how sample-size requirements depend on the assumed effect. Using a smaller fraction of the observed effect leads to larger illustrative per-arm requirements. Such calculations help frame future planning, but they do not explain the original trial design: the original sample-size assumptions are not reported in the registry record. They also do not measure the achieved power of the completed study.

Finally, the registry’s incomplete analytic details are consequential. Missing-data procedures, analysis populations, multiplicity handling, and results at other scheduled time points are not reported. Those details affect how confidently readers can interpret posted comparisons. The example demonstrates the value of treating registry results as a record of particular summaries rather than as a complete statistical report.

18. 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.

Several limitations are specific to the posted record. The primary endpoint relies on self-reported VAS adherence and classifies participants by a >95% cutoff. The registry does not post the full VAS distributions, so the extent of score variation within the threshold groups cannot be assessed. It reports the six-month outcome, although the stated assessment schedule also includes post-intervention and three-month assessments; those results are not reported in the registry record.

The available group descriptions are incomplete, and the registry does not report intervention attendance, fidelity, or exposure to other services. Masking is recorded as none. The record does not specify outcome-assessor procedures or whether the people collecting or entering outcome data were masked. These are limitations of what can be evaluated from the registry record, not claims that particular procedures were or were not used.

The enrollment field reports 106, while the registry summary describes a trial among 256 people. The record does not explain this difference. The outcome denominators are reported by group, but there is no account of missing outcomes, exclusions, or the analysis population. The original sample-size justification, missing-data strategy, multiplicity procedure, and detailed statistical plan are also not reported in the registry record.

The secondary result is unadjusted, and the registry does not describe a strategy for interpreting multiple outcomes or repeated assessment times. Planning calculations are based on the observed effects and should not be mistaken for the original design assumptions. Together, these limitations counsel against extending the posted estimates beyond the endpoints, time point, and groups actually described.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Secondary HIV Prevention and Adherence Among HIV-infected Drug Users — NCT01741311.
• Registry record last updated 2025-08-08; status last verified 2025-08.
• Results first posted 2025-08-08.
• 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.

22. Record Summary

NCT01741311 is a completed randomized, unmasked, parallel-group behavioral trial sponsored by the University of Connecticut. It compares 3H+ (Holistic Health for HIV) with HHRP+ (Holistic Health Recovery Program) among HIV-infected people in drug treatment who report HIV-related risk behavior. The registry records a start of 2012-09 and primary completion of 2018-06.

The primary six-month outcome is the count of participants meeting a self-reported ART adherence threshold of >95% on the VAS. The unadjusted primary comparison has a confidence interval spanning zero and p = 0.854. Viral suppression is the posted secondary endpoint; its unadjusted comparison has p = 0.005. The registry does not report multiplicity handling, missing-data methods, analysis populations, or results for the other stated assessment times. It also does not explain the difference between the enrollment field of 106 and the summary’s stated 256 people.