Brief Acceptance and Commitment Therapy for HIV-infected At-risk Drinkers: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Brief Acceptance and Commitment Therapy for HIV-infected At-risk Drinkers (NCT03974061), a randomized na study. The primary outcome is Number of Drinking Days: Baseline (at Baseline).

2. Clinical Question

3. Trial Design

The registry describes a randomized, double-masked, parallel-group behavioral trial, marked completed. It records an enrollment of 49 and a phase of NA. Syracuse University is listed as the sponsor. The recorded start date is 2019-11-01, and the primary completion date is 2022-11-10. These administrative details describe the trial record; they do not establish how many participants contributed data to any particular outcome.

Participants were assigned to Brief Acceptance and Commitment Therapy or Brief Alcohol Intervention. The ACT arm description specifies one, 1-hour telephone intervention session followed by five weekly sessions lasting 30-45 minutes. The BI arm description identifies telephone sessions over six weeks, including a 30-45 minute brief alcohol intervention session, a 5-10 minute booster call, a reminder call, and further session details. The full remaining description is not reported in the registry record.

The primary posted measure is number of drinking days at baseline. Arm-level means and standard deviations are reported for 24 participants in ACT and 25 in BI. Because this measure is explicitly at baseline, its between-arm contrast is a description of the groups before the assigned intervention could produce a treatment response. The registry record does not report a post-intervention primary drinking-days result or the trial's original design assumptions. Although the record lists additional outcomes at baseline and 6 months, reported inferential analyses are not listed.

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: There were two phases to this study. Phase I was the development of a treatment, and Phase II was a pilot randomized clinical trial. Only the second phase involved participants who were individually randomization to a treatment condition and to a graduate student (who was not enrolled) interventionist within that tx condition. In Phase I, individual in-depth interviews and focus groups were conducted with HIV providers (n = 10) and HIV patients (n = 13) - who were NOT enrolled in the trial.

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 Drinking Days: Baseline (at Baseline), measured over Baseline.

The primary measure is the number of drinking days, measured at baseline in days. The registry says alcohol consumption was assessed by retrospective self-report using the Time Line Follow Back interview method. The measure counts drinking days over the last 42-day period. A mean describes the average number of reported drinking days in each arm, while the standard deviation describes the spread of participants' reported values around that mean.

Drinking frequency is a direct description of alcohol consumption and is relevant to the trial's stated focus on at-risk drinking among people living with HIV. However, the timing is central to interpretation: this primary measure is recorded at baseline, not after the intervention. It can describe the starting groups and their baseline contrast, but it cannot show whether drinking changed during follow-up or whether one intervention altered drinking more than the other.

The registry record does not report a primary endpoint definition for a follow-up assessment, a change-from-baseline outcome, or a treatment-effect analysis of drinking days. The posted baseline comparison should therefore be read as a baseline profile, not as evidence of an intervention effect.

7. Results Posted in the Registry

• Brief Alcohol Intervention: mean 21.20 versus 26.21 on control; difference -5.01 (95% CI -12.48 to 2.46), standardized effect d = -0.38; z-test p = 0.189.

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.

Symptoms of Experiential Avoidance: Baseline (at Baseline)

• 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 deviations.
• Result:
  • Brief Alcohol Intervention: mean 50.48 versus 47.83 on control; difference 2.65 (95% CI -5.18 to 10.48), standardized effect d = 0.19; z-test p = 0.507.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Brief Alcohol Intervention and the control. The interval gives the range of effects that remain compatible with the data.

Symptoms of Experiential Avoidance: 6-months (at 6-months Post-baseline)

• 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 deviations.
• Result:
  • Brief Alcohol Intervention: mean 49.65 versus 42.00 on control; difference 7.65 (95% CI -2.38 to 17.68), standardized effect d = 0.51; z-test p = 0.135.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Brief Alcohol Intervention and the control. The interval gives the range of effects that remain compatible with the data.

Symptoms of Depression: Baseline (at Baseline)

• 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 deviations.
• Result:
  • Brief Alcohol Intervention: mean 16.76 versus 14.50 on control; difference 2.26 (95% CI -0.08 to 4.60), standardized effect d = 0.54; z-test p = 0.058.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Brief Alcohol Intervention and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes span psychological symptoms and other substance-use days, with assessments listed at baseline and 6 months for experiential avoidance, depression, and anxiety, and at baseline and 6 months for days of other substance use. The posted secondary summaries include three contrasts in detail, while the registry lists eight secondary outcomes overall. The overall pattern is mixed in direction and precision, rather than a consistent set of clearly separated arm means.

These measures can help characterize participants and broaden the outcome picture, but they do not replace the primary outcome. In particular, baseline secondary comparisons are descriptions of the randomized groups at entry, not responses to treatment. The posted 6-month secondary measures are follow-up summaries, but the registry record lists no reported inferential analyses for them. The primary drinking-days result itself is at baseline, and no primary follow-up drinking-days comparison is reported. As a result, the secondary data cannot supply the missing primary treatment comparison.

Unadjusted secondary results carry less weight as evidence because multiple outcomes and time points create more opportunities for apparently notable findings to arise by chance. The registry record does not report a multiplicity strategy or a hierarchy for interpreting the secondary outcomes. Without that information, isolated unadjusted p-values should be viewed as exploratory rather than confirmatory. Differences in measurement scales and timing also mean that results across outcomes are not interchangeable, and should not be combined into a single conclusion about intervention impact.

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

• Symptoms of Experiential Avoidance: Baseline (at Baseline)
• Symptoms of Experiential Avoidance: 6-months (at 6-months Post-baseline)
• Symptoms of Depression: Baseline (at Baseline)
• Symptoms of Depression: 6-months (at 6-months Post-baseline)
• Symptoms of Anxiety: Baseline (at Baseline)
• Symptoms of Anxiety: 6-months (at 6-months Post-baseline)
• Number of Days Other Substances Used: Baseline (at Baseline)
• Number of Days Other Substances Used: 6-months (6-months Post-baseline)

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous: it is a mean number of drinking days, expressed in days. The posted arm summaries pair each mean with a standard deviation. A mean gives a central summary of the observations, while the standard deviation indicates how much individual observations vary around that mean. The mean difference expresses the contrast between two arm means on the original outcome scale, so its units are days.

What does the contrast represent?

The registry comparison identifies ACT as the reference arm and BI as the other arm. The reported mean difference is therefore interpreted as BI minus ACT. A negative estimate means the posted BI mean is lower than the ACT mean; a positive estimate means the posted BI mean is higher. The sign describes the direction of the contrast, not whether an intervention caused a change. For the primary measure, both arm summaries refer to baseline.

The 95% confidence interval gives a range of values compatible with the data and the calculation's assumptions. When an interval for a difference includes zero, the data are compatible with no mean difference as well as with differences in either direction covered by the interval. A p-value is another summary of how inconsistent the data are with a specified null hypothesis under the calculation's assumptions. It does not measure the probability that the null hypothesis is true, the size or importance of a difference, or the probability that a treatment works.

What is the status of these comparisons?

The posted comparisons are unadjusted recalculations from the summary statistics. The registry record lists zero reported analyses and no reported inferential analyses for the secondary outcomes. Therefore, the calculated comparisons should not be confused with a sponsor-reported adjusted analysis, a prespecified model, or a complete analysis plan. The record does not report the trial's original statistical analysis plan, the intended analysis population, or any covariate-adjustment strategy. The discrepancy indicator is false, so no disagreement with a sponsor analysis is flagged; however, the absence of reported analyses still limits what can be inferred about the trial's planned or definitive analysis.

Unadjusted comparisons use the posted arm summaries without controlling for other variables. This can be useful for a transparent descriptive contrast, but it does not account for baseline prognostic factors or other analysis choices. For a randomized trial, an appropriate prespecified analysis can improve precision or address design features, but the registry record does not establish what such an analysis was. No adjusted treatment-effect estimate should be inferred from the simple comparisons.

Why does variability matter?

Participant responses commonly vary, and the standard deviation reflects that variation for a continuous outcome. Greater spread relative to a mean contrast generally makes the estimate less precise. The pooled standard deviation used in the recalculated standardized contrast summarizes within-arm variation across the two groups. Cohen's d expresses the mean contrast relative to that pooled spread; it is a scale-free description, but it does not replace the original-unit result. The reported d is -0.376 for the primary baseline contrast. It should be read as a standardized baseline difference, not an intervention effect.

A normal approximation is used for the planning illustrations, not as evidence that the trial's own analysis used that method. In general, statistical methods make assumptions about the outcome distribution, the independence of observations, and the way participants enter the analysis. The registry record does not report diagnostic checks or model details. With small groups, estimates and standard errors can be sensitive to individual observations, and the interval width is important when judging uncertainty.

What remains unreported?

The registry record does not report a primary follow-up drinking-days estimate, a prespecified significance threshold for the trial analysis, a sample-size justification, interim analyses, missing-data methods, or the populations used for efficacy analyses. The planning illustration separately specifies a two-sided significance level of 0.05, equal allocation, and a normal approximation; those are assumptions of that illustration, not evidence of the original trial's design or analysis plan. A baseline difference and its unadjusted p-value cannot substitute for those missing details or establish the trial's intervention effect.

11. Confidence Intervals and Precision

The primary baseline mean difference is -5.01 days, with a 95% confidence interval from -12.48 to 2.46. This interval is broad enough to include zero and values in either direction. It therefore conveys substantial uncertainty about the size and direction of the baseline mean contrast. The interval's crossing of zero does not prove that the groups are identical; it indicates that the posted data do not pin down a nonzero difference with precision under this calculation.

Confidence intervals are useful because they show a range of estimates compatible with the observed data and the calculation's assumptions, rather than reducing interpretation to a thresholded p-value. For a mean difference, zero represents no difference. An interval that includes zero leaves open both no difference and nonzero differences within the interval. The interval does not assign equal probability to every value it contains and should not be read as a probability statement about the true value.

Precision is limited by the amount of information and the variability in the measurements. The primary arm summaries have standard deviations of 13.68 and 12.97 days. In general, a smaller sample or greater outcome variability tends to yield a wider interval. The posted arm counts and standard deviations give context for the interval, but do not eliminate uncertainty or replace a planned analysis.

Most importantly, this interval concerns a baseline contrast. Even a more precise baseline estimate would not show a treatment effect. The registry record does not report a primary post-treatment or 6-month drinking-days contrast, so the precision of an intervention comparison on the primary drinking outcome cannot be assessed from the posted primary result.

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 for 80% power and participants per arm for 90% power. They are not total events: the event-count convention applies to time-to-event calculations, whereas these continuous-outcome planning illustrations use participants per arm. The associated curve should be read as a planning aid relating the assumed effect size to the required number of participants, not as an observed result.

The calculation assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the stated fraction of the observed effect as the effect to detect. The rows describe planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The 80% power column represents a design that would detect the assumed effect in 80% of repeated trials if the assumptions and effect were correct. The 90% power column represents a higher probability of detecting that assumed effect, and typically requires more participants.

Smaller effects are harder to distinguish from random variation, so planning to detect a smaller fraction of the observed effect requires more participants. The figures are illustrations based on the observed contrast, not the original trial's design assumptions; those original assumptions are not reported in the registry record. This is not observed power. It does not quantify how likely the completed trial was to find a result, nor does it establish that the observed effect is a reliable estimate of a future effect.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -5.010; pooled standard deviation σ = 13.322.
2. n = 2 × (1.96 + 0.842)² × 13.322² / -5.010² = 111.0, rounded up to 111 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
delta <- -5.01                      # observed difference in means
sigma <- 13.3221754021935                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(3974061)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 111 (80% power), 149 (90% power)
 75% of observed effect: n per arm = 198 (80% power), 265 (90% power)
 50% of observed effect: n per arm = 444 (80% power), 595 (90% power)
power.t.test: 112 
Simulated power at n = 111 per arm: 0.794 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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

Multiplicity arises when a study evaluates several outcomes, time points, or contrasts. Even when each individual test uses a conventional threshold, the chance of at least one apparently notable result can increase as more tests are considered. This is why a prespecified outcome hierarchy, adjustment method, or explicitly exploratory interpretation can matter. The registry lists multiple secondary measures at baseline and 6 months, but a multiplicity plan is not reported in the registry record.

The posted unadjusted comparisons should therefore be interpreted as individual summaries, not as a family-wise-confirmed set of findings. No reported analyses are listed for the secondary outcomes. The record does not say whether any adjustment was planned or conducted, whether outcomes were prioritized, or whether the posted contrasts were prespecified. These omissions limit confidence in using any isolated secondary p-value as confirmatory evidence.

Missing-data handling is also not reported in the registry record. Some posted follow-up arm summaries have fewer observations than the baseline summaries, but the record does not explain why. It does not report whether missing measurements resulted from withdrawal, missed visits, unavailable assessments, or another reason; nor does it report imputation, weighting, or sensitivity analyses. Consequently, the follow-up summaries may describe participants with observed measurements, but the representativeness of those observations cannot be assessed from the registry record.

The analysis populations are not described. The record does not state whether analyses followed randomized assignment, included only participants who completed treatment, or used another definition. It also does not report a participant flow description linked to each outcome. Without these details, readers cannot determine how missing outcomes or deviations from assigned intervention were handled, or how closely the posted estimates correspond to a prespecified intention-to-treat analysis.

The registry record also does not report interim analyses, the original sample-size justification, or a complete statistical analysis plan. These are distinct from the planning illustration, which states its own assumptions. Their absence means the unadjusted calculations should be treated as limited statistical summaries rather than a complete account of the trial's inferential approach.

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 registry records zero serious adverse events among the 24 participants at risk in the ACT arm and zero among the 25 participants at risk in the BI arm. It also records zero other adverse events in each arm and zero deaths in each arm. No serious adverse-event terms are listed.

These figures indicate that no events in those categories were posted for the recorded risk groups. They do not establish that there was no risk, and they cannot show whether the interventions differ in safety with precision. Event counts can be difficult to interpret when the number of participants and the observation period are limited, and the registry record does not provide event narratives, definitions beyond the serious/other categories, or detailed timing.

Absence of a posted event is not the same as proof that an event could not occur. Safety conclusions should remain limited to the counts and categories in the registry record.

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

The primary posted result describes baseline drinking frequency in two randomized groups. It does not show a change after treatment and does not establish that ACT or BI caused an improvement, worsening, or no change. The mean difference and confidence interval characterize the baseline contrast only. Since the interval includes zero and spans values in both directions, the baseline estimate is uncertain about the direction and size of a group difference.

The randomized design is an important feature, but randomization does not guarantee identical baseline measurements, particularly in a small study. Nor does the baseline comparison alone establish the effect of treatment. To assess whether the assigned interventions differed in drinking outcomes, a post-intervention comparison or an appropriate change analysis would be needed; such a primary drinking-days result is not reported in the registry record.

Secondary outcomes add context about symptoms and other substance use, but their unadjusted comparisons are not definitive evidence. The multiplicity approach, missing-data methods, analysis populations, and full analysis plan are not reported. The 6-month secondary results therefore require cautious reading, and they cannot compensate for the absence of a posted primary follow-up result.

The safety record reports no serious adverse events, other adverse events, or deaths in either arm. This is a statement about the posted counts, not a guarantee of safety or proof that risks are equal. In the same way, an imprecise or nonsignificant statistical result does not demonstrate equivalence. The registry results support descriptive statements about recorded measures and events, while leaving the intervention's comparative effect on drinking unanswered.

17. Why This Trial Matters Statistically

This trial is statistically instructive because the registry labels a baseline measure as the primary outcome. That timing changes the question the posted comparison can answer: it describes the randomized groups at entry, rather than their response to intervention. Clear separation of baseline characteristics from post-treatment outcomes is essential when interpreting trial results.

The study also illustrates how a randomized design, descriptive arm summaries, and inferential evidence are different pieces of information. Random assignment supports a fair comparison in principle, but small groups can still have baseline variation. The unadjusted mean difference and confidence interval make that variation visible while also showing uncertainty. Neither the p-value nor the direction of the estimate turns a baseline contrast into a causal treatment effect.

The record includes multiple secondary measures, but reported inferential analyses are absent. That makes multiplicity and analysis transparency especially relevant: readers need to know which comparisons were planned, how missing outcomes were treated, and what population was analyzed before treating a pattern as confirmatory. The planning illustrations also demonstrate how assumed effect size and desired power affect resource requirements, while remaining separate from the trial's original design.

Together, these features reinforce a core biostatistical lesson: the interpretation of a number depends on its timing, estimand, uncertainty, and analysis context. A precise description of what is recorded—and what is not—prevents descriptive evidence from being overstated as a treatment conclusion.

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.

A central limitation is that the posted primary endpoint is measured at baseline. The registry record does not report a primary follow-up drinking-days comparison, leaving the principal treatment question unanswered by the posted primary result. The baseline contrast cannot establish a treatment effect, regardless of how it is interpreted statistically.

The registry record lists an enrollment of 49, while outcome-specific arm counts vary by measure and time point. It does not explain the differences between those counts, report reasons for missing observations, or describe missing-data methods. Follow-up summaries may therefore be affected by which participants contributed measurements, and the extent of any such effect cannot be evaluated from the record.

Further limitations include the absence of reported inferential analyses, a full statistical analysis plan, analysis populations, multiplicity handling, interim-analysis information, and the original sample-size justification. The reported comparisons are unadjusted recalculations from summary statistics. They do not establish whether the trial's planned analysis used covariate adjustment or other methods.

The primary outcome is based on retrospective self-report using the Time Line Follow Back method. The registry does not report additional validation or corroborating measures for the posted drinking-day result. Finally, the intervention description for BI is incomplete in the registry record, limiting a full comparison of the intended intervention schedules from the posted description alone. These limitations constrain interpretation without implying that any particular unreported procedure was or was not used.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Brief Acceptance and Commitment Therapy for HIV-infected At-risk Drinkers — NCT03974061.
• Registry record last updated 2026-04-01; status last verified 2026-03.
• Results first posted 2026-04-01.
• 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

The registry record describes a completed randomized, double-masked, parallel-group behavioral trial sponsored by Syracuse University. It compares Brief Acceptance and Commitment Therapy with a Brief Alcohol Intervention among people living with HIV who were at-risk drinkers.

The primary posted outcome is mean drinking days at baseline, measured by retrospective self-report over the last 42-day period. The reported contrast is an unadjusted baseline comparison, not a treatment-effect estimate. A primary follow-up drinking-days result is not reported in the registry record.

The record lists secondary outcomes at baseline and 6 months, but no reported inferential analyses. It records zero serious adverse events, zero other adverse events, and zero deaths in each arm. Details on missing-data handling, analysis populations, multiplicity, and the original sample-size assumptions are not reported in the registry record.