Cocaine Use Reduction With Buprenorphine: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Cocaine Use Reduction With Buprenorphine (NCT01402492), a randomized phase 2, phase 3 study. The primary outcome is Cocaine Use Days as Measured by Self-report, Corroborated by Thrice-weekly Urine Drug Screens.

2. Clinical Question

3. Trial Design

This was a randomized, double-masked, parallel-group study listed as Phase 2 and Phase 3. The registry records enrollment of 302 participants and identifies cocaine dependence as the condition. The sponsor was University of California, Los Angeles. The recorded study start is 2011-09, primary completion is 2013-01, and status is completed.

Three arms are described. The BUP4+XR-NTX arm received 4mg buprenorphine plus naltrexone for 8 weeks of treatment. The BUP16+XR-NTX arm received 16mg buprenorphine plus naltrexone for 8 weeks. The PLB+XR-NTX arm received naltrexone for 8 weeks. Although the interventions list identifies buprenorphine plus naltrexone and placebo plus naltrexone, the arm descriptions give the specific regimens used in these three groups.

The primary outcome is a continuous measure summarized by means and standard deviations. The registry reports 100 participants in each buprenorphine arm and 102 in the naltrexone-only arm for this outcome. These outcome counts are distinct from the overall enrollment figure; the registry record does not explain the relationship between enrollment and the numbers contributing to the outcome.

The record does not report the original sample-size justification, allocation ratio in the trial's design, sequence-generation details, concealment procedures, masking procedures, or protocol deviations. It also does not describe treatment adherence or participant flow. Randomization, masking, and parallel-group structure are registry design labels; additional operational details are not reported in the registry record.

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

Reasons for not completing this period:

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 Cocaine Use Days as Measured by Self-report, Corroborated by Thrice-weekly Urine Drug Screens, measured over final 30 days of Treatment Phase, study days 25-54.

The primary endpoint is cocaine-use days measured by self-report and corroborated with urine drug screens. It covers the final 30 days of the treatment phase, identified as study days 25-54. The outcome is expressed in days of cocaine use and summarized as a mean with a standard deviation for each arm.

A count of use days gives a measure of frequency over a defined observation window. The final-treatment-period window makes the reported endpoint specific to that portion of the study, rather than a measure across the entire treatment period or follow-up. It does not by itself describe patterns of use on individual days or changes from baseline; baseline and longitudinal outcome results are not reported in the registry record.

Self-report captures participant-reported use, while urine drug screens offer a biological source of corroborating information. The registry states that screens were conducted thrice weekly. It does not report the rule used to reconcile self-report and test findings, how missing or discordant observations were handled, or whether the outcome incorporated any other information. Those details matter for understanding how a day was classified as a cocaine-use day, but they are not reported in the registry record.

The endpoint summarizes group averages and variation. It does not describe any one participant's experience, and it is not a safety outcome. The registry posts one outcome measure and no secondary outcome results.

7. Results Posted in the Registry

• BUP16+XR-NTX: mean 7.20 versus 6.60 on control; difference 0.60 (95% CI -1.08 to 2.28), standardized effect d = 0.10; z-test p = 0.484.
• PLB+XR-NTX: mean 7.70 versus 6.60 on control; difference 1.10 (95% CI -0.48 to 2.68), standardized effect d = 0.19; z-test p = 0.172.

8. Statistical Interpretation

9. Statistical Methods Explained

The endpoint is continuous and is summarized using a mean and standard deviation. The comparisons are expressed as mean differences, with the 4mg buprenorphine plus naltrexone group as the reference. The posted comparison estimates and confidence intervals are unadjusted calculations from the group summaries. No discrepancy between those calculations and the registry results is indicated.

What does a mean difference represent?

A mean is the arithmetic average of the recorded outcome values in an arm. A mean difference subtracts the reference-arm mean from the other arm's mean. For the 16mg arm, the posted difference is 0.6 days; for naltrexone alone, it is 1.1 days. In this comparison convention, a positive number means the comparison arm's mean is higher. The estimate describes the difference between group averages over the stated endpoint window, not a difference for every participant.

The standard deviation describes spread among observed values around an arm's mean. The reported values are 5.25 in the 4mg arm, 6.77 in the 16mg arm, and 6.16 in the naltrexone-only arm. A standard deviation is not the same as the uncertainty in the mean or the confidence interval for a difference. It describes variation in the outcome values, while a confidence interval expresses uncertainty about an estimated quantity.

How should the confidence intervals be understood?

A confidence interval is a range calculated using a statistical procedure. In general, its width reflects the precision of the estimate under the assumptions used in that procedure: narrower intervals indicate greater precision, and wider intervals indicate less precision. The intervals for the posted mean differences are -1.079 to 2.279 for the 16mg comparison and -0.477 to 2.677 for the naltrexone-only comparison. Both span zero, meaning the intervals include no mean difference as well as values in either direction.

The registry record does not report a named statistical analysis plan, confidence-interval method, adjustment for covariates, or the sponsor's own inferential analysis. The posted estimates can therefore be interpreted as unadjusted comparisons based on the arm summaries, rather than as evidence about any unreported adjusted model. The unadjusted p-values are 0.484 and 0.172, respectively. A p-value is a measure of how compatible observed data are with a specified null model under the assumptions of the test; it is not the probability that the null hypothesis is true, nor a measure of clinical importance.

Why can a small estimate still be uncertain?

Precision depends on both the amount of observed variation and the number of participants contributing data, as well as the statistical procedure. The arm standard deviations are several days, while the estimated mean differences are less than two days. That relationship is one reason the confidence intervals extend across zero. This description does not establish that the groups are equivalent: the intervals also include nonzero differences.

The posted comparisons use the arm counts of 100, 100, and 102. The registry does not say whether these are all randomized participants, all participants with endpoint data, or another analysis population. It also does not report missing-data methods, so the effect of incomplete outcome data cannot be evaluated from these summaries.

What assumptions matter?

General statistical methods for comparing means rely on assumptions about the data and calculation. Distributional shape, independence of observations, and the treatment of missing or unusual values can affect inference. The registry record does not report diagnostic checks or the methods used to assess these assumptions. The use of self-report corroborated by thrice-weekly urine drug screens is described, but the outcome-construction rule and handling of discordant information are not reported.

The design is listed as randomized, double-masked, and parallel, but the record does not provide procedural detail sufficient to assess randomization implementation or masking success. Nor does it report a prespecified statistical analysis plan, the original sample-size rationale, interim analyses, or the handling of multiple comparisons. These omissions limit how fully the numerical results can be connected to a planned confirmatory analysis.

10. Confidence Intervals and Precision

The estimated mean difference for the 16mg buprenorphine plus naltrexone arm relative to the 4mg arm is 0.6 days. Its 95% confidence interval runs from -1.079 to 2.279. The estimate for naltrexone alone relative to the 4mg arm is 1.1 days, with a 95% confidence interval from -0.477 to 2.677. These intervals represent uncertainty around the mean differences, not ranges containing a specified proportion of individual participants' outcomes.

Both confidence intervals include zero and include values on either side of zero. Thus, the posted data do not determine the direction of the underlying mean difference with precision. The interval for each comparison also allows differences greater than the point estimate in either direction. A confidence interval is not a guarantee that the true value lies within its endpoints; in general, it is produced by a procedure with stated coverage properties when its assumptions hold.

The standard deviations show considerable dispersion in the observed use-day counts: 5.25 days in the reference arm, 6.77 in the 16mg arm, and 6.16 in the naltrexone-only arm. This within-arm variation is distinct from the uncertainty around a mean difference. The registry record does not provide additional precision measures, adjusted intervals, or results from other time points.

These intervals are unadjusted. The registry record does not report whether the comparisons were part of a larger family of planned tests or whether any multiplicity adjustment was intended. Consequently, the intervals and p-values should be understood as the posted unadjusted comparisons rather than as multiplicity-adjusted inference.

11. 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 sample-size figures are planning illustrations based on the observed effect, not the original trial's design rationale. They give participants per arm for 80% power and participants per arm for 90% power; these are not total event counts. The calculations assume 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 original trial's sample-size assumptions are not reported in the registry record.

The 80% power column represents an illustrative design that, under its assumptions and if the specified effect were the true effect, would have an 80% chance of meeting the statistical significance criterion. The 90% power column uses the same type of interpretation with a 90% chance. These are planning quantities, not evidence about what the completed trial was capable of detecting in practice. This is not observed power.

For the 16mg comparison, the planning rows use 100%, 75%, and 50% of the observed effect. Participants per arm for 80% power are 1,601, 2,845, and 6,401, respectively; for 90% power they are 2,143, 3,809, and 8,569. For the comparison with naltrexone alone, the corresponding figures are 426, 757, and 1,703 participants per arm for 80% power, and 570, 1,013, and 2,280 for 90% power.

Smaller effects require more participants to detect under the same planning assumptions. The rows based on a smaller fraction of the observed effect therefore call for larger group sizes. The illustrations do not change the trial's observed enrollment or outcome counts, and they should not be mistaken for a retrospective judgment of whether the trial achieved a particular level of power.

12. 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 = 0.600; pooled standard deviation σ = 6.058.
2. n = 2 × (1.96 + 0.842)² × 6.058² / 0.600² = 1,600.2, rounded up to 1,601 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 <- 0.600000000000001                      # observed difference in means
sigma <- 6.05786265938738                     # 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(1402492)
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 = 1,601 (80% power), 2,143 (90% power)
 75% of observed effect: n per arm = 2,845 (80% power), 3,809 (90% power)
 50% of observed effect: n per arm = 6,401 (80% power), 8,569 (90% power)
power.t.test: 1601.2 
Simulated power at n = 1,601 per arm: 0.798 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record reports one outcome measure and no secondary outcome results. It does not report a prespecified statistical analysis plan, a hierarchy of outcomes, the number of planned comparisons, or a method for controlling multiplicity. The posted primary-outcome comparisons include two unadjusted p-values. Without a reported multiplicity strategy, it is not possible to determine whether those comparisons were selected from a broader set of planned tests or how any family-wise error concerns were addressed.

Missing-data handling is not reported in the registry record. The record gives outcome counts of 100 in the 4mg arm, 100 in the 16mg arm, and 102 in the naltrexone-only arm, but does not specify whether these counts represent everyone randomized, everyone treated, or only participants with outcome data. It does not describe withdrawals, missing endpoint values, imputation, or sensitivity analyses. The effect of missing data on the reported arm summaries therefore cannot be assessed from the registry record.

The analysis population is also not reported. There is no stated intention-to-treat, per-protocol, or other analysis-set definition, and no account of deviations from assigned treatment. Randomization is listed as a design feature, but the record does not say how participants were handled in the outcome analysis after randomization. This limits interpretation of the comparisons as estimates under a particular analysis population.

Baseline outcome values, covariate adjustment, interim analyses, and subgroup analyses are not reported. The registry record also does not provide a detailed protocol or explain how self-report and urine-screen results were combined when they did not agree. These omissions do not alter the numerical summaries, but they leave important aspects of the planned and completed analyses unclear.

14. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: drug detoxification (2.0%), sinusitis (2.0%), chest pain (2.0%), depression (1.0%), psychotic disorder (1.0%).

The serious adverse event summaries give the number of participants affected and the number at risk in each arm. Serious adverse events affected 13 of 100 participants in the BUP4+XR-NTX arm, 8 of 100 in the BUP16+XR-NTX arm, and 12 of 102 in the PLB+XR-NTX arm. These are descriptive counts, not estimates adjusted for differences in exposure or follow-up.

The record also lists serious-event terms with frequencies: Drug Detoxification, 2.0%; Sinusitis, 2.0%; Chest Pain, 2.0%; Depression, 1.0%; Psychotic Disorder, 1.0%; and Major Depression, 1.0%. The record does not assign these listed terms to particular arms in the available information, so they should not be attributed to one group. The count of participants with other adverse events was 66 of 100, 64 of 100, and 61 of 102 in the respective arms.

Deaths are not reported in the registry record. The summaries do not provide event timing, duration, severity beyond the serious-event category, or a comparative statistical analysis. They therefore describe the recorded counts but do not establish whether observed differences between arms are meaningful.

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

The posted primary-outcome summaries describe mean cocaine-use days during the final 30 days of treatment. The mean was 6.6 days in the 4mg buprenorphine plus naltrexone arm, 7.2 days in the 16mg arm, and 7.7 days in the naltrexone-only arm. The estimated differences relative to the 4mg arm were 0.6 and 1.1 days, respectively. Both confidence intervals include zero and extend in both directions, so the estimates are imprecise about the direction and magnitude of the underlying mean differences.

These results do not establish that the arms have identical outcomes, because the intervals also include nonzero differences. They also do not establish that one regimen is better or worse. The endpoint is limited to a specified 30-day period late in treatment, and no baseline or follow-up outcome results are reported. The results cannot describe how use changed over time or whether the pattern was sustained beyond that window.

The findings do not speak to outcomes that were not posted. The registry lists one outcome measure and no secondary outcome results. The outcome summaries also do not report participant-level distributions, responder definitions, or subgroup results. Mean differences cannot be used to infer what happened to any particular participant.

The adverse-event summaries are separate descriptive counts. They should not be combined with the primary endpoint to draw a broader conclusion about benefit or harm. The record does not report deaths, the original analysis plan, missing-data methods, or the analysis population. Those limits constrain interpretation of both the outcome comparisons and the safety summaries.

The registry describes a randomized, double-masked, parallel-group study and an aim of investigating safety and effectiveness. The posted figures can be read as statistical descriptions of the recorded endpoint and adverse-event counts, but they are not medical advice and do not by themselves establish treatment effects beyond the reported comparisons.

16. Why This Trial Matters Statistically

This trial illustrates why an estimated difference and its precision need to be read together. The posted mean differences are 0.6 days and 1.1 days, but their confidence intervals extend across zero and include values in both directions. The point estimates alone do not convey how uncertain the comparisons are.

The outcome also demonstrates the distinction between variability among participants and uncertainty in a group comparison. The arm standard deviations range from 5.25 to 6.77 days, while the comparisons are based on groups of 100, 100, and 102 participants. The means compress a varied outcome into a single summary; the standard deviations and confidence intervals add information about spread and precision.

The endpoint combines self-reported days with corroboration from thrice-weekly urine screens. That measurement approach makes the outcome more than a simple self-report, but interpretation still depends on how the two information sources were reconciled. The registry does not report that rule, illustrating how outcome definitions can leave important methodological details unresolved even when the measure's general description is clear.

The registry also highlights the difference between trial enrollment and the counts reported for an outcome. Enrollment is 302, while arm outcome counts are 100, 100, and 102. The record does not explain the analysis population or missing data, so the relationship between those counts cannot be fully evaluated.

Finally, planning illustrations should be distinguished from the completed study's observed evidence. The sample-size calculations use stated assumptions and fractions of observed effects; they do not recover the trial's original planning rationale. Keeping design planning, observed estimates, uncertainty, and reporting limitations separate is essential to a careful statistical reading.

17. 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 gives limited detail about how the study was conducted and analyzed. It lists randomization, double masking, and a parallel model, but does not describe sequence generation, concealment, implementation of masking, or treatment adherence. It does not report participant flow, withdrawals, or reasons for missing endpoint data.

The outcome counts are 100, 100, and 102, but the analysis population and relationship between those counts and the overall enrollment of 302 are not explained. Missing-data handling is not reported, and no sensitivity analyses are described. The record also does not provide baseline values, adjusted estimates, or results for other time points.

The endpoint description states that self-report was corroborated by urine drug screens conducted thrice weekly, but it does not explain how self-report and test results were combined, how discordant findings were treated, or how incomplete screen schedules affected classification. These details could affect the interpretation of a day counted as cocaine use.

The registry record does not report the original sample-size justification, a statistical analysis plan, interim analyses, or multiplicity handling. It contains one outcome measure and no secondary outcome results. The posted comparisons are unadjusted, and the available record does not establish whether these were the only comparisons planned.

The safety information is also limited: event counts are descriptive, the listed serious-event terms are not assigned to arms in the available information, and deaths are not reported in the registry record. These limitations warrant caution when interpreting the scope and precision of the posted results.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Cocaine Use Reduction With Buprenorphine — NCT01402492.
• Registry record last updated 2021-10-29; status last verified 2021-06.
• Results first posted 2021-10-29.
• 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.

21. Record Summary

NCT01402492, titled Cocaine Use Reduction With Buprenorphine (CURB), is listed as a completed randomized, double-masked, parallel-group Phase 2 and Phase 3 study sponsored by University of California, Los Angeles. The condition is cocaine dependence, and enrollment is 302.

The three treatment arms were 4mg buprenorphine plus naltrexone, 16mg buprenorphine plus naltrexone, and naltrexone alone, each described as 8 weeks of treatment. The primary outcome was mean cocaine-use days during the final 30 days of treatment, study days 25-54, measured by self-report and corroborated by thrice-weekly urine drug screens.

The registry reports arm means, standard deviations, and two unadjusted comparisons against the 4mg arm. It lists one outcome measure and no secondary outcome results. Details of the original sample-size rationale, statistical analysis plan, missing-data methods, and analysis population are not reported in the registry record.