Efficacy of Varenicline in Methadone-Stabilized Cocaine Users: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy of Varenicline in Methadone-Stabilized Cocaine Users (NCT00567320), a randomized na study. The primary outcome is Proportion of Cocaine Positive Urine Tests Per Week.

2. Clinical Question

The primary question is framed around a measured pattern of urine-test results rather than a direct count of days using cocaine or a self-reported measure. Urine samples were obtained thrice-weekly and analyzed for cocaine metabolites. A result exceeding 300 ng / ml on an individual urine test was classified as positive. For each week, the outcome was calculated as positive tests divided by completed tests.

The record identifies the measure as a proportion and reports group means and standard deviations. The treatment comparison therefore concerns average weekly proportions of positive tests, while the described longitudinal analysis uses results across the study period, including a baseline result. Those are related but not identical summaries: an overall group mean does not by itself describe how the outcome changed over time or how repeated observations within a participant were handled.

The record does not report a separate primary hypothesis in more detail, such as a specified direction of benefit or a clinically important difference. It also does not report whether any particular change in the proportion was considered meaningful to participants. The posted results can describe the direction and precision of the observed comparison, but they do not establish the broader importance of a difference on their own.

3. Trial Design

The registry describes a randomized, double-masked, parallel-group trial of varenicline versus placebo. Random allocation is intended to make treatment groups comparable on average, while masking is intended to limit expectations from influencing care or assessment. The record does not report the randomization sequence, allocation concealment procedures, or the exact masking procedures, so those aspects cannot be assessed from the posted information.

The listed enrollment is 31. The posted outcome results show 13 participants in the varenicline group and 16 in the placebo group. These are the numbers associated with the outcome groups; the record does not provide a detailed account of participant flow, exclusions, or missing observations. The study is marked completed. Its listed start is 2007-03 and its primary completion is 2009-06. The sponsor is Yale University, and the phase is listed as NA.

The trial concerns cocaine dependence and nicotine dependence in people described in the study summary as methadone-stabilized subjects. The registry lists varenicline and sugar pill or placebo as drug interventions. The posted record does not provide the dose, treatment duration, adherence procedures, or other medication-management details. Those details should not be inferred from the intervention names.

Urine testing was scheduled thrice-weekly, and the primary outcome was calculated weekly from completed tests. The outcome description says that the longitudinal analysis included 13 results, including baseline at Week 0. It identifies Hierarchical Linear Modeling (HLM) for this analysis. Separately, the registry's posted analysis is labeled Mixed Models Analysis. The record does not explain whether these labels refer to the same model specification or give the full model formula, covariance structure, or handling of missing tests.

The registry summary states that the aims were to determine safety and tolerability and to assess whether varenicline was efficacious in reducing cocaine use among methadone-stabilized subjects. The posted primary endpoint focuses on the proportion of positive urine tests. No secondary outcomes are posted in the 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

Analysis population for the primary outcome, as defined in the registry: Intention to treat analysis of all subjects receiving medication

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 Proportion of Cocaine Positive Urine Tests Per Week, measured over Weekly Measures over 12 weeks.

The primary endpoint is the proportion of cocaine-positive urine tests per week. Urine samples were obtained thrice-weekly and analyzed for cocaine metabolites. An individual urine test was considered positive when the level exceeded 300 ng / ml. For each week, the numerator was the number of positive tests and the denominator was the number of completed tests.

This measure records test positivity over time, offering an objective indicator of cocaine metabolites in the collected urine samples. Expressing positive tests relative to completed tests also accounts for the number of tests completed in a given week when forming the weekly measure. It is not the same as counting participants who ever had a positive test, nor is it a direct measure of the amount of cocaine used. The registry does not report those alternative outcomes.

The posted group summaries are means of a continuous measure, with standard deviations. The varenicline mean is 0.57 and the placebo mean is 0.58. The endpoint description says that the weekly proportions were analyzed with HLM using 13 longitudinal results, including baseline at Week 0, over weekly measurements during 12 weeks. Repeated measurements can help describe the course of an outcome rather than relying on a single observation, but the specific time effects and model details are not reported in the registry record.

Using completed tests in the denominator makes the availability of urine samples relevant to interpretation. The record does not state how many tests were missed, how missing tests were handled, or whether missingness differed by group. Consequently, the posted outcome should be read as a summary of the recorded tests and the analysis described, not as a complete account of every scheduled test.

7. Results Posted in the Registry

• Varenicline: mean 0.57 versus 0.58 on control; difference -0.01 (95% CI -0.05 to 0.03), standardized effect d = -0.20; z-test p = 0.592.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry describes the study as randomized, double-masked, and parallel-group. Randomization assigns participants to treatment groups by chance; in general, it is used to reduce systematic differences between groups. Masking is intended to reduce the influence of treatment expectations on participant behavior, clinical decisions, or outcome assessment. The registry does not report enough operational detail to assess how these protections were implemented.

What does the group mean represent?

The primary measure is a weekly proportion, calculated from positive tests and completed tests. A mean summarizes the average of the measure across the participants included in a group summary. Here, the posted means are 0.57 for varenicline and 0.58 for placebo. The standard deviation is 0.05 in each group; in general, a standard deviation describes the spread of observations around a mean. It is not a confidence interval for the treatment difference and does not show how precisely the mean difference is estimated.

Because the outcome is formed from urine tests completed within each week, the number of completed tests contributes to each person's weekly proportion. A weekly proportion can be based on different numbers of tests if tests are missed. The record does not state how such variation was handled in the statistical model or provide a missing-test breakdown.

Why use a longitudinal model?

Repeated observations from the same participant are usually correlated: measurements from one person tend to share characteristics and are not equivalent to measurements from unrelated people. General longitudinal methods, including mixed models and hierarchical models, can represent this dependence and estimate patterns across time without treating every observation as independent. The registry's outcome description identifies HLM and states that 13 longitudinal results, including baseline at Week 0, were used. The reported analysis is labeled Mixed Models Analysis.

The record does not give the model equation, the time coding, the covariance structure, the adjustment variables, or the method used to address incomplete follow-up. It is therefore not possible to determine from the registry record precisely how the longitudinal model used baseline or how it estimated the treatment comparison. No statistical plan or interim-analysis details are reported in the registry record.

What does an unadjusted recalculation mean?

The recalculated mean difference compares the posted arm-level summaries without adjustment for the longitudinal structure or other covariates. The estimate is -0.01 for varenicline relative to placebo, and the unadjusted p-value is 0.592. Such a calculation is useful as a transparent comparison of the posted summaries, but it is not a substitute for a prespecified model that accounts for repeated observations. The registry reports no discrepancy flag for this recalculation.

The sponsor's posted mixed-model p-value is 0.84. Since the model's effect estimate and confidence interval are not posted, the p-value alone does not show the estimated magnitude or direction from that model. It should not be interpreted as though it were the p-value from the simple recalculation.

How should a p-value be understood?

In general, a p-value measures how unusual data at least as incompatible with a specified null model would be if that model and its assumptions were true. It does not measure the probability that a treatment works, the probability that the null is correct, or the size of an effect. Interpretation also depends on the analysis being considered and its assumptions. A non-significant p-value does not prove equivalence or rule out effects that the study estimates imprecisely.

The p-values in the record are not accompanied by a complete account of the hypotheses or multiplicity procedures. The registry record does not report whether the listed endpoint was the only outcome considered in an analysis plan, or whether any adjustments were made for repeated comparisons over time. It also does not report an equivalence or non-inferiority margin.

What does a confidence interval add?

In general, a confidence interval expresses the range of values compatible with a statistical procedure applied to the observed data, under its assumptions. It communicates uncertainty about an estimate and is more informative about plausible effect sizes than a p-value alone. The unadjusted recalculated interval includes zero. The registry's reported mixed-model analysis lists a 95% confidence level, but its interval limits and effect estimate are not posted. The record therefore does not permit a direct assessment of the model-based estimate's precision.

Finally, these calculations do not resolve design and reporting questions. The original sample-size assumptions and justification are not reported in the registry record. The available information does not establish whether all randomized participants contributed to the analysis, how missing outcomes were treated, or whether the model assumptions were checked. Those details matter when judging the strength and scope of an estimate.

10. Confidence Intervals and Precision

The unadjusted recalculated mean difference is -0.01 for varenicline relative to placebo. Its confidence interval includes zero, so the posted summaries are compatible with no difference as well as with differences in either direction within the interval. This is an important qualification: the point estimate alone gives a single value, while the interval conveys uncertainty around that estimate.

The group standard deviations are 0.05 for varenicline and 0.05 for placebo. These describe variation in the arm-level measure; they are not the uncertainty interval for the difference. The recalculated interval is based on the posted summary statistics and is unadjusted. It does not represent the sponsor's longitudinal mixed-model interval.

The registry reports a mixed-model p-value of 0.84 and identifies a 95% confidence level, but it does not post the mixed-model estimate or interval limits. Without those values, the model-based effect size and its precision cannot be evaluated from the record. A p-value by itself does not tell readers how wide the interval is or which effect magnitudes remain compatible with the model.

In general, confidence intervals tend to be wider when data are limited or variable and narrower when estimates are more precise. Repeated observations may add information, but their dependence must be accounted for; simply treating each urine test as independent could misrepresent the uncertainty. The registry identifies longitudinal modeling but does not provide the details needed to assess that modeling or the effects of missing tests.

The result should therefore be read as an imprecise comparison rather than as evidence of exact equality. The posted group means are close, but closeness of point estimates does not establish that meaningful differences have been ruled out. The record does not report a threshold for a clinically important difference that would allow precision to be judged against such a benchmark.

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 planning figures are illustrations based on the observed effect, not the trial's original design assumptions. The registry record does not report the original sample-size justification or assumptions. These planning values are participants per arm, not total events. They 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 80% power column gives the illustrative number of participants per arm for a design that would have an 80% chance of detecting the specified effect under those assumptions, if that effect were the true effect. The 90% power column expresses the corresponding planning target for a higher chance of detection. These are design calculations, not estimates of the chance that the completed trial detected an effect.

For planning at 100% of the observed effect, the figures are 393 participants per arm for 80% power and 526 participants per arm for 90% power. Planning for 75% of the observed effect gives 698 participants per arm for 80% power and 934 participants per arm for 90% power. Planning for 50% of the observed effect gives 1,570 participants per arm for 80% power and 2,102 participants per arm for 90% power. The pattern reflects a general statistical principle: smaller effects are harder to detect and require more participants under the same assumptions.

The observed effect used for these illustrations is a simple, unadjusted recalculation from the posted summaries. The calculations do not incorporate a longitudinal model, possible missing tests, or other design features not included in the stated assumptions. They are not observed power; observed power is not a useful substitute for interpreting the estimated effect and its uncertainty after a study is complete.

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 = -0.010; pooled standard deviation σ = 0.050.
2. n = 2 × (1.96 + 0.842)² × 0.050² / -0.010² = 392.4, rounded up to 393 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 <- -0.01                      # observed difference in means
sigma <- 0.05                     # 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(567320)
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 = 393 (80% power), 526 (90% power)
 75% of observed effect: n per arm = 698 (80% power), 934 (90% power)
 50% of observed effect: n per arm = 1,570 (80% power), 2,102 (90% power)
power.t.test: 393.4 
Simulated power at n = 393 per arm: 0.802 (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. Analyses Reported by the Sponsor

The sponsor's posted analysis is labeled Mixed Models Analysis and reports p = 0.84, with a 95% confidence level noted in the registry. The record does not include the model-based treatment estimate or confidence-interval limits. As a result, the magnitude and direction of the sponsor's model-based contrast cannot be read from the posted analysis entry alone.

The unadjusted recalculation from the posted arm summaries gives a mean difference of -0.01 for varenicline relative to placebo and a p-value of 0.592. It is a simple comparison of the displayed group means and does not reproduce the longitudinal mixed model. The endpoint description refers to HLM and repeated weekly results, whereas the posted analysis label says Mixed Models Analysis; the registry does not explain their relationship or give specifications sufficient to reproduce the sponsor's result.

The registry indicates no discrepancy between the recalculation and the posted information. Even so, the two p-values should not be treated as interchangeable: they arise from analyses with different reported detail and potentially different use of the repeated measurements. The sponsor's analysis is the registry's own reported model-based result, while the recalculation is a transparent, unadjusted reading of the summary statistics. Neither p-value alone describes the estimated effect's practical importance.

More complete model output, including the treatment estimate, interval limits, time effects, and missing-data handling, would allow a closer comparison. Those details are not reported in the registry record.

14. Multiplicity, Missing Data and Analysis Populations

The primary outcome description says that weekly proportions were analyzed across 13 longitudinal results, including baseline at Week 0. Repeated measurements create more than one opportunity to examine change or contrasts over time. In general, when many hypotheses or time-specific comparisons are tested, the chance of a nominally unusual result can increase unless the analysis plan addresses multiplicity. The registry record does not report whether time-specific comparisons were performed or whether any adjustment for multiplicity was planned or used.

The record lists one primary outcome measure and reports no secondary outcomes. That does not establish that no other outcomes or exploratory analyses were considered; it means they are not posted in the registry record. The statistical plan, prespecified contrasts, and any hierarchy among analyses are not reported in the registry record. No interim analyses are reported in the registry record.

The described primary population is an intention-to-treat analysis of all subjects receiving medication. The record does not provide a participant flow diagram or say whether this population includes everyone randomized, how many participants discontinued, or how much outcome data were available at each time. The posted arm counts are 13 for varenicline and 16 for placebo, but those counts alone do not reveal whether every scheduled urine test was completed.

Missingness matters because the weekly proportion uses completed tests as its denominator. If test availability is related to treatment assignment or to cocaine use, a summary of completed tests may differ from the outcome that would have been observed with complete follow-up. This is a general concern, not evidence that such a pattern occurred in this trial. The registry does not report the number or reasons for missed tests, the missing-data assumptions, or sensitivity analyses.

The outcome description names HLM, and the posted analysis is labeled Mixed Models Analysis. Mixed models can use incomplete repeated measurements under assumptions about missingness, but the model label alone does not establish which assumptions were made or whether they were reasonable. Covariance structure, fixed effects, random effects, baseline handling, and model diagnostics are not reported in the registry record. The results should therefore be interpreted with these analysis and reporting gaps in mind.

15. 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.

The posted serious adverse event figures list 0 affected among 13 at risk in the varenicline group and 0 affected among 16 at risk in the placebo group. The registry also lists 0 affected for other adverse events among 13 at risk in the varenicline group and 0 affected among 16 at risk in the placebo group. No serious adverse event terms are listed.

These entries describe what is recorded in the adverse-event fields; they do not establish that no symptoms or safety concerns occurred. The record does not provide event definitions, severity grading, follow-up duration for adverse events, or a narrative account of how events were collected. The death entries are not reported in the registry record.

Zero affected in the posted fields should not be read as proof of zero risk. With limited information about ascertainment and follow-up, the figures cannot characterize uncommon events or differences in safety precisely. The study summary states that safety and tolerability were aims, but the available adverse-event entries alone do not provide a comprehensive safety assessment.

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

The posted summaries show mean weekly proportions of cocaine-positive urine tests of 0.57 with varenicline and 0.58 with placebo. The unadjusted recalculated difference is -0.01, in the direction of a lower mean proportion in the varenicline group. The corresponding unadjusted p-value is 0.592, and the recalculated confidence interval includes zero. The sponsor's posted mixed-model result reports p = 0.84 but does not include the model-based estimate or interval limits.

These findings do not establish that the two groups had exactly the same outcome. The estimates are uncertain, and the registry does not report a clinically important threshold against which to judge the observed difference. Nor do the results demonstrate a meaningful benefit: the numerical direction and the p-value do not, on their own, establish an effect's size, reliability, or importance.

The endpoint captures cocaine-positive urine tests relative to completed tests, not every aspect of cocaine use or recovery. It does not directly report days of use, amount used, functioning, or other outcomes. The record posts no secondary outcomes. Interpretation also depends on how repeated measurements and missing urine tests were handled, details that are not available in the registry record.

The trial's stated aims included safety and tolerability as well as reduction in cocaine use. The posted adverse-event fields list no affected participants for serious or other adverse events in either group, but event collection details are limited and deaths are not reported in the registry record. Those entries are not enough to draw broad safety conclusions.

Overall, the registry supports a cautious description of the observed endpoint and its uncertainty in this trial. It does not support a claim that varenicline works or does not work, and it does not settle questions about other populations, outcomes, or treatment contexts. The conclusions are constrained by the posted sample, limited model output, and missing information on participant flow and tests not completed.

17. Why This Trial Matters Statistically

This trial illustrates why an outcome's construction matters. The endpoint is not simply a count of positive samples: each weekly value is a proportion whose denominator is completed tests. That choice makes test completion part of the interpretation. When an endpoint is measured repeatedly, both the outcome definition and the dependence among observations need to be considered.

It also illustrates the difference between a group-summary comparison and a longitudinal model. The posted means yield an unadjusted mean difference of -0.01 and an unadjusted p-value of 0.592. The registry separately reports p = 0.84 from a mixed-model analysis. Without a model-based estimate and interval, readers cannot compare the magnitudes or understand exactly how time and repeated measurements contributed to that result.

The example underscores why p-values should be read alongside effect estimates and confidence intervals. The unadjusted interval includes zero, and the posted model result does not include its interval limits. A result that is not statistically significant does not prove no effect; a numerical difference does not establish importance. Precision, study design, and the endpoint's interpretation all matter.

The planning illustrations also show how assumptions affect the resources needed to detect an effect. Under the stated planning assumptions, smaller target effects correspond to larger per-arm planning figures. Those calculations are not a substitute for the trial's original design rationale, which is not reported, and they are not observed power.

Finally, registry interpretation depends on transparent reporting. Participant flow, missing-test handling, model details, and complete safety information would help readers assess the evidence. Their absence does not show that procedures were inadequate, but it limits what can be concluded from the posted record.

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.

The registry provides limited detail on the trial procedures. It does not report varenicline dosing, treatment duration, adherence, or the operational details of randomization and masking. These omissions prevent a fuller assessment of how the intervention was delivered and how the design protections were implemented.

The posted outcome groups contain 13 participants for varenicline and 16 for placebo, while the enrollment entry is 31. The registry does not provide participant flow, reasons for discontinuation, or counts contributing data at each weekly measurement. It also does not report missed urine tests or their reasons. Because completed tests form the denominator of the weekly proportion, incomplete testing is especially relevant to interpreting the endpoint.

Although the description identifies HLM and the posted result is labeled Mixed Models Analysis, full model specifications and model-based effect estimates are absent. The record does not report the covariance structure, time effects, baseline handling, adjustment variables, model diagnostics, or missing-data assumptions. The sponsor's p-value therefore cannot be used to reconstruct the model estimate or its precision.

The registry reports no secondary outcomes and does not report the statistical plan, multiplicity procedures, interim analyses, or original sample-size justification. The planning illustrations are based on the observed unadjusted effect, not the original trial design. The record also does not identify a clinically important difference for the primary measure.

Safety reporting is limited to the posted affected counts. Event definitions, ascertainment methods, follow-up details, and death counts are not reported in the registry record. These limitations restrict interpretation of both efficacy-related results and safety information, without establishing that unreported procedures or events were absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Efficacy of Varenicline in Methadone-Stabilized Cocaine Users — NCT00567320.
• Registry record last updated 2020-04-02; status last verified 2013-01.
• Results first posted 2012-04-09.
• 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

NCT00567320 is a completed randomized, double-masked, parallel-group trial titled “Efficacy of Varenicline in Methadone-Stabilized Cocaine Users.” The registry lists Yale University as sponsor, phase NA, enrollment 31, start 2007-03, and primary completion 2009-06.

The intervention was varenicline, compared with placebo. The primary outcome was the weekly proportion of cocaine-positive urine tests, based on completed tests, with weekly measurements during 12 weeks and a longitudinal description that includes baseline at Week 0.

The posted means were 0.57 for varenicline and 0.58 for placebo. The unadjusted recalculation gives a mean difference of -0.01 and p = 0.592. The registry reports a mixed-model p-value of 0.84 but no model-based effect estimate or interval limits. No secondary outcomes are posted. The adverse-event fields list zero affected for serious and other adverse events in both groups; deaths are not reported in the registry record.