The Effect of Naltrexone and Varenicline on Alcohol-Mediated Smoking Lapse: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effect of Naltrexone and Varenicline on Alcohol-Mediated Smoking Lapse (NCT00773422), a randomized phase 2 study. The primary outcome is Latency to Initiate Ad-lib Smoking Session.

2. Clinical Question

3. Trial Design

This completed phase 2 study was randomized, triple-masked, and used a factorial model. Yale University is listed as the sponsor. The registry gives a start date of 2008-01 and a primary completion date of 2016-11. It records an enrollment of 30 participants. Further details about how randomization was conducted, who was masked, or how the factorial structure was implemented are not reported in the registry record.

Three groups appear in the posted results: naltrexone plus varenicline, varenicline alone, and placebo. The arm descriptions identify the combination as naltrexone 25mg plus varenicline 2mg, and the varenicline-only arm as varenicline 2mg. The placebo arm is described as placebo control. The displayed arm sizes for the primary outcome are 11, 9, and 10, respectively. These sizes sum to the recorded enrollment, but the record does not explain participant flow or whether all enrolled participants contributed to each outcome.

The primary endpoint is a continuous measure reported as a mean with standard error. The outcome was assessed on day 8 during a smoking delay task, and the registry states that the task allowed a delay from 0 minutes to 50 minutes. A secondary endpoint is the number of cigarettes smoked during the ad-lib period, also measured on day 8 and reported as a mean with standard error.

The study description frames the investigation around a low-dose alcohol priming drink, resistance to smoking, and later ad-lib smoking among daily smokers who were not seeking treatment. The full protocol, planned contrasts across all factorial groups, original design assumptions, and detailed analysis plan are not reported in the registry record. Accordingly, the posted summaries support interpretation of the displayed outcomes and comparison, but do not establish that every possible factorial contrast was tested or reported.

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 Latency to Initiate Ad-lib Smoking Session, measured over day 8.

Latency to initiate the ad-lib smoking session measures how long a participant waits before beginning to smoke during the day 8 smoking delay task. The registry describes the measure in minutes and gives the possible task range as 0 minutes to 50 minutes. A longer recorded latency therefore represents a longer delay within this particular task, while a shorter latency represents an earlier start. The endpoint is reported as a group mean with its standard error.

This kind of task outcome is used to quantify an immediate behavioral response under a defined study condition. The registry’s description connects the task to the study question of resisting smoking after an alcohol priming drink. It is a measure of delay in that session, not a direct measure of sustained abstinence, later smoking behavior outside the study, or a participant’s long-term response to treatment.

For the primary comparison, the posted summaries contrast the naltrexone-plus-varenicline group with placebo. The group means are 28.13 minutes and 21.74 minutes, respectively. The simple unadjusted mean difference is 6.397 minutes, with a confidence interval extending from -9.393 to 22.19 minutes. The interval is wide and includes no difference, so the posted summary does not locate the underlying mean difference precisely. This is a description of the reported endpoint and its uncertainty, not a clinical recommendation or a conclusion about treatment efficacy.

The task has a bounded range, which matters when interpreting the mean: observed times cannot go below 0 minutes or above 50 minutes under the registry’s description. Details of how task stopping, non-initiation, or any special endpoint handling were analyzed are not reported in the registry record.

7. Results Posted in the Registry

• Naltrexone + Varenicline: mean 28.13 versus 21.74 on control; difference 6.40 (95% CI -9.39 to 22.19), standardized effect d = 0.35; z-test p = 0.427.

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.

Number of Cigarettes Smoked During the Ad-lib Period

• 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 errors.
• Result:
  • Naltrexone + Varenicline: mean 1.28 versus 2.23 on control; difference -0.95 (95% CI -1.80 to -0.09), standardized effect d = -0.96; z-test p = 0.030.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Naltrexone + Varenicline than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The posted secondary outcome is the number of cigarettes smoked during the ad-lib period on day 8. The group summaries show the lowest mean in the varenicline-only arm, a somewhat higher mean in the combination arm, and the highest mean in the placebo arm. The posted recalculated inferential comparison, however, is the combination arm against placebo; no formal comparison involving varenicline alone is listed.

The combination-versus-placebo secondary estimate points toward fewer cigarettes in the combination arm, and its unadjusted confidence interval excludes zero. Its unadjusted p-value is 0.03. This pattern differs from the primary latency result, whose confidence interval includes zero and whose estimate is imprecise. The two outcomes measure related but distinct behaviors: waiting before smoking and the number of cigarettes smoked during a later ad-lib period. A result on one does not automatically establish the same pattern for the other.

The secondary result should carry less evidential weight than a prespecified primary result, especially because the registry record does not report a multiplicity plan or formal analyses. When several outcomes or comparisons are examined, some can appear noteworthy by chance even if none reflects a stable underlying effect. The record lists two outcome measures but does not report how many contrasts were planned or whether any adjustment was made.

These observations are useful as context for the trial’s behavioral outcomes, but the secondary result should not be treated as definitive evidence or as a replacement for the primary question. The registry does not report whether the secondary analysis was prespecified, how missing observations were handled, or whether the reported comparison followed a full analysis plan. Those omissions limit the strength of interpretation.

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

• Number of Cigarettes Smoked During the Ad-lib Period

9. Statistical Interpretation

10. Statistical Methods Explained

The primary endpoint is a continuous measure: latency in minutes before a participant begins the ad-lib smoking session. Continuous outcomes are commonly summarized using a mean, which represents the arithmetic average of the observed values in a group. The primary outcome summaries give means and standard errors. The standard error describes the precision of an estimated group mean; it is not the spread of individual participant values. The registry does not provide standard deviations for the primary arm summaries, and the posted spread values are identified as standard errors.

What does a mean difference express?

The posted comparison expresses the combination-arm mean relative to the placebo-arm mean as a mean difference. A positive estimate means the combination mean is higher for this endpoint, while a negative estimate would mean it is lower. For latency, a higher value means more time elapsed before smoking began during the task. The recalculated difference is unadjusted: it is based on the posted group summaries and does not incorporate adjustment for other variables. It should not be confused with an adjusted model estimate or a reported sponsor analysis.

For the primary comparison, the displayed estimate is 6.397 minutes. Its confidence interval ranges from -9.393 to 22.19 minutes. The interval describes a set of values compatible with the observed data under the method’s assumptions. Because it includes zero, it does not distinguish clearly between a positive difference and no difference; because it also extends into negative values, it allows for a difference in the opposite direction. The breadth of this interval is central to interpretation: the point estimate alone would hide substantial uncertainty.

What does the p-value add?

The unadjusted p-value is 0.427 for the primary recalculated comparison. In general, a p-value measures how inconsistent the observed data, or more extreme data, would be with a specified null model if the assumptions of the test hold. It does not give the probability that the null model is true. It also does not measure the size or practical importance of a difference. A p-value should be considered alongside the effect estimate, its confidence interval, study design, and the scope of analyses performed.

The registry record does not post formal analyses, so the comparison is best understood as a simple unadjusted recalculation from the arm summaries. The record’s discrepancy indicator is false, so there is no stated conflict between the recalculation and a sponsor analysis. Nonetheless, the recalculation does not add detail about covariate adjustment, missing observations, or analysis populations that the registry record does not report.

Why does the factorial label matter?

A factorial design can organize treatment assignments so that the effects of more than one intervention, and sometimes their combined effects, can be studied. The record identifies a factorial model and lists naltrexone, varenicline, and placebo, but the exact assignment structure and planned factorial contrasts are not reported in the registry record. The posted primary comparison is specifically the combination arm against placebo. It should not be read as a complete account of the effects of each component or of an interaction between treatments. Those questions require defined contrasts and corresponding analyses.

Randomization is intended, in general, to make assigned groups comparable on average with respect to measured and unmeasured characteristics. Masking can reduce some forms of expectation or assessment bias. The record identifies the trial as randomized and triple-masked, but does not report the allocation procedure or who was masked. These design labels are useful context, not enough to reconstruct implementation or determine whether masking remained intact.

What does over-dispersion mean in general?

General statistical context: over-dispersion occurs when outcome variation is greater than a statistical model expects. It is particularly relevant when modeling counts or event data, because underestimating variation can make uncertainty appear too small. The secondary endpoint is a count of cigarettes, but no count-model analysis is posted. The displayed summaries and simple mean-difference recalculation do not establish whether over-dispersion was assessed or whether a model was used. Details of any such assessment are not reported in the registry record.

The primary endpoint is bounded by the task range, from 0 minutes to 50 minutes. General statistical context: bounded outcomes can have distributions that differ from an unbounded normal distribution, especially near a boundary. The record does not describe the distribution of individual latency values or report a model designed for bounded or time-to-event data. The summary mean and standard error remain interpretable as descriptive statistics, but they do not reveal the shape of the individual-level data.

Overall, the posted numerical comparison is a straightforward summary-level contrast. The design labels and outcome descriptions provide context, but the absence of reported analysis details means that assumptions beyond those used for the simple recalculation cannot be verified from the registry record.

11. Confidence Intervals and Precision

The primary mean difference is 6.397 minutes, with a confidence interval from -9.393 to 22.19 minutes. This interval is wide relative to the range of plausible values it covers and includes zero. It therefore communicates substantial uncertainty about both the direction and size of the difference. The group means alone give a more definite impression than the interval warrants; precision is assessed by considering the estimate together with its uncertainty.

In general, a confidence interval is a range produced by a statistical procedure that, under its assumptions, is designed to include the underlying parameter at its stated confidence level over repeated applications. It is not a range containing a fixed proportion of individual participants’ values, nor does it assign a probability to the true value after the data are observed. The interval’s interpretation depends on the method and assumptions used.

The arm sizes for this primary outcome are 11 for the combination and 10 for placebo. Small groups typically yield less precise estimates than larger groups when other factors are comparable, although the actual precision also depends on the variability of the outcome. The record reports standard errors for the group means, but no individual-level distribution or adjusted analysis. The 95% confidence interval shown for the recalculated contrast is based on posted summary statistics and should be understood as an unadjusted estimate, not as a registry-reported model result.

The upper confidence limit for the secondary comparison is just below zero, while its lower limit is -1.801 cigarettes. That interval is comparatively closer to excluding a zero mean difference, but it is still a summary-level unadjusted result for a secondary outcome. Its apparent precision does not address the possibility of multiple outcomes or contrasts. The registry record does not report a multiplicity adjustment.

Confidence intervals help distinguish a stable, narrowly estimated contrast from one that remains compatible with a broad range of effects. Here, the primary interval leaves considerable uncertainty. The posted data are informative about the means observed in this sample, but do not pinpoint the population contrast with high precision.

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 the two-arm comparison; they are not total sample sizes and are not total event counts. The registry’s planning illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers effects equal to 100%, 75%, and 50% of the observed effect. The original trial’s own sample-size assumptions are not reported in the registry record.

The 80% power column gives the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the chosen effect under the stated assumptions, if that effect is real and the model assumptions hold. The 90% power column makes the corresponding illustration for a 90% chance. These are planning targets for a hypothetical future study, not claims about the probability that the observed result is true or the chance that this completed trial detected an effect.

For the primary comparison, planning for 100% of the observed effect gives 130 participants per arm for 80% power and 174 participants per arm for 90% power. Planning for 75% of the observed effect gives 231 participants per arm for 80% power and 308 participants per arm for 90% power. Planning for 50% of the observed effect gives 518 participants per arm for 80% power and 693 participants per arm for 90% power. Smaller effects require more participants because they are harder to distinguish from random variation under the same assumptions.

This is not observed power. It is a planning illustration computed from the observed effect, not the trial’s original design calculation. Estimates based on an observed effect can be unstable, especially when the original groups are small, and should not be treated as a reliable forecast without a justified target effect and design assumptions.

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 = 6.397; pooled standard deviation σ = 18.367.
2. n = 2 × (1.96 + 0.842)² × 18.367² / 6.397² = 129.4, rounded up to 130 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 <- 6.397                      # observed difference in means
sigma <- 18.3665036210804                     # 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(773422)
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 = 130 (80% power), 174 (90% power)
 75% of observed effect: n per arm = 231 (80% power), 308 (90% power)
 50% of observed effect: n per arm = 518 (80% power), 693 (90% power)
power.t.test: 130.4 
Simulated power at n = 130 per arm: 0.797 (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

The registry lists two outcome measures: latency to initiate ad-lib smoking and number of cigarettes smoked during the ad-lib period. It posts no formal analyses. The available comparisons are simple unadjusted recalculations from the group summaries, and the record does not describe a prespecified multiplicity strategy. It is therefore not reported in the registry record whether the outcomes were organized into a testing hierarchy, whether the family of tests included other contrasts, or whether any adjustment for multiple testing was planned or applied.

Multiplicity matters because examining several outcomes, treatment contrasts, or analysis choices creates more opportunities for a nominally unusual result to occur by chance. An unadjusted p-value is interpreted for its particular comparison; it does not account for other tests unless a suitable strategy is used. The secondary unadjusted finding should consequently be read cautiously, especially alongside the absence of a reported analysis plan. The registry record does not establish that a multiplicity problem occurred; it leaves the handling of that issue unreported.

Information about missing data is also limited. The primary arm summaries have 11, 9, and 10 participants, and the secondary summaries show the same arm sizes. The record does not describe participant flow, whether outcomes were available for every randomized participant, reasons for missing measurements, or any imputation or sensitivity analyses. The listed outcome counts alone do not establish what happened to participants at each stage.

The analysis populations are not reported in the registry record. It is therefore unclear from the posted information whether the summaries use all randomized participants, participants who completed the task, or another defined population. The record also does not explain whether the analysis followed intention-to-treat principles or how protocol deviations were handled.

These gaps matter for interpreting both the point estimates and their uncertainty. Without a full statistical plan, missing-data description, and analysis-population definition, readers cannot determine whether the posted summaries represent the intended primary analysis or assess the sensitivity of conclusions to analytic choices.

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.

Most frequent non-serious adverse event terms

The serious adverse event figures report zero affected participants in each of the three groups: 0 of 11 in the naltrexone-plus-varenicline arm, 0 of 9 in the varenicline arm, and 0 of 10 in the placebo arm. The registry also reports zero deaths in each group. These figures describe the recorded counts during the study; they do not prove that serious events could not occur or that the groups have identical safety profiles.

With small groups, a count of zero provides limited information about uncommon events. It should be read alongside the number of participants at risk and the study’s size, rather than as evidence that risk is absent. The registry’s serious-event terms list is empty. The timing and duration of safety monitoring, definitions used for event classification, and details of event collection are not reported in the registry record.

The record also lists participants affected by other, non-serious adverse events, but those figures do not change the interpretation of the serious-event count. These descriptive safety summaries are not a substitute for a larger or longer safety assessment and do not support individual treatment decisions.

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

The primary result is an imprecise estimate of the difference in mean latency between the combination arm and placebo on the day 8 smoking delay task. The observed means were 28.13 minutes and 21.74 minutes, and the simple unadjusted mean difference was 6.397 minutes. The confidence interval, from -9.393 to 22.19 minutes, spans zero and includes effects in either direction. The posted summary therefore leaves substantial uncertainty about the size and direction of the population difference.

The trial also reports a secondary behavioral outcome, number of cigarettes smoked during the ad-lib period. Its unadjusted combination-versus-placebo recalculation points in a different direction from the primary latency comparison and has a nominal p-value of 0.03. Because this is a secondary result and the registry does not report multiplicity handling or formal analyses, it should be considered exploratory in interpretation rather than decisive evidence.

These results do not demonstrate that the interventions do or do not work. They concern outcomes measured in a small, specific study sample and setting: non-treatment-seeking alcohol-drinking daily smokers, a day 8 task, and an ad-lib smoking period. Latency during a brief task is not the same as sustained abstinence or long-term changes in smoking. The record does not report outcomes beyond the posted measures or establish that the observed patterns persist outside the study context.

The record’s design labels indicate randomization, triple masking, and a factorial model, but details of implementation and the full set of planned comparisons are not reported. No formal analyses are posted. As a result, the summary-level comparisons cannot answer every question about component effects, interactions, or the robustness of the findings to alternative analyses.

The most defensible reading is descriptive and cautious: the posted data show particular group means, with substantial uncertainty for the primary contrast and a nominal secondary finding. They do not establish a definitive treatment effect, clinical benefit, or absence of benefit.

17. Why This Trial Matters Statistically

This trial illustrates why a point estimate and its uncertainty should be read together. The primary mean difference is positive, but the confidence interval spans a wide range that includes zero and values in the opposite direction. Looking only at the observed means could give an overly certain impression; the interval reveals that the study does not estimate the contrast precisely.

It also shows how an outcome’s meaning depends on its measurement. Waiting time in a day 8 smoking delay task captures a specific behavior under study conditions. It is not interchangeable with cigarette consumption in a later ad-lib period, and neither outcome alone represents long-term cessation. Keeping the endpoints distinct helps prevent an immediate task result from being generalized beyond what was measured.

The combination of a factorial design label and three posted groups highlights the importance of identifying the actual contrast being interpreted. The registry posts a combination-versus-placebo comparison, but does not report every possible component or interaction analysis. A design description alone cannot substitute for a clearly reported statistical plan and results for each intended contrast.

Finally, the trial emphasizes the difference between exploratory signals and confirmatory evidence. The secondary comparison has a nominally notable unadjusted result, but the record does not report multiplicity handling or formal analyses. Reporting the estimate, interval, and limitations together makes the uncertainty visible rather than allowing a single p-value to carry more weight than the record supports. These are broadly useful principles for reading small clinical studies with multiple outcomes.

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 enrolled sample was 30, with primary outcome arm sizes of 11, 9, and 10. These are small groups, and the primary confidence interval is broad. Estimates from small samples can be sensitive to individual observations, but individual-level data are not reported, so that sensitivity cannot be assessed.

The primary endpoint is bounded by the task’s stated range of 0 minutes to 50 minutes. The registry does not describe the distribution of individual latency values, whether participants who did not smoke during the task were handled specially, or how censoring or task limits entered the analysis. Those details could matter for analysis of a bounded waiting-time measure.

Although the study is identified as factorial, the registry record does not report the detailed treatment assignment structure, planned component contrasts, or interaction analysis. The posted comparison addresses the combination against placebo; it does not resolve the effect of each intervention separately. A varenicline-only group is listed, but no inferential comparison for that group appears in the posted analyses.

The record posts no formal analyses and does not describe the original statistical plan, analysis populations, missing-data methods, participant flow, or multiplicity approach. The outcome summaries have matching arm sizes, but this alone does not establish complete follow-up or explain how the analysis set was defined. These omissions constrain evaluation of possible bias and robustness.

Generalizability is also limited by the population and setting described: non-treatment-seeking alcohol-drinking daily smokers, observed in a study task and ad-lib session on day 8. The record does not report longer-term smoking outcomes. These specific limitations do not negate the posted observations, but they narrow what can responsibly be inferred from them.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: The Effect of Naltrexone and Varenicline on Alcohol-Mediated Smoking Lapse — NCT00773422.
• Registry record last updated 2018-04-23; status last verified 2018-03.
• Results first posted 2018-04-23.
• 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 describes a completed phase 2 randomized, triple-masked factorial study sponsored by Yale University, with enrollment of 30. The study examined naltrexone and varenicline in non-treatment-seeking alcohol-drinking daily smokers. Its primary endpoint was latency to initiate ad-lib smoking during a day 8 smoking delay task, reported as a mean with standard error.

The primary posted comparison is naltrexone plus varenicline versus placebo. The simple unadjusted recalculation estimates a mean difference of 6.397 minutes, with a confidence interval from -9.393 to 22.19 minutes and an unadjusted p-value of 0.427. The interval includes zero and indicates substantial uncertainty. A secondary outcome measures cigarettes smoked during the ad-lib period; its unadjusted comparison is nominally notable, but multiplicity handling is not reported.

The registry reports no formal analyses. Details of the original sample-size assumptions, missing-data methods, analysis populations, and full statistical plan are not reported in the registry record. Serious adverse event counts and deaths are recorded as zero in all three groups. Overall, the posted data describe outcomes in a small sample and support cautious, task-specific interpretation rather than definitive conclusions.