Modeling Stress-precipitated Smoking Behavior for Medication Development: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Modeling Stress-precipitated Smoking Behavior for Medication Development (NCT00773357), a randomized phase 2 study. The primary outcome is Latency to Initiate Ad-lib Smoking Session.

2. Clinical Question

3. Trial Design

The registry describes a randomized, triple-masked, parallel phase 2 trial sponsored by Yale University. It lists guanfacine and placebo as the interventions, with guanfacine described as 3mg/day and placebo as the control. A parallel design compares groups assigned to different interventions rather than describing participants as crossing between the two groups. The registry does not report the sequence-generation or allocation-concealment procedures, or the identities of the parties included in the masking.

The record lists enrollment of 100. For the posted primary outcome, the guanfacine group has 50 participants and the placebo group has 50 participants. The trial status is completed; its listed start is 2008-10 and its primary completion is 2021-07-31. Those registry fields describe the study record but do not establish when each participant entered or completed follow-up.

The stated purpose was to examine whether guanfacine would attenuate stress-precipitated smoking lapse behavior among treatment-seeking and non-treatment-seeking daily smokers. The primary outcome was latency to initiate an ad-lib smoking session, measured in minutes during a 50-minute period. The posted results contain one outcome measure and no posted analyses beyond the arm-level summaries and comparison presented in the results record. The original design assumptions, eligibility details, and operational details of the stress procedure 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

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 50 minutes.

The primary endpoint is latency to initiate an ad-lib smoking session. It records the time, in minutes, until a participant began smoking during a 50-minute period. A longer latency corresponds to waiting longer to start the session within that measured period. This endpoint therefore captures an immediate, time-based response in a study designed around stress-precipitated smoking behavior.

The registry summarizes the outcome as a mean for each group, with standard error as the reported measure of dispersion. The posted mean is 31.55 minutes for guanfacine and 30.31 minutes for placebo. The endpoint is useful for comparing average timing between the assigned groups under the study conditions. It does not, by itself, describe the full distribution of individual times, establish how participants who did not initiate within the period were handled, or measure subsequent smoking behavior. Those details are not reported in the registry record.

Interpreting the endpoint requires keeping its scope in view: it concerns initiation of an ad-lib session during a defined observation period, not a direct measure of sustained abstinence, smoking frequency over time, or treatment-seeking outcomes. The registry does not report additional primary outcome definitions or validation information.

7. Results Posted in the Registry

• Guanfacine: mean 31.55 versus 30.31 on control; difference 1.24 (95% CI -13.65 to 16.13), standardized effect d = 0.03; z-test p = 0.870.

8. Statistical Interpretation

9. Statistical Methods Explained

The endpoint is a continuous measure summarized by a group mean. A mean gives a single description of the average observed latency in each group. Here, the registered outcome is measured in minutes, and the reported arm means are 31.55 for guanfacine and 30.31 for placebo. Means are easy to compare, but they do not show whether participant-level values were clustered near the mean or widely spread. The registry does not post the individual observations or a distributional summary beyond the reported standard errors.

What does the standard error describe?

A standard error describes the uncertainty in an estimated mean, rather than the variability among individual participants. The posted standard errors are 5.3 minutes for guanfacine and 5.44 minutes for placebo. In general, standard errors are useful for assessing how precisely a sample mean estimates a population mean under the assumptions of the analysis. They should not be interpreted as the typical distance of an individual participant's latency from the group mean. The registry labels these values as standard errors; it does not report standard deviations for the outcome.

The comparison is reported as a mean difference. It expresses the estimated separation between the group means on the endpoint's original scale, so the estimate is interpretable in minutes. The direction is guanfacine relative to placebo: the posted difference is 1.24 minutes, with the guanfacine mean higher than the placebo mean. The comparison record also gives the group means and sizes used in the posted result. The registry does not state the exact test or model used by the sponsor, so no particular modeling procedure should be inferred from the summary alone.

How should the p-value be read?

The unadjusted p-value is 0.87. In general, a p-value describes how unusual results at least as incompatible with a specified null model would be if that model and its assumptions were correct. It is not the probability that the null hypothesis is true, and it does not measure the probability that the result will replicate. The word unadjusted indicates that the value is presented without a reported adjustment for multiplicity. The registry does not report a broader plan for hypothesis testing or identify any adjustment procedure.

A p-value is not a measure of effect size or precision by itself. It is best read alongside the estimated mean difference and its confidence interval. In this trial, the estimate is 1.24 minutes and the interval ranges from -13.65 to 16.13 minutes. Together, these statistics show that the point estimate is small compared with the range of differences compatible with the posted interval. They do not establish equivalence or rule out potentially meaningful differences.

What does the confidence interval contribute?

In general, a confidence interval expresses uncertainty around an estimate using a method with stated coverage properties under its assumptions. Its endpoints describe a range of values compatible with the observed data and the method used. It is not a guarantee that the true effect lies inside the particular interval, and it does not assign probability to individual values after the data have been observed. The registry reports a confidence interval for the mean difference but does not state its confidence level or provide the detailed calculation method.

The interval's inclusion of negative and positive values means that the posted summary does not tightly resolve the direction of the difference. The interval should be considered together with the study context and outcome definition; it pertains to mean latency during the ad-lib session observation, not longer-term smoking outcomes.

Why can over-dispersion matter?

In general, over-dispersion occurs when observed variability is greater than a statistical model assumes. If a model understates variability, its uncertainty estimates can be too small, which can make intervals too narrow and tests too optimistic. The present endpoint is continuous, and the registry lists standard errors rather than a count model or an over-dispersion assessment. It does not report a diagnostic or modeling approach that would allow a determination of whether over-dispersion was relevant. The general issue is therefore a consideration in statistical interpretation, not a finding about this trial.

The record reports no posted analyses beyond the primary outcome result, and does not report model covariates, missing-data procedures, or analysis-population definitions. These omissions limit assessment of the assumptions and reproducibility of the sponsor's analysis. The posted result remains useful as a summary of the recorded comparison, but the registry does not offer enough methodological detail to reconstruct every analytical choice.

10. Confidence Intervals and Precision

The estimated mean difference is 1.24 minutes, with a confidence interval from -13.65 to 16.13 minutes. The interval is broad relative to the point estimate and covers differences in both directions. This means the estimate is not precise enough to establish the direction or magnitude of the group difference from the posted summary alone. The interval should be understood as uncertainty around the estimated mean difference, not as a range of individual participant latencies.

In general, confidence intervals combine information about the estimate and its uncertainty under a particular statistical method. A narrower interval would indicate greater precision, while a wider interval indicates less precision. The registry does not report the confidence level or detailed method used for this interval, so those aspects cannot be independently assessed from the record. The posted standard errors for the group means are 5.3 minutes and 5.44 minutes, but they are not substitutes for the interval on the group difference.

The interval includes zero, but this alone does not show that the groups are equivalent. Equivalence requires a prespecified margin and an analysis designed to assess whether uncertainty falls within that margin; neither is reported in the registry record. Likewise, the interval's width means that a small point estimate should not be mistaken for a precise estimate of no difference. The posted result leaves substantial uncertainty about the size and direction of the difference in mean latency.

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 display is a planning illustration based on the observed effect, not a report of the trial's original design calculation. The assumptions listed are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario asks how many participants per arm would be needed to plan for a stated fraction of the observed effect. These are participants per arm, not total events; the time-to-event exception described for other displays does not apply to this continuous outcome.

The display gives planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For 100% of the observed effect, it lists 14,723 participants per arm for 80% power and 19,710 participants per arm for 90% power. For 75% of the observed effect, it lists 26,174 participants per arm for 80% power and 35,040 participants per arm for 90% power. For 50% of the observed effect, it lists 58,891 participants per arm for 80% power and 78,838 participants per arm for 90% power.

The 80% power column represents the planning target of detecting the stated effect under the listed assumptions with 80% power. The 90% power column uses a higher planning target for detection, also under those assumptions. Smaller effects need more participants to detect under the same framework, as illustrated by the increasing planning counts for smaller fractions of the observed effect. These counts are not observed power. The original trial design assumptions and any sample-size justification are not reported in the registry record. The curve expresses the same general relationship between effect size and planning sample size; it should be read as an illustration, not as a description of enrollment or observed trial performance.

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 = 1.240; pooled standard deviation σ = 37.975.
2. n = 2 × (1.96 + 0.842)² × 37.975² / 1.240² = 14,722.7, rounded up to 14,723 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 <- 1.24                      # observed difference in means
sigma <- 37.9748601050748                     # 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(773357)
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 = 14,723 (80% power), 19,710 (90% power)
 75% of observed effect: n per arm = 26,174 (80% power), 35,040 (90% power)
 50% of observed effect: n per arm = 58,891 (80% power), 78,838 (90% power)
power.t.test: 14723.6 
Simulated power at n = 14,723 per arm: 0.801 (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 lists one outcome measure and no secondary outcomes. It also lists no posted analyses. This does not establish that no additional outcomes or analyses were collected or conducted; it means they are not reported in the registry record. The primary result includes an unadjusted p-value of 0.87. No multiplicity plan, family of hypotheses, or adjustment method is reported, so it is not possible to assess how the result relates to any broader testing strategy.

The registry record does not report how missing outcome data were handled, whether all participants contributed to the primary analysis, or how participants without an observed latency were treated. It also does not define an intention-to-treat, per-protocol, or other analysis population. The posted outcome groups each contain 50 participants, but those arm counts alone do not reveal whether any randomized participants were excluded from the analysis or whether outcome data were complete.

In general, multiplicity matters when several hypotheses or outcomes are tested because repeated testing can increase the chance of at least one apparently notable result. Missing-data methods also matter because an analysis can depend on why data are unavailable and how the method handles them. These are general methodological concerns, not claims that either issue affected this trial. Without a statistical analysis plan or additional registry entries, the appropriateness of any handling cannot be evaluated.

The record likewise does not report covariate adjustment, subgroup analyses, interim analyses, or a prespecified hierarchy of outcomes. Their absence from the registry record should not be read as proof that such procedures were not used. It does mean that the posted outcome is best interpreted as a standalone registry result, with important details about analysis populations and analytic decisions unresolved.

14. 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 adverse-event record lists 50 participants at risk in each group. It reports zero serious adverse events attributed in the guanfacine group and zero in the placebo group. Deaths are listed as zero in both groups. These are the posted counts for the categories shown; they do not, by themselves, establish that no other safety events occurred.

The record also lists other adverse events as affecting 35 participants in the guanfacine group and 12 in the placebo group, with 50 participants at risk in each group. These figures are distinct from the serious adverse-event counts. The registry does not provide event terms in the serious-event listing, and it does not report details such as timing, severity criteria, or the method used to determine attribution. No serious-event terms are listed.

In general, adverse-event counts describe recorded events under the study's reporting process. A zero count in a posted category is not proof that an intervention is free of risk, and counts alone do not establish a causal relationship. The registry safety figures should therefore be read as descriptive reporting for the groups and categories specified, not as a comprehensive assessment of safety.

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

The posted result addresses a specific question: whether average latency to begin an ad-lib smoking session differed between participants assigned to guanfacine and placebo during a 50-minute period. The mean was 31.55 minutes for guanfacine and 30.31 minutes for placebo, with a reported mean difference of 1.24 minutes. The confidence interval, from -13.65 to 16.13 minutes, indicates considerable uncertainty about the direction and size of that difference. The unadjusted p-value is 0.87.

These statistics do not establish that the groups are the same. Failure to distinguish a difference from no difference is not equivalent to demonstrating equivalence. The interval spans negative and positive values, and the registry does not report an equivalence margin or an equivalence analysis. Nor does the point estimate alone establish a meaningful difference. The endpoint's meaning is limited to time until initiating a smoking session in the measured period; it does not directly assess smoking behavior over longer periods.

The result also does not answer every question implied by the study purpose. The registry describes an aim concerning stress-precipitated smoking lapse behavior and includes treatment-seeking and non-treatment-seeking daily smokers, but the posted primary result does not separately report those groups or provide further subgroup results. No secondary outcomes are posted. The registry record does not report details needed to assess generalizability, including participant characteristics and eligibility criteria.

Accordingly, the result should be read as an imprecise estimate for the recorded primary outcome, rather than as a definitive conclusion about all smoking behavior or about whether guanfacine works. The posted comparison is informative about what was reported for this endpoint, while the interval and missing methodological details constrain stronger conclusions.

16. Why This Trial Matters Statistically

This trial illustrates why the estimated effect, its uncertainty, and the endpoint definition all matter together. The reported mean difference of 1.24 minutes is easy to read on the outcome's original scale, but the confidence interval from -13.65 to 16.13 minutes shows that the estimate is not precise. Looking only at the point estimate would conceal the range of differences compatible with the posted analysis. Looking only at the p-value would likewise omit the scale and uncertainty of the effect.

The endpoint also makes the scope of inference important. Latency to initiate an ad-lib smoking session during a 50-minute period captures a defined behavioral response. It does not substitute for longer-term smoking outcomes. Statistical interpretation must therefore match the outcome actually measured, rather than extending the finding to outcomes the registry does not report.

The registry makes a planning illustration available using fractions of the observed effect. That illustration demonstrates a general design principle: planning to detect smaller effects under the stated assumptions requires more participants per arm. It is not the trial's original sample-size rationale and is not observed power. Keeping planning calculations separate from actual design documentation helps prevent readers from treating a post-result illustration as evidence about the study's original statistical plan.

Finally, the record's limited reporting on analysis populations, missing data, and multiplicity is itself statistically relevant. These details affect how completely readers can evaluate a result, even when the group summaries and comparison are clearly stated. The trial is therefore a useful example of reading an effect estimate in context while recognizing both what a registry result says and what remains undocumented.

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 primary result is reported as a group mean and standard error, with no participant-level distribution or additional descriptive summaries. The registry does not report how latency was handled for participants who did not initiate smoking during the 50-minute period. That detail could affect interpretation of the endpoint and cannot be inferred from the summary statistics.

The record does not report the detailed statistical method used for the comparison, the confidence level for the interval, covariates, or any model diagnostics. It also does not report the analysis population, missing-data handling, or whether all randomized participants were included. These omissions limit independent evaluation of the analysis without establishing that the analysis was inappropriate.

The posted results include no secondary outcomes or subgroup comparisons, so the result cannot be used to characterize differences between treatment-seeking and non-treatment-seeking participants. The registry also does not report participant characteristics or detailed eligibility criteria, limiting assessment of how well the recorded groups represent particular populations of daily smokers.

The safety summary is limited to the reported categories and counts. The record does not describe event timing or detailed assessment procedures. More broadly, a registry record is not a complete account of every trial procedure or result. The primary completion date and completed status do not supply the missing methods or outcome details. These limitations constrain interpretation of this particular posted result; they do not, on their own, determine the quality of the trial or the validity of analyses not described in the record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Modeling Stress-precipitated Smoking Behavior for Medication Development — NCT00773357.
• Registry record last updated 2022-08-03; status last verified 2022-08.
• Results first posted 2022-08-01.
• 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.

21. Record Summary

The registry record describes a completed, randomized, triple-masked, parallel phase 2 study sponsored by Yale University. It lists enrollment of 100 and compares guanfacine, described as 3mg/day, with placebo. The stated purpose concerns whether guanfacine attenuates stress-precipitated smoking lapse behavior among treatment-seeking and non-treatment-seeking daily smokers.

The sole posted outcome measure is latency to initiate an ad-lib smoking session during a 50-minute period. The mean was 31.55 minutes for guanfacine and 30.31 minutes for placebo. The reported mean difference was 1.24 minutes, with a confidence interval from -13.65 to 16.13 minutes and an unadjusted p-value of 0.87. The registry also reports zero serious adverse events attributed and zero deaths in both groups, alongside other adverse events affecting 35 participants in the guanfacine group and 12 in the placebo group.

Important details—including the original sample-size rationale, analysis population, missing-data procedures, and full statistical plan—are not reported in the registry record.