This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for A Study of Cytisinicline for Vaping Cessation in Adult Smokers (NCT05431387), a randomized phase 2 study. The primary outcome is Percentage of Participants With Vaping Abstinence From Week 9 to 12.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT05431387 |
| Phase | Phase 2 |
| Condition | Vaping, E-Cig Use |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 160 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Achieve Life Sciences |
| Results posted | Yes |
2. Clinical Question
Population
The primary outcome population was all randomized participants. The registry describes adults using nicotine-containing e-cigarettes; the study title refers to adult smokers. The posted record does not give further eligibility details for interpreting which adults were represented.
Intervention
Participants assigned to cytisinicline received one tablet orally three times daily, together with behavioral support, for 12 weeks. The registry describes the study as evaluating 3 mg cytisinicline administered TID.
Comparator
The comparison group received one placebo tablet orally three times daily, together with behavioral support, for 12 weeks. Thus, the comparison concerns assignment to the cytisinicline regimen or placebo in the context of behavioral support, rather than either regimen without that support.
Primary question
Among all randomized participants, what proportion met the registry’s definition of vaping abstinence from Weeks 9 to 12 in each group, and how did those proportions compare? Abstinence required weekly saliva cotinine below the stated threshold for biochemical verification and participants’ self-report of no vaping.
This question is about a specified outcome over a specified period, not simply whether a participant ever stopped vaping. The endpoint combines a biochemical measure with self-report, so the recorded status depends on both components. The main comparison is between the cytisinicline-plus-support group and the placebo-plus-support group. The primary outcome is a percentage of participants, making the group results proportions with the event of interest: meeting the abstinence definition.
The trial’s randomized, placebo-controlled design makes the contrast between assigned groups the central statistical comparison. The results describe this study population and its recorded outcomes. They do not by themselves establish what would happen in other populations, settings, or treatment conditions. The registry record does not report detailed eligibility criteria or further information about participants’ prior smoking or vaping histories.
3. Trial Design
This was a completed Phase 2, multicenter, double-blind, randomized, placebo-controlled trial with a parallel-group model. It enrolled 160 participants. The study took place at sites within the United States, according to the registry summary. The record lists a start date of 2022-07-13 and a primary completion date of 2023-02-28.
Participants were randomized to cytisinicline plus behavioral support or placebo plus behavioral support. Both study regimens involved one tablet taken orally three times daily for 12 weeks. The registry describes masking as quadruple. In general, masking is intended to limit the influence of knowledge of assignment on participant experience, care, or assessment; the exact roles covered by the registry’s masking label are not reported in the registry record.
The primary outcome was assessed from Weeks 9 to 12 and was defined as vaping abstinence verified weekly using quantitative saliva cotinine levels below 10 ng/mL and self-report of no vaping. The primary analysis population is stated as all randomized participants. The record also lists secondary abstinence periods, seven-day point-prevalence rates at visits, and quantitative cotinine changes, although the posted results do not include every outcome named in the registry’s secondary-outcome list.
The arm counts for the primary outcome are 53 in the placebo-plus-support group and 107 in the cytisinicline-plus-support group. The record does not report the planned allocation ratio, the original sample-size justification, detailed randomization procedures, or the prespecified statistical analysis plan. It also does not report interim analyses. These omissions limit what can be inferred about the planning and conduct of the trial beyond the design features explicitly recorded.
The parallel-group design means the assigned groups are compared over the trial rather than participants crossing between regimens. The comparison therefore describes outcomes by randomized group. The posted information does not state whether participants changed or discontinued assigned treatment, how adherence was assessed, or how such events were incorporated into analyses.
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
| Stage | Placebo + Behavioral Support | Cytisinicline + Behavioral Support |
|---|---|---|
| STARTED | 53 | 107 |
| Randomized and Treated | 53 | 106 |
| COMPLETED | 42 | 89 |
| NOT COMPLETED | 11 | 18 |
Reasons for not completing this period:
| Reason | Placebo + Behavioral Support | Cytisinicline + Behavioral Support |
|---|---|---|
| Adverse Event | 1 | 0 |
| Withdrawal by Subject | 4 | 4 |
| Physician Decision | 0 | 1 |
| Lost to Follow-up | 5 | 9 |
| Other, Not Specified | 1 | 4 |
Analysis population for the primary outcome, as defined in the registry: All randomized participants
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.
| Characteristic | Unit | Placebo + Behavioral Support | Cytisinicline + Behavioral Support | Total |
|---|---|---|---|---|
| Participants analysed | 53 | 107 | 160 | |
| Age, Continuous | years | 33.5 (SD 10.94) | 33.6 (SD 11.15) | 33.6 (SD 11.05) |
| Sex: Female, Male: Female | Participants | 29 | 54 | 83 |
| Sex: Female, Male: Male | Participants | 24 | 53 | 77 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 5 | 4 | 9 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 48 | 103 | 151 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Race/Ethnicity, Customized: Asian | Participants | 3 | 3 | 6 |
| Race/Ethnicity, Customized: Black or African American | Participants | 5 | 9 | 14 |
| Race/Ethnicity, Customized: White | Participants | 43 | 92 | 135 |
| Race/Ethnicity, Customized: Other, Not Specified | Participants | 2 | 3 | 5 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants With Vaping Abstinence From Week 9 to 12, measured over Weeks 9 to 12.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants with vaping abstinence from Weeks 9 to 12. The registry defines abstinence using two elements: weekly quantitative saliva cotinine below 10 ng/mL for biochemical verification, and participants’ self-report of no vaping. The population for this outcome is all randomized participants.
This is a binary outcome: each participant either meets the stated abstinence definition for the endpoint or does not. Group percentages therefore describe the share meeting the definition, rather than the amount of change in a continuous measurement. Combining self-report with a biochemical measure gives the endpoint both a reported-behavior component and an objective verification component. That combination is relevant because self-report alone and a biochemical measure alone do not capture exactly the same information.
The Weeks 9 to 12 interval identifies a particular period near the end of the 12-week regimen. It should not be read as a measure of abstinence across the entire study or as evidence that abstinence continued after that interval. The registry also lists a secondary abstinence outcome from Weeks 9 to 16, but that is a different timeframe and is not the primary endpoint.
In general, a prespecified primary endpoint helps focus the main trial comparison on one defined outcome and time period. The registry record does not report the original protocol’s rationale for selecting this endpoint, nor does it provide further detail about the weekly verification schedule beyond the description in the endpoint definition. The endpoint tells readers what was counted; it does not, by itself, settle how broadly the result applies or how missing assessments were handled.
7. Results Posted in the Registry
- Cytisinicline + Behavioral Support: 31.8% (34/107) versus 15.1% (8/53) on control; risk difference 16.7 percentage points (95% CI 3.6 to 29.7), risk ratio 2.11 (1.05–4.22); unadjusted two-proportion z-test p = 0.024.
Risk difference: Cytisinicline + Behavioral Support
95% CI: 3.6 to 29.7 percentage points
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percentage of Participants With Vaping Abstinence From Week 3 to 6 | Binary Endpoint | Risk difference | +9.2 pts (-3.4 to 21.8) | 292 per arm |
| Percentage of Participants With Vaping Abstinence From Week 6 to 9 | Binary Endpoint | Risk difference | +13.9 pts (0.5 to 27.2) | 148 per arm |
| Percentage of Participants With Vaping Abstinence From Week 9 to 16 | Binary Endpoint | Risk difference | +10.2 pts (-2.0 to 22.3) | 227 per arm |
Percentage of Participants With Vaping Abstinence From Week 3 to 6
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Cytisinicline + Behavioral Support: 24.3% (26/107) versus 15.1% (8/53) on control; risk difference 9.2 percentage points (95% CI -3.4 to 21.8), risk ratio 1.61 (0.78–3.31); unadjusted two-proportion z-test p = 0.180.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Cytisinicline + Behavioral Support and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With Vaping Abstinence From Week 6 to 9
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Cytisinicline + Behavioral Support: 30.8% (33/107) versus 17.0% (9/53) on control; risk difference 13.9 percentage points (95% CI 0.5 to 27.2), risk ratio 1.82 (0.94–3.51); unadjusted two-proportion z-test p = 0.061.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Cytisinicline + Behavioral Support and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With Vaping Abstinence From Week 9 to 16
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Cytisinicline + Behavioral Support: 23.4% (25/107) versus 13.2% (7/53) on control; risk difference 10.2 percentage points (95% CI -2.0 to 22.3), risk ratio 1.77 (0.82–3.82); unadjusted two-proportion z-test p = 0.131.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Cytisinicline + Behavioral Support and the control. The interval gives the range of effects that remain compatible with the data.
The secondary abstinence outcomes show a generally higher posted percentage in the cytisinicline-plus-support group than in the placebo-plus-support group across the listed intervals. The pattern is not equally precise across outcomes: the unadjusted intervals for some comparisons include the no-difference value, while another interval is more compatible with a positive difference. The later-period outcome extending from Weeks 9 to 16 also points in the same descriptive direction as the primary comparison, but its uncertainty remains relevant.
These outcomes provide context for the Weeks 9 to 12 primary result because they assess abstinence over other time windows. They are not interchangeable with the primary endpoint: each uses a different interval, and the visit-based seven-day point-prevalence outcome is a distinct measure. The registry lists five secondary outcomes, but posted results include only some of the outcome descriptions; the seven-day visit rates and quantitative cotinine changes are not included in the secondary results listed in the record.
In general, secondary analyses are often interpreted as supportive or exploratory unless the analysis plan specifies otherwise. Multiple outcomes create multiple opportunities for apparently notable results, increasing the chance that at least one finding may arise from random variation. The registry record does not report a multiplicity adjustment or a hierarchy for secondary hypotheses. Consequently, unadjusted secondary results carry less inferential weight than a prespecified primary comparison and should be read as a pattern across measures, not as a series of independent confirmations.
The overall consistency in direction is descriptive; it does not prove that the effect is stable across time or that each secondary endpoint independently supports the same conclusion. Differences in endpoint definition, time period, event counts, and precision can produce varied estimates. The registry record does not report a formal longitudinal model or an overall test combining these time windows. Conclusions should therefore stay tied to each outcome’s own definition and uncertainty.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants With Vaping Abstinence From Week 3 to 6
- Percentage of Participants With Vaping Abstinence From Week 6 to 9
- Percentage of Participants Who Achieve Vaping Abstinence at Each Visit From Week 2 and Week 12 (Seven-Day Point Prevalence Rates)
- Changes From Baseline in Quantitative Cotinine Levels From Week 2 to Week 12
- Percentage of Participants With Vaping Abstinence From Week 9 to 16
9. Statistical Interpretation
For the primary outcome, abstinence was recorded for 15.1% of participants assigned to placebo plus behavioral support and 31.8% assigned to cytisinicline plus behavioral support. These are the posted group percentages for Weeks 9 to 12. The unadjusted recalculation describes a higher observed abstinence proportion in the cytisinicline group. It is a comparison of the posted summaries, not an adjusted estimate incorporating participant-level covariates.
The registry includes a sponsor-reported difference in proportions of 0.17, with a 95% confidence interval from 0.012 to 0.284 and p = 0.012 from a Cochran-Mantel-Haenszel analysis. It also lists exact computations for odds ratios: 2.64 with a 95% confidence interval from 1.062 to 7.098 and p = 0.035, and 2.62 with a 95% confidence interval from 1.133 to 6.491 and p = 0.035. These analyses express the group contrast using different effect measures and methods. The record does not explain why multiple sponsor-reported analyses appear or which one was designated as the principal inferential analysis.
In general, a p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not quantify the size or practical importance of an effect. The confidence interval gives a range of values compatible with the data and method at the stated confidence level. The primary sponsor-reported difference-in-proportions interval lies above zero, while the odds-ratio intervals lie above one; these are the respective no-difference reference values for those measures.
The trial was randomized, but the displayed comparison is not described as adjusted for other factors in the registry record. The study involved 160 participants overall, with unequal primary-outcome arm counts of 53 and 107. The estimates should therefore be read as results from a relatively limited trial population, rather than as highly precise values that would necessarily recur in another study. Confidence intervals convey some of this uncertainty, but do not account for every possible limitation, such as missing outcome data or differences between the trial population and other populations.
The record does not report how missing primary assessments were handled, whether any participants were excluded from the primary analysis, or the detailed prespecified analysis plan. Although the stated primary population is all randomized participants, the information posted does not resolve how that population was operationalized when outcome data were unavailable. Nor does the registry record report a multiplicity adjustment. As a result, the primary comparison is best considered in the context of the stated endpoint, the range of estimates, and the trial’s limited size, rather than interpreted solely from a threshold for statistical significance.
Overall, the posted primary percentages and reported analyses indicate a larger observed abstinence proportion in the cytisinicline-plus-support group than in the placebo-plus-support group for the specified Weeks 9 to 12 outcome. That description is not a claim about clinical benefit or lack of benefit. It is a summary of the observed contrast and its statistical uncertainty in this trial.
10. Statistical Methods Explained
Several statistical ideas help interpret the posted results. The primary outcome is binary, so each participant contributes an abstinence or non-abstinence status for the defined period. A percentage summarizes the proportion meeting the endpoint within an assigned group. In general, comparing two such percentages can be done through an absolute difference in proportions, a risk ratio, or an odds ratio. These measures describe the same underlying comparison in different ways, and their numerical values are not interchangeable.
What does a difference in proportions express?
A difference in proportions is an absolute contrast between the two group percentages, represented on a probability scale. A value of zero corresponds to equal proportions. The sponsor-reported estimate is 0.17, with a 95% confidence interval from 0.012 to 0.284. In general, this measure is often straightforward to interpret because it describes the gap between the groups on the outcome’s percentage scale. It is still an estimate, subject to sampling variability and the assumptions of the analysis.
How is an odds ratio different?
An odds ratio compares the odds of meeting the outcome in one group with the odds in the other. Odds are not the same as probabilities, so an odds ratio should not be read as a direct multiple of the group percentages. The sponsor lists exact-computation odds ratios of 2.64 and 2.62 in separate analyses. Their confidence intervals and p-values are also reported separately. The registry does not explain the distinction between these two exact computations, so they should not be treated as duplicate copies of one fully specified analysis without further information.
In general, an odds ratio of one represents equal odds in the compared groups; values above or below one indicate the direction of the contrast, depending on the order of groups. The posted analyses list the groups as placebo plus behavioral support and cytisinicline plus behavioral support. When communicating an odds ratio, it is useful to state the group order and avoid translating it directly into a probability or percentage change.
What do confidence intervals contribute?
A confidence interval conveys uncertainty around an estimate under the statistical method used. In general, a 95% confidence interval is produced by a procedure that, across repeated comparable studies under its assumptions, would cover the target value in 95% of repetitions. It is not a statement that there is a 95% probability that this particular interval contains the true value. Wider intervals indicate less precision than narrower intervals on the same scale.
The reported confidence intervals are tied to their respective measures and methods. For a difference in proportions, zero is the no-difference value; for an odds ratio, one is the no-difference value. The sponsor-reported intervals for the primary analyses do not include their respective reference values. That statistical feature should be considered alongside the estimate and the design, rather than treated as a complete judgment about the importance or reproducibility of the finding.
What do the p-values mean?
In general, a p-value measures how unusual data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the model assumptions were true. A small p-value is not the probability that the result occurred by chance, nor does it measure the size of the observed difference. The registry lists p-values for the primary analyses, including p = 0.012 for the Cochran-Mantel-Haenszel comparison and p = 0.035 for one exact odds-ratio analysis.
The Cochran-Mantel-Haenszel method is a general approach for comparing groups while accounting for specified strata. The registry names this method for a difference-in-proportions analysis but does not identify the strata or describe the implementation. It is not possible to infer from the method name alone what factors, if any, were used for stratification. The exact-computation analyses are identified as such, but the record does not provide additional technical detail about the exact procedure.
Why distinguish sponsor analyses from recalculation?
The recalculated comparison is an unadjusted calculation from posted group summaries. It does not substitute for an analysis using participant-level information, a stratification scheme, or an adjusted model. The sponsor’s posted analyses include a Cochran-Mantel-Haenszel difference in proportions and exact odds-ratio computations. Because these methods target different measures or may use different procedures, their numerical estimates and p-values need not match a simple unadjusted calculation exactly.
The registry record does not provide the full statistical analysis plan, details of covariate adjustment, or a rationale for each reported analysis. Those details matter when determining which analysis was prespecified and how to interpret multiple outputs. The posted results do not flag a discrepancy between the recalculation and the sponsor analyses. The sponsor’s reported values should nevertheless be kept distinct from a simple unadjusted re-calculation: each describes the group comparison through its stated measure and method.
General caution also applies to binary outcomes when group sizes are limited. Estimates can shift when a small number of participant outcomes differ, and intervals can remain broad even when the point estimate is notable. For that reason, interpreting an effect estimate together with its confidence interval is more informative than relying on a p-value alone. The trial’s design and endpoint definition establish what was compared, while the reported methods and their limitations determine how much statistical confidence to place in the numerical contrast.
11. Confidence Intervals and Precision
The primary outcome percentages are 15.1% in the placebo-plus-support group and 31.8% in the cytisinicline-plus-support group. The sponsor-reported difference in proportions is 0.17, with a 95% confidence interval from 0.012 to 0.284. This interval describes uncertainty for the difference-in-proportions estimate under the Cochran-Mantel-Haenszel method recorded by the sponsor.
The sponsor also reports odds-ratio estimates with 95% confidence intervals. One is 2.64, with an interval from 1.062 to 7.098; another is 2.62, with an interval from 1.133 to 6.491. These intervals are on the odds-ratio scale and should not be compared numerically with the difference-in-proportions interval. Their widths indicate that the exact magnitude of the odds ratio remains uncertain, even though the intervals are above the no-difference value of one.
In general, interval width reflects both the amount of information and the variability in the outcome, as well as the method used. A confidence interval is not a guarantee that the true value lies within its endpoints. It also does not address biases from missing outcomes, outcome measurement, or limitations in generalizability. Those concerns require information about the conduct and analysis that is not fully reported in the registry record.
The primary outcome arm counts were 53 and 107. The difference in group sizes and the overall trial enrollment are relevant context for precision, but they do not by themselves determine the width of an interval. The estimates are more informative when considered with their intervals and the explicit outcome definition than when read as single exact quantities. The posted results provide evidence about the trial’s observed comparison, while leaving uncertainty about the precise size of the contrast.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 101 | 134 |
| 75% of the observed effect | 168 | 224 |
| 50% of the observed effect | 350 | 468 |
The planning figures are illustrative requirements in participants per arm, not total event counts. They use the observed effect as a starting point and show scenarios that plan for 100%, 75%, or 50% of that observed effect. For the primary comparison, planning for 100% of the observed effect gives 101 participants per arm for 80% power and 134 participants per arm for 90% power. Planning for 75% gives 168 participants per arm for 80% power and 224 participants per arm for 90% power. Planning for 50% gives 350 participants per arm for 80% power and 468 participants per arm for 90% power.
The stated planning assumptions are 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. In general, the 80% power column describes a planning target under which a study with the stated assumptions would have an 80% chance of detecting the specified effect at the chosen significance level, if that effect and the model assumptions were correct. The 90% column uses a higher target probability under the same general planning framework.
Smaller effects are harder to distinguish from random variation, so the planning illustrations require more participants per arm when the assumed effect is reduced. These calculations are based on the observed trial effect and do not represent the trial’s original design justification. The registry record does not report the original sample-size assumptions or justification. The planning numbers are not observed power; they are hypothetical sample-size illustrations under the listed assumptions.
Equal allocation is an assumption for these planning illustrations, while the posted primary-outcome arm counts are 53 and 107. The planning figures therefore should not be read as a reconstruction of the actual enrollment plan or as a statement about what the trial was designed to detect. They indicate how required sample size changes under the specified hypothetical effect scenarios.
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 z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.151; treatment proportion p1 = 0.318; average p̄ = 0.234.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5990 = 1.1741.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5873 = 0.4943.
- n = (1.1741 + 0.4943)2 / (0.1668)2 = 100.0, rounded up to 101 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
p0 <- 0.150943396226415 # control proportion
p1 <- 0.317757009345794 # treatment proportion
n_per_arm <- function(power, frac = 1) {
q1 <- p0 + (p1 - p0) * frac # smaller effect = fraction of the observed difference
pbar <- (p0 + q1) / 2
z_b <- qnorm(power)
ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")
# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(5431387)
n <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))
Output from running the code
100% of observed effect: n per arm = 101 (80% power), 134 (90% power)
75% of observed effect: n per arm = 168 (80% power), 224 (90% power)
50% of observed effect: n per arm = 350 (80% power), 468 (90% power)
power.prop.test: 100
Simulated power at n = 101 per arm: 0.813 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Exact computations | Odds Ratio (OR) 2.64 | 1.062 to 7.098 | 0.035 |
| Exact computations | Odds Ratio (OR) 2.62 | 1.133 to 6.491 | 0.035 |
| Cochran-Mantel-Haenszel | Difference in proportions 0.17 | 0.012 to 0.284 | 0.012 |
The sponsor’s posted primary analyses include an odds ratio of 2.64 from exact computations, with a 95% confidence interval from 1.062 to 7.098 and p = 0.035. A second exact-computation odds ratio is 2.62, with a 95% confidence interval from 1.133 to 6.491 and p = 0.035. The sponsor also reports a Cochran-Mantel-Haenszel difference in proportions of 0.17, with a 95% confidence interval from 0.012 to 0.284 and p = 0.012.
The unadjusted recalculation is based on the posted group summaries and describes the same direction of observed difference as the sponsor’s reported difference in proportions. It is not identical in method to the Cochran-Mantel-Haenszel analysis or the exact odds-ratio analyses. Different effect measures and procedures can yield different estimates, intervals, and p-values while addressing the same broad group comparison.
The registry record does not explain why two exact odds-ratio results are listed, or provide enough detail to identify the precise implementation of each. It also does not provide the full analysis plan needed to establish which sponsor analysis was prespecified as primary for inference. The record does not flag a discrepancy between the recalculation and the sponsor analyses. The sponsor outputs should therefore be read as the analyses reported in the registry, while the recalculation remains a simple unadjusted comparison of the posted summaries.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several statistical hypotheses are examined. If each is tested separately at a chosen significance level, the chance of at least one apparently unusual result across the family of tests can be greater than for a single test. General methods for addressing multiplicity include defining a hierarchy of outcomes or adjusting the testing procedure, but the registry record does not report a multiplicity strategy for this trial. The listed secondary outcomes and multiple reported primary analyses make that absence relevant when interpreting nominal p-values.
The record identifies the primary endpoint and states that the primary population is all randomized participants. It does not report a detailed missing-data method, the number of participants with unavailable primary outcomes, or whether any sensitivity analyses examined alternative assumptions about missingness. A stated all-randomized population does not alone specify how participants without an observed endpoint were counted or modeled. Those details are not reported in the registry record.
In general, missing outcome data can affect both the estimated group proportions and their uncertainty. The direction and size of any effect depend on which outcomes are missing and why they are missing, information not contained in the posted results. It would be inappropriate to assume that every randomized participant had a complete assessment or that a particular imputation rule was used.
The record also does not report an analysis plan specifying whether the main comparison was adjusted, how the multiple sponsor analyses were selected, or whether interim analyses were conducted. The design description lists randomization and quadruple masking, but does not give operational details about allocation concealment or the roles masked. These reporting gaps limit assessment of how closely the displayed analyses follow a prespecified plan. They do not, on their own, establish that the analysis was inappropriate; they mark aspects that cannot be evaluated from the registry record.
Accordingly, the primary result can be described using its endpoint, assigned groups, estimate, and interval, while conclusions about multiplicity control, missing-data robustness, and prespecification remain limited. The secondary outcomes should be treated cautiously because their relationship to any testing hierarchy is not reported.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo + Behavioral Support | 0 | 53 | 0.0% |
| Cytisinicline + Behavioral Support | 0 | 106 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo + Behavioral Support | 0 of 53 |
| Cytisinicline + Behavioral Support | 0 of 106 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 2% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo + Behavioral Support | 26 of 53 |
| Cytisinicline + Behavioral Support | 42 of 106 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo + Behavioral Support | Cytisinicline + Behavioral Support |
|---|---|---|---|
| Abnormal dreams | Psychiatric disorders | 1 of 53 | 13 of 106 |
| Anxiety | Psychiatric disorders | 4 of 53 | 10 of 106 |
| Headache | Nervous system disorders | 5 of 53 | 7 of 106 |
| Insomnia | Psychiatric disorders | 1 of 53 | 11 of 106 |
| Nausea | Gastrointestinal disorders | 6 of 53 | 5 of 106 |
| COVID-19 | Infections and infestations | 7 of 53 | 4 of 106 |
| Upper respiratory tract infection | Infections and infestations | 3 of 53 | 6 of 106 |
| Fatigue | General disorders | 2 of 53 | 6 of 106 |
| Irritability | Psychiatric disorders | 2 of 53 | 3 of 106 |
| Dry mouth | Gastrointestinal disorders | 2 of 53 | 2 of 106 |
The posted serious adverse event figures list 0 affected participants among 53 at risk in the placebo-plus-support group and 0 among 106 at risk in the cytisinicline-plus-support group. The record lists 0 deaths in each group. No serious adverse event terms are listed in the posted serious-event summary.
For other adverse events, the record lists 26 affected participants among 53 at risk in the placebo group and 42 among 106 at risk in the cytisinicline group. These are counts of participants with an event, not counts of all event episodes. The safety denominators differ from the primary-outcome arm counts, including 106 in the cytisinicline safety group compared with 107 in the primary outcome group. The reason is not reported in the registry record.
Zero recorded serious events in these groups does not establish that the risk of serious events is absent. In general, rare events may not be observed in a trial of limited size, and the record gives no basis for estimating uncommon risks precisely. These figures describe the safety information posted for this trial and should not be interpreted as a complete account of all possible harms or as advice about treatment.
17. What the Result Does, and Does Not, Mean
The result describes a difference in recorded abstinence proportions between randomized groups for a defined endpoint and period. The primary percentages were 15.1% with placebo plus behavioral support and 31.8% with cytisinicline plus behavioral support. The sponsor’s reported difference-in-proportions analysis and odds-ratio analyses also describe a contrast favoring a higher observed abstinence proportion in the cytisinicline group. These are statements about the posted data, not recommendations about treatment.
The result does not establish the exact size of a true effect. Confidence intervals show that estimates remain uncertain, and statistical methods produce different scales for describing the same comparison. The trial enrolled 160 participants, and the primary endpoint group counts were 53 and 107. The precision and generalizability of findings from this trial should be considered in that context.
The endpoint was abstinence from Weeks 9 to 12, verified weekly by saliva cotinine below 10 ng/mL and self-report of no vaping. It does not show whether participants remained abstinent after that interval, whether they abstained throughout the whole trial, or how outcomes differed outside the specified definition. Although the registry lists an additional abstinence outcome through Week 16, an outcome over that period answers a different question.
The record does not provide detailed information about missing assessments, adherence, the original sample-size justification, or the full statistical analysis plan. It also does not report multiplicity handling for the secondary outcomes. Those gaps limit assessment of the robustness of the estimates and the weight to place on multiple analyses. The trial’s randomized and blinded design is important context, but does not remove uncertainty or resolve unreported methodological details.
Nor does the result show that the same percentages or contrasts would occur in other groups or settings. The registry describes adults using nicotine-containing e-cigarettes and sites in the United States, but does not provide further participant characteristics in the record. Differences in eligibility, setting, support, or follow-up could matter in other circumstances. The result should therefore be understood as a trial-specific statistical finding, with the stated outcome definition and uncertainty, rather than a universal conclusion.
Finally, a statistically notable result is not synonymous with clinical importance. The registry does not supply a threshold for what difference would be meaningful to participants or clinicians, nor does it establish how benefits and harms should be weighed. Statistical interpretation can describe the observed contrast and its precision; it cannot independently determine the practical or medical significance of that contrast.
18. Why This Trial Matters Statistically
This trial illustrates why a clinical result should be read through its endpoint definition, effect measure, uncertainty, and design rather than from a single p-value. The primary outcome is a binary abstinence measure that combines a cotinine threshold with participant report. That definition clarifies what the percentages represent and distinguishes the endpoint from a broader claim about all vaping behavior or longer-term abstinence.
The registry presents the primary comparison in more than one statistical form. A difference in proportions is an absolute contrast, while odds ratios compare odds. The methods yield estimates on distinct scales, and the confidence intervals provide information that a significance label alone cannot. The reported intervals help readers see the uncertainty around the group contrast, while the relatively limited trial size remains important context.
The trial also illustrates the interpretive challenge created by multiple outcomes and analyses. Secondary abstinence outcomes use different time periods, and the registry does not report a multiplicity plan or detailed analysis hierarchy. Similar directions across several endpoints can be informative descriptively, but multiple unadjusted analyses should not be treated as a collection of independent confirmatory tests.
Finally, the record separates what is known from what remains unclear. Randomization, masking, arm regimens, the primary population, and outcome definition are stated. Detailed missing-data handling, original sample-size justification, interim analyses, and aspects of the statistical plan are not reported in the registry record. Distinguishing these reported design details from unreported analysis details is essential for a calibrated reading of clinical trial evidence.
19. 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.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
Several trial-specific limitations affect interpretation. The study enrolled 160 participants, with primary outcome counts of 53 in the placebo-plus-support group and 107 in the cytisinicline-plus-support group. The imbalance is visible in the posted counts, but the registry record does not explain the planned allocation ratio or the reason for the final arm sizes. The planning illustrations assume equal allocation and should not be taken as the trial’s original design calculation.
The primary endpoint covers Weeks 9 to 12 and requires both weekly biochemical verification and self-report. That operational definition is specific to the trial; it does not directly represent every possible definition of cessation. The registry record does not give further detail about missing weekly measurements, adherence, or how participants with incomplete endpoint information were handled. This makes it difficult to assess the sensitivity of the estimates to missing data.
The registry lists several secondary outcomes and more than one sponsor-reported analysis for the primary comparison, but does not give the full prespecified statistical analysis plan, multiplicity approach, or rationale for the distinct exact-computation outputs. These omissions limit assessment of which secondary findings were confirmatory and how the analyses were selected. The method label for the Cochran-Mantel-Haenszel analysis is present, but the record does not state the strata.
The safety summaries report no serious adverse events or deaths in either group, but the number of participants is limited and the safety denominators do not exactly match the primary-outcome counts. The reason for the denominator difference is not reported in the registry record. Absence of listed serious events does not rule out uncommon harms or establish complete safety.
Finally, the record describes sites in the United States and adults using nicotine-containing e-cigarettes but does not provide additional participant characteristics or detailed eligibility criteria. Generalization to populations not described in the record is uncertain. These limitations qualify the interpretation of the posted estimates; they do not change the fact that the primary group percentages were higher in the cytisinicline-plus-support arm.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Study of Cytisinicline for Vaping Cessation in Adult Smokers — NCT05431387.
- Registry record last updated 2026-01-14; status last verified 2025-12.
- Results first posted 2026-01-14.
- 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.
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23. Record Summary
This completed, randomized, quadruple-masked, parallel-group Phase 2 trial enrolled 160 participants at sites in the United States. It compared cytisinicline plus behavioral support with placebo plus behavioral support, with both regimens given three times daily for 12 weeks.
The primary endpoint was vaping abstinence from Weeks 9 to 12 among all randomized participants, defined using weekly saliva cotinine below 10 ng/mL and self-report of no vaping. Posted abstinence percentages were 15.1% for placebo plus behavioral support and 31.8% for cytisinicline plus behavioral support. Sponsor-reported analyses included a difference in proportions of 0.17 and exact odds-ratio estimates.
Secondary abstinence outcomes generally had higher posted percentages in the cytisinicline group, with varying precision. The safety summary listed no serious adverse events or deaths in either group. The registry record does not report detailed missing-data handling, multiplicity procedures, the original sample-size justification, interim analyses, or the full statistical analysis plan.