Treatment of Smoking Lapses and Relapses: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Treatment of Smoking Lapses and Relapses (NCT01807871), a randomized phase 4 study. The primary outcome is Point-prevalent Abstinence at 4 Months.

2. Clinical Question

The comparison concerns what to do with the patch after a lapse, not whether participants should begin patch treatment. Both groups were recruited as smokers who wanted to quit and were to receive nicotine patch treatment and counseling. The primary outcome was assessed at the four-month follow-up, with abstinence defined by a specific survey response about smoking during the preceding seven days.

This is a question about a difference between randomized groups within the lapse-defined population. It is not a direct comparison of patch treatment with no patch treatment, and it does not estimate the effect of the assigned approach for all 701 enrolled participants. The registry record does not report a separate primary result for participants who never lapsed.

3. Trial Design

The registry record describes a randomized, parallel-group trial with no masking. It lists the study as phase 4 and reports enrollment of 701 participants. The study is marked completed. The listed start is 2013-03 and primary completion is 2016-02. The sponsor is the University of Vermont, and the condition is smoking cessation.

Participants were assigned to one of two nicotine-patch approaches. In the experimental-use group, participants were instructed to continue the patch after a lapse and resume smoking, provided smoking remained below 75% of pre-study levels. In the labeled-use group, participants were instructed to discontinue the patch when they resumed smoking. The registry describes this as the current FDA-approved use of the nicotine patches.

The brief description says the investigators planned to provide 10 weeks of nicotine patch treatment and 5 weeks of counseling. Treatment and study measures were to be conducted from home using paper, phone, or computer surveys. These details describe the intended study procedures; the registry record does not provide a detailed account of adherence or actual treatment exposure.

The primary outcome was measured at four months after the quit date and was restricted to participants who quit and then lapsed while using the patch. The result therefore pertains to a subgroup defined by events during the quit attempt. The registry record does not report the original sample-size justification, detailed randomization procedures, or whether analyses were adjusted for any baseline variables. It also does not report masking beyond listing the study as unmasked.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Analysis population for the primary outcome, as defined in the registry: Participants who lapsed while using the nicotine patch

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 Point-prevalent Abstinence at 4 Months, measured over 4 months after the quit date.

The primary endpoint is seven-day point-prevalent abstinence at four months after the quit date. It records whether a participant reported smoking on any day in the seven days covered by the four-month follow-up survey. A response of zero days smoking was classified as abstinent. Every other response, including a missing response, was classified as not abstinent.

This endpoint is a binary measure: each participant is placed in one of two categories, abstinent or not abstinent. It captures recent smoking status at a particular follow-up rather than continuous abstinence throughout the period since the quit date. A participant could have smoked earlier in the quit attempt and still meet this endpoint if they reported zero smoking days in the specified seven-day window.

Using a defined survey question makes the outcome classification explicit and allows the randomized groups to be compared on the same measure. The measure is relevant to the study question because the investigators wanted to compare post-lapse patch instructions on subsequent abstinence. However, the result should be read as an outcome at the four-month assessment, not as evidence about every aspect of quitting or longer-term smoking status. The registry record does not describe biochemical confirmation of abstinence.

7. Results Posted in the Registry

• Nicotine Patch, Labeled Use: 46.5% (59/127) versus 50.6% (90/178) on control; risk difference -4.1 percentage points (95% CI -15.5 to 7.3), risk ratio 0.92 (0.73–1.16); unadjusted two-proportion z-test p = 0.480.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a chi-squared comparison of the two randomized groups for a binary endpoint. The endpoint classifies each participant as abstinent or not abstinent at the four-month assessment. The posted group counts are 90 of 178 for experimental use and 59 of 127 for labeled use. The test asks whether the observed distribution of outcome categories differs between the groups under a null hypothesis of no group association.

What does the chi-squared test assess?

In general, a chi-squared test compares observed category counts with the counts expected if there were no association between group assignment and outcome. It summarizes how far the observed pattern departs from that null pattern, given the data. A small p-value can indicate that the observed pattern would be relatively unusual under the null model, while a larger p-value indicates that the data are not unusual enough under that model to provide strong evidence against it. The test does not measure the importance of an effect and does not establish that the groups are identical.

The registry reports p = 0.48 for the chi-squared analysis. The displayed unadjusted recalculation also gives p = 0.48. A p-value should be interpreted alongside the estimated difference and its confidence interval, not as a stand-alone conclusion. It is also conditional on the analysis approach and the data definition, including how missing outcome responses were handled.

How should the effect estimate be read?

The comparison reports a risk difference, which expresses the difference between the groups' proportions with the outcome. The posted estimate is for labeled use relative to experimental use and is negative. A negative value in that direction means the observed proportion classified as abstinent was lower in the labeled-use group than in the experimental-use group. The confidence interval extends across values on both sides of no difference, so it does not resolve whether the population difference is positive or negative.

Other relative measures are also listed in the record, including a risk ratio and an odds ratio. In general, these measures describe a group contrast on different scales. They do not replace the outcome counts, and they should be interpreted with their uncertainty intervals. Each of the posted ratio intervals includes its corresponding null value, consistent with the reported test not establishing a clear group difference. The primary reported analysis is the chi-squared test; the registry record does not describe a model-based adjusted analysis.

What does the recalculation add?

The unadjusted recalculation uses the posted summary counts to express the group contrast and its uncertainty. It is not a separate randomized trial analysis or a replacement for the sponsor's own analysis. The registry's reported test and the unadjusted recalculated p-value agree at p = 0.48, and the record does not flag a discrepancy. The recalculation therefore serves as a consistency check on the reported summary comparison, rather than as evidence from an independent dataset.

In general, recalculations based on aggregate counts cannot reproduce analyses that depend on participant-level information, adjustments, or additional design details that are not reported. The registry record does not specify any such adjusted analysis for this primary endpoint. Accordingly, the unadjusted comparison is the available quantitative description of the group contrast in this record.

Why does the lapse-defined population matter?

The primary question is explicitly restricted to people who quit smoking and then lapsed while using the patch. This is narrower than the full enrollment of 701. The posted primary counts apply to that outcome population, not to all randomized participants. A comparison in this subset addresses the stated post-lapse question, but it does not give the overall probability of quitting among all people who entered the trial.

In general, when an analysis population is defined by events after treatment begins, interpretation depends on how that population is identified and whether all relevant participants are included. The registry gives the primary population description and the group counts, but does not report further detail about the analysis-population rules. It also does not describe a separate analysis for participants who did not lapse.

How does outcome classification affect the analysis?

The registry defines abstinence as reporting zero smoking days in the last seven days at the four-month follow-up. All other responses, including missing, are classified as not abstinent. This is a conservative-looking classification in the sense that missing responses do not count as successes, but that label alone does not establish how the rule affects bias or the estimated contrast. In general, missing-data handling can affect both the counts and the group comparison, especially if missingness differs between groups or is related to smoking status. The registry record does not report sensitivity analyses using alternative assumptions.

The statistical interpretation is consequently tied to the specified binary definition and the reported test. It describes the observed classification under the registry's rule; it does not determine the unobserved smoking status of participants whose responses were missing.

10. Confidence Intervals and Precision

The point estimate gives a single summary of the observed group contrast, while the confidence interval describes a range of values compatible with the data and the method used to construct the interval. In general, a confidence interval is not a guarantee that the true effect lies within its limits. It communicates statistical uncertainty around an estimate and is more informative when read together with the estimate, the outcome definition, and the analysis population.

For the risk difference comparing labeled use with experimental use, the posted interval extends across zero. In general, zero is the no-difference value for a difference measure. Because the interval includes values on each side of zero, the data are compatible with a lower abstinence proportion in either group, as well as little or no difference. The width of the interval indicates that the direction and magnitude are not estimated precisely.

The registry also reports confidence intervals for relative measures. In general, the no-effect value for a ratio is the value at which the groups have the same outcome level. The posted ratio intervals span that value. These intervals reinforce that the group contrast is uncertain; they do not prove equivalence or rule out potentially meaningful differences.

Precision is affected by the number of observations contributing to the comparison and by the variability of the outcome. The primary counts are drawn from a subset of the 701 enrolled participants, specifically those described as having quit and then lapsed while using the patch. The interval therefore reflects information in that subset, not in the full enrollment. The registry does not report a prespecified precision target or a minimum clinically important difference for this endpoint.

The p-value of 0.48 should not be mistaken for a precision measure. It addresses compatibility with a null hypothesis under the test, whereas the confidence interval communicates the range of plausible group contrasts under its method. Together, the p-value and interval indicate that the observed comparison does not establish a clear difference, while leaving uncertainty about the size and direction of the underlying contrast.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning display gives illustrative participants per arm for binary-outcome comparisons. These are participant counts per group, not total events. The scenarios are based on 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each scenario, the display gives the number of participants per arm associated with 80% power and with 90% power.

In plain terms, the 80% power column shows the planned per-arm sample size under which a study would have an 80% chance of detecting the stated effect, if the planning assumptions and effect are correct. The 90% column uses a higher probability of detecting that effect and therefore has larger sample-size figures. For example, the display lists 2,326 participants per arm for 80% power and 3,113 participants per arm for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, the corresponding figures are 4,138 and 5,539; for 50%, they are 9,314 and 12,468.

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, smaller effects are harder to distinguish from random variation, so detecting a smaller effect requires more participants under otherwise similar assumptions.

These figures are a planning illustration based on the observed effect, not the trial's original design calculation. The trial's own sample-size justification and original design assumptions are not reported in the registry record. This is not observed power; it describes prospective sample-size requirements under the listed assumptions, not the probability that the completed study detected an effect.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.506; treatment proportion p₁ = 0.465; average p̄ = 0.485.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7068 = 1.3853.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.7062 = 0.5943.
4. n = (1.3853 + 0.5943)² / (-0.0411)² = 2,325.5, rounded up to 2,326 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 <- 0.50561797752809                          # control proportion
p1 <- 0.464566929133858                          # 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(1807871)
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 = 2,326 (80% power), 3,113 (90% power)
 75% of observed effect: n per arm = 4,138 (80% power), 5,539 (90% power)
 50% of observed effect: n per arm = 9,314 (80% power), 12,468 (90% power)
power.prop.test: 2325.5 
Simulated power at n = 2,326 per arm: 0.805 (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.

13. Analyses Reported by the Sponsor

The registry reports the sponsor's primary comparison as a chi-squared test, with p = 0.48. The unadjusted recalculation from the posted group counts also gives p = 0.48. The record does not flag a discrepancy between the reported analysis and the recalculation.

The recalculation is a simple comparison based on summary counts and should be understood as a check on the posted result, not as a substitute for any analysis using participant-level information. The registry record does not describe an adjusted primary model or provide additional details that would allow one to reproduce other possible analytic choices. The reported sponsor analysis remains the analysis explicitly identified in the registry.

Agreement in the p-value does not remove the uncertainty in the estimated effect. The risk-difference interval extends on either side of no difference, and the primary outcome applies to participants who lapsed while using the patch. The numerical test result should therefore be read alongside the population definition, the binary outcome rule, and the interval estimate. The recalculation and sponsor result support the same limited statistical reading: the posted data do not establish a clear difference between the randomized approaches on this endpoint.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists three outcome measures and reports two analyses. It names two secondary outcomes: mediators of the effect of post-lapse nicotine replacement therapy use on abstinence and adverse drug effects. The primary outcome is seven-day point-prevalent abstinence at four months. These listings indicate that the trial addressed more than one outcome, but the registry record does not report a multiplicity-adjustment plan or explain how the primary and secondary analyses were prioritized statistically.

In general, testing multiple outcomes or comparisons can increase the chance of obtaining at least one apparently unusual result by chance. Statistical plans sometimes address this through prespecified hierarchies or adjustments, but no such approach is reported in the registry record. The reported p = 0.48 concerns the primary comparison and should not be interpreted as a summary of every outcome examined.

Missing outcome responses were explicitly classified as not abstinent for the primary endpoint. This rule determines the posted binary classification but does not reveal how many responses were missing in either group. The registry record does not report sensitivity analyses under alternative missing-data assumptions or details about missingness for the secondary outcomes.

The primary population is described as participants who quit and then lapsed while using the nicotine patch. The registry gives counts for each randomized group within that comparison, but does not report a full participant flow or further details of the analysis-population rules. It does not specify whether the primary analysis followed an intention-to-treat approach, how participants with incomplete follow-up were otherwise handled, or whether any participants were excluded beyond the stated population definition.

The registry record also does not report an interim-analysis plan, stopping rules, or the original sample-size justification. These items should not be inferred from the completed status or from the sample-size planning illustration. Without those details, the reported analysis can be interpreted using the stated endpoint, population, and test, while broader claims about prespecification and multiplicity control remain unresolved.

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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: pancreas problems (0.6%), hospitalization (0.6%), stroke (0.3%), intestinal problems (0.3%), arrhythmia (0.3%).

The registry reports serious adverse events for two safety groups. In the experimental-use group, 356 participants were listed as at risk and 4 as affected by a serious adverse event. In the labeled-use group, 345 were listed as at risk and 4 were affected. The registry also lists 1 death in each group.

Other adverse events are reported separately: 196 affected participants among 356 at risk in the experimental-use group and 187 among 345 at risk in the labeled-use group. These counts should not be combined with the serious-event counts, since the registry presents them as distinct categories. The listed serious-event terms include pancreas problems and hospitalization at 0.6% each, and stroke, intestinal problems, and arrhythmia at 0.3% each.

These are descriptive safety counts. They do not by themselves establish whether an event was caused by the patch or whether the groups differ in risk. The registry record does not provide details about event definitions, severity adjudication, exposure time, or statistical comparisons of safety outcomes. The at-risk denominators for these safety listings differ from the primary outcome denominators, so they should be read as separate analysis populations rather than as interchangeable counts.

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

The primary result describes a comparison of two instructions for nicotine-patch use after a smoking lapse. Among the participants described as having quit and then lapsed while using the patch, the posted counts classified 90 of 178 in the experimental-use group and 59 of 127 in the labeled-use group as abstinent at the four-month follow-up. The chi-squared test gives p = 0.48, and the interval for the risk difference crosses no difference.

These findings do not establish a clear difference between the approaches on the specified endpoint. They also do not establish that the approaches are equivalent. The confidence interval remains compatible with contrasts in either direction, and the registry record does not state an equivalence margin or a target precision criterion. A non-significant test is not proof that any possible effect is absent.

The outcome is recent abstinence over the seven days before the four-month survey, not continuous abstinence from the quit date. Participants with missing responses were classified as not abstinent, so the result depends in part on that stated rule. The comparison applies to the lapse-defined population and should not be generalized automatically to all 701 enrolled participants or to people who did not lapse.

The record also contains serious adverse event counts, but these are descriptive and do not establish causation. The available information does not support a broad conclusion about overall safety, longer-term outcomes, or the effect of patch use outside the trial's defined instructions and population. The results are best understood as an uncertain estimate of a focused post-lapse comparison, rather than a definitive answer about quitting outcomes in all smokers.

17. Why This Trial Matters Statistically

This trial poses a statistically focused question: how do two post-lapse nicotine-patch instructions compare on a defined abstinence outcome? The random assignment and parallel-group structure provide a basis for comparing the groups, while the endpoint definition makes clear exactly what counted as abstinent at follow-up. These features help readers connect the numerical result to the study question rather than treating a p-value as a conclusion by itself.

The analysis also illustrates why the population matters. The primary comparison is not based on every enrolled participant, but on the subset described as having quit and then lapsed while using the patch. That is the group for whom the post-lapse instruction is directly relevant. At the same time, it means that the result cannot be treated as the overall quit outcome for the entire enrolled sample.

Another statistical lesson is the distinction between lack of clear evidence for a difference and evidence of equivalence. The reported p-value is 0.48, and the risk-difference interval spans no difference. Those features indicate uncertainty in the group contrast; they do not demonstrate that the approaches have the same effect. The interval is essential to understanding how broad that uncertainty remains.

The sample-size illustration reinforces the relationship between effect size and study scale. Under its stated planning assumptions, detecting a smaller fraction of the observed effect requires more participants per arm. That relationship is useful for planning, but the illustration is not a report of the trial's original design rationale and does not measure the completed trial's observed power.

Finally, the explicit handling of missing primary outcome responses matters for interpretation. Classifying missing responses as not abstinent defines the analysis, but readers still need information about the extent and pattern of missingness to assess how sensitive the comparison might be. The registry gives a clear outcome rule while leaving those additional details unreported.

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 primary comparison is restricted to participants who quit and then lapsed while using the patch. It therefore does not describe the overall outcome for all 701 enrolled participants, and the registry record does not report a separate primary comparison for participants who never lapsed. The result should be interpreted within this defined population rather than as an overall estimate for every smoker in the trial.

The outcome captures self-reported smoking during the seven days before the four-month follow-up survey. The registry defines a response of zero days as abstinent and classifies all other responses, including missing responses, as not abstinent. It does not report biochemical confirmation, the number of missing survey responses, or sensitivity analyses using alternative missing-data rules.

The trial is listed as randomized and unmasked, but the registry record does not provide detailed randomization procedures, adherence results, or information about how fully participants followed their assigned instructions. It also does not report an adjusted primary analysis or a detailed account of the analysis populations. These omissions limit assessment of analytic choices beyond the stated counts and chi-squared test.

The record lists multiple outcomes, but a multiplicity plan is not reported. The sample-size illustration is based on the observed effect and specified assumptions; it is not the original design justification. Interim analyses and other design assumptions are not reported in the registry record. Finally, the serious adverse event counts are descriptive, and the registry does not provide details sufficient to assess event attribution or compare safety outcomes statistically.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Treatment of Smoking Lapses and Relapses — NCT01807871.
• Registry record last updated 2017-10-13; status last verified 2017-09.
• Results first posted 2017-03-28.
• 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

NCT01807871, Treatment of Smoking Lapses and Relapses, is listed as a completed phase 4 randomized parallel-group study with no masking and enrollment of 701. The sponsor is the University of Vermont. The primary completion is listed as 2016-02.

The study compared continuing nicotine-patch use after a lapse with stopping the patch after resuming smoking. Its primary endpoint was seven-day point-prevalent abstinence at four months among participants who lapsed while using the patch. The registry reports a chi-squared p-value of 0.48; the unadjusted recalculation agrees, and no discrepancy is flagged. The confidence interval for the risk difference crosses no difference, leaving uncertainty about the direction and size of the comparison.

The registry also lists secondary outcomes and serious adverse event counts. Detailed multiplicity procedures, the original sample-size justification, and several analysis details are not reported in the registry record.