PATH Partnering to Achieve Tobacco-free Health: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for PATH Partnering to Achieve Tobacco-free Health (NCT01533974), a randomized phase 1, phase 2 study. The primary outcome is Number of Participants Who Stopped Smoking by 12 Month Post Treatment.

2. Clinical Question

3. Trial Design

PATH, or Partnering to Achieve Tobacco-free Health, is listed as a randomized, parallel-group study of ACT and CBT for smoking cessation. The record lists PHASE1 and PHASE2. Enrollment was 450, and the study status is COMPLETED. The recorded start is 2011-06 and primary completion is 2015-01. The study summary describes the project as a 5-year project and frames its aim as comparing ACT with standard CBT counseling in a real-world healthcare setting, with both approaches offered alongside nicotine replacement therapy.

The ACT arm is described as a five-session, group-delivered adaptation of Dr. Bricker's ACT treatment program, with 90 minutes per session. No comparable description of the CBT arm's delivery is reported in the registry record. The masking field says SINGLE, but who was masked and how masking was implemented are not reported in the registry record. The allocation field identifies randomization; details of sequence generation, concealment, and the allocation ratio are not reported in the registry record.

The primary outcome counts are listed for 224 participants in ACT and 226 in CBT. The outcome is binary: participants are counted according to whether they meet the registry definition of abstinence. The registry record lists one outcome measure and no posted analyses. It does not describe a prespecified statistical analysis plan, analysis populations, or sample-size justification. Those omissions limit the conclusions that can be drawn about how the reported comparison relates to the trial's original analysis plan.

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 Number of Participants Who Stopped Smoking by 12 Month Post Treatment, measured over 12 months.

The primary endpoint is the number of participants who stopped smoking by 12 months after treatment. Its description defines abstinence as 30 day point prevalence abstinence at 12 months. It also states that missing responses are counted as smoking and characterizes the measure as self-report. The registry gives counts rather than a continuous measure: 31 participants in ACT and 41 in CBT are recorded as meeting the endpoint.

A binary abstinence endpoint gives a direct count of how many participants met the specified smoking-status criterion at the assessment. It is useful for comparing the groups on a clinically interpretable outcome, while the accompanying comparison expresses the difference between group-level risks. The endpoint does not describe the timing of any change in smoking status within the follow-up period, nor does it distinguish among patterns of smoking outside the specified abstinence window. More detail about verification procedures, the handling of missingness beyond the stated rule, and the definition of the assessment window is not reported in the registry record.

Because the outcome is self-reported, the posted count reflects the registry's recorded measure, not an independently verified smoking-status measure. The record does not give further information about assessment completion or the characteristics of participants with missing responses.

7. Results Posted in the Registry

• Cognitive Behavioral Therapy (CBT): 18.1% (41/226) versus 13.8% (31/224) on control; risk difference 4.3 percentage points (95% CI -2.5 to 11.1), risk ratio 1.31 (0.85–2.01); unadjusted two-proportion z-test p = 0.213.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: each participant is classified according to whether the registry's abstinence criterion was met. The posted arm results are counts, and the comparison presents group risks and several ways to contrast those risks. The following explanations are general statistical context for interpreting those measures; details of the exact analysis procedures are not reported in the registry record.

What does a risk difference express?

A risk difference subtracts the risk in one group from the risk in the other. It describes an absolute contrast on the probability scale, rather than a relative change. The registry reports a risk difference of 0.043 for CBT relative to ACT. A positive estimate in this orientation means the observed risk is higher in the CBT group, while a negative estimate would indicate a higher risk in ACT. The value is an estimate from the recorded trial data, not a guarantee that the same contrast would occur in another sample or setting.

Absolute contrasts are often intuitive because they keep the comparison tied to the outcome probability. They can nevertheless depend on the population and context in which the risks are observed. The underlying group risks reported by the registry are 0.138 for ACT and 0.181 for CBT. No additional calculation is needed to interpret the posted risk difference, and no further adjustment is described in the registry record.

How do risk ratios and odds ratios differ?

A risk ratio divides one group's risk by the other group's risk. A value at the null corresponds to equal risks; values on either side indicate a relative increase or decrease according to the comparison's orientation. The registry reports a risk ratio of 1.311 for CBT relative to ACT, with an interval from 0.854 to 2.012.

An odds ratio compares the odds of the outcome between groups. Odds are related to, but are not the same as, risks. The odds ratio can therefore have a different numerical magnitude from a risk ratio, even when both describe the same binary outcome. The reported odds ratio is 1.38, with an interval from 0.83 to 2.294. As with the risk ratio, the null value is the value representing no contrast. The comparison orientation matters: reversing the reference group changes how the estimate is read.

Risk differences, risk ratios, and odds ratios answer related but distinct questions. They should not be read as though they were on the same scale. The registry record does not give a rationale for selecting these measures or specify whether one was the sole prespecified effect measure.

What does a confidence interval communicate?

In general, a confidence interval conveys the uncertainty associated with an estimate under a statistical procedure. A narrower interval indicates greater precision under that procedure, while a wider interval indicates less precision. The reported risk-difference interval is -0.025 to 0.111. Since it spans zero, the data do not rule out a zero risk difference at the level represented by that interval. The risk-ratio interval spans its no-difference value, as does the odds-ratio interval. Confidence intervals are not guarantees about the true effect, and their interpretation depends on the analysis method and assumptions.

The registry record gives confidence limits but does not identify the interval construction, confidence level, or model used. It also does not report adjusted estimates or covariates. These details matter when readers try to reproduce or compare an analysis, so the posted values should be described as reported rather than attributed to a specific unreported procedure.

What does the p-value contribute?

The unadjusted p-value is 0.213. In general, a p-value describes the compatibility of data with a specified null hypothesis under a statistical model and test. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. The p-value should be interpreted together with the effect estimate and its interval. Here, the interval conveys the range of contrasts compatible with the data under the stated interval procedure, while the p-value is a separate summary of the test result.

The word unadjusted indicates that the posted p-value is not reported as adjusted for other factors or for multiple comparisons. The registry does not state the test used, its assumptions, or whether this was the prespecified primary test. No conclusion about covariate adjustment or a broader testing strategy can be drawn from the available record.

Why does the outcome definition matter?

The primary measure is 30 day point prevalence abstinence at 12 months, and missing responses are counted as smoking. In general, an outcome rule determines which observations contribute to each category and therefore shapes the estimand being compared. Counting missing responses as smoking is a defined classification rule, but the registry does not provide enough detail to evaluate other missing-data procedures or the reasons responses were missing. It also does not state whether the analysis used an intention-to-treat population or another analysis population. These limitations make it important to describe the posted comparison according to its recorded definition, without assuming additional analysis choices.

10. Confidence Intervals and Precision

The risk-difference estimate is 0.043, and its reported confidence interval extends from -0.025 to 0.111. This interval is broad enough to include a zero contrast and values on both sides of zero. The point estimate therefore should not be read in isolation as a settled estimate of the difference between the groups. The data leave uncertainty about both the direction and magnitude of the underlying contrast.

The risk ratio is 1.311, with reported limits of 0.854 and 2.012. The odds ratio is 1.38, with limits of 0.83 and 2.294. Each interval includes the no-difference value for its scale. Intervals on different scales cannot be compared by their numerical width alone; each scale has its own interpretation. Taken together, these reported intervals indicate that the trial's primary comparison is not highly precise enough to distinguish a null contrast from a range of plausible contrasts.

In general, a confidence interval describes uncertainty around an estimate under the method used to construct it. It is not a range that is certain to contain the true value, and it does not assign probabilities to individual effect values. The interval method and confidence level are not reported in the registry record. The observed group counts and the reported estimates are therefore best interpreted alongside that limitation. The posted interval supports caution about treating the point estimate as a precise measure of the difference.

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 illustrations give participants per arm for 80% power and participants per arm for 90% power; they are not totals across the two arms and are not total event counts. They use the observed effect as a reference and show planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For 100% of the observed effect, the figures are 1,139 participants per arm for 80% power and 1,524 participants per arm for 90% power. For 75%, the figures are 1,969 and 2,635; for 50%, they are 4,304 and 5,762, respectively.

In general, power is the chance that a planned study would detect an effect of a specified size under its assumptions if that effect were present. The 80% and 90% columns show different planning targets: the higher target requires a larger planned sample under the same assumptions. Smaller effects are harder to distinguish from random variation and therefore require more participants in these illustrations.

The calculations use 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. These values are planning illustrations based on the observed effect, not the original trial's documented sample-size justification. The original design assumptions are not reported in the registry record. This is not observed power.

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 = 0.138; treatment proportion p₁ = 0.181; average p̄ = 0.160.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5183 = 1.0159.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5174 = 0.4355.
4. n = (1.0159 + 0.4355)² / (0.0430)² = 1,138.1, rounded up to 1,139 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 <- 0.138392857142857                          # control proportion
p1 <- 0.18141592920354                          # 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(1533974)
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 = 1,139 (80% power), 1,524 (90% power)
 75% of observed effect: n per arm = 1,969 (80% power), 2,635 (90% power)
 50% of observed effect: n per arm = 4,304 (80% power), 5,762 (90% power)
power.prop.test: 1138.1 
Simulated power at n = 1,139 per arm: 0.797 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists one outcome measure, the primary measure of participants who stopped smoking by 12 months, and no secondary outcomes. It also lists no posted analyses. This means the record does not provide a set of additional outcome estimates against which to assess how many statistical tests were conducted. A multiplicity plan, including any hierarchy of outcomes or adjustment for multiple testing, is not reported in the registry record. The unadjusted p-value should not be represented as adjusted for multiplicity.

The primary endpoint description states that missing responses are counted as smoking and that the measure is self-report. This is the only specific missing-response rule stated for the endpoint. The record does not report how many responses were missing, when missingness occurred, why participants did not respond, or whether any sensitivity analyses examined alternative assumptions. It also does not report a separate missing-data method or an imputation procedure. Consequently, the posted result should be read as applying the recorded endpoint definition, without assuming additional missing-data analyses.

The analysis population is not described. In particular, the registry does not state whether the primary comparison used all randomized participants, only participants with observed follow-up, or another defined population. The arm counts are listed as 224 for ACT and 226 for CBT, but the record does not explain how these denominators relate to randomization, eligibility after assignment, or endpoint availability. A numerical count in the outcome record alone cannot establish which analysis set was used.

The registry record does not state a prespecified statistical analysis plan, covariate adjustment strategy, subgroup approach, interim analysis procedure, or procedure for handling protocol deviations. These features should not be inferred from the fact that the study was randomized or from the presence of a p-value. Their absence limits assessment of whether the reported comparison represents the planned primary analysis and whether other analyses may have influenced interpretation.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent non-serious adverse event terms

The adverse-event record lists zero participants with serious adverse events in ACT among 224 at risk, and zero in CBT among 226 at risk. These are the serious-event figures recorded for the two arms. The registry also lists 17 participants affected by other adverse events in ACT and 5 in CBT. These counts are distinct from the serious-event counts and should not be combined or treated as a complete description of event types or severity.

The record does not list serious adverse-event terms, and death counts are not reported in the registry record. Further information about event definitions, collection methods, timing, attribution, or how events were reviewed is not reported in the registry record. The available counts therefore describe only what the adverse-event fields record; they do not establish that no events of any kind occurred or provide a complete comparative safety analysis.

In general, a count should be interpreted in relation to the population at risk and the way events were collected. These figures do not by themselves account for differences in exposure or follow-up, and the registry does not provide detail to assess those factors. The counts are descriptive and should not be treated as proof of a causal difference between the counseling groups.

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

The result describes a randomized comparison of ACT and CBT counseling for smoking cessation, with both approaches offered alongside NRT according to the study summary. At the 12-month assessment, the registry records 31 participants meeting its abstinence definition in ACT and 41 in CBT. The reported risk difference is 0.043 in the CBT-relative-to-ACT orientation. These figures describe the trial's posted primary endpoint, not every aspect of smoking behavior or treatment experience.

The confidence interval for the risk difference, -0.025 to 0.111, includes zero, and the unadjusted p-value is 0.213. The posted result therefore does not establish a statistically distinguishable difference on the reported comparison. It also does not establish equivalence or show that the approaches have identical effects. The interval leaves meaningful uncertainty about the direction and size of any underlying contrast. The relative measures and their intervals likewise include their no-difference values.

The result is limited to the endpoint as defined: self-reported 30 day point prevalence abstinence at 12 months, with missing responses counted as smoking. It does not report continuous abstinence, changes in smoking over time, or longer follow-up. The registry does not provide secondary outcome results, subgroup results, detailed analysis populations, or sensitivity analyses for missing responses. Those unreported elements cannot be inferred from the primary result.

These data also do not isolate the contribution of NRT, since the study summary describes both counseling approaches as offered with NRT. Nor do the posted counts alone explain why any difference arose. Interpretation should therefore remain focused on the observed, uncertain comparison between the two assigned counseling approaches under the recorded endpoint definition, rather than being extended to other settings, outcomes, or treatment components.

16. Why This Trial Matters Statistically

Statistically, this trial illustrates why a point estimate should be read alongside its uncertainty. The observed risk difference is positive in the CBT-relative-to-ACT orientation, but its confidence interval includes zero and extends to values in either direction. The unadjusted p-value of 0.213 is another summary of the comparison, not a substitute for examining the estimate, interval, outcome definition, and design.

The study also makes the scale of an effect measure important. A risk difference describes an absolute contrast, while risk and odds ratios describe relative contrasts. Each has a distinct interpretation, and the registry reports all three. Their intervals all include the respective no-difference values, underscoring that the result is uncertain across the reported measures rather than only on one scale.

The record is useful for teaching careful reading of a binary endpoint and its missing-response rule. The outcome is self-reported 30 day point prevalence abstinence at 12 months, and missing responses are counted as smoking. Such definitions determine what the recorded counts mean; without them, the arm counts would be harder to interpret. At the same time, the record's omissions about analysis populations, statistical procedures, and the original sample-size rationale show why registry results need to be read with attention to what is and is not documented.

Finally, the planning illustrations clarify that power calculations depend on the effect size a study is designed to detect. The listed participant requirements increase as the assumed effect becomes smaller, while the original trial's design assumptions are not reported. This distinction prevents planning illustrations derived from the observed result from being mistaken for evidence about the trial's prospective design or its ability to detect a particular effect.

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 registry record provides limited detail about the conduct and analysis of the study. It identifies randomization, a parallel design, and single masking, but does not explain sequence generation, allocation concealment, the allocation ratio, or who was masked. The ACT arm has a brief delivery description, whereas corresponding CBT delivery details are not reported. These omissions restrict assessment of implementation and potential sources of bias.

The primary result is defined as self-reported 30 day point prevalence abstinence at 12 months, with missing responses counted as smoking. The record does not report the number of missing responses, the analysis population, or sensitivity analyses for the missing-response assumption. It also does not explain whether participants with missing follow-up were included in the listed arm denominators. The resulting interpretation must remain tied to the endpoint and counts as recorded.

No posted analyses are listed, and the record does not describe the statistical test, confidence-interval method, confidence level, covariate adjustment, or prespecified analysis plan. No secondary outcome results are listed. The original sample-size justification and design assumptions are not reported in the registry record; the planning figures are illustrations based on the observed effect rather than the original design.

The adverse-event record gives counts but little detail about event definitions, collection, timing, or attribution. Death counts are not reported in the registry record. These gaps mean that the available safety entries cannot stand in for a comprehensive assessment of adverse events. Finally, the posted primary comparison concerns only the specified 12-month endpoint and does not supply information about longer-term outcomes or other settings.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: PATH Partnering to Achieve Tobacco-free Health — NCT01533974.
• Registry record last updated 2016-06-17; status last verified 2016-05.
• Results first posted 2016-05-09.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

NCT01533974 is the completed PATH study, listed as a randomized, parallel-group PHASE1 and PHASE2 study with enrollment of 450. It compares ACT with CBT counseling for smoking cessation; the summary says both approaches were offered with NRT. The primary outcome is the number of participants meeting 30 day point prevalence abstinence at 12 months, with missing responses counted as smoking.

The registry records 31 of 224 participants in ACT and 41 of 226 in CBT meeting the endpoint. The reported risk difference for CBT relative to ACT is 0.043, with a confidence interval from -0.025 to 0.111 and an unadjusted p-value of 0.213. The registry lists zero serious adverse events in each arm, alongside 17 and 5 participants affected by other adverse events, respectively. Analysis-plan details and the original sample-size assumptions are not reported in the registry record.