Cognitive and Emotional Skills to Aid Smoking Prevention: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Cognitive and Emotional Skills to Aid Smoking Prevention (NCT03058991), a randomized na study. The primary outcome is Specific Aim 1: Percentage of Participants Who Attended 13 or More Interventions.

2. Clinical Question

The clinical question is therefore about feasibility and attendance, not whether participants subsequently smoked or avoided smoking. The registry’s stated broader purpose was to investigate whether working memory training and distress tolerance interventions could affect cognitive and emotional processes related to smoking risk, and whether these approaches might complement standard no-smoking information. The primary result reported in this record addresses attendance only. It does not directly establish a change in smoking behavior, smoking risk, working memory, or distress tolerance.

3. Trial Design

The registry describes a randomized, parallel-group study of behavioral interventions, with no masking. The study phase is listed as NA. The three named groups were Working Memory Intervention, Distress Tolerance Intervention, and Control Informational Intervention. The registry lists enrollment as 124 and the study status as completed. It gives a start date of 2016-11-08 and a primary completion date of 2019-04-04.

The working memory intervention used the Cogmed RM program. Participants were asked to use it under supervision twice a week for an hour per session for 8 weeks, and on other days for 25-35 minutes. The distress tolerance intervention used a mindfulness-based stress reduction program adapted for adolescents. The control informational intervention was intended to match the session time of the other interventions and, according to its description, did not focus on smoking. Further protocol details are not reported in the registry record.

The primary outcome was attendance of at least 80% of interventions during the intervention period, identified as week 1 to week 8. The reported group denominators were 39 for working memory, 32 for control, and 37 for distress tolerance. The registry does not explain the relationship between these outcome denominators and the overall enrollment, or report participant flow and reasons for any unavailable outcome data. The record gives group outcome percentages and unadjusted comparisons with control, but does not report an analysis plan or adjusted estimates.

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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Percentage of individuals who attended at least 80% of interventions reported.

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 Specific Aim 1: Percentage of Participants Who Attended 13 or More Interventions, measured over Intervention (week 1 to week 8).

The primary endpoint measures attendance: the percentage of participants who attended 13 or more interventions. The registry’s description frames this measure as a way to assess feasibility and acceptability. It specifies a criterion in which at least 70% of the randomized sample would attend at least 80% of interventions. Thus, the endpoint concerns whether participants engaged with the intervention as intended, rather than whether the intervention changed smoking behavior or a cognitive or emotional measure.

Attendance can be useful in an intervention study because it indicates whether participants took part in enough sessions for the intervention to be delivered as planned. It is not, on its own, a measure of efficacy. Attendance may reflect practical aspects of participation as well as acceptability, and a group percentage does not explain why individual participants attended or missed sessions. The registry record does not report reasons for missed interventions or a separate measure of acceptability.

The posted results give percentages of 41.0 for the Working Memory Intervention, 50.0 for the Control Informational Intervention, and 40.5 for the Distress Tolerance Intervention. These are the outcome values reported for attendance at the defined threshold. The record does not report confidence intervals for the individual group percentages. It does report confidence intervals for the risk differences comparing each active intervention with control.

7. Results Posted in the Registry

• Working Memory Intervention: 41.0% (16/39) versus 50.0% (16/32) on control; risk difference -9.0 percentage points (95% CI -32.2 to 14.2), risk ratio 0.82 (0.49–1.37); unadjusted two-proportion z-test p = 0.450.
• Distress Tolerance Intervention: 40.5% (15/37) versus 50.0% (16/32) on control; risk difference -9.5 percentage points (95% CI -32.9 to 14.0), risk ratio 0.81 (0.48–1.37); unadjusted two-proportion z-test p = 0.431.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: a participant either met the attendance threshold or did not. The registry reports the group outcome as a percentage. General: for a binary outcome, a risk or event proportion describes the share of participants in a group who experienced the defined event. Here, the event is attendance of 13 or more interventions, not a smoking event.

What does the risk difference describe?

General: a risk difference subtracts the event proportion in one group from the event proportion in a reference group. A value of zero corresponds to equal event proportions; a negative value means the first group’s event proportion is lower than the reference group’s. The posted comparisons use the Control Informational Intervention as the reference. The reported risk differences are -0.090 for Working Memory Intervention versus control and -0.095 for Distress Tolerance Intervention versus control. These are unadjusted contrasts based on the posted group summaries.

The record also reports relative measures, including risk ratios and odds ratios, but the primary interpretation centers on risk differences because they express the contrast on the absolute event-proportion scale. General: a risk ratio compares proportions by division, while an odds ratio compares the odds of the event. Those measures use different scales, so their numerical values are not interchangeable. Their confidence intervals are broad in these comparisons, consistent with considerable uncertainty in the relative estimates.

How should the p-values be read?

The posted p-values are labeled unadjusted: 0.45 for working memory versus control and 0.431 for distress tolerance versus control. General: a p-value describes how compatible the observed data are with a specified null model, assuming that model and the analysis assumptions are appropriate. It is not the probability that the null hypothesis is true, nor does it measure the size or practical importance of an effect. The registry record does not report a more detailed testing procedure, such as covariate adjustment or a model specification.

Because the endpoint is binary, methods based on counts and proportions are relevant. The posted outcome counts are 16 in the control group, 16 in the working memory group, and 15 in the distress tolerance group. Their denominators are 32, 39, and 37, respectively. The record reports the arm percentages and comparison statistics, but it does not identify the exact method used to calculate the confidence intervals or p-values. It also does not report whether analyses accounted for any features of the intervention delivery or participant clustering.

Why does the confidence interval matter?

General: a confidence interval communicates the range of estimates reasonably compatible with the data under a specified statistical procedure. It reflects sampling uncertainty, not all possible sources of uncertainty. Both risk-difference intervals include zero: -0.322 to 0.142 for working memory versus control, and -0.329 to 0.14 for distress tolerance versus control. Their breadth indicates limited precision for these contrasts. The record does not report confidence intervals for the individual group percentages.

Random allocation supports comparisons between the assigned groups, but it does not by itself resolve questions about missing outcome data, adherence to assigned interventions, or the analysis population. The registry record does not report whether the primary comparison used an intention-to-treat population, a per-protocol population, or another defined set. It also does not report missing-data methods. Consequently, the posted estimates can be described as unadjusted group comparisons, but their relationship to the original randomized population is not fully specified.

What can be inferred from the posted analysis?

The estimates describe attendance in the posted outcome groups and quantify each intervention-control contrast. General: an estimate summarizes the observed contrast, while its interval indicates how uncertain that estimate is under the analysis method. The record does not report a statistical analysis plan, covariate-adjusted results, or analysis details sufficient to independently reproduce the inferential calculations. The registry lists seven outcome measures and no secondary outcomes posted in this record. It does not report an analysis of smoking outcomes among the posted results. Interpretation should therefore remain focused on the primary attendance endpoint and the reported unadjusted comparisons.

10. Confidence Intervals and Precision

Precision is limited for both comparisons. The risk difference for Working Memory Intervention versus control was -0.090, and its 95% confidence interval ranged from -0.322 to 0.142. The interval includes zero and allows estimates in either direction, so the point estimate alone does not give a precise account of the underlying attendance contrast. For Distress Tolerance Intervention versus control, the risk difference was -0.095, with a 95% confidence interval from -0.329 to 0.14. This interval also includes zero and spans both negative and positive values.

General: a confidence interval is a range generated by a statistical procedure that reflects uncertainty from sampling variation. It is not a guarantee that the true value lies within the particular interval, and it does not account automatically for unmeasured bias, missing-data problems, or choices in analysis. The exact method used to calculate these intervals is not reported in the registry record.

The reported outcome denominators were 39, 32, and 37 across the three groups, and the event counts were 16, 16, and 15, respectively. These group sizes and event counts provide context for why estimates may be uncertain, but no new interval for an individual group percentage is reported. The confidence intervals shown for the risk differences are the appropriate posted quantities for judging precision of the intervention-control contrasts. The registry record does not report a prespecified margin defining a clinically or practically important attendance difference, so the intervals cannot be judged against such a margin from this record alone.

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 figures are participants per arm for 80% power and participants per arm for 90% power. They are illustrations based on the observed effect, not a report of the trial’s original design calculation. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The figures are participants per arm; the note about total events applies only to time-to-event planning, not these binary-outcome comparisons.

For Working Memory Intervention versus control, planning for 100% of the observed effect gives 483 participants per arm for 80% power and 645 for 90% power. Planning for 75% of the observed effect gives 862 participants per arm for 80% power and 1,153 for 90% power. Planning for 50% of the observed effect gives 1,944 participants per arm for 80% power and 2,602 for 90% power.

For Distress Tolerance Intervention versus control, planning for 100% of the observed effect gives 434 participants per arm for 80% power and 580 for 90% power. Planning for 75% of the observed effect gives 775 participants per arm for 80% power and 1,037 for 90% power. Planning for 50% of the observed effect gives 1,750 participants per arm for 80% power and 2,342 for 90% power. In general, the 90% power column represents a higher chance of detecting the assumed effect than the 80% column, if that effect and the planning assumptions hold. Smaller effects require more participants. These are planning illustrations, 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 = 0.500; treatment proportion p₁ = 0.410; average p̄ = 0.455.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7043 = 1.3803.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.7014 = 0.5903.
4. n = (1.3803 + 0.5903)² / (-0.0897)² = 482.2, rounded up to 483 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 <- 0.5                          # control proportion
p1 <- 0.41025641025641                          # 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(3058991)
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 = 483 (80% power), 645 (90% power)
 75% of observed effect: n per arm = 862 (80% power), 1,153 (90% power)
 50% of observed effect: n per arm = 1,944 (80% power), 2,602 (90% power)
power.prop.test: 482.2 
Simulated power at n = 483 per arm: 0.795 (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 lists seven outcome measures, while this record reports a primary attendance result and no secondary outcomes posted. It does not report a statistical analysis plan describing how the primary endpoint was designated relative to the other outcomes, whether comparisons were prespecified, or whether any adjustment for multiple testing was planned. The two unadjusted intervention-versus-control p-values should therefore be understood as the reported comparisons, not as results adjusted for a family of tests.

The registry record does not report an analysis population definition, such as intention-to-treat or per-protocol, and does not explain how participants with unavailable attendance information were handled. It also does not report participant flow, reasons for missing attendance data, or sensitivity analyses evaluating assumptions about missingness. The listed enrollment is 124, whereas the reported outcome denominators are 39, 32, and 37. Without further information, the difference cannot be attributed to a particular reason, and the denominators should not be treated as an explanation of missingness.

The record does not report whether any covariates were included in adjusted analyses, whether an interim analysis was conducted, or whether stopping rules were used. These are aspects of the statistical plan that cannot be inferred from the posted estimates. The p-values are explicitly unadjusted, and no adjusted estimates are reported. These limitations affect the scope of interpretation: the results describe the posted group outcome summaries and contrasts, but they do not resolve how all planned outcomes or missing observations were treated.

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

The results describe attendance at the intervention threshold, not the effectiveness of the interventions at preventing smoking. The reported percentages meeting the threshold were 41.0 for working memory, 50.0 for control, and 40.5 for distress tolerance. The intervention-control risk differences were negative, but both confidence intervals include zero and extend into positive values. The posted comparisons therefore leave substantial uncertainty about the direction and size of the attendance differences.

The endpoint was chosen to assess feasibility and acceptability, with the registry describing a criterion of at least 70% of the randomized sample attending at least 80% of interventions. The reported group percentages are below that stated target. However, the record does not report a formal test of the target, intervals for the group percentages, or a combined analysis across the randomized sample. The reported values alone do not explain why participants did or did not attend.

Attendance does not establish whether participants changed their smoking behavior, became less susceptible to smoking, or improved in working memory or distress tolerance. Although those topics appear in the study’s stated rationale, the primary result described in the registry record is attendance. Secondary outcome results are not posted in this record. Nor does attendance demonstrate that participants received the same intervention exposure or experienced the intervention in the same way; those details are not reported.

The trial’s randomized design is relevant to the intervention-control comparison, but the registry record does not explain missing outcome handling or define the analysis population. Therefore, the posted contrasts should be interpreted as the reported unadjusted comparisons in the outcome groups, with those reporting gaps in mind. They do not support medical advice or a conclusion about whether an intervention prevents smoking.

15. Why This Trial Matters Statistically

This study raises a practical statistical question that differs from a conventional efficacy question: can participants attend enough sessions for an intervention to be delivered as intended? Measuring attendance can help distinguish a lack of participation from a lack of change in a target outcome, although attendance alone cannot explain either. The registry’s stated feasibility criterion makes the attendance threshold central to interpreting the primary endpoint.

The comparisons also show why estimates and their precision matter together. The risk-difference point estimates are negative, but both confidence intervals include zero and reach into positive values. Reporting only the point estimates would hide that uncertainty, while relying only on p-values would omit the range of effect sizes compatible with the data. The record also makes clear that unadjusted comparisons are not the same as a comprehensive analysis plan.

Finally, the planning illustrations demonstrate how the required number of participants depends on the effect assumed for planning. The illustrations use the observed effects and specified design assumptions; they are not the original trial’s design justification. This distinction matters because a planning calculation based on an observed estimate is not evidence that the trial had adequate power for its intended question. The original sample-size justification is not reported in the registry record.

16. 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.

The registry record has important reporting limits for interpreting this primary endpoint. It does not report participant characteristics in enough detail to describe the enrolled population, despite identifying low-SES youth as the study’s broader target. It also does not report the full eligibility criteria, participant flow, reasons for missed sessions, or reasons outcome denominators differ from the listed enrollment. The outcome denominators should therefore be read as the denominators used for the posted group results, without assuming why they differ from enrollment.

The endpoint captures attendance at a threshold, but the record does not provide session-by-session attendance, reasons for nonattendance, or a separate measure of acceptability. Group percentages alone cannot show whether participants missed sessions for similar reasons across groups. The record also does not report individual outcome confidence intervals, an analysis of the feasibility criterion as a formal hypothesis, or a defined threshold for an important between-group attendance difference.

Further limitations include the absence of reported missing-data methods, analysis-population definitions, a statistical analysis plan, adjusted estimates, and secondary outcome results. The registry identifies a parallel randomized study with no masking, but the record does not report other implementation details needed to evaluate delivery or potential biases. These gaps limit interpretation to the posted attendance results and the unadjusted intervention-control contrasts.

17. Related Tutorials

18. Related Statistical Calculators

19. Sources

• ClinicalTrials.gov: Cognitive and Emotional Skills to Aid Smoking Prevention — NCT03058991.
• Registry record last updated 2021-07-23; status last verified 2021-07.
• Results first posted 2020-02-17.
• 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.

20. Record Summary

NCT03058991 is a completed randomized, parallel-group behavioral study titled Cognitive and Emotional Skills to Aid Smoking Prevention. It lists enrollment of 124, no masking, and a study phase of NA. The primary endpoint was the percentage attending 13 or more interventions during week 1 to week 8, used to assess feasibility and acceptability.

The posted percentages were 41.0 for Working Memory Intervention, 50.0 for Control Informational Intervention, and 40.5 for Distress Tolerance Intervention. Both unadjusted risk-difference confidence intervals include zero. The registry record does not report the original sample-size justification, detailed missing-data handling, analysis-population definition, or secondary outcome results.