Shrinking the Size of the Tobacco Power Wall: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Shrinking the Size of the Tobacco Power Wall (NCT04632030), a randomized na study. The primary outcome is Proportion at Risk for Cigarette Smoking.

2. Clinical Question

The primary question concerns a short-term, self-reported risk measure rather than observed cigarette use. The outcome classified participants according to a summed response score from two questions: whether they would use an unflavored cigarette and whether they would use a menthol cigarette if offered by one of their best friends. Each response used a 10-point scale, with higher scores indicating greater stated willingness. A total score of 2 was coded as no risk; a score greater than 2 was coded as at risk.

The three randomized conditions varied the display size and number of products shown together. This allows the registry results to be read as comparisons among exposure conditions, with the typical large display serving as the control. The record describes an experimental evaluation of whether changing display size and product quantity influences tobacco-use risk in adolescents. It does not establish whether any participant subsequently used tobacco, or whether any change persisted beyond the stated assessment timeframe.

3. Trial Design

The registry describes a randomized, single-masked, parallel-group behavioral study. Participants were assigned to a control condition, a small-display condition, or a medium-display condition. The control presented a typical large power wall with three large cabinets. The small condition used one large cabinet, and the medium condition used two large cabinets. The registry's descriptions treat cabinet count as the operational definition of the display formats.

The study is listed as completed. Its recorded start date is 2020-10-30, and its primary completion date is 2022-08-29. The registry lists the phase as NA and identifies RAND as the sponsor. Enrollment is 275. The outcome-specific group sizes are 82.0 for Control, 80.0 for Small, and 78.0 for Medium; these are the numbers associated with the primary outcome, not a replacement for the overall enrollment figure.

Single masking is recorded, but the identity of the masked party or parties is not reported in the registry record. The randomization procedure, allocation concealment, and any details about how participants encountered the displays are not reported in the registry record. Nor is a protocol description given for how the behavioral exposure was delivered beyond the format descriptions.

The primary outcome was assessed within 5 minutes of the intervention. The registry lists 4 outcome measures and 8 analyses, but the full outcome and analysis details are not available in the record. The primary endpoint is a binary classification derived from a two-item self-report scale. No longer-term assessment of this endpoint is described in the primary outcome information.

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: Sample size may differ from baseline because of missing data.

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 Proportion at Risk for Cigarette Smoking, measured over within 5 minutes of the intervention.

The primary endpoint is the proportion of participants classified as at risk for cigarette smoking within 5 minutes of the intervention. Classification was based on two self-report questions about whether a participant would use an unflavored or menthol cigarette if offered by one of their best friends. Responses to each question were recorded on a 10-point scale, where 1 meant definitely not and 10 meant definitely yes. The two responses were summed.

A total score of 2 was coded as no risk, while any score greater than 2 was coded as at risk. The reported outcome is therefore a binary proportion, not the average score on the original response scale. It describes how many participants within each condition met the study's stated risk threshold, relative to the participants assessed in that condition.

This endpoint is used as a short-term measure of stated susceptibility or willingness, which can be studied experimentally after exposure to different display formats. It is not a direct measure of cigarette initiation, ongoing tobacco use, or later behavior. A response to a hypothetical offer may capture an aspect of risk, but the registry record does not establish how closely this measure predicts subsequent smoking for participants in this study. The brief assessment timeframe also means the endpoint addresses immediate reported responses rather than persistence of any response over time.

7. Results Posted in the Registry

• Small: 0.0% (0/80) versus 0.0% (0/82) on control; risk difference 0.0 percentage points (95% CI 0.0 to 0.0); unadjusted two-proportion z-test p = n/a.
• Medium: 0.0% (0/78) versus 0.0% (0/82) on control; risk difference 0.0 percentage points (95% CI 0.0 to 0.0); unadjusted two-proportion z-test p = n/a.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary: each assessed participant is classified as either at risk or not at risk under the registry's scoring rule. A proportion is a natural summary for this kind of outcome. The arm-level value represents the share of participants in that condition who met the at-risk definition. The registry gives a confidence interval for each proportion, expressing statistical uncertainty around its estimate rather than a range containing a specified share of individual participant responses.

General statistical explanation: a confidence interval reflects both the observed data and the method used to estimate uncertainty. A narrower interval indicates greater precision under that method; a wider interval indicates less precision. The interval does not remove potential bias in how participants were selected, how the intervention was delivered, how responses were measured, or how missing observations were handled. Nor does an interval by itself establish that a condition caused an outcome.

An odds ratio compares the odds of an event between two groups. Odds are not the same as proportions, although they are derived from them. An odds ratio of 1 corresponds to equal odds under the stated group ordering. Values above or below 1 indicate a contrast in one direction or the other, but the group order is necessary to identify that direction. The registry reports odds ratios and confidence intervals for the Control–Medium and Control–Small pairs, but does not report the analysis method or specify the direction convention. It also does not give p-values for these analyses.

General statistical explanation: the confidence interval for an odds ratio can be compared with 1 as a reference for no difference in odds. An interval containing 1 is compatible with equal odds under the analysis model at the confidence level used; an interval that excludes 1 is not. This comparison does not explain the size or practical importance of an association, and it depends on the validity of the model and data used. The registry's odds-ratio intervals can be described in those terms, but the missing method details limit assessment of how they were obtained.

A risk difference is a subtraction of two group proportions. It is expressed on the proportion scale and has a value of 0 when the two proportions are equal. The registry's listed risk-difference entries are 0.0 with 0.0-to-0.0 intervals for each comparison, while the arm-level proportions differ. Because these entries do not accord with the arm-level values, they cannot serve as a coherent estimate of the differences described by those arm results. The registry record does not explain the inconsistency. No alternative risk-difference estimate should be inferred from the entries.

General statistical explanation: the method used to estimate a confidence interval should match the data and the estimand. For a binary outcome, the precision of a proportion depends on the number of assessed participants and the observed proportion. A comparison between randomized groups also requires a clearly specified contrast and an appropriate uncertainty calculation. If the group values, analysis population, or calculation inputs are not consistent, the resulting estimate and interval may not summarize the intended comparison. This is why the arm-specific proportions and the separately listed risk-difference entries need to be kept distinct rather than treated as mutually confirming results.

The registry's sample-size assumptions describe a planning illustration based on the observed effect, with a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the target effect is described as a fraction of the observed effect. Such calculations are planning illustrations, not evidence of observed power and not necessarily the study's original design calculation. The registry record does not report the trial's own sample-size justification, the effect used in the original design, or an explanation of how the design accommodated three display conditions.

General statistical explanation: over-dispersion arises when observed variability is greater than a model assumes. If a statistical model underestimates variability, its standard errors and confidence intervals may be too small, making estimates appear more precise than warranted. The primary outcome is binary and the registry does not identify an over-dispersion model or describe a model-based adjustment. It would therefore be inappropriate to assume that over-dispersion was assessed or corrected. Details of model diagnostics and adjustments are not reported in the registry record.

The registry identifies randomization and single masking, but does not describe the allocation sequence, concealment, or which parties were masked. Those implementation details matter to assessing potential selection and measurement biases. The record also does not identify the analysis population used for the posted odds ratios, whether the comparisons were adjusted for other variables, or how observations with missing outcome data were treated beyond noting that outcome sample size may differ from baseline because of missing data.

10. Confidence Intervals and Precision

The arm-specific proportions have 95% confidence intervals: 0.11 to 0.29 for Control, 0.27 to 0.53 for Small, and 0.16 to 0.38 for Medium. These intervals show that the estimated proportions are not known with exact precision. The posted intervals are wider for Small and Medium than for Control, but the registry record does not explain the interval calculation method or report a formal comparison of precision between arms.

For the sponsor-reported odds ratios, the Control–Medium estimate is 1.58 with a 95% confidence interval of .69 to 3.6. The Control–Small estimate is 2.89 with a 95% confidence interval of 1.28 to 6.55. The first interval includes 1, while the second does not. This is a statement about the reported intervals and the usual reference value for an odds ratio; it does not resolve the missing direction convention or analysis-method information.

General statistical explanation: an interval is more informative when its endpoints are considered together with the estimate and the quantity being estimated. Wide intervals leave more uncertainty about the magnitude of a proportion or contrast. A confidence interval is not a probability statement that a particular fixed effect has a specified chance of lying in that realized interval. Its frequentist interpretation concerns the long-run performance of the method across repeated studies under its assumptions.

Arm-specific intervals do not substitute for a confidence interval on the difference or ratio between arms. Comparing their overlap by eye is not a formal test. The record's risk-difference entries are all zero-valued, despite the different arm-level proportions, so they do not provide a coherent measure of comparative precision. The sponsor-reported odds-ratio intervals offer a separate comparative summary, but their missing methodological details should be kept in view.

Precision is also limited by the outcome's definition and timing. The binary classification compresses two scale responses into a single threshold-based category, and the endpoint is measured within 5 minutes of the intervention. The intervals quantify sampling uncertainty for the reported outcome; they do not capture uncertainty about how well the measure reflects later behavior or how results might generalize beyond the study setting.

11. Analyses Reported by the Sponsor

The registry reports sponsor analyses as odds ratios for two group pairs. For Control and Medium, the reported odds ratio is 1.58 with a 95% confidence interval of .69 to 3.6. For Control and Small, the reported odds ratio is 2.89 with a 95% confidence interval of 1.28 to 6.55. The analysis method, p-values, and direction convention are not reported in the registry record. Accordingly, these estimates are best described with their group pairs and intervals, without assigning the odds-ratio direction to a particular condition.

The arm-level proportions are 0.18 for Control, 0.39 for Small, and 0.26 for Medium. The posted risk-difference calculations are 0.0 with 0.0-to-0.0 intervals for both comparisons, which does not align with those arm-level proportions. The registry record does not explain this. These zero-valued entries should not be used as a substitute for the sponsor's reported odds ratios or presented as if they reconcile the arm results.

The record's discrepancy indicator is false, but that flag does not provide methodological detail or explain the zero-valued risk-difference entries. The sponsor analyses are the reported comparative analyses; their interpretation remains constrained by the absent method and direction information. The record does not report enough detail to reproduce or independently assess those analyses.

12. Multiplicity, Missing Data and Analysis Populations

The registry lists 4 outcome measures and 8 analyses. It does not report whether the primary endpoint was the only confirmatory outcome, how the analyses were organized, or whether any adjustment was made for multiple outcomes or comparisons. No multiplicity strategy, testing hierarchy, or prespecified distinction between confirmatory and exploratory analyses is reported in the registry record. Without those details, the reported intervals should not be interpreted as adjusted for the number of analyses.

The primary endpoint information states that sample size may differ from baseline because of missing data. The group sizes associated with the primary outcome are 82.0 for Control, 80.0 for Small, and 78.0 for Medium. The registry does not report the number or pattern of missing outcome responses, reasons for missingness, or whether missingness differed across conditions. It also does not describe any imputation, complete-case rule, or sensitivity analysis for missing outcomes.

The analysis populations for the sponsor-reported odds ratios are not reported in the registry record. It is not specified whether participants were analyzed according to randomized assignment, whether any participants were excluded after assignment, or whether the posted analyses used all available observations. The record does not describe a prespecified statistical analysis plan or explain whether the outcome threshold and comparison methods were selected before results were examined.

These omissions affect interpretation rather than changing the values that are posted. Multiplicity can increase the chance of at least one apparently unusual result across a set of analyses, while missing-data handling can affect estimates if observed participants differ systematically from those without outcome data. These are general statistical considerations; the registry record does not establish that either issue altered the results in this trial. The absence of reported details means their influence cannot be evaluated from the record alone.

13. Safety Results

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

Deaths

Other (non-serious) adverse events

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

The registry's adverse-event information lists 0 serious adverse events in Control, Small, and Medium. The corresponding serious-event populations at risk are 96, 86, and 93. It also lists 0 other adverse events in each group and 0 deaths in each group. These safety counts are separate from the group sizes reported for the primary outcome, and the registry does not explain the difference between those populations.

The record lists no serious adverse-event terms. These entries describe what was recorded in the registry; they do not show that every participant was assessed identically or that no unrecorded event occurred. The registry does not provide event definitions, ascertainment procedures, reporting windows, or an explanation of how the safety populations were determined. It also does not describe whether events were actively solicited or reported in another way.

General statistical explanation: observing zero events in a group does not establish that the underlying event rate is zero. The precision of a safety estimate depends on the number monitored, the length and completeness of follow-up, and how events were collected. Because those details are not reported in the registry record, the zero counts should be read narrowly as the posted event counts, not as proof that an event is impossible or that all safety uncertainty has been eliminated.

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

The results describe the proportion of participants who crossed a specified self-report threshold for cigarette-smoking risk within 5 minutes of exposure to a tobacco display. The arm-level proportions are 0.18 for Control, 0.39 for Small, and 0.26 for Medium. They capture immediate reported responses under the study's binary scoring rule and are accompanied by arm-specific 95% confidence intervals.

The results do not directly measure whether participants began smoking, used cigarettes later, or maintained a particular intention over time. The outcome is based on hypothetical offers of unflavored and menthol cigarettes by a best friend. It therefore represents a stated response to those questions rather than observed behavior. The registry record does not report a longer-term primary outcome that would establish whether the short-term classification predicts later tobacco use.

The record also does not provide enough analysis detail to interpret the reported odds ratios fully. In particular, it does not specify their direction convention or method. The separate risk-difference entries are zero-valued despite the differences in arm-level proportions, and the record does not explain that inconsistency. These limitations mean the comparative results should be described with care rather than compressed into a simple claim about the relative effect of the display formats.

General statistical explanation: randomized assignment can support causal comparisons when allocation, follow-up, outcome measurement, and analysis are implemented appropriately. The registry identifies the study as randomized but does not report enough implementation detail to assess all of those conditions. Even a well-conducted randomized experiment would support conclusions about the measured outcome and study setting; extending findings to later behavior or other populations requires additional evidence.

The most defensible reading is therefore bounded: the posted results give short-term, threshold-based proportions across three randomized display conditions, with the stated intervals and sponsor-reported odds ratios. They do not by themselves establish a change in actual tobacco use, a durable behavioral effect, or the size of any effect in other settings. Nor do zero recorded adverse events establish absence of all safety risk.

15. Why This Trial Matters Statistically

This trial presents a useful statistical distinction between an outcome's measurement and the behavior researchers ultimately hope to understand. The primary endpoint is not cigarette use itself; it is a binary classification formed from two stated responses shortly after exposure. That makes the endpoint suitable for examining an immediate experimental response, while also limiting what can be concluded about later behavior.

The three conditions allow the observed proportions to be considered across a typical large display and smaller display formats. The arm-level values and their intervals are relatively straightforward to describe, but the record also illustrates why comparative estimates need to be internally coherent and methodologically transparent. The listed risk-difference entries are all zero-valued even though the arm proportions differ. Without an explanation, those entries cannot be treated as a reliable summary of the contrasts.

The sponsor-reported odds ratios add a comparative analysis, but the missing method and direction convention make precise interpretation harder. This is an important reporting lesson: a point estimate and interval are most useful when accompanied by a clear definition of the contrast, group ordering, analysis population, and statistical method. Reporting those details helps readers connect a model-based estimate with the underlying arm-level data.

The trial also highlights the role of timing, missing data, and multiplicity in reading clinical and behavioral research. The endpoint is immediate, sample size may differ from baseline because of missing data, and the registry lists multiple outcomes and analyses without describing how missingness or multiplicity was handled. These limitations do not establish that the findings are invalid, but they identify questions that the registry record alone cannot answer. Careful interpretation keeps the statistical evidence tied to the outcome actually measured.

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 primary endpoint is a brief self-report taken within 5 minutes of the intervention. It measures stated willingness in response to hypothetical offers, not observed smoking. The binary threshold also reduces the underlying two-item scale to an at-risk or no-risk classification. The registry does not report sensitivity analyses using another threshold or the original summed scale, so the effect of that categorization on the results cannot be assessed.

Although the study is described as randomized and single-masked, the registry does not identify who was masked or describe sequence generation and allocation concealment. It also does not explain the intervention delivery setting or whether exposure conditions were otherwise standardized. Such information would help assess the possibility of differences in implementation or measurement across conditions.

The registry notes that primary-outcome sample size may differ from baseline because of missing data but does not provide missingness counts, reasons, or handling methods. It does not identify the analysis population for the sponsor-reported odds ratios or report adjustment variables, model specification, or diagnostics. The reported method and direction convention for those odds ratios are also absent.

The zero-valued risk-difference entries do not accord with the reported arm-level proportions, and the record offers no explanation. In addition, it lists multiple outcome measures and analyses without describing multiplicity adjustment or a testing hierarchy. The sponsor's reported odds ratios are available, but their limited accompanying detail restricts independent interpretation. Finally, the short-term primary endpoint does not establish longer-term smoking behavior, and the safety record provides event counts without detailed ascertainment or follow-up information.

17. Related Tutorials

18. Related Statistical Calculators

19. Sources

• ClinicalTrials.gov: Shrinking the Size of the Tobacco Power Wall — NCT04632030.
• Registry record last updated 2023-10-25; status last verified 2023-10.
• Results first posted 2023-10-25.
• 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

NCT04632030 is a completed randomized, single-masked, parallel-group behavioral trial sponsored by RAND. It evaluated tobacco display formats described as Control, Small, and Medium, corresponding to three, one, and two large cabinets, respectively. The registry reports enrollment of 275 and lists the phase as NA.

The primary outcome was the proportion classified as at risk for cigarette smoking within 5 minutes of the intervention, based on two self-report items and a dichotomized summed score. The reported proportions were 0.18 for Control, 0.39 for Small, and 0.26 for Medium. The registry also reports odds ratios for Control–Medium and Control–Small comparisons, while method and direction details are absent. The separate zero-valued risk-difference entries do not align with the arm-level proportions.

The record notes possible differences between baseline and outcome sample size because of missing data, but does not describe missing-data handling or multiplicity procedures. It lists 0 serious adverse events, 0 other adverse events, and 0 deaths in each condition's safety group.