Testing Legally Feasible Options Studies 2/3: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Testing Legally Feasible Options Studies 2/3 (NCT05604508), a randomized na study. The primary outcome is Self-reported Cigarette Smoking Risk After Shopping in the StoreLab.

2. Clinical Question

The broader research aim is to experimentally evaluate legally viable approaches to reducing the impact of retail point-of-sale environments on adolescent tobacco-use risk. The study description identifies four product classes: cigarettes, e-cigarettes, smokeless tobacco, and little cigars or cigarillos. Studies 2 and 3 are described as examining whether changing the number and content of posters on outside retail doors reduces adolescents’ tobacco-use risk.

The primary outcome reported for this study is specifically cigarette-smoking risk after shopping in the StoreLab. The question is therefore narrower than the broader research aim: it concerns a dichotomized self-reported cigarette-risk measure at the experimental visit, rather than tobacco use across every product class or a later behavioral outcome. The record reports proportions for the three conditions and sponsor-reported odds ratios for the comparisons with Status Quo. It does not report a direct comparison between Reduced Poster and No Price.

3. Trial Design

The registry record describes a randomized, single-masked, parallel study. It lists phase as NA and reports enrollment of 445. The study status is completed. The recorded start date is 2022-10-12, and the primary completion date is 2024-03-07. RAND is listed as the sponsor.

Three conditions are represented in the primary outcome results. Status Quo permits many posters with pricing information. Reduced Poster permits a reduced number of posters with pricing information. No Price permits many posters without pricing information. These conditions distinguish poster quantity and price information in the retail point-of-sale environment. The registry also lists intervention names that describe many posters with prices, many posters without prices, and fewer posters without price restrictions.

The primary measure is assessed at one visit, within 5 minutes of the experimental manipulation. The posted outcome information gives an analysis sample of 142 for Status Quo, 145 for Reduced Poster, and 146 for No Price. The outcome description notes that some participants had missing data and that this accounts for differences in the reported n. The enrollment figure and these outcome-specific group counts describe different aspects of the record; the group counts should be read as the available primary-outcome data, not as a replacement for the enrollment figure.

The record’s description places the work within studies 2 and 3 of a broader research program and says those studies occurred concurrently. It does not report details about the randomization procedure, the unit assigned, the person or process masked, or how the study’s allocation was implemented. The protocol’s original statistical plan and design assumptions are not reported in the registry record.

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: Some participants were missing data, which accounts for differences in the n.

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 Self-reported Cigarette Smoking Risk After Shopping in the StoreLab, measured over There is one visit in this research: This variable is assessed at that visit, within 5 minutes of the experimental manipulation.

The primary endpoint is the proportion of participants in each condition classified as at risk of cigarette smoking. Participants answer three questions about trying a cigarette soon, trying one within the next year, and whether they would smoke if offered a cigarette by a best friend. Each response is on a scale from 1 (Definitely not) to 10 (Definitely yes). The responses are summed to create a total score ranging from 3 to 30.

The total score is then dichotomized: a score of 3 is coded as no risk, while a score greater than 3 is coded as at risk. The endpoint is thus a binary classification derived from a multi-item self-report scale, not a report of cigarette smoking behavior. Its reported unit is the proportion at risk within each condition.

This outcome is used to assess immediate self-reported risk in response to the experimental retail environment. Measuring it within 5 minutes of the manipulation links the response closely in time to the StoreLab experience. That timing does not establish whether any response persists or predicts later behavior. The registry record does not report longer-term follow-up for this primary endpoint.

Dichotomizing a scale makes the result easier to express as the share classified at risk, but it also discards variation among participants within each category. Participants with different scores above 3 are grouped together, as are participants whose score is exactly 3. Interpretation should therefore stay focused on this defined classification and not treat the proportions as measured rates of tobacco use.

7. Results Posted in the Registry

• Reduced Poster: 0.7% (1/145) versus 0.7% (1/142) on control; risk difference -0.0 percentage points (95% CI -1.9 to 1.9), risk ratio 0.98 (0.06–15.51); unadjusted two-proportion z-test p = 0.988.
• No Price: 0.7% (1/146) versus 0.7% (1/142) on control; risk difference -0.0 percentage points (95% CI -1.9 to 1.9), risk ratio 0.97 (0.06–15.40); unadjusted two-proportion z-test p = 0.984.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary at the analysis stage: each participant is classified as at risk or not at risk according to the stated score rule. A proportion is the number classified at risk relative to the number with outcome data in a condition. The record’s broad outcome type is a percentage of participants with an event, where the relevant event is classification as at risk. The endpoint is not a time-to-event measure, and the reported comparison metric is not a continuous mean difference.

What does the risk difference express?

A risk difference subtracts one group’s event proportion from another group’s event proportion. It is expressed on the probability scale, so zero corresponds to equal proportions. A negative estimate means the first condition in the stated comparison has a lower estimated proportion than the reference condition, assuming the comparison order is interpreted as presented. It is distinct from an odds ratio, which compares odds rather than probabilities.

The recalculated risk differences are reported as -< 0.001 for Reduced Poster versus Status Quo and -< 0.001 for No Price versus Status Quo. Their confidence intervals and unadjusted p-values are also posted. These values should be understood as simple unadjusted recalculations from posted summary statistics, not as a substitute for a fully described sponsor analysis. The record does not report the method used to produce the sponsor’s odds ratios.

How should an odds ratio be read?

An odds ratio compares the odds of an outcome between two groups. An odds ratio of 1 corresponds to equal odds. Values below 1 indicate lower odds in the numerator group relative to the denominator group, according to the comparison’s group ordering; values above 1 indicate higher odds. Odds are not the same as probabilities, particularly when the outcome is not rare. Therefore, an odds ratio should not be described as a proportional change in the risk or as a risk difference.

The sponsor-reported odds ratio for Status Quo compared with Reduced Poster is 0.735, and for Status Quo compared with No Price it is 0.471. The registry identifies the group pairs but does not give a method description for these analyses. The reported confidence intervals quantify uncertainty on the odds-ratio scale, not on the risk-difference scale.

What do confidence intervals and p-values contribute?

A confidence interval gives a range of values compatible with the estimate under the statistical procedure used, subject to its assumptions. Wider intervals indicate less precision than narrower intervals on the same scale. Whether an interval includes the null value helps describe how compatible the data are with no difference under that procedure, but it does not establish that the null is true or false. A p-value measures how unusual the observed data, or data more extreme, would be under a specified null model. It is not the probability that the null hypothesis is true, nor a measure of the size or importance of an effect.

The recalculated risk-difference results include unadjusted p-values. The sponsor-reported odds-ratio analyses have no p-values reported in the registry record. The record does not identify the sponsor analysis method or give enough detail to infer its model assumptions.

Why can over-dispersion matter?

In general, a simple binary model may assume that variation follows a particular probability structure. Over-dispersion means the observed variability is greater than that structure anticipates. If present and not accounted for, standard errors can be too small and confidence intervals too narrow, making results appear more precise than warranted. This is a general statistical consideration, not a reported feature of this study. The registry record does not report whether over-dispersion was assessed or whether an adjustment was used.

More generally, the analysis may need to account for how participants were assigned and how observations were collected. The record reports a randomized parallel design but does not report the randomization unit, clustering structure, covariate adjustment, model specification, or handling of repeated observations. The primary endpoint description indicates one visit, but that alone does not establish the full analysis plan.

What does dichotomizing the score imply?

The endpoint converts a score with multiple possible values into two categories. This creates a straightforward proportion but removes distinctions among scores within the at-risk category and within the no-risk category. The result depends on the prespecified cutoff stated in the endpoint description. The record does not report whether other cutoffs or continuous-score analyses were also conducted.

The record lists four outcome measures and eight analyses, but it does not identify all of them in the posted results summarized for the primary endpoint. It does not report a multiplicity adjustment or explain how the primary comparison was selected. Those omissions limit assessment of the broader analysis strategy and the role of the displayed comparisons within it.

10. Confidence Intervals and Precision

Precision is conveyed mainly by the confidence intervals. For the arm-level proportions, the 95% confidence interval is 0.45 to 0.73 for Status Quo, 0.38 to 0.65 for Reduced Poster, and 0.28 to 0.51 for No Price. Each interval spans a range of plausible values for the condition’s underlying proportion under the procedure used. The intervals overlap, but overlap alone is not a formal test of a difference between groups.

For the sponsor-reported odds ratios, the confidence interval for Status Quo compared with Reduced Poster ranges from 0.347 to 1.553. It includes 1, so the reported interval is compatible with equal odds as well as values on either side of equality. The interval for Status Quo compared with No Price ranges from 0.234 to 0.947 and does not include 1. This describes the interval’s relation to the null value on the odds-ratio scale; it does not establish clinical importance or resolve other limitations in the record.

The recalculated risk-difference intervals are -0.019 to 0.019 and -0.019 to 0.019. Both include zero, the null value for a risk difference. The associated recalculated estimates are very close to zero, but their interpretation should remain separate from the arm-level proportions and sponsor-reported odds ratios because the record does not reconcile those numerical displays.

Confidence intervals reflect sampling uncertainty under an analysis procedure; they do not account automatically for missing data, model misspecification, measurement limitations, or multiplicity. The registry record does not provide enough methodological detail to assess all such sources of uncertainty. In particular, it does not report the sponsor analysis method or the original statistical plan.

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 are not observed power. They use the recalculated observed effect as a starting point and show how many participants per arm would be needed under stated planning assumptions for the specified power targets. The figures are per arm, not total sample sizes or total event counts.

The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. Rows describing a smaller fraction of the observed effect represent a smaller target difference; detecting smaller effects generally requires more participants than detecting larger effects, all else held constant.

The 80% power column describes a planning scenario in which the test would have an 80% probability of rejecting the null under the assumed effect and analysis conditions, if those assumptions hold. The 90% power column uses a higher target probability of detecting the assumed effect. These are design calculations, not probabilities that the observed result is correct, and they do not describe the power actually achieved by the completed study.

Read across a row to compare the planning requirement for the two power targets, and read down the rows to see how the requirement changes as the assumed effect becomes smaller. The calculations are illustrations based on recalculated effects, not the trial’s original design calculations. The trial’s own sample-size justification and original design assumptions are not reported in the registry record.

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 = 0.007; treatment proportion p₁ = 0.007; average p̄ = 0.007.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.1177 = 0.2306.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.1177 = 0.0990.
4. n = (0.2306 + 0.0990)² / (-0.0001)² = 5,117,595.3, rounded up to 5,117,596 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 <- 0.00704225352112676                          # control proportion
p1 <- 0.00689655172413793                          # 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(5604508)
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 = 5,117,596 (80% power), 6,851,008 (90% power)
 75% of observed effect: n per arm = 9,121,556 (80% power), 12,211,175 (90% power)
 50% of observed effect: n per arm = 20,576,619 (80% power), 27,546,253 (90% power)
power.prop.test: 5117595 
Simulated power at n = 5,117,596 per arm: 0.801 (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 sponsor analyses as odds ratios for Status Quo compared separately with Reduced Poster and No Price. The reported odds ratios are 0.735 and 0.471, respectively, with 95% confidence intervals of 0.347 to 1.553 and 0.234 to 0.947. The sponsor analyses have no p-values reported in the registry record, and the method used to calculate them is not described.

The recalculated comparisons use risk differences and report estimates of -< 0.001 and -< 0.001, with unadjusted p-values of 0.988 and 0.984. These use a different effect measure from the sponsor’s odds ratios. They should not be treated as reproductions of the sponsor analyses or as interchangeable estimates.

The arm-level proportions and recalculated differences do not appear to convey the same numerical pattern, and the registry record does not explain the relationship. The record does not flag a discrepancy, but the available information still does not permit a detailed reconciliation. The sponsor’s reported analysis and the posted recalculations should therefore be identified separately, with their measures and uncertainty stated plainly.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists four outcome measures and eight analyses. The primary outcome information describes the cigarette-smoking-risk measure, but the record does not report secondary outcome results in the posted analyses. It does not explain how the eight analyses relate to the four outcome measures, which comparisons were designated primary, or whether any analyses were exploratory.

When several outcomes, comparisons, or analyses are considered, the chance of at least one apparently unusual result can increase. Statistical procedures that account for multiplicity can address this issue, but the record does not report whether an adjustment was planned or used. It also does not report a hierarchy of hypotheses or a strategy for interpreting the several analyses together. Consequently, the reported confidence intervals and recalculated unadjusted p-values should not be assumed to account for multiple testing.

Missing primary outcome data are acknowledged: the endpoint description says some participants were missing data and that this accounts for differences in n. The available group counts for the primary outcome are 142, 145, and 146. The registry record does not report the reasons for missingness, the amount missing by condition beyond those counts, or whether missingness was related to observed or unobserved participant characteristics. It also does not describe an imputation method, sensitivity analysis, or other missing-data strategy.

The record does not report which analysis population was used, such as whether all randomized participants were included in the primary analysis or whether eligibility for analysis depended on outcome availability. It does not provide a participant-flow account sufficient to assess exclusions or the handling of protocol deviations. These details matter because the interpretation of a randomized comparison depends partly on how participants are retained in the analysis. No assumptions about these procedures can be inferred from the arm counts alone.

The trial’s original statistical plan, including its prespecified primary analysis, missing-data strategy, and multiplicity approach, is not reported in the registry record. The stated limitations are reporting gaps, not evidence that a particular method was or was not used.

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 0% reporting threshold.

The adverse-event record reports zero serious adverse events in Status Quo, zero in Reduced Poster, and zero in No Price. It also reports zero other adverse events and zero deaths in each of the three conditions. These are the recorded event counts; they do not establish that no event of any kind occurred outside the categories or reporting procedures captured in the registry.

The adverse-event record lists 150 participants at risk in Status Quo, 147 in Reduced Poster, and 148 in No Price. These figures differ from the primary outcome analysis counts. They belong to the adverse-event reporting and should not be substituted for the primary endpoint denominators. The registry record does not explain the difference in these reporting counts.

No serious adverse-event terms are listed. The record does not provide additional detail about event definitions, collection procedures, follow-up duration for safety, or attribution. The absence of recorded events in these entries should therefore be described as a feature of the posted safety record, not as proof that the conditions had no possible adverse consequences.

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

The results describe self-reported cigarette-smoking risk shortly after a controlled retail-environment manipulation. The arm-level proportions range from 0.39 in No Price to 0.59 in Status Quo, with 0.52 in Reduced Poster. These values refer to the endpoint’s classification rule, not to observed cigarette smoking or subsequent tobacco use. The measure was assessed at one visit within 5 minutes of the manipulation.

The sponsor-reported odds ratios compare each intervention condition with Status Quo. The confidence interval for Reduced Poster includes 1, while the interval for No Price does not. The registry does not report p-values for these sponsor analyses, and it does not describe their model. Separate unadjusted risk-difference recalculations are also posted, but they do not align numerically with the arm-level proportions in an evidently reconciled way. The available record does not explain this issue, so the different results should not be blended into a single estimate.

The findings do not establish whether any condition changes later cigarette use, use of other tobacco products, or behavior outside the StoreLab setting. Nor do the reported figures determine how adolescents might respond to retail environments beyond the study conditions. The endpoint is a self-reported risk classification, and the record does not report longer-term follow-up for it.

These results also do not establish that poster quantity or price information alone explains any difference. The conditions vary in specified ways, but the record does not describe additional analyses that isolate mechanisms. Missing outcome data, unreported statistical methods, and the unexplained relationship among the posted analyses also constrain interpretation. The appropriate conclusion is descriptive: the registry reports the stated proportions and estimates under the defined conditions, with the uncertainty and reporting limitations.

17. Why This Trial Matters Statistically

This trial raises a useful statistical distinction between an outcome’s observed group proportions and the effect measure chosen for a comparison. Proportions describe the frequency of classification as at risk in each condition, while odds ratios and risk differences express contrasts on different scales. They cannot be interchanged without a clear explanation of the analysis and group ordering.

It also illustrates why uncertainty should be read alongside point estimates. Confidence intervals show how imprecise an estimate may be under the method used, and their relation to the null value helps describe compatibility with no difference. Neither a point estimate nor an interval alone addresses all questions about practical importance, bias, or generalizability.

The record’s endpoint is an immediate self-report converted from a multi-item score into a binary classification. That approach yields an interpretable proportion, but it loses information about score variation and does not directly measure smoking behavior. The timing of measurement is important to the meaning of the result: it captures reported risk soon after the manipulation, not persistence over time.

Finally, the record illustrates why analysis transparency matters. The sponsor-reported odds ratios, recalculated risk differences, available outcome counts, missing-data statement, and absence of a reported analysis method all shape how readers can interpret the results. Planning illustrations based on observed estimates can help explain the sample sizes associated with assumed effects, but they are not evidence of the study’s original design rationale or of achieved power.

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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The primary endpoint is self-reported and is based on a scale that is dichotomized at a stated cutoff. It measures a risk classification, not smoking behavior. Assessment occurs within 5 minutes of the experimental manipulation at one visit, so the reported outcome does not address whether responses persist or predict later behavior.

Some primary outcome data are missing, and the available analysis counts vary by condition. The record does not report reasons for missingness or describe the method used to handle missing data. The adverse-event reporting counts also differ from the primary outcome counts, and their relationship is not explained.

The posted arm-level proportions and recalculated risk differences do not appear to provide a readily reconciled numerical account of the same comparisons. Sponsor-reported odds ratios are presented on a different scale, without a reported analysis method or p-values. The registry record does not explain how these analyses relate, which limits a unified interpretation of the comparison results.

The record lists four outcome measures and eight analyses but does not describe a multiplicity strategy, analysis population, covariate adjustment, randomization procedure, or full statistical plan. The original sample-size justification and design assumptions are not reported. These omissions make it difficult to assess the extent to which the posted results reflect prespecified analyses.

The record describes a StoreLab experiment and identifies the broader aim as reducing adolescents’ tobacco-use risk in retail point-of-sale environments. It does not report enough participant or setting detail to determine how broadly the immediate self-reported findings apply to other populations or retail contexts. These are limits of what the registry record reports, not evidence that unreported procedures were absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Testing Legally Feasible Options Studies 2/3 — NCT05604508.
• Registry record last updated 2025-01-13; status last verified 2025-01.
• Results first posted 2025-01-03.
• 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

NCT05604508, titled Testing Legally Feasible Options Studies 2/3, is recorded as a completed randomized, single-masked, parallel study sponsored by RAND. The listed enrollment is 445. It compares Status Quo, Reduced Poster, and No Price retail poster conditions.

The primary outcome is the proportion classified as at risk of cigarette smoking after shopping in the StoreLab, assessed at one visit within 5 minutes of the manipulation. Posted condition proportions are 0.59, 0.52, and 0.39, respectively. The record also reports sponsor odds ratios and separate recalculated risk differences; these measures are not interchangeable, and their numerical relationship is not explained in the registry record.

The outcome description notes missing data. The record does not report the original statistical plan, analysis methods for the sponsor odds ratios, multiplicity handling, or a missing-data strategy. The planning illustrations use recalculated effects and stated assumptions, rather than the trial’s original design rationale.