Ecological Momentary Intervention of Implementation Intentions Delivered by Text Message to Reduce Cigarette Smoking: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Ecological Momentary Intervention of Implementation Intentions Delivered by Text Message to Reduce Cigarette Smoking (NCT04967885), a randomized na study. The primary outcome is Percent of Participants Completing Intervention Period.

2. Clinical Question

The study concerns whether a customized, text-message implementation-intentions approach can be evaluated for feasibility, acceptability, and initial effectiveness in a cigarette-smoking context. Its primary endpoint is about completing the intervention period, rather than a direct measure of smoking reduction. Smoking is identified as the condition, and the study description sets out an intervention intended to link situations in which smoking is likely with alternative responses. The primary outcome alone therefore addresses participation and completion, not whether smoking changed.

The registry identifies the design as randomized and crossover, with no masking. It records 80 participants enrolled. The brief description also refers to adults who smoke a minimum of 15 cigarettes per day and includes n=100; the relationship between that number and the recorded enrollment is not reported in the registry record. The endpoint results compare the Immediate Intervention and Waitlist conditions, but details of the crossover sequence and the analysis population are not reported.

3. Trial Design

The registry describes a randomized, unmasked crossover study of a behavioral intervention called the Ecological Momentary Implementation Intentions Intervention. The sponsor is Trustees of Dartmouth College. The registry records the study as completed and lists enrollment as 80. The recorded start date is 2021-06-08, and the primary completion date is 2021-12-31. The study phase is listed as NA.

The Immediate Intervention condition involved creating implementation-intention messages before a two-week EMA plus EMI-II period. Participants in that condition were to complete five daily ecological momentary assessments during the intervention period. The Waitlist condition began with a two-week period without intervention components. Participants in that initial period reported past-week smoking weekly. The arm description is truncated after describing what would happen at the end of the waitlist period, so subsequent procedures cannot be established from the registry record.

The primary outcome description places assessment of completion at Week 2 in the Immediate Intervention arm and week 4 in the Waitlist arm. This timing is consistent with the stated two-week intervention period and the initial two-week waitlist, but the record does not provide a full schedule of study periods. Although the design is labeled crossover, the sequence, period structure, washout procedures, and handling of possible period or carryover effects are not reported in the registry record.

The brief summary describes a micro-randomized trial and refers to a sample of adults who smoke a minimum of 15 cigarettes per day, with n=100. The registry separately records randomized allocation, crossover model, and enrollment of 80. How these descriptions relate to one another is not reported. The registry also does not report the original sample-size justification, the allocation ratio, or details of the randomization procedure. No inference about those design features can be made from the posted outcome counts.

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.

Week 1 Follow-Up

Reasons for not completing this period:

Week 2 Follow-Up

Reasons for not completing this period:

Week 3 Follow-Up

Reasons for not completing this period:

Week 4 Follow-Up

Reasons for not completing this period:

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.

Population: Participants

6. Primary Endpoint

The registry lists the primary outcome as Percent of Participants Completing Intervention Period, measured over 2 weeks.

The primary endpoint is titled “Percent of Participants Completing Intervention Period.” It is intended to assess feasibility by measuring completion of the two-week intervention period. The registry specifies the assessment point as Week 2 for the Immediate Intervention condition and week 4 for the Waitlist condition. Completion is relevant to feasibility because it describes whether participants reached the end of the planned period, rather than measuring a clinical change in smoking.

There is a distinction between the endpoint title and the posted values. The outcome parameter is listed as a count of participants, and the results give counts for each condition. Thus, the results directly report how many participants completed, not a percentage value. No percentage results are posted in the outcome record, and no completion definition beyond the endpoint description is reported in the registry record. The posted data should therefore be read as counts, with the condition-specific participant numbers as their denominators, rather than as directly reported percentages.

This endpoint can inform interpretation of participation in the two-week periods, but it cannot on its own establish acceptability, intervention engagement beyond completion, or smoking reduction. The study description identifies feasibility, acceptability, and initial effectiveness as broader interests, while the primary outcome specifically addresses completion. The registry lists three outcome measures, but details of secondary results are not posted. The completion outcome is consequently a narrow indicator of feasibility, and its interpretation depends on the precise completion criteria and the handling of missing assessments, neither of which is reported in the registry record.

7. Results Posted in the Registry

• Waitlist: 75.6% (31/41) versus 64.1% (25/39) on control; risk difference 11.5 percentage points (95% CI -8.5 to 31.5), risk ratio 1.18 (0.88–1.58); unadjusted two-proportion z-test p = 0.262.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary result is a binary completion outcome summarized as counts: participants either completed the intervention period or did not, according to the outcome definition. The registry reports the number completing and the participant count for each condition. Because the endpoint title uses the word “percent” but the parameter is a count, the reported results should be interpreted as counts rather than as posted percentages. No explicit operational definition of completion is reported in the registry record.

What does the risk difference describe?

A risk difference compares the outcome proportions in two conditions by subtracting one condition's proportion from the other's. Here, the reported contrast is Waitlist relative to Immediate Intervention, and the estimate is 0.115. A positive value in this orientation indicates a higher observed completion proportion in Waitlist; it does not, by itself, establish that the condition caused a difference. The confidence interval from -0.085 to 0.315 represents uncertainty around the estimate. Because the interval spans zero, the data are compatible with no difference and with differences in either direction.

How do relative measures differ?

The risk ratio compares the outcome proportions as a ratio, while the odds ratio compares the odds of completion. The posted risk ratio is 1.18, with a confidence interval from 0.881 to 1.58. The posted odds ratio is 1.736, with a confidence interval from 0.660 to 4.568. A relative measure equal to one corresponds to no relative contrast. Both intervals include one. Risk ratios and odds ratios use different scales, and an odds ratio should not be read as if it were a risk ratio. These measures summarize the same completion outcome and do not add separate evidence about smoking reduction.

What does the p-value tell the reader?

The reported unadjusted p-value is 0.262. In general, a p-value describes how compatible the observed data are with a specified null model, assuming that model and its conditions. It is not the probability that the null hypothesis is true, the probability that chance alone produced the result, or a measure of clinical importance. A p-value that is not small does not show that the conditions are equivalent. The registry record does not report the test specification or the sponsor's statistical analysis method, so the p-value should be read as the posted unadjusted result, not as a complete description of the inferential procedure.

The comparison is labeled as unadjusted re-calculation from posted summary statistics. Such a calculation summarizes the observed counts without accounting for unreported participant-level covariates or design features. In a crossover study, outcomes from the same participant across conditions can be related. General statistical practice would account for that dependence when estimating uncertainty if the analysis uses repeated observations. The registry record does not explain whether the posted comparison accounts for the crossover structure, period, sequence, or within-participant correlation. Therefore, the reported comparison cannot be assumed to incorporate those features.

Why can over-dispersion matter?

In general, over-dispersion occurs when observed variability is greater than a statistical model expects. If a model assumes less variability than the data contain, its uncertainty estimates can be too narrow and its inferential results can appear more decisive than warranted. That issue is relevant in settings with clustered or repeated observations, where responses may be more alike within a participant or group than a simple model assumes. The registry record does not report an over-dispersion assessment or a model for repeated measurements. This is a general consideration, not a claim that over-dispersion occurred in this study.

The word “crossover” indicates that the design is not simply described as two independent parallel groups, but the registry outcome summary provides condition-level counts and a single comparison. The sequence and period-level data are not reported. The number of participants contributing to each condition is stated, but the record does not clarify whether all participants contributed outcome data in both periods or how incomplete participation was handled. Without those details, the extent to which the published contrast reflects a paired comparison cannot be determined.

The outcome record lists one analysis and three outcome measures, while secondary posted results are listed as none. The particular method used for the primary outcome, any covariate adjustment, model diagnostics, and any interim analyses are not reported in the registry record. These omissions matter because different methods can produce different standard errors and confidence intervals, particularly when study designs involve repeated measurements. The posted estimates remain interpretable as summary contrasts, but their analytical basis is not fully documented.

10. Confidence Intervals and Precision

The confidence interval for the risk difference runs from -0.085 to 0.315 around an estimate of 0.115. In general, a confidence interval is a range of effect values compatible with the data under the method used to calculate it. It conveys uncertainty in the estimate, rather than a range containing a known fixed proportion of individual outcomes. Here the interval includes zero, so the result does not precisely distinguish a difference in either direction from no difference.

The relative measures also have broad intervals: 0.881 to 1.58 for the risk ratio and 0.660 to 4.568 for the odds ratio. In general, a ratio value of one represents no relative difference. Both intervals extend across that reference value. Together, the reported intervals show that the point estimates should not be treated as precise estimates of the size of a completion contrast. The possible values remain compatible with effects on either side of the no-difference reference.

Confidence intervals describe statistical uncertainty under the calculation method; they do not address every source of uncertainty. For example, they do not by themselves resolve possible bias from missing data, uncertainty about endpoint definitions, or the adequacy of the analysis for a crossover design. Those details are not reported in the registry record. The intervals should therefore be interpreted as precision summaries for the posted comparisons, not as a complete assessment of the reliability or generalizability of the result.

The p-value of 0.262 is consistent with the interval-based reading that the data do not sharply separate the observed contrast from no difference. It should not be used as a substitute for examining the estimate and interval. The confidence intervals are the more informative description of the range of effect sizes compatible with the posted summary statistics.

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 sample-size figures are planning illustrations based on the observed effect, not the trial's original design assumptions. The registry record does not report the original sample-size justification or design assumptions. For this binary completion outcome, the figures are participants per arm, not total events. The planning assumptions listed are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect.

The rows describe planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each assumed effect, the 80% power column gives the illustrative participants per arm for a design with an 80% chance of detecting that effect under the stated assumptions. The 90% power column gives the corresponding planning figure for a 90% chance. These are design-planning probabilities conditional on the assumptions, not probabilities that the intervention is effective.

The listed figures are 249 and 333 participants per arm for planning for 100% of the observed effect; 455 and 608 for planning for 75% of the observed effect; and 1,048 and 1,402 for planning for 50% of the observed effect. Each pair gives the 80% and 90% power planning figures, respectively. Smaller effects require more participants to detect under the same planning assumptions, which is why the figures increase as the assumed fraction of the observed effect decreases.

This is not observed power. It is a planning illustration derived from the observed effect, and it does not show what power the completed study actually had. The sample-size curve presents the same kind of planning relationship visually; it should be read under the stated assumptions rather than as a reconstruction of the trial's original design.

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 = 0.641; treatment proportion p₁ = 0.756; average p̄ = 0.699.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6490 = 1.2719.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6438 = 0.5419.
4. n = (1.2719 + 0.5419)² / (0.1151)² = 248.5, rounded up to 249 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 <- 0.641025641025641                          # control proportion
p1 <- 0.75609756097561                          # 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(4967885)
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 = 249 (80% power), 333 (90% power)
 75% of observed effect: n per arm = 455 (80% power), 608 (90% power)
 50% of observed effect: n per arm = 1,048 (80% power), 1,402 (90% power)
power.prop.test: 248.5 
Simulated power at n = 249 per arm: 0.802 (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 three outcome measures, while the primary outcome is completion of the two-week intervention period. It records one analysis and no posted secondary results. The registry record does not report a complete statistical analysis plan identifying all hypotheses, their order, or how results across outcomes were handled. It also does not report whether any multiplicity adjustment was planned or applied.

In general, multiplicity arises when several outcomes, comparisons, time points, or analyses are examined. The more opportunities there are to observe a result that appears unusual, the more important it is to know how the analyses were prespecified and interpreted. The presence of three registered outcome measures does not establish that all were tested in the same way, and the record does not give enough information to determine the scope of the analyses. The primary completion result should therefore be interpreted as the posted primary outcome, without assuming that a multiplicity procedure was or was not used.

The registry does not report how missing outcome data were defined, whether participants lost to follow-up were counted as not completing, or whether any imputation or sensitivity analysis was used. These details can affect a completion measure because non-completion and unobserved completion are not necessarily the same. The outcome counts and condition denominators are reported, but they do not explain the status or outcome handling of every participant.

The analysis population is not reported in the registry record. It is therefore unclear whether the comparison followed an intention-to-treat principle, included only participants with observed outcomes, or used another population definition. The record also does not describe exclusions after randomization, protocol deviations, or the handling of crossover periods. These absences limit assessment of how the reported estimate relates to the randomized allocation and whether missingness could have affected the comparison.

Finally, the registry does not report interim analyses or stopping rules. No assumptions about their presence or absence should be inferred from the single posted analysis. A fuller assessment of multiplicity and missing data would require the prespecified analysis plan and participant-level disposition information, neither of which is reported in the registry record.

14. 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 serious adverse event figures record zero events in the Immediate Intervention condition among 39 participants at risk and zero in the Waitlist condition among 41 participants at risk. The registry also records zero other adverse events in each condition and zero deaths in each condition. No serious adverse event terms are listed.

These entries mean that no events are recorded in the posted adverse-event fields for the stated groups. They should not be interpreted as proof that no adverse events occurred outside the registry's definitions, ascertainment process, or reporting period. The registry record does not provide further details about how adverse events were collected, what time window was used, or how the terms “serious” and “other” were operationalized.

Zero recorded events also does not establish that the intervention is free of risk. Safety interpretation depends on event definitions, follow-up, completeness of ascertainment, and the amount of information available. The posted figures are descriptive safety records, not a comparative safety analysis. They do not support a conclusion about safety differences between conditions, and they should be read separately from the completion endpoint.

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

The result shows the posted completion counts for the two conditions and an unadjusted contrast with considerable uncertainty. The risk difference estimate is 0.115 for Waitlist relative to Immediate Intervention, with a confidence interval from -0.085 to 0.315. The interval includes zero, and the relative-effect intervals include one. The reported p-value is 0.262. Taken together, these statistics do not precisely establish the direction or size of a completion difference.

The outcome is a feasibility measure: completion of a two-week period. It is not a direct measure of cigarettes smoked, smoking reduction, quit attempts, or longer-term behavior. The study description explains that EMI-II was intended to link situations where smoking is likely with alternative responses, but the primary results do not test whether those responses reduced cigarette use. No secondary results are posted in the registry record, so conclusions about the broader aims of acceptability and initial effectiveness are not supported by these outcome data.

The endpoint title refers to a percent, but the reported outcome is a count. Counts can be read alongside the participant numbers for each condition, but the registry does not post the corresponding percentages. The completion definition and missing-data procedures are also not reported. As a result, the exact meaning of completion and the handling of participants without recorded outcomes cannot be fully assessed.

The design is labeled randomized and crossover, yet the registry does not explain the sequence, period structure, or analysis of repeated observations. The posted comparison should therefore be understood as a summary contrast, not as a complete account of all design features. The result does not establish equivalence between conditions, nor does it establish a causal effect on smoking. It describes the completion data and their uncertainty, with important analytical and reporting details not available in the registry record.

16. Why This Trial Matters Statistically

Feasibility outcomes are important in intervention research because a behavior-change approach can only be evaluated further if participants can engage with and complete its procedures. This study combines ecological momentary assessment with implementation-intention messages delivered by text message, and its primary endpoint focuses on completing the two-week period. The outcome therefore addresses a practical question about participation in the intervention process, distinct from whether smoking behavior changed.

The statistical interpretation also illustrates why an estimate, confidence interval, and p-value should be read together. The point estimate alone suggests a direction for the completion contrast, but the interval spans values on either side of no difference. The p-value does not establish equivalence, and the relative-effect intervals are also broad. Looking at uncertainty prevents the point estimate from being treated as a definitive finding.

The distinction between the endpoint title and the reported count is another useful statistical reporting issue. A measure described as a percent can be difficult to interpret when the posted result is a count. Clear endpoint definitions, denominators, missing-data rules, and analysis populations are important for determining what a feasibility result means and how it can be compared across studies.

Finally, the crossover label makes transparent reporting of periods and analysis methods especially relevant. Repeated outcomes may be correlated within participants, and period or sequence features may affect interpretation. The registry record does not describe how these issues were handled. This does not negate the descriptive value of the posted counts, but it identifies why registry summaries alone may not support a full evaluation of the statistical analysis.

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 leaves several trial-specific details unresolved. Although the design is labeled crossover, it does not report the sequence of conditions, the full period schedule, washout procedures, or the method used to account for repeated measurements. Those details matter for interpreting a condition comparison when participants may contribute observations in more than one condition. The posted summary does not establish whether the analysis treated condition outcomes as independent or paired.

The primary endpoint title refers to a percent, but the posted result is a count. The registry does not report a detailed completion definition, assessment rules, or how missing outcome data were handled. It also does not identify the analysis population or explain whether participants with incomplete follow-up were included in a particular way. These omissions restrict interpretation of the completion counts and comparison.

The brief summary refers to a sample of adults who smoke a minimum of 15 cigarettes per day and includes n=100, while the enrollment field records 80. The relationship between those entries is not explained in the registry record. The registry also does not report the original sample-size rationale, full eligibility criteria, or a detailed account of the intervention content and delivery beyond the available arm descriptions. The Waitlist arm description is truncated, leaving its later procedures unclear.

There are three registered outcome measures, but no secondary results are posted. The statistical analysis plan, multiplicity procedures, interim analyses, and methods for assessing acceptability are not reported. These limitations concern what can be concluded from the registry record; they do not determine whether the unreported methods or results exist elsewhere.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Ecological Momentary Intervention of Implementation Intentions Delivered by Text Message to Reduce Cigarette Smoking — NCT04967885.
• Registry record last updated 2023-04-24; status last verified 2023-03.
• Results first posted 2023-03-27.
• 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

The registry identifies NCT04967885 as a completed, randomized, unmasked crossover study of the Ecological Momentary Implementation Intentions Intervention for cigarette smoking. The sponsor is Trustees of Dartmouth College. Enrollment is recorded as 80, with a start date of 2021-06-08 and primary completion date of 2021-12-31.

The primary outcome is completion of the two-week intervention period, assessed at Week 2 for Immediate Intervention and week 4 for Waitlist. The posted counts are 25 among 39 in Immediate Intervention and 31 among 41 in Waitlist. The unadjusted risk difference is 0.115, with a confidence interval from -0.085 to 0.315 and p = 0.262. The record does not post secondary outcome results or full details of the analysis, missing-data handling, or crossover procedures.