Lung Cancer Screening Eligibility Assessment: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Lung Cancer Screening Eligibility Assessment (NCT06133816), a randomized na study. The primary outcome is Full Survey Completion.

2. Clinical Question

This is a study of survey response behavior, not a trial of lung cancer screening itself. The tool was intended to estimate pack-year eligibility, and the main outcome was whether participants completed the survey. The registry describes the purpose as evaluating whether different messaging affects response rates and informing future work to increase responses to the tool. The endpoint therefore concerns engagement with a brief survey, rather than whether a participant was eligible for screening, received screening, or experienced a health outcome.

The posted comparisons address each of the other 11 arms against the reference arm. They do not directly compare every possible pair of message combinations, nor do they report a single combined estimate for the introductory message, tobacco-use message, or incentive factors. The registry record does not report a statistical plan explaining whether these individual comparisons were intended as the primary inferential approach.

3. Trial Design

The registry describes a completed, randomized, single-masked, factorial behavioral study. Enrollment was 6125. The study dates listed in the registry record are 2023-07-31 for start and 2024-01-31 for primary completion. The condition listed is lung cancer, but the activity evaluated was messaging around a text-message survey rather than a clinical treatment.

The 12 arms combine three introductory-message versions, two tobacco-use-message versions, and the presence or absence of a financial incentive. The reference arm received introductory message A and tobacco-use message A plus an incentive. The remaining arms vary one or more of those elements. This arrangement allows the study to examine a range of message packages, but the posted results are individual arm comparisons with the reference, not estimates of main effects or interactions for each factorial component.

Arm sizes in the primary outcome results range from 509.0 to 515.0 participants. The full survey outcome counts range from 335.0 to 402.0 across the 12 arms. The registry lists no reported analyses. It does not report the randomization procedure, the identity of the masked party, or whether the posted comparisons follow a prespecified analysis plan. Details of recruitment, participant characteristics, and the original sample-size justification are also not reported in the registry record.

The primary outcome timeframe was 7 days. A secondary outcome was partial survey completion, also assessed within 7 days. The registry record marks the study as completed. This design addresses whether the tested messaging packages were associated with survey completion in this study; it does not establish how the same packages would perform in a different setting or population.

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.

Before assignment: No significant events

Only the first 6 of 12 groups are shown.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Only the first 6 of 13 groups are shown.

6. Primary Endpoint

The registry lists the primary outcome as Full Survey Completion, measured over 7 days.

The primary endpoint is full survey completion: the number of participants who answered all three survey questions by text message among all participants randomized. The registry specifies a 7-day timeframe. The posted results give both the number completing the survey and the number randomized in each arm. For example, Arm 1 had 358.0 full completions among 509.0 participants, while Arm 8 had 402.0 among 509.0.

This endpoint is relevant to the study’s stated purpose because the simplified tool depends on people responding to questions about tobacco use in order to estimate pack-year eligibility for lung cancer screening. A response outcome can indicate how well a messaging approach engages participants with the survey. It does not measure whether the estimated eligibility was accurate, whether screening occurred, or whether a participant’s health changed.

Full completion is also distinct from partial completion. A participant who answered some, but not all three questions, would not meet the primary endpoint definition. Partial Survey Completion was posted as a secondary outcome. The registry does not report additional endpoint details such as how incomplete responses were handled beyond the stated definition, or whether any outcome adjudication was used.

Because the endpoint is binary at the participant level, the arm-level counts describe how many participants did or did not meet the completion definition. The reported risk differences compare the completion proportions between an arm and the reference arm. They express the absolute difference in those proportions, with positive values indicating a higher observed completion proportion in the named arm.

7. Results Posted in the Registry

• Arm 2 (Introductory Message A + Tobacco Use Message A): 74.9% (381/509) versus 70.3% (358/509) on control; risk difference 4.5 percentage points (95% CI -1.0 to 10.0), risk ratio 1.06 (0.99–1.15); unadjusted two-proportion z-test p = 0.106.
• Arm 3 (Introductory Message A + Tobacco Use Message B + Incentive): 74.4% (383/515) versus 70.3% (358/509) on control; risk difference 4.0 percentage points (95% CI -1.4 to 9.5), risk ratio 1.06 (0.98–1.14); unadjusted two-proportion z-test p = 0.149.
• Arm 4 (Introductory Message A + Tobacco Use Message B): 76.4% (389/509) versus 70.3% (358/509) on control; risk difference 6.1 percentage points (95% CI 0.7 to 11.5), risk ratio 1.09 (1.01–1.17); unadjusted two-proportion z-test p = 0.028.
• Arm 5 (Introductory Message B + Tobacco Use Message A + Incentive): 72.9% (372/510) versus 70.3% (358/509) on control; risk difference 2.6 percentage points (95% CI -2.9 to 8.1), risk ratio 1.04 (0.96–1.12); unadjusted two-proportion z-test p = 0.356.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Partial Survey Completion

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Arm 2 (Introductory Message A + Tobacco Use Message A): 79.6% (405/509) versus 74.1% (377/509) on control; risk difference 5.5 percentage points (95% CI 0.3 to 10.7), risk ratio 1.07 (1.00–1.15); unadjusted two-proportion z-test p = 0.038.
  • Arm 3 (Introductory Message A + Tobacco Use Message B + Incentive): 76.5% (394/515) versus 74.1% (377/509) on control; risk difference 2.4 percentage points (95% CI -2.8 to 7.7), risk ratio 1.03 (0.96–1.11); unadjusted two-proportion z-test p = 0.366.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Arm 2 (Introductory Message A + Tobacco Use Message A) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Arm 3 (Introductory Message A + Tobacco Use Message B + Incentive) and the control. The interval gives the range of effects that remain compatible with the data.

Partial Survey Completion is the posted secondary outcome and uses the same 7-day timeframe. The record gives completion counts for all 12 arms, with the reference arm at 377.0 of 509.0 participants. The partial-completion counts across the arms range from 345.0 to 414.0. The registry posts comparison statistics against the reference for Arm 2 and Arm 3, but does not post comparison analyses for the other arms or a complete set of secondary-outcome tests.

Full and partial completion represent different levels of survey response. The primary endpoint requires answers to all three questions, whereas partial completion concerns an incomplete survey. Together, these outcomes describe different aspects of engagement with the text-message tool. The registry does not specify whether partial completion includes every participant who did not complete all questions or provide a more detailed operational definition, so the two measures should not be assumed to be mutually exclusive categories beyond their stated descriptions.

The secondary counts offer additional context for the primary response pattern, but they do not replace the full-completion endpoint. The two posted secondary comparisons are not a basis for a comprehensive ranking of the message packages. They also do not establish that partial responses translate into successful eligibility estimates or subsequent screening.

Unadjusted secondary results generally carry less inferential weight when multiple outcomes and arm comparisons are considered, particularly when the registry does not report a prespecified hierarchy or multiplicity adjustment. These results are most appropriately viewed as descriptive or exploratory evidence about response behavior. The registry does not report a secondary-outcome analysis plan, additional adjusted analyses, or whether the findings were intended to support confirmatory claims.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Partial Survey Completion

9. Statistical Interpretation

10. Statistical Methods Explained

What does the risk difference represent?

A risk difference is the difference between the proportion meeting an outcome definition in one arm and the proportion in the reference arm. Here the outcome is full survey completion. A positive risk difference means the observed proportion completing all three questions was higher in the named arm; a negative difference means it was lower. The difference is expressed on a proportion scale, not as a relative percentage change. For instance, the posted Arm 8 risk difference is 0.086. That estimate describes the observed contrast; it does not by itself establish that the message package caused a reproducible change.

How should a confidence interval be read?

A confidence interval describes the statistical uncertainty around an estimate under the assumptions of its calculation. A wider interval indicates less precision, while a narrower interval indicates greater precision. For the risk differences, zero represents no absolute difference between the arm proportions. An interval entirely above zero is consistent with a positive difference at the stated confidence level; an interval entirely below zero is consistent with a negative difference. When the interval crosses zero, the data do not clearly distinguish the estimate from no difference at that level. This is a general interpretation of intervals, not a statement that every possible source of uncertainty has been captured.

What do the p-values add?

The posted p-values are unadjusted. In general, a p-value describes how compatible the observed data are with a specified null hypothesis, under the statistical test’s assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of a difference. Because there are multiple arm comparisons against one reference, unadjusted p-values do not account for the increased chance of at least one apparently unusual result across a family of tests. A multiplicity procedure or prespecified testing hierarchy is not reported in the registry record.

What is the role of randomization and the factorial layout?

Randomization is intended, in general, to make comparison groups similar on average with respect to factors other than assigned study conditions. The registry identifies the allocation as randomized, but the sequence generation and allocation concealment procedures are not reported. The factorial structure combines introductory-message versions, tobacco-use-message versions, and incentive conditions. Factorial designs can estimate separate component effects and interactions if the analysis plan and model are specified to do so. The posted results instead give separate comparisons for the 11 non-reference arms against Arm 1. The registry does not report analyses that isolate the independent contribution of each component or test interactions.

What is not documented about the analysis?

The registry lists zero reported analyses. It does not report a statistical model, covariate adjustment, handling of missing outcome data, analysis population, or original design assumptions. The risk differences, intervals, and p-values are presented as unadjusted comparisons. Without additional analysis documentation, readers should not infer that a particular regression model, stratification, or planned subgroup approach was used.

The outcomes are binary counts: a participant either met the full-completion definition or did not. General methods for binary outcomes compare proportions or model the probability of an event. The choice of method can affect intervals and tests, especially when accounting for covariates or a factorial structure. The posted record does not identify the method used to calculate the comparisons, so this explanation describes the statistics’ general meaning rather than asserting a particular model.

11. Confidence Intervals and Precision

The confidence intervals convey how precisely each arm contrast is estimated. For the primary outcome, the reported risk-difference intervals have different widths. Arm 8’s interval extends from 0.033 to 0.140, while Arm 12’s extends from -0.043 to 0.069. The former is wholly above zero, whereas the latter includes zero and spans both positive and negative differences. The interval is uncertainty around the comparison, not a range of individual participant outcomes.

Several intervals are compatible with a positive difference, while others include zero. This variation matters because an estimate alone can look more decisive than the underlying precision warrants. For example, the Arm 2 estimate is 0.045, but its interval from -0.009 to 0.100 includes zero. The Arm 4 estimate is 0.061, with an interval from 0.007 to 0.115 that lies above zero. Confidence intervals are generally more informative than treating a p-value as a yes-or-no conclusion, because they show both the direction and range of uncertainty in the estimated contrast.

Precision is affected by the number of participants and the frequency of the outcome, as well as the method used to calculate the interval. Arm sizes are similar, between 509.0 and 515.0, but similar group sizes do not make every estimate equally precise. The registry does not report the exact interval method or whether adjustment was made for any design features. The posted intervals therefore need to be read as the reported uncertainty for the individual comparisons, not as accounting for all uncertainty from multiple comparisons or unreported design details.

These intervals describe the precision of contrasts in the enrolled study sample. They do not guarantee that a future study would produce an estimate inside the same interval, and they do not resolve uncertainty about generalizability. For this survey-response outcome, the interpretation is limited to the posted population and 7-day follow-up context.

12. 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, not total events. They are illustrations based on the observed effect for a comparison, with alternative scenarios for detecting 100% of the observed effect, 75% of the observed effect, or 50% of the observed effect. The stated planning assumptions 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 registry’s original design assumptions and sample-size justification are not reported.

The 80% power column gives the estimated participants per arm for a planning scenario designed to have an 80% chance of detecting the specified effect under the stated assumptions, if that effect is the true one and the assumptions hold. The 90% power column gives the corresponding per-arm planning figure for a 90% chance. These are design probabilities used to plan a hypothetical comparison, not probabilities that the observed result is correct or that a finding will replicate.

Smaller effects require more participants to distinguish them from chance variation with the same planned power. This is why the displayed figures increase when the target is reduced from 100% of the observed effect to 75% or 50%. Scenarios based on the observed effect can be unstable, especially when that estimate is imprecise. These figures are not observed power: they do not tell how much power the completed trial had after seeing its results. For a factorial study with multiple arms, the illustrations are comparison-specific and should not be treated as the original total enrollment target.

13. 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 = 0.703; treatment proportion p₁ = 0.749; average p̄ = 0.726.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6308 = 1.2363.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6300 = 0.5302.
4. n = (1.2363 + 0.5302)² / (0.0452)² = 1,528.4, rounded up to 1,529 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 <- 0.703339882121807                          # control proportion
p1 <- 0.74852652259332                          # 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(6133816)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 1,529 (80% power), 2,046 (90% power)
 75% of observed effect: n per arm = 2,753 (80% power), 3,685 (90% power)
 50% of observed effect: n per arm = 6,271 (80% power), 8,394 (90% power)
power.prop.test: 1528.4 
Simulated power at n = 1,529 per arm: 0.797 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The study has multiple message packages and a common reference arm, and the primary results include 11 comparisons. A secondary outcome is also posted, with comparison statistics available for two arms. When many comparisons are examined, the probability of finding one result that appears statistically notable can increase even if there are no real differences. This is the general multiplicity problem. The posted p-values are unadjusted, and the registry record does not report a multiplicity correction, testing hierarchy, or prespecified strategy for interpreting the collection of comparisons.

The factorial arrangement creates further questions about whether the purpose was to compare the 12 complete packages or to estimate effects for individual message factors and their combinations. The posted comparisons address complete arms against Arm 1. The registry does not report separate estimates for introductory-message versions, tobacco-use-message versions, incentive effects, or interactions between these elements. The intended primary contrast structure is not reported in the registry record.

Missing-data procedures and analysis populations are also not reported. The endpoint definition uses all randomized participants as the denominator, and arm-level outcome counts are posted. However, the registry does not explain how unavailable or incomplete responses were classified for the primary endpoint, whether follow-up status was known for every randomized participant, or whether any participants were excluded from analyses. It does not identify an intention-to-treat or per-protocol analysis population.

The registry lists zero reported analyses. It also does not report covariate adjustment, subgroup analyses, interim analyses, or the method used to handle missing outcome data. These omissions limit assessment of whether the posted comparisons were prespecified and how robust they are to alternative analysis choices. They do not invalidate the counts, but they mean that inferences should be anchored to the reported arm-level results and their stated unadjusted uncertainty.

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 registry reports serious adverse events, other adverse events, and deaths for each of the 12 arms. For every listed arm, the serious adverse event count is 0, the other adverse event count is 0, and the death count is 0. The number at risk is listed separately for each arm; for example, Arm 1 has 509 participants at risk and Arm 3 has 515.

These entries describe what was recorded in the registry’s adverse-event fields. They should not be read as proof that no adverse event of any kind occurred outside what was captured or reported. The registry does not list serious adverse event terms, and it provides no further explanation of the collection or reporting procedures. Because this was a behavioral messaging and survey study, the posted safety counts concern the study record’s adverse-event reporting; they are not measures of survey completion or message effectiveness.

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

The results describe response to a brief text-message survey in a randomized study of message framing and a financial incentive. Across the 12 arms, the number of full completions and the reported completion proportions vary. Several arm-to-reference comparisons have positive risk-difference estimates with confidence intervals that exclude zero, while other comparisons have intervals that include zero. The posted data therefore show differences in observed completion patterns, with varying statistical precision.

The study does not test lung cancer screening uptake, the accuracy of the simplified eligibility tool, cancer detection, or health outcomes. A higher full-completion proportion would indicate more participants answered all three survey questions within the stated period; it would not establish that more eligible people were screened. Nor do these arm-level comparisons identify which individual message feature explains the observed differences. That would require analyses designed to separate the components of the factorial arrangement, which are not reported in the registry record.

The estimates are subject to uncertainty, and the p-values are unadjusted across multiple comparisons. The registry’s lack of a reported analysis plan, multiplicity procedure, and missing-data approach limits the strength of conclusions that can be drawn from the comparisons. Findings from a single completed trial also do not establish how the messages would perform in other settings or populations. Participant characteristics and recruitment details are not reported in the registry record.

The appropriate interpretation is therefore bounded: the posted results characterize completion of this 7-day text-message survey across the tested message packages. They can inform understanding of response behavior in this trial, but do not establish a clinical benefit, a universal best message, or a result that necessarily applies beyond the study context.

17. Why This Trial Matters Statistically

This trial is statistically informative because it treats survey response as an outcome that can itself be studied experimentally. A screening-eligibility tool depends on people answering the questions it asks; a tool that estimates eligibility but receives few complete responses may be difficult to use in later research. By randomizing participants across message packages, the study investigates whether the presentation surrounding a survey is associated with completion behavior.

The factorial arrangement illustrates both the opportunity and the analytic challenge of testing several components at once. Introductory framing, tobacco-use framing, and an incentive are combined in 12 packages. Such a design can be useful for separating component effects when the analysis plan specifies how those effects and interactions will be estimated. The posted arm-to-reference contrasts, however, answer a narrower question about each package relative to one particular package. They do not identify independent effects of each component.

The trial also makes clear why effect estimates, confidence intervals, and multiplicity deserve attention alongside p-values. Some estimated differences are more precise than others, and the many unadjusted comparisons complicate interpretation of individually notable results. The sample-size illustrations show how planned enrollment depends on the effect a future study aims to detect, but they are not evidence about the power of this completed trial.

More broadly, the record distinguishes survey-methodology outcomes from clinical outcomes. Full completion may matter for designing future screening research, but it is not equivalent to screening eligibility or screening participation. This distinction helps keep statistical conclusions aligned with what was actually measured.

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.

The outcome is a short-term response measure: full completion of three text-message survey questions within 7 days. It does not establish whether the simplified tool accurately estimates pack-year eligibility, whether participants proceed to lung cancer screening, or whether screening outcomes change. The registry does not report longer follow-up for these questions.

The arm comparisons use a single reference package, and the registry does not report a factorial analysis that separates the effects of introductory framing, tobacco-use framing, and incentive. The posted p-values are unadjusted despite multiple comparisons, and no multiplicity strategy is documented. The registry lists no reported analyses, leaving the statistical model and whether analyses were prespecified unclear.

Participant characteristics, recruitment details, the randomization procedure, the identity of the masked party, and the original sample-size justification are not reported in the registry record. Missing-data handling and the analysis population are also not reported. These omissions make it difficult to assess how representative the enrolled participants were, how fully the randomized groups were followed, and whether the posted analyses reflect all randomized participants as intended.

The interpretation is further limited by the nature of the endpoint: a completed survey is a behavioral response, not a direct measure of screening eligibility or subsequent care. Results describe the tested combinations in this study and should not be assumed to generalize to other populations or messaging contexts. The record does not report whether the messages were tested in additional settings.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Lung Cancer Screening Eligibility Assessment — NCT06133816.
• Registry record last updated 2025-05-31; status last verified 2025-05.
• Results first posted 2025-05-31.
• 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

NCT06133816, titled Lung Cancer Screening Eligibility Assessment, is a completed randomized, single-masked, factorial behavioral study sponsored by Abramson Cancer Center at Penn Medicine. The registry lists enrollment of 6125 and evaluates message combinations, with or without a financial incentive, for a text-message survey intended to estimate pack-year eligibility for lung cancer screening.

The primary outcome was full survey completion within 7 days, defined as answering all three questions among randomized participants. Partial Survey Completion was listed as a secondary outcome. The primary results report 12 arms and comparisons of 11 arms against Arm 1. Several unadjusted comparisons have confidence intervals excluding zero; interpretation is limited by multiple comparisons and analysis details not reported in the registry record.

All listed arms report zero serious adverse events, zero other adverse events, and zero deaths. The registry record does not report the original sample-size justification, detailed analysis plan, missing-data procedures, or participant characteristics.