Reducing Lung Cancer-Related Anxiety (RELAX): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Reducing Lung Cancer-Related Anxiety (RELAX) (NCT02063828), a randomized na study. The primary outcome is Retention - Number of Participants Who Complete the Final Assessment.

2. Clinical Question

The registry describes RELAX as a study comparing music and different levels of device-guided breathing for anxiety and shortness of breath in lung cancer survivors. The named groups, however, are low-dose device-guided breathing, high-dose device-guided breathing, and usual breathing. The record does not explain how music relates to those groups, so the intervention contrast should be understood from the named group descriptions rather than inferred from the study summary.

The primary outcome is retention, not a direct measure of anxiety or shortness of breath. The record also lists change in anxiety measured by the Hospital Anxiety and Depression Scale (HADS) as a secondary outcome. It does not post an analysis of that measure. Thus, the posted group comparisons address completion of the final assessment; they do not answer whether anxiety or shortness of breath changed.

3. Trial Design

RELAX (NCT02063828) is recorded as a randomized, parallel-group trial with quadruple masking. The registry lists the phase as NA. Wake Forest University Health Sciences is listed as sponsor. The record gives a start date of 2015-07-30 and a primary completion date of 2019-12-23, and the study status is terminated. The reason for termination is not reported in the registry record.

The registry lists an enrollment of 46. The posted group sizes are 14 for Group A, 14 for Group B, and 18 for Group C. Group A is device-guided breathing at low dose, Group B is device-guided breathing at high dose, and Group C is the usual-breathing control group. The record does not describe the randomization sequence, allocation concealment, or the details of the masking procedures; those details are not reported in the registry record.

The primary outcome is retention, defined as completion of the final assessment divided by the number randomized, with a 12-week timeframe. The record lists seven outcome measures and identifies one secondary outcome: change from baseline in anxiety measured by HADS. It posts no analyses for the listed outcomes. The results presented for retention are counts of participants completing the final assessment, with comparisons between Group A and each of the other groups.

The study summary refers to music as well as different levels of device-guided breathing. The three listed intervention descriptions do not identify a music group or explain its role. That discrepancy in description cannot be resolved from the registry record, so the group names are the clearest available basis for describing the randomized arms.

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: In this feasibility study, participants were stratified by baseline self-reported dyspnea score and randomized to a 12-week high-dose or low-dose device-guided breathing intervention versus a usual breathing control group with equal probability, using variable length permuted block randomization. All participants enrolled were randomized and included in analyses.

Overall Study

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.

6. Primary Endpoint

The registry lists the primary outcome as Retention - Number of Participants Who Complete the Final Assessment, measured over 12 weeks.

The primary endpoint is retention at the final assessment, with the assessment scheduled at 12 weeks. The registry defines retention as the number of participants who complete that assessment divided by the number randomized. The posted results give the completion counts within each group: 10 of 14 in Group A, 8 of 14 in Group B, and 14 of 18 in Group C.

Retention is used to describe whether participants remain available for assessment through the trial’s stated follow-up point. It is relevant to interpreting other outcomes because incomplete follow-up can leave some randomized participants without measurements at that time. The endpoint itself does not measure anxiety, shortness of breath, or a change in health status. It records completion of an assessment.

The registry’s definition refers to a proportion, but the posted group results are counts. The reported comparisons express differences in the proportion completing the assessment. They should be read as comparisons of observed retention in these groups, not as estimates of treatment effects on symptoms. The record does not describe how missing final assessments were handled in analyses of other outcomes, and it does not post an analysis of the HADS secondary outcome.

Completion counts can indicate how much follow-up was achieved in each group, but they do not explain why participants did or did not complete the assessment. Reasons for non-completion are not reported in the registry record. Nor does the endpoint establish whether missingness was related to participants’ symptoms, treatment experience, or other characteristics.

7. Results Posted in the Registry

• Group B: 57.1% (8/14) versus 71.4% (10/14) on control; risk difference -14.3 percentage points (95% CI -49.4 to 20.8), risk ratio 0.80 (0.46–1.40); unadjusted two-proportion z-test p = 0.430.
• Group C: 77.8% (14/18) versus 71.4% (10/14) on control; risk difference 6.3 percentage points (95% CI -24.1 to 36.8), risk ratio 1.09 (0.72–1.65); unadjusted two-proportion z-test p = 0.681.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: a participant either completed the final assessment or did not. The registry reports the number completing the assessment and the group size. A risk is the proportion of participants with the event of interest; in this outcome, the event is completion. A risk difference subtracts the reference group’s risk from the comparison group’s risk. A negative difference means the observed completion proportion was lower in the comparison group, while a positive difference means it was higher. The posted contrasts compare Group B with Group A and Group C with Group A.

In general, a risk difference is expressed on the absolute probability scale. It describes the separation between two proportions rather than a relative change. The reported estimates are -0.143 for Group B versus Group A and 0.064 for Group C versus Group A. These are the registry’s posted comparison estimates; no additional arithmetic is needed to interpret their direction. They do not account for any covariates in the information available in the registry record.

The registry also posts relative measures, including risk ratios and odds ratios. In general, a risk ratio compares the event risks between groups, while an odds ratio compares event odds. A value on the null scale for either relative measure corresponds to no relative contrast; for a risk difference, the corresponding no-difference value is zero. Relative measures can be harder to interpret when the event is common, and the odds ratio should not be read as though it were a risk ratio. The most direct interpretation for retention is usually the absolute completion difference, alongside its uncertainty.

A confidence interval describes a range of estimates compatible with the data and the method used to calculate the interval. It is not a guarantee that the true value lies inside the particular interval, nor does it describe the probability that a treatment is beneficial. In these comparisons, both risk-difference intervals include zero and extend in both directions. That pattern means the data are compatible with either lower or higher retention in the comparison group than in Group A, as well as little or no difference. The wide spans indicate limited precision.

The p-values posted for these comparisons are unadjusted. In general, a p-value measures how unusual data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the test assumptions held. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of a difference. The p-values should be interpreted alongside the effect estimates and confidence intervals, not as stand-alone evidence. The statistical analysis plan, including any prespecified testing approach, is not reported in the registry record.

The registry identifies the comparison metric as a risk difference and reports counts, group sizes, relative measures, intervals, and unadjusted p-values. The record does not report a model specification, adjustment variables, handling of protocol deviations, or the analysis population used for these comparisons. It is therefore not possible to determine from the record whether any analyses beyond the posted group-level comparisons were planned or conducted.

In general, missing outcome data can affect interpretation if the probability of missingness differs between groups or is related to the unobserved outcome. Here, retention is itself the primary endpoint, so non-completion is counted as an outcome rather than treated as an unobserved retention status. For other outcomes, however, the registry does not state how missing observations were handled. Reasons for non-completion and the relationship between missingness and participant characteristics are not reported in the registry record.

In general, masking is intended to reduce the influence of knowledge about group assignment on trial conduct or assessment. The registry labels the trial quadruple-masked, but does not identify which people or roles were masked, how masking was maintained, or whether it could be assessed. No further inference about the success of masking can be made from the label alone.

In general, a randomized parallel-group design assigns participants to groups and compares outcomes across those groups. Randomization can support fair comparisons when properly implemented, but the registry record does not provide the sequence-generation or concealment details needed to assess those procedures. The group-level retention estimates describe the randomized groups as posted; the record does not specify an alternative analysis population or report adjusted estimates.

The registry lists a HADS anxiety change outcome but posts no analysis. It also lists seven outcome measures and reports zero analyses. Consequently, the posted retention results cannot be used as a substitute for analyses of the symptom outcomes or as evidence about the trial’s broader stated purpose. The sponsor’s statistical analysis plan and the trial’s original analysis methods are not reported in the registry record.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an estimated effect. The risk-difference estimate for Group B versus Group A is -0.143, with a 95% confidence interval from -0.494 to 0.208. For Group C versus Group A, the estimate is 0.064, with a 95% confidence interval from -0.241 to 0.368. Each interval includes zero, the value corresponding to no absolute difference in completion.

The intervals also extend meaningfully in both directions. For Group B, the compatible values include lower retention in Group B and higher retention in Group B relative to Group A. The same is true for Group C relative to Group A. The point estimates alone therefore do not convey the full uncertainty: the ranges allow interpretations that differ in direction as well as magnitude.

These intervals are wide in relation to the point estimates, consistent with limited precision in the posted comparisons. Small group sizes contribute to uncertainty, although the registry record does not provide a detailed precision analysis or adjusted estimates. The results do not tightly distinguish a small difference from a larger difference in either direction.

A confidence interval is not a measure of clinical importance, and it cannot identify which possible difference matters to patients or researchers. The registry does not provide a threshold for a meaningful retention difference. The intervals apply to the retention comparisons, not to anxiety or shortness of breath; analyses and uncertainty estimates for those outcomes are not reported in the registry record.

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 illustrations are planning calculations based on the observed retention effects, not a report of the trial’s original design. The figures are participants per arm for 80% power and participants per arm for 90% power. They are not total event counts. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each illustration uses the stated fraction of the observed effect as the effect to detect.

For Group B versus Group A, planning for 100% of the observed effect gives 176 participants per arm for 80% power and 235 participants per arm for 90% power. Planning for 75% of the observed effect gives 306 participants per arm for 80% power and 409 participants per arm for 90% power. Planning for 50% of the observed effect gives 670 participants per arm for 80% power and 897 participants per arm for 90% power.

For Group C versus Group A, planning for 100% of the observed effect gives 737 participants per arm for 80% power and 986 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,338 participants per arm for 80% power and 1,790 participants per arm for 90% power. Planning for 50% of the observed effect gives 3,068 participants per arm for 80% power and 4,107 participants per arm for 90% power.

In plain terms, the 80% column describes the planned number per group for a design with an 80% chance of detecting the specified effect under the stated assumptions; the 90% column describes the corresponding target for a 90% chance. The curve expresses how planning sample size changes with the effect being targeted. Smaller effects need more participants, and higher target power also requires more participants. These are planning illustrations, not observed power. The trial’s own original sample-size 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 = 0.714; treatment proportion p₁ = 0.571; average p̄ = 0.643.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6776 = 1.3281.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6701 = 0.5639.
4. n = (1.3281 + 0.5639)² / (-0.1429)² = 175.4, rounded up to 176 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 <- 0.714285714285714                          # control proportion
p1 <- 0.571428571428571                          # 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(2063828)
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 = 176 (80% power), 235 (90% power)
 75% of observed effect: n per arm = 306 (80% power), 409 (90% power)
 50% of observed effect: n per arm = 670 (80% power), 897 (90% power)
power.prop.test: 175.4 
Simulated power at n = 176 per arm: 0.800 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The registry lists seven outcome measures, identifies one secondary outcome, and reports zero analyses. The listed secondary outcome is change from baseline in anxiety measured by HADS. No result for that outcome is posted. The analyses available for interpretation are the retention comparisons, so the record does not show how many outcomes were tested or whether any outcome-specific analyses were completed outside the posted results.

Multiplicity arises when several outcomes or comparisons are tested: the chance of at least one apparently noteworthy result can increase as the number of tests grows. In general, adjustment or a prespecified hierarchy can address some multiplicity concerns, but the registry record does not report an adjustment method, testing hierarchy, or statistical analysis plan. The p-values shown for retention are explicitly unadjusted. They should not be treated as multiplicity-adjusted evidence.

Retention is based on completion of the final assessment. The registry gives the counts of participants completing that assessment and group sizes. It does not report reasons for missing assessments, whether non-completion differed by participant characteristics, or how missing values were handled for other endpoints. Since HADS is listed as a change-from-baseline outcome, interpretation would require information about available baseline and follow-up measurements and the analysis approach; those details and results are not reported in the registry record.

The record does not describe an intention-to-treat, per-protocol, or other analysis population. It also does not provide information about protocol deviations, exclusions after randomization, or imputation. These omissions prevent assessment of how the posted comparisons relate to a prespecified analysis population. The trial’s termination status is recorded, but its reason and any implications for outcome availability are not 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 5% reporting threshold.

The serious adverse event figures report zero serious adverse events among the participants at risk in Group A, zero in Group B, and zero in Group C. The registry also reports zero other adverse events in each group. One death is recorded in Group C; no deaths are recorded in Group A or Group B. The record does not provide a cause for the death or establish whether it was related to the intervention or study procedures.

These are counts, not comparative safety estimates. Zero recorded events in a group does not prove that the risk is absent, particularly when the number of participants observed is limited. The counts also do not show when events occurred or how they were assessed. The registry lists no top serious adverse-event terms. Further details about event definitions, attribution, timing, and the safety monitoring process are not reported in the registry record.

Accordingly, the figures should be read as the adverse events posted for the listed groups, rather than as evidence that an intervention caused or prevented an event. The registry does not provide enough detail to make a causal safety comparison.

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

The posted results describe completion of the 12-week final assessment in the three randomized groups. The counts are 10 of 14 in the low-dose device-guided breathing group, 8 of 14 in the high-dose group, and 14 of 18 in the usual-breathing control group. The registry’s risk-difference comparisons put Group B below Group A and Group C above Group A by their point estimates, but both confidence intervals include zero and span differences in either direction.

These findings do not establish that one group had better retention than another. The estimates are imprecise, and the unadjusted p-values do not provide strong evidence against a zero risk difference. Nor do these retention results answer the trial’s stated questions about anxiety or shortness of breath. The registry lists HADS anxiety change as a secondary outcome but posts no analysis of it, and no symptom results are reported in the registry record.

The record also does not explain why the trial was terminated, why some participants did not complete the final assessment, or how missing data were handled for outcomes other than retention. Those gaps limit interpretation of both follow-up and the broader study aims. The study summary mentions music, while the listed groups describe only breathing approaches and usual breathing; the record does not clarify the role of music.

In general, randomized comparisons are intended to estimate differences between assigned groups, but interpretation depends on implementation, follow-up, analysis choices, and the outcome being measured. The posted retention estimates are specific to this registry record and should not be treated as evidence about symptom benefit, clinical importance, or effects in other populations. No medical conclusion follows from these completion counts alone.

16. Why This Trial Matters Statistically

Retention is statistically important because the completeness of follow-up affects how much outcome information is available for a trial. Reporting the number of participants who complete the final assessment makes one part of that follow-up visible. It also places the symptom outcomes in context: without knowing how many participants were assessed, readers cannot judge the extent of observed follow-up from the outcome results alone.

In RELAX, the primary endpoint is retention itself, and the registry supplies completion counts for each group. The comparisons show why counts should be accompanied by uncertainty estimates: the point estimates differ, but the intervals are broad and include zero. A ranked list of group percentages or a p-value alone would not communicate that uncertainty as clearly as the estimates and intervals together.

The record also illustrates the distinction between a trial’s stated purpose and its posted results. The study summary refers to anxiety and shortness of breath, and the secondary outcome list includes HADS anxiety change, but no analyses are posted. That means the available statistical evidence addresses completion rather than the stated symptom questions. Keeping outcome definitions and results distinct prevents retention findings from being misread as symptom findings.

Finally, planning calculations based on observed effects can show how much larger a future study might need to be under specified assumptions, but they do not reconstruct the trial’s original design or establish what the original study could detect. Clear separation between observed results, uncertainty, and planning scenarios is central to statistical interpretation.

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 trial is recorded as terminated, but the reason for termination is not reported in the registry record. Without that context, it is not possible to determine whether termination was related to recruitment, feasibility, safety, or another issue. The record lists enrollment as 46 and gives the posted group sizes, but it does not describe the recruitment process, participant characteristics, or eligibility criteria in detail.

The primary outcome is retention, and the registry provides completion counts and unadjusted group comparisons. It does not report the reasons participants missed the final assessment, a missing-data analysis, or adjustment for possible baseline differences. The record also does not describe the analysis population or provide a full statistical analysis plan. These omissions restrict assessment of how robust the comparisons are to analytic choices.

The outcome reporting is incomplete for the trial’s stated purpose. HADS anxiety change is listed as a secondary outcome, but no analysis is posted. The registry reports seven outcome measures and zero analyses. No posted results address shortness of breath, and the role of music is unclear because the summary mentions music but the listed intervention groups do not. Further outcome definitions and results are not reported in the registry record.

The safety information is limited to group-level event counts. The record gives no serious adverse-event terms, and does not report the cause or relationship of the death recorded in Group C. The masking label and randomized designation are present, but procedural details are not reported in the registry record. These features limit conclusions about trial conduct, safety, and generalizability beyond the posted retention findings.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Reducing Lung Cancer-Related Anxiety (RELAX) — NCT02063828.
• Registry record last updated 2021-03-05; status last verified 2021-03.
• Results first posted 2021-02-18.
• 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

NCT02063828, RELAX, is a randomized, parallel-group, quadruple-masked trial sponsored by Wake Forest University Health Sciences. The registry records the status as terminated, with a start date of 2015-07-30 and primary completion date of 2019-12-23. The listed groups are low-dose device-guided breathing, high-dose device-guided breathing, and usual-breathing control.

The primary endpoint is completion of the final assessment at 12 weeks. The posted counts are 10 of 14 for Group A, 8 of 14 for Group B, and 14 of 18 for Group C. Comparisons against Group A have risk differences of -0.143 for Group B and 0.064 for Group C; both 95% confidence intervals include zero. The record lists HADS anxiety change as a secondary outcome but posts no analyses. The reason for termination and further details about outcome analyses are not reported in the registry record.