Innovation in Pulmonary Rehabilitation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Innovation in Pulmonary Rehabilitation (NCT00123422), a randomized na study. The primary outcome is Exercise Endurance.

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group study of three behavioral interventions. Participants were assigned to exercise training with computerized breathing retraining, exercise training with heliox, or exercise training alone. The study summary calls the intervention an 8-week study. The primary outcome was measured at 14 weeks, so the outcome assessment occurred at a different time point from the stated intervention duration.

The registry records enrollment of 103 and a completed status. The recorded start is 2005-10 and primary completion is 2009-08. The sponsor is the US Department of Veterans Affairs. The study is listed for pulmonary disease and pulmonary emphysema, and its summary describes participants with moderate to severe chronic obstructive pulmonary disease.

Randomization is relevant because, in principle, it supports comparisons between groups by reducing systematic differences in baseline characteristics. The registry record does not report the randomization sequence method or allocation concealment, so those details cannot be assessed from this record. Masking is listed as single, but the registry record does not specify who was masked. It also does not report further details about how adherence to the exercise or breathing interventions was assessed.

The primary outcome description reports an intent-to-treat analysis using last observation carried forward and states that all participants were included in the final analysis. This explains the stated analysis population and missing-data approach, but does not establish how many measurements were missing or whether the assumptions behind carrying the last value forward were appropriate. The trial's original sample-size assumptions and detailed statistical plan 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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: We used an intent-to treat analysis using the last value carried forward. All participants were included in the final analysis.

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 Exercise Endurance, measured over 14 weeks.

The primary endpoint was exercise endurance, measured in minutes on a constant-workrate treadmill test at 14 weeks. In this test, participants exercised at a workload tied to the grade and speed they had reached on a symptom-limited treadmill test at 85% of their peak oxygen uptake. Thus, the endpoint reflects how long participants could sustain a defined exercise workload rather than simply whether they could complete a test.

Exercise endurance is relevant to a pulmonary rehabilitation study because it provides a functional measure of capacity during exercise. A time-based endpoint can capture differences in how long participants sustain the test workload. The interpretation depends on the test protocol, the workload selected for each participant, and the timing of assessment; the registry describes the workload selection and the 14-week measurement time.

The posted arm summaries report means and standard deviations. A mean describes the group average, while the standard deviation describes variation among measured outcomes within a group. The mean is useful for comparing group-level performance, but it does not describe every participant's result or show the full distribution of outcomes. The posted comparisons are expressed as mean differences against breathing retraining, so a negative value indicates a lower reported mean in the comparison group than in the breathing-retraining group. The endpoint is an exercise-test measure, not a direct measure of every aspect of daily functioning or pulmonary health.

7. Results Posted in the Registry

• Heliox: mean 14.50 versus 18.10 on control; difference -3.60 (95% CI -9.35 to 2.15), standardized effect d = -0.30; z-test p = 0.220.
• Exercise: mean 11.50 versus 18.10 on control; difference -6.60 (95% CI -11.61 to -1.59), standardized effect d = -0.62; z-test p = 0.010.

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.

Inspiratory Capacity

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Heliox: mean 2.00 versus 2.40 on control; difference -0.40 (95% CI -0.71 to -0.09), standardized effect d = -0.61; z-test p = 0.011.
  • Exercise: mean 2.10 versus 2.40 on control; difference -0.30 (95% CI -0.63 to 0.03), standardized effect d = -0.43; z-test p = 0.073.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Heliox 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 Exercise and the control. The interval gives the range of effects that remain compatible with the data.

Inspiratory capacity is the posted secondary endpoint. At a broad level, its descriptive pattern is consistent with the primary outcome in that the breathing-retraining group has the highest reported group mean, while the other groups have lower means. This shared direction across the two outcomes can be noted as a pattern, but it does not demonstrate that the outcomes are measuring the same construct or that one explains the other.

The sponsor reports an overall ANCOVA result for inspiratory capacity with p < 0.05. The recalculated pairwise comparisons are unadjusted and should not be treated as the sponsor's adjusted contrasts. As with the primary outcome, the registry record does not provide adjusted effect estimates or confidence intervals for the overall analysis. The secondary endpoint's relationship to the primary finding is therefore best described as broadly similar in the direction of the group summaries, with limited information about adjusted magnitude and precision.

Secondary outcomes generally carry less confirmatory weight than a prespecified primary outcome. Testing multiple outcomes and contrasts creates more opportunities for apparently notable findings to arise by chance. The registry record does not report a multiplicity adjustment, a testing hierarchy, or enough detail to establish how secondary analyses were prioritized. The unadjusted secondary results should consequently be treated as supportive or exploratory evidence rather than as independent confirmation of the primary result. The record lists one posted secondary outcome, but does not establish whether any other outcomes were considered in the original analysis plan.

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

• Inspiratory Capacity

9. Statistical Interpretation

10. Statistical Methods Explained

What does the mean represent?

Exercise endurance is a continuous outcome measured in minutes. For each group, the posted mean is the arithmetic average of the recorded values included in that summary. A mean gives a compact description of the group's central result, but individual outcomes may lie above or below it. The standard deviation describes how dispersed the observations are around the group mean. It is not the same as the uncertainty in the mean: uncertainty also depends on the amount of information available in the group.

What does a mean difference represent?

The recalculated comparisons subtract the breathing-retraining mean from the mean in each comparison group. On that scale, a negative estimate means that the comparison group's posted mean is lower than the breathing-retraining mean. The estimate is a difference in minutes, so its size is interpretable in the outcome's original units. These calculations are unadjusted: they compare the posted group summaries without accounting for covariates or other features of an adjusted model.

How should the confidence interval be read?

A confidence interval gives a range of values compatible with the data and the calculation's assumptions. It represents uncertainty around an estimate, rather than a range containing a stated proportion of individual participant outcomes. An interval that includes zero does not establish that the groups are identical; it indicates that the data and calculation remain compatible with no mean difference as well as with other differences in the interval. An interval excluding zero signals greater incompatibility with a zero difference under the same assumptions, but does not by itself establish clinical importance.

The recalculated intervals are based on unadjusted comparisons of posted means and standard deviations. They should not be read as adjusted ANCOVA intervals. The registry's sponsor-reported analysis is an ANCOVA across the three groups, and its reported result is an overall p-value. The record does not include the ANCOVA's adjusted estimates, standard errors, or confidence intervals, so the adjusted effect size and precision cannot be reconstructed from the registry record.

What does ANCOVA contribute?

Analysis of covariance, or ANCOVA, compares outcome means across groups while accounting for specified covariates. In a randomized study, adjustment can improve precision when the included covariates are related to the outcome and can account for chance baseline imbalance. The value of an adjusted analysis depends on which covariates were included, how they were measured, and whether the model assumptions are reasonable. Those covariates and model details are not reported in the registry record. The reported ANCOVA p-value is for the three-group analysis; it does not supply a separate adjusted estimate for each pair of groups.

Why distinguish an overall test from pairwise comparisons?

An overall test addresses whether the data provide evidence of a difference somewhere among the groups, according to the fitted model. It does not identify which pair differs or quantify every pairwise contrast. Pairwise comparisons answer narrower questions, but conducting several tests raises the chance of obtaining a small p-value by chance if no adjustment is made. The registry record does not report a multiplicity adjustment or a prespecified hierarchy of comparisons. Therefore, the recalculated pairwise p-values should be read as unadjusted exploratory comparisons, not as substitutes for an adjusted sponsor analysis.

What is the role of randomization and masking?

Random allocation is intended to make treatment groups comparable, on average, with respect to factors that could affect the outcome. It does not guarantee that every baseline characteristic is balanced in a particular trial. The registry labels the study randomized and single-masked, but the sequence generation, concealment procedures, and identity of the masked parties are not reported in the registry record. These omissions limit assessment of how assignment and masking were implemented.

What does last observation carried forward assume?

The primary outcome description states that the analysis used last observation carried forward and included all participants. This approach replaces a missing later measurement with an earlier observed value. It implicitly assumes that the carried-forward value is a reasonable stand-in for the unobserved endpoint, which may be unsuitable if outcomes change over time or missingness is related to participants' condition or treatment experience. The registry record does not report the extent or pattern of missing data, or sensitivity analyses using alternative assumptions. The stated intent-to-treat approach describes the analysis population, but it does not remove uncertainty created by missing outcomes.

11. Confidence Intervals and Precision

Precision concerns how much uncertainty surrounds an estimate. The recalculated confidence intervals provide more information than the point estimates alone because they show a range compatible with the posted data under the unadjusted calculation. For heliox compared with breathing retraining, the estimated difference is -3.6 minutes and the interval runs from -9.348 to 2.148. That span includes zero, as well as values in either direction. The unadjusted result therefore does not pin down the direction of the mean difference precisely.

For exercise alone compared with breathing retraining, the estimated difference is -6.6 minutes and the interval runs from -11.61 to -1.591. The interval is entirely below zero, but it still covers a range of possible magnitudes. Neither interval says how much individual outcomes vary; that is what the group standard deviations describe. Nor does either interval establish whether a difference is meaningful to patients, since the registry record does not report a threshold for clinical importance.

These intervals are recalculated from posted summary statistics and are unadjusted. They are not the sponsor's ANCOVA intervals. The registry record reports no adjusted confidence interval for the sponsor's overall analysis, so its precision cannot be evaluated from a reported interval. The sponsor's analysis takes precedence where it differs from the recalculation, but its overall p-value alone does not convey the magnitude or range of adjusted effects.

Uncertainty also includes features not represented by a confidence interval, such as missing outcome data, model choices, and whether the findings generalize beyond the trial population. The last-value-carried-forward method is stated, but the amount of missingness and sensitivity to alternative approaches are not reported in the registry record. The confidence intervals should therefore be interpreted as statistical precision for the particular recalculated comparisons, not as a complete account of uncertainty in the trial.

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 for 80% power and participants per arm for 90% power. They are based on a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect: the full observed effect, 75% of the observed effect, or 50% of the observed effect. These assumptions describe the planning illustration, not the trial's original design. The original design assumptions are not reported in the registry record.

The 80% power column gives the number of participants per arm estimated to provide an 80% chance of detecting the specified effect under those assumptions, if that effect is present and the model assumptions hold. The 90% column uses a higher target chance of detection and therefore generally requires more participants per arm for the same effect. These are planning targets, not guarantees about what a future study will find. A curve expresses the same general relationship between the assumed effect and the required group size.

Smaller effects are harder to distinguish from random variation, so planning for a smaller fraction of the observed effect requires more participants per arm. The observed effect may itself be imprecise, and using it as a planning value can produce optimistic estimates for a future study. The figures are not observed power; they are sample-size planning illustrations calculated from the observed effect and the stated assumptions. They should not be interpreted as a reconstruction of the trial's original sample-size justification or as evidence that the completed study had a particular probability of detecting an effect.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -3.600; pooled standard deviation σ = 12.166.
2. n = 2 × (1.96 + 0.842)² × 12.166² / -3.600² = 179.3, rounded up to 180 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
delta <- -3.6                      # observed difference in means
sigma <- 12.165973413209                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(123422)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 180 (80% power), 241 (90% power)
 75% of observed effect: n per arm = 319 (80% power), 427 (90% power)
 50% of observed effect: n per arm = 718 (80% power), 961 (90% power)
power.t.test: 180.2 
Simulated power at n = 180 per arm: 0.800 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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. Analyses Reported by the Sponsor

The registry reports a sponsor analysis using ANCOVA across the breathing-retraining, heliox, and exercise groups, with p = 0.015. This is the reported overall analysis. The registry does not give adjusted mean differences, confidence intervals, or a pairwise breakdown from that model, so the result cannot be used to identify the adjusted difference for a particular pair of groups.

The recalculated comparisons are simple unadjusted calculations from the posted group means and standard deviations. They are not the same analysis as ANCOVA and do not adjust for covariates. For that reason, their estimates and p-values may differ from the sponsor's result. The registry record flags a discrepancy, so the sponsor's own analysis takes precedence when describing the trial's inferential result. The recalculation can still help readers understand the scale and direction of differences in the posted descriptive means, but it should not override or be presented as a correction to the sponsor's analysis.

The record does not report the covariates included in the ANCOVA, model diagnostics, or a detailed statistical analysis plan. Without those details, it is not possible to assess fully how the sponsor's adjusted result was obtained or to reproduce it from the posted summary. The overall p-value is evidence about the fitted overall test, not a measure of effect size, clinical importance, or the probability that the null hypothesis is true.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study evaluates several outcomes, group contrasts, time points, or other hypotheses. Without a planned adjustment or hierarchy, repeated testing can increase the chance of at least one small p-value even when no underlying effect exists. This study has three intervention groups, a primary outcome, and a posted secondary outcome. The registry record reports an overall ANCOVA result for each outcome and also allows simple pairwise recalculations against the breathing-retraining group. The record does not report a multiplicity adjustment, a prespecified ordering of tests, or a statistical analysis plan explaining how these results were to be interpreted together.

The overall ANCOVA and the pairwise recalculations address different questions. An overall result does not establish which specific group pairs differ. Conversely, unadjusted pairwise p-values do not account for the fact that more than one comparison is available. The sponsor-reported overall analyses should be kept distinct from the recalculated pairwise results, and the latter should not be interpreted as confirmatory evidence without a reported testing strategy.

For missing data, the primary outcome description states that the study used an intent-to-treat analysis, carried the last value forward, and included all participants in the final analysis. This reports the intended analysis population and a missing-data procedure. It does not reveal how many outcome values were missing, when they were missing, or whether missingness differed by group. The registry record does not report sensitivity analyses or alternative missing-data models. Last observation carried forward can be biased if the carried value does not adequately represent the unobserved later outcome.

The registry record also does not report details of the original sample-size justification, interim analyses, or a fuller statistical plan. These omissions prevent a complete assessment of whether the analyses and multiplicity strategy were defined before results were known.

16. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: cardiac event (8.6%), lung cancer (2.9%), intracerebral bleed (2.9%).

The adverse-event figures are counts of participants affected within each group, as recorded in the registry. For serious adverse events, the record lists 1 participant in breathing retraining, 0 in heliox, and 5 in exercise alone. The separate counts for other adverse events are 1, 2, and 1, respectively. These categories should be kept distinct: a count of participants with a serious event is not interchangeable with a count of all events, and the registry does not provide event narratives or timing for these group summaries.

The record also lists cardiac event, lung cancer, and intracerebral bleed among the leading serious-event terms, with the displayed percentages. It does not provide enough detail in these summaries to determine the clinical course, relatedness to an intervention, or whether participants experienced more than one event. Death counts are not reported in the registry record. The posted safety figures are descriptive and should not be treated as a basis for comparing risk without considering the small group sizes, event definitions, follow-up, and missing information.

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

The results describe average exercise-test endurance in three randomized groups and report an overall sponsor ANCOVA result. The descriptive means differ across groups, with the breathing-retraining group having the highest mean. The sponsor's overall result is reported as p = 0.015, while the recalculated unadjusted pairwise comparisons provide estimates and intervals for comparisons against breathing retraining. Because the registry record flags a discrepancy, the sponsor's analysis takes precedence for the trial's inferential result.

These findings do not establish the size of an adjusted difference between any particular pair of groups. The sponsor's ANCOVA is reported only as an overall p-value, without adjusted group estimates or confidence intervals. The unadjusted recalculations are informative about the posted summaries, but they do not replace that analysis. A p-value does not show the probability that a treatment is effective, and it does not express whether a difference is important to participants.

The endpoint is a treadmill endurance measure at 14 weeks, with an individually determined workload based on a symptom-limited test. It does not directly capture every aspect of daily activity, symptoms, or quality of life. The study summary describes an 8-week intervention, but the outcome assessment is recorded at 14 weeks. The record does not report longer-term outcomes or the clinical threshold that would define a meaningful change in endurance.

The results also have limitations related to missing data, multiplicity, and incomplete reporting of the analysis. The last-observation-carried-forward approach is stated, but the amount and pattern of missing data are not. The record does not report an adjustment for multiple outcomes or pairwise testing, or enough information to reconstruct the sponsor's ANCOVA. The trial therefore provides a report of group summaries and an overall statistical result, not a complete account of adjusted effects, clinical importance, or how results might apply to populations beyond those studied.

18. Why This Trial Matters Statistically

This trial illustrates why a reported group comparison should be read together with the analysis that generated it. The posted means and standard deviations permit transparent, unadjusted recalculations, while the sponsor reports an ANCOVA across all three groups. Those analyses answer related but not identical questions. When a discrepancy is recorded, keeping the analyses separate prevents a simple recalculation from being mistaken for the trial's own adjusted result.

It also highlights the difference between an overall test and pairwise estimates. An overall p-value can indicate evidence of variation across groups without identifying which contrast accounts for that result. Pairwise estimates and confidence intervals are more directly interpretable as differences in outcome units, but unadjusted comparisons do not account for multiplicity or covariate adjustment. Readers need both the analysis structure and the estimates to understand the strength and scale of evidence.

The endpoint and follow-up timing matter statistically as well as clinically. Exercise endurance is measured under a defined treadmill workload, and the assessment is recorded at 14 weeks after an intervention described as lasting 8 weeks. This offers a specific functional measure, but does not itself describe the broader experience of pulmonary rehabilitation or longer-term outcomes.

Finally, the missing-data method and limited reporting affect how precisely the results can be interpreted. An intent-to-treat label does not remove the assumptions introduced by carrying an earlier observation forward, and the registry record does not report how much data were missing. The case emphasizes that effect estimates, uncertainty intervals, analysis methods, and reporting completeness all matter alongside p-values.

19. 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.

Several limitations are specific to the information recorded for this trial. The registry lists single masking but does not identify who was masked or describe how masking was maintained. It records randomization but does not report the sequence-generation method or allocation concealment. These omissions make it difficult to assess implementation of the design from the registry record alone.

The sponsor's primary analysis is identified as ANCOVA, but the registry does not report the covariates, adjusted estimates, confidence intervals, or model diagnostics. The overall p-value therefore cannot be translated into an adjusted effect size or a clear pairwise interpretation. The record also flags a discrepancy with the simple unadjusted recalculations, making it especially important not to conflate those analyses.

The primary outcome description states that last observation carried forward was used and all participants were included, but the registry does not report missingness by group, the amount of missing outcome data, or sensitivity analyses. This limits assessment of how robust results are to the missing-data assumptions. The registry also does not report a multiplicity plan, despite the primary and secondary outcomes and possible pairwise comparisons.

The intervention is described as 8 weeks, while the primary endpoint was assessed at 14 weeks. The record does not give more detail about adherence, the timing of changes in exercise endurance, or longer-term follow-up. It also does not report a clinically meaningful threshold for the endpoint. These limits constrain judgments about clinical importance and durability. They do not negate the posted results, but they define what can be concluded from the registry record.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Innovation in Pulmonary Rehabilitation — NCT00123422.
• Registry record last updated 2014-10-16; status last verified 2014-10.
• Results first posted 2014-10-07.
• 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.

23. Record Summary

NCT00123422 is a completed, randomized, single-masked, parallel-group study sponsored by the US Department of Veterans Affairs. It compared exercise training with computerized breathing retraining, exercise training with heliox, and exercise training alone in people described as having moderate to severe chronic obstructive pulmonary disease. The intervention period is described as 8 weeks.

The primary outcome was exercise endurance on a constant-workrate treadmill test at 14 weeks. Inspiratory capacity was also posted as a secondary outcome at 14 weeks. The primary analysis description states that all participants were included under an intent-to-treat approach using last observation carried forward. The sponsor reports an overall ANCOVA result for the primary outcome, while the posted recalculations are unadjusted pairwise comparisons.

The registry record does not report adjusted effect estimates, detailed ANCOVA specifications, the original sample-size assumptions, or a multiplicity strategy. The sponsor's own analysis takes precedence over recalculated comparisons where the registry flags a discrepancy.