This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for A Study to Assess the Effect of CK-2127107 on Physical Function in Subjects With Chronic Obstructive Pulmonary Disease (NCT02662582), a randomized phase 2 study. The primary outcome is Change From Period Baseline at Week 2 in Constant Work Rate (CWR) Endurance Time Relative to Placebo.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02662582 |
| Phase | Phase 2 |
| Condition | Chronic Obstructive Pulmonary Disease (COPD) |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | Double |
| Enrollment | 46 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Astellas Pharma Global Development, Inc. |
| Results posted | Yes |
2. Clinical Question
Population
Participants with chronic obstructive pulmonary disease (COPD) entered a Phase 2a trial. The registry reports 46 enrolled participants. The primary outcome population was the full analysis set: randomized participants who received at least one dose, had at least one baseline measurement, and had at least one post-baseline measurement within a period, with data available at the specified time point.
Intervention
CK-2127107, also named reldesemtiv in the intervention listing. The arm descriptions state that participants received 500 mg orally twice daily for two weeks in one treatment period. The two treatment periods were separated by a two-week washout.
Comparator
Matching placebo, taken orally twice daily for two weeks in the other treatment period. Participants were assigned to one of the two sequences: CK-2127107 followed by placebo, or placebo followed by CK-2127107.
Primary question
Did change from period baseline in constant work rate (CWR) cycle-ergometer endurance time at week 2 differ between CK-2127107 and placebo? The outcome is measured in seconds; a positive change from baseline indicates improvement. The registry reports a mixed-model estimate of the between-treatment difference, with a 90% confidence interval and p-value.
The study also assessed cardiopulmonary and neuromuscular measures, resting spirometry, safety and tolerability, and pharmacokinetics. The primary question is specifically about exercise endurance, not a broad measure of COPD symptoms or daily functioning. The registry record does not report a clinical threshold defining what size of change in endurance time would be important to participants.
3. Trial Design
This was a Phase 2a randomized, double-blind, placebo-controlled crossover study. In a crossover design, each participant receives both study treatments in different periods, so the treatment comparison can use measurements made under both conditions in the same participant. The registry describes two sequences: CK-2127107 in the first period followed by placebo, or placebo first followed by CK-2127107. Each treatment period lasted two weeks, with a two-week washout between them.
The arm descriptions state that CK-2127107 was given as 500 mg orally twice daily, with matching placebo given twice daily during the other period. The listed sequence labels refer to CK-2127107 1000 mg, while the descriptions specify 500 mg twice daily. The registry record does not explain this difference in wording.
The study enrolled 46 participants and is recorded as completed. The registry gives a start date of 2016-06-30 and a primary completion date of 2018-06-08. For the primary outcome, the full analysis set included randomized participants who received at least one dose and had baseline and post-baseline measurements within a period; analyses used participants with available data at each specified time point. The posted arm summaries have 32 participants for placebo and 35 for CK-2127107, which are analysis counts rather than the overall enrollment count.
Randomization and double masking are stated in the registry. Further details such as the randomization procedure, allocation concealment, the washout's rationale, and the statistical handling of sequence or period effects are not reported in the registry record. The registry reports that the primary comparison used a mixed models analysis, but the full model specification is 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.
Before assignment: Participants with a clinical diagnosis of moderate to severe chronic obstructive pulmonary disease (COPD) between 40 to 75 years of age inclusive and met all of the inclusion and none of the exclusion criteria were enrolled in this study.
Treatment Period 1 (14 Days)
| Stage | CK-2127107 1000 mg, Then Placebo | Placebo, Then CK-212710 1000 mg |
|---|---|---|
| STARTED | 23 | 23 |
| COMPLETED | 18 | 19 |
| NOT COMPLETED | 5 | 4 |
Reasons for not completing this period:
| Reason | CK-2127107 1000 mg, Then Placebo | Placebo, Then CK-212710 1000 mg |
|---|---|---|
| Adverse Event | 3 | 2 |
| Miscellaneous | 0 | 1 |
| Protocol Deviation | 1 | 0 |
| Withdrawal by Subject | 1 | 1 |
Washout Period (14 Days)
| Stage | CK-2127107 1000 mg, Then Placebo | Placebo, Then CK-212710 1000 mg |
|---|---|---|
| STARTED | 18 | 19 |
| COMPLETED | 18 | 19 |
| NOT COMPLETED | 0 | 0 |
Treatment Period 2 (14 Days)
| Stage | CK-2127107 1000 mg, Then Placebo | Placebo, Then CK-212710 1000 mg |
|---|---|---|
| STARTED | 18 | 19 |
| COMPLETED | 18 | 19 |
| NOT COMPLETED | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: The full analysis set (FAS) consisted of all participants who were randomized and received ≥ 1 dose of study drug and had ≥ 1 baseline measurement and 1 post baseline measurement within a period. FAS population with available data at each specified time point.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: The safety analysis set (SAF) consisted of all randomized participants who took ≥ 1 dose of study medication.
| Characteristic | Unit | CK-2127107 1000mg, Then Placebo | Placebo, Then CK-2127107 1000mg | Total |
|---|---|---|---|---|
| Participants analysed | 23 | 23 | 46 | |
| Age, Continuous | Years | 62.8 (SD 7.9) | 63.1 (SD 8.3) | 63 (SD 8) |
| Sex: Female, Male: Female | Participants | 13 | 12 | 25 |
| Sex: Female, Male: Male | Participants | 10 | 11 | 21 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 0 | 1 | 1 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 23 | 22 | 45 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 5 | 8 | 13 |
| Race (NIH/OMB): White | Participants | 18 | 14 | 32 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 1 | 1 |
| Constant work rate (CWR) Endurance Time | Seconds | 334.5 (SD 80.0) | 346.4 (SD 89.1) | 340.4 (SD 84.0) |
6. Primary Endpoint
The registry lists the primary outcome as Change From Period Baseline at Week 2 in Constant Work Rate (CWR) Endurance Time Relative to Placebo, measured over Baseline and week 2 of each treatment period.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | seconds |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change from period baseline at week 2 in constant work rate (CWR) endurance time, compared between CK-2127107 and placebo. It is measured in seconds during cycle-ergometer exercise. The registry describes CWR time to intolerance as the time until a participant reaches symptom limitations while being monitored; this determines the CWR endurance time. Time to intolerance was assessed with a stopwatch and verified from electronic cycle-ergometer recordings. Measurements used a breath-by-breath metabolic system with integrated electrocardiogram monitoring.
Change from period baseline makes the outcome a within-period change rather than a comparison of raw endpoint values alone. The crossover structure means each participant could contribute observations under both treatment conditions, which can help control for stable differences between people when treatments are compared. That general benefit depends on suitable design and analysis; it does not remove possible period, sequence, carryover, or missing-data concerns.
The registry states that a positive change indicates improvement from baseline, so the direction of a treatment contrast must be read with the outcome definition in mind. The endpoint is intended to quantify exercise tolerance under a standardized workload. It does not, by itself, establish how participants function in ordinary daily life or how meaningful a particular change would be to them. A threshold for clinical importance is not reported in the registry record.
7. Results Posted in the Registry
- CK-2127107: mean -13.40 versus -1.40 on control; difference -12.00 (95% CI -72.16 to 48.16), standardized effect d = -0.10; z-test p = 0.696.
Mean difference: CK-2127107
95% CI: -72.16 to 48.16
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change From Period Baseline at Week 2 in Inspiratory Capacity (IC) Change From Peak to Rest | Continuous Endpoint | Mean difference | 0.05 (-0.09 to 0.19) | 476 per arm |
| Change From Period Baseline at Week 2 in Forced Vital Capacity (FVC) | Continuous Endpoint | Mean difference | -0.10 (-0.23 to 0.03) | 108 per arm |
| Change From Period Baseline at Week 2 in Forced Expiratory Volume 1 (FEV1) | Continuous Endpoint | Mean difference | -0.01 (-0.08 to 0.07) | 8,112 per arm |
Change From Period Baseline at Week 2 in Inspiratory Capacity (IC) Change From Peak to Rest
- 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 errors.
- Result:
- CK-2127107: mean 0.04 versus -0.01 on control; difference 0.05 (95% CI -0.09 to 0.19), standardized effect d = 0.18; z-test p = 0.458.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between CK-2127107 and the control. The interval gives the range of effects that remain compatible with the data.
Change From Period Baseline at Week 2 in Forced Vital Capacity (FVC)
- 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 errors.
- Result:
- CK-2127107: mean -0.10 versus 0.00 on control; difference -0.10 (95% CI -0.23 to 0.03), standardized effect d = -0.38; z-test p = 0.118.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between CK-2127107 and the control. The interval gives the range of effects that remain compatible with the data.
Change From Period Baseline at Week 2 in Forced Expiratory Volume 1 (FEV1)
- 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 errors.
- Result:
- CK-2127107: mean -0.04 versus -0.03 on control; difference -0.01 (95% CI -0.08 to 0.07), standardized effect d = -0.04; z-test p = 0.857.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between CK-2127107 and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists a broad range of secondary measures, including oxygen uptake, ventilation, ventilatory efficiency, inspiratory capacity, perceived exertion, respiratory exchange ratio, carbon dioxide output, and end-tidal carbon dioxide. It records 25 posted secondary outcomes. The available detailed results in the record include inspiratory capacity, forced vital capacity, and forced expiratory volume in one second.
Across those available detailed comparisons, the estimated directions are not uniform: one measure has a positive treatment contrast, while the spirometry contrasts are negative or close to zero. The reported intervals for these three comparisons cross zero. Taken together, these results do not form a clear, consistent pattern that independently reinforces the primary endurance-time result. They also do not establish that the treatments have identical effects.
Secondary outcomes can help describe whether an intervention's effects appear across related physiological measures, but they are not substitutes for the prespecified primary question. If many outcomes are tested, chance alone can produce apparently notable findings. The registry record does not report a multiplicity adjustment or identify a hierarchy for interpreting the secondary outcomes. For that reason, unadjusted secondary results carry less weight than the primary analysis and should be treated as exploratory unless the analysis plan states otherwise. Details of the remaining posted secondary results are not reported in the registry record available for this analysis, so a broader endpoint-by-endpoint pattern cannot be established from these results.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change From Period Baseline at Week 2 in Oxygen Uptake (VO2)
- Change From Period Baseline at Week 2 in Ventilation (VE)
- Change From Period Baseline at Week 2 in Ventilatory Equivalent for Carbon Dioxide (VE/VCO2)
- Change From Period Baseline at Week 2 in Inspiratory Capacity (IC) Change From Peak to Rest
- Change From Period Baseline at Week 2 in Perceived Exertion for Dyspnea and Leg Discomfort (BORG CR10)
- Change From Period Baseline at Week 2 in Respiratory Exchange Ratio (RER)
- Change From Period Baseline at Week 2 in Carbon Dioxide Output (VCO2)
- Change From Period Baseline at Week 2 in End-tidal PCO2 (PETCO2)
9. Statistical Interpretation
The registry's mixed models analysis estimates a CK-2127107 minus placebo least-squares mean difference of -12.0 seconds in change in CWR endurance time. Its 90% confidence interval ranges from -71.2 to 47.2 seconds, and the reported p-value is 0.734. The interval includes zero and includes estimates in either direction. The posted result therefore does not pin down a precise treatment contrast: it is compatible with a range of values, including a modest advantage for either treatment and a larger difference in either direction.
The posted arm summaries show mean changes of -1.4 seconds with placebo and -13.4 seconds with CK-2127107. These are least-squares means, and the reported treatment comparison comes from a mixed models analysis. They should not be treated as independent raw group means or as a substitute for the crossover model's estimate. The comparison's p-value does not measure the probability that either treatment is effective, nor does it establish equivalence. The registry does not report an equivalence or non-inferiority objective.
A simple unadjusted re-calculation from the posted summary statistics gives a mean difference of -12.0 seconds, with a 95% interval from -72.16 to 48.16 and an unadjusted p-value of 0.696. This calculation is a rough comparison of the summaries and is not the same analysis as the sponsor's mixed model. The two approaches yield similar central estimates but different uncertainty intervals and p-values because their methods differ. The registry's own mixed-model analysis is the trial's reported result.
The secondary outcomes listed in the record span exercise physiology, inspiratory capacity, perceived exertion, and spirometry. The available posted secondary comparisons do not establish a consistent pattern that would strengthen the primary finding. Their interpretation also warrants caution because multiple outcomes were assessed and an adjustment strategy for multiplicity is not reported in the registry record.
These results describe estimates and uncertainty in this trial, not a recommendation about treatment. Enrollment was 46, while the primary analysis summaries include 32 and 35 observations by treatment. In a crossover trial, those treatment counts may represent available period-specific data rather than distinct sets of participants. The registry's analysis-population definition is stated, but the number excluded for each reason and the handling of missing observations are not reported in the registry record.
10. Statistical Methods Explained
The primary endpoint is continuous: it measures a change in endurance time in seconds. The registry reports least-squares means for each treatment and a least-squares mean difference from a mixed models analysis. Least-squares means are model-based estimates adjusted according to the model's terms. The registry record does not give the complete model formula, covariance structure, or list of included covariates, so the precise adjustments cannot be described.
What does a mixed model contribute?
General statistical explanation: mixed models can represent both treatment effects and correlations among repeated observations. In a crossover trial, the same participant contributes measurements during more than one treatment period, so those observations are not generally independent. A model that accounts for this dependence can estimate a treatment contrast while reflecting the repeated-measures structure. The registry identifies a mixed models analysis, but the details needed to determine exactly how within-participant correlation, period, sequence, or carryover were handled are not reported in the registry record.
Randomization helps limit systematic differences in treatment assignment, and double masking can reduce bias in care or outcome assessment. Those design features do not guarantee that all sources of bias are absent. The registry identifies the study as randomized and double-blind but does not report the randomization method, concealment details, or assessment of masking.
How should the contrast and p-value be read?
The reported least-squares mean difference is -12.0 seconds for CK-2127107 relative to placebo. Because the endpoint is change from baseline, the contrast is a difference between treatment-period changes, not simply a difference in final endurance times. The reported 90% interval is -71.2 to 47.2 seconds. A confidence interval describes the range of estimates compatible with the data and the statistical procedure at its stated confidence level. It is not a range containing a fixed proportion of individual participant outcomes, nor is it the probability that the true value lies in that particular interval.
The reported p-value is 0.734. General statistical explanation: a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be if that null hypothesis and the analysis assumptions held. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. A p-value alone also does not show whether a result is precise; the confidence interval provides useful information about the range of compatible treatment contrasts.
What is the recalculated comparison?
The posted re-calculation uses the treatment-specific summary values and standard errors to construct a simple, unadjusted comparison. It estimates a mean difference of -12.0 seconds, a 95% interval from -72.16 to 48.16, and an unadjusted p-value of 0.696. It is not a reconstruction of the mixed model and does not use the full participant-level crossover data. The standard deviations used in this calculation are approximate, inferred from the posted summaries, so it is best read as a rough check rather than a competing primary analysis. The registry record does not mark a discrepancy between this calculation and the sponsor result.
Why can an interval be wide?
General statistical explanation: an interval's width depends on the amount and variability of information, as well as the method used to estimate uncertainty. Smaller samples and more variable measurements tend to produce less precise estimates. Repeated measures can provide useful within-person information, but the gain depends on the correlation between measurements and the analysis model. The registry reports the treatment-specific analysis counts and standard errors, but not enough detail to isolate how each design feature contributed to the interval's width.
The posted arm values are least-squares means with standard errors. A standard error describes the estimated uncertainty of a mean, not the spread of individual participants' outcomes. It should not be read as a standard deviation. The uncertainty for the treatment difference is reflected directly in its confidence interval.
What analysis details remain unknown?
The registry record does not report the original sample-size calculation, its assumptions, or the rationale for the enrollment target. It also does not report an interim-analysis plan, adjustment for multiple comparisons, a detailed missing-data strategy, or sensitivity analyses. Those omissions limit how far readers can assess the full analysis plan. The stated analysis population requires baseline and post-baseline data within a period and availability at the specified time point, but exclusions and missingness patterns are not described.
General statistical explanation: over-dispersion is a concern when observed variability exceeds what a statistical model assumes. It can make standard errors too small if ignored, leading to overly narrow intervals or overly optimistic tests. The primary outcome is continuous, and no over-dispersion assessment is reported in the registry record; this issue should not be assumed to have occurred in this analysis. More broadly, statistical methods should match outcome type, design, and data structure, and the registry's brief method label does not provide enough detail to verify every modeling choice.
11. Confidence Intervals and Precision
The primary estimate from the registry's mixed models analysis is -12.0 seconds, with a 90% confidence interval from -71.2 to 47.2 seconds. The interval includes zero, so the posted data are compatible with no difference as well as with differences in either direction. Its breadth means that the point estimate alone should not be mistaken for a precise estimate of the treatment contrast.
General statistical explanation: a confidence interval summarizes uncertainty under the statistical model and its assumptions. A 90% interval is constructed by a procedure that, over repeated use under those assumptions, would cover the target value at the stated rate. It is not a statement that 90% of participants' outcomes lie in the interval. The interval also does not account for unreported sources of uncertainty, such as possible bias from missing data or model misspecification.
The simple recalculation uses a 95% interval from -72.16 to 48.16 seconds. It is based on posted summary statistics and an approximate standard deviation, rather than the sponsor's participant-level mixed-model analysis. Its interval and the sponsor's 90% interval should not be compared as if they were generated by the same method and confidence level. The registry's mixed-model result is the reported trial analysis; the recalculation is only a supplementary unadjusted estimate.
For the posted secondary comparisons, the reported sponsor intervals also cross zero. That indicates uncertainty around those estimates, not proof that the treatments are identical. No clinical-importance threshold is reported in the registry record, so the intervals cannot be classified against a stated threshold for meaningful change. More precise estimates would narrow the range of compatible effects, but precision by itself would not establish clinical relevance.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 1,717 | 2,299 |
| 75% of the observed effect | 3,053 | 4,087 |
| 50% of the observed effect | 6,868 | 9,194 |
The planning figures are illustrations based on the observed effect, not the trial's original design calculation. They assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning row considers detecting a stated fraction of the observed effect. The entries are participants per arm for 80% power or participants per arm for 90% power; these are not total enrollment counts and are not total event counts. The outcome is continuous, so an event-count interpretation does not apply.
In plain language, the 80% power column gives the estimated number of participants per arm that would be needed for the specified effect under the listed assumptions, with an 80% chance of statistical significance if that effect were the true effect and the assumptions held. The 90% column gives the corresponding planning number for a higher chance of detecting that effect. These are planning concepts, not guarantees about what a future study would find. This is not observed power.
The rows for 100%, 75%, and 50% of the observed effect show how the planning requirement changes when the target effect is smaller. Smaller effects need more participants to distinguish them from random variation under the same assumptions. The large calculated numbers should not be read as a recommendation for a future crossover study: the illustration assumes equal allocation between two arms and a normal approximation, while the registry describes a crossover trial. The original trial's sample-size assumptions and justification are not reported in the registry record.
The planning calculations use the observed estimate, which is uncertain and may not be a stable estimate of the effect a future trial would see. They are therefore useful for understanding how power calculations respond to assumed effect size, but should not be treated as a validated design recommendation. The planning figures are not a reanalysis of the original trial's 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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = -12.000; pooled standard deviation σ = 125.498.
- n = 2 × (1.96 + 0.842)2 × 125.4982 / -12.0002 = 1,716.9, rounded up to 1,717 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 <- -12 # observed difference in means
sigma <- 125.497832037664 # 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(2662582)
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 = 1,717 (80% power), 2,299 (90% power)
75% of observed effect: n per arm = 3,053 (80% power), 4,087 (90% power)
50% of observed effect: n per arm = 6,868 (80% power), 9,194 (90% power)
power.t.test: 1717.9
Simulated power at n = 1,717 per arm: 0.798 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | LSMean difference -12.0 | -71.2 to 47.2 | 0.734 |
The registry's own primary analysis is a mixed models analysis. It reports a least-squares mean difference of -12.0 seconds, a 90% confidence interval from -71.2 to 47.2 seconds, and p = 0.734. This is the reported treatment comparison from the trial.
The unadjusted recalculation from the posted summary statistics also estimates a difference of -12.0 seconds, but gives a 95% interval from -72.16 to 48.16 and p = 0.696. It uses approximate standard deviations derived from the summary values and does not reproduce the mixed model or the full crossover analysis. The identical central estimate does not mean the methods are interchangeable; their intervals and p-values differ.
The registry record does not flag a discrepancy between the recalculation and the reported analysis. Accordingly, the sponsor's mixed-model result remains the primary result to interpret, while the recalculation offers a simple summary-statistic comparison. The registry does not provide enough model details to independently reproduce the sponsor analysis from participant-level data.
15. Multiplicity, Missing Data and Analysis Populations
The registry identifies one primary outcome: change in CWR endurance time at week 2 relative to placebo. It also lists numerous secondary outcomes and reports 25 posted secondary outcomes overall. Testing multiple outcomes increases the chance that at least one result may appear unusual by chance when each is assessed separately.
General statistical explanation: multiplicity refers to the increased false-positive risk that can arise when several hypotheses are tested. Common approaches include adjusting significance thresholds, defining a hierarchy for outcomes, or explicitly labeling analyses exploratory. The registry record does not report whether such an adjustment or hierarchy was used. Therefore, secondary p-values should not be treated as if each were the only test conducted.
The primary analysis population is described as randomized participants who received at least one dose and had at least one baseline and one post-baseline measurement within a period, with available data at each time point. The registry reports treatment-specific analysis counts, but the reasons for unavailable data or exclusions are not reported in the registry record. The missing-data assumptions, imputation procedures, and sensitivity analyses are also not reported in the registry record. Those details matter because an analysis based on available observations can be affected if data availability is related to treatment response or other factors.
The crossover design also makes period and sequence considerations relevant. The registry identifies a mixed models analysis, but does not report whether period, sequence, or possible carryover effects were included or evaluated. Nor does it report interim analyses or the full statistical analysis plan. These missing details do not prove that the analysis was inadequate; they limit what can be assessed from the registry record alone.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo | 1 | 41 | 2.4% |
| CK-2127107 | 2 | 42 | 4.8% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo | 0 of 41 |
| CK-2127107 | 0 of 42 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo | 1 of 41 |
| CK-2127107 | 3 of 42 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | CK-2127107 |
|---|---|---|---|
| Renal cell carcinoma | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 41 | 1 of 42 |
| IIIrd nerve paralysis | Nervous system disorders | 0 of 41 | 1 of 42 |
| Haematuria | Renal and urinary disorders | 1 of 41 | 0 of 42 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | CK-2127107 |
|---|---|---|---|
| Dizziness | Nervous system disorders | 1 of 41 | 3 of 42 |
Serious events with the highest arm-level rate: haematuria (2.4%), renal cell carcinoma (2.4%), iiird nerve paralysis (2.4%).
The registry reports serious adverse events among 1 of 41 participants at risk in the placebo group and 2 of 42 at risk in the CK-2127107 group. No deaths were reported in either group. These counts describe the serious adverse events recorded during the trial; the at-risk counts are the relevant denominators for those summaries.
The listed serious-event terms are haematuria, renal cell carcinoma, and IIIrd nerve paralysis, each reported as 2.4%. These terms describe events recorded in the study and do not by themselves establish causation by a treatment. The registry also reports other adverse events affecting 1 of 41 participants at risk with placebo and 3 of 42 at risk with CK-2127107. These counts should be read as observed safety summaries, not as a complete account of event severity, timing, relatedness, or clinical course.
The study's size and duration limit how much can be concluded about uncommon or delayed adverse events. The registry record does not report enough detail to assess the attribution or comparative risk of individual events. These figures are descriptive and do not support medical advice.
17. What the Result Does, and Does Not, Mean
The primary result is an estimate of the difference between CK-2127107 and placebo in change in cycle-ergometer endurance time after two weeks of treatment in each crossover period. The registry's mixed-model estimate is -12.0 seconds, with a 90% confidence interval from -71.2 to 47.2 seconds and p = 0.734. The interval includes zero and spans values in both directions, so the result is uncertain about the size and direction of the treatment contrast.
This finding does not establish that the treatments are equivalent. A failure to demonstrate a difference is not the same as evidence that any difference is small enough to be unimportant. The registry does not report an equivalence margin, a non-inferiority objective, or a threshold for clinically meaningful change. It also does not establish that CK-2127107 improves endurance or that it worsens it. The data describe the estimate and its uncertainty in this trial.
The endpoint is a measured exercise-tolerance outcome under cycle-ergometer conditions. It does not automatically translate into changes in daily activities, symptoms outside the test, or long-term health outcomes. Those broader outcomes are not established by this primary measure. The study also assessed physiological and spirometric secondary outcomes, but the available detailed results do not form a consistent pattern that resolves the uncertainty in the primary result.
The trial was Phase 2a and enrolled 46 participants. The primary treatment summaries include fewer available observations by treatment than the enrollment count, and the registry does not describe missingness in detail. The posted findings therefore should be interpreted in the context of the studied population, short treatment periods, analysis methods, and remaining uncertainty. They do not determine how the intervention would perform in other populations or under other treatment durations.
18. Why This Trial Matters Statistically
This trial is statistically informative because it uses a randomized, double-blind crossover comparison for a continuous exercise-tolerance outcome. A crossover design can make within-person comparisons possible, which is useful when measurements vary substantially between people. It also creates analysis considerations: measurements from the same participant are related, and period or sequence effects may matter. The registry identifies a mixed models analysis but does not provide enough detail to evaluate all of those choices.
The result illustrates why an estimate, its interval, and the design context should be considered together. The central estimate is -12.0 seconds, but the 90% interval extends from -71.2 to 47.2 seconds. The interval communicates that the trial does not tightly locate the treatment contrast. A single p-value cannot convey the full range of plausible effects or indicate whether a difference would be meaningful to participants.
The posted summary also demonstrates the limits of a summary-statistic recalculation. Its point estimate matches the mixed-model estimate, but the interval and p-value differ because the recalculation does not reproduce the trial's model. Readers can use a simple recalculation as a check on the broad direction and scale, but the registry's reported mixed-model result is the primary analysis.
Finally, the many secondary outcomes make transparent multiplicity handling important. The registry record does not report a multiplicity strategy, detailed missing-data methods, or the original sample-size justification. Those gaps do not change the posted estimates, but they limit how comprehensively the trial's statistical planning and robustness can be assessed.
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.
The primary estimate is imprecise, with a 90% confidence interval extending from -71.2 to 47.2 seconds. The sample was small, with 46 enrolled participants, and treatment-specific primary analysis counts were 32 and 35. The registry record does not explain the differences between enrollment and available analysis counts or describe missing-data patterns. This leaves uncertainty about how incomplete observations may have affected the estimates.
The crossover design is potentially efficient for within-person comparisons, but interpretation depends on handling repeated measurements, period effects, sequence effects, and possible carryover. The registry reports a mixed models analysis but does not provide its full specification or state which of these design features were modeled or assessed. A two-week washout is described; the rationale and any evaluation of residual treatment effects are not reported in the registry record.
The registry record does not report the trial's original sample-size calculation, the intended detectable effect, an interim-analysis plan, multiplicity handling, or a clinical-importance threshold for the primary outcome. The recalculated planning figures are not substitutes for the trial's design justification and rely on the observed effect. The registry also does not report detailed missing-data methods or sensitivity analyses.
Follow-up for each treatment was two weeks, so these results do not describe longer-term effects. The primary endpoint is measured during cycle-ergometer exercise, and the record does not establish how the observed test outcome relates to daily functioning. Finally, safety summaries are descriptive and come from a relatively small study; they cannot characterize uncommon or delayed events with precision.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Study to Assess the Effect of CK-2127107 on Physical Function in Subjects With Chronic Obstructive Pulmonary Disease — NCT02662582.
- Registry record last updated 2024-11-14; status last verified 2024-10.
- Results first posted 2021-02-05.
- 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.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
23. Record Summary
NCT02662582 is a completed Phase 2a randomized, double-blind, placebo-controlled crossover study of CK-2127107 in participants with COPD. The registry reports 46 enrolled participants and two two-week treatment periods separated by a two-week washout. Participants received CK-2127107 in one period and matching placebo in the other.
The primary outcome was change in CWR cycle-ergometer endurance time at week 2. The reported mixed-model comparison was -12.0 seconds, with a 90% confidence interval from -71.2 to 47.2 seconds and p = 0.734. The interval includes zero and is broad, so the treatment contrast remains uncertain. The registry also lists secondary physiological and spirometric outcomes and reports descriptive adverse-event counts. The detailed statistical plan, multiplicity strategy, original sample-size rationale, and missing-data methods are not reported in the registry record.