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Heart Failure, Diastolic Phase 2 Continuous Endpoint NCT03133793

CoQ10 and D-ribose in Patients With Diastolic Heart Failure: Complete Statistical Analysis

This analysis examines a randomized, double-masked, parallel-group trial of CoQ10, D-ribose, their combination, and placebo in people with diastolic heart failure. It focuses on change in KCCQ health-status scores from baseline to Week 12 and explains the posted secondary outcomes, safety counts, and planning illustrations.

Trial start: 2018-02-05  ·  Enrollment: 216  ·  Sponsor: University of Kansas Medical Center
Scope of this record

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 CoQ10 and D-ribose in Patients With Diastolic Heart Failure (NCT03133793), a randomized phase 2 study. The primary outcome is Change in Health Status of Patients With HFpEF.

216
Enrollment
Phase 2
4
Arms
In the primary outcome
22.41
Mean difference
CoQ10 Only
12.51–32.31
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03133793
PhasePhase 2
ConditionHeart Failure, Diastolic
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment216
Arms in the primary outcome4
Lead sponsorUniversity of Kansas Medical Center
Results postedYes

2. Clinical Question

Population

People with diastolic heart failure, also described in the registry record as heart failure with preserved ejection fraction (HFpEF). The registry record notes that a few participants refused the questionnaire or left the study because of COVID-19.

Intervention

CoQ10 pills, D-ribose oral powder, or both. The arm descriptions pair each active treatment with placebo for the other treatment form when applicable.

Comparator

Placebo pills and placebo powder. The randomized groups were placebo only, CoQ10 only, D-ribose only, and CoQ10 plus D-ribose.

Primary question

How did KCCQ health-status scores change from baseline to Week 12 in each treatment group compared with placebo? Higher KCCQ scores represent better health status, with lower scores indicating more severe symptoms or limitations.

The clinical question concerns patients’ perceptions of health, rather than a single physiological measurement. The KCCQ captures several domains of health status relevant to HFpEF. The trial’s stated purpose was to compare the clinical benefits of CoQ10 and D-ribose in people with diastolic heart failure. The registry record identifies change in KCCQ score as the primary outcome and lists changes in vigor, ejection fraction, septal E/e', walking distance, BNP, lactate, and ATP among secondary outcomes.

The randomized comparisons describe group averages over the stated follow-up interval. They do not, by themselves, establish which individuals experienced improvement, how the treatments might act, or whether any observed score changes would be important to every patient. The interpretation also depends on the uncertainty around the estimated group differences and on how the results were analyzed.

3. Trial Design

The registry record describes a completed Phase 2 randomized, double-masked, parallel-group study sponsored by the University of Kansas Medical Center. Enrollment was 216. The recorded start date was 2018-02-05, and primary completion was 2021-03-12. The study compared placebo only, CoQ10 only, D-ribose only, and CoQ10 plus D-ribose. In the treatment groups receiving only one active product, the other product form was placebo; the placebo-only group received placebo pills and placebo powder.

A parallel-group design assigns participants to a group and compares outcomes across groups over time. Random allocation is intended to reduce systematic differences between groups at the start, though it does not guarantee that all characteristics are balanced. Double masking means the record identifies the trial as masked at two levels, but the particular roles masked are not reported in the registry record. The allocation procedure, masking procedures, and details of treatment adherence are not reported in the registry record.

The primary outcome was change in health status from baseline to Week 12, measured with the KCCQ. The posted primary outcome is a mean change with standard deviation. The record also names seven secondary outcomes: vigor, ejection fraction, septal E/e', six-minute walk test, venous blood BNP, lactate, and ATP. Numerical posted results are available for vigor, ejection fraction, and septal E/e'; numerical results for the other named secondary outcomes are not reported in the registry record.

The registry record does not report the original sample-size assumptions, the planned statistical model, an analysis population, or an interim-analysis plan. Those details should not be inferred from the observed group sizes or from planning illustrations based on observed effects. The trial is marked completed, but that status alone does not explain how participants who discontinued or missed an assessment were handled.

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: Trial included a 7 day run-in period where the participant was asked to take placebo capsules and powder. They had to consume 80% of both placebo items to be randomized into the study. There were many subjects who signed the consent form and started on the run-in period but never returned for data collection (n=63).

Overall Study

StagePlacebo OnlyCoQ10 (Ubiquinol) OnlyD-ribose OnlyCoQ10 (Ubiquinol) + D-ribose
STARTED39393738
COMPLETED38353333
NOT COMPLETED1445

Reasons for not completing this period:

ReasonPlacebo OnlyCoQ10 (Ubiquinol) OnlyD-ribose OnlyCoQ10 (Ubiquinol) + D-ribose
Withdrawal by Subject0424
Lost to Follow-up1020
Death0001

Analysis population for the primary outcome, as defined in the registry: A few of the subjects refused to complete the questionnaire or drop out of the study due to COVID-19.

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.

CharacteristicUnitPlacebo OnlyCoQ10 OnlyD-ribose OnlyCoQ10 + D-riboseTotal
Participants analysed39393738153
Age, Categorical: <=18 yearsParticipants00000
Age, Categorical: Between 18 and 65 yearsParticipants1112141249
Age, Categorical: >=65 yearsParticipants28272326104
Age, Continuousyears69.0 (SD 9.3)67.0 (SD 10.6)72.0 (SD 10.6)69.5 (SD 9.4)69 (SD 10.1)
Sex: Female, Male: FemaleParticipants2321222086
Sex: Female, Male: MaleParticipants1618151867
Race/Ethnicity, Customized: Ethnicity : Hispanic or LatinoParticipants13149
Race/Ethnicity, Customized: Ethnicity : Non-HispanicParticipants37363634143
Race/Ethnicity, Customized: Ethnicity : UnknownParticipants10001
Race/Ethnicity, Customized: Race : African AmericanParticipants776626
Race/Ethnicity, Customized: Race: American Indian or Alaska NativeParticipants00123
Race/Ethnicity, Customized: Race: AsianParticipants00011
Race/Ethnicity, Customized: Not ReportedParticipants00011
Race/Ethnicity, Customized: OtherParticipants02114
Race/Ethnicity, Customized: WhiteParticipants32302927118
Region of Enrollment: United Statesparticipants39393738153
Kansas City Cardiomyopathy Questionnaireunits on a scale48.52 (SD 24.23)51.88 (SD 23.17)44.05 (SD 19.11)45.63 (SD 21.6)47.52 (SD 22.03)
Vigor Scaleunits on a scale13.79 (SD 5.7)13 (SD 5.49)13.94 (SD 7.11)12.21 (SD 5.57)13.24 (SD 5.97)
Ejection Fraction (EF)percentage of ejection fraction51.04 (SD 7.43)51.89 (SD 5.68)50.79 (SD 4.38)51.28 (SD 4.76)51.25 (SD 5.56)
6-minute walking test (6MWT)meters247.87 (SD 150.96)322.69 (SD 124.18)265.58 (SD 135.96)237.85 (SD 131.05)268.49 (SD 135.54)
B-type natriuretic peptide (BNP) levelpg/mL232 (SD 388.28)182.51 (SD 211.23)152.48 (SD 141.52)157.09 (SD 155.27)181.02 (SD 224.08)
lactatemmol/L2.45 (SD 1.13)2.58 (SD 1.04)2.34 (SD 1.12)2.72 (SD 1.59)2.52 (SD 1.22)
Septal E/e'ratio9.41 (SD 5.54)9.8 (SD 4.27)11.2 (SD 5.97)9.35 (SD 4.24)9.94 (SD 5.05)
Adenosine Phosphate (ATP)Relative Light Units (RLU)3332.87 (SD 844.33)3222.63 (SD 1040.44)3312.18 (SD 915.98)3383.24 (SD 954.03)3312.73 (SD 938.695)

6. Primary Endpoint

The registry lists the primary outcome as Change in Health Status of Patients With HFpEF, measured over Change from Baseline to Week 12.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
UnitScores on a scale
Endpoint classificationContinuous Endpoint

The primary endpoint is change from baseline to Week 12 in the Kansas City Cardiomyopathy Questionnaire (KCCQ). The KCCQ is a self-administered 24 item questionnaire that measures patients’ perceptions across five health-status domains relevant to HFpEF. The registry record states that scores are transformed to a 0-to-100-point scale. Higher scores reflect better health status; lower scores correspond to more severe symptoms or limitations, while a score of 100 indicates no symptoms, no limitations, and excellent quality of life.

This endpoint is used because symptoms and limitations are central parts of the health status experienced by people with HFpEF. A questionnaire can capture patients’ own reports rather than relying only on measurements such as ejection fraction or blood biomarkers. Change over time compares a participant’s later score with their baseline score, while group summaries describe average change among participants included in the reported outcome.

The measure is not a direct count of clinical events, nor does the average change indicate that every participant changed in the same way. Standard deviations describe the spread of individual changes around the group mean. The registry record notes that a few participants refused to complete the questionnaire or left the study due to COVID-19. The handling of these missing endpoint observations is not reported in the registry record, which matters because the posted means represent the available outcome summaries rather than a description of every enrolled participant’s experience.

7. Results Posted in the Registry

Mean difference: CoQ10 Only

22.41

95% CI: 12.51 to 32.31

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-8.02.613.123.634.244.7Placebo Only (n=37)CoQ10 Only (n=35)D-ribose Only (n=33)CoQ10 + D-ribose (n=33)Scores on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CoQ10 OnlyD-ribose OnlyCoQ10 + D-ribose-3.166.0015243443mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Change in VigorContinuous EndpointMean difference7.65 (4.75 to 10.55)11 per arm
Change in Ejection Fraction (EF)Continuous EndpointMean difference7.08 (3.60 to 10.56)17 per arm
Change in Septal E/e'Continuous EndpointMean difference-2.66 (-5.56 to 0.24)88 per arm

Change in Vigor

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CoQ10 OnlyD-ribose Only-0.891.694.286.879.4512mean difference vs control (95% CI)

Change in Ejection Fraction (EF)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CoQ10 OnlyD-ribose Only-0.911.724.356.989.6012mean difference vs control (95% CI)

Change in Septal E/e'

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CoQ10 (Ubiquinol) OnlyD-ribose Only-6.12-4.50-2.89-1.280.331.95mean difference vs control (95% CI)

The registry names seven secondary outcomes, spanning patient-reported vigor, cardiac function measures, walking performance, BNP, lactate, and ATP. Numerical results are posted for vigor, ejection fraction, and septal E/e'. The overall pattern is not uniform across those measured domains: the displayed comparisons for vigor and ejection fraction favor higher mean changes relative to placebo, whereas the septal E/e' estimates are negative and their intervals include zero. Numerical results for the remaining named outcomes are not reported in the registry record.

These measures address different aspects of health and physiology, so they are not interchangeable with the primary KCCQ outcome. A secondary measure can provide complementary context, but it does not independently confirm a patient-reported health-status result. Agreement across outcomes may strengthen coherence, while disagreement may reflect different constructs, variation, or chance; the registry record does not provide enough information to distinguish among those explanations.

Unadjusted secondary results carry less weight because multiple outcomes and comparisons increase the opportunity for apparently notable findings to arise by chance. The registry record does not report a multiplicity adjustment, a hierarchy for testing endpoints, or a prespecified secondary analysis plan. The listed secondary comparisons should therefore be treated as exploratory descriptions rather than as a collection of confirmatory claims. Their estimates and confidence intervals are more informative than p-values alone, but they remain subject to missing-data and analysis limitations.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary KCCQ outcome, the placebo-only group had a mean change of 4.15 points, with a standard deviation of 24.04. The CoQ10-only group had a mean change of 26.56 points, the D-ribose-only group 29.97 points, and the CoQ10 plus D-ribose group 33.0 points. The posted unadjusted comparisons against placebo estimate mean differences of 22.41 points for CoQ10 only, 25.82 points for D-ribose only, and 28.85 points for the combination. Each reported confidence interval is entirely above zero, and each unadjusted p-value is <0.001.

These estimates describe differences in average score change, not the experience of every participant. The KCCQ scale runs from 0 to 100, with higher scores indicating better health status. Thus the direction of the posted mean changes and mean differences is toward higher scores in the active-treatment groups than in the placebo-only group. The confidence intervals express uncertainty about the estimated mean differences under the simple unadjusted comparison; they do not establish that the effect is identical across patients or settings.

The group standard deviations are sizable relative to the group means, indicating considerable variation in individual change scores. The reported outcome counts also differ across arms, and the registry notes that some participants did not complete the questionnaire or left due to COVID-19. The missing-data method and the characteristics of participants with missing results are not reported in the registry record. These limitations make it important not to treat the posted group averages as a complete account of all randomized participants.

The comparisons are unadjusted recalculations from posted summary statistics, and the registry record lists no reported analyses. They should therefore be read as descriptive statistical contrasts, not as a substitute for a prespecified sponsor analysis. The record does not report a multiplicity adjustment, an analysis model, or a primary analysis population. In a study with multiple arms and outcomes, those omissions limit how confidently p-values can be interpreted as confirmatory evidence.

The secondary results have a mixed pattern: the posted vigor and ejection-fraction comparisons show positive mean differences against placebo, while the septal E/e' estimates are negative and their confidence intervals include zero. These outcomes provide context but do not change the fact that KCCQ was designated primary. The secondary findings are exploratory in the absence of reported multiplicity procedures and an analysis plan. No conclusion about treatment benefit or lack of benefit should be drawn from these statistical summaries alone.

10. Statistical Methods Explained

The primary outcome is continuous: it is a numeric score that can take values across a scale. The registry reports means and standard deviations for change from baseline to Week 12. A mean describes the group’s average change; a standard deviation describes how dispersed the individual changes are around that average. The mean is useful for comparing groups, but it can conceal different response patterns within each group. The standard deviation gives information about that spread, but it is not itself a measure of uncertainty in the estimated group mean.

What does a mean difference represent?

Each posted primary comparison contrasts an active-treatment group’s mean change with the placebo-only group’s mean change. The estimate is the difference between these group averages, expressed in KCCQ score points. A positive estimate means the active-treatment group’s average change was higher than the placebo-only group’s average change. Because higher KCCQ scores indicate better health status, direction can be interpreted using that scale definition. The estimate does not mean that every participant had a change of that size, and it does not show how many participants improved.

The comparison uses the reported group summaries and is an unadjusted recalculation. It is not an adjusted estimate from a reported regression model, and it does not account for any covariates or trial features beyond the summary statistics used in the calculation. The registry record does not report the sponsor’s statistical model or a formal set of reported analyses. When such analyses are absent, recalculated comparisons are useful for understanding the posted numbers but cannot establish which analysis was prespecified or how the trial investigators handled all design and data issues.

What does the confidence interval add?

A confidence interval gives a range of values reasonably compatible with the observed data under the calculation’s assumptions. It conveys precision as well as direction: a narrower interval indicates a more precise estimate than a wider interval, while an interval spanning zero is compatible with no group difference under the corresponding procedure. A confidence interval is not a range containing every participant’s response, nor does it assign a probability to the true value after the data have been observed. The primary intervals lie above zero, while some secondary intervals include zero.

The interval should be interpreted together with the trial context. These are unadjusted comparisons using posted summary statistics, and the original analytic plan is not reported in the registry record. Confidence intervals do not correct for missing outcome data, multiplicity, or bias from departures from the planned trial procedures. Their stated precision is conditional on the method used to calculate them.

Why do sample sizes and variation matter?

Precision depends in part on how many outcome observations contribute to a comparison and how variable those observations are. More variable results generally make it harder to estimate a group mean difference precisely, while more observations can improve precision when other assumptions hold. In this trial, the primary standard deviations are 24.04 for placebo only, 18.61 for CoQ10 only, 21.95 for D-ribose only, and 21.45 for the combination. These describe participant-level spread in changes; they should not be confused with the confidence interval width or with standard errors.

The outcome group counts are 37.0 for placebo only, 35.0 for CoQ10 only, 33.0 for D-ribose only, and 33.0 for the combination. They are outcome-specific counts, not necessarily the total randomized group sizes. The record does not report the reason for every difference between enrollment and outcome counts or the method used to address missing values. Loss of observations can affect both precision and the interpretation of group comparisons if missingness is related to health status or treatment experience.

Why can over-dispersion matter?

As a general statistical concept, over-dispersion occurs when data vary more than a model assumes. If a method assumes less variation than is actually present, standard errors may be too small and confidence intervals too narrow. A method that accommodates greater variability can better reflect uncertainty. For this trial’s primary endpoint, the posted outcome is continuous and summarized with standard deviations, so the central issue is the observed spread and the assumptions behind the comparison; the registry record does not describe a model or an over-dispersion adjustment. Over-dispersion is more commonly discussed with count outcomes, but the broader lesson is that uncertainty calculations depend on an appropriate account of variability.

The comparison p-values are unadjusted. In general, a p-value measures how incompatible the observed data are with a specified null hypothesis under a statistical procedure; it is not the probability that the null hypothesis is true and does not quantify the size or clinical importance of an effect. A small p-value is not a substitute for an effect estimate and its confidence interval. Here, no multiplicity strategy or prespecified hierarchy is reported, so the p-values do not account for the number of outcomes and comparisons considered.

Finally, statistical significance and clinical importance are different questions. The registry record does not provide a threshold for a clinically important KCCQ change, so the clinical meaning of a particular point difference cannot be classified using a trial-specific threshold from this record. The observed mean difference, scale direction, uncertainty, missing-data context, and analysis limitations all contribute to interpretation.

11. Confidence Intervals and Precision

The primary mean-difference estimates are 22.41 points for CoQ10 only versus placebo only, 25.82 points for D-ribose only versus placebo only, and 28.85 points for CoQ10 plus D-ribose versus placebo only. Their respective confidence intervals are 12.51 to 32.31, 15.05 to 36.59, and 18.19 to 39.51. Each interval is on the positive side of zero, so each unadjusted comparison is consistent with a higher average KCCQ change in the active-treatment group than in the placebo-only group under the calculation used.

The intervals also show that the exact size of each mean difference is uncertain. A confidence interval is not a guarantee about the range of effects in other patients or settings; it reflects sampling uncertainty under the statistical method and its assumptions. The widths are affected by the outcome variability and the numbers contributing to each comparison. The standard deviations show substantial spread in individual changes, so the mean estimates should not be understood as uniform responses.

The posted intervals do not address uncertainty from missing observations, departures from the study procedures, or unreported analytic choices. The registry record notes questionnaire refusals and departures related to COVID-19, but does not report the missing-data method. The intervals are unadjusted, and the record does not report a multiplicity procedure. Consequently, their nominal interpretation should not be extended to a family of comparisons as though multiplicity had been controlled. They describe precision for each simple comparison, not certainty about all outcomes collectively.

For the secondary septal E/e' comparisons, both confidence intervals include zero, illustrating that an estimate’s direction alone does not establish a clear difference. The registry record does not define a clinically important difference for that measure either. Statistical precision and clinical relevance must therefore remain distinct considerations.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect1520
75% of the observed effect2635
50% of the observed effect5978
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10205010020040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: CoQ10 Only.

The planning illustrations report participants per arm for the continuous outcomes. They are not total-event counts. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the target effect is a stated fraction of the observed effect. The original trial design assumptions are not reported in the registry record, so these illustrations should not be mistaken for the enrollment calculation used to plan this trial.

The 80% power column gives the illustrated number of participants per arm for a planning scenario with an 80% chance of detecting the assumed effect under the stated calculation assumptions, if that effect and assumptions held. The 90% power column gives the corresponding illustration for a 90% chance. These are planning concepts, not guarantees about the result of a future study. They depend on the assumed effect size, variability, allocation, significance level, and statistical approximation.

Rows for 100% of the observed effect use the observed contrast as the planning effect; rows for 75% or 50% use smaller fractions of it. Smaller effects are harder to distinguish from chance variation and therefore require more participants per arm under the same assumptions. The table and curve communicate how those planning counts change as the target effect is made smaller. The figures are not observed power and do not measure the probability that this completed trial’s finding is true.

Because the observed effect can be imprecise and may be larger or smaller than a future study’s true effect, planning directly from it can be optimistic. The registry record does not report an original design target, recruitment allowance, or the assumptions used for its planned enrollment. These recalculated figures are illustrations only, not a reconstruction of the trial’s original design.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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 = 22.410; pooled standard deviation σ = 21.574.
  2. n = 2 × (1.96 + 0.842)2 × 21.5742 / 22.4102 = 14.5, rounded up to 15 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 <- 22.41                      # observed difference in means
sigma <- 21.5739489066923                     # 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(3133793)
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 = 15 (80% power), 20 (90% power)
 75% of observed effect: n per arm = 26 (80% power), 35 (90% power)
 50% of observed effect: n per arm = 59 (80% power), 78 (90% power)
power.t.test: 15.6 
Simulated power at n = 15 per arm: 0.783 (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.

Very small required sample. The formula gives a very small requirement because the observed effect is very large relative to the variability. Normal-approximation formulas are unreliable at such sizes, and the simulation above shows the power actually achieved. An exact or simulation-based design would be needed in practice.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when researchers examine several outcomes or make several comparisons. Even when each individual statistical test uses a conventional significance threshold, considering many tests without adjustment can increase the chance of at least one apparently significant result by chance. This trial lists a primary endpoint and seven secondary outcomes, and the primary outcome has comparisons for three active-treatment groups against placebo. The registry record does not report a multiplicity correction, a testing hierarchy, or a plan distinguishing confirmatory from exploratory comparisons.

The primary endpoint is identified in the registry, but its analysis model, analysis population, and handling of repeated or incomplete measurements are not reported. The record lists no reported analyses. The posted mean differences and associated unadjusted p-values are simple recalculations from summary statistics rather than a reported adjusted sponsor analysis. A recalculation cannot establish whether the trial’s investigators used another method or whether a prespecified approach differed.

Missing outcome data are relevant. The registry record says a few participants refused to complete the KCCQ or left the study due to COVID-19. It does not report the number missing by reason for every endpoint, the timing of missingness, or the method used to address it. If participants with missing outcomes differed systematically from those with observed outcomes, the observed means could be less representative of all randomized participants. This is a general concern, not a claim that such bias occurred in this trial.

The registry record also does not specify whether results were analyzed according to assigned group, whether adherence was considered, or how protocol deviations were handled. These are analysis-population and data-handling decisions that can affect interpretation. Without those details, the posted summaries support a description of available outcome data but cannot resolve how missingness, treatment discontinuation, or multiplicity was handled in the original analysis.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo Only83821.1%
CoQ10 Only103528.6%
D-ribose Only53315.2%
CoQ10 + D-ribose73321.2%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo Only21.1%CoQ10 Only28.6%D-ribose Only15.2%CoQ10 + D-ribose21.2%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo Only0 of 38
CoQ10 Only0 of 35
D-ribose Only0 of 33
CoQ10 + D-ribose1 of 33

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 1% reporting threshold.

ArmParticipants affected of at risk
Placebo Only2 of 38
CoQ10 Only1 of 35
D-ribose Only1 of 33
CoQ10 + D-ribose2 of 33

Most frequent serious adverse event terms

Event termOrgan systemPlacebo OnlyCoQ10 OnlyD-ribose OnlyCoQ10 + D-ribose
Heart FailureCardiac disorders3 of 382 of 350 of 331 of 33
Lung InfectionRespiratory, thoracic and mediastinal disorders1 of 381 of 353 of 331 of 33
Chest painCardiac disorders0 of 381 of 351 of 330 of 33
Urinary Tract InfectionRenal and urinary disorders0 of 380 of 350 of 332 of 33
SyncopeNervous system disorders0 of 382 of 350 of 330 of 33
FallMusculoskeletal and connective tissue disorders1 of 381 of 350 of 330 of 33
PneumonitisRespiratory, thoracic and mediastinal disorders0 of 380 of 350 of 331 of 33
Skin infectionInfections and infestations0 of 380 of 350 of 331 of 33
Non-cardiac chest painGastrointestinal disorders0 of 380 of 350 of 331 of 33
HypotensionCardiac disorders0 of 380 of 351 of 330 of 33

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo OnlyCoQ10 OnlyD-ribose OnlyCoQ10 + D-ribose
DiarrheaGastrointestinal disorders1 of 380 of 350 of 331 of 33
Soft tissue infectionInfections and infestations0 of 380 of 350 of 331 of 33
Bullous DermatitisInfections and infestations0 of 380 of 351 of 330 of 33
ConstipationGastrointestinal disorders0 of 381 of 350 of 330 of 33
HypertensionCardiac disorders1 of 380 of 350 of 330 of 33

Serious events with the highest arm-level rate: lung infection (9.1%), heart failure (7.9%), urinary tract infection (6.1%), syncope (5.7%), chest pain (3.0%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The serious-adverse-event figures are counts of affected participants and the corresponding numbers at risk in each arm, as recorded in the registry. For placebo only, 8 participants were reported with serious adverse events among 38 at risk; for CoQ10 only, 10 among 35; for D-ribose only, 5 among 33; and for CoQ10 plus D-ribose, 7 among 33. Deaths were recorded as 0, 0, 0, and 1 in those same groups, respectively. These are descriptive counts and do not establish that a treatment caused an event.

The record lists serious-event terms including Lung Infection at 9.1%, Heart Failure at 7.9%, Urinary Tract Infection at 6.1%, Syncope at 5.7%, Chest pain at 3.0%, and Pneumonitis at 3.0%. These percentages are presented as recorded; the event-term denominator and whether individuals could contribute to multiple terms are not reported in the registry record. Comparisons should be cautious because the group sizes are limited and the record does not provide a causal safety analysis, event timing, or adjustment for differences in exposure.

Other adverse events are also listed, but counts alone do not show severity, duration, or attribution. Safety findings should be read as registry-reported observations, not proof for or against a treatment effect.

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

The posted primary results show larger average KCCQ score changes in each active-treatment group than in the placebo-only group over the interval from baseline to Week 12. The KCCQ scale direction means higher changes correspond to better reported health status. The unadjusted mean differences are accompanied by confidence intervals that do not cross zero. These statistics describe the observed group summaries and the precision of simple comparisons; they do not establish a causal conclusion by themselves.

The results do not show that every participant improved, that the treatments would produce the same pattern in another population, or that one active regimen is superior to another. The comparisons are each against placebo, not direct head-to-head tests between the active groups. No statistical comparison among the active-treatment arms is reported. The registry record also does not define a threshold for clinical importance, so the point estimates cannot be classified as clinically meaningful on the basis of a trial-specific threshold.

Nor do these results establish effects on outcomes not reported numerically. The registry names multiple secondary outcomes, but numerical findings are only posted for some of them. Measures such as ejection fraction and BNP assess different constructs from a patient-reported questionnaire. A result on one measure does not automatically imply an effect on another, and absence of a posted numerical result is not evidence of no effect.

The record does not report an analysis plan, missing-data approach, or multiplicity strategy. The KCCQ outcome has incomplete observations noted, and the posted comparisons are unadjusted recalculations. Those features limit how far the statistics can support confirmatory claims. Safety counts are descriptive and cannot establish causation. Taken together, the results are best read as a set of registry-posted group summaries and simple contrasts requiring cautious interpretation, rather than as definitive evidence about treatment efficacy or safety.

17. Why This Trial Matters Statistically

This trial is statistically informative because it combines a patient-reported primary outcome with several physiological and functional secondary measures. The KCCQ captures symptoms, limitations, and health status from the patient’s perspective, while the named secondary outcomes include measures of vigor, cardiac function, walking performance, and laboratory markers. Considering distinct outcome types helps readers see why a treatment comparison cannot be reduced to a single number or measurement domain.

The four randomized groups also allow the record to present separate comparisons for CoQ10, D-ribose, and their combination against placebo. The posted primary means and confidence intervals make it possible to examine both estimated differences and their uncertainty. At the same time, they highlight the need to distinguish group averages from individual experiences and to distinguish statistical evidence from clinical importance.

The trial also illustrates why registry completeness matters. The record marks the study completed and identifies the primary endpoint, but does not report its original statistical plan, missing-data methods, multiplicity procedures, or analysis population. Those details help readers judge whether reported comparisons were planned, how incomplete outcomes were addressed, and whether multiple tests were accounted for. Without them, even apparently clear unadjusted contrasts have limits as confirmatory evidence.

Finally, the sample-size illustrations show how planning depends on the target effect and assumptions. They are not a substitute for the original design rationale and should not be confused with a retrospective measure of the trial’s power. Reading effect estimates, intervals, design context, outcome availability, and analytic transparency together is central to sound biostatistical interpretation.

18. Limitations

Several limitations are specific to the information recorded for this trial. The registry notes questionnaire refusals and departures related to COVID-19, but does not report how missing KCCQ scores were handled or whether missingness differed across groups. The outcome counts are below enrollment, and the registry does not explain every gap between enrolled participants and those contributing to each outcome. Missing observations could affect the representativeness of the posted mean changes.

The registry does not report the original statistical analysis plan, the model used by investigators, the analysis population, or an approach to multiplicity. The comparison statistics are unadjusted recalculations from summary values, and the record lists no reported analyses. As a result, the calculations do not show whether the original analysis accounted for baseline values, other covariates, or trial-specific features. No adjustment for multiple comparisons is documented.

The primary endpoint is a patient-reported scale, and the record does not provide a clinically important difference threshold. The averages and standard deviations do not reveal the distribution of individual responses or the proportion of participants experiencing a particular degree of change. The posted primary results therefore cannot alone resolve the clinical importance or consistency of the observed changes.

The registry record identifies the study as double-masked but does not describe who was masked or how masking was maintained. It also does not report adherence, treatment exposure, or reasons for discontinuation beyond the note about COVID-19 and questionnaire refusal. Numerical results are not reported for all named secondary outcomes. These gaps limit interpretation of both efficacy patterns and safety counts.

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22. Record Summary

NCT03133793 is a completed Phase 2 randomized, double-masked, parallel-group trial sponsored by the University of Kansas Medical Center. The registry lists enrollment of 216 and compares placebo only, CoQ10 only, D-ribose only, and CoQ10 plus D-ribose in people with diastolic heart failure or HFpEF.

The primary endpoint is change in KCCQ health-status score from baseline to Week 12. Posted group means and unadjusted comparisons show higher average changes in the active-treatment groups than in placebo only, with confidence intervals reported for the mean differences. Secondary outcomes include several patient-reported, functional, physiological, and laboratory measures, though numerical results are not posted for all named outcomes.

The record notes some incomplete KCCQ assessments or departures due to COVID-19, and it does not report the original statistical plan, missing-data method, multiplicity procedure, or analysis population. Safety counts are descriptive. The statistical results therefore require interpretation in light of incomplete analysis details and should not be treated as definitive causal conclusions.

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