Mitochondria and Chronic Kidney Disease: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Mitochondria and Chronic Kidney Disease (NCT03177798), a randomized phase 2 study. The primary outcome is Phosphocreatine (PCR) Recovery Time After Knee Extension Assessed by 31 Phosphorus Magnetic Resonance Spectroscopy (31P-MRS).

2. Clinical Question

3. Trial Design

This was a phase 2, randomized, quadruple-masked, crossover study. The registry lists total enrollment of 11 and a completed status. The study began on 2017-08-01, with primary completion on 2018-06-30. The summary describes a randomized, placebo-controlled, double-blind crossover study; the registry separately records quadruple masking.

Participants were assigned to one of two sequences: icatibant followed by placebo, or placebo followed by icatibant. The descriptions state that a 1 week washout separated the treatment periods. In the icatibant-then-placebo description, icatibant was infused at 50 ug/kg/h for 1 hour before dialysis and continued through hemodialysis (4 hours); placebo was described as infused at the same rate for 1 hour before dialysis. In the reverse sequence, placebo was described as continuing through hemodialysis (4 hours), while icatibant was described as infused for 1 hour before dialysis. The registry does not clarify these differences in the sequence descriptions.

A crossover design exposes participants to both treatments, allowing treatment comparisons to use measurements from the same people. This can make within-participant differences informative, but the interpretation depends on accounting for the pairing, treatment order, period, and any carryover. The statistical model and handling of these design features are not reported in the registry record. The registry lists systolic blood pressure as a secondary outcome, and one secondary outcome is posted; numerical results for that outcome 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

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: Patients on hemodialysis three times a week for at least six months

6. Primary Endpoint

The registry lists the primary outcome as Phosphocreatine (PCR) Recovery Time After Knee Extension Assessed by 31 Phosphorus Magnetic Resonance Spectroscopy (31P-MRS), measured over Up to 2 hours after completion of drug infusion.

The primary endpoint was phosphocreatine (PCR) recovery time after knee extension, measured in seconds with 31-phosphorus magnetic resonance spectroscopy (31P-MRS). The endpoint is the time constant tau of phosphocreatine recovery: the time required to reach 66.3% of maximal concentration during recovery. The registry uses this measure to assess mitochondrial function.

During the described assessment, participants underwent basal measurements, performed 90 seconds of knee extension, and then rested for 4 minutes. The exercise-and-rest cycle was repeated 3 times. Magnetic resonance spectra were used to calculate concentrations of inorganic phosphate (Pi), phosphocreatine (PCr), and adenosine triphosphate (ATP). The primary outcome focuses on PCr recovery rather than reporting all measured phosphate-energy carrier concentrations as separate primary endpoints.

As a general measurement principle, a recovery time is a continuous outcome: larger or smaller values express a difference in elapsed time, rather than a count of events or a yes-or-no response. The registry identifies 31P-MRS as the method for evaluating mitochondrial function and describes it as the gold standard method. The recorded timeframe is up to 2 hours after completion of drug infusion. This endpoint concerns a measured physiological response under the study assessment conditions; it is not, by itself, a direct summary of broader clinical outcomes.

7. Results Posted in the Registry

• Icatibant: mean 60.59 versus 62.66 on control; difference -2.07 (95% CI -21.30 to 17.16), standardized effect d = -0.09; z-test p = 0.833.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous and is reported as a mean with a standard deviation for each treatment. A mean describes the central value of the observed measurements, while a standard deviation describes their spread. For icatibant, the posted mean was 60.59 seconds and the standard deviation was 13.94 seconds. For placebo, the mean was 62.66 seconds and the standard deviation was 29.4 seconds. These summaries describe the recorded observations; they do not show the distribution of individual participant values or the within-person treatment differences.

What does the mean difference represent?

The posted mean difference compares the icatibant mean with the placebo mean and is -2.07 seconds. A negative value indicates that the displayed icatibant mean was lower than the displayed placebo mean. The registry does not describe the method used to estimate this contrast. In particular, it does not say whether the calculation used each participant's paired measurements, adjusted for treatment sequence or period, or used another model. Those details are especially relevant in a crossover study, where each participant receives both treatments.

As a general statistical concept, a paired analysis uses the within-person contrast between treatment periods. It can account for the fact that measurements from the same participant are related. Treating observations from the same person as independent can misrepresent uncertainty. Crossover analyses may also need to consider treatment order, period effects, and carryover. Whether and how these issues were addressed is not reported in the registry record.

How should the p-value be read?

The posted unadjusted p-value is 0.833. In general, a p-value describes how compatible the observed result is with a specified null hypothesis under the assumptions of a statistical test. It is not the probability that the null hypothesis is true, and it does not quantify the size or clinical importance of a difference. The test specification and model assumptions are not reported in the registry record, so the p-value should be interpreted as the posted unadjusted result, not as evidence that all possible analyses would give the same result.

General statistical context: adjustment refers to accounting for design variables or other factors in a model; an unadjusted comparison does not incorporate such factors. The registry gives no analysis plan or model details. It also lists 0 analyses, so the record does not document an analysis set, a prespecified model, or an inferential procedure beyond the posted summary comparison.

What role does the confidence interval play?

The confidence interval for the mean difference extends from -21.3 to 17.16 seconds. General explanation: a confidence interval expresses uncertainty around an estimated contrast under the assumptions of the method used to calculate it. A narrower interval indicates greater precision, whereas a wider interval indicates less precision. Here, the interval spans zero and permits both negative and positive contrasts. Its width means the point estimate alone should not be treated as a precise estimate of the treatment difference.

The interval does not assign probabilities to particular treatment effects, and it does not resolve the uncertainty created by unreported analysis details. The method used to calculate it is not reported in the registry record. The displayed interval should therefore be read as the uncertainty statement associated with the posted comparison, with the crossover analysis details remaining unknown.

Why does variability matter?

The standard deviations differ between the treatment summaries: 13.94 seconds for icatibant and 29.4 seconds for placebo. General statistical context: over-dispersion means that observations vary more than a model's assumptions anticipate. When variability is greater, estimates are often less precise; if a model assumes an inappropriate variance structure, its uncertainty estimates may also be unreliable. The registry does not state whether the analysis examined variance assumptions or used a method that allows different variability between treatment periods.

The comparison also reports a pooled standard deviation of 23.01 and a standardized difference of -0.09. These are scale-based summaries of the posted contrast and observed variability. They do not replace the treatment-unit estimate in seconds, nor do they correct for the unreported paired structure. The record does not explain the role of these summaries in the original analysis.

Finally, general statistical interpretation must distinguish an observed estimate from a design target. The planning illustrations use fractions of the observed effect and stated assumptions; they are not evidence about the trial's original design or about the probability that the completed study detected an effect. The registry does not report its original sample-size justification, statistical plan, interim analyses, missing-data methods, or analysis populations.

10. Confidence Intervals and Precision

The mean difference is -2.07 seconds, and its confidence interval ranges from -21.3 to 17.16 seconds. The point estimate is close to zero in the scale of the endpoint, but the interval is broad and includes both negative and positive values. That breadth means the posted data do not pin down the size or direction of the treatment contrast with much precision.

A confidence interval is an uncertainty range calculated under a statistical method and its assumptions. In general, a narrow interval is more precise than a wide interval. The interval is consistent with the point estimate being only one among a substantial range of possible contrasts. It does not show that all values within the interval are equally plausible, and it does not establish equivalence or absence of an effect.

Precision is limited in the context of total enrollment of 11 and the observed variation in the treatment summaries. The registry lists 11 observations for each treatment arm, but those entries arise from a crossover study and should not be interpreted as separate groups of 11 different people. The reported comparison does not provide the within-participant correlation or the distribution of paired differences, information that would help readers understand the precision of a crossover estimate.

The confidence-interval method and the model used to obtain it are not reported in the registry record. That absence matters because the design is paired and the reported arm-level standard deviations do not convey the variability of within-person contrasts. The interval is useful as the posted uncertainty summary, but its statistical assumptions and treatment of the crossover design cannot be independently evaluated from the registry record.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. The planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers detecting 100%, 75%, or 50% of the observed effect. These are planning assumptions for an illustration based on the observed effect; the trial's own original design assumptions are not reported in the registry record.

The 80% power column gives the illustrated number of participants per arm for a design intended to have an 80% chance of detecting the specified effect if that effect is the true one and the planning assumptions hold. The 90% power column gives the corresponding number for a design intended to have a 90% chance. These are prospective planning concepts, not descriptions of what happened in the completed trial.

For 100% of the observed effect, the illustration gives 1,940 participants per arm for 80% power and 2,597 participants per arm for 90% power. For 75% of the observed effect, it gives 3,448 participants per arm for 80% power and 4,616 participants per arm for 90% power. For 50% of the observed effect, it gives 7,757 participants per arm for 80% power and 10,385 participants per arm for 90% power. Smaller effects need more participants to detect under the same assumptions, which is why the planning figures rise as the target effect becomes smaller.

The curve represents the same planning relationship visually. These figures are not observed power: they are illustrations based on the observed effect, not calculations of the completed study's probability of detecting a true effect. They should not be read as the trial's prespecified target or as a justification for its enrollment.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -2.070; pooled standard deviation σ = 23.007.
2. n = 2 × (1.96 + 0.842)² × 23.007² / -2.070² = 1,939.2, rounded up to 1,940 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 <- -2.06999999999999                      # observed difference in means
sigma <- 23.0074292349232                     # 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(3177798)
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 = 1,940 (80% power), 2,597 (90% power)
 75% of observed effect: n per arm = 3,448 (80% power), 4,616 (90% power)
 50% of observed effect: n per arm = 7,757 (80% power), 10,385 (90% power)
power.t.test: 1940.2 
Simulated power at n = 1,940 per arm: 0.797 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry identifies phosphocreatine recovery time as the primary outcome and lists systolic blood pressure as a secondary outcome. It reports one secondary outcome, but the numerical result for systolic blood pressure is not reported in the registry record. The registry does not report a multiplicity plan describing how inference across outcomes was to be handled.

General statistical context: when several outcomes or several analyses are considered, the chance of at least one apparently unusual result can increase unless the analysis plan addresses that issue. The registry record does not say whether the primary outcome was the sole confirmatory test, whether secondary outcomes were considered exploratory, or whether any adjustment was planned. The posted primary p-value is described as unadjusted; no adjusted result is reported.

The record lists 0 analyses. It does not report a prespecified statistical analysis plan, an interim-analysis plan, a stopping rule, or a hierarchy of tests. The original sample-size justification is also not reported. No specific approach to missing data, exclusions, protocol deviations, or analysis populations is described.

These are reporting gaps, not proof that the study did not use such methods. They do mean that readers cannot determine from the registry record whether all randomized participants contributed to the primary analysis, whether measurements from both treatment periods were available for every participant, or how any incomplete observations were handled. The registry's arm counts do not resolve those questions because the design is crossover and total enrollment is 11.

General statistical context: analysis-population definitions clarify which participants and observations are included in each result. Missing-data methods clarify how incomplete outcomes are treated. Both are important to interpreting a crossover comparison, where results can depend on the availability of measurements across treatment periods. Neither the population definitions nor the missing-data methods are reported in the registry record.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hospitalization for cardiac catheterization (9.1%), hypovolemia (9.1%).

The posted serious adverse event figures list 0 affected participants among 11 at risk for icatibant and 2 among 11 at risk for placebo. The listed counts for other adverse events are 1 among 11 for icatibant and 1 among 11 for placebo. No deaths are listed in either group.

The serious adverse event terms shown are hospitalization for cardiac catheterization and hypovolemia, each listed as 9.1%. The registry does not attribute these terms to a particular treatment group in the term listing, so they should not be assigned to a group on that basis. The group-level serious-event counts and the terms are different kinds of information: one reports affected participants by group, while the term listing names serious events.

These are descriptive counts from a study with total enrollment of 11. They are not a comparative safety analysis, and the registry does not report a statistical test or detailed causal attribution. The counts alone do not establish whether an event was caused by a treatment. Adverse-event definitions, collection procedures, timing, and the relationship of each event to treatment are not reported in the registry record.

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

The primary-outcome comparison describes phosphocreatine recovery time measured after knee extension using 31P-MRS. The posted mean was 60.59 seconds with icatibant and 62.66 seconds with placebo. The mean difference was -2.07 seconds, with a confidence interval from -21.3 to 17.16 seconds and an unadjusted p-value of 0.833. These results show a small point estimate relative to the uncertainty expressed by the interval, not a precise estimate of the treatment contrast.

The confidence interval includes zero and extends in both directions. As a result, the posted comparison does not distinguish a difference in either direction from no difference under the reported unadjusted analysis. It does not establish that the treatments are equivalent, and it does not demonstrate that there is no effect. The study's enrollment and the breadth of the interval leave substantial uncertainty.

The study addresses a focused physiological measure in people undergoing hemodialysis. It does not, from this primary result alone, establish effects on symptoms, longer-term outcomes, or other aspects of mitochondrial function. Systolic blood pressure is listed as a secondary outcome, but its numerical result is not reported in the registry record. No broader clinical outcome should be inferred from the primary endpoint.

The crossover design has potential to compare treatment periods within the same participants, but the registry does not describe the analysis model or whether the comparison accounted for pairing, period, sequence, or carryover. Therefore, the displayed arm summaries and contrast are not enough to assess every design-specific feature of the analysis. The safety counts are also descriptive and do not establish causation.

In practical statistical terms, the result is inconclusive as an estimate of the treatment difference: the point estimate is available, but its precision and the unreported analytic details limit interpretation. This is a statement about what the registry record reports, not advice about treatment or a claim about the clinical value of either intervention.

16. Why This Trial Matters Statistically

This trial is statistically notable because its randomized crossover design asks for a treatment comparison in which the same participants receive icatibant and placebo in different periods. Such a design can make within-person comparisons valuable, because each participant can serve as their own reference. It also makes the analysis structure important: pairing, sequence, period, and potential carryover can affect how treatment differences and their uncertainty should be estimated.

The registry reports a mean difference and confidence interval, but not the statistical model used to obtain them. That gap prevents readers from determining whether the posted estimate reflects the crossover structure. The arm-level means and standard deviations alone do not reveal the variability of the paired differences, which is central to understanding precision in a within-person comparison.

The second statistical lesson is the distinction between a point estimate and its uncertainty. The mean difference is -2.07 seconds, while the confidence interval extends from -21.3 to 17.16 seconds. The estimate's direction is not enough to settle interpretation because the interval is broad and spans zero. Reporting the interval alongside the point estimate makes that imprecision visible.

Finally, the enrollment of 11 underscores how a small study can yield an estimate with substantial uncertainty, even when its design is randomized. The planning illustrations are based on the observed effect and stated assumptions; they do not reveal the original design rationale. Together, the design and reporting features make the record a useful example of why readers need both an effect estimate and sufficient detail about the model that produced it.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The total enrollment was 11, limiting the amount of information available for estimating the primary treatment contrast. The posted confidence interval is broad, and the treatment summaries have different standard deviations. The record does not provide participant-level data or the distribution of within-person differences, so readers cannot inspect the paired observations or assess outliers and distributional features.

The registry does not report how the crossover analysis handled pairing, treatment order, period effects, or carryover. Although a 1 week washout is described, the record does not state how the washout was selected or whether carryover was assessed. The sequence descriptions also differ in whether the infusion is said to continue through hemodialysis (4 hours), and the record does not clarify that discrepancy.

Other limitations are reporting-related. The original sample-size justification, statistical analysis plan, interim analyses, multiplicity approach, missing-data procedures, and analysis populations are not reported in the registry record. Numerical results for the listed secondary outcome, systolic blood pressure, are also not reported. The registry does not give detailed eligibility criteria or participant characteristics, limiting assessment of the population to which the result might apply.

The adverse-event information is descriptive and does not report detailed attribution or a comparative safety analysis. These limitations do not establish that the methods were inadequate; they identify what cannot be evaluated from the registry record. Interpretation should remain tied to the posted primary-outcome summaries and their uncertainty.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Mitochondria and Chronic Kidney Disease — NCT03177798.
• Registry record last updated 2019-10-29; status last verified 2019-10.
• Results first posted 2019-10-29.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes a completed phase 2 randomized, quadruple-masked crossover study sponsored by Vanderbilt University Medical Center. It enrolled 11 participants and compared icatibant with placebo in two treatment sequences, with a 1 week washout described between periods. The stated primary endpoint was phosphocreatine recovery time after knee extension measured by 31P-MRS.

The posted means were 60.59 seconds for icatibant and 62.66 seconds for placebo. The mean difference was -2.07 seconds, with a confidence interval from -21.3 to 17.16 seconds and an unadjusted p-value of 0.833. The record lists systolic blood pressure as a secondary outcome, but its numerical result is not reported. The crossover analysis details, missing-data methods, original sample-size justification, and statistical analysis plan are not reported in the registry record.