Exercise Training and Cognitive Function in Kidney Disease: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Exercise Training and Cognitive Function in Kidney Disease (NCT03197038), a randomized na study. The primary outcome is Composite Global Cognitive Function.

2. Clinical Question

3. Trial Design

NCT03197038, titled Exercise Training and Cognitive Function in Kidney Disease, is recorded as a completed randomized, parallel-group study with no masking. The registry lists University of Illinois Chicago as sponsor and an enrollment of 39. The study began on 2017-09-01, and its primary completion date is 2019-11-26. The listed phase is NA.

Participants were assigned to home-based walking exercise or control. The intervention was behavioral, as was the control condition. The primary endpoint was a continuous measure: change from baseline in composite global cognitive function at 6 months, reported as a Z-score. The record identifies the primary outcome summary as a mean with standard deviation.

The primary outcome summaries list 18 participants in the exercise group and 17 in the control group. These endpoint counts are not the same as the registry’s total enrollment of 39. The reason for the difference is not reported in the registry record. The outcome record does not describe the allocation ratio, how the random sequence was generated, or whether allocation was concealed. Masking is listed as none, but further detail about who knew participants’ assignments is not reported in the registry record.

The study also registered secondary outcomes covering cognition, brain imaging, motor function, and vascular health. The available outcome summaries include several of these measures, with different numbers of participants contributing to different outcomes. The registry record does not report the original sample-size justification or the trial’s planned statistical analysis details.

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.

6. Primary Endpoint

The registry lists the primary outcome as Composite Global Cognitive Function, measured over Change from baseline in composite global cognitive function at 6 months.

The primary endpoint was change from baseline in composite global cognitive function at 6 months. It is a continuous Z-score, with the endpoint summary expressed as a mean and standard deviation. The composite was formed by converting individual cognitive test scores to standardized Z-scores and averaging them. The listed tests cover memory, attention and processing, executive function, fluency, and digit span.

A composite can combine information across several related tests rather than treating one task as the whole of cognition. The registry describes the component measures and states that an increase in change from baseline was considered improvement. The measure therefore represents overall performance across the selected tests, not a diagnosis or a single cognitive ability in isolation.

The outcome was chosen to address the study’s stated question about cognitive function in older patients with kidney disease and preclinical cognitive impairment. The registry also describes MRI-based measures of brain structure and blood flow, alongside behavioral and physical measures. Those outcomes can provide related but distinct information; they do not replace the primary cognitive endpoint. The record does not report the rationale for selecting this exact composite, the weighting of its components beyond averaging standardized scores, or a clinically meaningful threshold for interpreting a change.

7. Results Posted in the Registry

• Home-based Walking Exercise: mean 0.15 versus 0.02 on control; difference 0.13 (95% CI -0.10 to 0.36), standardized effect d = 0.37; z-test p = 0.272.

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.

White Matter Integrity

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Home-based Walking Exercise: mean -0.00 versus 0.00 on control; difference -0.01 (95% CI -0.02 to 0.01), standardized effect d = -0.33; z-test p = 0.448.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Home-based Walking Exercise and the control. The interval gives the range of effects that remain compatible with the data.

Cerebral Blood Flow

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Home-based Walking Exercise: mean 1.60 versus 0.30 on control; difference 1.30 (95% CI -7.32 to 9.92), standardized effect d = 0.12; z-test p = 0.768.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Home-based Walking Exercise and the control. The interval gives the range of effects that remain compatible with the data.

Vascular Health - Young's Elastic Modulus

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Home-based Walking Exercise: mean -3,175 versus 1,279 on control; difference -4,454 (95% CI -10,624 to 1,716), standardized effect d = -0.49; z-test p = 0.157.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Home-based Walking Exercise and the control. The interval gives the range of effects that remain compatible with the data.

The registered secondary outcomes extend beyond the primary cognitive composite to include brain imaging, vascular health, motor function, and additional cognitive measures. This broad set reflects related domains of interest, but each measure addresses a distinct question and may have a different scale, participant count, and amount of uncertainty.

Across the three secondary outcome summaries with quantitative comparisons in the registry record, the estimated directions are not uniform. That variation does not automatically conflict with the primary result: the measures assess different constructs, and a single cognitive composite need not move in parallel with brain imaging, blood-flow, or vascular indices. Nor does a mixed pattern establish that any one domain changed reliably. Each result must be interpreted on its own scale and with its own interval and uncertainty.

The secondary outcomes are best considered supportive or exploratory in relation to the primary question unless the analysis plan establishes otherwise. The registry record does not report that plan or a procedure for adjusting for multiple comparisons. When many outcomes are examined, some estimates can appear unusual by chance even if there is no underlying effect for those outcomes. Unadjusted p-values do not account for that broader set of comparisons, so they carry less weight than a prespecified primary analysis when drawing an overall conclusion.

Different outcome-specific participant counts also complicate comparison across measures. The record does not explain all reasons for those differences or report a common analysis population. The secondary results can describe patterns across domains, but they should not be combined informally into a single claim about cognitive or brain effects. The primary endpoint remains the designated measure for the central trial question; secondary measures add context while retaining their own limitations.

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

• White Matter Integrity
• Hippocampal Volume - Right
• Cerebral Blood Flow
• Vascular Health - Young's Elastic Modulus
• Cognitive Function - Total Cognition
• Motor Function - Grip Strength
• Vascular Health - Pulse Wave Velocity
• Vascular Health - Augmentation Index

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous, so the registry reports a mean change and standard deviation for each group. A mean describes the group’s average change, while a standard deviation describes how spread out individual changes are around that average. These summaries answer different questions: the mean concerns the group-level location, and the standard deviation concerns variation among participants.

What does the mean difference represent?

The posted contrast compares the mean change in the home-based walking exercise group with the mean change in control. Its direction is defined as exercise minus control. A positive value therefore indicates a higher mean change in the exercise group; a negative value indicates a higher mean change in control. The registry’s primary outcome description defines an increase in change from baseline as improvement, but the size of a mean difference alone does not establish whether a change is important to patients.

The reported means are 0.15 for exercise and 0.02 for control, with an unadjusted mean difference of 0.13. The group standard deviations are 0.37 and 0.33, respectively. These quantities should be read as the registry reports them; they do not convey individual participant trajectories or show how many participants improved. The endpoint is a composite average of standardized test scores, rather than a direct measure of one test.

How should the interval be understood?

The interval for the mean difference runs from -0.102 to 0.362. In general, a confidence interval expresses uncertainty about an estimated quantity under a statistical model: estimates nearer the center are more compatible with the observed data than values far from it, subject to the interval’s construction and assumptions. Because this interval spans zero, it does not distinguish clearly between a negative and a positive underlying mean difference. The confidence level and interval-construction method are not reported in the registry record, so those details should not be presumed.

The interval is not a range containing a fixed proportion of individual participants’ changes. Nor does it show that all values inside it are equally plausible. It describes uncertainty about the group contrast, not the spread of individual outcomes. The standard deviations describe participant-level spread, while the interval describes uncertainty in the estimated difference.

What does the p-value add?

The posted p-value is unadjusted and equals 0.272. In general, a p-value measures how unusual data at least as discrepant as the observed data would be under a specified null model and its assumptions. It does not measure the probability that the null is true, the probability that the result will replicate, or the clinical importance of the estimate. The registry record does not report a more detailed model specification or an adjusted p-value for the primary result.

Interpreting the p-value alongside the point estimate and interval is more informative than using it alone. The point estimate gives the direction and magnitude of the observed contrast; the interval conveys uncertainty about that contrast; the p-value provides a test-based summary under a null model. None of these quantities resolves limitations arising from incomplete reporting of the analysis population or missing-data methods.

Why are the planning illustrations separate from the trial result?

The sample-size planning illustrations use the observed effect as a reference and consider smaller fractions of it. They apply a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The original trial’s own design assumptions and sample-size justification are not reported in the registry record. The planning illustrations are not observed power: they are conditional projections for future planning under stated assumptions, not a retrospective measure of the trial’s ability to detect an effect.

More generally, planning calculations depend on the effect size chosen, the variability assumed, the significance level, the desired power, and the analysis design. If an effect smaller than the observed estimate is the target, more participants are generally needed to distinguish it from random variation under otherwise similar assumptions. The observed estimate can be unstable in a small study, so using it as a planning reference does not guarantee that a future study will have the same underlying effect or variability.

Several secondary outcomes are also continuous and have their own group summaries and unadjusted comparisons. Their interpretation follows the same general principles: examine the contrast, its interval, and the measure’s scale, while recognizing that multiple outcomes create additional opportunities for apparently notable results by chance. The registry record does not report a multiplicity adjustment or a comprehensive analysis plan.

11. Confidence Intervals and Precision

The primary mean difference is 0.13 Z-score units, with an interval from -0.102 to 0.362. The interval spans zero, so the data do not pin down the direction of the underlying difference. Values below zero and above zero remain within the reported interval. The interval’s width reflects substantial uncertainty around the point estimate relative to the estimate itself.

Precision depends in part on how many participants contribute outcome data and how much their changes vary. The primary summaries list 18 participants in the exercise group and 17 in control, with standard deviations of 0.37 and 0.33. Those group sizes are modest, and the spread in scores means individual variation contributes to uncertainty in the estimated contrast. The interval provides a more direct view of that uncertainty than the point estimate alone.

The confidence level and the method used to construct the interval are not reported in the registry record. As a result, the interval can be described by its endpoints, but its exact coverage interpretation and model assumptions cannot be fully evaluated from the registry entry. The posted p-value is also unadjusted and should not be treated as a substitute for the interval.

The interval concerns the difference between group means; it does not describe the range of individual responses or indicate how consistently participants changed. It also does not resolve uncertainty about the analysis population, because the record does not explain the difference between total enrollment and the primary outcome counts or report how missing data were handled. The available estimate is therefore informative about the observed group contrast but limited in how precisely it characterizes the effect in the intended population.

12. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total event counts. They illustrate sample sizes under a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning effect is set to the stated fraction of the observed effect, with illustrations for 100%, 75%, and 50% of that effect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

The column for 80% power describes the number of participants per arm in a hypothetical study designed to have an 80% chance of detecting the specified effect under the planning assumptions, if that effect and model assumptions were correct. The 90% power column describes the corresponding planning target for a 90% chance. These are design concepts, not guarantees about results in a future study.

As the target effect becomes smaller, the distinction from random variation becomes harder to detect, so more participants are generally needed. The illustrations use the observed effect as a reference, but an observed estimate from a small trial can be uncertain. These figures are planning illustrations, not observed power. They do not describe the power of the completed trial or establish that any particular future sample size is sufficient under different assumptions.

13. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = 0.130; pooled standard deviation σ = 0.351.
2. n = 2 × (1.96 + 0.842)² × 0.351² / 0.130² = 114.6, rounded up to 115 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 <- 0.13                      # observed difference in means
sigma <- 0.351175515126329                     # 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(3197038)
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 = 115 (80% power), 154 (90% power)
 75% of observed effect: n per arm = 204 (80% power), 273 (90% power)
 50% of observed effect: n per arm = 459 (80% power), 614 (90% power)
power.t.test: 115.5 
Simulated power at n = 115 per arm: 0.800 (20000 replicates)

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

14. Multiplicity, Missing Data and Analysis Populations

The registry identifies composite global cognitive function as the primary outcome and lists multiple secondary outcomes. Examining multiple outcomes can increase the chance of obtaining an apparently notable result by chance. Statistical methods can address this issue through prespecified testing sequences or adjustments, but such a plan is not reported in the registry record. The posted comparisons are unadjusted, and no multiplicity adjustment is described.

The record lists zero reported analyses. It therefore does not provide a fuller account of the model specification, covariates, hypothesis-testing sequence, or any sensitivity analyses. The registry does provide outcome summaries and unadjusted comparisons, but those do not reveal all decisions that may have been made in an analysis plan. The original trial’s statistical analysis plan is not reported in the registry record.

Missing-data handling is also not reported. The primary endpoint summaries list 18 participants in the exercise group and 17 in control, while total enrollment is 39. The registry does not say whether the difference reflects missing endpoint measurements, exclusions, or another reason. It does not report imputation, methods for handling incomplete follow-up, or whether analyses followed an intention-to-treat principle.

Analysis-population definitions are not reported in the registry record. It is therefore unclear whether the endpoint summaries include all randomized participants with available measurements, a specified subset, or another population. The record also does not describe how adherence to the exercise program was assessed or incorporated into analysis. These omissions limit evaluation of potential bias and make it difficult to determine whether the reported comparison corresponds to the effect of assignment among all randomized participants.

15. 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 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: transient ischemic attack (4.5%).

The registry safety record lists serious adverse events for 22 participants at risk in the home-based walking exercise group and 17 in control. It records one serious adverse event in the exercise group and none in control. The listed serious-event term is transient ischemic attack, with a reported value of 4.5%. The registry does not provide further detail in the record summarized for this comparison about event timing, relatedness, or clinical course.

For other adverse events, the record lists 14 affected participants among 22 at risk in the exercise group and 10 among 17 at risk in control. It reports zero deaths in both groups. These are counts as recorded, not evidence that events were caused by or unrelated to the assigned condition. The safety at-risk counts differ from the primary endpoint counts; the reason is not reported in the registry record.

These figures should be read descriptively. The registry entry does not provide enough detail to assess event severity beyond the serious-event designation, adjudication procedures, or comparative statistical testing. The counts alone do not establish a difference in safety between groups.

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

The posted primary result is a comparison of average change in a composite cognitive score over the 6-month outcome period. The exercise group had a higher observed mean change than control, but the estimated difference has considerable uncertainty: its interval includes values in both directions. The result therefore describes the observed data without resolving the size or direction of an underlying difference with precision.

The result does not establish that exercise caused the observed contrast, despite random assignment. Randomization is intended to support a fair comparison, but the registry record does not fully describe allocation procedures, outcome missingness, or the analysis population. Those details matter when judging whether the posted analysis preserves the benefits of randomization.

The result also does not show how many individuals improved or worsened, whether any change was meaningful to participants, or whether outcomes continued after 6 months. The composite averages standardized results from several tests and is not itself a diagnosis. The registry record does not report a clinically meaningful threshold for the score.

Nor does the primary result settle the secondary questions about brain structure, blood flow, vascular health, or motor function. Those outcomes measure different domains and have their own uncertainty. Their unadjusted results should be interpreted cautiously because the record does not report a multiplicity plan.

The appropriate statistical reading is bounded: the group summaries and unadjusted contrast describe the registered primary outcome, while the interval indicates that the estimate is imprecise. The registry record does not report enough information to establish the broader analysis strategy, explain all outcome counts, or determine the practical importance of the observed difference.

17. Why This Trial Matters Statistically

This trial is statistically interesting because it links a cognitive outcome with a behavioral intervention in a population identified by the registry as older adults with kidney disease and preclinical cognitive impairment. Its primary endpoint combines standardized results from several cognitive tasks, making the choice and construction of the composite central to interpretation. The registry describes the component tests and the averaging approach, allowing readers to understand the broad content of the score.

The record also illustrates why a point estimate should not be read alone. The mean difference gives the direction of the observed contrast, while the interval shows that the estimate remains compatible with a range of underlying differences. A single p-value does not convey that range or answer whether a change is meaningful.

There is a further planning lesson in separating retrospective results from prospective sample-size calculations. Illustrations based on the observed effect can help explore how a future study might be planned under explicit assumptions, but they are not evidence of the completed trial’s power and do not substitute for the original design rationale. That rationale is not reported in the registry record.

Finally, the registry includes a range of secondary domains and safety counts. These broaden the questions that can be asked, while also increasing the need for transparent analysis plans, clear population definitions, and careful handling of multiplicity and missing data. The gaps in those reporting details are important to the statistical interpretation, independent of the direction of the primary point estimate.

18. 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 endpoint summaries include fewer participants than the total enrollment listed in the registry, and the reason is not reported. Without a description of missing outcomes, exclusions, or analysis populations, it is not possible to determine how completely the primary comparison represents the randomized groups. Different participant counts across secondary outcomes add another source of uncertainty about comparability among results.

The registry lists masking as none. It does not give further detail about whether outcome assessment or data analysis was masked. The exercise and control conditions are behavioral and described differently, but the record does not report procedures intended to limit awareness of assignment or its influence on measurements.

The exercise description is incomplete in the registry record. It identifies a home-based walking program, an educational session, an exercise prescription, and a heart rate monitor, but does not fully report the exercise schedule or the extent of supervision. The control description also does not fully state the content of follow-up contacts. This limits assessment of intervention delivery and the distinction between the two conditions.

The primary endpoint is a composite, and the record does not report a clinically meaningful threshold or the rationale for the chosen composition. The confidence interval level and construction method, original sample-size rationale, complete statistical analysis plan, multiplicity handling, and missing-data methods are also not reported in the registry record.

The registered primary outcome is measured at 6 months. Longer-term outcomes are not described in the available record, so persistence of any observed change cannot be assessed. The study’s enrollment of 39 also means the estimates are based on a limited participant count; the uncertainty interval makes that imprecision visible, but does not by itself indicate what the result would be in a larger or different population.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Exercise Training and Cognitive Function in Kidney Disease — NCT03197038.
• Registry record last updated 2021-07-02; status last verified 2021-06.
• Results first posted 2021-07-02.
• 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.

22. Record Summary

NCT03197038 is a completed randomized, parallel-group study sponsored by University of Illinois Chicago. It compared partially supervised home-based walking exercise with control among older patients with kidney disease and preclinical cognitive impairment. The registry lists enrollment of 39 and no masking.

The primary outcome was change from baseline in composite global cognitive function at 6 months. The posted mean difference was 0.13 Z-score units, with an interval from -0.102 to 0.362 and an unadjusted p-value of 0.272. The registry also lists secondary cognitive, imaging, vascular, and motor outcomes, along with adverse-event counts.

The registry record does not report the original sample-size rationale, a full statistical analysis plan, missing-data methods, or definitions of the analysis populations. Those limitations are relevant to interpreting the posted comparisons.