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 Relationship of Exercise, Sleep, and Inflammation Markers in People Living With HIV (NCT04946994), a randomized na study. The primary outcome is Sleep Quality.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT04946994 |
| Phase | NA |
| Condition | Hiv, Sleep |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 52 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Christine Horvat Davey |
| Results posted | Yes |
2. Clinical Question
Population
Older people living with HIV. The registry record describes the study as a sub-study at the University of Washington site of the HEALTH-HIV study. It does not report detailed eligibility criteria or the age threshold used to define older participants.
Intervention
High-intensity interval training (HIIT), a behavioral exercise intervention. The arm description includes walking or jogging and resistance exercise, but its text ends before the full progression schedule is specified.
Comparator
Continuous moderate-intensity exercise (CME), also a behavioral exercise intervention. Its posted description includes walking or jogging and resistance exercise; the schedule text is likewise incomplete in the registry record.
Primary question
How does change in self-reported sleep quality over 0–16 weeks compare between HIIT and CME? The trial also describes an aim to relate sleep quality to inflammation markers, with assessments at baseline, week 8, and week 16.
The primary outcome is change in sleep quality assessed with the Pittsburgh Sleep Quality Index (PSQI). Higher PSQI scores indicate poorer sleep quality. The record describes a hypothesis that HIIT would lead to greater improvement in sleep quality than CME. This is a stated hypothesis, not a result. The posted primary comparison is between the arms’ mean changes over the stated timeframe.
The inflammation aims concern interferon gamma, C-reactive protein, and tumor necrosis factor alpha. The registry describes these as secondary outcomes and proposes examining their relationship with sleep quality. The posted secondary comparisons report arm-level changes for the markers, but the record does not report a detailed analysis of the association between sleep and inflammation. Nor does it provide separate results for the planned baseline, week 8, and week 16 assessments. Those details are not reported in the registry record.
3. Trial Design
The registry describes a randomized, parallel-group trial with no masking. Participants were assigned to HIIT or CME. The trial is listed as completed, with enrollment of 52. The registry lists the phase as not applicable. It identifies the study as a sub-study associated with HEALTH-HIV and states that data were collected at the University of Washington site.
The two interventions are behavioral exercise programs. The posted descriptions for both arms include walking or jogging for 50 continuous minutes at 55% VO2peak. They also describe an initial resistance-exercise goal of 3 sets of 8-10 repetitions of 4 exercises, beginning at 50% 1-RM and progressing to 70-80% 1-RM. The descriptions say exercise intensity would increase every 4, but do not include the remainder of that schedule. The registry record therefore does not provide a complete account of how the exercise programs differed in practice.
The primary outcome is change in PSQI sleep-quality score over 0–16 weeks. The outcome description states that the possible score range is 0-21 and that higher scores indicate poorer sleep quality. The registry’s study summary describes baseline, week 8, and week 16 assessments for sleep and inflammation, while the outcome listings specify a 0–16-week timeframe. The record does not report detailed visit-level outcome values.
The primary posted comparison includes 20 participants in the HIIT arm and 23 in the CME arm. The secondary marker comparisons include 15 and 19 participants, respectively. These outcome-specific numbers differ; the registry record does not explain the reasons. Its overall enrollment figure should not be treated as the denominator for every outcome.
The record does not report the original sample-size justification, the intended statistical analysis plan, or whether any interim analyses were planned or conducted. It also does not report masking beyond stating that the trial was unmasked, or provide further details about allocation procedures.
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
| Stage | High Intensity Interval Training | Continuous Moderate Intensity Exercise |
|---|---|---|
| STARTED | 25 | 27 |
| COMPLETED | 20 | 24 |
| NOT COMPLETED | 5 | 3 |
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.
| Characteristic | Unit | High Intensity Interval Training | Continuous Moderate Intensity Exercise | Total |
|---|---|---|---|---|
| Participants analysed | 25 | 27 | 52 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 21 | 21 | 42 |
| Age, Categorical: >=65 years | Participants | 4 | 6 | 10 |
| Age, Continuous | years | 58.68 (SD 6.47) | 59.22 (SD 6.85) | 58.96 (SD 6.61) |
| Sex: Female, Male: Female | Participants | 3 | 4 | 7 |
| Sex: Female, Male: Male | Participants | 22 | 23 | 45 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 1 | 1 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 3 | 4 | 7 |
| Race (NIH/OMB): White | Participants | 22 | 19 | 41 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 3 | 3 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 1 | 8 | 9 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 24 | 18 | 42 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 1 | 1 |
| Sleep Quality | Score on a scale | 8.88 (SD 3.44) | 8.46 (SD 3.09) | 8.67 (SD 3.24) |
| Sleep Fragmentation Index | index | 32.25 (SD 15.30) | 36.82 (SD 12.74) | 34.73 (SD 14.00) |
| Sleep Efficiency | percentage of time asleep | 80.28 (SD 9.40) | 78.92 (SD 6.87) | 79.54 (SD 8.06) |
| Mean Sleep Duration | minutes per night | 395.82 (SD 65.59) | 375.31 (SD 67.21) | 384.67 (SD 66.55) |
| Interleukin Inflammation Markers IL-6 | pg/mL | 1.63 (SD 2.15) | 1.34 (SD 1.45) | 1.47 (SD 1.79) |
| Interleukin Inflammation Markers IL-8 | pg/mL | 4.58 (SD 1.53) | 6.53 (SD 3.14) | 5.64 (SD 2.70) |
| Interleukin Inflammation Markers IL-10 | pg/mL | 34 (SD 0.30) | 0.29 (SD 0.12) | 0.32 (SD 0.22) |
| Interleukin Inflammation Markers IL-13 | pg/mL | 3.06 (SD 1.18) | 3.31 (SD 1.48) | 3.20 (SD 1.34) |
| Interleukin Inflammation Markers IL-1β | pg/mL | 0.17 (SD 0.09) | 0.19 (SD 0.10) | 0.18 (SD 0.09) |
6. Primary Endpoint
The registry lists the primary outcome as Sleep Quality, measured over 0-16 weeks.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | score on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change in sleep quality measured with the Pittsburgh Sleep Quality Index (PSQI), a validated self-report instrument. The registry describes the score as ranging from 0-21, with higher scores indicating poorer sleep quality. The measure is used to capture participants’ reported sleep quality rather than an objective measure of sleep.
Change is relevant because the trial compares exercise interventions over time. The posted comparison estimates the difference between the arms’ mean changes during 0–16 weeks. A negative mean change indicates a reduction in the score; given the scale’s stated direction, a lower score corresponds to better reported sleep quality. The primary arm means are -2.15 for HIIT and -1.43 for CME. The recalculated mean difference, expressed as CME minus HIIT, is 0.72. This direction indicates that the mean change was numerically less negative in CME than in HIIT. It does not, by itself, establish a reliable difference between the interventions.
Self-report is useful for measuring a participant’s experience of sleep, but a score can be affected by recall and perception. The registry record does not report objective sleep measures alongside the PSQI results. It also does not provide individual-level change patterns or results for each planned assessment time, so the posted primary summary gives a limited view of how sleep scores changed across the study.
7. Results Posted in the Registry
- Continuous Moderate Intensity Exercise: mean -1.43 versus -2.15 on control; difference 0.72 (95% CI -1.00 to 2.44), standardized effect d = 0.26; z-test p = 0.413.
Mean difference: Continuous Moderate Intensity Exercise
95% CI: -1.00 to 2.44
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Interferon Gamma Inflammation Marker | Continuous Endpoint | Mean difference | -0.05 (-2.21 to 2.11) | 54,710 per arm |
| C-reactive Protein Inflammation Marker | Continuous Endpoint | Mean difference | 0.95 (0.29 to 1.61) | 16 per arm |
| Tumor Necrosis Factor Alpha Inflammation Marker | Continuous Endpoint | Mean difference | -0.07 (-0.18 to 0.04) | 95 per arm |
Interferon Gamma Inflammation Marker
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Continuous Moderate Intensity Exercise: mean 0.10 versus 0.15 on control; difference -0.05 (95% CI -2.21 to 2.11), standardized effect d = -0.02; z-test p = 0.964.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Continuous Moderate Intensity Exercise and the control. The interval gives the range of effects that remain compatible with the data.
C-reactive Protein Inflammation Marker
- 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:
- Continuous Moderate Intensity Exercise: mean 0.65 versus -0.30 on control; difference 0.95 (95% CI 0.29 to 1.61), standardized effect d = 1.00; z-test p = 0.005.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Continuous Moderate Intensity Exercise than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Tumor Necrosis Factor Alpha Inflammation Marker
- 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:
- Continuous Moderate Intensity Exercise: mean -0.02 versus 0.05 on control; difference -0.07 (95% CI -0.18 to 0.04), standardized effect d = -0.41; z-test p = 0.231.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Continuous Moderate Intensity Exercise and the control. The interval gives the range of effects that remain compatible with the data.
Across the three posted inflammation outcomes, the arm differences do not all point in the same numerical direction, and their intervals differ in whether they include zero. The registry’s primary focus is change in sleep quality; the secondary markers add outcome-specific information but do not replace that primary comparison.
The study summary describes an aim to quantify inflammation markers associated with sleep quality. However, the posted secondary results are comparisons between exercise arms for marker changes. Those comparisons alone do not estimate an association between each participant’s sleep quality and inflammation, nor do they show whether changes in sleep and markers occurred together. A direct analysis of the proposed sleep-inflammation relationship is not reported in the registry record.
The registry lists 15 outcome measures and 15 analyses, while detailed secondary results are posted for three inflammation markers. It is not reported in the registry record how the other listed measures were analyzed or what results they produced. The record also does not report whether the analyses were prespecified or how the number of outcomes was handled statistically.
Unadjusted secondary results carry less weight when many outcomes or comparisons are examined. General statistical context: making multiple tests increases the opportunity for at least one result to appear notable by chance, even when no underlying differences exist. Adjustments or a clear hierarchy of hypotheses can address that issue, but the registry record does not state whether a multiplicity procedure was used. Accordingly, the C-reactive protein result should be viewed as a secondary, unadjusted finding rather than as conclusive evidence for the broader hypothesis.
These secondary results are also based on fewer outcome observations than the primary comparison. The record does not explain the differences in analysis counts. That limits direct comparison of precision across endpoints and makes it important not to treat a secondary finding as if it were the trial’s primary result.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Interferon Gamma Inflammation Marker
- C-reactive Protein Inflammation Marker
- Tumor Necrosis Factor Alpha Inflammation Marker
9. Statistical Interpretation
For the primary endpoint, the mean change in PSQI score was -2.15 in the HIIT arm and -1.43 in the CME arm. Because higher PSQI scores indicate poorer sleep, both arm means represent reductions in the score. The recalculated mean difference, CME minus HIIT, is 0.72, with a confidence interval from -1.003 to 2.443 and an unadjusted p-value of 0.413. The interval includes values on either side of no difference, so the posted summary does not pin down the direction or size of an arm difference with much precision.
The registry reports a two-sided t-test p-value of 0.42 for the primary comparison. This is close to the unadjusted recalculation from the posted means and standard deviations. Neither value establishes that the arms differ. A p-value also does not quantify the probability that a hypothesis is true or the probability that the observed difference arose by chance; it describes how compatible the data are with a specified no-difference model under the test’s assumptions.
The secondary results are mixed in their numerical directions. The recalculated comparison for C-reactive protein is positive, whereas those for interferon gamma and tumor necrosis factor alpha are negative. The C-reactive protein interval excludes zero, while the intervals for the other two markers include zero. These results should be interpreted cautiously: they concern secondary outcomes, and the registry record does not report whether or how multiple comparisons were handled. The study summary’s proposed relationship between sleep and inflammation is not itself demonstrated by arm-level marker comparisons alone.
The posted results do not give enough detail to assess the effect of missing outcome data, adjustment for baseline values, or participant-level adherence. Those aspects are not reported in the registry record. The endpoint-specific participant counts are smaller for the inflammation outcomes than for the primary outcome, but the record does not explain why or identify the analysis populations in detail.
Overall, the posted primary comparison is compatible with a range of possible differences between the arms. It does not establish that one exercise intervention produced a greater change in sleep quality. The secondary findings provide outcome-specific estimates, not a definitive account of the broader sleep-inflammation relationship described in the study aims.
10. Statistical Methods Explained
What does the mean difference represent?
For a continuous outcome, a mean summarizes the average observed value in a group. Here the outcome is change in PSQI score or change in an inflammation marker over the listed timeframe. The posted comparison is expressed as the CME mean minus the HIIT mean. Thus, a positive mean difference means the CME change is numerically higher than the HIIT change; a negative value means it is numerically lower. Whether a higher or lower value is favorable depends on the measure and its direction. For PSQI, higher scores indicate poorer sleep; the registry gives units for the inflammatory markers but does not state a clinical direction of benefit for them.
A mean difference preserves the outcome’s original units. For the primary endpoint, it is expressed in PSQI score points. For C-reactive protein, it is in ng/mL; for interferon gamma and tumor necrosis factor alpha, it is in pg/ml and pg/mL, respectively. The posted estimates are not interchangeable across these different scales.
What does the standard deviation describe?
A standard deviation describes the spread of individual observations around a group mean. Greater spread means that participant values vary more within that group. It is not the same as the uncertainty around the mean difference. The primary outcome and two of the posted inflammation outcomes report standard deviations. Interferon gamma is reported with a standard error instead, so its spread value should not be read as a standard deviation. The registry record does not explain the choice of dispersion measure for that outcome.
General statistical context: when the individual values vary substantially, a group mean may be less precisely estimated for a given number of observations. Standard errors and confidence intervals convey uncertainty in estimates, while standard deviations describe variability among observations. These quantities answer related but different questions.
How should the p-values be read?
The reported analysis method for each posted comparison is a two-sided t-test. A two-sided test considers departures in either direction from a no-difference value. The registry reports p-values of 0.42 for sleep quality, 0.86 for interferon gamma, 0.009 for C-reactive protein, and 0.22 for tumor necrosis factor alpha. The recalculations from the posted summary statistics give unadjusted p-values of 0.413, 0.964, 0.005, and 0.231, respectively.
A p-value is not an effect size, and it is not a measure of clinical importance. It does not show whether a difference is large enough to matter, nor does it show the chance that the observed result is a false positive. Its interpretation depends on the statistical model and analysis choices. General statistical context: a smaller p-value indicates that results at least as incompatible with the no-difference model would be less common under that model, assuming the model and test conditions hold.
What is a standardized effect?
The recalculated comparisons also include standardized effect values, denoted by d. A standardized effect expresses a difference relative to a pooled measure of variability, rather than in the original outcome units. This can help describe the size of a difference on a scale that is less dependent on the outcome’s units. It does not replace the original-unit estimate or its interval, and it does not establish practical importance. General statistical context: standardized effects can be difficult to interpret when the underlying measure or population differs, and estimates from small samples can be imprecise.
Why might over-dispersion matter?
General statistical context: over-dispersion occurs when observations vary more than a model assumes. If a method assumes less variability than is present, standard errors can be too small and uncertainty can be understated. This is especially relevant for count or highly skewed outcomes, though the posted endpoints are continuous measures. The registry record does not provide distribution plots or diagnostic checks, so the fit of a normal-based comparison cannot be assessed from the posted summary alone.
What does the recalculation add?
The recalculated estimates are simple, unadjusted comparisons based on the posted arm summary statistics. They allow readers to see the size, direction, and uncertainty of a difference derived from those summaries. They are not a substitute for a sponsor analysis using participant-level data, covariate adjustment, or any prespecified analysis plan. No adjusted estimates or detailed model specifications are reported in the registry record.
For the primary outcome, the recalculated mean difference is 0.72, with an interval from -1.003 to 2.443. For the secondary outcomes, the corresponding differences are -0.05 for interferon gamma, 0.95 for C-reactive protein, and -0.07 for tumor necrosis factor alpha. Their intervals are reported alongside the posted results and should be read as ranges of values compatible with the summary data under the calculation’s assumptions. The registry record does not specify the confidence level for these intervals, so no confidence percentage should be inferred from the listing.
The recalculation uses the published summary values as its input. It cannot reconstruct details that are not in the registry, such as individual observations, missing-data handling, baseline adjustment, or whether an analysis followed a prespecified plan. The posted sponsor analyses are separately reported t-tests. Differences between sponsor p-values and recalculated p-values can arise because the recalculation is based on summary statistics and may not reproduce the sponsor’s exact analysis choices.
11. Confidence Intervals and Precision
A confidence interval describes a range of values that are reasonably compatible with the data and the calculation’s assumptions. It gives more information about precision than a point estimate alone: a narrow interval indicates less uncertainty about the estimated difference, while a wide interval leaves more values plausible. The registry record does not specify the confidence level for the posted intervals, so that level is not reported in the registry record.
For the primary sleep-quality comparison, the recalculated mean difference is 0.72, and its interval extends from -1.003 to 2.443. It includes zero, the value representing no mean difference. The data therefore do not precisely distinguish between no difference and differences in either direction across the range covered by the interval. The point estimate alone should not be treated as the definitive arm difference.
The secondary intervals also vary in precision. The interval for interferon gamma extends from -2.212 to 2.112, which spans values on both sides of zero. The interval for C-reactive protein runs from 0.287 to 1.613 and lies above zero. The tumor necrosis factor alpha interval runs from -0.184 to 0.044 and includes zero. These ranges describe uncertainty in the arm differences, not the range of individual participant values.
Precision depends on the amount of information in the outcome data and on variability. The posted outcome-specific participant counts and dispersion values differ across measures. General statistical context: estimates based on smaller analysis groups or more variable observations tend to be less precise, all else equal. The record does not report why the analysis counts differ, nor does it provide participant-level data to examine the distributions.
Intervals do not, by themselves, resolve questions about bias, missing data, multiplicity, or clinical importance. They quantify uncertainty under the calculation’s assumptions. The primary interval is compatible with a range that includes no difference, so the estimate is not precise enough to establish a clear comparative effect from the posted summary.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 239 | 319 |
| 75% of the observed effect | 424 | 567 |
| 50% of the observed effect | 953 | 1,275 |
The planning illustrations express the number of participants per arm for the continuous outcomes. They do not give total event counts. The assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each illustration uses a stated fraction of the observed effect as the effect to detect. The original trial’s own sample-size assumptions and justification are not reported in the registry record.
The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under the stated assumptions, if that effect is the true one. The 90% power column gives the analogous planning number for a 90% chance. These are design illustrations, not guarantees: actual power depends on the true effect, variability, analysis choices, and other conditions.
Each outcome has its own observed difference and variability, so its planning figures differ. For sleep quality, planning for 100% of the observed effect gives 239 participants per arm for 80% power and 319 participants per arm for 90% power. Planning for 75% of the observed effect gives 424 participants per arm for 80% power and 567 participants per arm for 90% power; planning for 50% gives 953 and 1,275 participants per arm, respectively. These examples illustrate that smaller effects need more participants to detect under the same assumptions.
The same reading applies to the other outcomes: the listed counts are participants per arm, not total participants. These figures are planning illustrations based on observed effects, not observed power. They should not be read as a recommendation or as evidence that the trial was originally designed to those targets.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.
Worked calculation for this trial
- Observed difference Δ = 0.720; pooled standard deviation σ = 2.804.
- n = 2 × (1.96 + 0.842)2 × 2.8042 / 0.7202 = 238.0, rounded up to 239 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 <- 0.72 # observed difference in means
sigma <- 2.80365701948844 # 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(4946994)
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 = 239 (80% power), 319 (90% power)
75% of observed effect: n per arm = 424 (80% power), 567 (90% power)
50% of observed effect: n per arm = 953 (80% power), 1,275 (90% power)
power.t.test: 239
Simulated power at n = 239 per arm: 0.793 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| t-test, 2 sided | not reported | 0.420 |
The registry reports sponsor analyses using two-sided t-tests. The reported p-values are 0.42 for sleep quality, 0.86 for interferon gamma, 0.009 for C-reactive protein, and 0.22 for tumor necrosis factor alpha. The recalculated unadjusted p-values from posted summary statistics are 0.413, 0.964, 0.005, and 0.231, respectively.
The primary sponsor p-value is close to the recalculation. The C-reactive protein sponsor p-value and recalculated p-value both indicate a difference under conventional unadjusted testing, while the other secondary comparisons have larger p-values in both sets of results. The numbers are not identical. The recalculations use posted group summaries and do not reproduce analyses from individual-level data or any unreported sponsor choices.
The registry record does not report a detailed statistical analysis plan, adjustments, or model specifications beyond the t-test description. Therefore, the sponsor’s reported results should be read as the record’s own analyses, while the recalculations serve as transparent, simple comparisons based on the summaries. The record does not identify a discrepancy flag for these results.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists 15 outcome measures and 15 analyses, but the posted results include a primary sleep-quality comparison and three inflammation-marker comparisons. The registry record does not report a multiplicity adjustment, a hierarchy for testing the outcomes, or a prespecified plan for deciding which results would be considered confirmatory. Without those details, the secondary p-values should be interpreted as unadjusted results rather than as evidence that accounts for all analyses.
General statistical context: when many hypotheses are tested, the chance of at least one small p-value can rise even if the underlying effects are absent. Multiplicity methods can control or describe that risk, but their choice depends on the study’s aims and analysis plan. The registry does not state whether such methods were used outside the posted results.
Missing-data handling is also not reported in the registry record. The primary endpoint includes 20 participants in HIIT and 23 in CME, while each posted inflammation comparison includes 15 in HIIT and 19 in CME. The record does not explain whether these differences reflect missing measurements, eligibility for a particular analysis, assay availability, or another reason. It does not describe imputation, complete-case analysis, or sensitivity analyses.
The analysis populations are not specified in detail. Although the design is randomized, the record does not say whether the reported comparisons follow an intention-to-treat principle, include only participants with available outcome data, or use another population definition. Nor does it report whether participants were analyzed according to their randomized assignment or exercise adherence.
Adjustment for baseline outcome values, other covariates, and repeated observations is not described. The study summary refers to baseline, week 8, and week 16 assessments, but the posted result summaries do not provide visit-specific estimates or explain how repeated measurements were modeled. These omissions make it difficult to assess whether the posted summary captures all planned analyses or how robust the estimates are to alternative assumptions.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| High Intensity Interval Training | 2 | 25 | 8.0% |
| Continuous Moderate Intensity Exercise | 1 | 27 | 3.7% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| High Intensity Interval Training | 0 of 25 |
| Continuous Moderate Intensity Exercise | 0 of 27 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| High Intensity Interval Training | 14 of 25 |
| Continuous Moderate Intensity Exercise | 17 of 27 |
Most frequent serious adverse event terms
| Event term | Organ system | High Intensity Interval Training | Continuous Moderate Intensity Exercise |
|---|---|---|---|
| infection related (including COVID) | Infections and infestations | 1 of 25 | 0 of 27 |
| infection related (including COVID); neurologic | Infections and infestations | 1 of 25 | 0 of 27 |
| other | Nervous system disorders | 0 of 25 | 1 of 27 |
Most frequent non-serious adverse event terms
| Event term | Organ system | High Intensity Interval Training | Continuous Moderate Intensity Exercise |
|---|---|---|---|
| Joint, Tendon or Muscle Pain | Musculoskeletal and connective tissue disorders | 10 of 25 | 13 of 27 |
| Respiratory infection | Infections and infestations | 2 of 25 | 5 of 27 |
| Diarrhea, nausea or vomiting | Gastrointestinal disorders | 1 of 25 | 4 of 27 |
| Fatigue | General disorders | 3 of 25 | 1 of 27 |
| COVID infection | Infections and infestations | 2 of 25 | 1 of 27 |
Serious events with the highest arm-level rate: infection related (including covid) (4.0%), infection related (including covid); neurologic (4.0%), other (3.7%).
The adverse-event record gives serious and other adverse-event counts separately by intervention group, with the number at risk specified for each category. For serious adverse events, 2 of 25 participants at risk in the HIIT group and 1 of 27 in the CME group were affected. For other adverse events, the corresponding figures are 14 of 25 and 17 of 27. The record reports 0 deaths in each group.
These are descriptive counts, not estimates of a causal difference between interventions. The registry record does not provide a statistical comparison, event-level timing, severity details, or an explanation of how events were attributed to the intervention. The figures at risk for safety outcomes also differ from the outcome-specific counts for sleep and inflammation, so they should not be substituted for those analysis denominators.
The listed serious-event terms include infection related (including COVID) at 4.0%, infection related (including COVID); neurologic at 4.0%, and other at 3.7%. The record does not provide enough detail to determine whether terms overlap or how these percentages relate to participant-level event counts. These entries should be read as registry safety descriptions rather than as comparative risk estimates.
17. What the Result Does, and Does Not, Mean
The posted primary result describes mean change in PSQI sleep-quality score in the two randomized groups. The average change was -2.15 with HIIT and -1.43 with CME. Since higher PSQI scores indicate poorer sleep, both group means are reductions in the score. The recalculated difference is 0.72 for CME minus HIIT, but its interval includes zero and spans values in either direction. The result therefore does not establish a clear difference between the interventions in this summary.
That interpretation is about the available group-level data, not a judgment about whether either program is useful in other settings. The record does not show whether individual participants improved or worsened, how consistently changes occurred, or whether any change was important to participants. It also does not report objective sleep measurements or detailed adherence information.
The secondary marker results provide additional comparisons, but they do not by themselves answer whether inflammation is associated with sleep quality. The study summary describes that relationship as an aim, while the posted marker estimates compare changes between exercise arms. The record does not report a direct participant-level analysis linking sleep scores to inflammation-marker values.
These results also do not establish the size or persistence of any longer-term effect. The listed outcome timeframe is 0–16 weeks, and longer follow-up is not reported in the registry record. Nor can the posted summary show whether effects vary across participant subgroups, because subgroup estimates are not reported.
In short, the posted data provide estimates of average changes and uncertainty for the stated outcomes. They do not establish a definitive comparative effect on sleep, provide a complete account of the proposed sleep-inflammation relationship, or resolve questions about missing outcomes and multiple testing.
18. Why This Trial Matters Statistically
This trial is statistically informative because it reports both a primary patient-reported outcome and several biological markers, making clear that different endpoints can tell different parts of a study’s story. A single primary estimate should not be conflated with a collection of secondary findings, particularly when the registry does not report whether multiplicity was addressed.
The primary comparison illustrates why effect estimates and uncertainty matter together. The mean difference is 0.72, but its interval includes zero and extends to values in either direction. A point estimate alone might suggest a directional contrast; the interval shows that the posted summary leaves substantial uncertainty about the comparative effect.
The secondary analyses also illustrate how evidence can differ across outcomes. The inflammation markers are measured on different scales and have different amounts of variability and different analysis counts. Their results cannot be reduced to one overall marker effect from the posted information. In particular, an arm comparison for a marker is not equivalent to an analysis of whether that marker is associated with sleep quality.
Finally, the record highlights the importance of transparent reporting. Information on the original sample-size justification, missing-data procedures, analysis populations, baseline adjustment, and multiplicity would help readers evaluate the reliability and intended interpretation of the estimates. The posted results support a careful reading of the observed summaries, while leaving those design and analysis questions unresolved.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The registry record leaves several trial-specific questions unanswered. It does not report detailed eligibility criteria, the threshold used to define older participants, or participant characteristics that would help readers judge how well the results apply to other groups of people living with HIV.
The posted descriptions of both exercise arms are incomplete. They share a walking or jogging component and a resistance-exercise progression, but the schedule text ends after stating that intensity would increase every 4. The registry record therefore does not fully describe the intervention schedules or clarify the distinction between the two programs. This limits interpretation of what participants actually received and how reproducible the interventions are from the public description.
The study is unmasked, and the primary endpoint is self-reported. The registry does not report objective sleep measures, adherence summaries, or information about how outcome assessments were administered. These factors may affect interpretation of reported sleep changes, although their specific impact cannot be determined from the registry.
Outcome-specific analysis counts differ, and the record does not explain why. Missing-data methods, analysis-population definitions, baseline adjustment, repeated-measures methods, and sensitivity analyses are not reported. The summary also does not give results for each planned visit or describe a direct analysis of the association between sleep quality and inflammation markers.
Lastly, the record does not report the original sample-size rationale or a detailed multiplicity plan. The posted planning illustrations are based on observed effects and are not evidence of the trial’s original design assumptions. These gaps limit how fully readers can assess precision, risk of bias, and the confirmatory status of secondary findings.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Relationship of Exercise, Sleep, and Inflammation Markers in People Living With HIV — NCT04946994.
- Registry record last updated 2026-06-22; status last verified 2026-05.
- Results first posted 2026-06-22.
- 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.
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23. Record Summary
NCT04946994 is a completed randomized, unmasked, parallel-group study comparing HIIT with CME in older people living with HIV. The registry lists enrollment of 52 and identifies the study as a sub-study conducted at the University of Washington site of HEALTH-HIV.
The primary outcome is change in PSQI sleep-quality score over 0–16 weeks. Mean changes were -2.15 for HIIT and -1.43 for CME. The recalculated mean difference is 0.72, with an interval from -1.003 to 2.443 and an unadjusted p-value of 0.413; the registry reports a two-sided t-test p-value of 0.42.
Three inflammation-marker comparisons are also posted. Their interpretation is limited by the absence of reported details about multiplicity, missing data, and analysis populations. The registry record does not report the original sample-size justification or a detailed statistical analysis plan.