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 Internet and Telephone Support Intervention for Stroke Caregivers (NCT04348851), a randomized na study. The primary outcome is Change in Depressive Symptoms.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT04348851 |
| Phase | NA |
| Condition | Depression, Quality of Life, Recovery of Function |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 53 |
| Arms in the primary outcome | 4 |
| Lead sponsor | VA Office of Research and Development |
| Results posted | Yes |
2. Clinical Question
Population
Caregivers of veterans with stroke. The registry record describes caregiver outcomes and veteran functional abilities as areas of interest; it does not give further eligibility details in the material summarized for this analysis.
Intervention
A combined Internet and telephone caregiver problem-solving intervention delivered by registered nurses. The trial had a 4-Week Intervention arm and an 8-Week Intervention arm.
Comparator
The main recalculated comparisons use 8-Week Attention Control, which involved active listening and paraphrasing, as the reference group. Standard Care was a separate randomized arm and is also compared with attention control in the posted results.
Primary question
At 9 weeks after baseline, how did mean change in depressive symptoms differ between each intervention arm and 8-Week Attention Control? The measure was the Center for Epidemiologic Studies Depression scale. The posted summary statistics allow unadjusted comparisons of group means, but the registry record does not report the sponsor’s inferential analysis.
The comparison is about differences in average change over the stated follow-up, not about whether an individual caregiver improved or worsened. The CES-D scale assigns higher scores to more symptoms, so the direction of a mean change can be interpreted against that scale definition. The calculated mean differences use attention control as the reference and are not adjusted for other characteristics or for the trial’s multiple outcome comparisons.
The registry record describes random assignment and a parallel-group design. Randomization can help make groups comparable at baseline, but it does not guarantee balance in a small trial. The posted summary does not provide enough detail to determine how allocation was implemented, what analysis population was used, or how missing measurements were handled.
3. Trial Design
The registry record describes a randomized, double-masked, parallel-group trial with an enrollment of 53. It is listed as completed, with a start date of 2014-10-01 and primary completion on 2016-09-19. The phase is recorded as NA. The sponsor is the VA Office of Research and Development.
Four groups appear in the outcome results: 4-Week Intervention, 8-Week Intervention, 8-Week Attention Control, and Standard Care. The intervention is described as a combined Internet and telephone problem-solving and support program for caregivers, conducted by registered nurses. The attention-control description says nurses used active listening and paraphrasing and did not provide advice. Standard Care is described simply as caregivers receiving standard of care. Further details of the intervention descriptions are not reported in the registry record.
The trial’s stated focus includes caregiver depression, burden, stress, problem-solving abilities, self-efficacy, and quality of life, as well as veteran functional abilities. The primary outcome was change in depressive symptoms, measured 9 weeks after baseline. The registry record also lists 18 outcome measures and reports secondary outcomes that include perceived stress, health-related quality of life, stroke knowledge, problem-solving abilities, self-efficacy, and veteran functional abilities.
The registry record does not report the original sample-size justification, the intended allocation procedure beyond randomization, the masking procedures, or a detailed statistical analysis plan. It also does not report whether interim analyses were planned or conducted. These omissions limit assessment of how the completed study was intended to address its questions. The arm sizes displayed for outcomes should not be treated as a full account of participant flow, because the record does not explain the relationship between enrollment, outcome availability, and the analysis population.
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.
Post-Test 1
| Stage | 4-Week Intervention | 8-Week Intervention | 8-Week Attention Control | Standard Care |
|---|---|---|---|---|
| STARTED | 13 | 13 | 13 | 14 |
| COMPLETED | 13 | 11 | 13 | 14 |
| NOT COMPLETED | 0 | 2 | 0 | 0 |
Reasons for not completing this period:
| Reason | 4-Week Intervention | 8-Week Intervention | 8-Week Attention Control | Standard Care |
|---|---|---|---|---|
| Withdrawal by Subject | 0 | 1 | 0 | 0 |
| Lost to Follow-up | 0 | 1 | 0 | 0 |
Post-Test 2
| Stage | 4-Week Intervention | 8-Week Intervention | 8-Week Attention Control | Standard Care |
|---|---|---|---|---|
| STARTED | 13 | 11 | 13 | 14 |
| COMPLETED | 13 | 10 | 13 | 13 |
| NOT COMPLETED | 0 | 1 | 0 | 1 |
Reasons for not completing this period:
| Reason | 4-Week Intervention | 8-Week Intervention | 8-Week Attention Control | Standard Care |
|---|---|---|---|---|
| Stroke survivor death | 0 | 1 | 0 | 1 |
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 | 4-Week Intervention | 8-Week Intervention | 8-Week Attention Control | Standard Care | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 13 | 13 | 13 | 14 | 53 | |
| Age, Continuous | years | 63.8 (SD 8.9) | 58.2 (SD 12.0) | 57.1 (SD 9.9) | 61.9 (SD 9.5) | 60.3 (SD 10.2) |
| Sex: Female, Male: Female | Participants | 12 | 13 | 12 | 12 | 49 |
| Sex: Female, Male: Male | Participants | 1 | 0 | 1 | 2 | 4 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 1 | 0 | 1 | 0 | 2 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 12 | 13 | 12 | 14 | 51 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 1 | 0 | 0 | 1 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 6 | 3 | 3 | 2 | 14 |
| Race (NIH/OMB): White | Participants | 7 | 8 | 10 | 11 | 36 |
| Race (NIH/OMB): More than one race | Participants | 0 | 1 | 0 | 1 | 2 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
| Region of Enrollment: United States | participants | 13 | 13 | 13 | 14 | 53 |
6. Primary Endpoint
The registry lists the primary outcome as Change in Depressive Symptoms, measured over 9 weeks after baseline.
| 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 depressive symptoms at 9 weeks after baseline. The registry record says symptoms were measured with the Center for Epidemiologic Studies Depression (CES-D) scale. It is a 20-item, 4-point Likert scale, with response options ranging from never (0) to most of the time (3); possible total scores range from 0-60. Higher scores indicate more symptoms. The registry description notes that the scale has been used in caregiver studies and has good reliability and validity.
Using change rather than a single follow-up score is intended to describe how the measured symptom level shifts over the period of observation. Comparing group mean changes can summarize differences between assigned groups. It does not show the distribution of individual trajectories, and a group average does not establish that every participant changed in the same direction.
For interpretation, a negative mean change corresponds to a decrease in CES-D score, while a positive mean change corresponds to an increase. A difference in mean change between two groups is expressed in score units. The recalculated comparisons are unadjusted contrasts based on the posted group means and standard deviations. The sponsor’s own inferential analysis is not reported in the registry record, so the recalculated results should not be mistaken for a reported trial analysis.
The endpoint is relevant to the trial’s stated focus on caregiver depression, but it is only one aspect of caregiver experience. It does not directly measure burden, stress, quality of life, or the veteran’s functional abilities; those are addressed as separate outcomes in the registry record.
7. Results Posted in the Registry
- 4-Week Intervention: mean -2.31 versus 0.08 on control; difference -2.39 (95% CI -8.93 to 4.15), standardized effect d = -0.28; z-test p = 0.474.
- 8-Week Intervention: mean 1.00 versus 0.08 on control; difference 0.92 (95% CI -6.54 to 8.38), standardized effect d = 0.10; z-test p = 0.809.
- Standard Care: mean 3.90 versus 0.08 on control; difference 3.82 (95% CI -3.70 to 11.34), standardized effect d = 0.39; z-test p = 0.319.
Mean difference: 4-Week Intervention
95% CI: -8.93 to 4.15
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change in Health-Related Quality of Life - Physical Scale | Continuous Endpoint | Mean difference | 3.88 (-2.42 to 10.18) | 71 per arm |
| Change in Perceived Stress | Continuous Endpoint | Mean difference | 1.08 (-0.85 to 3.01) | 86 per arm |
| Change in Stroke Knowledge | Continuous Endpoint | Mean difference | -0.30 (-1.33 to 0.73) | 314 per arm |
Change in Health-Related Quality of Life - Physical Scale
- 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:
- 4-Week Intervention: mean 0.70 versus -3.18 on control; difference 3.88 (95% CI -2.42 to 10.18), standardized effect d = 0.47; z-test p = 0.228.
- 8-Week Intervention: mean 1.91 versus -3.18 on control; difference 5.09 (95% CI -1.71 to 11.89), standardized effect d = 0.58; z-test p = 0.142.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 4-Week Intervention and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 8-Week Intervention and the control. The interval gives the range of effects that remain compatible with the data.
Change in Perceived Stress
- 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:
- 4-Week Intervention: mean 1.23 versus 0.15 on control; difference 1.08 (95% CI -0.85 to 3.01), standardized effect d = 0.43; z-test p = 0.274.
- 8-Week Intervention: mean 0.27 versus 0.15 on control; difference 0.12 (95% CI -1.86 to 2.10), standardized effect d = 0.05; z-test p = 0.906.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 4-Week Intervention and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 8-Week Intervention and the control. The interval gives the range of effects that remain compatible with the data.
Change in Stroke Knowledge
- 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:
- 4-Week Intervention: mean -0.15 versus 0.15 on control; difference -0.30 (95% CI -1.33 to 0.73), standardized effect d = -0.22; z-test p = 0.568.
- 8-Week Intervention: mean 0.27 versus 0.15 on control; difference 0.12 (95% CI -0.82 to 1.06), standardized effect d = 0.10; z-test p = 0.803.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 4-Week Intervention and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 8-Week Intervention and the control. The interval gives the range of effects that remain compatible with the data.
The registry record lists a broad set of secondary outcomes spanning caregiver stress, health-related quality of life, stroke knowledge, problem-solving abilities, self-efficacy, and veteran functional abilities. The results summarized for several secondary measures show a similar statistical pattern to the primary outcome: recalculated mean differences are uncertain, and the reported confidence intervals include zero. This means the available contrasts do not sharply distinguish group differences from no average difference.
The secondary outcomes provide related but distinct perspectives. Measures of stress and quality of life describe caregiver experience, while stroke knowledge and problem-solving abilities concern other possible aspects of the intervention’s intended impact. Veteran functional abilities are a separate outcome domain. Taken together, these measures can help describe whether the observed pattern is consistent across different outcomes, but they do not replace the primary comparison or independently establish a treatment effect.
The numerical summaries available for secondary comparisons are not equally complete across the listed outcomes. The registry record does not report inferential analyses for the secondary outcomes. As a result, broad conclusions about the entire secondary-outcome set would go beyond the reported material. A pattern across the posted summaries should not be read as proof that every secondary measure behaved similarly.
Secondary results carry less weight when many outcomes and comparisons are examined without a reported adjustment or prespecified hierarchy. Unadjusted testing can produce apparently notable findings by chance, especially when several outcomes are considered. The registry record does not report how multiplicity was handled. These secondary findings are therefore best treated as exploratory context for the primary result, rather than as confirmatory evidence. They can indicate what was measured and where estimates are uncertain, but they cannot on their own resolve the uncertainty in the primary comparison.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change in Health-Related Quality of Life - Physical Scale
- Change in Perceived Stress
- Change in Stroke Knowledge
- Changes in Problem-Solving Abilities
- Caregiving Self-efficacy
- Change in Veteran Functional Abilities
- Change in Health-Related Quality of Life - Physical Scale
- Change in Perceived Stress
9. Statistical Interpretation
For the primary outcome, the posted mean change in CES-D score was -2.31 in the 4-Week Intervention arm and 0.08 in the 8-Week Attention Control arm. The unadjusted recalculated mean difference, intervention minus attention control, was -2.39, with a 95% confidence interval from -8.929 to 4.149 and p = 0.474. The interval includes no difference and also includes differences in either direction. Thus, these summary statistics do not estimate the contrast precisely enough to distinguish a lower mean change from a higher one with confidence.
The 8-Week Intervention arm had a mean change of 1.0, compared with 0.08 in attention control. The unadjusted recalculated difference was 0.92, with a 95% confidence interval from -6.543 to 8.383 and p = 0.809. Standard Care had a mean change of 3.9; compared with attention control, its unadjusted difference was 3.82, with a 95% confidence interval from -3.699 to 11.34 and p = 0.319. Each interval crosses zero. These comparisons are not evidence that the groups were equivalent; they indicate that the estimates are uncertain and compatible with a range of differences.
The direction of a mean change should be read using the CES-D scoring description: higher scores indicate more symptoms. The 4-Week Intervention group’s mean was negative, while the other displayed group means were positive. Those within-group summaries alone do not establish a treatment effect. The relevant question is the between-group contrast, and its uncertainty is substantial in these recalculations.
The trial had modest outcome-group sizes, and the standard deviations were sizeable relative to the mean differences. This makes estimates less precise. The posted p-values are unadjusted; they do not account for multiple comparisons or possible covariates. No sponsor-reported analysis is listed, and the registry record does not report whether adjusted analyses, repeated-measures methods, or a prespecified testing hierarchy were used. The simple recalculations therefore describe the posted summaries, rather than replacing an analysis conducted under the trial’s original plan.
There is no discrepancy flag for the recalculated results. The sponsor’s own analysis takes precedence if it is available elsewhere, but a sponsor analysis is not reported in the registry record. No conclusion about effectiveness should be drawn from these estimates alone. The posted results are best read as uncertain group comparisons at the stated time point, not as a definitive demonstration of benefit, harm, or equivalence.
10. Statistical Methods Explained
The primary outcome is continuous: it is a score, and the registry reports each arm’s mean and standard deviation. A mean describes the group’s average score change. A standard deviation describes how dispersed individual scores are around that average. A mean difference then compares the average change in one arm with the average change in the reference arm. It is expressed in the scale’s score units, which makes its direction interpretable using the scale’s scoring rules.
What does the recalculated comparison represent?
The posted recalculations subtract the attention-control mean from each other arm’s mean. These are simple, unadjusted contrasts derived from the arm-level summary statistics. They do not control for baseline characteristics, account for repeated measurements through a fitted model, or incorporate a sponsor-specific analysis plan. A recalculated contrast is useful for describing the observed summaries, but it is not a substitute for the trial’s intended analysis. That analysis is not reported in the registry record.
A confidence interval describes a range of values compatible with the data and the method used to calculate it. Wider intervals indicate less precision. When an interval for a mean difference includes zero, the data are compatible with no average difference as well as with differences on either side of zero. That does not prove the groups are the same. Conversely, an interval that excludes zero would not by itself establish clinical importance; the size and relevance of the difference would also matter.
Why do the arm sizes and variation matter?
For a continuous outcome, precision depends in part on the amount of information in each arm and on how variable the scores are. Smaller groups generally yield less precise estimates, while greater variation makes it harder to distinguish a group difference from sampling fluctuation. Here, the outcome arms are small and the reported standard deviations show variation within groups. The resulting intervals are broad relative to the point estimates, which is consistent with substantial uncertainty.
The recalculated p-values are unadjusted. A p-value describes how unusual data at least as incompatible with a specified no-difference hypothesis would be under the assumptions of the test. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. Because the record lists multiple outcomes and comparisons, unadjusted p-values should be treated cautiously. Testing many hypotheses without accounting for multiplicity increases the chance that some apparently notable result arises by chance. Whether the trial’s sponsor used a correction, hierarchical strategy, or other approach is not reported in the registry record.
What can the reported summaries not establish?
Arm means and standard deviations do not show individual-level data, the shape of each score distribution, or whether there were influential observations. They also do not establish that baseline values were balanced. Although random allocation can support comparisons, the record does not give the allocation details or baseline outcome values needed to assess that balance. Nor does it report the analysis population, exclusions, missing-data strategy, or whether all randomized participants were included in the outcome summaries.
The primary outcome is measured at one stated follow-up, 9 weeks after baseline. The registry record does not report a longitudinal model or other approach to using measurements over time. It is therefore not possible to say whether the sponsor’s analysis compared change scores, adjusted follow-up scores for baseline, or used another method. The posted mean-change summaries support the straightforward contrasts, but not a reconstruction of a more complex analysis.
General statistical interpretation should also distinguish statistical uncertainty from clinical importance. A confidence interval can show the range of values compatible with an estimate, but it does not define what difference would matter to caregivers. A threshold for a clinically important CES-D change is not reported in the registry record. Without such a threshold, these summary statistics cannot establish whether a difference, even if estimated more precisely, would be meaningful in practice.
The registry’s planning illustrations use observed effects and stated assumptions. They concern hypothetical future-study planning, not the precision or power that the completed trial actually had. The original trial’s sample-size assumptions and justification are not reported in the registry record. Thus, planning illustrations should be kept separate from interpretation of the completed trial’s estimates.
11. Confidence Intervals and Precision
The primary mean-difference estimates have broad 95% confidence intervals. For the 4-Week Intervention comparison with attention control, the interval runs from -8.929 to 4.149 score units. For 8-Week Intervention, it runs from -6.543 to 8.383. For Standard Care, it runs from -3.699 to 11.34. Each interval includes zero and spans values on both sides of no difference.
This means that the point estimates alone provide an incomplete picture. The 4-Week Intervention estimate is negative, but its interval also allows a positive difference. The 8-Week Intervention and Standard Care point estimates are positive, but their intervals also allow negative differences. The observed data therefore do not tightly locate the underlying group contrasts. An interval crossing zero is not proof of no effect; it reflects that the data do not rule out a range of possibilities under the calculation method.
Precision is limited in part by the small arm sizes and observed score variation. The record gives outcome group sizes of 13, 11, 13, and 14 across the four arms, and standard deviations from 4.8 to 11.03 for the primary outcome. With limited information and variability in scores, the estimated mean differences have considerable uncertainty.
The confidence intervals are recalculated, unadjusted intervals based on the posted summary statistics. They are not reported as the sponsor’s own model-based intervals, and no adjustment for multiple comparisons is included. The registry record does not report a threshold for a meaningful CES-D difference, so the intervals cannot be judged against a prespecified clinical-importance boundary. They should be read as measures of statistical precision around the recalculated contrasts, not as guarantees about the true effect or individual outcomes.
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 | 199 | 267 |
| 75% of the observed effect | 354 | 474 |
| 50% of the observed effect | 796 | 1,065 |
The planning figures are participants per arm, not total event counts. They are illustrations based on the observed comparison effect and assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. For each comparison, the planning exercise considers detecting 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The original trial’s own sample-size assumptions and justification are not reported in the registry record.
The 80% power column gives the estimated participants per arm for a future study to have an 80% chance of detecting the specified effect under those assumptions, if that effect is the true one. The 90% power column uses the same idea but aims for a 90% chance. These are design-planning quantities, not guarantees that a study will produce a particular result. They depend on the assumptions used, including the effect size and variability.
Smaller effects are harder to distinguish from random variation, so the planning illustrations require more participants per arm when the target is a smaller fraction of the observed effect. In this record, the number required rises when planning for 75% or 50% of the observed effect rather than the full observed effect. Very large planning estimates can arise when the observed contrast is small relative to its variability; they should not be interpreted as evidence that such an effect is real.
These figures are not observed power. They are hypothetical sample-size calculations for future planning and are not a retrospective measure of whether the completed trial was adequately powered. They also do not establish the sample-size plan that was used when the trial was designed. That original design information is not reported in the registry record.
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 = -2.390; pooled standard deviation σ = 8.506.
- n = 2 × (1.96 + 0.842)2 × 8.5062 / -2.3902 = 198.8, rounded up to 199 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 <- -2.39 # observed difference in means
sigma <- 8.50590677117966 # 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(4348851)
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 = 199 (80% power), 267 (90% power)
75% of observed effect: n per arm = 354 (80% power), 474 (90% power)
50% of observed effect: n per arm = 796 (80% power), 1,065 (90% power)
power.t.test: 199.8
Simulated power at n = 199 per arm: 0.799 (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 record lists multiple outcome measures, including the primary depressive-symptom endpoint and secondary outcomes across several domains. It does not report a multiplicity strategy, such as a hierarchy of hypotheses, a family-wise error adjustment, or a false-discovery approach. The recalculated p-values are unadjusted. When many comparisons are considered, the chance of at least one apparently unusual result can increase, so isolated secondary findings should be interpreted cautiously.
The record does not report a detailed statistical analysis plan, including whether the primary comparison was prespecified in the form recalculated here, whether covariate adjustment was intended, or how outcomes at different time points were to be handled. It also does not report interim analyses. These details matter because analysis choices can affect estimates, uncertainty, and the interpretation of multiple tests. No assumptions about them can be made from the posted summaries.
Missing-data handling is not reported in the registry record. Although arm-specific outcome group sizes are displayed, the record does not explain whether participants lacked follow-up data, whether any measurements were excluded, or why the outcome group sizes differ. It does not state whether missing values were imputed, handled by a model, or omitted from the summary. The displayed sizes alone do not establish the amount or pattern of missing data.
The analysis population is also not reported. It is therefore unclear whether the results use all randomized caregivers, participants with available outcome measurements, or another population. The record does not describe adherence to intervention assignment or any per-protocol definition. These omissions prevent assessment of whether the posted estimates preserve the benefits of randomization or could be affected by selection into the analyzed group. They also limit comparison with any sponsor analysis that may exist outside the registry record.
15. 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 |
|---|---|---|---|
| 4-Week Intervention | 1 | 13 | 7.7% |
| 8-Week Intervention | 0 | 13 | 0.0% |
| 8-Week Attention Control | 0 | 13 | 0.0% |
| Standard Care | 0 | 14 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| 4-Week Intervention | 0 of 13 |
| 8-Week Intervention | 0 of 13 |
| 8-Week Attention Control | 0 of 13 |
| Standard Care | 0 of 14 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| 4-Week Intervention | 0 of 13 |
| 8-Week Intervention | 0 of 13 |
| 8-Week Attention Control | 0 of 13 |
| Standard Care | 0 of 14 |
Most frequent serious adverse event terms
| Event term | Organ system | 4-Week Intervention | 8-Week Intervention | 8-Week Attention Control | Standard Care |
|---|---|---|---|---|---|
| Seizures | Nervous system disorders | 1 of 13 | 0 of 13 | 0 of 13 | 0 of 14 |
Serious events with the highest arm-level rate: seizures (7.7%).
The registry safety record lists serious adverse events for each group. It reports one serious adverse event in the 4-Week Intervention arm, with seizures identified as the serious-event term and listed at 7.7%. The other groups have zero serious adverse events recorded. The record lists zero deaths in every group.
For other, non-serious adverse events, the recorded number affected is zero in each group. The serious-event and other-event figures are separate categories, so a zero in the other-event column does not erase the serious event recorded for the 4-Week Intervention arm.
These counts are descriptive. With small outcome and safety groups, a low count does not establish that an event could not occur, and differences in observed counts do not by themselves show that an intervention caused or prevented an event. The registry record does not provide further detail about event timing, severity beyond the serious classification, relatedness to the intervention, or the method used to collect adverse events. The figures should therefore be read as the safety events recorded in the registry, not as a complete causal assessment.
16. What the Result Does, and Does Not, Mean
The posted results describe group-average changes in CES-D scores at 9 weeks after baseline and recalculated unadjusted comparisons with attention control. The point estimates differ in direction across arms, but all of the primary confidence intervals include zero and are broad. The estimates therefore leave substantial uncertainty about the direction and size of the average differences.
That uncertainty does not establish that the groups are equivalent, nor does it establish that any one approach is better or worse. A non-significant unadjusted p-value is not proof of no effect. It indicates that the recalculated data do not provide strong evidence against the no-difference hypothesis under the test used. The registry record does not report an equivalence or non-inferiority design, so the results cannot be interpreted as showing equivalence.
The outcome is a measure of depressive symptoms, not a diagnosis or a full account of caregiver well-being. The trial also lists other caregiver and veteran outcomes, but the available summaries and the absence of a reported multiplicity plan limit the strength of conclusions across those measures. The registry record does not report a threshold for a clinically important CES-D change, so statistical estimates cannot be translated into a claim about practical importance.
These results also cannot show what happened to every caregiver. Group means and standard deviations summarize overall patterns but do not reveal individual changes, experiences, or reasons for missing measurements. The record does not report the analysis population, missing-data methods, or detailed adjustment strategy. Those gaps matter when judging how representative the posted estimates are of all randomized participants.
In short, the registry record documents a completed randomized trial and posts outcome summaries, but the primary comparisons remain imprecise and unadjusted. The results should be understood as uncertain statistical estimates rather than a definitive judgment about the intervention. They do not support medical advice or a causal conclusion beyond what the reported design and analysis details can substantiate.
17. Why This Trial Matters Statistically
This trial raises several statistical issues common in behavioral and caregiver research. The intervention is compared with both an active listening control and standard care, so the choice of comparator matters: each comparison addresses a different question. An attention control may help separate the intervention’s problem-solving content from contact and listening, while standard care provides a distinct reference. The registry record’s recalculations use attention control as the reference for the displayed contrasts.
The outcome is continuous, which allows estimation of mean differences in the original scale units. But interpretable estimates still require enough information to achieve useful precision. The relatively small outcome groups and variation in CES-D scores lead to broad confidence intervals. This illustrates why point estimates and p-values should not be read without their uncertainty intervals.
The record also lists many outcomes. Measuring several aspects of caregiver and veteran experience can be valuable, but it creates a multiplicity problem if each is tested and interpreted independently. Without a reported hierarchy or adjustment strategy, secondary findings are most responsibly viewed as exploratory. A prespecified plan would help readers distinguish confirmatory questions from additional measures.
Finally, registry summaries are not a complete statistical report. Missing information about the original sample-size justification, analysis population, missing data, and model specification limits what can be inferred from posted arm means and standard deviations. Clear reporting of those elements is important for reproducibility and for judging how closely observed results answer the trial’s intended question. The case shows that transparent outcome summaries are useful, but they do not replace a full account of the design and analysis.
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 primary limitation is the imprecision of the recalculated comparisons. The outcome arms are small, the score variability is substantial, and the confidence intervals span differences in both directions. This limits the conclusions that can be drawn from the point estimates.
The recalculations use unadjusted group summaries rather than a reported sponsor analysis. The registry record does not report the statistical model, any baseline adjustment, the analysis population, or the handling of missing data. It is therefore not possible to determine whether the summaries include all randomized participants or how exclusions and incomplete follow-up may have affected results.
Although the trial is described as randomized and double-masked, the registry record does not describe how allocation or masking was implemented. In a behavioral intervention, the practical details of who was masked and how masking was maintained would be relevant to assessing potential bias; those details are not reported in the registry record.
The record also does not report a sample-size justification, a multiplicity plan, a clinically meaningful difference for the CES-D scale, or whether interim analyses were planned. Many outcomes are listed, while the inferential analyses for secondary outcomes are not reported. This makes secondary findings difficult to interpret as confirmatory evidence. In addition, the intervention descriptions are incomplete in the registry record, limiting assessment of what was delivered across the two intervention arms. The safety record gives event counts but not detailed timing, relatedness, or collection procedures. These reporting gaps do not invalidate the posted summaries, but they constrain how confidently they can be interpreted.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Internet and Telephone Support Intervention for Stroke Caregivers — NCT04348851.
- Registry record last updated 2020-06-02; status last verified 2020-05.
- Results first posted 2020-05-18.
- 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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22. Record Summary
NCT04348851 is a completed, randomized, double-masked, parallel-group trial of Internet and telephone support for caregivers of veterans with stroke. The registry record lists four groups: 4-Week Intervention, 8-Week Intervention, 8-Week Attention Control, and Standard Care. Enrollment is recorded as 53.
The primary outcome was change in depressive symptoms on the CES-D scale at 9 weeks after baseline. Recalculated unadjusted comparisons with attention control have broad confidence intervals that include zero. The registry record lists secondary outcomes across caregiver and veteran domains, but does not report a detailed analysis plan, multiplicity handling, missing-data methods, or the original sample-size justification.
The safety record lists one serious event, seizures, in the 4-Week Intervention group, no serious events in the other groups, and no deaths. These registry summaries are descriptive and do not establish causation. Overall, the posted results are informative about the observed group means but leave substantial uncertainty about comparative effects.