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 Improving the Recovery and Outcome Every Day After the ICU (NCT03095417), a randomized na study. The primary outcome is Cognitive Status Outcome at 6 Months.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03095417 |
| Phase | NA |
| Condition | Delirium, Alzheimer Disease |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 249 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Indiana University |
| Results posted | Yes |
2. Clinical Question
Population
The clinical question concerns ICU survivors aged 50 and older. The registry lists delirium and Alzheimer disease among the conditions studied. For the primary cognitive outcome, the analysis included only participants able to complete the Repeatable Battery for the Assessment of Neuropsychological Status (RBANS) scale. The registry record does not report further eligibility details in the information available for this analysis.
Intervention
The primary intervention of interest is combined physical exercise and cognitive training. The trial also assigned participants to physical exercise with cognitive control, cognitive training with stretching control, or cognitive control with stretching control. The stated primary aim was to assess the combined program’s effect on cognitive function. The brief summary describes the combined intervention as lasting 12 weeks.
Comparator
The sponsor’s reported analysis considered all four groups together. The recalculated pairwise contrasts use physical exercise and cognitive control as the reference group. That comparison isolates the posted mean for the combined exercise-and-cognitive-training group against the exercise-and-cognitive-control group, while the other recalculations compare the cognitive-training-and-stretching group and the cognitive-control-and-stretching group with the same reference. These contrasts are not the same as the overall four-group test.
Primary question
At 6 months after randomization, how did cognitive status, measured by the RBANS overall z-score, compare across the randomized groups? Higher z-scores represent better cognitive outcomes. The sponsor’s mixed models analysis reported an overall p-value of 0.747. Recalculated unadjusted mean differences against the physical-exercise-and-cognitive-control group were small in the posted summaries, with confidence intervals that include zero. Together, these statistics do not establish a clear difference in the primary outcome; they also do not establish equivalence among the groups.
3. Trial Design
The registry describes a completed, randomized, double-masked, parallel-group trial sponsored by Indiana University. The enrollment was 249. The study began on 2017-09-25, and primary completion was 2022-12-15. The registry lists the phase as NA. The posted record does not explain who was masked or how masking was maintained, and it does not report the original sample-size assumptions or justification.
There were four intervention combinations: physical exercise and cognitive training; physical exercise and cognitive control; cognitive training and stretching control; and cognitive control and stretching control. The brief summary describes the combined physical exercise and cognitive training program as a 12-week intervention. The arm descriptions also mention stretching and cognitive-control activities, but some of those descriptions are incomplete in the registry record. Details beyond the activities and schedules stated in those descriptions are not reported in the registry record.
The primary outcome was cognitive status at 6 months after randomization, assessed using the RBANS. The stated primary aim focused on cognitive function, with planned assessment at 3 and 6 months described in the brief summary. The posted primary outcome is specifically the 6-month assessment. Secondary outcomes include physical performance, cardiovascular fitness, depression, and anxiety at different follow-up times. The registry lists 12 outcome measures and 12 analyses, while 10 secondary outcomes are posted in the information available for this analysis.
The posted arm summaries do not include every randomized participant: the primary outcome analysis was restricted to participants able to complete the scale. Group counts in the outcome summaries therefore describe participants included in those particular summaries, not necessarily the full randomized groups. The registry record does not report a full account of participant flow, reasons for missing measurements, or the methods used to handle missing outcomes.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: Per protocol subjects were considered to be enrolled in the study at the time of completion of the informed consent process. 249 subjects were enrolled. 153 subjects were randomized to one of the four study groups.
Overall Study
| Stage | Physical Exercise and Cognitive Training | Physical Exercise and Cognitive Control | Cognitive Training and Stretching Control | Cognitive Control and Stretching Control |
|---|---|---|---|---|
| STARTED | 41 | 41 | 36 | 35 |
| COMPLETED | 28 | 30 | 27 | 24 |
| NOT COMPLETED | 13 | 11 | 9 | 11 |
Reasons for not completing this period:
| Reason | Physical Exercise and Cognitive Training | Physical Exercise and Cognitive Control | Cognitive Training and Stretching Control | Cognitive Control and Stretching Control |
|---|---|---|---|---|
| missed | 1 | 2 | 0 | 1 |
| Lost to Follow-up | 2 | 2 | 1 | 0 |
| refusal | 0 | 1 | 0 | 1 |
| Withdrawal by Subject | 8 | 2 | 5 | 4 |
| Physician Decision | 1 | 2 | 2 | 2 |
| Death | 1 | 2 | 1 | 3 |
Analysis population for the primary outcome, as defined in the registry: Only participants who were able to complete the scale are included in the analysis.
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 | Physical Exercise and Cognitive Training | Physical Exercise and Cognitive Control | Cognitive Training and Stretching Control | Cognitive Control and Stretching Control | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 41 | 41 | 36 | 35 | 153 | |
| Age, Continuous | years | 64.3 (50 to 83) | 64.4 (50 to 83) | 64.6 (50 to 89) | 65.4 (52 to 81) | 64.7 (50 to 89) |
| Sex: Female, Male: Female | Participants | 31 | 29 | 22 | 18 | 100 |
| Sex: Female, Male: Male | Participants | 10 | 12 | 14 | 17 | 53 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 0 | 0 | 0 | 0 | 0 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 41 | 41 | 36 | 35 | 153 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 | 0 | 0 |
| 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 | 10 | 14 | 13 | 17 | 54 |
| Race (NIH/OMB): White | Participants | 30 | 27 | 21 | 17 | 95 |
| Race (NIH/OMB): More than one race | Participants | 1 | 0 | 2 | 1 | 4 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
| Region of Enrollment: United States | participants | 41 | 41 | 36 | 35 | 153 |
6. Primary Endpoint
The registry lists the primary outcome as Cognitive Status Outcome at 6 Months, measured over 6 months post study randomization.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | Z-score |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is cognitive status at 6 months after study randomization, measured with the Repeatable Battery for the Assessment of Neuropsychological Status. The reported measure is an overall z-score, calculated in the endpoint description as the mean of the seven item z-scores. The subscale z-scores are described as having a mean of 0 and a standard deviation of 1. Higher z-scores represent better cognitive outcomes.
A standardized score expresses a measurement relative to a reference scale, which can make results easier to interpret across measures that otherwise use different units. In this trial, the z-score is the stated summary of performance across the RBANS subscales. The registry reports means and standard deviations for each group. For the combined exercise-and-cognitive-training group, the posted mean was 0.24 with a standard deviation of 0.64; for the physical-exercise-and-cognitive-control group, the mean was 0.36 with a standard deviation of 0.59. The cognitive-training-and-stretching-control group had a mean of 0.21 and standard deviation of 0.58, while the cognitive-control-and-stretching-control group had a mean of 0.35 and standard deviation of 0.64.
The primary analysis included only participants who were able to complete the scale. That qualification matters because the endpoint summaries do not represent every randomized participant unless all were able to complete the measure. The registry record does not report further details about completion, the reference population used to form the z-scores, or how incomplete measurements were addressed. As a general statistical point, a continuous endpoint summarized by a mean conveys the group’s average score, while the standard deviation describes variation among participants; neither alone describes the full score distribution.
7. Results Posted in the Registry
- Physical Exercise and Cognitive Training: mean 0.24 versus 0.36 on control; difference -0.12 (95% CI -0.44 to 0.20), standardized effect d = -0.20; z-test p = 0.463.
- Cognitive Training and Stretching Control: mean 0.21 versus 0.36 on control; difference -0.15 (95% CI -0.45 to 0.15), standardized effect d = -0.26; z-test p = 0.334.
- Cognitive Control and Stretching Control: mean 0.35 versus 0.36 on control; difference -0.01 (95% CI -0.34 to 0.32), standardized effect d = -0.02; z-test p = 0.953.
Mean difference: Physical Exercise and Cognitive Training
95% CI: -0.44 to 0.20
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 |
|---|---|---|---|---|
| Physical Performance Scores at 3 Months | Continuous Endpoint | Mean difference | -1.20 (-4.88 to 2.48) | 217 per arm |
| Physical Performance Scores at 6 Months | Continuous Endpoint | Mean difference | -2.07 (-5.76 to 1.62) | 83 per arm |
| Cardiovascular Fitness Scores at 3 Months | Continuous Endpoint | Mean difference | 1.63 (-32.38 to 35.64) | 9,925 per arm |
Physical Performance Scores at 3 Months
- 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:
- Physical Exercise and Cognitive Training: mean 6.60 versus 7.80 on control; difference -1.20 (95% CI -4.88 to 2.48), standardized effect d = -0.27; z-test p = 0.523.
- Cognitive Training and Stretching Control: mean 4.92 versus 7.80 on control; difference -2.88 (95% CI -6.17 to 0.41), standardized effect d = -0.67; z-test p = 0.086.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Physical Exercise and Cognitive Training 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 Cognitive Training and Stretching Control and the control. The interval gives the range of effects that remain compatible with the data.
Physical Performance Scores at 6 Months
- 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:
- Physical Exercise and Cognitive Training: mean 5.00 versus 7.07 on control; difference -2.07 (95% CI -5.76 to 1.62), standardized effect d = -0.44; z-test p = 0.271.
- Cognitive Control and Stretching Control: mean 7.00 versus 7.07 on control; difference -0.07 (95% CI -3.47 to 3.33), standardized effect d = -0.02; z-test p = 0.968.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Physical Exercise and Cognitive Training 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 Cognitive Control and Stretching Control and the control. The interval gives the range of effects that remain compatible with the data.
Cardiovascular Fitness Scores at 3 Months
- 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:
- Physical Exercise and Cognitive Training: mean 47.30 versus 45.67 on control; difference 1.63 (95% CI -32.38 to 35.64), standardized effect d = 0.04; z-test p = 0.925.
- Cognitive Training and Stretching Control: mean 27.67 versus 45.67 on control; difference -18.00 (95% CI -50.50 to 14.50), standardized effect d = -0.44; z-test p = 0.278.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Physical Exercise and Cognitive Training 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 Cognitive Training and Stretching Control and the control. The interval gives the range of effects that remain compatible with the data.
The posted secondary outcomes cover physical performance, cardiovascular fitness, depression, and anxiety at follow-up assessments. The brief summary also identifies quality of life as a secondary aim, but the posted secondary results in the information available for this analysis do not include quality-of-life estimates. The overall pattern should be read alongside the primary result: the sponsor’s overall primary test had p = 0.747, while secondary outcomes address different aspects of recovery and are not substitutes for the primary cognitive endpoint.
The registry lists 12 outcome measures and 12 analyses, while 10 secondary outcomes are posted. Results available for physical performance and cardiovascular fitness include group means and standard deviations, as well as sponsor-reported mixed-model overall p-values. The posted summaries have varying group counts across endpoints and follow-up times. This means the evidence base differs by outcome, and a result for one measure should not be assumed to describe another domain or follow-up time.
Unadjusted secondary comparisons carry less weight when many outcomes and contrasts are considered. As a general statistical point, testing multiple outcomes creates more opportunities for chance findings, and a nominal p-value does not account for that unless an adjustment or testing hierarchy is specified. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for the secondary outcomes. Consequently, the secondary estimates are best treated as supportive or exploratory descriptions rather than isolated confirmatory evidence.
Different secondary measures also use different scales and capture distinct constructs. Physical performance scores and step-test counts are not directly interchangeable with mood measures or quality of life. The posted secondary evidence can help describe the breadth of outcomes evaluated, but it does not resolve the primary cognitive question or establish an overall benefit across recovery domains. The registry record does not report results for every listed secondary outcome in the information available for this analysis.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Physical Performance Scores at 3 Months
- Physical Performance Scores at 6 Months
- Cardiovascular Fitness Scores at 3 Months
- Cardiovascular Fitness Scores at 6 Months
- Depression Scores at 3 Months
- Depression Scores at 6 Months
- Anxiety Scores at 3 Months
- Anxiety Scores at 6 Months
9. Statistical Interpretation
The sponsor’s reported primary analysis used mixed models analysis across all four groups and gave a p-value of 0.747. This is an overall test reported for the groups together. The registry does not provide the model estimate, confidence interval, or further specification of that analysis, so the p-value cannot by itself indicate the size or direction of every group contrast. It is evidence about the overall comparison under the sponsor’s model, not a direct estimate of the combined intervention versus each other group.
In the posted arm summaries, mean cognitive z-scores ranged from 0.21 to 0.36. The recalculated unadjusted contrast between physical exercise and cognitive training and the physical-exercise-and-cognitive-control group was -0.12, with a confidence interval from -0.441 to 0.201 and an unadjusted p-value of 0.463. The recalculated contrast for cognitive training and stretching control versus the reference group was -0.15, with a confidence interval from -0.454 to 0.154 and an unadjusted p-value of 0.334. For cognitive control and stretching control versus the reference group, the estimate was -0.01, with a confidence interval from -0.342 to 0.322 and an unadjusted p-value of 0.953.
These recalculations are simple, unadjusted comparisons of posted group summaries. Their intervals include zero, so the estimates are compatible with a range of possibilities that includes no mean difference as well as differences in either direction. The estimates are not adjusted for other variables or for multiple comparisons. They should not be treated as a replacement for the sponsor’s mixed-model analysis, which addresses a different, overall question and is the sponsor’s reported result. No discrepancy is flagged between the sponsor’s analysis and the recalculated summaries.
The outcome summaries are based on relatively small analyzed groups, with the number included varying by group. The registry states that only participants able to complete the scale were included, and does not report a missing-data analysis or the characteristics of those without completed measurements. This limits how confidently the observed group means can be generalized to all randomized participants. The posted results describe cognitive scores at the specified follow-up; they do not establish that the groups are equivalent, and they do not establish a treatment effect beyond the comparisons and analyses reported.
10. Statistical Methods Explained
The main statistical results combine an overall analysis reported by the sponsor with simple recalculations from the posted group means and standard deviations. These answer related but distinct questions. The sponsor reports a mixed models analysis across the four randomized groups. The recalculations compare each of three groups with the physical-exercise-and-cognitive-control group using unadjusted mean differences. The registry record does not report enough model details to reconstruct the sponsor’s mixed model.
What does a mean difference describe?
A mean difference is the first group’s average minus the reference group’s average in the posted comparisons. A negative estimate means the first group’s posted mean is lower than the reference group’s mean; a positive estimate would mean it is higher. For the primary outcome, the recalculated difference for physical exercise and cognitive training versus physical exercise and cognitive control was -0.12. The cognitive-training-and-stretching-control contrast was -0.15, and the cognitive-control-and-stretching-control contrast was -0.01. These are unadjusted calculations from summary statistics, not model-adjusted estimates.
As a general statistical explanation, an unadjusted comparison does not account for covariates or for the structure of repeated observations unless those features are explicitly built into the calculation. The registry record does not state that these recalculations adjust for baseline values, participant characteristics, or repeated measurements. They should therefore be read as descriptive pairwise contrasts rather than as the sponsor’s full analysis.
How should the overall p-value be understood?
The sponsor reports a mixed models analysis with p = 0.747 for the four groups. A p-value is a measure of how compatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of a difference. The record identifies the method as mixed models analysis but does not report the model formula, covariance structure, included covariates, exact contrast tested, or handling of missing observations. Those details are not reported in the registry record.
As a general statistical point, mixed models can account for correlations among repeated observations when repeated measurements are modeled. The presence of a mixed-model label alone does not reveal which repeated measurements or covariance assumptions were used in this trial. The reported overall p-value is therefore best described as the sponsor’s test across groups, without inferring unreported model features.
What do the unadjusted p-values add?
The recalculated pairwise p-values are 0.463 for physical exercise and cognitive training versus the reference group, 0.334 for cognitive training and stretching control versus the reference group, and 0.953 for cognitive control and stretching control versus the reference group. Each tests a particular pairwise contrast under the unadjusted recalculation. They are not the sponsor’s overall four-group p-value. A p-value does not convey precision by itself; the confidence interval gives a range of estimates compatible with the data and calculation assumptions.
Multiple comparisons create an interpretive issue because testing several contrasts increases the chance of observing an apparently unusual result by chance. The registry record does not report a multiplicity adjustment for the posted pairwise results, nor does it state a hierarchy of tests. Accordingly, the pairwise p-values should be treated as unadjusted and exploratory in relation to a set of possible comparisons, rather than as independently confirmatory findings.
What do the planning illustrations mean?
The sample-size planning illustrations use observed effects and assumptions stated with those calculations: a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The illustrated target effect is a stated fraction of the observed effect. These are planning scenarios, not evidence about the trial’s original design. The original design assumptions and sample-size justification are not reported in the registry record. The figures are participants per arm for continuous outcomes.
As a general statistical explanation, power is the probability that a planned analysis will reject its null hypothesis under a specified effect and model assumptions. The 80% and 90% columns describe different target probabilities for detecting the stated effect under the planning assumptions. A smaller effect is harder to distinguish from random variation and generally requires more participants. The illustration does not show the probability that the completed trial found a real effect.
The primary endpoint summaries report means and standard deviations, and the recalculated comparisons use those quantities. As a general statistical point, the standard deviation reflects the spread of individual scores around a group mean; the standard error reflects uncertainty in an estimated mean and depends on both variability and the number analyzed. The registry supplies standard errors for the group means used in the recalculations, but it does not report a confidence-interval level for the pairwise intervals. No confidence level should be inferred from the record.
11. Confidence Intervals and Precision
The primary pairwise confidence intervals are broad relative to their point estimates and include zero. For physical exercise and cognitive training versus physical exercise and cognitive control, the estimated mean difference was -0.12, with an interval from -0.441 to 0.201. For cognitive training and stretching control versus that reference group, the estimate was -0.15, with an interval from -0.454 to 0.154. For cognitive control and stretching control versus the reference group, the estimate was -0.01, with an interval from -0.342 to 0.322. These intervals show uncertainty around the recalculated unadjusted contrasts; they do not establish that the true differences are exactly zero.
A confidence interval is a range of values compatible with the data and the statistical method used. As a general explanation, narrower intervals indicate more precise estimates, while wider intervals indicate greater uncertainty. The registry record does not state the confidence level for these recalculated intervals, so their level is not reported in the registry record. They should not be assigned a conventional level by assumption.
Precision is limited in part by the number of participants included in the primary outcome summaries: 27 in the combined-intervention group, 30 in the physical-exercise-and-cognitive-control group, 27 in the cognitive-training-and-stretching-control group, and 24 in the cognitive-control-and-stretching-control group. Only participants able to complete the scale were included. These analysis counts are not the same as the trial’s enrollment, and the registry record does not explain the difference or report how missing outcomes affected the estimates.
The means and standard deviations also indicate variability in scores within groups. As a general statistical point, participant-level variation and the number of observations both influence the precision of a mean difference. The uncertainty intervals are therefore essential context: the point estimates alone would give an incomplete account. The sponsor’s overall analysis provides a p-value but no estimate or interval in the posted record, so its precision cannot be judged from an interval for that model.
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 | 412 | 551 |
| 75% of the observed effect | 731 | 979 |
| 50% of the observed effect | 1,645 | 2,202 |
The planning figures are participants per arm, not total participants or total events. This is a continuous-outcome illustration; the record’s planning description distinguishes it from time-to-event calculations, which would express totals of events. The assumptions stated for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses the stated fraction of the observed effect as the effect to detect. These figures are planning illustrations, not observed power.
The 80% power column gives the illustrated number of participants per arm for a design that would have an 80% probability of detecting the specified effect under those assumptions. The 90% column gives the corresponding number per arm for a higher target probability of detection. Neither column reports a feature of the completed trial’s results. The original trial design assumptions and sample-size justification are not reported in the registry record.
Rows that plan for 75% or 50% of the observed effect use smaller target effects than the row based on 100% of the observed effect. Smaller effects are generally harder to detect against background variability, so the planning figures increase as the target effect becomes smaller. The large variation in figures across contrasts reflects the different observed effects used in each illustration; it is not evidence that one comparison is more important or that the original study was designed around these recalculations.
As a general statistical point, a sample-size calculation depends on the effect size, variability, significance level, power target, allocation, and analysis assumptions. Changing any of these can change the resulting planning number. These illustrations should be used to understand the scale of sample sizes associated with the stated assumptions, not as a retrospective judgment of the trial’s design or a statement about the probability that its results are correct.
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 = -0.120; pooled standard deviation σ = 0.614.
- n = 2 × (1.96 + 0.842)2 × 0.6142 / -0.1202 = 411.2, rounded up to 412 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 <- -0.12 # observed difference in means
sigma <- 0.614143897855158 # 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(3095417)
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 = 412 (80% power), 551 (90% power)
75% of observed effect: n per arm = 731 (80% power), 979 (90% power)
50% of observed effect: n per arm = 1,645 (80% power), 2,202 (90% power)
power.t.test: 412.1
Simulated power at n = 412 per arm: 0.804 (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 |
|---|---|---|---|
| Mixed Models Analysis | not reported | 0.747 |
The sponsor’s primary result is a mixed models analysis across all four groups, reported with p = 0.747. The registry does not provide the model’s estimated group differences or confidence intervals. That overall analysis is distinct from the recalculated pairwise comparisons, which use posted means and standard deviations to compare each of three groups with physical exercise and cognitive control.
The recalculated mean differences are -0.12 for physical exercise and cognitive training, -0.15 for cognitive training and stretching control, and -0.01 for cognitive control and stretching control, each against the same reference group. Their unadjusted p-values are 0.463, 0.334, and 0.953, respectively. These calculations do not reproduce the sponsor’s mixed model and should not be interpreted as if they did. They omit any model adjustments or repeated-measure structure not represented in the posted summary statistics.
No discrepancy is flagged between the sponsor analysis and the recalculations. The sponsor’s analysis remains the direct report of the planned overall analysis in the registry. The recalculations are supplementary descriptions of pairwise group means, useful for seeing the direction and uncertainty of selected comparisons, but they are not a replacement for the sponsor’s analysis. Details of the sponsor’s model specification and analysis population beyond the posted endpoint qualification are not reported in the registry record.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several outcomes, time points, or group contrasts are tested. Even if each individual test uses the same nominal threshold, the chance of at least one seemingly noteworthy result can rise as the number of tests increases. This is a general statistical consideration, not a claim that any particular result in this trial is false. The registry lists 12 outcome measures and 12 analyses, and the posted secondary results cover 10 outcomes. The record does not describe a multiplicity correction or a prespecified testing hierarchy for these analyses.
The primary sponsor analysis is reported as an overall mixed models test with p = 0.747. The additional recalculated pairwise p-values are unadjusted. They address selected contrasts rather than the same overall question, and the record does not report an adjustment across those contrasts. Secondary results likewise span multiple measures and follow-up times. Without reported multiplicity procedures, individual unadjusted results should be interpreted cautiously and in the context of the full set of outcomes rather than in isolation.
Missing data are also relevant. The primary endpoint description says that only participants able to complete the scale are included. Primary outcome analysis counts are 27, 30, 27, and 24 across the four groups. Counts also vary in the secondary outcome summaries. The registry record does not report the reasons for missing outcome measurements, the number of participants who were unable to complete each measure, or the methods used to handle missing data in the sponsor’s model.
The analysis population is therefore only partly described: the primary endpoint includes scale completers, but further details about analysis eligibility and handling of incomplete observations are not reported in the registry record. It is not possible to determine from the posted information whether missingness differed by group or whether the analysis assumptions adequately addressed it. This uncertainty limits interpretation of how representative the analyzed summaries are of all randomized participants. The registry record also does not report sensitivity analyses for missing data or the model’s treatment of repeated measurements.
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 |
|---|---|---|---|
| Physical Exercise and Cognitive Training | 0 | 41 | 0.0% |
| Physical Exercise and Cognitive Control | 1 | 41 | 2.4% |
| Cognitive Training and Stretching Control | 0 | 36 | 0.0% |
| Cognitive Control and Stretching Control | 0 | 35 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Physical Exercise and Cognitive Training | 1 of 41 |
| Physical Exercise and Cognitive Control | 2 of 41 |
| Cognitive Training and Stretching Control | 1 of 36 |
| Cognitive Control and Stretching Control | 3 of 35 |
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 |
|---|---|
| Physical Exercise and Cognitive Training | 2 of 41 |
| Physical Exercise and Cognitive Control | 3 of 41 |
| Cognitive Training and Stretching Control | 1 of 36 |
| Cognitive Control and Stretching Control | 0 of 35 |
Most frequent serious adverse event terms
| Event term | Organ system | Physical Exercise and Cognitive Training | Physical Exercise and Cognitive Control | Cognitive Training and Stretching Control | Cognitive Control and Stretching Control |
|---|---|---|---|---|---|
| elevated heart rate | Cardiac disorders | 0 of 41 | 1 of 41 | 0 of 36 | 0 of 35 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Physical Exercise and Cognitive Training | Physical Exercise and Cognitive Control | Cognitive Training and Stretching Control | Cognitive Control and Stretching Control |
|---|---|---|---|---|---|
| elevated heart rate | Cardiac disorders | 1 of 41 | 1 of 41 | 1 of 36 | 0 of 35 |
| O2 saturation lower than 88% | Respiratory, thoracic and mediastinal disorders | 1 of 41 | 2 of 41 | 0 of 36 | 0 of 35 |
Serious events with the highest arm-level rate: elevated heart rate (2.4%).
The registry reports serious adverse events, other adverse events, and deaths by intervention group. For serious adverse events, the numbers affected were 0 of 41 in physical exercise and cognitive training, 1 of 41 in physical exercise and cognitive control, 0 of 36 in cognitive training and stretching control, and 0 of 35 in cognitive control and stretching control. For other adverse events, the corresponding affected counts were 2 of 41, 3 of 41, 1 of 36, and 0 of 35. The registry lists deaths as 1, 2, 1, and 3 in those groups, respectively.
These figures are counts within the groups reported as at risk for the relevant adverse-event category. The registry lists elevated heart rate at 2.4% among the top serious adverse-event terms. The posted information does not establish that any listed event or death was caused by an intervention. It also does not provide further detail in the information about event timing, severity classifications beyond the serious/other categories, or relatedness assessments. The counts are descriptive safety information, not a basis for attributing causation or comparing risk without accounting for the study design and event definitions.
17. What the Result Does, and Does Not, Mean
The primary results describe average cognitive z-scores at 6 months among participants able to complete the RBANS scale. The sponsor’s reported overall mixed models analysis gave p = 0.747. The recalculated unadjusted pairwise estimates against the physical-exercise-and-cognitive-control group were -0.12, -0.15, and -0.01, with confidence intervals that include zero. These results do not provide clear evidence of differences in the primary outcome under the analyses reported.
That interpretation is not the same as concluding that all four interventions are equivalent. A non-significant p-value does not show that any possible difference is absent, and the confidence intervals remain compatible with differences in either direction. The registry record does not report a prespecified equivalence or noninferiority margin. Without such a margin and an analysis designed for that question, equivalence cannot be established from these results.
The result also does not determine whether the interventions affect every aspect of recovery. Secondary outcomes concern other constructs and follow-up times, and the posted record contains results for only some of the listed measures. The primary endpoint is a cognitive measure at a specific follow-up, not a general measure of health, function, or long-term outcomes. The results should be understood within that scope.
Interpretation is further limited by the primary endpoint’s completion-based analysis population, the variation in analyzed group counts, and the absence of reported detail about missing-data handling. The sponsor’s model specification and the original sample-size justification are also not reported in the registry record. These omissions do not erase the posted estimates, but they constrain what can be inferred from them. The results describe the registry’s reported group summaries and analysis; they do not, by themselves, prove a treatment effect, rule out a meaningful difference, or support a claim about outcomes not measured or reported.
18. Why This Trial Matters Statistically
This trial is statistically informative because it compares four combinations of physical activity, cognitive training, and control activities, while reporting a cognitive endpoint and several secondary recovery measures. The four-arm structure makes it possible to see how the reported groups were organized, but the primary sponsor analysis is an overall comparison and the available recalculations address selected pairwise contrasts. Keeping those questions distinct prevents an overall p-value from being mistaken for an estimate of one specific intervention contrast.
The posted primary estimates also illustrate why effect estimates and uncertainty matter alongside p-values. The pairwise mean differences are close to zero in the posted summaries, but their confidence intervals include values on both sides of zero. The evidence is therefore not a demonstration that group outcomes are identical. Reporting the estimate, interval, and analysis population gives a more complete account than interpreting a p-value alone.
The trial also highlights the importance of outcome completion and multiplicity. The primary analysis includes only scale completers, group counts vary across outcomes, and the registry does not report a missing-data strategy or multiplicity procedure. Those issues affect how much weight readers should place on individual results, particularly across several outcomes and follow-up times.
Finally, the sample-size illustrations are tied to observed effects and stated planning assumptions, not the trial’s original design. Separating retrospective planning scenarios from the sponsor’s analysis helps avoid treating them as evidence of observed power or as a judgment about the study’s initial design. The registry record is most useful when its reported results are read with their scope and methodological gaps clearly in view.
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.
Several limitations are specific to the information reported for this trial. The primary outcome analysis includes only participants who were able to complete the RBANS scale. The registry does not report why some participants did not contribute primary endpoint data, whether completion differed across groups, or how incomplete measurements were handled in the sponsor’s mixed models analysis. This leaves uncertainty about the relation between the analyzed participants and all randomized participants.
The sponsor’s primary result is an overall p-value without a posted model estimate or confidence interval. The model is labeled mixed models analysis, but the registry record does not report its specification, covariates, repeated-measure structure, or exact contrast. The pairwise calculations are unadjusted comparisons of summary statistics and cannot fill in those details. The reported recalculations also do not account for multiplicity across the several outcomes, time points, and possible comparisons; adjustment procedures are not reported in the registry record.
Secondary outcomes are not all available in the posted information, despite 12 outcome measures and 12 analyses being listed. The available secondary summaries have varying analyzed group counts. Some intervention descriptions are incomplete in the registry record, which limits interpretation of the activities and delivery beyond the stated descriptions. The record labels the trial double-masked but does not state who was masked or how masking was maintained.
The original sample-size assumptions and justification, interim analyses, and detailed statistical plan are not reported in the registry record. The sample-size illustrations are separate planning calculations based on observed effects and stated assumptions. Finally, adverse-event counts are descriptive; the posted information does not provide enough detail to attribute events or deaths to an intervention or to assess their timing and relatedness.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Improving the Recovery and Outcome Every Day After the ICU — NCT03095417.
- Registry record last updated 2024-03-27; status last verified 2024-02.
- Results first posted 2024-03-27.
- 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
NCT03095417, titled Improving the Recovery and Outcome Every Day After the ICU, is a completed randomized, double-masked, parallel-group trial sponsored by Indiana University. Enrollment was 249. The primary endpoint was RBANS cognitive status at 6 months after randomization, analyzed among participants able to complete the scale. The registry reports a four-group mixed models analysis with p = 0.747.
Recalculated unadjusted pairwise mean differences against physical exercise and cognitive control were -0.12 for physical exercise and cognitive training, -0.15 for cognitive training and stretching control, and -0.01 for cognitive control and stretching control. Each confidence interval includes zero. These calculations are distinct from the sponsor’s overall analysis. The registry record does not report the original sample-size justification, full model specification, multiplicity procedures, or missing-data handling.