A Trial of Rehabilitation Therapy in Older Acute Heart Failure Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Trial of Rehabilitation Therapy in Older Acute Heart Failure Patients (NCT02196038), a randomized na study. The primary outcome is Short Physical Performance Battery (SPPB) at Month 3.

2. Clinical Question

The clinical question is about a measured physical-function score at a defined follow-up, rather than directly about rehospitalization. The registry describes rehospitalization as one of the key clinical outcomes motivating the trial and lists all-cause rehospitalization as a secondary outcome. The primary endpoint is the Month 3 SPPB score.

The trial randomized 349 participants overall. For the primary outcome, the registry states that the analysis was completed on all participants alive with a Month 3 SPPB result obtained, with an analysis population of 304. The comparison therefore pertains to the participants included in that endpoint analysis. The registry record does not report enough detail to establish how missing Month 3 scores were handled beyond that stated analysis population.

The intervention and comparator both involved study contact, but the registry describes their content differently: individualized progressive rehabilitation versus usual care with regular staff contact. The primary question is whether the average recorded score differed between these randomized groups at the stated follow-up; it does not by itself answer every question about longer-term clinical outcomes or the experience of all randomized participants.

3. Trial Design

REHAB-HF was a multicenter, randomized, attention-controlled, single-blind, parallel-group trial. The record lists the sponsor as Wake Forest University Health Sciences. The trial status is completed; the recorded start was 2014-09 and primary completion was 2020-06-15. Phase is recorded as NA.

The enrollment was 349. Participants were assigned to a multi-domain rehabilitation intervention or attention control. The rehabilitation arm is described as an individual, tailored, progressive physical-function rehabilitation intervention. The trial summary says it was added to standard care, began early during hospitalization, and continued for 12 weeks. The attention-control arm is described as usual care with bi-weekly contact from study staff.

Randomization and the parallel-group structure support a between-group comparison. The record identifies the trial as single-blind, but does not report who was blinded or how blinding was maintained. It also does not report the allocation ratio or further details of the randomization procedure. Those design details should not be inferred from the arm sizes in the endpoint analysis.

The primary outcome was the Short Physical Performance Battery score at Month 3. The registry reports a primary-outcome analysis population of 304 participants who were alive and had that score obtained. The arm-level endpoint summaries list 155 participants in attention control and 149 in rehabilitation. The record also lists 26 outcome measures, one posted secondary outcome, and two analyses. All-cause rehospitalization is the secondary outcome named in the record.

The registry describes the study's broad purpose as examining physical function and key clinical outcomes, including rehospitalization. The original sample-size justification, detailed protocol, and planned statistical analysis details beyond the posted analysis descriptions are not reported in the registry record. The trial's recorded status and design features describe the study, but do not on their own establish how broadly its endpoint result applies outside the analyzed participants.

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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Analysis completed on all participants alive with Month 3 SPPB obtained (n=304).

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Short Physical Performance Battery (SPPB) at Month 3, measured over Month 3.

The primary endpoint is the Short Physical Performance Battery score at Month 3. The SPPB is a score on a scale of 0-12, with a higher score indicating better physical function. It provides a numerical measure of physical function that can be compared between the randomized groups at a defined follow-up time.

Using a continuous score preserves information across its scale rather than reducing the result to a binary classification. A group mean and a mean difference describe the average score and the average separation between groups. The registry reports least-squares means with standard errors for the arms, and the sponsor's posted analysis reports a mean difference in final values.

The endpoint is relevant to the stated intervention because the rehabilitation program is designed around physical function. It is nevertheless distinct from the trial's secondary outcome of all-cause rehospitalization. A score difference should be interpreted as a difference in the measured endpoint, not as a direct estimate of rehospitalization or of every aspect of recovery.

The primary analysis included participants alive with Month 3 SPPB obtained, with a reported analysis population of 304. The registry does not report a clinical threshold for interpreting the size of a score difference, so statistical separation should not be equated with a particular level of practical importance.

7. Results Posted in the Registry

• Rehabilitation Intervention: mean 8.30 versus 6.90 on control; difference 1.40 (95% CI 0.85 to 1.95), standardized effect d = 0.57; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous: each participant's SPPB result is a score on a 0-12 scale. For a continuous outcome, a group mean describes the average observed score, and a mean difference describes the separation between the group averages. Positive differences in this comparison correspond to a higher average score in the rehabilitation group, given the direction used in the posted results.

The registry lists least-squares means and standard errors for the arm summaries. A standard error describes the estimated uncertainty in a mean, rather than the spread of individual participant scores. The reported arm means are 6.9 for attention control and 8.3 for rehabilitation, each with a standard error of 0.2. Those standard errors should not be read as ranges containing most individual scores.

The unadjusted recalculation uses posted summary statistics to estimate a simple between-group mean difference. It reports 1.4 points and p < 0.001. This is a summary-statistic recalculation, not the sponsor's joint model. The recalculation also uses an approximate pooled standard deviation derived from the posted standard errors and sample sizes; its status as approximate is important when interpreting any standardized effect derived from those summaries. The original participant-level data and detailed model specification are not reported in the registry record.

The sponsor reports a joint model with the parameter described as mean difference in final values. It gives an estimate of 1.5, a 95% confidence interval from 0.9 to 2.0, and p < 0.001. The record does not report the joint model's covariates, covariance structure, or other implementation details. It is therefore appropriate to describe the posted result and its method label without filling in unreported model assumptions.

A mean difference is expressed in the original score units, which in this case are SPPB points. A standardized effect expresses a difference relative to a measure of score variability, which can make results on different scales easier to compare. Such standardization does not replace the original-unit result, and the recalculated standardized value depends on the approximate variability estimate used. The registry does not report a sponsor-provided standardized effect for this endpoint.

A p-value assesses how compatible the observed data are with a specified null hypothesis under the statistical model. Smaller p-values can indicate stronger evidence against that null model, but do not quantify the probability that a treatment is beneficial or the probability that the result will be reproduced. The recalculated p-value and sponsor p-value are attached to their respective analyses and should not be treated as interchangeable.

A confidence interval expresses uncertainty around an estimated parameter under the analysis model. The sponsor's 95% interval ranges from 0.9 to 2.0 points. In repeated use of a procedure with the same assumptions, intervals constructed in this way would cover the true parameter at the stated rate. For an individual interval, the practical reading is the range of values compatible with the data and model, not a guarantee that the true value lies within it.

Random allocation supports a comparison between assigned groups, but a valid interpretation still depends on how outcomes and missing observations are handled and on the suitability of the analysis. Here, the primary endpoint population is explicitly restricted to participants alive with a Month 3 score obtained. The record does not report an intention-to-treat analysis, imputation strategy, sensitivity analysis for missing outcomes, or the detailed treatment of participants who died before the assessment.

Over-dispersion is a general concern for count outcomes when their variability exceeds what a chosen count model expects. It is not a direct feature of the primary continuous SPPB score in the way it is for count data. More generally, model choice should reflect the outcome's scale and distribution. The registry does not report diagnostic checks or enough detail to assess the sponsor's joint model assumptions, so no such checks should be presumed.

Multiplicity is a general issue when multiple outcomes or analyses are examined, because the chance of at least one apparently unusual result can increase across a family of tests. The record lists 26 outcome measures and two analyses, but does not report whether or how the primary and secondary comparisons were adjusted for multiplicity. The posted p-values should therefore be read as reported for their analyses, without claiming a particular family-wise error control.

Finally, the planning calculations based on the observed effect are not the trial's original design calculations. They use stated illustration assumptions and help show how required sample size changes with a target effect. They are not evidence about the probability that the completed study would have found a result, and they do not replace a protocol-based sample-size justification, which is not reported in the registry record.

10. Confidence Intervals and Precision

The sponsor's posted estimate is a mean difference of 1.5 SPPB points, with a 95% confidence interval from 0.9 to 2.0. The interval describes uncertainty around the estimated group contrast under the sponsor's joint model. Its lower and upper bounds are both above zero, indicating that the reported interval is compatible with a positive difference rather than no difference under that model.

The interval also shows that the point estimate is not known with exact precision. Values across the reported range remain compatible with the data and model, and the range should be considered alongside the score's 0-12 scale. The registry does not report a threshold for a clinically important SPPB difference, so the interval alone cannot establish whether the difference is practically important to patients.

The unadjusted recalculation reports a mean difference of 1.4 and p < 0.001. It is distinct from the sponsor's joint-model estimate and interval. The recalculated confidence limits are not needed to interpret the sponsor's posted precision, and the registry record does not provide the details needed to reconcile every feature of the two analyses.

Precision applies to the analyzed population of participants alive with a Month 3 score obtained. The record does not provide a sensitivity analysis showing how the interval might change under alternative assumptions about missing outcomes or deaths before measurement. Thus, the interval quantifies model-based uncertainty for the reported analysis, not uncertainty from every possible source of bias or incomplete follow-up.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm for this continuous endpoint. The assumptions state that time-to-event calculations would instead report total events, but that convention does not apply to the SPPB planning illustration. The figures are based on a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. They use the observed effect as a reference, with the target set at the stated fraction of that effect.

For planning for 100% of the observed effect, the illustration gives 49 participants per arm for 80% power and 66 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 87 participants per arm for 80% power and 116 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 195 participants per arm for 80% power and 261 participants per arm for 90% power.

The 80% power column means the calculated per-arm sample size is intended to give an 80% chance of detecting the chosen effect under the stated assumptions if that effect is the true one. The 90% column uses a higher target chance of detection and therefore calls for more participants in each corresponding planning scenario. Smaller effects are harder to distinguish from random variation, so the illustration requires more participants per arm as the target effect becomes smaller.

The curve communicates this same planning relationship across effect sizes: as the target effect shrinks, the required sample size rises. These figures are planning illustrations based on the observed effect, not the trial's original design assumptions; the original sample-size justification is not reported in the registry record. This is not observed power.

12. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = 1.400; pooled standard deviation σ = 2.466.
2. n = 2 × (1.96 + 0.842)² × 2.466² / 1.400² = 48.7, rounded up to 49 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 <- 1.4                      # observed difference in means
sigma <- 2.46624899512605                     # 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(2196038)
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 = 49 (80% power), 66 (90% power)
 75% of observed effect: n per arm = 87 (80% power), 116 (90% power)
 50% of observed effect: n per arm = 195 (80% power), 261 (90% power)
power.t.test: 49.7 
Simulated power at n = 49 per arm: 0.796 (20000 replicates)

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

13. Analyses Reported by the Sponsor

The sponsor's posted analysis is a joint model of final values. It reports a mean difference of 1.5 points, a 95% confidence interval from 0.9 to 2.0, and p < 0.001. That is the registry's own reported analysis and should be distinguished from a simple recalculation based on the posted arm-level summaries.

The unadjusted recalculation gives a mean difference of 1.4 points and p < 0.001. It is derived from the reported group summaries and does not reproduce the sponsor's joint model. The estimates are close in direction and size, but the registry does not report the full model specification needed to identify why their values differ. It would be unwarranted to attribute the difference to a particular adjustment or modeling choice not described in the record.

Both analyses point to a higher Month 3 average score in the rehabilitation group among the analyzed participants. The recalculation is useful as a transparent check on the scale and general direction of the posted contrast, while the sponsor's joint-model result remains the study's reported model-based result. The record does not indicate a discrepancy flag for these results.

14. Multiplicity, Missing Data and Analysis Populations

The primary-outcome analysis population is described as all participants alive with Month 3 SPPB obtained, with n=304. The registry lists 155 participants in the attention-control endpoint summary and 149 in the rehabilitation endpoint summary. These are the numbers associated with the posted endpoint summaries, not a complete account of how every randomized participant was handled across all outcomes.

The record does not report the detailed missing-data strategy. It does not say whether unobserved Month 3 scores were imputed, whether a sensitivity analysis was conducted, or how outcome availability was addressed beyond defining the primary analysis population. It also does not report the primary endpoint result for participants who were not alive at Month 3. The result should therefore be understood as applying to the stated analysis population, with the implications of that restriction not fully assessable from the registry record.

The trial lists 26 outcome measures, one posted secondary outcome, and two analyses. All-cause rehospitalization is the secondary outcome identified. The record does not report a multiplicity adjustment or a prespecified hierarchy controlling interpretation across outcomes and analyses. The primary comparison can be described as reported, but it should not be assumed that family-wise error or another multiplicity procedure was applied.

The registry identifies the sponsor's method as a joint model but does not provide enough detail to assess the full analysis plan, covariate adjustment, or assumptions used for incomplete observations. It also does not report an intention-to-treat analysis label in the posted primary result. No conclusions about unreported analysis populations, imputation procedures, interim analyses, or multiplicity controls should be inferred.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: heart failure exacerbation (36.8%), injurious fall (9.2%), non-cardiac chest pain (3.4%), acute kidney injury (3.4%), implantable cardioverter defibrillator implantation (3.4%).

The registry lists serious adverse events and other adverse events by group. In attention control, 174 participants were at risk for serious adverse events and 115 were affected; 174 were at risk for other adverse events and 69 were affected. In the rehabilitation intervention group, 175 were at risk for serious adverse events and 106 were affected; 175 were at risk for other adverse events and 60 were affected. Deaths are listed as 16 in attention control and 21 in the rehabilitation group.

The most frequent serious adverse-event terms listed are heart failure exacerbation at 36.8%, injurious fall at 9.2%, non-cardiac chest pain at 3.4%, acute kidney injury at 3.4%, implantable cardioverter defibrillator implantation at 3.4%, and chest pain at 3.4%. These are the registry's listed terms and percentages; they do not by themselves establish whether an event was caused by the intervention.

Counts of participants affected are not the same as counts of event episodes, and the registry excerpt does not provide enough context to infer comparative risk or causality from these figures alone. The event figures are descriptive and should be read separately from the primary SPPB analysis.

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

The posted primary result describes a higher average Month 3 SPPB score in the rehabilitation group than in attention control among participants alive with a score obtained. The sponsor's model-based estimate is 1.5 points, with a 95% confidence interval from 0.9 to 2.0. The unadjusted recalculation is 1.4 points. Higher SPPB scores indicate better physical function on the 0-12 scale.

This is a statistical description of a group contrast, not a complete account of every outcome or every participant randomized. The endpoint result does not establish the finding for all-cause rehospitalization, even though rehospitalization was a stated clinical outcome and is listed as secondary. No rehospitalization estimate is included in the registry record for this analysis.

Randomization is a design strength for comparing assigned groups, but the primary endpoint analysis is limited to participants alive with a Month 3 score obtained. Because missing-data handling and sensitivity analyses are not reported in the registry record, the impact of this analysis-population restriction cannot be determined from these results alone. The report also does not give a threshold for a clinically important SPPB difference, so the statistical result does not settle the practical importance of the size of the score contrast.

The result should not be generalized automatically to populations, settings, or follow-up periods not described by the trial. The study focused on older patients hospitalized with acute decompensated heart failure and used an attention-control comparison. The registry record does not provide the detailed eligibility criteria or other information needed to define all limits to generalizability.

In short, the reported data support a positive between-group difference in the measured Month 3 physical-function score under the sponsor's analysis. They do not, by themselves, show why the scores differed, establish effects on unreported outcomes, or answer whether the difference meets a clinical importance threshold.

17. Why This Trial Matters Statistically

This trial offers a useful statistical example of interpreting a continuous functional outcome in a randomized, attention-controlled design. The SPPB is recorded on a bounded 0-12 scale, and the result can be expressed in its original units as a mean difference. That makes the estimate directly interpretable as a difference in average score, while still requiring attention to uncertainty and clinical context.

The registry also allows readers to distinguish a sponsor-reported joint-model result from a simple recalculation using posted arm summaries. The estimates are similar in direction and close in size, but method labels matter: a summary-statistic recalculation does not reproduce a participant-level model. Recognizing that distinction helps prevent an independent arithmetic check from being mistaken for the trial's full analysis.

The endpoint population matters too. The primary result is based on participants alive with a Month 3 score obtained, not necessarily every randomized participant. This makes the analysis population part of the interpretation rather than a technical footnote. The record's lack of detail on missing outcomes illustrates why a reported estimate and confidence interval cannot resolve every question about potential bias.

Finally, the planning illustration shows how a target effect and desired power influence participant requirements under stated assumptions. It is a separate question from the trial's observed result and from the original design justification. Keeping estimation, uncertainty, missingness, multiplicity, and planning distinct is central to a careful reading of clinical trial statistics.

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 registry record does not provide the detailed eligibility criteria, so the precise population to which the result may generalize cannot be fully characterized. It describes older patients with acute decompensated heart failure, but further clinical and demographic detail is not reported in the registry record for this analysis.

The primary endpoint analysis includes participants alive with a Month 3 SPPB result obtained. The record does not report the reasons for unavailable scores, methods for handling missing outcomes, or sensitivity analyses. As a result, it is not possible to assess from this record how those missing observations might affect the estimate.

The sponsor's analysis is labeled a joint model, but its specification is not reported. Details of adjustment, model assumptions, and diagnostic assessment are also not reported in the registry record. The unadjusted recalculation is necessarily more limited because it relies on arm-level summaries and an approximate variability estimate.

The record lists 26 outcome measures and two analyses but does not report a multiplicity strategy. The primary endpoint result should be interpreted without assuming that adjustments across outcome measures or analyses were made. The original sample-size justification and design assumptions are also not reported, so the planning illustration based on the observed effect cannot be treated as a description of the original design.

Finally, the primary endpoint is a Month 3 physical-function score. The record identifies all-cause rehospitalization as a secondary outcome, but the numerical result for it is not included in the registry record for this analysis. The SPPB result therefore cannot substitute for a separate assessment of rehospitalization or other outcomes.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Trial of Rehabilitation Therapy in Older Acute Heart Failure Patients — NCT02196038.
• Registry record last updated 2021-06-24; status last verified 2020-09.
• Results first posted 2021-06-23.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

REHAB-HF was a completed, multicenter, randomized, single-blind, parallel-group, attention-controlled trial sponsored by Wake Forest University Health Sciences. Enrollment was 349, and the recorded primary completion date was 2020-06-15.

The comparison was an individual, tailored, progressive rehabilitation intervention added to standard care versus usual care with bi-weekly staff contact. The primary endpoint was SPPB score at Month 3, on a 0-12 scale, with higher scores indicating better physical function. The primary analysis included participants alive with a Month 3 score obtained, reported as n=304.

The sponsor's joint-model analysis reported a mean difference of 1.5 points, a 95% confidence interval from 0.9 to 2.0, and p < 0.001. The unadjusted recalculation reported a mean difference of 1.4 and p < 0.001. The registry lists all-cause rehospitalization as a secondary outcome, but its numerical result is not reported in the registry record.