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Parkinson's Disease NA Continuous Endpoint NCT03335150

Cognitive Rehabilitation for PD: Complete Statistical Analysis

This analysis examines a randomized, double-masked, parallel-group trial of cognitive rehabilitation for people with Parkinson’s disease and mild cognitive impairment. The primary outcome was change in WAIS-IV Matrix Reasoning scaled score from baseline to Week 10, comparing CogSMART-PD with supportive care.

Trial start: 2015-11-02  ·  Enrollment: 110  ·  Sponsor: VA Office of Research and Development
Scope of this record

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 Cognitive Rehabilitation for PD (NCT03335150), a randomized na study. The primary outcome is Wechsler Adult Intelligence Scale-IV (WAIS-IV) Matrix Reasoning Test Total Scaled Score.

110
Enrollment
NA
2
Arms
In the primary outcome
0.20
Mean difference
CogSMART-PD
-0.76–1.16
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03335150
PhaseNA
ConditionParkinson's Disease
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment110
Arms in the primary outcome2
Lead sponsorVA Office of Research and Development
Results postedYes

2. Clinical Question

The trial asked whether a compensatory cognitive rehabilitation program for people with Parkinson’s disease and mild cognitive impairment would be associated with a different change in executive-function test scores than a supportive-care group. The intervention was CogSMART-PD, described in the registry as cognitive rehabilitation for PD-MCI; the comparator was a support group for PD-MCI.

The primary measure was the WAIS-IV Matrix Reasoning Test Total Scaled Score. It is described as an objective, validated measure of executive function, with higher scores indicating better executive function. The recorded endpoint was change from baseline to Week 10. The registry also lists secondary measures addressing executive functioning, cognitive decline, memory strategies, memory for intentions, quality of life, Parkinson’s disease-related quality of life, and neuropsychiatric symptoms.

Population

People with Parkinson’s disease and mild cognitive impairment. The registry record describes 110 enrolled participants overall. For the primary measure, it reports that 45 participants in Supportive Care and 50 in CogSMART-PD completed the measure.

Intervention

CogSMART-PD, a behavioral cognitive rehabilitation program for PD-MCI.

Comparator

Supportive Care, described as a support group for PD-MCI.

Primary question

Did mean change in WAIS-IV Matrix Reasoning scaled score from baseline to Week 10 differ between CogSMART-PD and Supportive Care?

This is a question about a between-group difference in a continuous score over a specified assessment period. It is not simply a question of whether either group’s mean score changed from baseline: the comparative question is whether the average changes differ between groups. The registry record does not report a prespecified threshold for a clinically important score difference, so statistical estimates alone cannot establish the practical importance of any difference.

3. Trial Design

The registry describes a randomized, double-masked, parallel-group behavioral trial, with CogSMART-PD compared against Supportive Care. The trial status is completed, and the record lists 110 participants enrolled. The study’s stated purpose was to investigate a compensatory cognitive rehabilitation program for people with Parkinson’s disease and mild cognitive impairment. The sponsor is the VA Office of Research and Development.

The primary endpoint was assessed at baseline and Week 10. The registry describes the reported values as change scores. For the primary measure, 54 participants were enrolled in Supportive Care; 6 left before the group started, 1 left before baseline, and 2 left during the group, leaving 45 who completed the measure. In CogSMART-PD, 55 were enrolled; 3 left before the group started and 2 left during the group, leaving 50 who completed the measure. These counts describe the primary measure’s analysis population and should not be assumed to represent every secondary outcome.

Randomization and masking are identified, but the method used to generate the random sequence, the allocation-concealment procedures, and the people or roles covered by masking are not reported in the registry record. The protocol’s intended sample size, its original sample-size justification, and the planned statistical analysis details beyond the reported analyses are also not reported in the registry record.

The registry lists secondary outcomes involving executive function, informant reports of cognitive decline, memory-strategy use, memory for intentions, quality of life, Parkinson’s disease-related quality of life, and neuropsychiatric symptoms. These outcomes broaden the range of domains assessed, but their presence does not establish that every measure was analyzed in the same population or with the same statistical model. Such outcome-specific details are not reported in the registry record.

The design compares the two assigned groups at the end of a short assessment period. The registry record does not describe a longer follow-up period for the primary endpoint. Accordingly, the primary results address change through Week 10, not durability at later times. It also does not report details of treatment attendance, adherence, or intervention delivery that would help characterize the amount of rehabilitation participants received.

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

StageSupportive CareCogSMART-PD
STARTED5555
Enrolled + Assigned Group5455
PRE Testing Session5355
Commenced Group4752
POST Testing Session4550
COMPLETED4550
NOT COMPLETED105

Reasons for not completing this period:

ReasonSupportive CareCogSMART-PD
Withdrawal by Subject104
Adverse Event01

Analysis population for the primary outcome, as defined in the registry: 54 enrolled in Supportive Care: 6 dropped before group started, 1 dropped before baseline, 2 dropped during group. Therefore, 45 completed measure. 55 were enrolled in CogSMART-PD: 3 dropped before group started and 2 dropped during group. Therefore, 50 completed measure.

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.

CharacteristicUnitSupportive CareCogSMART-PDTotal
Participants analysed5455109
Age, Continuousyears70.59 (SD 7.06)68.22 (SD 7.98)69.39 (SD 7.60)
Sex: Female, Male: FemaleParticipants201232
Sex: Female, Male: MaleParticipants344377
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants437
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants5052102
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants000
Race/Ethnicity, Customized: Race – American Indian or Alaskan NativeParticipants000
Race/Ethnicity, Customized: Race – AsianParticipants101
Race/Ethnicity, Customized: Race – Black or African AmericanParticipants123
Race/Ethnicity, Customized: Race – Hispanic or LatinoParticipants235
Race/Ethnicity, Customized: Race – Native Hawaiian or Pacific IslanderParticipants112
Race/Ethnicity, Customized: Race – White or CaucasianParticipants494998
Educationyears16.15 (SD 2.41)15.8 (SD 2.29)15.97 (SD 2.34)
Duration of Diseasemonths69.02 (SD 55.97)73.27 (SD 45.43)71.18 (SD 50.68)
Cognitive Status: Normal CognitionParticipants14923
Cognitive Status: Mild Cognitive ImpairmentParticipants404585
Motor Symptomsseconds12.28 (SD 4.85)11.76 (SD 3.73)12.01 (SD 4.30)
Baseline Medicationmilligrams685.26 (SD 445.71)764.17 (SD 483.10)725.09 (SD 464.46)

6. Primary Endpoint

The registry lists the primary outcome as Wechsler Adult Intelligence Scale-IV (WAIS-IV) Matrix Reasoning Test Total Scaled Score, measured over Baseline and Week 10.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitscore on a scale
Endpoint classificationContinuous Endpoint

The primary endpoint is the change in total scaled score on the WAIS-IV Matrix Reasoning Test from baseline to Week 10. The registry describes this test as a validated, objective measure of executive function. Scaled scores range from 0 to 26, and higher scores indicate better executive function. The outcome is a continuous score, so the reported group summaries are means accompanied by standard deviations.

A change score represents the difference between a participant’s recorded score at follow-up and the baseline score. Comparing mean change between randomized groups focuses on whether the average movement over the assessment period differed between the intervention and comparator groups. This differs from comparing the groups’ follow-up scores alone, and the registry’s primary description explicitly identifies the posted values as change scores.

Matrix Reasoning is used as an objective performance measure of executive function. That makes it distinct from the secondary outcomes based on informant reports, memory-strategy use, quality of life, or other domains. A test score is still a measure of one aspect of functioning; it does not by itself represent every aspect of cognition or daily life. The registry record does not report a threshold for a change considered clinically important, so the magnitude should be interpreted as a score difference rather than translated into a claim about practical benefit.

The endpoint’s baseline and Week 10 timing defines the period represented by the change. It does not establish whether a difference persists after Week 10. Nor does the score alone describe the mechanism behind any group difference. Those interpretations require evidence beyond the endpoint summary.

7. Results Posted in the Registry

Mean difference: CogSMART-PD

0.20

95% CI: -0.76 to 1.16

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-0.6-0.20.10.50.91.2Supportive Care (n=45)CogSMART-PD (n=50)score on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CogSMART-PD-0.92-0.47-0.020.420.871.32mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Delis-Kaplan Executive Functioning System (D-KEFS): 20 Questions Test Total Questions Asked Scaled ScoreContinuous EndpointMean difference1.15 (-0.03 to 2.33)103 per arm
Informant Questionnaire on Cognitive Decline in the Elderly-Self Report (IQCODE-SR) Total ScoreContinuous EndpointMean difference-3.35 (-6.59 to -0.11)91 per arm
Cognitive Problems and Strategies Assessment (CPSA) Memory Strategies Use ScoreContinuous EndpointMean difference10.41 (4.61 to 16.21)31 per arm

Delis-Kaplan Executive Functioning System (D-KEFS): 20 Questions Test Total Questions Asked Scaled Score

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CogSMART-PD-0.210.330.881.421.972.51mean difference vs control (95% CI)

Informant Questionnaire on Cognitive Decline in the Elderly-Self Report (IQCODE-SR) Total Score

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CogSMART-PD-7.12-5.59-4.06-2.53-1.000.53mean difference vs control (95% CI)

Cognitive Problems and Strategies Assessment (CPSA) Memory Strategies Use Score

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CogSMART-PD-1.302.466.239.991418mean difference vs control (95% CI)

The secondary outcomes cover several distinct domains, including executive function, informant-reported cognitive decline, and use of memory strategies. The three measures with detailed numerical summaries do not produce a uniform pattern: the direction and precision vary, and the recalculated intervals do not all fall in the same relation to zero. This heterogeneity is a reason to avoid treating the secondary results as one coherent measure of a single effect.

The D-KEFS 20 Questions measure has a recalculated mean difference of 1.15, with an unadjusted p-value of 0.055 and an interval extending across zero. The IQCODE-SR comparison has a mean difference of -3.35 and an unadjusted p-value of 0.043; its interval is below zero. The CPSA Memory Strategies Use comparison has a mean difference of 10.41 and an unadjusted p-value of < 0.001, with its interval above zero. These outcomes have different scales and constructs, so the numerical values should not be compared as though they represented the same kind of change.

The primary result does not show a similarly clear separation in the unadjusted comparison. The secondary pattern therefore does not provide a simple confirmation of the primary result. It may generate questions about particular domains for further study, but it cannot establish a definitive overall effect across cognition or daily functioning. The registry’s mixed-model results are also distinct analyses, and their reported estimates should not be conflated with the unadjusted comparisons.

Unadjusted secondary p-values carry less weight when many outcomes are examined because the chance of at least one apparently notable result can rise across a collection of tests. A multiplicity adjustment or a clearly prespecified hierarchy could help contextualize that issue, but such a plan is not reported in the registry record. In addition, the secondary domains differ in measurement source and meaning, making a single combined interpretation inappropriate without a specified synthesis method.

The registry names other secondary measures, including informant questionnaires, memory for intention, quality-of-life scales, and neuropsychiatric symptoms. Numerical summaries for the remaining named measures are not reported in the registry record. Their outcomes therefore cannot be used to characterize the direction or consistency of the full secondary-outcome set.

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

9. Statistical Interpretation

Clinical Biostats interpretation

On the primary change-score summary, the Supportive Care group had a mean change of 0.22, with a standard deviation of 2.35, among 45 participants. The CogSMART-PD group had a mean change of 0.42, with a standard deviation of 2.43, among 50 participants. The recalculated unadjusted mean difference, comparing CogSMART-PD with Supportive Care, is 0.2 points. Its 95% confidence interval extends from a value below zero to a value above zero, and the unadjusted p-value is 0.684.

The estimate is close to zero relative to the variation in individual change scores. The interval crossing zero means that the posted summary statistics are compatible with a range of between-group differences on either side of zero. The p-value does not indicate strong evidence against a null hypothesis of no mean difference under the unadjusted comparison. These statements describe statistical evidence from this outcome; they do not establish whether a particular score difference would matter in practice.

The recalculation uses the posted group means, standard deviations, and participant counts to make a simple unadjusted comparison. The registry also reports mixed-model analyses for the primary outcome, with three mean-difference values and associated p-values. The record does not provide confidence intervals for those entries or identify in the displayed descriptions which analysis specification each entry represents. They are therefore not interchangeable with the simple unadjusted summary comparison. The registry’s reported model results should be read as separate analyses rather than as values reconstructed from the group summaries.

The secondary outcomes present a more varied pattern. Among the three secondary outcomes with numerical summaries described in detail, the recalculated unadjusted comparisons differ in direction and strength: one interval includes zero, while the other two do not. The corresponding unadjusted p-values range from 0.055 to < 0.001. These findings are exploratory in the absence of a reported multiplicity plan, and they should not be treated as independent confirmation of the primary result. Numerical estimates for the remaining named secondary measures are not reported in the registry record.

The primary result is a comparison of group averages, not a statement that every participant’s score changed in the same direction. The standard deviations show substantial variation around the mean changes, and individual outcomes may differ from the average. The registry does not report the distribution of individual changes or subgroup results, so those features cannot be assessed from the posted summaries.

In short, the primary unadjusted estimate is small and imprecise relative to its uncertainty. The record includes model-based results as well, but the available descriptions do not supply enough detail to reconstruct those models. The evidence should be read at the level the reported outcomes support: a short-term between-group comparison on the specified test score, alongside secondary findings that require cautious interpretation.

10. Statistical Methods Explained

The primary outcome is continuous: each participant contributes a scaled test score, and the group summaries use means and standard deviations. A mean describes the average score change, while a standard deviation describes how spread out the observed changes are around that average. The standard deviation is not the uncertainty in the mean; uncertainty in a group mean also depends on the number of participants contributing data.

What does the unadjusted comparison represent?

The recalculated comparison subtracts the Supportive Care mean change from the CogSMART-PD mean change. It is an unadjusted difference between group means based on the posted summary statistics. It does not account for baseline values through a participant-level model, nor does it incorporate covariates or repeated observations beyond what is already represented in the summary change scores. No such adjustments can be inferred from this calculation.

The recalculated standard error reflects the uncertainty associated with the two group means under the simple comparison. The confidence interval is formed around the estimated difference and expresses a range of values compatible with the data and the assumptions of that calculation. A wider interval indicates less precision. An interval containing zero means that no difference is among the values compatible with that interval; it does not prove that the groups are identical.

How does this differ from a mixed model?

A mixed model can account for the structure of repeated measurements and can estimate a group contrast using a specified model. The registry lists mixed-model analyses for the primary outcome and for three secondary outcomes. However, the registry record does not report the model formulas, covariates, covariance structure, handling of missing observations, or the mapping of all reported model entries to specific analysis choices. Those details matter because different specifications can yield different estimates and standard errors.

For that reason, the simple recalculation and the mixed-model entries answer related but not necessarily identical statistical questions. The recalculation is useful for understanding the direction and approximate precision of the raw summary comparison. It is not a substitute for the sponsor’s model-based analysis. The record does not identify a discrepancy flag for the primary results; where a sponsor analysis is reported, it should be read as the registry’s model-based result, not silently replaced by a summary-statistic calculation.

What does a p-value convey?

In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be under the assumptions of a statistical model. A smaller p-value can indicate greater incompatibility with that null model, but it is not the probability that the null hypothesis is true. It also does not measure the size or practical importance of an effect. Interpretation depends on the analysis being tested, the model assumptions, and whether the analysis was prespecified.

The primary unadjusted p-value is 0.684. That value is consistent with the estimate’s confidence interval spanning zero; neither statistic on its own establishes equivalence or rules out differences that could matter. A formal equivalence conclusion would require a prespecified equivalence margin and an analysis designed for that question. Such a margin is not reported in the registry record.

Why do secondary outcomes need caution?

When a trial assesses multiple outcomes, each test creates an opportunity for a chance finding. General statistical practice recognizes that unadjusted p-values do not account for the full set of tests. A multiplicity procedure can control a chosen error rate, or outcomes can be interpreted as exploratory with the number and relationships of tests in mind. The registry record does not report a multiplicity adjustment or a complete statistical plan for the secondary outcomes. Consequently, the secondary p-values should be treated as unadjusted evidence rather than as confirmatory results with controlled family-wise error.

General statistical interpretation also distinguishes a prespecified primary endpoint from secondary measures. The primary endpoint generally anchors the main comparison, while secondary measures can offer supporting or hypothesis-generating information. Here, the secondary measures cover different constructs, so they are not all interchangeable replications of the Matrix Reasoning result. Their meanings, scales, and sources of measurement differ.

What can the analysis population tell us?

The record gives primary-measure counts and reasons for some losses before or during the group period. It does not fully describe the analysis population for each model or how missing measurements were handled. In general, an analysis using only participants with completed measurements can be affected if the probability of having an observed score is related to outcomes or group assignment. Methods such as likelihood-based modeling or imputation may address some missing-data settings under assumptions, but the registry record does not state which missing-data method was used.

The methods information therefore supports a limited reading: the posted means and standard deviations permit an unadjusted summary comparison; the registry separately reports mixed-model analyses; and the model details needed to reproduce or fully evaluate those analyses are not reported in the registry record. General statistical concepts help explain these distinctions, but they cannot fill in missing protocol information.

11. Confidence Intervals and Precision

The primary recalculated mean difference is 0.2 points, with a 95% confidence interval that extends from below zero to above zero. The interval is broad enough to include both a negative and a positive difference. In practical terms, the posted summaries do not pin down the direction of the underlying mean difference with much precision. The estimate is centered near zero, but the interval also allows for differences farther from zero than that point estimate.

In general, a confidence interval conveys the precision of an estimate under the assumptions used to calculate it. A narrower interval indicates that the data constrain the estimate more tightly; a wider interval leaves more uncertainty. A 95% confidence interval is not a statement that there is a 95% probability that this particular interval contains the true value. It is a procedure that, under its assumptions, would cover the true value at the stated rate across repeated applications.

The primary groups’ standard deviations, 2.35 and 2.43, are large relative to the mean changes of 0.22 and 0.42. That contrast highlights the difference between average movement and variation among participants. The confidence interval for the between-group estimate reflects that uncertainty in the group comparison. It is not an interval describing where most individual participant scores lie.

The secondary comparisons show varying precision. For the D-KEFS measure, the unadjusted interval extends across zero; for IQCODE-SR and CPSA memory-strategy use, the reported unadjusted intervals lie on one side of zero. These differences in interval placement do not remove the need to consider multiplicity, analysis choices, and the distinct constructs measured. The secondary estimates are not a substitute for the primary endpoint.

The registry does not report confidence intervals alongside the listed mixed-model estimates. As a result, the precision of those model-based estimates cannot be judged from interval bounds in the registry record. The unadjusted confidence intervals are informative about the simple summary comparisons, but they do not describe every uncertainty associated with trial conduct, missing outcomes, or model choice.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect2,2473,008
75% of the observed effect3,9945,347
50% of the observed effect8,98612,029
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2,0005,00010,00020,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: CogSMART-PD.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original sample-size justification. The listed values are participants per arm for 80% power and participants per arm for 90% power. These are not total events, because this is not a time-to-event calculation. For example, the primary-outcome illustration gives 2,247 participants per arm for 80% power and 3,008 participants per arm for 90% power when planning for 100% of the observed effect.

The stated planning assumptions 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. The figures describe hypothetical future-study planning under those assumptions; they do not describe the number enrolled in this trial or show that the trial had a particular probability of finding an effect.

The 80% power column gives the planned number per arm for a design that, under the assumptions and specified effect, would have an 80% chance of rejecting the null hypothesis if that effect were the true effect. The 90% column represents a higher chance under the same type of assumptions and generally requires more participants per arm. Smaller target effects require more participants because they are harder to distinguish from sampling variation.

For the primary outcome, the planning illustrations increase as the assumed effect is reduced from 100% to 75% and then 50% of the observed effect. This is the expected direction: detecting a smaller difference with the same design assumptions calls for a larger study. These numbers are not observed power, and they should not be interpreted as a retrospective measure of whether the completed trial was adequate.

The original design assumptions and the sample-size justification used when the trial was planned are not reported in the registry record. These illustrations instead use the observed result as their reference, which makes them sensitive to the uncertainty and possible over- or underestimation in that observed effect. They are planning aids, not evidence that the observed effect is stable or that a future trial would reproduce it.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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

Worked calculation for this trial

  1. Observed difference Δ = 0.200; pooled standard deviation σ = 2.392.
  2. n = 2 × (1.96 + 0.842)2 × 2.3922 / 0.2002 = 2,246.3, rounded up to 2,247 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 <- 0.2                      # observed difference in means
sigma <- 2.39248397484549                     # 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(3335150)
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 = 2,247 (80% power), 3,008 (90% power)
 75% of observed effect: n per arm = 3,994 (80% power), 5,347 (90% power)
 50% of observed effect: n per arm = 8,986 (80% power), 12,029 (90% power)
power.t.test: 2247.3 
Simulated power at n = 2,247 per arm: 0.798 (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

MethodEstimate95% CIP-value
Mixed Models AnalysisMean Difference (Final Values) 0.4856not reported0.666
Mixed Models AnalysisMean Difference (Final Values) 0.2415not reported0.162
Mixed Models AnalysisMean Difference (Final Values) 0.5087not reported0.624

The registry reports mixed-model analyses for the primary outcome, listing three mean-difference values and three associated p-values. Confidence intervals are not included for those entries, and their descriptions do not identify which particular model specification or analysis population each line represents. The registry also reports a mixed-model result for each of the three secondary outcomes with detailed numerical summaries.

The recalculated primary comparison is a simple, unadjusted difference between the posted group mean change scores. It gives a mean difference of 0.2 points and an unadjusted p-value of 0.684. This summary-statistic calculation does not reproduce the mixed-model analysis. The available record does not provide the model details needed to explain the relationship between each model estimate and the unadjusted estimate, so the different values should not be treated as a direct contradiction or as interchangeable estimates.

The registry’s mixed-model results are the sponsor’s reported analyses. The unadjusted recalculation serves as a transparent check based on the group summaries, while the model-based entries reflect the analyses reported by the sponsor. The registry record does not report enough model specification detail to independently reconstruct those results or explain the three primary entries in greater depth.

For the secondary outcomes, the same distinction applies: unadjusted comparisons derived from the posted group summaries are not the same analysis as the listed mixed-model estimates. Their p-values and estimates should be interpreted in the context of their respective analysis methods, and the record does not report a multiplicity adjustment for the set of secondary outcomes.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a trial assesses several outcomes or conducts several related comparisons. Even if each test is interpreted at a conventional significance threshold, the chance of observing at least one low p-value by chance can increase across a family of tests. This does not mean that any particular secondary result is false; it means that isolated unadjusted results require more caution when many analyses are considered together.

The registry lists a primary outcome and multiple secondary outcomes, and it reports more than one mixed-model analysis for the primary endpoint. The analysis hierarchy, the intended role of each secondary outcome, and any multiplicity adjustment are not reported in the registry record. The reader therefore cannot determine from the registry record whether the secondary analyses were intended as confirmatory tests, exploratory analyses, or part of a formal testing sequence. The unadjusted p-values should not be read as if they controlled the error rate across all outcomes.

The record reports that some participants left before the group began, before baseline, or during the group, and it gives the number who completed the primary measure in each arm. Those details indicate that the primary analysis did not include every enrolled participant. The registry record does not provide a complete account of missing observations at each assessment, the analysis population definitions for every outcome, or the method used to handle missing data in the mixed models.

In general, missing-data methods rely on assumptions about why outcomes are absent and how observed information relates to missing values. If participants with missing scores differ systematically from those with observed scores, a complete-case comparison may not represent the originally randomized groups. A mixed model can use incomplete repeated-measure information under assumptions, but the presence of a mixed-model label alone does not establish which assumptions or implementation were used.

The registry record also does not report an intention-to-treat definition, a per-protocol definition, sensitivity analyses for missing data, or the handling of deviations from assigned intervention. These are important details for judging how closely the analysis preserves the randomized comparison and how robust the findings are to alternative assumptions. Their absence limits methodological appraisal; it does not justify assuming that a particular approach was or was not used.

The trial’s original sample-size justification and broader statistical analysis plan are not reported in the registry record. Without those details, the posted results cannot establish whether the outcome hierarchy, multiplicity handling, missing-data strategy, or model specifications followed a prespecified plan.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Supportive Care0550.0%
CogSMART-PD1551.8%
Participants with at least one serious adverse event
Serious adverse events by armSupportive Care0.0%CogSMART-PD1.8%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Supportive Care0 of 55
CogSMART-PD0 of 55

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Supportive Care0 of 55
CogSMART-PD0 of 55

Most frequent serious adverse event terms

Event termOrgan systemSupportive CareCogSMART-PD
Clinical Motor ExamSurgical and medical procedures0 of 551 of 55

Serious events with the highest arm-level rate: clinical motor exam (1.8%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The serious adverse event summaries report zero affected participants among 55 at risk in Supportive Care and 1 among 55 at risk in CogSMART-PD. The registry also reports zero deaths in each group. For other adverse events, the record lists zero affected participants among 55 at risk in both groups. The listed serious-event term is Clinical Motor Exam, reported as 1.8%.

These are counts over the adverse-event reporting period recorded in the registry; that period’s detailed definition is not reported in the registry record. A count of participants affected is not necessarily the same as a count of event episodes, and the record’s summary does not provide details about event timing, duration, severity beyond the serious-event classification, or relationship to the intervention. The listing does not establish causation.

The figures are descriptive and involve a small number of reported events. Zero reported events in a group does not prove that an event could never occur, and a difference in counts alone does not establish a treatment-related risk difference. The registry record does not report further adjudication details or a statistical comparison of adverse events. These summaries should therefore be read as the recorded event counts, not as a definitive comparison of safety.

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

The primary result describes a short-term comparison of mean change in an objective executive-function test score between participants assigned to CogSMART-PD and Supportive Care. The recalculated difference is 0.2 points, and its confidence interval spans zero. This indicates that the simple unadjusted summary does not precisely distinguish the groups’ average changes. It does not establish that the groups are equivalent, nor does it rule out every difference that might be important.

The outcome is one scaled test of executive function, not a complete assessment of cognition, independence, quality of life, or daily performance. Higher Matrix Reasoning scores indicate better executive function, but the registry record does not provide a clinically important difference threshold for this scale. The numerical difference therefore cannot be translated from these registry entries into a claim about meaningful change in participants’ lives.

The secondary results address other constructs, and some unadjusted comparisons are more separated from zero than the primary comparison. Those findings are subject to the limitations of multiple testing, differing measurement scales, and incomplete reporting of the statistical plan. They do not change what the primary outcome itself shows, and they do not establish a broad effect across all cognitive or functional domains.

The registry reports mixed-model analyses as well as summary statistics. Because the model specifications and confidence intervals are not reported, the model-based results cannot be fully assessed or independently reproduced from the registry record. The unadjusted estimates provide one clear view of the posted summaries, but they are not a replacement for the sponsor’s model-based analysis.

The findings apply to the participants and assessment period described in the record. The primary measure was completed by 45 participants in Supportive Care and 50 in CogSMART-PD, after recorded losses before or during the group period. Longer-term outcomes, the completeness of all secondary measurements, and the effect of missing-data assumptions are not reported in the registry record.

Overall, the posted evidence supports a cautious statistical description: the primary unadjusted comparison is centered near no group difference and is imprecise, while some secondary comparisons show different patterns. Neither statistical significance on a secondary measure nor a non-significant primary p-value should be used alone to make a claim about clinical effectiveness. The registry summary does not resolve the practical importance or durability of the observed score changes.

18. Why This Trial Matters Statistically

This trial is statistically informative because it places an objective continuous measure of executive function at the center of a randomized comparison and reports both group summaries and model-based analyses. Those different presentations illustrate why an estimated group difference should be considered alongside its uncertainty and the method used to obtain it. The means alone do not convey the precision of the comparison, while a p-value alone does not convey its magnitude.

The primary score changes show how large within-group variation can coexist with a small difference between group averages. That distinction matters in clinical research: individual outcomes may vary, while the trial’s central comparative estimate concerns the average difference between assigned groups. The confidence interval communicates that the average contrast remains uncertain in the posted summary-statistic analysis.

The record also illustrates the interpretive challenge of multiple outcomes. A trial can assess several cognitive, informant-reported, and quality-of-life domains, but mixed results across measures do not automatically combine into a single conclusion. Without a reported multiplicity plan and a clearly described hierarchy of outcomes, secondary findings are more appropriately viewed as exploratory signals than as a set of definitive confirmatory tests.

Finally, the presence of a mixed-model analysis alongside simple group summaries highlights the value of transparent reporting. Model specifications, analysis populations, and missing-data procedures are necessary to understand how an analysis was conducted and whether it can be reproduced. Their absence from the registry record limits what readers can infer, even when estimates and p-values are posted.

19. Limitations

A specific limitation is the difference between the total enrollment and the number completing the primary measure. The record gives reasons for some departures in each arm and reports 45 and 50 primary-measure completers. It does not describe outcomes for participants who left, so the direction or influence of missing primary scores cannot be determined from the registry record.

The registry’s model-based entries are not accompanied by confidence intervals or detailed model specifications. The primary outcome has three mixed-model entries with different reported values and p-values, but the record does not explain their respective analysis choices. This makes it difficult to identify which model result should be emphasized or to assess its precision. The unadjusted recalculation is transparent but does not resolve those reporting gaps.

The primary endpoint is measured through Week 10. The record does not report longer-term primary results, so persistence of any score change cannot be assessed. It also does not report a threshold for a clinically important difference on the Matrix Reasoning scale, limiting interpretation of the score magnitude in practical terms.

The registry lists multiple secondary measures, while the detailed numerical summaries in the available record cover only some of them. The remaining named measures’ numerical results are not reported in the registry record. A full assessment of consistency across secondary outcomes is therefore not possible. No multiplicity adjustment or testing hierarchy is reported, which further limits the confirmatory interpretation of isolated secondary p-values.

Details needed to evaluate the conduct and analysis are also absent from the registry record, including the randomization procedure, who was masked, the original sample-size justification, missing-data methods, outcome-specific analysis populations, and the full model specifications. These are reporting limitations; the record does not establish that the procedures were inadequate, only that they cannot be evaluated from the available descriptions.

The two groups’ interventions are described at a broad level as cognitive rehabilitation and a support group. Details about session content, attendance, adherence, and treatment delivery are not reported in the registry record. The amount of intervention actually received and the extent of similarity between the groups beyond those descriptions therefore cannot be characterized.

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22. Sources

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23. Record Summary

NCT03335150, titled “Cognitive Rehabilitation for PD,” is a completed randomized, double-masked, parallel-group behavioral trial sponsored by the VA Office of Research and Development. It enrolled 110 participants and compared CogSMART-PD cognitive rehabilitation with a Supportive Care support group for people with Parkinson’s disease and mild cognitive impairment.

The primary outcome was change from baseline to Week 10 in WAIS-IV Matrix Reasoning scaled score. The primary-measure summaries include 45 Supportive Care participants and 50 CogSMART-PD participants. The recalculated unadjusted mean difference was 0.2 points, with a 95% confidence interval spanning zero and an unadjusted p-value of 0.684. The registry also reports mixed-model analyses, but does not provide model confidence intervals or full specifications.

Secondary outcomes span executive function, cognitive decline, memory strategy use, memory, quality of life, and neuropsychiatric symptoms. The available detailed comparisons vary in direction and precision; unadjusted secondary results warrant caution because a multiplicity plan is not reported. Serious adverse event counts were 0 of 55 in Supportive Care and 1 of 55 in CogSMART-PD; deaths were zero in both groups.

Important details—including the original sample-size justification, analysis plan, missing-data procedures, and longer-term primary outcomes—are not reported in the registry record.

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