Patient Centered-Rehabilitation ver111090.1: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Patient Centered-Rehabilitation ver111090.1 (NCT03034954), a randomized na study. The primary outcome is Object Location Touchscreen Task (Version C) Free Recall Total Error.

2. Clinical Question

This question is narrower than the study’s broader description of cognition. The primary endpoint assesses object-location association memory, rather than every aspect of working memory, learning, or memory. The registry also lists secondary outcomes concerning blinding and endorsement of several symptoms during the stimulation session. Those additional outcomes do not change the definition of the primary comparison. The record does not report enough detail to establish how the primary comparison was selected in relation to the other outcomes.

3. Trial Design

The registry describes a randomized, double-masked, parallel-group trial sponsored by the University of Michigan. The study is marked completed and has no applicable phase. Enrollment is listed as 42. The registry dates are 2016-10 for study start and 2017-06 for primary completion. These are record-level design details; they do not establish when each participant was enrolled or assessed.

Participants were assigned to active HD-tDCS or sham HD-tDCS. The active description specifies 3 milliamps for 20 minutes during a single session. The sham description says participants underwent the same procedures but received sham stimulation, also in a single session. The allocation and masking fields indicate randomization and double masking, but the method used to generate the allocation sequence, conceal assignments, or maintain masking is not reported in the registry record.

The primary outcome record gives 19 participants in the active arm and 20 in the sham arm. It also notes missing data for one participant. These outcome counts are distinct from the registry’s enrollment figure. The record does not explain the flow from enrollment to the primary outcome analysis, or state which analysis population was used.

The study’s primary endpoint was collected 15 minutes after encoding and reflects free recall of object locations. The registry lists 24 outcome measures and 15 analyses, while the posted secondary outcomes include measures of blinding and reports of headache, neck pain, scalp pain, tingling, itching, burning, and skin redness. The protocol’s original sample-size rationale, planned analysis details, and any interim-analysis plan are not reported in the registry record.

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: Two participants were excluded after consent due to failing the tDCS safety screen. One participant endorsed a skin condition with lesions at site of electrode placement. One participant disclosed a prior head injury.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Missing data for one participant

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.

Population: One participant was a statistical outlier for several behavioral measures and was excluded from baseline data and all analyses

6. Primary Endpoint

The registry lists the primary outcome as Object Location Touchscreen Task (Version C) Free Recall Total Error, measured over 15 minutes after encoding.

The primary endpoint is the Object Location Touchscreen Task (Version C) Free Recall Total Error, recorded in centimeters 15 minutes after encoding. The task assesses object-location association memory: participants learn the locations of 15 object-location associations and then try to recall locations by touching a touchscreen. During free recall, the screen is black, and participants indicate where an object had been located. The total score combines the error across the trials; error is measured as distance from the targeted location. A lower score represents better performance.

This endpoint is useful for studying a particular, measurable aspect of memory. Because error is recorded as a continuous distance, the reported arm summaries can describe average performance and its spread, and a mean difference can quantify the contrast between arm averages. The task’s touchscreen format also permits continuous measurement of location accuracy, as described in the registry. These features do not make it a comprehensive measure of cognition: the endpoint concerns object-location recall, not every domain named in the study summary.

The posted primary outcome data give a mean of 121.5 centimeters with a standard deviation of 26.37 for active HD-tDCS, and a mean of 99.77 centimeters with a standard deviation of 27.84 for sham HD-tDCS. Since lower error means better task performance, the active arm’s posted average is numerically higher. The registry does not report additional endpoint-level details about scoring beyond the description above.

7. Results Posted in the Registry

• Active HD-tDCS: mean 121.50 versus 99.77 on control; difference 21.73 (95% CI 4.71 to 38.74), standardized effect d = 0.80; z-test p = 0.012.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry lists the sponsor’s primary analysis method as repeated measures ANOVA, with p = .300 for the active and sham groups. ANOVA is a general family of methods for comparing means. A repeated-measures version is generally used when measurements are related because they come from the same participants or another repeated structure. The registry does not report the repeated observations included in this analysis, the model terms, or which measurements were used. Those details are therefore not possible to infer from the method label alone.

What does the unadjusted recalculation describe?

The recalculated contrast is an unadjusted difference between the posted group means. It is based on the continuous endpoint’s mean, standard deviation, and group size, rather than on the sponsor’s repeated-measures analysis. In general, an unadjusted comparison summarizes the observed separation between group averages without accounting for additional covariates or repeated-measure structure. The registry does not report a covariate-adjusted estimate in the posted results.

The reported recalculated mean difference is 21.73 centimeters, defined as active minus sham. Its positive direction corresponds to a higher mean error in the active group. The task description says lower errors represent better performance, so the sign of the difference has a direct descriptive interpretation. The recalculation is not a replacement for the sponsor’s model, especially because the two reported p-values differ and the registry provides no details that would reconcile them.

How should a p-value be understood?

In general, a p-value describes how compatible the observed data are with a statistical model’s null hypothesis, under the assumptions of that model. It is not the probability that the null hypothesis is true, nor a measure of the size or importance of an effect. A smaller p-value does not resolve concerns about model choice, missing observations, or the many outcomes and analyses listed in a record. Here, the sponsor p-value and the unadjusted recalculated p-value refer to different analyses, and the registry does not describe the sponsor model in sufficient detail for a direct methodological comparison.

The sponsor’s reported p-value is .300. The recalculated p-value is 0.012. Because the discrepancy flag is true, the sponsor’s own analysis takes precedence for interpreting the trial’s reported analysis. The unadjusted calculation remains a transparent summary of the posted arm-level data, but it must be labeled as a recalculation and not presented as the sponsor’s result.

What does the confidence interval add?

In general, a confidence interval gives a range of estimates compatible with the data and the calculation’s assumptions, while conveying uncertainty around an estimate. The recalculated 95% confidence interval for the mean difference runs from 4.714 to 38.74 centimeters. It is based on the unadjusted comparison of the posted summaries, not on a confidence interval reported for the sponsor’s repeated-measures analysis. The registry does not report a sponsor confidence interval for this result.

A confidence interval is not a guarantee that the true effect lies within its endpoints, and its interpretation depends on the assumptions behind the method. The interval’s width reflects imprecision in this particular recalculation; it does not capture every uncertainty about the study, including unreported model details or how missing data were handled.

Why do distribution and spread matter?

The outcome is continuous, and the registry reports means and standard deviations. A mean describes the group’s average score; a standard deviation describes the spread of individual scores around that average. In general, the mean alone does not show how similar or different participants’ scores were, and it does not reveal the outcome’s full distribution. The posted standard deviations are 26.37 centimeters in the active arm and 27.84 centimeters in the sham arm. The registry does not report distribution plots or other summaries that would show the shape of scores.

For count outcomes, over-dispersion is a concern when variability exceeds what a simple count model assumes; in general, that can make standard errors too small if the model is not suited to the data. That concept does not describe the primary endpoint here, which is continuous distance error. It should not be used to infer a problem with the trial’s analysis: the registry does not report a count model for this endpoint.

What does the analysis record leave unclear?

The record identifies a repeated measures ANOVA and its p-value but does not describe the outcome structure, model specification, missing-data method, or analysis population. It also does not state whether an adjustment for multiple outcomes or analyses was made. These omissions limit independent assessment of the sponsor’s result. The reported registry entries do not support guessing which model choices were made or why the sponsor analysis differs from the unadjusted recalculation.

In general, an analysis plan specifies how outcomes, comparisons, missing observations, and multiplicity will be handled. The original statistical plan and original sample-size assumptions are not reported in the registry record. The assumptions used for the separate planning illustration are known and are described with the sample-size figures; they should not be confused with the trial’s original design plan.

10. Confidence Intervals and Precision

The unadjusted recalculated mean difference is 21.73 centimeters, with a 95% confidence interval from 4.714 to 38.74 centimeters. The interval describes uncertainty around the active-minus-sham contrast under the recalculation’s assumptions. It is not a confidence interval from the sponsor’s repeated-measures ANOVA; no interval for that sponsor analysis is reported in the registry record.

In general, a confidence interval is more informative than a point estimate alone because it shows a range of estimates compatible with the data and method. A narrower interval indicates greater precision for that estimate, while a wider interval indicates more uncertainty. The interval spans values that correspond to a higher average error in the active group, given the direction active minus sham and the fact that lower scores are better. That interpretation applies to the unadjusted recalculation only.

The interval does not incorporate uncertainty about unreported analysis choices, missing-data handling, or the difference between the recalculated method and the sponsor’s analysis. It also does not establish the practical importance of the estimated difference. The registry does not report a threshold for judging the relevance of a change in centimeters, nor a sponsor estimate with which to compare the recalculated interval.

The sponsor’s p-value is .300, while the recalculated p-value is 0.012. The discrepancy means that precision should not be described using the recalculated interval as if it were the sponsor’s primary result. The sponsor’s own analysis takes precedence. The posted arm means and standard deviations remain useful descriptive information, but they do not resolve the difference between analyses.

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 sample-size figures are planning illustrations based on the observed effect, not the trial’s original design justification. The original design assumptions are not reported in the registry record. The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; it considers effects that are the stated fractions of the observed effect.

These entries are participants per arm for 80% power and participants per arm for 90% power. They are not total events: this is a continuous-outcome comparison, and the figures are expressed per arm. The 80% power column gives the illustrated number of participants in each arm under the assumptions for a design intended to have an 80% chance of detecting the specified effect if that effect is present. The 90% power column gives the corresponding per-arm planning figure for a 90% chance under those same assumptions.

The rows describe planning for 100%, 75%, and 50% of the observed effect. The listed per-arm figures are 25 and 33 for 100% of the observed effect, 44 and 59 for 75%, and 98 and 132 for 50%, for 80% and 90% power respectively. Smaller effects require more participants because they are harder to distinguish from sampling variation under the stated assumptions. The curve represents the same planning relationship across effect sizes; it is not an additional analysis of trial outcomes.

This is not observed power. It is a forward-looking planning illustration that uses the observed effect as its starting point, with the assumptions stated above. It should not be interpreted as evidence that the completed trial had a particular probability of detecting an effect, and it does not show what the original investigators used to choose enrollment.

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 = 21.728; pooled standard deviation σ = 27.136.
2. n = 2 × (1.96 + 0.842)² × 27.136² / 21.728² = 24.5, rounded up to 25 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 <- 21.728                      # observed difference in means
sigma <- 27.1355574462534                     # 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(3034954)
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 = 25 (80% power), 33 (90% power)
 75% of observed effect: n per arm = 44 (80% power), 59 (90% power)
 50% of observed effect: n per arm = 98 (80% power), 132 (90% power)
power.t.test: 25.5 
Simulated power at n = 25 per arm: 0.792 (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 reported analysis is a repeated measures ANOVA comparing the active and sham groups, with p = .300. No estimated contrast, confidence interval, model details, or further statistical output for this analysis is reported in the registry record.

A separate unadjusted recalculation from the posted arm means and standard deviations gives an active-minus-sham mean difference of 21.73 centimeters, a 95% confidence interval from 4.714 to 38.74, and p = 0.012. This uses the posted summary statistics and is not the sponsor’s analysis. The registry marks the results as discrepant. In that circumstance, the sponsor’s own analysis takes precedence; the recalculation should be presented as a different, unadjusted summary rather than as a correction to the sponsor’s result.

The registry does not explain whether the sponsor’s repeated-measures ANOVA used additional measurements, a different analysis population, covariates, or another model structure. It is therefore not possible to attribute the discrepancy to any particular choice. Nor can the recalculated confidence interval be treated as the interval for the sponsor’s model. The sponsor result is reported as a p-value only, limiting assessment of its estimated effect and precision.

Read together, the posted arm-level summaries describe the observed group averages, while the sponsor analysis reports the trial’s own inferential result. These answer related but not identical statistical questions as recorded. The available details do not justify choosing an explanation for the difference or merging the results into a single estimate.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 24 outcome measures and 15 analyses. It also lists secondary outcomes concerning blinding and reports of headache, neck pain, scalp pain, tingling, itching, burning, and skin redness. With multiple outcomes and analyses, there may be more than one opportunity to observe a seemingly notable result. In general, multiplicity procedures address the increased chance of false-positive findings when many hypotheses are tested. The registry does not report whether any adjustment was planned or applied, or how the primary outcome was treated in relation to the other analyses.

The record does not provide the protocol’s full statistical analysis plan, so it is not possible to determine which analyses were prespecified, whether all planned outcomes are posted, or how any outcome hierarchy was defined. The number of listed outcomes and analyses alone does not establish that multiplicity adjustment was required or omitted; the analysis plan is not reported in the registry record.

The primary outcome notes missing data for one participant. The arm summaries contain 19 active participants and 20 sham participants, but the record does not explain the missing-data mechanism, the method used to handle missing observations, or whether participants with missing data were included in another analysis. It does not report imputation, sensitivity analyses, or a comparison of participants with and without observed outcomes. No assumptions about the missing participant’s score should be made.

The analysis population is also not reported in the registry record. Although the trial is randomized, the record does not say whether the primary analysis followed assignment regardless of treatment received, included only participants who completed the session, or used another population definition. Those distinctions can affect interpretation, but the available information does not support inferring the approach.

The enrollment figure is 42, while the posted primary outcome summaries cover the arm counts noted above. The record does not provide a complete participant flow explaining that difference. Nor does it report interim analyses or stopping rules. These are reporting gaps, not evidence that a particular procedure was or was not used.

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 non-serious adverse event terms

The serious adverse event record lists zero serious events among 19 participants at risk in the active HD-tDCS group and zero among 21 participants at risk in the sham HD-tDCS group. Deaths are listed as zero in each group. These are the recorded serious-event counts for the listed at-risk groups.

The record separately lists other adverse events affecting 16 of 19 active participants and 19 of 21 sham participants. These counts are not serious adverse event counts. The registry’s secondary outcomes name several specific symptom items, including headache, neck pain, scalp pain, tingling, itching, burning, and skin redness, but the serious-event summary does not provide event-by-event detail. The registry also does not report the duration or severity of the other events in this safety summary.

Zero serious events in the listed groups does not prove that serious events cannot occur or establish a general safety profile. The figures describe reported events in this trial record and the participants at risk as recorded. The study involved a single session, so these data do not describe repeated exposure or longer-term follow-up. The record’s adverse-event information should be read as descriptive counts, not as a basis for medical advice or a broader conclusion about risk.

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

The primary task measured free-recall error in locating objects on a touchscreen. The posted means were 121.5 centimeters for active HD-tDCS and 99.77 centimeters for sham HD-tDCS; lower scores represent better performance. Descriptively, the active group had the higher average error. The recalculated unadjusted contrast is 21.73 centimeters in the active-minus-sham direction.

The inferential results require particular care. The unadjusted recalculation has a 95% confidence interval from 4.714 to 38.74 and p = 0.012, whereas the sponsor’s repeated measures ANOVA reports p = .300. Because the record flags a discrepancy, the sponsor’s own analysis takes precedence. The registry does not report enough detail to explain the difference, and the sponsor result does not include an estimate or interval in the posted record. Neither result should be rewritten as though it were the other.

The findings concern this endpoint and its stated measurement time, 15 minutes after encoding, in a trial of a single stimulation session. They do not establish effects on other forms of memory, broader cognition, everyday functioning, repeated sessions, or longer-term outcomes. The study description includes wider interests in working memory, learning, and memory, but the primary endpoint is specifically object-location association memory.

The record also does not provide a clinical or practical threshold for interpreting centimeters of error. Statistical estimates, even when they are precise, do not by themselves determine practical importance. Missing-data handling, the analysis population, multiplicity procedures, and the sponsor model details are not reported, limiting what can be concluded from the record.

Accordingly, the defensible reading is that the posted arm summaries show different mean errors, with higher mean error in the active arm, while the sponsor’s reported analysis gives p = .300. The discrepancy and incomplete analysis reporting prevent treating the unadjusted calculation as the definitive trial result. The registry evidence describes this trial’s reported measurements; it does not support a general claim about treatment efficacy or absence of efficacy.

17. Why This Trial Matters Statistically

This trial is statistically instructive because the posted group summaries and the sponsor’s reported analysis do not tell the same inferential story. The unadjusted recalculation yields a mean difference of 21.73 centimeters and p = 0.012, while the sponsor reports p = .300 from a repeated measures ANOVA. The record flags the discrepancy, making it important to distinguish a transparent recalculation from the trial’s own analysis rather than treating all reported statistics as interchangeable.

The example also illustrates why the analysis method matters. A comparison of arm-level means is not necessarily equivalent to a repeated-measures model. In general, the model’s specification and the measurements it includes determine what is being estimated and how uncertainty is calculated. Because those details are not reported, readers cannot establish the source of the differing results from the registry record alone.

The endpoint makes direction important. It measures error, and lower values represent better performance; therefore, a higher group mean is not automatically a favorable outcome simply because it is numerically larger. Clear description of the outcome scale and contrast direction is essential to interpreting an estimate.

The record further shows the distinction between observed results and planning illustrations. Sample-size figures based on fractions of the observed effect can help readers understand how planning needs change when a target effect is smaller. They are not the original trial design rationale and are not observed power. The registry does not report the trial’s original sample-size assumptions.

Finally, the number of listed outcomes and analyses, the missing primary outcome observation, and unreported analysis populations and multiplicity procedures all matter to interpretation. These are not reasons to dismiss the recorded data; they identify where additional protocol and analysis reporting would be needed for a fuller statistical assessment.

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 most important limitation for interpreting the primary result is the discrepancy between the sponsor’s repeated measures ANOVA p-value of .300 and the unadjusted recalculated p-value of 0.012. The registry does not provide model details or a sponsor estimate and confidence interval, so the reason for the difference cannot be established. The sponsor analysis takes precedence, but its limited reporting makes the size and precision of that result difficult to assess.

The primary outcome notes missing data for one participant. The record does not explain how missing observations were handled, define the analysis population, or provide a participant-flow account connecting enrollment of 42 with the outcome summaries. These omissions limit assessment of whether the posted summaries represent all randomized participants or a defined subset.

The record lists 24 outcome measures and 15 analyses, but does not report whether multiplicity was addressed or how the primary outcome related to the other analyses. The original statistical analysis plan, protocol details, interim-analysis plan, and original sample-size assumptions are not reported in the registry record. The sample-size illustration based on the observed effect should not be mistaken for those original design decisions.

The trial evaluated a single session and measured the primary endpoint 15 minutes after encoding. The record therefore does not describe longer-term outcomes or repeated sessions. The endpoint captures object-location free recall, not all cognitive domains. Participant eligibility and other baseline characteristics beyond the description of healthy, cognitively intact older adults are not reported in the registry record.

The safety record gives event counts but limited detail about the types, timing, and severity of other adverse events. Finally, no threshold for interpreting the practical importance of the endpoint difference is reported. These limitations concern what can be concluded from the registry record; they do not establish that a particular unreported procedure was absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Patient Centered-Rehabilitation ver111090.1 — NCT03034954.
• Registry record last updated 2018-08-16; status last verified 2018-07.
• Results first posted 2018-08-16.
• 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

NCT03034954 is a completed, randomized, double-masked, parallel-group study sponsored by the University of Michigan. Enrollment is listed as 42. It compared a single active HD-tDCS session with sham stimulation in healthy, cognitively intact older adults. The primary endpoint was free-recall total error on the Object Location Touchscreen Task, measured 15 minutes after encoding; lower scores represent better performance.

The posted primary arm means were 121.5 centimeters for active stimulation and 99.77 centimeters for sham. An unadjusted recalculation gives an active-minus-sham mean difference of 21.73 centimeters, with a 95% confidence interval from 4.714 to 38.74 and p = 0.012. The sponsor’s repeated measures ANOVA reports p = .300. The record flags a discrepancy, so the sponsor’s analysis takes precedence; the reason for the difference is not reported.

The registry lists 24 outcome measures and 15 analyses. It notes missing primary outcome data for one participant, but does not report the missing-data method or analysis population. Serious adverse events and deaths are listed as zero in both at-risk groups.