Brain Training to Enhance Frontal Lobe Reasoning: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Brain Training to Enhance Frontal Lobe Reasoning (NCT01552473), a randomized na study. The primary outcome is Glasgow Outcome Scale-Extended.

2. Clinical Question

3. Trial Design

This was a completed, randomized, double-blind, parallel-group study sponsored by The University of Texas at Dallas. The registry lists enrollment of 108. The recorded start was 2012-03 and primary completion was 2015-07. The phase is listed as NA.

The two named arms were Strategic Memory Advanced Reasoning Training (SMART) and the Brain Health Workshop (BHW). The intervention entries classify the programs as behavioral. The SMART description emphasizes strategies to address cognitive issues following traumatic brain injury, while the BHW description emphasizes educational information about those issues. The registry does not report which roles were masked or how masking was maintained.

The primary outcome was the Glasgow Outcome Scale-Extended, assessed at a pre-training baseline neuropsychological test. The posted group summaries include 52 participants for BHW and 56 for SMART. The primary outcome description identifies community-dwelling individuals aged 19 to 65 years with chronic traumatic brain injury, specified as more than 6 months post-injury. The brief study summary instead describes chronic stages as greater than 12 months, a difference in wording that the registry does not explain.

The registry lists 18 outcome measures and posts 12 secondary outcomes. The named secondary measures include mood, post-traumatic stress, substance involvement, attention, resilience, memory, and brain connectivity measures. This range indicates that the study considered outcomes beyond the primary disability scale, but the posted results do not establish that each measure had a prespecified role in the analysis.

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.

Pre-training Testing

Post-training Testing

Delayed Post-training Testing

Analysis population for the primary outcome, as defined in the registry: Community dwelling individuals between the ages of 19 and 65 years with a history of chronic TBI (\> 6 months post-injury).

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 Glasgow Outcome Scale-Extended, measured over Pre-training (Baseline) Neuropsychological Test.

The primary endpoint was the Glasgow Outcome Scale-Extended (GOS-E), reported as a mean and standard deviation in units on a scale. The registry describes it as an assessment of disability after brain injury. Scores run from 1, dead, to 8, good recovery; higher scores indicate a better outcome. This provides a broad summary of functional outcome rather than a direct measure of one specific cognitive skill targeted by training.

The recorded timeframe is a pre-training baseline neuropsychological test. That timing is central to interpretation: the posted GOS-E values describe the two groups before the training period, not their outcomes after training or their change from baseline. The group mean at baseline can show how the groups compared on this measure when assessed, but it cannot establish the effect of training. A post-training primary GOS-E result or a change-from-baseline result is not reported in the registry record.

Using a mean and standard deviation makes the groups' average scores and the spread of individual scores easy to compare. It also simplifies a complex disability scale to a numerical summary. The registry record does not report whether the scale was analyzed in another form, such as an ordinal model, or explain the rationale for the reported summary approach.

7. Results Posted in the Registry

• Strategic Memory Advanced Reasoning Training (SMART): mean 6.30 versus 6.21 on control; difference 0.09 (95% CI -0.19 to 0.37), standardized effect d = 0.12; z-test p = 0.536.

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.

Beck Depression Inventory (BDI)

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Strategic Memory Advanced Reasoning Training (SMART): mean 18.41 versus 18.28 on control; difference 0.13 (95% CI -4.43 to 4.69), standardized effect d = 0.01; z-test p = 0.955.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Strategic Memory Advanced Reasoning Training (SMART) and the control. The interval gives the range of effects that remain compatible with the data.

Post Traumatic Stress Disorder (PTSD) Checklist

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Strategic Memory Advanced Reasoning Training (SMART): mean 44.09 versus 46.76 on control; difference -2.67 (95% CI -9.33 to 3.99), standardized effect d = -0.16; z-test p = 0.432.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Strategic Memory Advanced Reasoning Training (SMART) and the control. The interval gives the range of effects that remain compatible with the data.

Alcohol, Smoking and Substance Involvement Screening Test

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Strategic Memory Advanced Reasoning Training (SMART): mean 22.18 versus 19.40 on control; difference 2.78 (95% CI -3.91 to 9.47), standardized effect d = 0.16; z-test p = 0.415.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Strategic Memory Advanced Reasoning Training (SMART) and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary outcomes cover several domains, including depression, post-traumatic stress symptoms, substance involvement, attention, resilience, memory, and brain connectivity. The registry lists 18 outcome measures overall and posts 12 secondary outcomes. The secondary results posted with numeric comparisons are measured at 10 weeks post-training for the measures described in the record.

Across the reported secondary comparisons, the unadjusted confidence intervals include zero. This broad pattern does not establish that the groups had identical outcomes, nor does it show a consistent, clearly separated difference across the measured domains. The estimates remain uncertain, and each outcome has its own scale, variability, and amount of available data. The secondary results should be interpreted in their individual measurement contexts rather than combined into a single overall effect.

The primary GOS-E result is a baseline comparison, whereas the posted secondary measures are described at 10 weeks post-training. The primary result therefore cannot serve as evidence that the secondary results confirm or contradict a post-training functional outcome. A formal relationship between these measures, such as a joint or mediation analysis, is not reported in the registry record.

Unadjusted secondary results carry less weight when many outcomes are examined because the chance of obtaining at least one apparently notable result can increase across multiple tests. In general, multiplicity procedures can address this issue, but they may change the thresholds or uncertainty used for interpretation. The registry record does not report a multiplicity adjustment, a hierarchy among secondary endpoints, or a prespecified strategy for selecting among them. The absence of such information makes these secondary comparisons best viewed as descriptive rather than definitive evidence.

The record does not list reported analyses for the posted secondary measures. The numerical group comparisons can describe the posted summaries, but they do not reveal whether additional adjusted analyses were conducted or how missing observations were treated. Those analysis details are not reported in the registry record.

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

• Network Based Statistics in Brain Connectivity
• Beck Depression Inventory (BDI)
• Post Traumatic Stress Disorder (PTSD) Checklist
• Alcohol, Smoking and Substance Involvement Screening Test
• Alcohol Use Disorders Identification Test
• Digit Vigilence Test
• Connor-Davidson Resilience Scale
• Wechsler Memory Scale

9. Statistical Interpretation

10. Statistical Methods Explained

The primary result is a comparison of two group means on a continuous measure. The GOS-E values are reported as means with standard deviations: 6.21 with a standard deviation of 0.75 for BHW and 6.3 with a standard deviation of 0.76 for SMART. The comparison is expressed as a mean difference, with SMART minus BHW as the direction. The estimated difference is 0.09 units.

What does a mean difference represent?

In general, a mean difference expresses how far apart two group averages are on the original measurement scale. A positive value in this comparison means the SMART mean is higher than the BHW mean; a negative value would mean it is lower. Because higher GOS-E scores represent better outcomes, the direction can be described in terms of the scale, but the measurement occurred before training. The difference is therefore a baseline contrast, not an estimate of a training effect.

The standard deviation describes the spread of scores within a group. It is not the standard error of the mean and is not a confidence interval. In general, the standard error reflects uncertainty in an estimated mean, with its size affected by both the variability among observations and the number of observations. The posted summaries give group sizes and standard deviations, but do not provide individual-level data.

How should the confidence interval be read?

The primary comparison has a 95% confidence interval from -0.195 to 0.375. In general, a confidence interval is a range of values compatible with the data and the statistical procedure used, under its assumptions. It conveys uncertainty around the estimated difference; it is not a range containing a stated proportion of individual participants' scores. The interval crossing zero means that a zero difference is among the values compatible with the unadjusted comparison. It also includes values on both sides of zero, so the direction of any underlying baseline difference is uncertain.

The interval's width reflects the precision of the comparison. Greater precision generally means a narrower interval, while more variability or fewer observations can make estimates less precise. These are general statistical relationships, not a reconstruction of the trial's design choices. The registry record does not report the original sample-size justification or the assumptions used when the study was planned.

What does the p-value add?

The unadjusted p-value is 0.536. In general, a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model, assuming that model and the analysis assumptions hold. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of a difference. Here, it should be read alongside the mean difference and confidence interval, and in the context that the outcome is a baseline measure.

The term unadjusted indicates that the posted p-value is not adjusted for multiple comparisons. The registry record does not report a multiplicity procedure for the outcomes. There is also no reported primary post-training comparison to interpret as a treatment effect.

Why can standardized effects be useful?

The standardized effect estimate is 0.119. In general, standardization expresses a difference relative to a measure of variability, which can help compare measurements recorded on different scales. It does not replace the original-scale result: the GOS-E mean difference remains 0.09 units, and interpretation of the standardized estimate still depends on the study context and analysis. The registry record does not report a clinically meaningful threshold for either measure.

The posted comparison is an unadjusted summary-statistic comparison. The record does not describe a covariate-adjusted model, an analysis of repeated measurements, or a method for handling missing outcomes. These methods cannot be assumed. Statistical methods and analysis populations beyond the posted summaries are not reported in the registry record.

11. Confidence Intervals and Precision

The primary mean difference is 0.09 GOS-E units, with a 95% confidence interval from -0.195 to 0.375. This interval communicates uncertainty about the baseline contrast. Since it spans zero and values on either side, the posted data do not pin down whether the underlying mean difference is positive, negative, or absent. The interval should not be read as evidence that the groups are equivalent.

The interval is expressed in the original scale units, which helps relate it to the GOS-E score range of 1, dead, to 8, good recovery. The interval describes uncertainty about the group mean difference, not the range of scores expected for individual participants. The group standard deviations, 0.75 for BHW and 0.76 for SMART, describe observed score spread rather than precision of the treatment comparison.

Precision is affected by the number of observations and by variability, among other features of the analysis. The posted primary summaries include 52 BHW participants and 56 SMART participants. The registry record does not report confidence intervals for the group means themselves, nor details of missing data or a model that might alter the estimate or its precision.

Because the endpoint was recorded at baseline, even a more precise estimate would only refine the comparison of pre-training scores. It would not establish what happened after training. A follow-up estimate and its uncertainty are not reported in the registry record.

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.

The planning figures describe participants per arm, not total events. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is the stated fraction of the observed effect. These are planning assumptions for an illustration; the original trial's sample-size assumptions are not reported in the registry record.

For the primary comparison, planning for 100% of the observed effect gives 1,106 participants per arm for 80% power and 1,480 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,965 participants per arm for 80% power and 2,631 participants per arm for 90% power. Planning for 50% of the observed effect gives 4,422 participants per arm for 80% power and 5,919 participants per arm for 90% power.

In general, power is the probability that a study will detect an effect of a stated size under specified assumptions if that effect is present. The 80% and 90% columns therefore represent different planning targets: the 90% target seeks a higher chance of detecting the specified effect, and the listed participant requirement is larger. The figures are not a retrospective measure of this study's ability to detect an effect. This is not observed power.

The pattern across the planning rows illustrates a general principle: smaller effects require more participants to detect reliably under the same assumptions. These calculations use the observed baseline difference as their reference effect. Since the primary result is a baseline comparison rather than a post-training treatment effect, the planning values should not be taken as a definitive design recommendation for a future efficacy study.

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 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 = 0.090; pooled standard deviation σ = 0.755.
2. n = 2 × (1.96 + 0.842)² × 0.755² / 0.090² = 1,105.3, rounded up to 1,106 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 <- 0.0899999999999999                      # observed difference in means
sigma <- 0.755205207649138                     # 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(1552473)
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 = 1,106 (80% power), 1,480 (90% power)
 75% of observed effect: n per arm = 1,965 (80% power), 2,631 (90% power)
 50% of observed effect: n per arm = 4,422 (80% power), 5,919 (90% power)
power.t.test: 1106.3 
Simulated power at n = 1,106 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. Multiplicity, Missing Data and Analysis Populations

The registry lists 18 outcome measures and posts 12 secondary outcomes, in addition to the primary measure. When several outcomes are tested, the chance of at least one result appearing unusual by chance can rise. In general, multiplicity methods can control or otherwise address that concern, but the choice depends on the planned questions and analysis strategy. A multiplicity adjustment, testing hierarchy, or prespecified prioritization of secondary outcomes is not reported in the registry record.

The posted comparison p-values are unadjusted. They should therefore be interpreted as individual comparisons rather than as results with a reported correction across the set of outcomes. This matters especially for secondary endpoints, which often provide supporting or exploratory evidence and should not be treated as independent confirmation without context about the analysis plan.

Missing-data handling is also not reported in the registry record. The primary baseline outcome includes 52 participants in BHW and 56 in SMART. For the posted secondary measures, the available group counts differ across outcomes. The record does not explain why counts vary, whether observations were unavailable, how missing values were handled, or whether any imputation or sensitivity analysis was used. As a general matter, missingness can affect both the representativeness of the analyzed participants and the uncertainty of an estimate, depending on its pattern and the methods used.

The analysis population is not described beyond the counts attached to the posted outcome summaries. It is not reported whether analyses followed an intention-to-treat principle, used a per-protocol population, or applied another inclusion rule. The registry record also does not report participant flow, adherence, protocol deviations, or the handling of exclusions in the outcome analyses. These gaps limit assessment of how closely the posted summaries represent all randomized participants.

Likewise, the registry record does not report a detailed statistical analysis plan, covariate adjustments, interim analyses, or a sample-size justification. Their absence from the record does not show that they did not exist; it means they cannot be characterized from the registry record.

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.

The serious adverse event figures report zero serious events among 56 participants in the Strategic Memory Advanced Reasoning Training group and zero among 52 participants in the Brain Health Workshop group. The record also reports zero deaths in each group. These figures describe what was posted for the groups and the stated numbers at risk.

A zero count means that no serious adverse events were recorded in these group summaries; it does not establish that no adverse events of any kind occurred, or that the programs are free of risk. The registry also reports zero other adverse events in each group. The record does not provide event terms, event-level descriptions, an ascertainment period, or details about how adverse events were collected. No serious adverse event terms are listed.

Safety counts depend on the population observed and the completeness and duration of event reporting. Those details are not reported in the registry record. The figures should therefore be read as registry-reported counts, not as a comprehensive assessment of safety or as a comparison demonstrating a difference between the groups.

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

The posted primary result describes the groups' GOS-E scores before training. BHW had a mean of 6.21, and SMART had a mean of 6.3. Their unadjusted mean difference was 0.09, with a 95% confidence interval from -0.195 to 0.375 and an unadjusted p-value of 0.536. The interval includes zero, and the available result does not establish a baseline difference between the groups.

This finding does not show that either program improved or failed to improve functioning. The measurement was taken pre-training, so it is not an estimate of change or a post-training treatment effect. Although the study description states an aim related to diagnosis and functional recovery, the registry record does not report a post-training primary GOS-E comparison that could address whether the programs changed this outcome.

The result also does not show equivalence. A nonsignificant p-value is not proof that two groups are identical, and the confidence interval gives a range of compatible baseline differences rather than a guarantee about the true value. Nor does the result establish that the training programs are interchangeable, effective, ineffective, or beneficial. Those claims would require appropriately timed outcome analyses and supporting evidence.

The secondary results offer measurements from other domains, but their unadjusted nature, multiple outcomes, and unreported analysis details limit the weight they can carry. Their existence does not change the timing of the primary result or substitute for a reported post-training primary analysis. The most defensible interpretation is restricted to the posted baseline comparison and the specific summary statistics in the registry record.

17. Why This Trial Matters Statistically

This study illustrates why the timing of an endpoint matters as much as its name. The GOS-E is described as assessing disability after brain injury, and it is the primary outcome, but the posted timeframe is pre-training baseline. A baseline contrast answers a different question from a treatment comparison after the intervention. Reading the result without attending to timing could lead to an incorrect claim about functional recovery.

The registry also makes clear why effect estimates and uncertainty should be read together. The mean difference is small on the stated scale, while the confidence interval includes values on both sides of zero. The p-value alone cannot establish equivalence or practical importance. A careful interpretation distinguishes the observed estimate from what remains uncertain.

The study provides an example of a randomized, double-blind, parallel design with behavioral programs and multiple outcome domains. Yet important statistical details—such as the analysis population, missing-data methods, multiplicity strategy, and original sample-size justification—are not reported in the registry record. Their absence limits reproducibility and the ability to judge how the posted comparisons were selected and analyzed.

Finally, the planning illustrations show how sample-size requirements depend on the effect one aims to detect and the desired power target. Since the primary effect used is a baseline difference, the calculations should be read as illustrations rather than a blueprint for a follow-up efficacy trial. The trial is statistically informative as a lesson in separating baseline description, treatment-effect estimation, and precision.

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.

A central limitation of the posted primary result is that its timeframe is pre-training baseline. It therefore does not provide the post-training GOS-E comparison needed to assess a treatment effect on the primary measure. The registry's study summary refers to chronic stages greater than 12 months, while the primary population description specifies more than 6 months post-injury. The record does not explain this difference in eligibility wording.

The posted comparison is unadjusted and based on summary statistics. Individual-level data, distributional details, covariate-adjusted estimates, and an analysis plan are not reported in the registry record. The record also does not state how the measure was analyzed beyond its summary as a mean and standard deviation.

Available participant counts differ across the posted secondary outcomes, but reasons for those differences and the approach to missing data are not reported. The analysis population and participant flow are also not described in sufficient detail to determine how the posted outcomes relate to all randomized participants.

There are multiple outcome measures, yet a multiplicity strategy and hierarchy among outcomes are not reported. The secondary comparisons are unadjusted, and the record does not list reported analyses for those measures. This limits the strength of inferences drawn from a pattern across secondary endpoints.

Other details that would support fuller appraisal—including who was masked, adherence, protocol deviations, the original sample-size justification, and any interim analyses—are not reported in the registry record. These limitations concern the information available in the record and do not establish that the study did not collect or analyze such information elsewhere.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Brain Training to Enhance Frontal Lobe Reasoning — NCT01552473.
• Registry record last updated 2025-03-10; status last verified 2025-02.
• Results first posted 2025-03-10.
• 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

NCT01552473, titled “Brain Training to Enhance Frontal Lobe Reasoning,” is a completed randomized, double-blind, parallel study sponsored by The University of Texas at Dallas. The recorded enrollment is 108. The study compared SMART with a Brain Health Workshop in adults with chronic traumatic brain injury.

The primary measure was the GOS-E at pre-training baseline. The unadjusted mean difference for SMART versus BHW was 0.09 units, with a 95% confidence interval from -0.195 to 0.375 and an unadjusted p-value of 0.536. Because this was a baseline assessment, it does not estimate the effect of training.

The registry posts secondary outcomes spanning several domains, along with zero reported serious adverse events and deaths in both groups. Details of multiplicity, missing-data handling, analysis populations, and the original sample-size justification are not reported in the registry record.