Problem Solving Training for Care Partners of Adults With Traumatic Brain Injury: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Problem Solving Training for Care Partners of Adults With Traumatic Brain Injury (NCT03739450), a randomized na study. The primary outcome is Changes From T2 to T3 in the Patient Health Questionnaire (PHQ9).

2. Clinical Question

The trial concerns support for care partners of adults with TBI during the transition from inpatient rehabilitation to home. Its stated aims were to assess whether PST could be provided during the rehabilitation stay and to compare PST plus education with education alone for caregiver burden, depressive symptoms, and coping skills. The primary posted result concerns depressive symptoms, measured with the PHQ-9. The registry also posts results for alcohol use and coping. Those outcomes offer related but distinct information and do not replace the primary comparison.

3. Trial Design

The registry describes a randomized, single-masked, parallel-group trial of PST plus education versus education alone. Both interventions are classified as behavioral. The masking field says single, but which people were masked is not reported in the registry record. The allocation ratio, method of sequence generation, and procedures for concealing assignments are also not reported in the registry record.

The registry lists the study status as completed, an enrollment of 94, a start date of 2018-11-20, and a primary completion date of 2022-10-22. Its brief summary describes a plan to enroll 172 care partners. The record does not explain the difference between that planned enrollment and the enrollment figure it lists. The listed phase is NA.

The stated study setting for PST delivery was the inpatient rehabilitation stay of an adult with TBI. The summary describes a baseline assessment and follow-up at 1 month and 6 months post-discharge. The primary outcome compares change between those follow-up times; the posted PHQ-9 analysis includes only participants with both T2 and T3 data. The record does not report how participants were assigned to the two arms, whether treatment delivery or adherence was monitored beyond the feasibility aim, or whether the analysis followed the original randomization for all participants.

The trial aimed to assess feasibility as well as efficacy. Feasibility was to include the number of PST sessions completed and care partner satisfaction. Posted numeric results for those feasibility measures are not reported in the registry record. The trial's own sample-size justification and original design assumptions 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.

Overall Study

Analysis population for the primary outcome, as defined in the registry: The participants not analyzed here were lost to follow-up. These numbers do not match directly with the numbers in the participant flow since these are change scores. Therefore, participants had to have BOTH T2 and T3 data to be included in analysis.

5. Baseline Characteristics

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

Population: n = 14 participants (n = 6 allocated to PST; n = 8 allocated to Education) who consented did not complete baseline assessment and no information is available for these participants. Therefore, of the 94 consented, baseline data are available for n=80 participants (n=37 PST, n=43 education only)

6. Primary Endpoint

The registry lists the primary outcome as Changes From T2 to T3 in the Patient Health Questionnaire (PHQ9), measured over 1-month (T2), 6-month (T3) post-discharge between both arms.

The primary endpoint is the change in Patient Health Questionnaire-9 (PHQ-9) score from T2, at 1-month post-discharge, to T3, at 6-month post-discharge. The PHQ-9 asks about the frequency of nine symptoms of a major depressive episode over the preceding two weeks. Its total score ranges from 0-27. The registry describes symptom cutoffs from none through severe, with the severe category listed as >20. It labels a positive change as improvement.

A change score focuses on how the measure shifts over the period between the two follow-up assessments. Comparing mean change between randomized arms addresses whether the average change differed between PST plus education and education alone among participants included in this analysis. It does not describe each participant's course, and a group mean does not show how many people improved or worsened.

The registry says participants needed both T2 and T3 data to be included in the change-score analysis. It also notes that these outcome counts do not correspond directly to participant-flow counts because the endpoint is based on paired follow-up data. The clinical interpretation of an average change depends on the scale and the trial context; a threshold for a clinically important between-arm difference is not reported in the registry record.

7. Results Posted in the Registry

• Education: mean 1.50 versus 2.90 on control; difference -1.40 (95% CI -4.62 to 1.82), standardized effect d = -0.36; z-test p = 0.394.

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.

Alcohol Use Disorders Identification Test (AUDIT)

• 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:
  • Education: mean 1.14 versus 0.59 on control; difference 0.55 (95% CI -0.70 to 1.80), standardized effect d = 0.27; z-test p = 0.387.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Education and the control. The interval gives the range of effects that remain compatible with the data.

Brief Coping Orientation to Problems Experienced

• 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:
  • Education: mean 0.41 versus -1.00 on control; difference 1.41 (95% CI -2.52 to 5.34), standardized effect d = 0.30; z-test p = 0.481.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Education and the control. The interval gives the range of effects that remain compatible with the data.

The registry posts secondary results for alcohol use measured with the AUDIT and for coping measured with the Brief Coping Orientation to Problems Experienced. These outcomes cover related aspects of care partner experience, but they are not interchangeable with the primary PHQ-9 measure. Their time frames also differ: AUDIT change is reported from baseline to 6-month post-discharge, while the coping change is reported between 1-month and 6-month post-discharge.

Across the posted secondary comparisons, the estimated contrasts do not all point in the same numerical direction. The record does not provide enough interpretive detail to translate that pattern into a common judgment about benefit: the scales measure different constructs, and the registry does not state a positive-improvement convention for these secondary change scores. The primary outcome's sign convention should not be assumed to apply to them.

The secondary results do not resolve the uncertainty in the primary result. They can offer context about other measured outcomes, but they do not serve as independent confirmation of the PHQ-9 finding. The analysis groups are limited, the intervals for the comparisons include zero, and the registry does not report investigator analyses for these outcomes. Those features make the estimates uncertain and their direction difficult to treat as definitive.

Multiple outcomes create an interpretive challenge because examining more than one result increases the opportunity for a seemingly notable finding to arise by chance. The registry does not report whether outcomes were ranked, whether a multiplicity adjustment was planned, or whether secondary findings were intended to be confirmatory. For that reason, unadjusted secondary comparisons carry less weight than a prespecified primary analysis. They are best treated as descriptive signals that may inform future research questions, not as conclusive evidence for a broad pattern across care partner outcomes.

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

• Alcohol Use Disorders Identification Test (AUDIT)
• Brief Coping Orientation to Problems Experienced

9. Statistical Interpretation

10. Statistical Methods Explained

The posted measures are continuous outcomes summarized by arm means and standard deviations. A mean is the arithmetic average of the measured values in an analysis group. It gives a compact description of the group's central value, but it does not show the full distribution, whether observations cluster, or whether a small number of values have an unusually large influence. A standard deviation describes the spread of individual observations around their group mean. It is not the uncertainty of the mean itself.

What does a mean difference represent?

A mean difference subtracts one arm's average from the other's, using a stated ordering. The primary comparison is expressed as education relative to PST plus education. For the primary PHQ-9 change score, the estimate is -1.4. Since positive change is defined as improvement, the sign indicates that the education mean change was lower than the PST plus education mean change in these posted summaries. The sign must be read together with the ordering of the arms and the outcome's direction. Reversing the arm order would reverse the sign without changing the underlying contrast.

This comparison is unadjusted: it is calculated from posted group summaries and does not account for other variables. An adjusted analysis could use information about participant characteristics or the study design, but such an analysis is not reported in the registry record. The recalculated comparisons should not be mistaken for a model-based estimate reported by the investigators.

How should the standard deviation be read?

Standard deviations describe participant-to-participant variability in the measured changes. Greater spread means individual results are more dispersed around the mean. With continuous outcomes, such variation matters because the group average can be estimated less precisely when measurements vary widely, especially when the analysis group is small. Standard deviations are descriptive and do not, by themselves, show whether a difference between arms is statistically persuasive.

The comparisons also include pooled standard deviations and standardized effect-size estimates. A pooled standard deviation combines information about variability across the two groups, and a standardized effect expresses the mean difference relative to that spread. Standardized effects can help describe a contrast on a scale independent of the outcome's original units. They do not convey clinical importance on their own, and they can be unstable when based on limited observations. The registry does not report a threshold for a clinically important effect.

What information does a confidence interval add?

A confidence interval gives a range of values compatible with the estimate under the statistical method used. In general, it reflects sampling uncertainty: repeated studies using the same method would produce intervals that cover the underlying value at the stated rate. It is not a range containing a fixed proportion of individual participant outcomes, nor does it assign a probability to the true effect after the data have been observed.

For the primary comparison, the 95% confidence interval runs from -4.619 to 1.819. Because it includes zero, the posted summaries are compatible with no mean difference as well as with differences in either direction. Its width also conveys limited precision. A point estimate alone would conceal that uncertainty, while the interval makes the range of plausible values visible.

What does the unadjusted p-value mean?

A p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that null hypothesis and the statistical model were true. It is not the probability that the null hypothesis is true, the probability that the result occurred by chance, or a measure of the size or importance of an effect. The primary unadjusted p-value is 0.394. Interpreting it requires considering the estimate and its confidence interval, not treating it as a standalone verdict.

Unadjusted comparisons also do not account for testing several outcomes. When multiple outcomes or analyses are examined, the chance of at least one apparently unusual result can increase. The registry does not report a multiplicity strategy, so the posted secondary comparisons should be treated as exploratory rather than as a set of confirmatory tests.

General statistical context is useful when reading these summaries: variability, analysis-group size, and missing observations affect precision and interpretation. The registry does not report diagnostic checks for distributional assumptions, transformations, covariate adjustment, or robust methods. It is therefore not possible to assess from the registry record whether alternative models were considered or how sensitive results were to analytic choices.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data locate the between-arm difference. The primary estimate is -1.4, and its 95% confidence interval extends from -4.619 to 1.819. That range includes zero and values on both sides of zero. It therefore does not identify the direction of the underlying difference with confidence, and it permits a range of magnitudes rather than a single precise value. The point estimate should not be read without this uncertainty.

The analysis groups are 11.0 and 17.0 participants, and the posted standard deviations are 4.8 and 3.2. These summaries describe a modest set of paired observations with variation in change scores. In general, greater variability and fewer observations make estimates less precise. The confidence interval reflects uncertainty in the calculated contrast, but it does not address possible bias from loss to follow-up, unreported analytic choices, or differences between included and excluded participants.

The interval is not a prediction interval for individual care partners and does not show the likely range of personal outcomes. Nor does it specify whether a difference would matter clinically; a minimally important difference is not reported in the registry record. The breadth and placement of the interval support a cautious reading: the posted data do not distinguish a meaningful effect in one direction from little difference or an effect in the other direction. More complete follow-up and a prespecified analysis could help address uncertainty, but those details 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 sample-size figures are planning illustrations expressed as participants per arm, not total event counts. They are based on the observed effect in the posted summaries, with calculations for detecting 100%, 75%, or 50% of that observed effect. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The original trial's sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under those planning assumptions, if that effect is the true one and the assumed model applies. The 90% power column gives the corresponding planning number for a 90% chance. These are design calculations, not guarantees that a future study will achieve those operating characteristics. They also do not change the uncertainty in the current trial's observed estimate.

The rows for smaller fractions of the observed effect require more participants per arm. This is the expected pattern: a smaller difference is harder to distinguish from random variation than a larger one under otherwise similar assumptions. The figures are not the trial's original target enrollment and do not show what the investigators used to design the study. They are not observed power; observed power is not a useful substitute for interpreting the estimate and its confidence interval. Read the calculations as conditional planning illustrations, not as evidence about whether the present result is reliable or whether an intervention has an effect.

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 = -1.400; pooled standard deviation σ = 3.894.
2. n = 2 × (1.96 + 0.842)² × 3.894² / -1.400² = 121.4, rounded up to 122 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -1.4                      # observed difference in means
sigma <- 3.89397957404465                     # 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(3739450)
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 = 122 (80% power), 163 (90% power)
 75% of observed effect: n per arm = 216 (80% power), 290 (90% power)
 50% of observed effect: n per arm = 486 (80% power), 651 (90% power)
power.t.test: 122.4 
Simulated power at n = 122 per arm: 0.796 (20000 replicates)

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

14. Multiplicity, Missing Data and Analysis Populations

The registry identifies a primary PHQ-9 outcome and posts secondary results for AUDIT and the Brief Coping Orientation to Problems Experienced. It does not report how the investigators handled the possibility of multiple comparisons. A prespecified hierarchy, adjustment to control the family-wise error rate, or a decision to treat secondary outcomes as exploratory is not reported in the registry record. Without that information, unadjusted secondary p-values should not be interpreted as though each were the only hypothesis tested.

The record lists four outcome measures, while it posts results for the primary outcome and two secondary outcomes. The details of any additional outcome measure or its results are not reported in the registry record. The record also lists zero reported analyses. This means that investigator-reported inferential analyses are not available in the registry results; it does not establish that no analyses were performed.

Missing data are directly relevant to the primary result. The registry states that participants not analyzed were lost to follow-up and that both T2 and T3 measurements were required for inclusion in the change-score analysis. It notes that endpoint counts therefore do not match participant-flow counts directly. The number and reasons for missing assessments by arm, the timing of loss to follow-up, and any comparison of included and excluded participants are not reported in the registry record.

Methods for handling missing data are also not reported. There is no registry description of imputation, weighting, sensitivity analysis, or a model using incomplete follow-up information. The target analysis population, any exclusions after randomization, and whether the analysis followed intention-to-treat principles are not reported in the registry record. These omissions limit assessment of whether the analyzed participants remained comparable as randomized and whether the observed change scores could be affected by selective follow-up. They also make it difficult to judge how well the posted results represent the originally randomized groups.

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.

For the PST plus education group, the registry lists 43 participants at risk for serious adverse events and 43 at risk for other adverse events; it records zero affected participants in each category and zero deaths. For the education group, it lists 51 at risk for serious adverse events and 51 at risk for other adverse events; it likewise records zero affected participants in each category and zero deaths.

These figures indicate that the registry reports no serious or other adverse events and no deaths for the listed groups during the recorded safety assessment. They do not establish that no events occurred outside the assessment period, were missed, or were not entered into the record. The registry does not report event-collection procedures, observation duration for safety, definitions used for event categories, or attribution to either intervention. The listed safety groups should not be assumed to be the same participants included in the primary change-score analysis.

Zero recorded events are a descriptive finding, not proof that an intervention has no risk. The registry figures are useful for understanding what was reported, but limited event information and the absence of further safety methods constrain interpretation.

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

The primary posted summaries describe average PHQ-9 change between 1-month and 6-month post-discharge among participants with both assessments. The point estimate favors a larger positive mean change in the PST plus education arm under the registry's definition of positive change as improvement. However, the confidence interval includes zero and extends in both directions, so the result does not establish a clear between-arm difference. Its uncertainty should remain central to any interpretation.

This finding does not show that PST works or does not work. It also does not show that the two approaches are equivalent. A nonzero point estimate can coexist with substantial uncertainty, and a confidence interval that includes zero does not rule out effects that may matter. The registry does not report a threshold for clinical importance, so statistical summaries alone cannot determine whether the estimated change would be meaningful to care partners.

The endpoint measures depressive symptoms over a defined follow-up interval; it does not capture every potential benefit, burden, or experience of care partners. The trial's stated feasibility aims include session completion and satisfaction, but numeric results for those measures are not reported in the registry record. The posted secondary outcomes address alcohol use and coping, and their results are also subject to uncertainty and the unreported multiplicity approach.

Finally, the primary analysis is limited to participants with paired follow-up data, and the registry describes those not analyzed as lost to follow-up. Without details about missing-data handling, participant characteristics by follow-up status, or the investigators' full analysis, the extent to which the posted comparison represents all randomized participants cannot be determined. The defensible conclusion is about the posted summaries and their precision, not about a general clinical recommendation or a definitive treatment effect.

17. Why This Trial Matters Statistically

This trial is statistically informative because it makes the distinction between a point estimate and the strength of evidence visible. The PHQ-9 comparison has a numerical direction, but its confidence interval spans zero and values on either side. Interpreting the estimate together with its uncertainty avoids treating the observed direction as a settled result.

It also illustrates how follow-up requirements shape an analysis. A change between T2 and T3 requires both measurements, so the analyzed group is not simply everyone enrolled. The registry explicitly connects exclusion from the change-score analysis with loss to follow-up. That makes transparency about missingness, analysis populations, and sensitivity analyses essential to evaluating the result. Those details are not reported in the registry record.

The study addresses a population and intervention context for which the registry summary describes limited ongoing support and identifies feasibility as an aim. Statistical interpretation must keep that context distinct from the strength of the efficacy evidence. Feasibility measures and clinical outcome measures answer different questions; the record does not post numeric feasibility results alongside the outcome summaries.

Finally, the record demonstrates why a sample-size illustration should not be confused with the original trial design or with evidence about the observed effect. The planning figures are conditional on stated assumptions and fractions of the observed effect, while the original design justification is not reported. Separating planning calculations, observed estimates, and missing design information helps readers assess what the registry can support without making stronger claims than the available results warrant.

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 primary comparison is based on 11.0 participants in the PST plus education arm and 17.0 in the education arm, with inclusion requiring both follow-up assessments. The registry identifies loss to follow-up as the reason some participants were not analyzed, but does not describe the amount or pattern of missingness by arm. This limits assessment of selection bias and the generalizability of the change-score estimates to everyone randomized.

The listed enrollment is 94, while the brief summary describes a planned enrollment of 172. The registry does not explain this difference. It also does not report the trial's sample-size justification, original power assumptions, allocation ratio, sequence-generation details, or allocation-concealment procedures. The single-masking field does not identify who was masked.

Investigator-reported analyses are not posted. Adjustment for baseline or other participant characteristics, the handling of missing data, model diagnostics, and sensitivity analyses are not reported. The registry also does not describe a multiplicity strategy despite posting more than one outcome. These gaps restrict evaluation of analytic choices and the robustness of results.

The record's measure count and posted results are not fully aligned: it lists four outcome measures but posts a primary result and two secondary results. Numeric feasibility results for PST session completion and care partner satisfaction are not reported. A threshold for clinically important change is also not reported. These trial-specific limitations mean that the outcome summaries should be read as incomplete registry reporting rather than as a full account of trial conduct and analysis.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Problem Solving Training for Care Partners of Adults With Traumatic Brain Injury — NCT03739450.
• Registry record last updated 2025-03-05; status last verified 2025-02.
• Results first posted 2025-03-05.
• 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

NCT03739450 is a completed, randomized, single-masked, parallel-group trial of Problem Solving Training plus TBI-specific education versus education alone for care partners of adults with TBI. The registry lists enrollment of 94 and describes follow-up after discharge. The primary posted outcome is PHQ-9 change from 1-month to 6-month post-discharge, with positive change defined as improvement.

The primary unadjusted recalculated comparison is -1.4 for education relative to PST plus education, with a 95% confidence interval from -4.619 to 1.819 and p = 0.394. The interval includes zero and indicates substantial uncertainty about the between-arm difference. Secondary results are posted for alcohol use and coping, but investigator-reported analyses and a multiplicity plan are not reported in the registry record. Missing-data methods, the original sample-size justification, and numeric feasibility results are also not reported.