Reward Function and Therapy for Late-Life Depression: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Reward Function and Therapy for Late-Life Depression (NCT03688139), a randomized na study. The primary outcome is Change in Late Positive Potential to Rewarding Stimuli.

2. Clinical Question

3. Trial Design

The registry describes a randomized, double-masked, parallel-group study comparing Engage Therapy with supportive therapy. The listed phase is NA. The registry records enrollment of 65 and marks the study as completed. The start date is 2019-03-14, and the primary completion date is 2024-01-18.

Both therapies were delivered over 9 weeks. Research assessments were planned before therapy and at weeks 3, 6, and 9. These included questionnaires, computer tasks, and recordings of electrical brain activity using electroencephalography (EEG). The record’s stated aim was to learn about brain changes during Engage and how they may differ from changes during supportive therapy.

The primary endpoint concerns change in the LPP response to rewarding stimuli from baseline to week 9. The registry also lists change in anhedonia as a secondary outcome. The endpoint summaries report different available participant counts for different measures, and the record notes dropouts before baseline as well as missing data due to poor quality or missed assessments. The original sample-size justification, intended enrollment for each arm, and detailed analysis-population definitions are not reported in the registry record.

Random allocation describes how participants are assigned to groups; double masking describes the registry’s masking designation. The record does not explain which people were masked or how masking was maintained. It also does not provide enough information to characterize the implementation of allocation or the therapy-delivery procedures beyond the descriptions of the two interventions.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Two participants dropped out before baseline and some data points are missing due to poor data quality or missed study assessments.

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 Change in Late Positive Potential to Rewarding Stimuli, measured over Change from baseline to week 9.

The primary endpoint is change from baseline to week 9 in the late positive potential, measured in microvolts. The LPP is derived from EEG recordings and is described in the registry as a measure of emotional engagement with positively valenced images. The study’s stated focus on rewarding stimuli makes this measure relevant to its investigation of reward-related brain function during therapy.

Change over time can address a different question from a single measurement at the end of treatment: it captures how the measure changes relative to a participant’s baseline. The registry describes assessments at baseline and several treatment visits, while the primary endpoint specifies the baseline-to-week-9 change. Its reported mixed-model analysis uses a difference in slopes, which reflects group trajectories over observed assessments rather than simply subtracting the two posted week-9 mean changes.

The clinical meaning of a difference in LPP is not established by the endpoint description alone. The registry does not report a threshold for a meaningful change, nor does it specify how a change in microvolts should be interpreted for an individual. The endpoint is a research measure of brain activity, not a direct measure of a participant’s overall clinical status.

7. Results Posted in the Registry

• Supportive Therapy: mean 0.07 versus 0.80 on control; difference -0.73 (95% CI -2.57 to 1.11), standardized effect d = -0.22; z-test p = 0.436.

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.

Change in Anhedonia

• 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:
  • Supportive Therapy: mean -2.07 versus -3.37 on control; difference 1.30 (95% CI -1.90 to 4.50), standardized effect d = 0.21; z-test p = 0.425.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Supportive Therapy and the control. The interval gives the range of effects that remain compatible with the data.

The registry identifies change in anhedonia as a secondary outcome. Its posted summaries and analyses offer a less clear basis for comparing the therapies than would be needed to establish a consistent secondary pattern. The recalculated contrast is uncertain, and the registry’s mixed-model secondary analyses do not report evidence of a clear between-group separation. These findings do not resolve the uncertainty in the primary EEG endpoint; they address a different outcome.

Secondary outcomes can add context by examining effects beyond the primary measure, but they generally carry less weight when many outcomes or analyses are considered. Testing multiple outcomes increases the chance that some results may appear notable through chance alone. In general, multiplicity procedures can adjust interpretation or testing to account for that possibility. Whether such a procedure was planned or applied is not reported in the registry record.

The registry lists five outcome measures and seven analyses, while one secondary outcome is identified in the posted secondary results. The record does not explain how the listed measures and analyses relate to one another, whether all were prespecified, or whether unposted outcomes were analyzed. Without that context, the secondary findings should be treated as exploratory rather than as independent confirmation of the primary result. They also do not establish a broader clinical effect based on the EEG endpoint.

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

• Change in Anhedonia

9. Statistical Interpretation

10. Statistical Methods Explained

The registry reports a mixed-model analysis for the primary comparison, expressed as a difference in slopes. A mixed model is a general statistical approach for repeated observations, such as measurements collected from the same participant at multiple visits. In general, it can represent how outcomes change over time while accounting for the fact that observations from the same participant are related. The registry does not report the model specification, the covariance structure, the fixed effects included, or the method used to handle missing observations.

What does a difference in slopes represent?

In general, a slope describes the direction and rate of change in an outcome over time. A difference in slopes compares the modeled trajectories between groups. That differs from comparing only the group means of change from baseline to week 9: the slope analysis may use information from intermediate visits, while the simple recalculation uses the posted summary changes. The reported mixed-model value is 0.23 and its p-value is .08. The registry does not provide an interval estimate for this result or enough modeling detail to determine precisely how the estimate is parameterized.

What does the recalculation represent?

The recalculated primary comparison is an unadjusted difference between the posted group mean changes. It uses the posted mean change and standard deviation for each group to estimate a mean difference and an interval. In general, a standard deviation describes variability among observations within a group; it is not the same as the uncertainty around the group mean. The reported pooled standard deviation is 3.245, and the standardized difference is -0.225. These are descriptive recalculations from summary statistics, not outputs from the registry’s mixed model.

The unadjusted p-value for this recalculation is 0.436. In general, a p-value describes how compatible data are with a specified null model, under the assumptions of the analysis. It does not give the probability that the null hypothesis is true, and it does not measure the clinical importance of a finding. This recalculated p-value should not be substituted for the sponsor’s mixed-model p-value because the analyses address different summaries and may use different assumptions.

Why can repeated measurements matter?

Repeated assessments can provide information about the shape of change during treatment, not only the endpoint contrast. In general, a mixed model can use this structure to estimate group trajectories and can accommodate some incomplete records under its assumptions. That does not mean missingness is harmless: the validity of estimates can depend on why observations are absent and on how the model represents the data. Here, the registry notes missing data due to poor data quality or missed assessments, but the specific missing-data assumptions and procedures are not reported in the registry record.

What does randomization contribute?

In general, random allocation is intended to reduce systematic differences between groups at the point of assignment. It does not guarantee that the groups will be identical, particularly in a study with limited enrollment, and it does not resolve missing-data or measurement issues. The registry identifies the study as randomized but does not report details of the randomization sequence or allocation concealment.

All statistical explanations in this methods discussion are general unless they refer to an explicitly reported registry result. The original sample-size justification, prespecified model details, handling of multiplicity, and analysis-population rules are not reported in the registry record. The recalculations are descriptive illustrations based on posted summary statistics and should be read separately from the registry’s own model-based analysis.

11. Confidence Intervals and Precision

The recalculated primary mean difference is -0.73 microvolts, with an interval from -2.568 to 1.108. This interval includes zero and extends to values on either side of it. The posted summaries therefore do not pin down the between-group difference precisely: estimates compatible with the interval include a difference favoring either group as well as no difference. The registry does not state the confidence level for this recalculated interval, so a confidence percentage should not be inferred from the record.

In general, a confidence interval expresses uncertainty around an estimate under the assumptions of the method used. A narrower interval indicates greater precision, while a wider interval indicates less precision. An interval that includes zero does not prove that the true difference is exactly zero; it means the data and method do not rule out zero at the interval’s stated confidence level. Because that level is not reported for this recalculation, the interval is best read as the posted range of uncertainty without assigning it an unstated coverage percentage.

The registry’s mixed-model estimate has no confidence interval reported. Its p-value alone does not show the full range of effect sizes compatible with the model. The interval from the unadjusted recalculation should not be attached to the mixed-model estimate, because it comes from a different analysis. Together, the reported material supports a cautious reading: the primary comparison is uncertain, and the precision of the sponsor’s model-based estimate cannot be assessed from an interval 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 are participants per arm, not total events. They illustrate the sample sizes associated with detecting specified fractions of the observed recalculated effect under the stated planning assumptions. The assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the participants per arm associated, under those assumptions, with an 80% chance of rejecting the null hypothesis if the assumed effect were the true effect. The 90% power column gives the corresponding per-arm planning figure for a 90% chance. These are design calculations conditional on the assumptions, not guarantees about the result of a future study.

The rows for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect show that planning for a smaller effect requires more participants per arm. For the primary comparison, the posted figures are 311 and 416 participants per arm for 80% and 90% power when planning for 100% of the observed effect; 552 and 739 when planning for 75%; and 1,241 and 1,661 when planning for 50%. These are illustrations based on the observed recalculated effect, not the trial’s original plan. This is not observed power: it does not measure the probability that the completed trial detected 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 = -0.730; pooled standard deviation σ = 3.245.
2. n = 2 × (1.96 + 0.842)² × 3.245² / -0.730² = 310.1, rounded up to 311 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 <- -0.73                      # observed difference in means
sigma <- 3.24478645374927                     # 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(3688139)
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 = 311 (80% power), 416 (90% power)
 75% of observed effect: n per arm = 552 (80% power), 739 (90% power)
 50% of observed effect: n per arm = 1,241 (80% power), 1,661 (90% power)
power.t.test: 311.1 
Simulated power at n = 311 per arm: 0.805 (20000 replicates)

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

14. Analyses Reported by the Sponsor

The registry’s own primary analysis is a mixed-model comparison of slopes, reported as 0.23 with p = .08. The recalculation from the posted mean changes is an unadjusted supportive-therapy-minus-Engage contrast of -0.73, with an interval from -2.568 to 1.108 and p = 0.436. These are different statistical summaries: the sponsor’s analysis compares modeled trajectories, while the recalculation compares posted group mean changes.

The values also have opposite signs as reported. The registry does not provide enough information about model coding, time parameterization, or the full analysis to reconcile that difference. The recalculation should therefore not be presented as a replacement for the sponsor’s model-based result. Conversely, the sponsor’s p-value does not supply the interval information missing from its reported estimate. No discrepancy flag is recorded, but the underlying analyses remain distinct and should be interpreted according to what each estimates.

The registry also reports an Engage-only mixed-model slope with p = .14. That is a within-group result, not the between-group contrast. The registry does not report confidence intervals for either mixed-model result, so their precision cannot be evaluated from the posted model statistics alone.

15. Multiplicity, Missing Data and Analysis Populations

The registry reports several outcome measures and analyses, but the multiplicity plan is not reported in the registry record. When researchers examine multiple outcomes, time points, or contrasts, the chance of observing at least one apparently notable result can increase. In general, prespecified prioritization and appropriate adjustment can help readers distinguish confirmatory tests from exploratory ones. The record does not state whether any adjustment was made, which analyses were designated primary beyond the stated endpoint, or how the reported analyses were selected for posting.

Missing data are relevant to the primary interpretation. The registry says that two participants dropped out before baseline and that some data points were missing because of poor data quality or missed study assessments. It does not report the amount or pattern of missingness by assessment, the reasons for each missing observation, or the method used to handle missing data in the mixed models. It also does not report sensitivity analyses examining the effect of alternative missing-data assumptions.

The analysis population is not defined in sufficient detail to determine which participants or observations contributed to each model. The posted primary summaries list 25.0 for Engage Therapy and 23.0 for supportive therapy, whereas the safety figures use different at-risk counts. The registry does not explain the relationship between these sets of counts. It also does not report whether the primary analysis followed an intention-to-treat principle, a per-protocol approach, or another rule.

These omissions do not by themselves show that the analyses are invalid. They limit the ability to assess how robust the results are to missing observations, choices among analyses, and differences between analysis populations. The original statistical analysis plan and its details are not reported in the registry record.

16. 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 registry reports zero serious adverse events in each group, with 32 participants at risk in Engage Therapy and 33 at risk in supportive therapy. It reports one other adverse event in the Engage Therapy group and seven in the supportive therapy group. No deaths are listed in either group. The registry does not list serious adverse-event terms.

These are descriptive counts, not a statistical comparison of risk. The at-risk counts differ from the participant counts in the primary endpoint summaries, and the registry does not explain the relationship between those populations. It also does not provide details about event definitions, severity, relatedness to therapy, timing, or how events were collected. The reported counts should therefore be read as the safety information recorded in the registry, not as a complete characterization of comparative safety.

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

The posted results describe a randomized comparison of two therapies on an EEG-derived measure of emotional engagement with rewarding images. The registry’s mixed-model analysis reports a difference in slopes of 0.23 with p = .08. The unadjusted recalculation based on posted mean changes gives a difference of -0.73 microvolts, with an interval from -2.568 to 1.108 and p = 0.436. The analyses address different quantities, and neither provides a precise, fully contextualized estimate of the between-group contrast in the record.

These statistics do not establish that the therapies are equivalent. Failure to obtain a small p-value is not proof that there is no difference; it may reflect uncertainty, limited information, or a small effect. At the same time, the numerical estimates do not establish that one therapy has a meaningful advantage. The registry does not report a threshold for clinically meaningful LPP change, and the EEG endpoint should not be treated as a direct substitute for clinical outcomes.

The endpoint concerns the change in an EEG measure, not every aspect of late-life depression or treatment experience. The registry also lists anhedonia as a secondary outcome, but it does not report enough information to support broad conclusions across multiple outcomes. Missing assessments and incomplete model details further limit interpretation of the estimates.

The findings are best understood as evidence about the posted endpoint summaries and reported analyses in this study. They do not, on their own, establish a treatment recommendation, a mechanism of action, or a general conclusion about all older adults with depression. The registry record does not provide the detail needed to evaluate all design and analysis assumptions.

18. Why This Trial Matters Statistically

This trial raises several statistical issues that are common in studies with repeated measures and behavioral interventions. Its primary endpoint is measured at multiple visits, and the registry reports a mixed-model comparison of slopes. That makes the distinction between a trajectory-based model estimate and a simple endpoint-change contrast important: the two summaries answer related but different questions and can yield different estimates.

The record also illustrates why estimates should be read together with their precision. The recalculated primary interval spans zero and a broad range of possible differences, while the sponsor’s model-based estimate has no interval reported. A p-value alone cannot convey the likely magnitude or precision of an effect. Clear reporting of interval estimates and model details would make the comparison easier to assess.

Missing data and outcome multiplicity are also central. The registry identifies missing observations and multiple outcome measures and analyses, but does not describe the missing-data methods or multiplicity approach. Those details matter because they help readers judge the robustness of results and distinguish confirmatory evidence from exploratory findings.

The statistical lesson is not that one analysis is automatically preferable in every setting. Rather, the estimand, model, analysis population, missing-data assumptions, and uncertainty all shape the meaning of a result. Reporting these elements alongside the estimates is essential for transparent interpretation of clinical research.

19. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record leaves important details about the primary analysis unclear. It reports the mixed-model difference in slopes and p-value but not a confidence interval, model specification, covariance structure, or time coding. The simple recalculation supplies an interval for a different estimand and cannot fill that reporting gap.

The record notes missing data due to poor quality or missed assessments and dropouts before baseline, but does not describe their distribution across visits or the methods used to address them. Without the analysis-population definition and missing-data assumptions, readers cannot fully assess how incomplete observations may affect the estimates.

The registry does not report the original sample-size justification, detailed randomization procedures, or a multiplicity plan. It also does not give a clinically meaningful threshold for change in the LPP. These omissions limit assessment of design rationale, robustness, and practical importance.

The primary measure is an EEG-derived endpoint, and its posted results do not by themselves establish effects on broader clinical outcomes. The registry identifies anhedonia as a secondary outcome but does not provide sufficient context about prespecification and adjustment across the listed outcomes and analyses. Safety reporting is also limited: event counts and at-risk counts are posted, but event details and the relationship between safety and endpoint populations are not explained.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Reward Function and Therapy for Late-Life Depression — NCT03688139.
• Registry record last updated 2024-11-14; status last verified 2024-10.
• Results first posted 2024-11-14.
• 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.

23. Record Summary

NCT03688139 is a completed randomized, double-masked, parallel-group study of Engage Therapy and supportive therapy for older adults with depression. Enrollment is recorded as 65. Each therapy was delivered for 9 weeks, with research assessments before treatment and at weeks 3, 6, and 9.

The primary endpoint is change from baseline to week 9 in the EEG-derived late positive potential response to rewarding stimuli. The registry reports a mixed-model difference in slopes of 0.23 with p = .08. An unadjusted recalculation from the posted group mean changes gives a difference of -0.73 microvolts, with an interval from -2.568 to 1.108 and p = 0.436. These analyses estimate different quantities and both require cautious interpretation.

The registry notes missing observations and does not report several details needed to evaluate the analysis fully, including the original sample-size justification, missing-data methods, and multiplicity plan. The posted statistics describe the recorded outcomes; they do not establish a clinically meaningful effect or broader conclusions beyond those measures.