tDCS for Increasing Exercise Adherence in Depressed Individuals: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for tDCS for Increasing Exercise Adherence in Depressed Individuals (NCT03178903), a randomized na study. The primary outcome is Physical Activity Levels.

2. Clinical Question

The study's stated purpose was to examine tDCS for increasing exercise adherence among low active individuals with elevated depressive symptoms. Its summary also describes an interest in the role of tDCS in changing the affective experience of exercise. The primary endpoint posted measures physical activity, rather than directly measuring the affective experience of exercise. The registry record does not report a separate posted outcome for exercise adherence or affective experience.

3. Trial Design

This was a randomized, double-masked, parallel-group study, with 51 participants enrolled. The registry lists the study as completed and gives Butler Hospital as the sponsor. The listed phase is NA. The study start date is 2017-02-01, and the primary completion date is 2019-12-31.

The two posted groups both received aerobic exercise alongside their assigned stimulation condition. One group received tDCS and aerobic exercise; the other received sham tDCS and aerobic exercise. The active and sham descriptions specify a 20-minute stimulation session followed immediately by a supervised 30-minute moderate-intensity exercise bout. The descriptions identify the dorsolateral prefrontal cortex as the stimulation target. The registry record does not report the full schedule of these procedures in the posted arm descriptions.

The endpoint results are based on fewer participants than the enrollment figure: 19 in the tDCS and exercise group and 17 in the sham tDCS and exercise group. The registry states that only participants meeting the accelerometer valid-wear requirement were included in the primary-outcome analysis. These analysis counts should not be mistaken for the total enrolled population or for the safety denominators.

Randomization and double masking are listed, but the registry record does not report the randomization sequence method, allocation concealment procedures, or who was masked. The original design's sample-size assumptions and justification are not reported in the registry record. The planning figures displayed with the results are calculations based on the observed effect, not a report of the original design target.

The parallel design compares outcomes between groups rather than reporting a within-person crossover. Because both groups received supervised exercise, the contrast addresses the added stimulation condition in that setting. The record does not describe an exercise-only group, so the posted comparison does not estimate an exercise-versus-no-exercise contrast.

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 numbers analyzed include only individuals that provided valid wear-time data on the primary outcome measure, using accelerometry. Specifically, only participants that provided 3 days of 8 hours/day valid wear time were included in the analysis of the primary outcome.

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 Physical Activity Levels, measured over 8 week assessment.

The primary endpoint is physical activity at the 8 week assessment, described as accelerometry-based moderate-to-vigorous physical activity (MVPA). It is summarized as a mean in minutes per day, with standard deviation as the measure of spread. Accelerometry records movement over wear periods and provides an objective basis for summarizing activity, rather than relying only on participants' recall. The registry's endpoint description does not specify the accelerometer model, processing rules, or intensity thresholds.

The registry states a specific validity requirement for inclusion in the primary-outcome analysis: 3 days of 8 hours/day valid wear time. This defines which participants contributed to the posted endpoint analysis, but it also means the analyzed sample is not simply everyone enrolled. The posted group counts are 19 for tDCS and exercise and 17 for sham tDCS and exercise.

MVPA is relevant to the study's interest in physical activity and exercise adherence, but a measured activity level is not itself a direct measure of adherence to the supervised exercise sessions. Nor is it a direct measure of the affective experience of exercise mentioned in the study summary. The registry record does not report those as additional posted primary outcomes. Results should therefore be interpreted as a comparison of the stated accelerometry endpoint at the stated assessment, not as a direct answer to every broader motivation described for the study.

7. Results Posted in the Registry

• tDCS and Aerobic Exercise: mean 17.40 versus 21.00 on control; difference -3.60 (95% CI -12.97 to 5.77), standardized effect d = -0.26; z-test p = 0.452.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a randomized, double-masked, parallel-group design and an ANCOVA analysis for the primary comparison. The displayed recalculation is a separate, unadjusted comparison derived from the posted group summaries. These methods answer related but not necessarily identical questions, so keeping their roles distinct is important when reading the results.

What the group summaries describe

For each group, the registry posts a mean and standard deviation for MVPA at the 8 week assessment. A mean summarizes the group outcome as a single average value. A standard deviation describes how dispersed individual measurements are around that average; it is not the uncertainty in the group mean and is not a confidence interval. The reported means are 17.4 and 21.0 minutes per day, with standard deviations of 9.8 and 17.4, respectively.

The recalculated mean difference compares the active group mean with the sham group mean, using the ordering indicated by the posted estimate. It is an unadjusted contrast: it uses the displayed summaries rather than modeling participant-level outcomes and covariates. The recalculated estimate is -3.6 minutes per day. Its accompanying confidence interval and p-value quantify uncertainty under the recalculation's assumptions, not under the sponsor's ANCOVA model.

What ANCOVA means

ANCOVA, or analysis of covariance, compares group outcomes while accounting for one or more covariates included in the model. In general, adjusting for relevant baseline measurements can make a group comparison more precise or account for chance differences in those measurements. The registry record does not report which covariates were included, their coding, or the model specification. It is therefore not possible to explain exactly what adjustment produced the reported ANCOVA value of .678 or to reproduce it from the posted group summaries.

The registry describes the ANCOVA result as a mean difference in final values and reports p = .87. It does not report a confidence interval for that estimate. The absence of a posted interval limits how directly a reader can assess the range of values compatible with that particular adjusted analysis. The unadjusted interval should not be substituted for the missing ANCOVA interval, because it comes from a different calculation.

How to read a p-value

In general, a p-value describes how unusual data at least as discrepant from a specified null model would be if that model and the analysis assumptions held. It does not give the probability that the null hypothesis is true, and it does not measure the size or importance of an effect. Here, the registry reports p = .87 for its ANCOVA, while the unadjusted recalculation reports p = 0.452. Those values belong to their respective analyses. The registry record does not report a prespecified threshold or a fuller inferential plan, so the p-values should be read as reported evidence summaries rather than as a complete account of the analysis plan.

Why dispersion and valid wear time matter

MVPA varies among participants, as reflected in the posted standard deviations. In general, greater variability makes it harder to estimate a group mean or difference precisely when other features are held constant. The posted standard deviations differ between groups, and the confidence interval is broad enough to include values on both sides of zero. No individual-level data are posted to examine the distribution, outliers, or whether the analysis assumptions were checked.

The outcome analysis also depends on the valid-wear rule. The registry includes only participants with 3 days of 8 hours/day valid accelerometer wear time. This is a measurement-quality criterion, but it also defines the analysis population. The record does not state how many participants failed to meet the criterion, what happened to partial wear records, or whether missing activity measurements were handled in another way. Those details matter because available-case analyses can represent a selected subset if inclusion is related to participants' activity or group assignment.

Why the recalculation is not the sponsor analysis

A recalculation from summary statistics is useful as a transparent check on the posted means and spread, but it cannot recover all features of a participant-level model. ANCOVA may incorporate covariates and model choices that are not visible in group means and standard deviations. The displayed unadjusted estimate, interval, and p-value should therefore be regarded as a simple supplementary analysis. The trial's own reported ANCOVA remains the registry's reported analysis, while important details of its implementation are not reported in the registry record.

10. Confidence Intervals and Precision

The unadjusted recalculated mean difference is -3.6 minutes per day, with a 95% confidence interval from -12.97 to 5.772. In general, a confidence interval describes a range of estimates compatible with the observed data and the method's assumptions. It is not a guarantee that the true value lies inside the particular interval, and it does not show that every value inside the range is equally plausible.

This interval crosses zero, so the posted summary data do not determine a single direction of difference with precision. The interval includes negative and positive values, meaning that the summary-based comparison is compatible with differences in either direction. Its span also indicates that the data do not tightly identify the size of the difference. This uncertainty is important alongside the point estimate; focusing only on -3.6 would leave out the range of estimates compatible with the data.

The confidence interval belongs to the unadjusted recalculation, not to the sponsor's ANCOVA. For the ANCOVA, the registry reports a mean difference in final values of .678 and p = .87, but no confidence interval. Because the covariates and model details are not reported in the registry record, the unadjusted interval cannot be treated as an interval for the adjusted result.

Precision is also affected by the analysis population and measurement requirements. The endpoint comparison includes 19 and 17 participants, selected by the valid-wear rule, rather than all 51 enrolled participants. The registry record does not report an analysis of how the excluded or missing measurements might affect the estimate. The interval therefore describes uncertainty in the displayed summary-based comparison, not all possible uncertainty about the broader enrolled population or outcomes beyond the endpoint.

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 planning table gives participants per arm, not total event counts. Its figures are illustrations computed from the observed effect rather than the trial's original sample-size plan. The planning 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 set to the stated fraction of the observed effect. The original trial's design assumptions and sample-size justification are not reported in the registry record.

For 100% of the observed effect, The table shows 235 participants per arm for 80% power and 314 participants per arm for 90% power. For 75% of the observed effect, it lists 417 participants per arm for 80% power and 558 participants per arm for 90% power. For 50% of the observed effect, it lists 937 participants per arm for 80% power and 1,254 participants per arm for 90% power.

In plain language, the 80% power column describes the planned number per arm under the stated assumptions for a study intended to have an 80% chance of detecting the specified effect if that effect is the true one and the assumptions hold. The 90% power column gives the corresponding planning figure for a higher chance of detection under those assumptions. These are design illustrations, not guarantees about what any particular study will detect. The displayed table is not observed power.

The rows show why smaller effects require more participants: when the target is a smaller fraction of the observed effect, the table's planning numbers increase. This relationship is a general feature of power calculations, not evidence that the smaller effects are more likely or more important. The table does not describe the enrollment target actually used in this trial, and it should not be used to infer the original investigators' assumptions.

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 = -3.600; pooled standard deviation σ = 13.904.
2. n = 2 × (1.96 + 0.842)² × 13.904² / -3.600² = 234.2, rounded up to 235 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 <- -3.6                      # observed difference in means
sigma <- 13.9039562715078                     # 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(3178903)
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 = 235 (80% power), 314 (90% power)
 75% of observed effect: n per arm = 417 (80% power), 558 (90% power)
 50% of observed effect: n per arm = 937 (80% power), 1,254 (90% power)
power.t.test: 235.1 
Simulated power at n = 235 per arm: 0.800 (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 registry's own reported analysis is ANCOVA, described as mean difference in final values. It reports a value of .678 and p = .87, with no confidence interval. The registry record does not report which covariates were included or enough model detail to reconstruct this analysis.

The recalculation uses the posted group means and standard deviations without adjustment. It gives a mean difference of -3.6 minutes per day, a 95% confidence interval from -12.97 to 5.772, and p = 0.452. Because this is an unadjusted calculation from summary statistics, it is not a replacement for the trial's ANCOVA. The reported analyses differ in method, and the values should not be compared as though they came from the same model.

Both results are summaries of the primary endpoint, but the available record does not provide the information needed to explain why the estimates and p-values differ. The recalculation is useful for describing the posted group summaries and their uncertainty under its assumptions. For the trial's own analysis, readers should refer to the sponsor's reported ANCOVA result while noting that its confidence interval and model details are not reported in the registry record.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure and one analysis, and no secondary outcomes are posted. This makes the posted record appear focused on a single endpoint comparison, but the registry does not provide a complete statistical analysis plan. The multiplicity strategy, including whether any adjustment was planned or applied, is not reported in the registry record. The number of hypotheses considered beyond those posted is also not reported, so the listed outcome and analysis do not establish how many comparisons were examined during the study.

The primary-outcome analysis included participants who met the stated accelerometer criterion of 3 days of 8 hours/day valid wear time. The group counts in that analysis are 19 and 17, whereas enrollment was 51. The registry record does not report the flow from enrollment to the endpoint analysis, reasons for unavailable or invalid wear data, or whether missing measurements were imputed. It also does not report sensitivity analyses addressing missing outcome data.

The record identifies the study as randomized but does not state whether the primary analysis followed an intention-to-treat population, a per-protocol population, or another prespecified analysis set. The endpoint population is described by its valid-wear requirement, but that alone does not establish how participants were handled in all analyses. The safety denominators are 25 and 26, different from the endpoint analysis counts; the record does not provide a full explanation of how the safety and endpoint populations were defined.

The registry reports an ANCOVA, but the covariates, model diagnostics, treatment of any missing covariates, and detailed analysis procedures are not reported in the registry record. It is also not reported whether there were interim analyses or a prespecified plan for handling multiple outcomes or comparisons. These omissions limit assessment of analysis choices and the possible influence of missingness or selective reporting. They do not establish that a particular procedure was or was not used; they mean the registry record does not document it.

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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: psychiatric inpatient hospitalization (4.0%), medical hospitalization (4.0%).

The serious adverse event figures use safety denominators of 25 participants in the tDCS and exercise group and 26 in the sham tDCS and exercise group. The registry lists 4 serious adverse events for the first group and 0 for the second. It names Psychiatric Inpatient Hospitalization and Medical Hospitalization among the serious adverse event terms, each reported as 4.0%. Deaths are reported as 0 in both groups.

The registry also lists other adverse events for the same safety groups: 2 in the tDCS and exercise group and 1 in the sham tDCS and exercise group. These are separate from the serious adverse event figures. The record does not provide detailed event descriptions, timing, duration, relatedness assessments, or participant-level information in the registry record.

These counts describe what the registry posts; they should not be read as a complete characterization of safety or as proof that an event was caused by the assigned intervention. The safety denominators differ from the primary-outcome analysis counts, which were based on valid accelerometer wear time. The registry record does not report the reasons for those differing denominators or additional methods for assessing adverse events.

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

The posted results describe an imprecise comparison of accelerometry-based MVPA at the 8 week assessment between participants assigned to tDCS plus aerobic exercise and those assigned to sham tDCS plus aerobic exercise. The group means were 17.4 and 21.0 minutes per day, and the unadjusted recalculation estimated a difference of -3.6 minutes per day. Its confidence interval spans values on both sides of zero. The sponsor's ANCOVA reports a mean difference in final values of .678 with p = .87, but no confidence interval.

These data do not establish a clear difference between the groups, nor do they establish that the groups are equivalent. A non-significant p-value is not proof of no effect, and the broad unadjusted interval leaves uncertainty about the direction and magnitude of the difference. The sponsor's adjusted result also cannot be fully interpreted without its covariates and model details.

The comparison is specifically between two stimulation conditions when paired with supervised aerobic exercise. It does not estimate the effect of exercise compared with no exercise, since both groups received exercise. The primary endpoint is activity recorded by accelerometry, not a direct measure of adherence to exercise sessions or the affective experience of exercise. The registry record does not report separate results for those broader concepts.

The endpoint analysis includes only participants meeting the valid-wear criterion, so its results apply directly to that analyzed group. How missing or invalid accelerometer data might affect the comparison is not reported in the registry record. The study's enrollment and the smaller endpoint analysis groups should be kept distinct when considering how broadly to interpret the findings.

This statistical summary is not a medical recommendation and does not determine what an individual should do. It describes the posted endpoint values, the uncertainty around an unadjusted comparison, and the limits of what can be concluded from the registry record.

17. Why This Trial Matters Statistically

This trial offers a useful example of why a study question, endpoint, and analysis need to be read together. The stated motivation includes exercise adherence and the affective experience of exercise, while the posted primary endpoint is accelerometry-based MVPA at the 8 week assessment. Those concepts are related to physical activity but are not interchangeable. A result for recorded activity should not automatically be described as a result for adherence or affect.

The design also makes the comparison precise in scope. Both groups received supervised aerobic exercise, and the assigned conditions differed in active versus sham tDCS. The study therefore addresses the stimulation contrast in an exercise setting. It does not provide a direct estimate of exercise compared with no exercise. Clear description of the comparator prevents a broader causal interpretation than the design supports.

Statistically, the record illustrates the difference between a sponsor-reported ANCOVA and an unadjusted calculation from group summaries. The latter is transparent and can help readers understand the raw group contrast, but it cannot reproduce an adjusted model without its covariates and details. The ANCOVA result has no reported confidence interval, leaving a gap in the precision information for the trial's own analysis.

The endpoint's valid-wear rule is another important part of interpretation. The published analysis counts are smaller than enrollment, and the registry record does not explain the full flow or missing-data handling. Reporting those details would help readers assess how the analyzed group relates to the randomized population. The planning illustrations also show how strongly sample-size requirements depend on the chosen target effect, but they are not evidence of the original design assumptions.

Together, these features make the record valuable for statistical reading: they show why endpoint definition, analysis population, uncertainty, comparator, and reporting completeness all shape what a trial result can support.

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 endpoint is based on valid accelerometer wear time, and the registry specifies the inclusion threshold as 3 days of 8 hours/day. The posted analysis includes 19 and 17 participants, compared with 51 enrolled. The registry record does not report the participant flow, reasons for missing or invalid wear data, or whether those excluded differed from those analyzed. This limits assessment of how representative the endpoint analysis is of the enrolled group.

The primary endpoint captures accelerometry-based MVPA, but the stated study purpose also concerns exercise adherence and the affective experience of exercise. The registry record does not post separate outcome results for those concepts. The timing and measurement procedures beyond the 8 week assessment and valid-wear rule are not reported in the registry record.

The comparison includes aerobic exercise in both groups, so it cannot isolate exercise versus no exercise. The registry record also does not report the full schedule of stimulation and exercise procedures in the posted arm descriptions. Randomization and double masking are listed, but sequence generation, allocation concealment, masking details, and assessment of masking are not reported in the registry record.

The sponsor's ANCOVA is reported without a confidence interval, covariate list, or full model specification. This limits interpretation and reproducibility. The unadjusted recalculation has an interval, but it is not an interval for the ANCOVA. The record does not report a complete statistical analysis plan, multiplicity procedures, interim analyses, or sensitivity analyses for missing data.

Finally, the planning table is based on the observed effect and stated assumptions rather than the original trial design. It cannot establish whether the trial met its intended sample-size target, because that target and its justification are not reported in the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: tDCS for Increasing Exercise Adherence in Depressed Individuals — NCT03178903.
• Registry record last updated 2023-02-27; status last verified 2023-01.
• Results first posted 2023-02-27.
• 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

NCT03178903, titled “tDCS for Increasing Exercise Adherence in Depressed Individuals,” is listed as a completed, randomized, double-masked, parallel-group study sponsored by Butler Hospital. It enrolled 51 participants and compared tDCS plus aerobic exercise with sham tDCS plus aerobic exercise.

The primary endpoint was accelerometry-based MVPA in minutes per day at the 8 week assessment. The analysis included participants meeting the stated valid-wear requirement, with 19 in the active group and 17 in the sham group. The posted means were 17.4 and 21.0 minutes per day. The unadjusted recalculation gives a mean difference of -3.6 minutes per day, with a 95% confidence interval from -12.97 to 5.772 and p = 0.452. The registry's ANCOVA reports a mean difference in final values of .678 and p = .87, without a confidence interval.

The estimates are uncertain, and the registry record does not report several details needed to reproduce the adjusted analysis or assess missing outcome data. The study comparison concerns stimulation conditions in the context of exercise, not exercise versus no exercise.