Home-based tDCS and Mindfulness-based Meditation for Self-management of Clinical Pain and Symptoms: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Home-based tDCS and Mindfulness-based Meditation for Self-management of Clinical Pain and Symptoms (NCT04375072), a randomized na study. The primary outcome is Change in Numeric Rating Score (NRS) of Pain.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, parallel-group trial with quadruple masking. The study status is completed, and the recorded enrollment is 208. The phase is listed as NA. The sponsor is the University of Arizona. The recorded study start is 2020-08-13 and the primary completion date is 2025-01-30. These registry entries describe the study’s overall structure and timing, but do not establish how participants were randomized, what masking procedures were used, or how adherence was assessed; those details are not reported in the registry record.

Four intervention combinations are listed: active tDCS paired with active MBM, sham tDCS paired with active MBM, active tDCS paired with sham MBM, and sham tDCS paired with sham MBM. The primary outcome results list 53.0 participants in the active tDCS plus active MBM group, 53.0 in the sham tDCS plus active MBM group, 50.0 in the active tDCS plus sham MBM group, and 52.0 in the sham tDCS plus sham MBM group. Arm descriptions in the record are empty, so further details of the assigned regimens are not available there.

The primary outcome timeframe is baseline and week 2, after 10 tDCS sessions. The registry also posts a secondary outcome of change in the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) over the same timeframe. Although the record lists two outcome measures, it posts results for one secondary outcome and no reported analyses. The protocol’s original sample-size assumptions, allocation procedures, planned analysis model, analysis populations, and handling of missing outcome data are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: A total of 208 participants consented to participate in the study. However, 8 participants withdrew due to being unable to attend the remaining sessions and assessments.

Overall Study

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 Numeric Rating Score (NRS) of Pain, measured over baseline, week 2 (after 10 tDCS sessions).

The primary endpoint is change in Numeric Rating Scale (NRS) pain score, measured from baseline to week 2 after 10 tDCS sessions. The NRS is described as a subjective measure of pain intensity, with a scale from 0 (no pain) to 100 (most intense pain imaginable). Change is defined as the week 2 score minus the baseline score. Under this definition, a negative change means the recorded score is lower at week 2 than at baseline, which the registry describes as improvement.

A continuous measure such as this can be summarized by a group mean, which describes the average observed change, and a standard deviation, which describes how spread out individual changes are around that average. A mean difference between groups summarizes how far apart their average changes are. It is not the same as a change experienced by every participant: individual responses may vary around the group mean.

Measuring change across the stated timeframe gives a direct summary of the outcome at the end of the intervention period relative to baseline. However, the registry does not report individual-level observations, the distribution of scores, or additional measurement details. The posted group summaries therefore characterize average short-term changes, not the full range of participants’ experiences or outcomes beyond week 2.

7. Results Posted in the Registry

• active tDCS paired with active MBM: mean -19.41 versus -7.16 on control; difference -12.25 (95% CI -20.26 to -4.24), standardized effect d = -0.58; z-test p = 0.003.
• active tDCS paired with sham MBM: mean -16.78 versus -7.16 on control; difference -9.62 (95% CI -17.40 to -1.84), standardized effect d = -0.48; z-test p = 0.015.
• sham tDCS paired with sham MBM: mean -6.20 versus -7.16 on control; difference 0.96 (95% CI -6.77 to 8.69), standardized effect d = 0.05; z-test p = 0.808.

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 Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC).

• 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:
  • active tDCS paired with active MBM,: mean -6.98 versus -7.90 on control; difference 0.92 (95% CI -4.31 to 6.15), standardized effect d = 0.07; z-test p = 0.730.
  • active tDCS paired with sham MBM: mean -8.08 versus -7.90 on control; difference -0.18 (95% CI -5.51 to 5.15), standardized effect d = -0.01; z-test p = 0.947.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between active tDCS paired with active MBM, and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between active tDCS paired with sham MBM and the control. The interval gives the range of effects that remain compatible with the data.

The registry posts change in WOMAC as a secondary outcome over baseline to week 2, the same timeframe as the primary NRS outcome. The posted group means show decreases in all four arms, and the recalculated comparisons against sham tDCS plus active MBM are close to zero relative to the reported variation. Their confidence intervals include zero, and the unadjusted p-values do not indicate clear separation in these comparisons.

This overall pattern differs from the primary NRS comparisons involving active tDCS, where the recalculated mean differences are negative and the confidence intervals do not include zero. The measures capture different aspects of pain and osteoarthritis-related symptoms, so their patterns need not be identical. The secondary results neither reproduce the apparent separation in the primary comparisons nor directly contradict it; they estimate a different outcome on its own scale. The registry record does not report a formal analysis testing whether the primary and secondary outcome results differ.

Secondary results generally carry less confirmatory weight when multiple outcomes and comparisons are available, especially if the analysis hierarchy and multiplicity procedure are unknown. Repeated testing can increase the chance of at least one apparently notable result by chance. The registry lists two outcome measures, posts one secondary outcome, and reports no analyses. It does not state whether WOMAC was prespecified as a key secondary endpoint, how missing secondary measurements were handled, or whether any adjustment for multiple testing was planned. Its estimates are therefore best read as descriptive evidence alongside the primary result, not as an independent confirmation.

General statistical context: consistency across different measures can strengthen interpretation when outcomes are prespecified and analyses are planned, but lack of consistency may reflect different constructs, measurement variability, precision, or chance. The available summaries do not identify which explanation applies. No clinical threshold for interpreting WOMAC change is reported in the registry record.

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

• Change in Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC).

9. Statistical Interpretation

10. Statistical Methods Explained

The registry posts continuous outcome summaries as means and standard deviations. A mean represents the arithmetic average of the observed change scores in a group. The standard deviation describes the spread of individual scores around that mean. A standard deviation is not a confidence interval and does not directly describe the uncertainty in the mean; uncertainty in a group mean depends on both variability and the number of observations.

What does a mean difference represent?

For each comparison, the unadjusted mean difference is calculated as the comparison group’s mean change minus the mean change in the sham tDCS plus active MBM group. The sign must be interpreted in the context of the outcome’s direction. For NRS change, a decrease is described as improvement, so a negative difference indicates a more negative average change in the comparison group. For example, the active tDCS plus active MBM comparison has an estimate of -12.25. This is a difference between group averages, not an estimate that every participant’s score changed by that amount.

These are simple unadjusted recalculations from posted summary statistics. They do not account for baseline covariates or other possible adjustment variables. The registry record does not report a sponsor analysis, an adjusted model, or a model specification. There are no reported analyses in the record, so the recalculated comparisons should not be represented as the trial’s prespecified analysis.

How should a confidence interval be understood?

A confidence interval gives a range of estimates compatible with the observed data under the calculation’s assumptions. It conveys precision: a narrower interval indicates greater precision, while a wider interval indicates more uncertainty about the size and direction of the group difference. An interval that crosses zero includes no difference as one value compatible with the data. It can also include differences in either direction. An interval that does not cross zero indicates that zero is not within that interval, but it does not establish clinical importance or remove uncertainty about the precise effect size.

The posted comparison intervals are recalculated from the group summary statistics. They should be read alongside the estimate and not as a range containing a fixed proportion of individual participants’ results. The record does not report whether a confidence-interval method was prespecified or whether any adjustment for multiple comparisons was planned.

What does a p-value contribute?

A p-value describes how unusual data at least as inconsistent with a specified null hypothesis would be under the assumptions of a statistical test. It is not the probability that the null hypothesis is true, nor is it a measure of effect size. Smaller p-values indicate greater incompatibility with the null model under those assumptions, but interpretation also depends on study design, analysis choices, precision, and the number of comparisons considered.

The p-values posted for the primary comparisons are unadjusted recalculations. They do not account for the fact that several group comparisons and outcomes are available. Since no multiplicity plan or sponsor-reported analysis is listed, the p-values should not be treated as a family-wise confirmatory test. The estimates and intervals provide important context beyond a threshold-based reading of p-values.

Why does variability matter?

Variation among participants affects how precisely group means and their differences can be estimated. Greater variation generally makes a comparison less precise when other features are held constant. The group standard deviations for NRS change range from 17.9 to 22.24. The calculation uses pooled standard deviations for the comparisons; these summarize variability across the two groups being compared under the calculation’s assumptions. The record does not report individual data, so distribution shape, outliers, or subgroup variation cannot be examined from these summaries.

General statistical context: if outcome variability differs substantially between groups, or if score distributions depart from assumptions used by a simple mean-based comparison, the validity of a standard unadjusted analysis may be affected. Whether such issues arose in this trial cannot be determined from the posted group summaries. The registry record does not report diagnostic checks or alternative analyses.

What can the design support?

Randomization can support comparisons among assigned groups by reducing systematic differences at allocation, provided it is implemented and analyzed appropriately. The registry identifies the study as randomized and parallel-group, but does not report the randomization method or the analysis population. Quadruple masking is also listed, but the record does not state which roles were masked or how masking was maintained. Consequently, the labels describe the reported design without supplying details needed to assess implementation.

General statistical context: when more than two groups are present, separate pairwise comparisons do not necessarily answer whether the treatment components interact or whether one component’s effect depends on the other. Such questions require a suitable prespecified analysis. The record lists four combinations, but does not report an interaction test or a model that jointly estimates component effects. The posted pairwise estimates therefore address only their stated comparisons.

11. Confidence Intervals and Precision

The primary comparison of active tDCS plus active MBM with sham tDCS plus active MBM has an estimated mean difference in NRS change of -12.25. Its 95% confidence interval extends from -20.26 to -4.241. The interval lies below zero, while still allowing a range of possible magnitudes for the difference. The point estimate is not known with exactness; the interval communicates uncertainty around it under the unadjusted calculation.

For active tDCS plus sham MBM versus sham tDCS plus active MBM, the estimate is -9.62 and the 95% confidence interval is -17.4 to -1.844. This interval also lies below zero, but spans a range of possible differences. For sham tDCS plus sham MBM versus sham tDCS plus active MBM, the estimate is 0.96 and its interval is -6.77 to 8.69. That range includes zero and values on both sides of zero, so the direction and size of the underlying difference are uncertain from this comparison.

Confidence intervals describe uncertainty in a group-level estimate, not the distribution of individual participant changes. A wide interval can reflect limited precision, while a narrow interval generally indicates more precision, subject to the calculation assumptions. The group standard deviations show substantial variation in individual NRS changes, but individual data and diagnostic information are not reported.

These intervals are unadjusted recalculations from the posted group means, standard deviations, and sample sizes. They are not reported sponsor confidence intervals, and no multiplicity adjustment is reported. They should therefore be interpreted as uncertainty ranges for the individual recalculated comparisons, not as a simultaneous guarantee covering all outcomes and comparisons. The registry does not report a threshold for clinical importance, so statistical precision alone cannot establish whether any estimated difference is meaningful to patients.

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 illustrations translate an observed comparison effect into hypothetical requirements for future planning. The figures are participants per arm, not total participants, because these comparisons are between two groups and the stated illustration assumes equal allocation. The posted 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 trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed for an 80% chance of detecting the specified effect under those assumptions, if that effect and the calculation assumptions were correct. The 90% power column gives the corresponding planning number for a 90% chance. These are planning probabilities for a hypothetical future study, not probabilities that a treatment effect is true. Smaller effects are harder to distinguish from random variation, so planning to detect a smaller fraction of an observed effect requires more participants.

For the primary comparison of active tDCS plus active MBM with sham tDCS plus active MBM, the illustration gives 47 participants per arm for 80% power and 62 for 90% power when planning for 100% of the observed effect. Planning for 75% of the observed effect gives 83 and 111 participants per arm, respectively; planning for 50% gives 186 and 248. The other primary comparisons have their own illustrations based on their respective observed estimates. Those figures are not design recommendations without considering the intended analysis, attrition, multiplicity, and clinical priorities; such protocol assumptions are not reported. These are planning illustrations, not observed power.

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 = -12.250; pooled standard deviation σ = 21.037.
2. n = 2 × (1.96 + 0.842)² × 21.037² / -12.250² = 46.3, rounded up to 47 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 <- -12.25                      # observed difference in means
sigma <- 21.0365776684327                     # 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(4375072)
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 = 47 (80% power), 62 (90% power)
 75% of observed effect: n per arm = 83 (80% power), 111 (90% power)
 50% of observed effect: n per arm = 186 (80% power), 248 (90% power)
power.t.test: 47.3 
Simulated power at n = 47 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.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary NRS outcome and a WOMAC secondary outcome, along with four randomized intervention combinations. The posted primary comparisons each use the sham tDCS plus active MBM group as the reference. Multiple outcomes and group comparisons create a multiplicity issue: if many statistical tests are considered, some may appear notable by chance even when there is no underlying difference. The registry record does not report a planned testing hierarchy, a family-wise error procedure, or another multiplicity adjustment.

The displayed p-values for the primary comparisons and WOMAC comparisons are unadjusted recalculations. They should not be interpreted as though they account for all comparisons. The record reports no sponsor analyses, so it is not possible to determine whether an analysis plan specified a different model, a particular contrast, or a correction for multiple testing. No interaction analysis is reported for the four intervention combinations.

Missing data are also important for interpreting trial outcomes. The registry provides group sizes for the posted outcome results, but does not describe whether those numbers represent all randomized participants, participants with observed outcomes, or another analysis population. It does not report the amount or pattern of missing outcome data, reasons for missingness, imputation methods, or sensitivity analyses. Therefore, the potential effect of missing results on the estimates cannot be assessed from the record.

The registry identifies the study as randomized and quadruple-masked, but does not report whether analyses followed an intention-to-treat principle, whether participants were excluded after randomization, or how deviations from assigned interventions were addressed. These are not details that can be inferred from the group summaries. They matter because different analysis populations and missing-data choices can change the interpretation of randomized comparisons. No claim about the analysis population or completeness of follow-up is warranted from the posted results alone.

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 registry reports serious adverse event figures for each of the four treatment groups. The number at risk is 53 in the active tDCS plus active MBM group, 53 in the sham tDCS plus active MBM group, 50 in the active tDCS plus sham MBM group, and 52 in the sham tDCS plus sham MBM group. The reported number affected by serious adverse events is 0 in each group, and deaths are reported as 0 in each group. The record lists no serious adverse event terms.

These figures describe the adverse-event counts posted in the registry for the stated groups. A zero count in these results means no affected participants are reported in that category; it does not prove that an event is impossible or that there is no safety uncertainty. The record does not provide event timing, exposure duration, ascertainment details, or further context for interpreting safety beyond the posted counts. These figures should be read as registry reporting, not as a comprehensive assessment of risk.

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

The posted primary outcome summaries indicate that average NRS change was more negative in the two groups assigned active tDCS than in the sham tDCS plus active MBM reference group. The unadjusted recalculated confidence intervals for those two comparisons lie below zero. The comparison between the two sham tDCS groups is less precise and its interval includes zero. These are statements about observed group averages and the uncertainty of recalculated comparisons, not statements about what each participant experienced.

The registry does not report sponsor analyses, an analysis plan, adjustment for multiple comparisons, or details about missing data and analysis populations. That limits how strongly the comparisons can be treated as confirmatory. In particular, unadjusted p-values alone cannot resolve the effect of considering several groups and outcomes. The record also does not report a clinical-importance threshold for NRS change, so the estimates cannot be classified as clinically important or unimportant from the posted statistical results alone.

The endpoint is measured at week 2 after 10 tDCS sessions. It therefore describes short-term change over the stated timeframe. The results do not establish whether differences persisted beyond that point, whether participants maintained use of the assigned interventions, or whether effects differed across patient characteristics. Those questions require information and analyses not reported in the registry record.

The findings also do not demonstrate the contribution of each intervention component independently or whether the components interact. Although four combinations are listed, the available pairwise comparisons do not substitute for a reported model estimating main effects and interaction. Nor do these results establish a mechanism for any observed change. The registry results are a limited statistical description of the posted group summaries and should not be used alone to make treatment decisions.

17. Why This Trial Matters Statistically

This trial is statistically notable for evaluating four combinations of active and sham tDCS and MBM in a randomized, parallel-group design, with pain change as its primary outcome. Such a set of groups raises questions beyond whether any one group differs from a reference: readers may also want to distinguish the contribution of each component and whether the components work differently in combination. The registry record lists the combinations but does not report an interaction analysis, making clear the difference between available pairwise evidence and broader component-level questions.

The comparison estimates illustrate why effect size and precision should be read together. The primary recalculations involving active tDCS have intervals below zero, while the sham-versus-sham comparison has a wider interval that includes zero. A point estimate alone would conceal this difference in precision. Conversely, a p-value alone would not convey the range of possible group differences. Confidence intervals offer a useful way to examine both direction and uncertainty, while still requiring care about the unadjusted nature of the calculations.

The contrast between the posted primary and secondary outcome patterns also has statistical relevance. WOMAC measures a different outcome from NRS, and its estimates do not show the same pattern of group separation. Multiple endpoints increase the importance of knowing the planned analysis hierarchy and multiplicity approach. Those plans are not reported, so the outcome pattern is informative descriptively but does not establish a single confirmatory conclusion.

Finally, the sample-size illustrations show how planning depends on the size of the effect a future study is intended to detect. Smaller target effects require larger per-arm enrollment under the stated assumptions. These illustrations are distinct from the trial’s original design rationale, which is not reported. Together, the results underscore why design details, analysis plans, missing-data methods, and clinically meaningful thresholds are important alongside outcome estimates.

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.

Several trial-specific details needed for a fuller statistical assessment are not reported in the registry record. The arm descriptions contain no additional information about the assigned regimens, and the record does not state eligibility criteria beyond the broad population of older adults with knee osteoarthritis. Randomization is listed, but the sequence-generation and allocation-concealment methods are not described. Quadruple masking is listed without identifying the roles masked or the masking procedures.

The record does not provide the sponsor’s analysis plan or any reported analyses. The estimates and confidence intervals discussed are unadjusted recalculations from summary statistics. The analysis population, handling of participants who did not complete assigned interventions, and treatment of missing endpoint values are not reported. The extent to which these issues could affect the observed comparisons cannot be evaluated from group summaries alone.

The primary endpoint is measured at week 2 after 10 tDCS sessions. No longer-term outcome timeframe is posted for this primary result. The record does not report a clinical-importance threshold, so statistical estimates cannot be mapped to a defined meaningful-change criterion. The posted results also do not report an interaction analysis for the intervention combinations, limiting conclusions about how the components relate to one another.

Finally, more than one outcome and group comparison is available, but a multiplicity strategy is not reported. This makes the unadjusted p-values less suitable for broad confirmatory claims. These limitations do not negate the posted estimates; they define the scope of what can be inferred from the available registry information.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Home-based tDCS and Mindfulness-based Meditation for Self-management of Clinical Pain and Symptoms — NCT04375072.
• Registry record last updated 2025-11-12; status last verified 2025-10.
• Results first posted 2025-11-12.
• 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

The registry record describes a completed randomized, quadruple-masked, parallel-group trial sponsored by the University of Arizona, with enrollment of 208. It lists four combinations of active or sham tDCS and active or sham MBM for older adults with knee osteoarthritis. The primary outcome is change in NRS pain score from baseline to week 2 after 10 tDCS sessions, with a decrease indicating improvement.

The posted NRS means show more negative average changes in the groups assigned active tDCS than in the sham tDCS plus active MBM reference group; the recalculated estimates are unadjusted. WOMAC is posted as a secondary outcome, with no reported analyses listed. Serious adverse event and death counts are reported as 0 in each group. The registry does not report the trial’s original sample-size justification, analysis plan, multiplicity procedure, or missing-data methods.