Transcranial Direct Current Stimulation for Chronic Low Back Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Transcranial Direct Current Stimulation for Chronic Low Back Pain (NCT02768129), a randomized na study. The primary outcome is West Haven-Yale Multidimensional Pain Inventory (General Activity Subscale) Rating.

2. Clinical Question

The study’s stated aim was to examine whether stimulating brain regions involved in behavioral responses to chronic pain could affect the emotional component of pain, functioning, and quality of life. The registered primary outcome was the General Activity Subscale of the West Haven-Yale Multidimensional Pain Inventory (WHY-MPI), a measure of chronic pain’s effects on functioning. Its score ranges from 0-108, with higher scores indicating more activity and therefore a better outcome on this measure.

The posted results compare the group mean scores for active and sham tDCS. The active group mean was 48.4 among 10 participants, and the sham group mean was 35.3 among 11 participants. The estimated mean difference was 13.1 points in favor of the active group, with an interval estimate that extends from -3.695 to 29.89. The registry record does not describe the detailed analysis population or explain how the outcome time point was selected within the stated 8 weeks total.

3. Trial Design

The registry record describes a completed, randomized, triple-masked, parallel-group study of tDCS for chronic low back pain. Butler Hospital is listed as the sponsor. The study began in 2014-11, and primary completion is listed as 2018-04. The registered phase is NA. Enrollment is listed as 30.

Participants were assigned to active tDCS or sham tDCS. Each arm description specifies 10 sessions. The outcome results include 11 participants in the sham group and 10 in the active group. These outcome counts are not the same as the overall enrollment listing; the registry record does not provide a participant-flow account explaining the difference. It also does not report whether the masking applied to participants, care providers, outcome assessors, or another set of roles, so the specific masking arrangements cannot be described.

The primary outcome was a continuous score on the WHY-MPI General Activity Subscale, with a stated timeframe of 8 weeks total. The registry record lists two outcome measures, but no secondary outcome results are posted. It lists no statistical analyses. The record does not report the trial’s original sample-size justification, allocation ratio as a design target, or detailed analysis plan. The planning figures associated with the posted group results are separate illustrations, not the trial’s documented design assumptions.

The registered study description frames tDCS as a way to investigate central neural pathways involved in chronic pain and the behavioral response to pain. That research rationale is not itself an outcome finding. The results available for statistical interpretation concern the activity subscale scores and the reported safety counts.

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: Of the 30 participants that were consented, 9 participants were ineligible, withdrew, or were lost to contact before commencing tDCS.

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.

Population: The data collected from the 21 participants who completed tDCS treatment (either active or sham) is included in the analysis.

6. Primary Endpoint

The registry lists the primary outcome as West Haven-Yale Multidimensional Pain Inventory (General Activity Subscale) Rating, measured over 8 weeks total.

The primary endpoint is the West Haven-Yale Multidimensional Pain Inventory General Activity Subscale rating. It measures functioning in the context of chronic pain. The registry describes Subscale C as a validated measure of chronic pain’s effects on functioning and gives a possible score range of 0-108. Higher scores indicate more activity and are defined as a better outcome on this scale.

A continuous score preserves gradations in participants’ reported activity rather than reducing the measure to a simple category. Comparing group means therefore describes the average score difference between the active and sham groups. The posted mean was 48.4 in the active group and 35.3 in the sham group, with a reported mean difference of 13.1.

The registered timeframe is 8 weeks total. The record does not explain whether this refers to the full intervention and assessment period, nor does it specify the exact assessment visit used for the posted group summaries. It also does not state a threshold for a clinically important difference on this scale. Accordingly, the numerical score contrast can be described, but its clinical importance cannot be determined from the registry record alone.

7. Results Posted in the Registry

• Active tDCS: mean 48.40 versus 35.30 on control; difference 13.10 (95% CI -3.69 to 29.89), standardized effect d = 0.67; z-test p = 0.126.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the mean difference describe? A mean is the arithmetic average of the observed scores in a group. The posted mean difference compares the average score in the active tDCS group with the average in the sham group. Here the registry reports group means of 48.4 and 35.3 and a mean difference of 13.1. This is an absolute difference in score units, not a percentage change. The score’s direction matters: higher activity-subscale scores are defined as better on this measure. The result is therefore expressed as a difference in reported activity scores, not as a change in pain severity or a direct measure of emotional response.

What does the interval estimate add? A point estimate gives one value for the group contrast, but sampling variation means the underlying difference is uncertain. A confidence interval describes a range of values compatible with the data and a specified statistical procedure. In this registry result, the interval extends from -3.695 to 29.89. Because the registry record does not report the interval’s confidence level or the procedure used to construct it, those details should not be inferred. The interval’s inclusion of zero indicates that the posted estimate does not rule out no difference under the interval procedure.

What does a p-value mean? The posted unadjusted p-value is 0.126. In general, a p-value describes how unusual data at least as incompatible with a null model would be if that model and the test assumptions held. It is not a measure of effect size, clinical importance, or the chance that a hypothesis is true. Because the statistical test and any planned decision threshold are not reported in the registry record, the p-value cannot be tied to a fully documented analysis plan. The estimate and interval provide essential context for interpreting it.

Why does the small outcome count matter? In general, estimates based on relatively few observations tend to be less precise than estimates based on larger samples, all else being equal. The posted outcome groups contain 11 sham participants and 10 active participants. Their standard deviations are 17.7 and 21.2, respectively, indicating substantial variation in scores within each group. The registry record does not explain why these outcome counts differ from the overall enrollment of 30, or whether the posted summaries include all participants with available outcome data. No cause for the difference can be determined from the record.

What does the spread measure? The posted group summaries use means and standard deviations. A standard deviation describes how dispersed individual scores are around a group mean; it is not the uncertainty around the mean itself. The comparison also reports a pooled standard deviation of 19.44 and a standardized difference of 0.674. A standardized difference expresses the mean contrast relative to a measure of score spread, placing it on a scale without the original score units. It does not replace the absolute mean difference, and it does not by itself establish clinical importance.

Why can over-dispersion matter? General statistical explanation: a model that assumes less variability than the data actually contain can produce uncertainty estimates that are too small and tests that appear more conclusive than warranted. Conversely, allowing for more variability generally widens uncertainty. The posted outcome is analyzed as a continuous measure with standard deviations; the registry record does not report a model assessment or identify an over-dispersion adjustment. The concept is relevant to evaluating statistical models, but the record does not establish that over-dispersion occurred in this trial.

What analysis can be reconstructed? The posted comparison gives a mean difference, interval limits, pooled standard deviation, and unadjusted p-value. The record lists zero statistical analyses, so it does not document the sponsor’s inferential method, covariate adjustment, handling of repeated measurements, or analysis population. A recalculated contrast from summary statistics, if presented, would be a simple unadjusted recalculation and would not substitute for the sponsor’s own analysis. The registry record does not provide a sponsor analysis to compare with such a calculation.

What cannot be inferred? Statistical methods depend on design details such as the prespecified primary analysis, outcome timing, allocation handling, missing-data strategy, and multiplicity plan. Those details are not reported in the registry record. The randomized designation and parallel design describe broad trial features, but they do not reveal the exact statistical model. No particular assumption or analysis method should be attributed to this trial without a registry entry documenting it.

10. Confidence Intervals and Precision

The mean difference is 13.1 points, with an interval estimate from -3.695 to 29.89. This range conveys uncertainty around the estimated contrast: it includes zero and spans values below and above the point estimate. It therefore does not support a narrowly precise estimate of the size or direction of the group difference. The confidence level and construction method for the interval are not reported in the registry record.

Precision depends in part on the amount of information in the data and the variability of the measure. The posted groups include 11 participants in the sham arm and 10 in the active arm. Their standard deviations are 17.7 and 21.2. With these group sizes and observed spread, substantial uncertainty in the estimated difference is consistent with the broad interval. The posted values do not establish why the outcome counts are smaller than overall enrollment of 30.

The interval should not be interpreted as a range containing every participant’s response. It concerns uncertainty about the group contrast, not the distribution of individual scores. Nor does it establish which values are clinically important: no threshold for a meaningful difference is reported. The interval is most informative when read with the means, scale direction, and study’s limited posted outcome counts.

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 figures are participants per arm, not total events. They are illustrations based on the observed effect, not a record of the trial’s original design calculation. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses the stated fraction of the observed effect as the effect to detect. The trial’s own original sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect is the true one and the model assumptions hold. The 90% power column gives the corresponding per-arm number for a 90% chance under those same conditions. These are design-planning quantities, not properties measured after a trial has been completed.

The scenarios range from planning for 100% of the observed effect to planning for 75% and 50% of that effect. Smaller target effects require more participants per arm to achieve the same target power under the stated assumptions. For example, the listed 80% power figures increase from 35 participants per arm for 100% of the observed effect, to 62 for 75%, and 139 for 50%. The corresponding 90% power figures are 47, 83, and 186 participants per arm.

These calculations are planning illustrations based on the observed estimate, which is itself uncertain. They are not observed power and should not be used to claim that the completed trial had a particular probability of finding a result.

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 = 13.100; pooled standard deviation σ = 19.437.
2. n = 2 × (1.96 + 0.842)² × 19.437² / 13.100² = 34.6, rounded up to 35 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 <- 13.1                      # observed difference in means
sigma <- 19.4366176394752                     # 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(2768129)
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 = 35 (80% power), 47 (90% power)
 75% of observed effect: n per arm = 62 (80% power), 83 (90% power)
 50% of observed effect: n per arm = 139 (80% power), 186 (90% power)
power.t.test: 35.5 
Simulated power at n = 35 per arm: 0.790 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists two outcome measures, but no secondary outcome results are posted. It also lists zero statistical analyses. It does not report whether the investigators tested multiple outcomes, multiple time points, or multiple contrasts, or whether any multiplicity adjustment was planned. Without those details, the risk of inflated false-positive findings from multiple testing cannot be evaluated. The posted unadjusted p-value should not be treated as evidence that multiplicity was or was not addressed.

Missing-data handling is also not reported in the registry record. The overall enrollment is 30, while the primary outcome summaries include 11 participants in the sham group and 10 in the active group. The record does not provide a participant flow, reasons for absent outcome values, the number randomized to each group, or whether any participants were excluded from the outcome analysis. It is therefore not possible to identify the amount or pattern of missing outcome data or to judge whether a complete-case analysis, imputation, or another approach was used.

The analysis population is not reported. The registry does not say whether the posted results use all randomized participants, participants who received treatment, participants with available outcomes, or another defined group. It also does not describe adherence, protocol deviations, or any prespecified population definitions. These omissions matter because the population included in an analysis can affect the interpretation of a randomized comparison.

The record does not report the original statistical analysis plan, adjustment for baseline scores or other covariates, or any interim analyses. No conclusions about those choices can be drawn from the posted means and unadjusted p-value alone. The absence of these details limits reproducibility and makes it difficult to compare the reported result with a prespecified analysis, but it does not establish that a particular practice was or was not used.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The serious adverse event counts are zero in both groups. The registry lists 11 participants at risk in the sham group and 10 in the active group, with zero serious adverse events affecting participants in either group. The death count is also zero for each group. The registry’s serious adverse event terms list is empty.

The separate counts for adverse events other than serious adverse events are also zero in both groups: 0 of 11 in the sham group and 0 of 10 in the active group. These are the posted counts; they do not establish that no unrecorded events occurred. The registry record does not describe the event collection period, definitions, ascertainment process, or relationship assessment, so the scope and completeness of safety reporting cannot be evaluated from these figures alone.

Zero recorded events in these small outcome groups should be read as a description of the registry entries, not as proof that an event cannot occur. The counts are not a comparative estimate of risk with a reported uncertainty interval, and they do not establish a safety difference between groups.

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

The posted primary outcome summaries show a mean activity score of 48.4 in the active tDCS group and 35.3 in the sham group. The estimated mean difference of 13.1 points is in the direction of a higher average activity score for active tDCS, consistent with the scale’s definition that higher scores indicate more activity. The interval estimate, from -3.695 to 29.89, includes zero and is broad. The unadjusted p-value is 0.126.

Taken together, these figures describe an uncertain estimate rather than a definitive group contrast. The point estimate alone does not show how precisely the difference was estimated, and the p-value does not quantify the probability that the treatment has an effect. The interval allows for no difference as well as differences in either direction. The registry record does not report a threshold for a clinically important change, so the score contrast cannot be classified as clinically meaningful from the posted information.

The result does not establish that active tDCS improves functioning, nor does it establish that active and sham tDCS have equivalent effects. A conclusion either way would require a supported interpretation of the study’s prespecified analysis, outcome completeness, and analysis population. Those details are not reported in the registry record.

The finding also concerns one registered functioning measure over a timeframe of 8 weeks total. It does not directly report changes in pain intensity, emotional response, quality of life, or longer-term outcomes. Although those topics appear in the study rationale, the registry record does not post secondary outcome results for them. The available evidence should therefore be understood as a limited description of this particular score comparison, not as a broad conclusion about chronic low back pain or tDCS.

16. Why This Trial Matters Statistically

This trial is statistically informative because the observed point estimate and its uncertainty tell different parts of the story. The mean difference of 13.1 points favors a higher active-group average on a scale where higher scores indicate more activity. But the interval from -3.695 to 29.89 includes zero and remains broad. A single favorable point estimate cannot substitute for an assessment of precision.

The outcome groups are small: the posted summaries include 11 participants receiving sham tDCS and 10 receiving active tDCS. That limited information, together with the observed score variation, is relevant when interpreting the breadth of the interval. The registry record lists enrollment of 30 but does not account for the difference between enrollment and the primary outcome counts. Participant flow and outcome completeness are important to understanding what population the estimate describes.

The record also illustrates why statistical interpretation depends on more than a p-value. The unadjusted p-value is 0.126, but the registry does not report the test, analysis plan, multiplicity handling, or analysis population. Without that context, the p-value cannot serve as a complete account of the evidence.

Finally, the trial’s scientific rationale and its posted outcome result should remain distinct. The study set out to investigate central pain pathways and behavioral responses to chronic pain, while the primary posted result is a functioning score. The result can inform understanding of that measured comparison, but the registry record does not support conclusions about every aspect of the study’s broader rationale.

17. 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 limitation for interpreting the result is the small number of participants represented in the posted outcome groups: 11 in sham and 10 in active tDCS. The record lists overall enrollment of 30 but does not explain the outcome counts or provide a participant-flow account. Without that information, the extent and reasons for missing outcomes cannot be assessed.

The statistical analysis is not documented in detail. The registry lists no statistical analyses and does not report the test used, the interval confidence level, the prespecified analysis population, or any adjustment for baseline values or other covariates. It also does not report an original sample-size rationale. These gaps make it difficult to assess whether the posted summaries match a prespecified plan.

The primary outcome timeframe is stated as 8 weeks total, but the exact assessment visit and the timing relative to treatment sessions are not specified. The record does not report a clinically important difference threshold for the activity scale. Therefore, the practical importance of a 13.1-point mean difference cannot be determined from the registry entries alone.

Secondary outcome results are not posted, despite two outcome measures being listed. The record does not provide enough information to assess multiplicity or to interpret outcomes beyond the primary score. The masking designation is triple, but the record does not describe which roles were masked. Finally, safety counts are zero in the listed groups, but details of event definitions and ascertainment are not reported. These limitations constrain interpretation; they do not by themselves demonstrate that the trial procedures were inadequate.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Transcranial Direct Current Stimulation for Chronic Low Back Pain — NCT02768129.
• Registry record last updated 2019-08-20; status last verified 2019-07.
• Results first posted 2019-08-20.
• 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.

21. Record Summary

The registry record describes a completed, randomized, triple-masked, parallel-group study sponsored by Butler Hospital, with enrollment of 30. It compares 10 sessions of active tDCS with 10 sessions of sham tDCS in adults with chronic low back pain. The registered primary outcome is the WHY-MPI General Activity Subscale score over 8 weeks total, with higher scores indicating more activity.

The posted outcome summaries include 11 participants in the sham group and 10 in the active group. Their means are 35.3 and 48.4, respectively; the reported mean difference is 13.1, with an interval from -3.695 to 29.89 and an unadjusted p-value of 0.126. Serious and other adverse event counts, as well as deaths, are zero in both groups. The registry record does not report the detailed statistical plan, participant flow, missing-data handling, or analysis population.