Efficacy of the Quell Wearable Device for Chronic Low Back Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy of the Quell Wearable Device for Chronic Low Back Pain (NCT02944513), a randomized na study. The primary outcome is Pain Intensity (Average).

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group trial with no masking. The experimental group was assigned to receive the Quell device, while the control group was assigned not to receive it. The intervention is classified as a device. The registry record reports enrollment of 68 and identifies Brigham and Women's Hospital as the sponsor. It lists the study as completed, with a start date of 2016-10 and primary completion in 2018-08.

The brief description calls this a 1-year trial designed to gather information about Quell use among people with chronic musculoskeletal low back pain. The primary outcome reported for this analysis is measured at 3 months. The registry record therefore gives both a broad study duration description and a specific primary-outcome timeframe; the 3-month result should be interpreted as an assessment at that stated time, not as a result across the full year.

The record reports 35 subjects consented in the experimental group, of whom 4 dropped out and 2 did not complete the 3-month questionnaire; 29 were analyzed. In the control group, 33 subjects were consented, 1 dropped out and 1 did not complete the questionnaire; 31 were analyzed. The enrollment figure and the arm-specific consent and analysis counts describe different stages or record fields. The posted primary analysis is based on the reported analyzed groups.

One secondary outcome is listed: the Post-study Helpfulness Questionnaire. The record lists 6 outcome measures overall and 0 analyses. It does not report the original sample-size justification, the planned statistical analysis, allocation concealment, the method used to generate the random sequence, or details of the device-use protocol. Those design details are not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: For the experimental group, 35 subjects were consented, 4 subjects dropped out, 2 subjects did not complete the 3-month questionnaire, so 29 subjects were analyzed. For the control group, 33 subjects were consented, 1 subject dropped out, 1 subject did not complete the 3-month questionnaire, so 31 subjects were analyzed.

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 Pain Intensity (Average), measured over 3 months.

The primary endpoint is average pain intensity, measured as a score on a scale at 3 months. The record specifies a visual analog scale from 0 to 10: 0 means no pain and 10 means the worst possible pain. Higher scores indicate a worse outcome. The endpoint is treated as a continuous measure, and the posted group summaries are means with standard deviations.

General: A continuous pain score preserves information about the location and spread of responses across a scale. Comparing group means provides a summary of the average score in each group, while the standard deviations describe variability among participants. The mean alone does not show the full distribution of individual ratings, nor whether every participant's experience was similar.

Average pain intensity is relevant to the stated question because it expresses participants' ratings of pain at the trial's specified assessment. It is not a measure of every aspect of low back pain or functioning. The registry record does not specify a clinically important threshold for interpreting score changes, nor does it report how the scale was administered beyond identifying it as a visual analog scale. The posted result therefore describes the group-average scores and their estimated difference, rather than establishing the clinical importance of that difference.

The experimental group mean was 4.0, with a standard deviation of 2.5; the control group mean was 5.7, with a standard deviation of 1.9. These summaries refer to the participants analyzed at 3 months. They do not, on their own, describe changes from baseline, since baseline pain results are not reported in the registry record.

7. Results Posted in the Registry

• Experimental: mean 4.00 versus 5.70 on control; difference -1.70 (95% CI -2.83 to -0.57), standardized effect d = -0.77; z-test p = 0.003.

8. Statistical Interpretation

9. Statistical Methods Explained

General: A randomized parallel-group design assigns participants to groups intended to differ in the intervention under study, then compares outcomes between those groups. Random assignment can help balance measured and unmeasured characteristics on average, but it does not guarantee identical groups, especially in a trial with finite group sizes. The registry record identifies the study as randomized and parallel but does not report how the random sequence was generated or how assignment was concealed.

What does the mean difference represent?

The reported group means are 4.0 for the experimental group and 5.7 for the control group. The recalculated contrast is expressed as experimental minus control, giving -1.7. Because the scale is oriented so that higher scores mean worse pain, a negative contrast means the experimental group's average score was lower at the stated assessment. This is a description of the direction of the group-average difference, not a claim that all participants had lower scores.

The calculation is unadjusted: it compares the reported summary values without incorporating baseline scores or other participant characteristics. An adjusted estimate could differ if an analysis accounted for such information, but no adjusted estimate is reported in the registry record. The record also does not identify the statistical test or model used for an original sponsor analysis. The displayed contrast is a recalculation from the posted summary statistics, not a substitute for an undocumented analysis plan.

How should standard deviations be understood?

General: A standard deviation describes the spread of individual values around a group's mean. It is not the same as a standard error, which describes uncertainty in an estimated mean, and it is not a confidence interval. The posted standard deviations are 2.5 in the experimental group and 1.9 in the control group. They indicate that participant scores were not all concentrated exactly at their respective group means, but they do not show the shape of the score distributions or the presence of outliers.

General: Standard deviations matter in a comparison because the variability of observations contributes to the uncertainty of the estimated difference. With more variability, the group mean is generally less precise for a fixed number of participants. The recalculation uses the reported group sizes and variability; the registry record does not report a separate model accounting for other sources of variation.

What does the confidence interval add?

The 95% confidence interval for the mean difference extends from -2.829 to -0.571. General: A confidence interval is a range produced by a statistical procedure that, under its assumptions, has a stated long-run coverage property. It represents uncertainty in the estimated contrast. It is not a range containing a fixed proportion of individual participants' scores, and it does not mean that there is a 95% probability that the true value lies inside this particular interval.

The interval is entirely on the negative side of the zero-difference value. General: Zero represents no difference between the group means on the contrast scale. The interval therefore indicates that the recalculated unadjusted data are compatible with a negative mean difference under the calculation's assumptions. The interval does not address whether the size of the difference matters to participants, because a clinically important threshold is not reported.

What is the role of the p-value?

The posted unadjusted p-value is 0.003. General: A p-value is calculated under a null hypothesis and model assumptions; it describes how unusual data at least as extreme as those observed would be if the null model held. It is not an effect-size measure and is not a measure of the probability that a result happened “by chance.” The p-value does not account for unreported choices about outcome selection, analysis populations, or multiplicity.

The record lists 6 outcome measures and 0 analyses. It does not report whether the primary comparison was selected before data inspection, whether other analyses were planned, or how multiple outcomes or time points were handled. Consequently, the p-value should be interpreted as an unadjusted result for the posted primary endpoint, not as a result adjusted for a broader family of comparisons.

What is known about the analyzed groups?

The reported primary analysis includes 29 experimental-group participants and 31 control-group participants. The registry describes the group flow from consent through dropout, questionnaire completion, and analysis. It does not report an intention-to-treat analysis, the handling of missing questionnaire responses, or whether all randomized participants were included in any other analysis. The reasons for dropout and noncompletion are not reported in the registry record.

General: An analysis population is the set of participants whose data are included in a particular analysis. Different choices can affect interpretation, particularly when outcomes are missing. An intention-to-treat approach generally aims to analyze participants according to randomized assignment, while other approaches may use only participants with available outcomes or otherwise defined populations. The record's stated analyzed counts are informative, but the analysis-population label and missing-data method are not reported.

Overall, the statistical result is a clear numerical summary of the posted 3-month means, with a confidence interval and unadjusted p-value. The record does not contain enough detail to reconstruct a full prespecified statistical analysis plan or determine how alternative assumptions and analysis choices would affect the result.

10. Confidence Intervals and Precision

The recalculated unadjusted mean difference is -1.7, with a 95% confidence interval from -2.829 to -0.571. In the contrast's direction, experimental minus control, both interval limits are negative. The interval therefore conveys that the reported group means are compatible with a lower average score in the experimental group under the calculation's assumptions. It also shows that the exact size of the difference is uncertain.

General: A confidence interval combines an estimate with information about its precision. A narrower interval indicates less uncertainty on the same measurement scale than a wider interval, while a wider interval leaves more possible values compatible with the data. The interval is not a prediction range for individual scores and is not a guarantee that the population value lies within its limits.

The endpoint's standard deviations were 2.5 for the experimental group and 1.9 for the control group, with analyzed groups of 29 and 31. Those summaries help describe the information underlying the comparison, but they do not show participant-level distributions. The confidence interval should not be interpreted as describing the range of pain ratings among individuals.

The record does not report a clinically important difference threshold, so the interval alone cannot determine whether every value within it would be important in practice. It also does not provide an adjusted estimate, a baseline comparison, or a separate result at a later assessment. The interval applies to the recalculated unadjusted contrast for the posted 3-month outcome; broader claims are not supported by this estimate.

The unadjusted p-value is 0.003. General: Statistical significance and precision are related but distinct concepts. The p-value summarizes compatibility with a null model, whereas the interval displays a range of plausible contrast values under its calculation assumptions. Neither measure, by itself, answers whether the size of the observed group difference is meaningful to participants.

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 planning illustrations based on the observed effect, with scenarios that use 100%, 75%, and 50% of that observed effect. The assumptions listed for these illustrations 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 80% power column means the illustrated number of participants per arm for a design with an 80% chance of detecting the specified effect if that effect and the planning assumptions are correct. The 90% power column gives the corresponding planning number for a 90% chance under those assumptions. These are design calculations, not results from the trial. The registry record's original design assumptions and sample-size justification are not reported in the registry record.

General: Power is a property of a planned test under specified assumptions. The planning values use the observed effect as a starting point, but an observed estimate can be uncertain and may not be the effect a future study should expect. Smaller effects require more participants to detect with the same target power, all else equal. The figures are therefore useful for understanding how assumptions about the effect size influence planning, not as a guarantee that a future study would obtain a particular result.

This is not observed power. The figures do not describe the chance that the completed trial detected its observed result, and they do not replace interpretation of the estimate and its confidence interval. They are illustrative participant counts per arm under the stated planning 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 = -1.700; pooled standard deviation σ = 2.210.
2. n = 2 × (1.96 + 0.842)² × 2.210² / -1.700² = 26.5, rounded up to 27 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -1.7                      # observed difference in means
sigma <- 2.21008659527646                     # 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(2944513)
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 = 27 (80% power), 36 (90% power)
 75% of observed effect: n per arm = 48 (80% power), 64 (90% power)
 50% of observed effect: n per arm = 107 (80% power), 143 (90% power)
power.t.test: 27.5 
Simulated power at n = 27 per arm: 0.798 (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 6 outcome measures, including the primary outcome of average pain intensity and the secondary outcome Post-study Helpfulness Questionnaire. It reports 0 analyses. The record does not state whether all listed outcomes were measured, which were analyzed, or whether there were additional time points or comparisons. The registry record does not report a multiplicity adjustment or a plan for controlling the chance of false-positive findings across multiple outcomes or analyses.

General: Multiplicity arises when several hypotheses or outcomes are examined. If many comparisons are made, the chance of at least one apparently notable result can increase unless the analysis plan addresses that issue. A single unadjusted p-value should therefore be read as applying to its stated comparison, rather than automatically as accounting for all outcomes or analyses that may have been considered. The record does not provide enough information to determine the broader analysis family.

The primary-outcome record describes 35 experimental-group subjects consented, 4 dropped out, 2 did not complete the 3-month questionnaire, and 29 were analyzed. It describes 33 control-group subjects consented, 1 dropped out, 1 did not complete the questionnaire, and 31 were analyzed. These counts identify missing outcome data and attrition before the reported analysis. Reasons for dropout and noncompletion are not reported in the registry record.

The method for handling missing outcomes is not reported in the registry record. There is no reported imputation method, sensitivity analysis, or comparison of participants with and without observed scores. It is also not reported whether the analysis followed an intention-to-treat principle or used another defined analysis population. The analyzed counts can be stated, but the record does not allow a reader to assess how assumptions about missing outcomes might affect the estimate.

General: Missingness matters because conclusions can depend on whether participants with observed outcomes differ systematically from those without them. Without information about the reasons for missing data and the analysis method, the direction and size of any resulting bias cannot be determined. The result should be understood as a comparison among the participants included in the reported 3-month analysis.

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 registry reports 0 serious adverse events in the experimental group among 35 at risk and 0 in the control group among 33 at risk. It also reports 0 other adverse events among 35 at risk in the experimental group and 0 among 33 at risk in the control group. Deaths are reported as 0 in each group. No serious adverse-event terms are listed.

These are the registry's reported counts for the groups and categories specified. A count of zero means that no events were posted in that category for the stated group; it does not by itself establish that no event occurred outside the record's collection or reporting procedures. The record does not provide further detail about event definitions, surveillance, severity grading, relatedness assessment, or the duration of safety follow-up.

General: Adverse-event counts are descriptive safety information. They do not alone establish that an intervention is safe or unsafe, and interpretation depends on how events were solicited, defined, followed, and reported. The registry record gives the at-risk group counts and event counts, but does not report additional safety-analysis details. The figures should be read as the posted record, not as a comprehensive accounting of all possible harms.

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

The posted primary result describes average pain intensity at 3 months. The experimental-group mean was 4.0 and the control-group mean was 5.7 on a 0-to-10 scale where higher scores indicate worse pain. The recalculated unadjusted mean difference was -1.7, with a 95% confidence interval from -2.829 to -0.571 and an unadjusted p-value of 0.003. These values indicate that the reported group averages differed at the stated assessment, with the experimental group having the lower mean score.

This finding does not show that every participant receiving the device had a lower score, or that every control participant had a higher score. Group means do not reveal individual trajectories, and the registry does not report baseline scores in the posted primary result. The comparison therefore cannot be described as a change from baseline based on the information reported.

The result also does not establish the clinical importance of the difference. The registry record does not report a threshold for a meaningful difference on the pain scale. Statistical evidence and practical importance are separate questions: the estimate and interval describe the size and uncertainty of the group-average contrast, but they do not by themselves define its value to patients.

The result applies to the reported 3-month outcome and analyzed participants. It does not establish whether any difference persisted through the 1-year trial description, whether the same pattern occurred at other assessments, or whether other outcomes differed. The listed secondary outcome is a Post-study Helpfulness Questionnaire, but results for that outcome are not reported in the registry record.

The trial was randomized, but masking was listed as none. The posted comparison is an unadjusted recalculation, and the registry record does not report the full analysis plan, missing-data method, or multiplicity handling. These limits do not erase the numerical result; they define what can be concluded from it. The result is best read as a statistical description of the reported groups at the specified time, rather than a broad statement about all uses of the device or all people with chronic low back pain.

16. Why This Trial Matters Statistically

This trial is statistically informative because it reports a continuous primary outcome with group means, standard deviations, analyzed group sizes, and an estimated contrast with a confidence interval. Together, these quantities allow readers to consider both the direction of the group-average difference and the uncertainty around its size. The negative mean difference is interpretable in context because the scale direction is specified: higher pain scores mean worse outcomes.

The record also makes attrition visible. It reports the numbers consented, dropped out, missing the 3-month questionnaire, and analyzed in each group. These details matter because the primary comparison reflects participants with reported outcome data, while the registry record does not state how missing outcomes were handled. The group-flow information helps identify where interpretation depends on information not included in the record.

The example also distinguishes a posted result from a complete statistical analysis plan. An unadjusted recalculation can clarify the summary comparison, but the record lists 0 analyses and does not report adjustment, multiplicity handling, or a sample-size justification. Reporting an estimate, interval, and p-value does not answer every question about design or analysis.

Finally, the record pairs a 1-year study description with a primary endpoint at 3 months. Keeping those timeframes separate prevents a single assessment from being mistaken for evidence about the whole study period. The statistical value of the result lies in what it directly quantifies: a 3-month difference between reported group means, with uncertainty and important reporting limitations made explicit.

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 registry record describes a randomized trial but lists masking as none. It does not report details of random-sequence generation or allocation concealment. Those omissions limit assessment of how assignment was implemented. The record also does not describe the device-use schedule, participant instructions, adherence, or whether use was monitored, so the intervention's implementation cannot be characterized further.

The primary result is reported at 3 months, while the brief description calls the study a 1-year trial. Other assessment-time results are not reported in the registry record. Baseline pain scores are also not reported with the primary outcome, so the posted comparison cannot establish a difference in change from baseline. The registry record does not report a clinically important threshold for the scale.

The analyzed primary groups include 29 experimental-group participants and 31 control-group participants, following the reported consent, dropout, and questionnaire-completion counts. The record does not report why participants dropped out or did not complete the questionnaire, how missing values were handled, or whether sensitivity analyses were conducted. This leaves uncertainty about the effect of missing outcomes on the comparison.

The statistical comparison is an unadjusted recalculation from the posted summary statistics. The record lists 0 analyses and does not report a prespecified statistical plan, multiplicity approach, original sample-size justification, or adjusted analysis. One secondary outcome is listed, but its results are not reported in the registry record. Safety reporting gives zero posted adverse events in the listed categories, but further information about event ascertainment and follow-up is not reported.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Efficacy of the Quell Wearable Device for Chronic Low Back Pain — NCT02944513.
• Registry record last updated 2022-04-25; status last verified 2022-04.
• Results first posted 2019-02-26.
• 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

NCT02944513 is a completed randomized, unmasked, parallel-group device trial sponsored by Brigham and Women's Hospital. It studied the Quell wearable device for chronic musculoskeletal low back pain and had reported enrollment of 68. The registry record lists a start date of 2016-10 and primary completion in 2018-08.

The primary endpoint was average pain intensity at 3 months, rated on a 0-to-10 visual analog scale, with higher scores indicating worse pain. The experimental-group mean was 4.0 and the control-group mean was 5.7. The recalculated unadjusted mean difference was -1.7, with a 95% confidence interval from -2.829 to -0.571 and an unadjusted p-value of 0.003.

The registry record lists the Post-study Helpfulness Questionnaire as a secondary outcome, 6 outcome measures, and 0 analyses. It reports 0 serious adverse events, 0 other adverse events, and 0 deaths in each group. The original sample-size justification, detailed analysis plan, and missing-data method are not reported in the registry record.