An Acupuncture Functional Magnetic Resonance Imaging (fMRI) Study on Chronic Pain: Response Reliability and Dose Effect: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for An Acupuncture Functional Magnetic Resonance Imaging (fMRI) Study on Chronic Pain: Response Reliability and Dose Effect (NCT01079390), a randomized na study. The primary outcome is Knee Injury and Osteoarthritis Outcome Score (KOOS Pain Rating) at 5-7 Weeks Post-Treatment.

2. Clinical Question

3. Trial Design

The study was a randomized, single-masked, parallel-group trial of acupuncture in people with knee osteoarthritis. The registry lists 44 participants as enrolled and reports the study as completed. Its recorded dates are a start in 2010-01 and primary completion in 2013-01. The study is listed as phase NA. Massachusetts General Hospital is the listed sponsor.

Three groups are described: high-dose acupuncture, low-dose acupuncture, and placebo acupuncture. The high-dose arm description says six needles were applied; the low-dose description says two needles were applied. The placebo arm is described as sham acupuncture. The allocation is recorded as randomized, masking as single, and model as parallel. The identity of the person or people masked, the randomization procedure, and the methods used to maintain masking are not reported in the registry record.

The registry's brief summary describes a plan to examine brain responses across multiple treatment sessions, including response reliability and the effects of different acupuncture doses. It also describes an aim to investigate acupuncture efficacy. The clinical result posted for interpretation is a KOOS pain-rating outcome, while fMRI findings and other brain-response results are not reported in the registry record.

The primary outcome is identified as a mean on the KOOS pain rating, with standard deviation as the dispersion measure. Its title places the measurement at 5-7 weeks post-treatment, while the timeframe describes one post-treatment measurement 5-7 weeks after baseline. The record does not clarify this wording. The posted outcome groups each contain 10 participants. The adverse-event groups list 15, 15, and 14 participants at risk, respectively; the record does not explain the difference between the safety counts and the outcome counts.

Further trial details, including the original sample-size justification, the full treatment schedule, participant flow, and the analysis population definitions, 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: Fourteen subjects did not complete the study due to problems with scheduling (6), ineligibility at screening (3), disinterest (2), claustrophobia (1), or inability to adhere to study requirements in scanner (2). Of the 14 subjects who dropped, four dropped out after randomization.

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 Knee Injury and Osteoarthritis Outcome Score (KOOS Pain Rating) at 5-7 Weeks Post-Treatment, measured over One post-treatment measurement 5-7 weeks after baseline.

The posted primary endpoint is the Knee Injury and Osteoarthritis Outcome Score (KOOS) pain rating. It is intended to measure pain-related symptoms in people with knee osteoarthritis. The registry description says KOOS includes five subscales: pain, other symptoms, function in daily living, function in sport and recreation, and knee-related quality of life. It says the pain, daily-living function, and sport-and-recreation function subscales were selected as primary outcomes in the study description. However, the posted primary result is specifically titled as the KOOS pain rating.

The registry describes an original KOOS scale from 0 to 4, where 0 means no pain and 4 means extreme pain, and also describes normalized subscale scores from 0 to 100, where 0 indicates the most extreme symptoms or pain and 100 indicates no symptoms or pain. The posted endpoint is reported in units on the KOOS scale, with a mean and standard deviation. This difference in scale descriptions is not clarified in the registry record; readers should interpret the displayed group summaries in the context of the normalized-score description and the stated endpoint units rather than assume an unreported transformation.

The outcome is a clinical measure, distinct from the study's stated fMRI aims. The registry gives its timing as one post-treatment measurement 5-7 weeks after baseline, while the endpoint title says 5-7 weeks post-treatment. The exact timing relative to treatment is therefore not fully clear from the record. No additional primary outcome results are posted.

7. Results Posted in the Registry

• High Dose Acupuncture: mean 59.00 versus 56.00 on control; difference 3.00 (95% CI -11.27 to 17.27), standardized effect d = 0.18; z-test p = 0.680.
• Low Dose Acupuncture: mean 53.00 versus 56.00 on control; difference -3.00 (95% CI -16.03 to 10.03), standardized effect d = -0.20; z-test p = 0.652.

8. Statistical Interpretation

9. Statistical Methods Explained

For the primary continuous outcome, the registry reports a mean and standard deviation for each group. A mean describes the average observed score among participants included in that group summary. A standard deviation describes how dispersed individual scores are around that group mean; it is not the uncertainty interval for the mean. The posted group summaries are 59.0 with a standard deviation of 13.0 for high-dose acupuncture, 53.0 with a standard deviation of 9.0 for low-dose acupuncture, and 56.0 with a standard deviation of 19.0 for placebo acupuncture. Each summary includes 10 participants.

The posted comparisons express each acupuncture group's mean relative to the placebo group's mean. For high-dose acupuncture, the mean difference is 3.0; for low-dose acupuncture, it is -3.0. The sign gives the direction relative to the placebo mean under the registry's comparison convention. These are differences between group averages, not the size of change within a participant, and the registry does not post baseline outcome means that would permit interpretation as before-and-after changes.

A confidence interval describes a range of values compatible with the observed data under the statistical procedure used. In general, a wider interval indicates less precision, while an interval that includes zero does not establish a nonzero mean difference at the corresponding confidence level. The high-dose comparison has a 95% confidence interval from -11.27 to 17.27; the low-dose comparison has a 95% confidence interval from -16.03 to 10.03. Both intervals include zero. They also include differences in both directions, so the estimates do not sharply distinguish a benefit-direction difference from a difference in the opposite direction. Confidence intervals do not by themselves tell whether a difference matters clinically; the registry does not report a meaningful-difference threshold.

The registry posts unadjusted p-values of 0.68 for high-dose acupuncture versus placebo and 0.652 for low-dose acupuncture versus placebo. A p-value is a measure of how incompatible the observed result is with a specified null model, under the assumptions of the test. It is not the probability that the null hypothesis is true, nor is it a measure of the probability that a result occurred by chance. The registry does not identify the exact test or give the full analysis procedure, so the p-values should be read as posted rather than attributed to a more detailed method that is not documented.

The comparison estimates also include recalculated quantities based on posted summary statistics. These are simple, unadjusted recalculations, not additional participant-level analyses. The registry does not flag a discrepancy between those recalculations and the posted comparison results. They do not replace an analysis using individual participant data, and they cannot account for adjustment or modeling choices that are not reported.

General statistical context: small groups and substantial variation can make a mean difference difficult to estimate precisely. Greater dispersion relative to the difference tends to make confidence intervals wider. The posted placebo standard deviation, 19.0, is larger than the standard deviations reported for either acupuncture group, but no distributional plots or participant-level values are reported, so the pattern of individual scores cannot be assessed from the means and standard deviations alone.

General statistical context: when an outcome has a distribution with more variability than a simple model assumes, over-dispersion can make model-based standard errors too small if it is ignored. The reported primary endpoint is analyzed as a continuous mean, and the registry does not report an over-dispersion assessment or model specification. There is not enough detail to determine whether this issue was relevant to the trial's original analyses.

The study's original statistical plan, including its analysis model, covariate adjustment, handling of repeated measurements, and any interim analyses, is not reported in the registry record. The study description mentions multiple sessions and response reliability, but that aim alone does not establish how repeated data were analyzed. The posted primary result is a single post-treatment measurement, and the record does not document whether baseline values or other covariates were included.

Power calculations are also distinct from the observed comparisons. The posted planning illustrations use the observed effect and evaluate smaller fractions of that effect under stated assumptions. They do not disclose the trial's original design justification. The interpretation of those illustrations is addressed separately in the sample-size discussion; they should not be mistaken for evidence that the trial had a particular probability of detecting an effect.

10. Confidence Intervals and Precision

The confidence intervals show that both posted mean-difference estimates are uncertain. For high-dose acupuncture compared with placebo, the estimated difference is 3.0, with a 95% confidence interval from -11.27 to 17.27. For low-dose acupuncture compared with placebo, the estimate is -3.0, with a 95% confidence interval from -16.03 to 10.03. Both intervals cross zero, meaning the compatible values include no difference as well as differences in either direction.

The intervals are broad relative to the point estimates. They do not isolate a narrow range of plausible group differences, so the precise magnitude and direction remain uncertain. The outcome groups each include 10 participants, and the reported standard deviations range from 9.0 to 19.0. Variation among observed scores, alongside the small group summaries, is relevant to the limited precision. The registry does not post individual observations, so the distribution of scores and potential influence of unusual values cannot be evaluated.

A confidence interval is not a guarantee that the true difference lies within its endpoints, nor does inclusion of zero prove that the groups are equivalent. Demonstrating equivalence would require a prespecified margin and an analysis designed for that question; neither is reported in the registry record. Likewise, the record does not give a threshold for a clinically important KOOS difference. Statistical uncertainty can therefore be described, but clinical importance cannot be determined from the posted interval alone.

The confidence intervals are presented for each comparison, while the registry does not report a multiplicity adjustment. Their interpretation should be understood as applying to the posted comparisons individually, rather than as simultaneous coverage for a larger set of outcomes or analyses.

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 the trial's original design assumptions; those original assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect.

The 80% power column gives the estimated number of participants per arm under those assumptions for a design with an 80% chance of detecting the specified effect, if that effect and the assumptions were correct. The 90% power column gives the corresponding number per arm for a 90% chance. These are planning concepts, not properties measured from the trial's results. This is not observed power.

For high-dose acupuncture versus placebo, planning for 100% of the observed effect gives 463 participants per arm for 80% power and 619 for 90% power. Planning for 75% of the observed effect gives 822 participants per arm for 80% power and 1,101 for 90% power. Planning for 50% of the observed effect gives 1,849 participants per arm for 80% power and 2,476 for 90% power.

For low-dose acupuncture versus placebo, planning for 100% of the observed effect gives 386 participants per arm for 80% power and 517 for 90% power. Planning for 75% of the observed effect gives 686 participants per arm for 80% power and 918 for 90% power. Planning for 50% of the observed effect gives 1,542 participants per arm for 80% power and 2,065 for 90% power.

The pattern reflects a general principle: smaller effects are harder to distinguish from random variation and therefore require more participants under the same assumptions. Because the observed effects come from small groups and are uncertain, these illustrations should not be treated as definitive sample-size recommendations. A curve, where displayed, visualizes the same planning relationship rather than adding evidence about the trial's observed outcomes.

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 = 3.000; pooled standard deviation σ = 16.279.
2. n = 2 × (1.96 + 0.842)² × 16.279² / 3.000² = 462.2, rounded up to 463 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                      # observed difference in means
sigma <- 16.2788205960997                     # 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(1079390)
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 = 463 (80% power), 619 (90% power)
 75% of observed effect: n per arm = 822 (80% power), 1,101 (90% power)
 50% of observed effect: n per arm = 1,849 (80% power), 2,476 (90% power)
power.t.test: 463.2 
Simulated power at n = 463 per arm: 0.802 (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 posts two comparisons for the primary KOOS result: high-dose acupuncture versus placebo and low-dose acupuncture versus placebo. It gives an unadjusted p-value for each. The record does not report whether these comparisons were designated as co-primary, whether one was the principal contrast, or whether a multiplicity adjustment was planned or applied. It also does not report a hierarchy or a prespecified strategy for interpreting multiple tests. The p-values should therefore be understood as unadjusted results, without assuming they control error across a larger family of analyses.

The record lists two outcome measures overall, but no secondary outcome results are posted. The brief study summary refers to brain-response reliability and dose effects, yet fMRI results are not present in the posted results. The record does not clarify whether those measures were planned secondary outcomes, exploratory outcomes, or collected but not reported. Results for the other KOOS subscales mentioned in the outcome description are also not reported in the registry record.

Missing-data handling is not reported in the registry record. There is no posted account of how many participants lacked the primary outcome, whether imputation was used, or how missing observations were handled in the analysis. The outcome summaries list 10 participants per group, whereas the safety summaries list 15, 15, and 14 participants at risk. The registry does not explain this difference, and the posted information does not establish why the counts differ.

Analysis populations are not described. The record does not state whether the primary comparison used an intention-to-treat population, a per-protocol population, or another defined set of participants. It also does not describe exclusions after randomization or participant flow by arm. These omissions limit assessment of how the randomized groups were represented in the posted outcome analysis.

The protocol-level statistical analysis plan, interim analyses, and any adjustments for baseline characteristics are not reported in the registry record. No conclusion about those procedures should be inferred from the posted summary statistics alone.

14. Safety Results

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

Other (non-serious) adverse events

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

The registry lists serious adverse events as zero affected participants in each group: high-dose acupuncture had 0 among 15 at risk, low-dose acupuncture had 0 among 15 at risk, and placebo acupuncture had 0 among 14 at risk. It also lists other adverse events as zero affected participants in each of those respective groups. No serious-event terms are listed. These entries describe what is recorded in the registry, not proof that no events occurred outside the reported definitions, observation period, or reporting process.

The safety denominators differ from the primary outcome summaries, which list 10 participants per arm. The registry does not explain the denominator difference. It also does not give details such as event collection procedures, event definitions, follow-up duration for safety, or whether the listed at-risk counts refer to everyone randomized or another group. Death counts are not reported in the registry record.

Zero reported affected participants should not be interpreted as evidence that the groups have identical safety profiles. With limited group counts and no further safety detail, the registry entries provide a narrow description of reported event counts rather than a complete characterization of risk.

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

The posted clinical results show average KOOS scores of 59.0 for high-dose acupuncture, 53.0 for low-dose acupuncture, and 56.0 for placebo acupuncture, with 10 participants included in each outcome summary. The estimated high-dose mean difference relative to placebo is 3.0, and the estimated low-dose difference is -3.0. Both confidence intervals include zero and extend in both directions. The results therefore do not precisely determine the direction or magnitude of either comparison.

These findings do not establish that acupuncture is effective or ineffective, and they do not show that the groups are equivalent. The registry does not report a clinically meaningful threshold for the KOOS score or an equivalence margin. The intervals leave room for multiple possible differences, and the observed averages are not a substitute for a prespecified clinical interpretation.

The record's description concerns both clinical outcomes and brain responses to repeated acupuncture sessions. Only the KOOS pain result is posted for the primary clinical outcome. No fMRI results are reported, so the available results do not answer whether brain responses were reliable across sessions or whether dose altered brain response. Nor do they allow conclusions about the other KOOS subscales described in the record.

The results also do not establish what occurred for participants whose outcomes may not be included in the summaries. Missing-data procedures, analysis populations, and participant flow are not reported. The outcome groups are smaller than the safety at-risk groups, and the reason is not documented. This limits the ability to assess whether the reported outcome summaries represent all randomized participants.

The appropriate statistical reading is therefore limited: the registry posts small-group mean comparisons with broad uncertainty, alongside incomplete information about analysis methods and outcome reporting. These results can describe the posted scores and their uncertainty, but they do not support stronger conclusions about clinical importance, brain mechanisms, or the full pattern of trial outcomes.

16. Why This Trial Matters Statistically

This trial illustrates how a study can have several related scientific aims while the available registry results address only part of them. Its description emphasizes session-to-session brain-response reliability and the effect of acupuncture dose, while the posted primary clinical result is a KOOS pain score. Because fMRI findings are not reported, the clinical summaries cannot be used as a substitute for the stated brain-response outcomes.

It also illustrates why point estimates need to be read with their confidence intervals. The observed differences are 3.0 and -3.0, but the respective intervals extend across zero and include values in opposite directions. The means alone could suggest a directional pattern; the intervals make clear that the data are not precise enough to settle the direction or size of the comparisons.

The difference between the outcome and safety counts is another useful statistical consideration. Outcome summaries include 10 participants per group, whereas safety counts at risk are 15, 15, and 14. Without participant flow or analysis-population details, readers cannot determine why the counts differ. Transparent accounting is important for understanding which participants contribute to each result.

Finally, planning illustrations based on observed effects are not the same as the trial's original sample-size justification. The registry does not report the original design assumptions, and the posted planning figures depend on the observed estimates. This distinction prevents an illustrative calculation from being mistaken for evidence about the study's original planning or its observed probability of detecting a result.

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 leaves important details unavailable for evaluating these results. It does not report participant characteristics beyond the knee osteoarthritis condition, detailed eligibility criteria, treatment schedule, or the procedures used for randomization and masking. The record also does not identify who was masked or how the sham procedure was implemented.

The primary outcome timing is described in two ways: the endpoint title says 5-7 weeks post-treatment, while the timeframe says 5-7 weeks after baseline. The record does not resolve that difference. It also describes the KOOS original 0-4 scale and normalized subscale scores from 0 to 100, while the endpoint is expressed in units on the KOOS scale. The exact score presentation is not clarified.

Outcome summaries include 10 participants in each group, while the adverse-event counts at risk are 15, 15, and 14. Participant flow and reasons for these different counts are not reported. The record does not describe missing-data handling, analysis populations, exclusions, or whether the comparisons were adjusted for baseline factors. These gaps prevent a full assessment of the analysis set and robustness of the estimates.

Only the primary clinical result is available for interpretation. No fMRI findings are reported, despite the study's stated brain-response aims, and no secondary outcome results are posted. The original statistical analysis plan, original sample-size justification, interim analyses, and multiplicity strategy are not reported in the registry record. The registry also gives no clinical-importance threshold for the KOOS score, limiting interpretation of the practical meaning of the estimated differences.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: An Acupuncture Functional Magnetic Resonance Imaging (fMRI) Study on Chronic Pain: Response Reliability and Dose Effect — NCT01079390.
• Registry record last updated 2017-08-10; status last verified 2017-02.
• Results first posted 2017-08-10.
• 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 completed study NCT01079390 examined acupuncture dose, placebo acupuncture, and chronic pain in knee osteoarthritis. It was randomized, single-masked, and parallel-group, with 44 participants enrolled. The listed sponsor is Massachusetts General Hospital. The primary posted clinical outcome is the KOOS pain rating, measured at a post-treatment time described as 5-7 weeks, although the timing wording differs within the record.

The posted outcome summaries include 10 participants in each arm. The high-dose versus placebo mean difference is 3.0, with a 95% confidence interval from -11.27 to 17.27 and unadjusted p-value 0.68. The low-dose versus placebo mean difference is -3.0, with a 95% confidence interval from -16.03 to 10.03 and unadjusted p-value 0.652. Both intervals include zero and are broad. No fMRI results are posted. Serious and other adverse events are recorded as zero affected participants in each group, with safety at-risk counts of 15, 15, and 14. Additional analysis details, missing-data procedures, and the original design assumptions are not reported in the registry record.