Role of the Supraspinal Opioidergic Circuit in Prefrontal TMS-Induced Analgesia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Role of the Supraspinal Opioidergic Circuit in Prefrontal TMS-Induced Analgesia (NCT01643798), a randomized na study. The primary outcome is Pain Rating.

2. Clinical Question

This is a mechanistic question, not simply a comparison of two treatments. The contrast of real with sham stimulation addresses whether ratings differed after active rather than sham stimulation under a given drug condition. Comparing those patterns under saline and naloxone would address whether opioid blockade modifies the stimulation-associated response. A direct test of that modification is not reported in the registry record.

3. Trial Design

The registry describes a randomized, triple-masked, crossover study, marked completed. Enrollment was 15. The phase is listed as not applicable. The study dates are recorded as 2011-01 for start and 2012-05 for primary completion. The sponsor was the Medical University of South Carolina.

There were two experimental visits separated by one week. During the experiments, pain ratings were collected every 30 minutes. Preliminary testing at 30 minutes was used to select a temperature for inducing pain throughout the experiment. The primary outcome record identifies baseline testing at 60 minutes, post-sham testing at 90 minutes, and post-real testing at 120 minutes.

The arm descriptions specify intravenous saline or naloxone immediately before sham and real rTMS of the left dorsolateral prefrontal cortex. The listed stimulation parameters were 10 Hz, 5 seconds on, 10 seconds off, 20 minutes, and 4000 pulses. The naloxone dose was 0.1mg/kg. The record names sham rTMS and real rTMS as procedures.

A crossover design means that participants contribute observations under more than one study condition, so observations from the same person may be related. Randomization describes assignment by chance, while masking means information about assigned conditions was concealed from specified parties; the registry labels masking as triple but does not identify those parties. The registry record does not report the treatment sequence, washout rationale, or details of the randomization and masking procedures. The posted group sizes are 14 for each of the four outcome conditions, while overall enrollment is 15; the reason for the difference is 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: Healthy volunteers were randomized to receive I.V. saline or naloxone immediately prior to sham and real rTMS on the same experimental visit. One week later, each participant received the novel pretreatment but the same stimulation paradigm. One participant dropped out after her first experimental visit. These data were not included.

Pretreatment 1 and Stimulation

Reasons for not completing this period:

Pretreatment 2 and Stimulation

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 Rating, measured over Baseline (60 minutes into experiment), Post-Sham (90 minutes), Post-Real (120 minutes).

The primary outcome is mean pain rating, measured in units on a scale. Ratings used an 11-point Visual Analog Scale, where 0 represented no pain and 10 represented unbearable pain. The outcome is continuous: it can take values along a scale rather than being limited to categories such as pain present or absent.

Ratings were taken at baseline, after sham rTMS, and after real rTMS. The record places these assessments at 60, 90, and 120 minutes into the experiment, respectively. The displayed group means therefore describe pain ratings at the identified assessment times, rather than the proportion of participants meeting a responder definition. The registry record does not report an endpoint definition based on change from baseline or a prespecified summary across time.

Repeated ratings can help describe how the measured experience changes across an experiment and across stimulation conditions. A scale also retains more gradation than a binary outcome, though interpretation depends on the scale and measurement procedure. These ratings concern pain elicited in a laboratory protocol; they are not by themselves a measure of longer-term clinical outcomes. The posted means are accompanied by standard errors, which describe the precision of the estimated means rather than the spread of individual participants’ ratings. The registry record does not report the scale’s measurement properties or a threshold for a clinically important difference.

7. Results Posted in the Registry

• Real rTMS With Saline: mean 5.61 versus 7.36 on control; difference -1.75 (95% CI -2.44 to -1.06), standardized effect d = -1.87; z-test p = <0.001.
• Sham rTMS With Naloxone: mean 7.54 versus 7.36 on control; difference 0.18 (95% CI -0.37 to 0.73), standardized effect d = 0.24; z-test p = 0.525.
• Real rTMS With Naloxone: mean 6.75 versus 7.36 on control; difference -0.61 (95% CI -1.24 to 0.02), standardized effect d = -0.72; z-test p = 0.056.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports ANOVA for two analyses: the sham and real rTMS groups under saline, and the sham and real rTMS groups under naloxone. The registry gives a 95% confidence level for both analyses and reports p < 0.001 for the saline comparison and p = 0.04 for the naloxone comparison. It does not report the ANOVA model specification, test statistic, degrees of freedom, adjustment variables, or a confidence interval for either sponsor analysis.

What a mean difference represents

A mean is the average outcome in a group. A mean difference expresses the contrast between two group means, with the direction determined by which group is treated as the reference. The unadjusted recalculations compare each listed group with sham rTMS with saline. For real rTMS with saline, the recalculated difference is -1.75. For sham rTMS with naloxone, it is 0.18. For real rTMS with naloxone, it is -0.61. These are simple contrasts from the posted summary statistics, not estimates from a reported crossover model.

A negative difference means the mean in the compared group is lower than the reference mean under the stated subtraction order; a positive difference means it is higher. A difference is expressed in the outcome’s original scale units. These contrasts are useful descriptions, but they do not automatically account for within-person correlation, period effects, sequence effects, or other features of a crossover experiment. The registry record does not report whether or how those features were included in the sponsor’s analyses.

How to read a p-value

A p-value describes how incompatible the observed data are with a specified null model, given the assumptions of the test. A small p-value is not the probability that the null hypothesis is true, nor is it a measure of the size or importance of an effect. The sponsor reports p < 0.001 for the saline ANOVA and p = 0.04 for the naloxone ANOVA. The recalculated, unadjusted p-values are p < 0.001, p = 0.525, and p = 0.056 for the three contrasts against sham rTMS with saline. Those recalculated tests do not replace the sponsor’s analyses when the contrast or model differs.

In particular, p = 0.056 does not show that there is no difference, just as a result below a conventional threshold does not by itself show that an effect is important. Interpretation should include the estimate, interval, analysis design, and clinical context. The registry record does not state a threshold for statistical significance or describe whether its reported analyses were adjusted for multiple testing.

Why repeated measures matter

In a crossover study, a participant can contribute ratings under multiple conditions. Those ratings are generally not independent because they come from the same person. A model that accounts for this relationship can differ from a calculation that treats group summaries as independent. The posted standard errors and means allow simple summary-based recalculations, but they do not reveal the covariance between repeated measurements. The recalculated results should consequently be understood as unadjusted illustrations, not as a reconstruction of the full trial analysis.

Standard error describes uncertainty in an estimated mean. It is not the same as the standard deviation, which describes variation among individual observations. For example, the outcome groups list means and standard errors, but the registry does not provide participant-level ratings or the within-person correlations needed to reproduce a crossover analysis. The recalculated intervals and tests depend on the posted summary information and should be interpreted with that limitation in mind.

Why over-dispersion can matter

General statistical context: a count or binary-outcome model can be over-dispersed when the observed variability exceeds what its assumed probability model allows. That can make standard errors too small if the extra variability is ignored. The primary outcome in this record is continuous, so over-dispersion is not the central issue for these mean comparisons. In general, the appropriate variance model should reflect the outcome and design; the registry record does not provide enough detail to assess all modeling assumptions.

The essential distinction is between the sponsor’s reported ANOVA results and the simple unadjusted recalculations based on posted summaries. They are not interchangeable whenever their group contrast or treatment of repeated observations differs. The registry record’s limited analysis details prevent a full evaluation of model assumptions or reproduction of the sponsor’s results.

10. Confidence Intervals and Precision

A confidence interval gives a range of effect estimates compatible with the data and the method used to construct the interval. It expresses statistical uncertainty; it is not a guarantee that the true effect lies within the interval, and it does not describe the range of individual participants’ ratings. The recalculated intervals are unadjusted and use the posted summary statistics.

For real rTMS with saline versus sham rTMS with saline, the mean difference is -1.75 and the 95% confidence interval runs from -2.444 to -1.056. The interval lies on the negative side of zero, indicating that the estimate is compatible with lower ratings after real rTMS in that contrast. Its width still matters: the data support a range of possible magnitudes, not one exact value.

For sham rTMS with naloxone versus sham rTMS with saline, the difference is 0.18 and the 95% confidence interval is -0.375 to 0.735. This interval includes zero and is compatible with effects in either direction. It does not establish equivalence or exclude potentially relevant differences.

For real rTMS with naloxone versus sham rTMS with saline, the estimate is -0.61 and the 95% confidence interval is -1.235 to 0.015. This interval also includes zero. It describes uncertainty for that particular recalculated contrast, not the sponsor’s within-naloxone ANOVA comparison. The sponsor’s analyses do not include reported confidence intervals in the registry record.

Precision is limited by the small posted groups and by the absence of participant-level data and model details. Standard errors are reported for the group means, but the registry does not report standard errors or intervals for its ANOVA contrasts. The uncertainty estimates should not be treated as adjusted for the crossover structure unless the analysis is documented as doing so; that is not reported in the registry record.

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 for the continuous outcome, not total event counts. They are illustrations based on the observed effect, not the trial’s original design justification. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The trial’s own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants per arm under those assumptions for an 80% chance of detecting the specified effect if that effect is real. The 90% power column gives the corresponding number per arm for a 90% chance. These are prospective planning quantities, not a probability that the trial’s result is correct. This is not observed power.

The rows describe planning for 100%, 75%, and 50% of the observed effect. A smaller effect is harder to distinguish from random variation, so detecting a smaller effect generally requires more participants. For the saline real-versus-sham contrast, the displayed figures range from 5 and 7 participants per arm for planning at 100% of the observed effect, to 18 and 25 for planning at 50%. For the sham naloxone-versus-saline contrast, the corresponding figures range from 272 and 364 to 1,087 and 1,455. For real rTMS with naloxone versus sham rTMS with saline, they range from 31 and 41 to 121 and 161.

These values are sensitive to the observed effect used as the starting point. Because the estimates come from small groups, their magnitude may be uncertain, and the planning figures should not be treated as a recommendation for a future study without a separate design analysis. The crossover design and any within-person correlation are not represented in the listed two-arm 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 = -1.750; pooled standard deviation σ = 0.936.
2. n = 2 × (1.96 + 0.842)² × 0.936² / -1.750² = 4.5, rounded up to 5 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 <- -1.75                      # observed difference in means
sigma <- 0.936162379077476                     # 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(1643798)
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 = 5 (80% power), 7 (90% power)
 75% of observed effect: n per arm = 8 (80% power), 11 (90% power)
 50% of observed effect: n per arm = 18 (80% power), 25 (90% power)
power.t.test: 5.6 
Simulated power at n = 5 per arm: 0.736 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The registry reports sponsor ANOVA results for sham versus real rTMS within each drug condition: p < 0.001 under saline and p = 0.04 under naloxone. The unadjusted recalculations instead compare posted means using sham rTMS with saline as the reference. The saline real-versus-sham comparison matches the groups in the sponsor’s saline analysis in broad contrast, and its recalculated result is p < 0.001. The registry record does not report enough model detail to determine whether the estimates and tests were otherwise calculated in the same way.

The recalculated real-rTMS-with-naloxone comparison is against sham rTMS with saline, not against sham rTMS with naloxone. It is therefore not the same comparison as the sponsor’s naloxone ANOVA, which uses the two naloxone groups. The sponsor’s own analysis takes precedence for its stated comparison. The recalculated value should not be used to contradict or replace the sponsor’s p = 0.04 result.

The difference in contrast is important for the study’s mechanistic question. Establishing whether naloxone alters the response to real versus sham stimulation calls for a direct comparison of the stimulation effect between drug conditions, such as an interaction analysis. Such an estimate is not reported in the registry record. The posted group means alone do not supply that inferential test.

14. Multiplicity, Missing Data and Analysis Populations

The primary outcome description identifies pain rating at baseline, after sham rTMS, and after real rTMS. The registry lists two outcome measures and four analyses, but the record does not report a complete statistical analysis plan or explain the status of every analysis. It reports two ANOVA results. Whether there were additional planned or exploratory comparisons, and whether any adjustment for multiple testing was used, is not reported in the registry record.

Multiplicity arises when several hypotheses are tested. The more tests considered, the greater the chance that at least one result may appear notable by chance if all tests are treated separately. Adjustments can address that issue, but the registry record does not report whether the sponsor used one. This absence limits interpretation of the reported p-values across the full set of study questions; it does not alter the values as posted.

The registry record does not report a detailed missing-data method, the number of participants with incomplete primary outcome measurements, or how incomplete crossover sequences were handled. It also does not report whether analysis used all randomized participants, only participants completing each condition, or another analysis population. Although the overall enrollment is 15 and each posted outcome group has 14 participants, the record does not state why those counts differ. No assumptions about the missing observations or their handling can be inferred from the summaries.

For a crossover study, analysis populations and missing observations can be especially consequential because measurements across conditions are linked within participants. The record does not report how period, sequence, or carryover effects were evaluated, or whether the model included participant-level effects. These are questions about the analysis, not evidence that a particular problem occurred. Without those details, the sponsor’s reported ANOVA cannot be fully assessed for its handling of the design.

15. 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 5% reporting threshold.

The registry lists a pretreatment and stimulation safety group with 15 participants at risk. It reports 0 serious adverse events and 0 other adverse events in that group. The list of top serious adverse event terms is empty. Deaths are not reported in the registry record.

These figures describe events recorded for the specified safety group and period; they do not establish that no other events occurred outside the registry’s reporting categories or observation window. The record does not provide event definitions, severity grading details, follow-up duration for safety, or a participant-level account. It also does not explain how adverse events were collected or whether the group includes all enrolled participants.

With 15 participants at risk, the absence of a recorded event should be read as a description of this small study’s posted safety data, not as proof that an event cannot occur. The figures do not support conclusions about comparative safety between saline and naloxone or between sham and real rTMS, because separate condition-specific adverse event results are not reported in the registry record.

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

The posted results describe pain ratings during a laboratory experiment with sham and real prefrontal rTMS under saline and naloxone. Under saline, the mean rating was lower after real than after sham rTMS, and the recalculated contrast had a 95% confidence interval entirely below zero. The sponsor’s ANOVA for the saline groups reports p < 0.001. These results characterize the reported outcome under that study condition; they do not establish the size or persistence of any effect outside the measurement times and setting.

Under naloxone, the sponsor reports p = 0.04 for the ANOVA comparing sham and real rTMS within that drug condition. The recalculated contrast against sham rTMS with saline is a different comparison, with an interval that includes zero. Neither result alone answers whether opioid blockade changes the real-versus-sham stimulation effect. A direct interaction estimate and its uncertainty are not reported in the registry record.

The study was designed to investigate a proposed mechanism involving opioid blockade and pain circuitry. The results may be relevant to that research question, but they do not directly measure a mechanism or establish that opioid signaling explains the rating pattern. Statistical significance, where reported, is not the same as clinical importance, and the registry record does not give a threshold for a clinically meaningful rating change.

The sample was small, the posted outcome groups contain 14 participants, and the record does not provide participant-level data or full analysis details. Those limits make the estimates less definitive than the exact-looking decimals may suggest. The findings should be interpreted as results from an experimental protocol with repeated pain ratings, not as a basis for medical decisions or a claim about treatment effectiveness in clinical practice.

17. Why This Trial Matters Statistically

This trial illustrates a common challenge in mechanistic studies: the most interesting scientific claim may concern a difference in effects across conditions, while the posted analyses report separate comparisons within conditions. The sponsor’s saline and naloxone ANOVAs address real versus sham stimulation separately. To establish that the stimulation contrast itself differs under opioid blockade, an explicit comparison of those contrasts is needed. That analysis is not reported in the registry record.

The crossover design is another important statistical feature. Repeated observations from the same participant can be more informative than unrelated observations, but they require analysis that accounts for within-person dependence and the timing and sequence of conditions. The registry identifies the design as crossover without describing the analysis details needed to evaluate those features. This distinction helps readers understand why simple comparisons based on group summaries are not necessarily equivalent to the sponsor’s model.

The record also shows how effect estimates and uncertainty complement p-values. The saline contrast has a negative estimate with an interval that does not include zero, while other recalculated contrasts have intervals that include zero. Those patterns describe different degrees of compatibility with a range of effects; they do not prove equality or explain biological mechanisms. Planning illustrations further demonstrate that the participant requirements vary considerably depending on the effect size targeted, and they are based on observed estimates rather than the trial’s original design assumptions.

For clinical researchers, the lesson is to distinguish the scientific hypothesis, the statistical contrast, and the reported analysis. A result can be relevant to a hypothesis without directly testing its central interaction. Clear reporting of the model, analysis population, missing data, multiplicity, and uncertainty would make the evidence easier to evaluate and reproduce.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record gives limited detail about the statistical analysis. It reports ANOVA and p-values but not the model specification, the handling of repeated measurements, the participant-level covariance structure, or any adjustment variables. The recalculations use posted summary statistics and are unadjusted; they cannot reconstruct a crossover model without the underlying data and additional design information.

The number of participants in the posted outcome groups is 14, while enrollment is 15. The reason for that difference is not reported in the registry record. The record also does not state the analysis population, explain missing measurements, or describe the handling of participants who may not have completed every condition. These omissions limit assessment of attrition and the reach of the reported estimates.

The primary outcome is a laboratory pain rating measured at defined points in an experiment. The record does not report a threshold for clinical importance or longer-term outcomes. The results therefore have a limited scope beyond those ratings and conditions. Participant characteristics and further details about the pain-induction protocol are not reported in the primary outcome record.

The study’s stated mechanistic question concerns whether opioid blockade changes the response to prefrontal stimulation. The sponsor reports separate sham-versus-real ANOVAs for saline and naloxone, but a direct interaction estimate is not reported. Separate p-values are not themselves a test that the effects differ. The registry record does not report multiplicity procedures, sample-size assumptions for the original trial, or detailed methods for sequence, period, and carryover effects in the crossover design. These uncertainties warrant caution when interpreting the results as evidence for a mechanism.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Role of the Supraspinal Opioidergic Circuit in Prefrontal TMS-Induced Analgesia — NCT01643798.
• Registry record last updated 2014-04-15; status last verified 2012-06.
• Results first posted 2014-04-15.
• 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

NCT01643798 is a completed randomized, triple-masked crossover study of pain ratings after sham and real left dorsolateral prefrontal rTMS with saline or naloxone. Enrollment was 15. The primary outcome was mean Visual Analog Scale pain rating at baseline and after sham and real stimulation.

The sponsor reports ANOVA results of p < 0.001 for the sham-versus-real comparison under saline and p = 0.04 under naloxone. Summary-based recalculations give a saline real-versus-sham mean difference of -1.75, with a 95% confidence interval from -2.444 to -1.056. A direct test of whether naloxone changes the stimulation effect is not reported in the registry record. The posted safety group reports 0 serious and 0 other adverse events among 15 participants at risk.