Placebo In Chronic Back Pain - Double-Blind Randomized Control Trial: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Placebo In Chronic Back Pain - Double-Blind Randomized Control Trial (NCT02013427), a randomized phase 4 study. The primary outcome is Change in Pain Assessed by Visual Analogue Scale (VAS).

2. Clinical Question

The trial concerns chronic low back pain and a study of placebo response. The registry describes a randomized, partially blinded study intended to examine brain properties associated with placebo response and to evaluate how placebo response relates to medication treatment. The primary posted outcome is change in self-reported pain after six weeks.

The main posted comparison is between participants assigned to take placebo capsules and participants assigned to observation without study treatment. The outcome is percentage change in pain measured with a visual analogue scale. The reported comparison describes the difference between the mean percentage change in the placebo group and the mean change in the observational group. A negative change reflects a lower post-intervention score than baseline under the registry’s stated calculation; it is a summary of reported scores, not by itself an explanation of why the scores changed.

A third arm was assigned naproxen and omeprazole. Its reported outcome group was very small, and the posted comparison is specifically placebo versus observation rather than a direct estimate contrasting the active medication arm with either of the other arms. The registry’s research description also refers to studying brain imaging parameters and the relationship between placebo response and medication treatment. The posted primary outcome summaries do not report brain imaging results, responder classification results, or a statistical test of that interaction.

3. Trial Design

The registry identifies this as a Phase 4, randomized, parallel-group study with single masking. The study status is completed. The enrollment field reports 82, while the primary outcome description reports 67 participants randomized among the three outcome groups: 20 in the observational arm, 4 in the naproxen-and-omeprazole arm, and 43 in the placebo-only arm. The registry record does not explain the difference between the enrollment figure and the primary-outcome group counts.

The observational arm received no study treatment and was described as unblinded to participants and study staff. The placebo-only arm was described as blinded to participants and study staff. The naproxen-and-omeprazole arm was also described as double-blind. The registry’s overall masking field says single, so the record contains different descriptions of masking at the overall and arm levels. The study is characterized as partially blind in its official title and research description.

Participants in each arm were asked to discontinue their current pain medications for the length of the study. The active-treatment arm was assigned naproxen and omeprazole, while the placebo arm was assigned placebo capsules. The observational arm received no study treatment. The registry describes the primary outcome assessment at baseline and post-intervention, with the post-intervention measurement at six weeks.

The posted results contain one primary outcome measure and no posted secondary outcomes. The record reports no posted analyses, although arm-level outcome summaries and a recalculated unadjusted comparison are available. It does not report the trial’s original sample-size assumptions, allocation ratio targets, detailed randomization procedures, or a prespecified analysis plan. The enrollment and group-size figures describe the recorded trial, but do not establish how the study’s original design decisions were made.

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

Analysis population for the primary outcome, as defined in the registry: 67 patients were randomized into an Observational arm (no treatment, n = 20), Naproxen \& Omeprazole (active treatment, n=4) and Placebo only (placebo, n = 43).

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: 25 patients received no treatment. Of the 57 treated individuals, 52 were allocated to placebo treatment (PTx) and 5 were allocated to active treatment (MTX, Naproxen + Esomeprazole) in a double-blind fashion. Note: the MTx group was included for blinding purposes (i.e., so that we could tell patients they may receive a placebo or active treatment) hence why the large imbalance between groups. Participants were not informed about the odds for receiving active versus placebo treatment.

6. Primary Endpoint

The registry lists the primary outcome as Change in Pain Assessed by Visual Analogue Scale (VAS), measured over 6 weeks.

The primary endpoint is change in self-reported pain measured with a visual analogue scale from 0, meaning no pain, to 10, meaning worst imaginable pain. The registry reports the outcome as percentage change from baseline to the six-week post-intervention assessment. Its formula is post-intervention pain minus baseline pain, divided by baseline pain. The reported group summaries are means with standard deviations.

This type of measure captures participants’ own reports of pain rather than an externally observed event. Comparing baseline and follow-up scores expresses the direction and relative size of reported change for each participant, while group means summarize those changes within each randomized arm. The registry describes the posted results as the largest percentage change before and after intervention. The record does not further clarify how that wording relates to the stated percentage-change formula.

A percentage-change outcome can be sensitive to its baseline denominator: the same absolute change can correspond to different relative changes when baseline values differ. The registry does not report how baseline values of zero, if any, were handled, or provide participant-level values that would allow that issue to be assessed. The endpoint is useful for describing change in reported pain over the stated follow-up period, but the summary alone does not explain the causes of change or establish whether the groups were comparable on all relevant features.

7. Results Posted in the Registry

• Placebo Only: mean -0.21 versus -0.03 on control; difference -0.18 (95% CI -0.27 to -0.09), standardized effect d = -0.94; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each participant’s percentage change in visual-analogue pain score can take values across a numerical scale. The registry reports a mean and standard deviation for each arm. A mean describes the group’s average outcome, while the standard deviation describes how dispersed individual outcomes are around that average. Neither statistic reveals the full distribution or whether a small number of participants had unusually large changes.

What does the mean difference represent?

The comparison subtracts the observational-group mean from the placebo-group mean. The resulting unadjusted mean difference is -0.18. It expresses the difference on the posted outcome scale, not as a percentage-point conversion or a standardized effect. The negative sign follows the order of the groups in the comparison and indicates that the placebo mean was lower than the observational mean. The result is unadjusted: it is based on the reported group summaries and does not account for baseline covariates or other factors.

Randomization is intended to create groups that are comparable on average, including with respect to characteristics that are not measured. However, the registry record does not report the randomization method or an analysis adjusting for baseline pain or other characteristics. The small active-treatment group is not part of the reported placebo-versus-observation contrast. The result therefore should not be read as a three-arm comparison.

How should the p-value be understood?

The reported p-value is <0.001 for the unadjusted mean comparison. In general, a p-value evaluates how compatible the observed data are with a specified null model, usually one that assumes no group difference. A small p-value is not the probability that the null model is true, and it does not measure the size or importance of the effect. It also does not show whether the model’s assumptions are appropriate. The registry does not report a prespecified analysis plan or a sponsor analysis for this endpoint.

The comparison is a recalculation from the arm-level means, standard deviations, and group sizes. Such a calculation uses aggregate summaries rather than individual participant records. It cannot incorporate participant-level features, assess the shape of outcome distributions, or directly address missing observations. The record reports no posted analyses, and the comparison should not be mistaken for an adjusted or prespecified model.

Why does variability matter?

Standard deviations describe the observed spread in individual outcomes. Greater variability makes a group mean less precisely estimated when other features are similar. The placebo arm’s standard deviation is 0.21, and the observational arm’s is 0.14. These values describe variability within each arm; they do not say how much outcomes overlap between participants in the two arms. General statistical methods often use a pooled standard deviation when summarizing a standardized difference. The comparison lists a pooled standard deviation of 0.191, but the mean difference itself remains on the endpoint’s original scale.

Over-dispersion is a general concern when observed variability exceeds what a chosen model assumes. If present and unaccounted for, standard errors and confidence intervals can be too optimistic. The registry record does not report a distributional diagnostic or a separate over-dispersion assessment. Since only summary statistics are posted, the distribution of individual percentage changes cannot be inspected from those summaries alone.

What does a confidence interval add?

A confidence interval represents uncertainty around an estimated effect under a specified method and its assumptions. The reported interval for the mean difference is entirely below zero. This gives information about the range of values compatible with the unadjusted calculation, beyond the single point estimate. It does not cover uncertainty from every possible source, such as outcome missingness, measurement choices, or bias arising from study conduct. The registry does not report an adjusted interval or a model-based analysis using participant-level data.

Effect size can also be expressed in standardized units, which scale the mean difference by variability. The posted comparison includes a standardized effect estimate, but it does not replace the raw mean difference. Standardized measures can aid comparison across differently scaled measures, while their interpretation depends on the variability estimate used. Neither raw nor standardized estimates alone determine whether a difference is important for participants.

What limits the analysis?

The placebo and observational group sizes are unequal, and the active-treatment arm has only 4 participants. Unequal sample sizes do not automatically invalidate a mean comparison, but precision depends on the amount of information in each group and the variability of outcomes. No participant-level data, baseline balance summaries, missing-data description, or analysis-population definitions are posted. The registry also does not report how the stated percentage-change outcome was handled in edge cases or whether any transformations or adjustments were planned.

These methods explain the posted contrast, not a complete reanalysis of the trial. The interpretation relies on the accuracy of the registry’s arm summaries and on the assumptions behind the unadjusted calculation. The registry record does not report whether an interim analysis was planned or conducted, nor does it provide the trial’s original statistical analysis plan.

10. Confidence Intervals and Precision

The mean difference for placebo versus observation is -0.18. Its confidence interval is reported entirely below zero, so the interval is consistent with a negative mean difference under the recalculated unadjusted method. The registry reports the interval endpoints with more decimal places than can be reproduced in this explanation; the direction and interval interpretation are therefore more useful than extra numerical precision.

Confidence intervals communicate uncertainty in an estimate. In general, an interval is constructed so that a procedure would capture the true parameter at its stated confidence level over repeated use under the model assumptions. It is not a guarantee that the particular interval contains the true effect, nor is it a range for individual participants’ outcomes. The interval around a mean difference addresses sampling uncertainty for that contrast, not all possible uncertainty from study conduct or analysis choices.

The p-value is <0.001, but this does not make the estimate exact. The standard deviations show variation among participant outcomes, and the reported interval gives a range of plausible mean differences under the unadjusted calculation. The group sizes—43 in the placebo arm and 20 in the observational arm—also matter to precision. In general, estimates based on fewer participants are less precise when other features are alike.

The reported interval does not adjust for baseline characteristics, and no adjusted estimate or interval is posted. It also cannot quantify the impact of unreported missing outcomes or differences between the enrollment figure and the primary outcome counts. Thus, precision within the calculation should be distinguished from certainty about the result’s broader interpretation.

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 an illustrative two-group study, not total events. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed placebo-versus-observation effect. These are planning illustrations based on the observed comparison, not the original trial’s design assumptions; the registry record does not report those original assumptions.

For planning around 100% of the observed effect, the figures are 18 participants per arm for 80% power and 24 participants per arm for 90% power. For 75% of the observed effect, they are 32 and 43 participants per arm, respectively. For 50% of the observed effect, they are 71 and 95 participants per arm, respectively.

The 80% power column represents the number of participants per arm that the stated assumptions estimate would give an 80% chance of detecting the chosen effect if that effect were the true one. The 90% column gives the corresponding planning target for a 90% chance. These are design probabilities under the planning model, not guarantees for a future study. Smaller effects require more participants to detect under the same assumptions, which is why the figures rise as the assumed fraction of the observed effect falls.

This is not observed power. The figures should not be interpreted as the power achieved by the completed trial or as evidence that a result is reliable. The illustration uses the observed effect as its starting point, and the observed estimate itself is uncertain. The registry record does not report the trial’s original sample-size justification or whether the original design used these 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 = -0.180; pooled standard deviation σ = 0.191.
2. n = 2 × (1.96 + 0.842)² × 0.191² / -0.180² = 17.7, rounded up to 18 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 <- -0.18                      # observed difference in means
sigma <- 0.190968197506853                     # 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(2013427)
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 = 18 (80% power), 24 (90% power)
 75% of observed effect: n per arm = 32 (80% power), 43 (90% power)
 50% of observed effect: n per arm = 71 (80% power), 95 (90% power)
power.t.test: 18.7 
Simulated power at n = 18 per arm: 0.782 (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 lists one primary outcome measure and no posted secondary outcomes. It reports no posted analyses. The trial description discusses brain imaging, placebo response, and interaction with medication treatment, but the available primary outcome summaries do not provide statistical results for those aims. The registry record does not report a multiplicity strategy, such as an adjustment for testing multiple outcomes, time points, or subgroup contrasts. Without a posted analysis plan, it is not possible to determine which analyses were prespecified or how multiple testing was handled.

Missing-data handling is also not reported in the registry record. The outcome description reports 67 participants across the three arms, while the enrollment field reports 82. The record does not explain whether the difference reflects participants without outcome data, exclusions, or another reason. It also does not state how many participants contributed to each endpoint analysis beyond the arm counts in the outcome description, or how incomplete measurements were treated.

The analysis population is not defined in the registry record. It does not say whether participants were analyzed according to randomized assignment, whether any participants were excluded after randomization, or whether the analysis included only participants who completed the intervention. These distinctions can affect the interpretation of a randomized comparison, particularly if inclusion depends on events after assignment.

The posted placebo-versus-observation comparison is unadjusted and based on summary statistics. The record does not report adjustment for baseline pain, other covariates, or possible clustering, and it does not give a model specification or a detailed statistical analysis plan. The absence of these details does not establish that any particular method was or was not used outside the posted record. It means that the registry record does not permit evaluation of those choices.

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 serious adverse events, other adverse events, and deaths separately for the listed safety groups. The observational group had 25 participants at risk, the placebo group had 52, and the naproxen-and-omeprazole group had 5. For each of these groups, the reported number affected by serious adverse events was 0, the number affected by other adverse events was 0, and deaths were 0. No serious adverse event terms are listed.

These figures are counts in the reported at-risk groups. They do not establish that no adverse events occurred outside the registry’s defined reporting categories or period, and the registry record does not provide additional event descriptions or follow-up detail. The safety group counts differ from the primary outcome group counts, and the record does not explain that difference. Consequently, the safety denominators should be read as reported rather than assumed to represent the same analysis population as the primary outcome.

Zero reported events in these groups is a description of the posted safety data, not a general statement about risk. The registry record does not report a comparative statistical analysis of adverse events.

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

The posted primary outcome data show that the mean percentage change in self-reported pain was -0.21 in the placebo-only group and -0.03 in the observational group at six weeks. The recalculated unadjusted mean difference is -0.18, with a reported p-value of <0.001 and a confidence interval lying below zero. These results describe the groups’ recorded changes and the uncertainty from the unadjusted comparison.

They do not establish why the groups differed. The comparison cannot separate possible effects of expectation, study participation, reporting behavior, or other influences. The observational group was unblinded, while the placebo arm was described as blinded; those differences are relevant context when interpreting a self-reported outcome. The registry does not report details sufficient to assess how masking was implemented or maintained.

The result is not a direct estimate of the naproxen-and-omeprazole effect. The active-treatment arm included 4 participants in the primary outcome description, and the posted comparison contrasts placebo with observation. Nor do these summaries answer the stated research questions about brain imaging predictors, placebo responder classification, or the interaction between placebo response and medication treatment.

The enrollment figure is 82, while the primary outcome description reports 67 participants in the three arms. Reasons for the difference and the handling of missing outcomes are not reported in the registry record. The absence of those details limits assessment of how representative the analyzed groups are of all enrolled participants.

Statistical evidence for a difference is not the same as evidence of clinical importance. The registry does not report a threshold for a meaningful change in pain, and the mean difference alone does not describe the range of individual experiences. These posted results should therefore be read as an unadjusted summary of one comparison at one follow-up point, rather than as a complete account of all trial aims or outcomes.

16. Why This Trial Matters Statistically

This trial is statistically notable because it separates a placebo-only arm from an observational arm that received no study treatment, while measuring change in participants’ self-reported pain. Such a contrast raises methodological questions beyond the mean difference itself: masking differs across arms, the endpoint is reported by participants, and the placebo and observational groups have unequal sizes. Those design features matter when deciding what the comparison can describe.

The record also illustrates the distinction between an outcome estimate and the broader research questions motivating a study. The study description emphasizes brain properties, placebo response, and medication interaction, but the posted primary outcome result is a mean change comparison between placebo and observation. The available summaries cannot answer all of the stated mechanistic questions.

Reporting completeness is important to interpretation. The enrollment field and primary outcome group counts do not match, the safety group counts differ from the outcome counts, and the record does not explain these differences. Missing-data procedures, analysis populations, multiplicity handling, and the original statistical plan are not reported. These are not minor details when readers need to determine which participants and analyses underpin a result.

Finally, the sample-size illustrations demonstrate how planning requirements depend on the effect a future study aims to detect. Smaller assumed effects require more participants under the stated planning assumptions. Because the observed effect is itself uncertain, those figures are best treated as illustrations rather than as a definitive design recommendation.

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 outcome group sizes are 20 for observation, 4 for naproxen and omeprazole, and 43 for placebo. The active-treatment group is particularly small, so its reported mean and standard deviation provide limited information about that arm. The posted statistical comparison does not include the active-treatment group and cannot be used to infer its contrast with placebo or observation.

The enrollment field reports 82, whereas the primary outcome description reports 67 participants randomized across the three arms. Safety denominators are 25, 52, and 5, rather than those primary outcome counts. The registry record does not explain these differences, identify which participants lacked outcome data, or describe how missing measurements were handled. This complicates assessment of the relationship between enrollment, outcome analyses, and safety reporting.

Masking descriptions also vary by level: the overall registry field identifies single masking, while the arm descriptions distinguish an unblinded observational arm and double-blind medication arms. The study is described as partially blind. The record does not provide further procedural detail to assess implementation or possible unmasking.

The endpoint is percentage change based on baseline pain. The registry does not report how zero baseline values or incomplete measurements were handled. Nor does it provide participant-level distributions, baseline balance summaries, a detailed statistical analysis plan, analysis-population definitions, or an adjusted comparison. The description’s reference to the largest percentage change is not further clarified.

The registry record does not report a multiplicity approach, interim analyses, or original sample-size justification. It also does not post results for the brain imaging aims, responder classifications, or medication interaction described in the study rationale. These limitations concern what can be evaluated from the registry record; they do not establish what was or was not done outside that record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Placebo In Chronic Back Pain - Double-Blind Randomized Control Trial — NCT02013427.
• Registry record last updated 2023-03-03; status last verified 2023-03.
• Results first posted 2023-03-03.
• 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 Phase 4 study is described as randomized, parallel-group, and partially blinded, and concerns chronic low back pain. Its primary posted endpoint is percentage change in visual-analogue pain scores from baseline to six weeks. The outcome description reports 67 participants across observation, naproxen and omeprazole, and placebo arms, while the enrollment field reports 82.

The posted primary comparison is placebo versus observation. Their mean changes were -0.21 and -0.03, respectively, yielding an unadjusted mean difference of -0.18 and a reported p-value of <0.001. The record does not report posted secondary outcomes or analyses, or results for the brain imaging and medication-interaction aims described in the study rationale. Missing-data procedures, analysis populations, multiplicity handling, and the original sample-size assumptions are not reported.