This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for The Safety and Efficacy of the Buprenorphine Transdermal System (BTDS) in Subjects With Chronic Back Pain. (NCT00315445), a randomized phase 3 study. The primary outcome is Pain on the Average, Mean Change From Baseline Days 21-84 (Last Observation Carried Forward [LOCF]).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00315445 |
| Phase | Phase 3 |
| Condition | Back Pain |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 134 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Purdue Pharma LP |
| Results posted | Yes |
2. Clinical Question
Population
People with chronic back pain enrolled in a phase 3 clinical trial. The registry reports enrollment of 134 and states that all randomized subjects received study drug and were included in the intent-to-treat and safety analyses. Efficacy data were available for 133 subjects.
Intervention
Buprenorphine transdermal patches at 5, 10, or 20 mcg/hour, described in the registry as BTDS. Supplemental non-steroidal anti-inflammatory drugs were allowed for all subjects during the treatment period.
Comparator
The trial included placebo transdermal patches and placebo oxycodone/acetaminophen tablets, as well as 5 mg oxycodone/325 mg acetaminophen tablets, identified as OXY/APAP. The primary outcome results compare BTDS and OXY/APAP separately with the placebo group.
Primary question
How did mean change from baseline in average pain ratings over days 21–84 compare among the study groups? Participants rated average pain on a scale from 0, no pain, to 10, pain as bad as they could imagine it. The primary outcome uses last observation carried forward for the stated period.
The registry describes a double-blind, randomized, parallel-group study. Its objective was to assess safety of the buprenorphine transdermal system in comparison with placebo and immediate-release oxycodone/acetaminophen in subjects with chronic back pain. The primary outcome is a measure of reported pain intensity, while the listed secondary outcomes include health-status domains from the MOS SF-36. The results address comparisons among the trial groups during the recorded study period; they do not by themselves establish how results would apply to people outside the enrolled trial population.
3. Trial Design
The registry describes a phase 3 randomized, double-blind, parallel-group study of treatments for chronic back pain. Enrollment was 134. The primary completion date was 1998-05, and the study status is completed. The recorded start was 1997-12. The registry states that all 134 randomized subjects received study drug and were included in the intent-to-treat and safety analyses. It also reports efficacy data for 133 subjects, with one subject withdrawn because informed consent was never obtained and no efficacy data available for that subject.
The study groups included BTDS, OXY/APAP, and placebo. The BTDS arm description gives patch strengths of 5, 10, or 20 mcg/hour. OXY/APAP tablets are described as 5 mg oxycodone/325 mg acetaminophen. The placebo group received placebo oxycodone/acetaminophen tablets and a placebo transdermal patch. The registry summary states that supplemental non-steroidal anti-inflammatory drugs were allowed for all subjects in addition to study drug.
The double-blind treatment intervention duration was 84 days. The primary pain measure was collected on baseline day 1 and days 21, 30, 45, 60, 75, and 84, and, if applicable, at early termination. The primary endpoint summarizes mean change from baseline during days 21–84 using last observation carried forward. Outcome-level group counts differ across the reported analyses; the primary outcome lists 45 for placebo, 42 for OXY/APAP, and 46 for BTDS.
The registry record does not report the original sample-size justification, detailed randomization procedures, or the full statistical analysis plan. Those details should not be inferred from the observed enrollment or from planning calculations based on the posted results.
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: This study was designed to evaluate the efficacy and safety of BTDS in comparison with current pharmacotherapeutic pain management practice and placebo in opioid-naïve or opioid-experienced adult subjects with chronic back pain not manageable with nonopioid analgesics alone (range, 19-85 years).
Overall Study
| Stage | Placebo | OXY/APAP | BTDS |
|---|---|---|---|
| STARTED | 45 | 43 | 46 |
| COMPLETED | 18 | 27 | 22 |
| NOT COMPLETED | 27 | 16 | 24 |
Reasons for not completing this period:
| Reason | Placebo | OXY/APAP | BTDS |
|---|---|---|---|
| Adverse Event | 7 | 12 | 15 |
| Lack of Efficacy | 16 | 1 | 7 |
| Lost to Follow-up | 1 | 0 | 1 |
| Protocol Violation | 2 | 0 | 1 |
| Other | 1 | 3 | 0 |
Analysis population for the primary outcome, as defined in the registry: All 134 subjects randomized and received study drug were included in the intent-to-treat (ITT) and safety analyses. ITT Subjects With Efficacy Data (N = 133) 1 subject was withdrawn from study because the informed consent was never obtained. This subject had no efficacy data but was included the analysis of discontinuation due to lack of efficacy.
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.
| Characteristic | Unit | Placebo | OXY/APAP | BTDS | Total |
|---|---|---|---|---|---|
| Participants analysed | 45 | 43 | 46 | 134 | |
| Age Continuous | years | 52 (SD 2.2) | 49 (SD 2.5) | 54 (SD 2.2) | 52 (SD 1.31) |
| Sex: Female, Male: Female | Participants | 25 | 27 | 28 | 80 |
| Sex: Female, Male: Male | Participants | 20 | 16 | 18 | 54 |
| Opioid Experience: Opioid naive | participants | 39 | 34 | 34 | 107 |
| Opioid Experience: Opioid experienced | participants | 6 | 9 | 12 | 27 |
6. Primary Endpoint
The registry lists the primary outcome as Pain on the Average, Mean Change From Baseline Days 21-84 (Last Observation Carried Forward [LOCF]), measured over On baseline day 1 and days 21, 30, 45, 60, 75, and 84, and, if applicable, at early termination..
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Units on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is mean change from baseline in average pain ratings during days 21–84, with last observation carried forward (LOCF). Participants were asked to rate their pain “on the average since your last visit” by choosing a number on a scale from 0, no pain, to 10, pain as bad as you can imagine it. The registry lists baseline day 1 and follow-up days 21, 30, 45, 60, 75, and 84, with an early-termination assessment if applicable.
A change-from-baseline outcome compares each participant’s follow-up pain rating with their own baseline rating, then summarizes change for the group. Because lower values on the rating scale indicate less reported pain, a negative mean change represents a decrease in ratings from baseline. The arm results are least-squares means with standard errors, according to the registry outcome description. The posted outcome values are -1.01 for placebo, -1.82 for OXY/APAP, and -1.92 for BTDS.
Repeated pain assessments can describe how ratings evolve during the study period, while a summary over days 21–84 provides a group-level comparison across that interval. LOCF uses the last recorded observation for a participant in place of later missing measurements. This method allows a summary to be calculated when some later observations are absent, but it does not ensure that the carried-forward value represents the participant’s unobserved later pain rating. The registry record does not report enough detail to determine the extent or pattern of missing primary outcome observations.
7. Results Posted in the Registry
- OXY/APAP: mean -1.82 versus -1.01 on control; difference -0.81 (95% CI -1.82 to 0.20), standardized effect d = -0.34; z-test p = 0.117.
- BTDS: mean -1.92 versus -1.01 on control; difference -0.91 (95% CI -1.89 to 0.07), standardized effect d = -0.38; z-test p = 0.070.
Mean difference: OXY/APAP
95% CI: -1.82 to 0.20
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| "Physical Functioning" Scale of the Medical Outcomes Survey (MOS) 36 Item Short-Form Health Survey (SF-36): Mean Percent ± Standard Error of the Mean (SEM) at Day 84 (LOCF) | Continuous Endpoint | Mean difference | -1.90 (-12.85 to 9.05) | 2,961 per arm |
| "Physical Role" Scale (MOS SF-36): Mean Percent ± SEM at Day 84(LOCF) | Continuous Endpoint | Mean difference | 5.50 (-9.41 to 20.41) | 645 per arm |
| "Bodily Pain" (MOS SF-36): Mean Percent at Day 84 (LOCF) | Continuous Endpoint | Mean difference | 3.70 (-5.32 to 12.72) | 526 per arm |
"Physical Functioning" Scale of the Medical Outcomes Survey (MOS) 36 Item Short-Form Health Survey (SF-36): Mean Percent ± Standard Error of the Mean (SEM) at Day 84 (LOCF)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- OXY/APAP: mean 44.50 versus 46.40 on control; difference -1.90 (95% CI -12.85 to 9.05), standardized effect d = -0.07; z-test p = 0.734.
- BTDS: mean 46.50 versus 46.40 on control; difference 0.10 (95% CI -10.45 to 10.65), standardized effect d = 0.00; z-test p = 0.985.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between OXY/APAP and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between BTDS and the control. The interval gives the range of effects that remain compatible with the data.
"Physical Role" Scale (MOS SF-36): Mean Percent ± SEM at Day 84(LOCF)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- OXY/APAP: mean 24.40 versus 18.90 on control; difference 5.50 (95% CI -9.41 to 20.41), standardized effect d = 0.16; z-test p = 0.470.
- BTDS: mean 33.90 versus 18.90 on control; difference 15.00 (95% CI 0.24 to 29.76), standardized effect d = 0.42; z-test p = 0.046.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between OXY/APAP and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for BTDS than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
"Bodily Pain" (MOS SF-36): Mean Percent at Day 84 (LOCF)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- OXY/APAP: mean 39.00 versus 35.30 on control; difference 3.70 (95% CI -5.32 to 12.72), standardized effect d = 0.17; z-test p = 0.421.
- BTDS: mean 41.90 versus 35.30 on control; difference 6.60 (95% CI -1.99 to 15.19), standardized effect d = 0.32; z-test p = 0.132.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between OXY/APAP and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between BTDS and the control. The interval gives the range of effects that remain compatible with the data.
The posted secondary outcomes cover health-status domains from the MOS SF-36, including physical functioning, physical role, bodily pain, general health, vitality, social functioning, emotional role, and mental health. The displayed secondary results include day-84 group means and unadjusted comparisons for some domains. Across those reported comparisons, estimates vary in direction and precision, and intervals often include zero. The registry record lists 14 posted secondary outcomes, while the outcome descriptions identify a broader set of measures.
The secondary results provide context about health-status measures alongside the primary pain-rating outcome, but they are not interchangeable with it. They assess different constructs and use day-84 levels rather than the primary endpoint’s mean change over days 21–84. As a result, agreement or disagreement across these measures would not directly replicate the primary comparison. The secondary findings do not remove the uncertainty around the primary recalculated intervals, nor do they establish the sponsor model’s effect estimates.
Unadjusted secondary results carry less weight because testing multiple outcomes increases the chance of finding apparently notable results by chance. The registry record does not report whether multiplicity was controlled, whether particular secondary outcomes were designated as confirmatory, or how the analyses were prioritized. The posted results should therefore be read as a collection of outcome-specific observations rather than as a set of independent confirmatory tests. The overall pattern can inform description of the recorded data, but it does not support selecting one favorable secondary result as definitive evidence.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- "Physical Functioning" Scale of the Medical Outcomes Survey (MOS) 36 Item Short-Form Health Survey (SF-36): Mean Percent ± Standard Error of the Mean (SEM) at Day 84 (LOCF)
- "Physical Role" Scale (MOS SF-36): Mean Percent ± SEM at Day 84(LOCF)
- "Bodily Pain" (MOS SF-36): Mean Percent at Day 84 (LOCF)
- "General Health" (MOS SF-36): Mean Percent ± SEM at Day 84 (LOCF)
- "Vitality" (MOS SF-36): Mean Percent ± SEM at Day 84 (LOCF)
- "Social Functioning" (MOS SF-36): Mean Percent ± SEM at Day 84 (LOCF)
- "Emotional Role" (MOS SF-36): Mean Percent ± SEM at Day 84 (LOCF)
- "Mental Health" (MOS SF-36):Mean Percent ± SEM at Day 84 (LOCF)
9. Statistical Interpretation
The posted primary outcome means show decreases from baseline in all three groups. The placebo mean change was -1.01, the OXY/APAP mean was -1.82, and the BTDS mean was -1.92. The recalculated unadjusted mean difference versus placebo is -0.81 for OXY/APAP, with a 95% confidence interval from -1.822 to 0.202, and -0.91 for BTDS, with a 95% confidence interval from -1.895 to 0.075. Each interval includes zero, so these unadjusted recalculations do not rule out no difference between the group means at the confidence level used for those intervals.
The registry’s own mixed models analysis reports p = 0.035 for placebo versus BTDS and p = 0.062 for placebo versus OXY/APAP. These are the sponsor-reported analyses and take precedence over the unadjusted recalculations. The registry does not report the corresponding sponsor-model effect estimates or confidence intervals in the available results. The difference between the sponsor’s BTDS p-value and the recalculated unadjusted comparison illustrates that the analyses are not interchangeable: the sponsor used mixed models, while the recalculation uses posted group summary statistics and approximations.
The observed group means are close in direction, with BTDS showing a more negative mean change than placebo and OXY/APAP also showing a more negative mean change than placebo. The confidence intervals from the recalculations are broad enough to include both a negative difference and a difference close to zero or positive. Thus, the group summaries alone do not precisely establish the size of the difference. A p-value is not a measure of the probability that a treatment effect is true, nor does it convey the magnitude or clinical importance of a difference.
The secondary outcomes describe several SF-36 health-status domains at day 84. Their unadjusted recalculated comparisons vary in direction and precision. These are additional analyses, and the registry record does not report a multiplicity adjustment or a prespecified hierarchy that would establish how they should influence interpretation of the primary result. Their results should therefore be viewed as exploratory context rather than independent confirmation.
Safety results should also be read descriptively. The registry reports serious adverse events affecting 2 participants in placebo, 3 in OXY/APAP, and 3 in BTDS. Counts of participants affected do not by themselves establish whether a difference is attributable to treatment, and the record does not report deaths. Taken together, the posted results describe observed outcomes in this study, but do not settle the size or reliability of all between-group differences or support conclusions beyond the recorded trial.
10. Statistical Methods Explained
The primary outcome is continuous: it is a numerical pain rating summarized as a mean change from baseline. The posted arm estimates are least-squares means with standard errors. A least-squares mean is a model-based group mean; the registry’s own primary comparison method is identified as mixed models analysis. The registry record does not provide the model specification, its covariates, or the detailed assumptions used in that analysis. Therefore, the sponsor-reported p-values can be described, but the exact model-based estimates cannot be reconstructed from the available information.
What does a mean difference represent?
The unadjusted recalculations compare the posted mean change in each active group with the placebo mean change. The estimate is the difference between those group means, expressed in the original scale units. A negative difference means the active-group mean change is more negative than the placebo mean change. For OXY/APAP, the recalculated difference is -0.81; for BTDS, it is -0.91. These are not adjusted mixed-model estimates. They are simple comparisons derived from the posted summary statistics.
What does a confidence interval convey?
A confidence interval gives a range of values compatible with the observed data under the calculation’s statistical assumptions. It communicates uncertainty about the estimated difference, rather than a range containing a stated percentage of individual participants. The recalculated 95% intervals for both primary comparisons include zero. This indicates that the posted summary data are compatible with no group difference as well as with differences in either direction within the interval. A confidence interval does not account for every possible source of uncertainty, such as model misspecification, missing-data bias, or selective reporting.
Why does the recalculation differ from the registry analysis?
The registry reports mixed models analyses and their p-values, but no model-based estimates or confidence intervals for the primary comparisons. The recalculation instead uses the posted arm means and standard errors to estimate unadjusted mean differences and intervals. For the primary endpoint, the standard deviations used in that recalculation are approximated from the standard errors and group sizes, as indicated by the calculation method. Such an approximation is not identical to fitting the sponsor’s mixed model, which may incorporate repeated measurements or other model features not reported in the record. Because the registry reports a discrepancy, the sponsor’s own analysis takes precedence.
How should p-values be read?
A p-value describes how incompatible the observed data are with a specified null model, conditional on the analysis assumptions. It is not the probability that the null hypothesis is true, nor a measure of treatment benefit, effect size, or clinical importance. The sponsor-reported values are 0.035 for placebo versus BTDS and 0.062 for placebo versus OXY/APAP. The recalculated unadjusted values are 0.07 and 0.117, respectively. These values come from different analyses, and should not be treated as competing versions of one identical calculation. The sponsor analysis is the relevant reported analysis; the simple recalculations offer a separate view based on the available summaries.
Why can repeated measurements require modeling?
Measurements collected repeatedly from the same participant are generally related rather than independent. A mixed model can account for such within-participant structure, depending on its specification. This is a general statistical point, not a claim about the exact model used in this trial: the registry identifies mixed models analysis but does not describe its form, covariance assumptions, or handling of every scheduled measurement. The primary outcome also uses LOCF, which substitutes the last observed value for a later missing value. This is a missing-data procedure, not a guarantee that the substituted value is unbiased.
What does over-dispersion mean in general?
For count outcomes, over-dispersion means that observed variation exceeds what a simple count model assumes. It can make standard errors too small if the extra variation is ignored. This is a general concept and is not a reported feature of this trial’s primary continuous pain outcome. The primary endpoint is a mean of a continuous measure, so count-model over-dispersion is not the central issue for its interpretation.
These methods distinguish the registry’s model-based analysis from the simple unadjusted re-calculation. Neither a small p-value nor a particular confidence interval should be interpreted without considering the endpoint definition, analysis population, missing-data approach, and the limits of the registry’s statistical detail.
11. Confidence Intervals and Precision
The primary recalculated differences are -0.81 for OXY/APAP versus placebo and -0.91 for BTDS versus placebo. Their 95% confidence intervals are -1.822 to 0.202 and -1.895 to 0.075, respectively. Both intervals include zero, and both extend across values representing differences in either direction. This indicates that the estimated differences are not highly precise from the posted summary statistics alone.
A confidence interval is not a guarantee that the true value lies inside its endpoints. Rather, it describes uncertainty under a specified method and its assumptions. These intervals arise from unadjusted recalculations, not the sponsor’s mixed models analysis. The sponsor analysis reports p-values but does not report corresponding estimates or confidence intervals in the registry results available for these comparisons. The two kinds of results therefore cannot be combined as if they came from the same model.
The intervals are also not measures of individual variation. Standard errors describe uncertainty in a group estimate, while the between-participant spread can be larger. For the primary outcome, the registry lists standard errors of 0.37 for placebo, 0.36 for OXY/APAP, and 0.34 for BTDS. The recalculated standard deviations are approximations based on those standard errors and group sizes, rather than separately reported individual-level variability.
Precision is limited by the information available in the registry record and by the number of observations contributing to each analysis. The record does not provide the original analysis model details or enough information to calculate model-based confidence intervals independently. The interpretation should therefore retain both details: the estimated differences favor a greater decrease in the active-group means, while the recalculated intervals include zero and leave substantial uncertainty about the magnitude.
12. 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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 140 | 187 |
| 75% of the observed effect | 248 | 332 |
| 50% of the observed effect | 557 | 745 |
The planning figures are participants per arm for the continuous outcomes in this trial. They are not total event counts. The illustrations use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. For each row, the effect to detect is a stated fraction of the observed effect: 100%, 75%, or 50%. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.
The 80% power column gives the illustrative number of participants per arm under those assumptions to have an 80% chance of detecting the specified effect if that effect is present and the assumptions hold. The 90% power column gives the corresponding planning number for a 90% chance. These are prospective planning illustrations, not estimates of what this trial’s design targeted.
The rows show why smaller effects require more participants: detecting 75% or 50% of the observed effect requires larger group sizes than detecting the full observed effect. When the observed effect is very small, the implied planning numbers can become very large. Such calculations are sensitive to the observed estimate, which itself is uncertain and may not represent the effect expected in a future study.
These figures are not observed power. They do not tell whether the completed trial had enough power to identify its true effect, and they do not turn a non-significant result into evidence of no effect. They are conditional illustrations based on the observed differences and listed assumptions. The original protocol’s planning choices, including any target effect or allowance for attrition, are not reported in the registry record.
13. 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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = -0.810; pooled standard deviation σ = 2.411.
- n = 2 × (1.96 + 0.842)2 × 2.4112 / -0.8102 = 139.1, rounded up to 140 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 <- -0.81 # observed difference in means
sigma <- 2.41132914287828 # 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(315445)
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 = 140 (80% power), 187 (90% power)
75% of observed effect: n per arm = 248 (80% power), 332 (90% power)
50% of observed effect: n per arm = 557 (80% power), 745 (90% power)
power.t.test: 140.1
Simulated power at n = 140 per arm: 0.801 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | not reported | 0.035 | |
| Mixed Models Analysis | not reported | 0.062 |
For the primary endpoint, the registry reports mixed models analyses comparing placebo with BTDS and placebo with OXY/APAP. The sponsor-reported p-values are 0.035 for placebo versus BTDS and 0.062 for placebo versus OXY/APAP. The registry does not report an effect estimate or confidence interval for either mixed-model comparison in the results available for these analyses.
The recalculated comparisons use the posted group means and standard errors to obtain unadjusted mean differences, confidence intervals, and p-values. They give -0.91 for BTDS versus placebo, with p = 0.07, and -0.81 for OXY/APAP versus placebo, with p = 0.117. These calculations are not a reproduction of the sponsor’s mixed models, and the primary recalculation uses approximated standard deviations.
Because the registry record identifies a discrepancy between the sponsor analysis and the recalculation, the sponsor’s own analysis takes precedence. The recalculations remain useful as a transparent, summary-statistic-based check of the direction and approximate precision of the differences, but they should not replace the reported mixed-model analyses. Without the sponsor’s model estimates, confidence intervals, and specification, the registry record does not allow a complete numerical reconciliation of the results.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists numerous outcome measures and analyses, including multiple secondary health-status domains and comparisons between each active-treatment group and placebo. Testing multiple outcomes creates a multiplicity concern: even when there is no underlying effect, the chance of at least one apparently unusual result can increase as more tests are considered. This is a general statistical issue, not evidence that any particular reported result is false.
The registry record does not report a multiplicity adjustment, a prespecified hierarchy of endpoints, or a confirmatory testing strategy. It also does not state whether the sponsor’s primary comparisons were adjusted for multiple group comparisons. Consequently, the reported p-values should be interpreted in the context of the analyses actually listed, without assuming a correction or a testing order that is not documented. The secondary comparisons are especially important to treat cautiously when they are considered together.
The primary endpoint uses LOCF. That method carries the participant’s last recorded pain value forward for later missing measurements. The registry does not report the number or pattern of missing primary observations, nor does it describe sensitivity analyses that might show how conclusions change under other missing-data assumptions. Missingness can matter if the chance of a missing observation is related to pain status or treatment response; this is a general concern, not a reported finding about this study.
The registry states that all 134 randomized subjects received study drug and were included in intent-to-treat and safety analyses, while efficacy data were available for 133 subjects. The reason given for the participant without efficacy data is that informed consent was never obtained, and that participant was included in the analysis statement as written in the record. Arm-level counts for individual outcomes are not identical across all analyses. The detailed analysis-population rules beyond these statements are not reported in the registry record.
These limitations affect how confidently outcome-specific estimates can be interpreted. They do not establish that the reported analyses are invalid, but they make it important to distinguish the stated analysis methods from undocumented choices and to avoid treating a collection of unadjusted findings as a single confirmatory conclusion.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo | 2 | 45 | 4.4% |
| OXY/APAP | 3 | 43 | 7.0% |
| BTDS | 3 | 46 | 6.5% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo | 20 of 45 |
| OXY/APAP | 35 of 43 |
| BTDS | 37 of 46 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | OXY/APAP | BTDS |
|---|---|---|---|---|
| Chest pain | General disorders | 0 of 45 | 1 of 43 | 0 of 46 |
| Fractured humerous | Investigations | 0 of 45 | 1 of 43 | 0 of 46 |
| Increased back pain | General disorders | 1 of 45 | 0 of 43 | 0 of 46 |
| Syncope | Cardiac disorders | 0 of 45 | 0 of 43 | 1 of 46 |
| Diverticulitis | Gastrointestinal disorders | 0 of 45 | 0 of 43 | 1 of 46 |
| Bowel obstruction | Gastrointestinal disorders | 1 of 45 | 0 of 43 | 0 of 46 |
| Obstructed right kidney | Renal and urinary disorders | 0 of 45 | 1 of 43 | 0 of 46 |
| Pyelonephritis | Renal and urinary disorders | 0 of 45 | 1 of 43 | 0 of 46 |
| Asthma | Respiratory, thoracic and mediastinal disorders | 0 of 45 | 0 of 43 | 1 of 46 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | OXY/APAP | BTDS |
|---|---|---|---|---|
| Nausea | Gastrointestinal disorders | 6 of 45 | 19 of 43 | 17 of 46 |
| Dizziness | Nervous system disorders | 7 of 45 | 14 of 43 | 14 of 46 |
| Somnolence | Nervous system disorders | 4 of 45 | 17 of 43 | 12 of 46 |
| Constipation | Gastrointestinal disorders | 7 of 45 | 14 of 43 | 10 of 46 |
| Headache | General disorders | 6 of 45 | 7 of 43 | 13 of 46 |
| Dry mouth | Gastrointestinal disorders | 5 of 45 | 9 of 43 | 10 of 46 |
| Vomiting | Gastrointestinal disorders | 0 of 45 | 12 of 43 | 12 of 46 |
| Pruritus at site | Skin and subcutaneous tissue disorders | 7 of 45 | 9 of 43 | 7 of 46 |
| Pruritus | Skin and subcutaneous tissue disorders | 2 of 45 | 4 of 43 | 6 of 46 |
| Dyspepsia | Gastrointestinal disorders | 4 of 45 | 1 of 43 | 6 of 46 |
Serious events with the highest arm-level rate: chest pain (2.3%), fractured humerous (2.3%), obstructed right kidney (2.3%), pyelonephritis (2.3%), increased back pain (2.2%).
The registry reports serious adverse events affecting 2 participants in the placebo group, 3 in the OXY/APAP group, and 3 in the BTDS group. The corresponding numbers at risk are 45, 43, and 46. These are counts of participants affected, not counts of every event, and the registry record does not report deaths.
For other adverse events, the registry reports 20 participants affected in placebo, 35 in OXY/APAP, and 37 in BTDS, with the at-risk group counts shown alongside the safety results. These are a separate reporting category from serious adverse events and should not be combined with the serious-event figures.
The registry lists serious-event terms with percentages, including Chest pain, Fractured humerous, Obstructed right kidney, and Pyelonephritis at 2.3%, and Increased back pain and Bowel obstruction at 2.2%. The record does not provide enough detail in these summary figures to determine event timing, recurrence, relatedness assessments, or comparative risk. These counts describe reported safety observations during the study; they do not alone establish that a treatment caused an event or quantify safety outside the trial.
17. What the Result Does, and Does Not, Mean
The posted results describe changes in average pain ratings and other outcomes among people enrolled in a randomized, double-blind trial of chronic back pain treatments. Mean pain ratings decreased from baseline in each group. The BTDS and OXY/APAP group means showed larger decreases than placebo in the posted primary outcome summaries. The registry’s mixed-model analyses report p = 0.035 for placebo versus BTDS and p = 0.062 for placebo versus OXY/APAP. Separate unadjusted recalculations yield confidence intervals that include zero; because the analyses differ, the sponsor’s own analysis takes precedence.
These findings do not, by themselves, establish the clinical importance of a difference. The registry does not supply a threshold for a clinically meaningful change in this pain scale, and the available sponsor results do not include model-based effect estimates or confidence intervals. A p-value alone cannot show the size of an effect or whether a difference matters to participants. The relatively broad recalculated intervals also leave uncertainty about the magnitude of the group differences.
The results apply to the recorded study population, interventions, outcome definitions, and follow-up period. The treatment period was 84 days, and the primary outcome uses LOCF. The registry record does not provide detailed information about missing-data patterns, the complete statistical model, or the original sample-size justification. These omissions limit independent assessment of analysis assumptions and generalizability.
The safety counts are descriptive and should not be read as proof of causation or as a complete account of all possible risks. Likewise, secondary findings should be interpreted cautiously because multiple outcomes are reported and the registry record does not describe multiplicity control. The evidence supports a careful account of what was observed in this trial, not a medical recommendation or a conclusion about outcomes beyond its recorded data.
18. Why This Trial Matters Statistically
This trial illustrates why clinical trial interpretation requires more than reading group means or a single p-value. The primary outcome is a repeated pain measure summarized over time, and the registry reports a mixed-model analysis. The posted summary statistics also permit an unadjusted recalculation, but that calculation does not reproduce the sponsor’s model. The difference between the sponsor p-values and recalculated p-values makes the distinction between analysis methods consequential rather than merely technical.
The example also shows the value of reporting effect estimates and confidence intervals alongside tests. The sponsor’s primary analyses include p-values but no corresponding estimates or intervals in the registry results available for those comparisons. The unadjusted recalculations supply an approximate view of magnitude and uncertainty, but they are not substitutes for model-based results. Clear reporting of model estimates, uncertainty intervals, analysis populations, and missing-data handling would make the evidence easier to assess.
Finally, this record includes multiple outcome measures, group comparisons, LOCF, and safety summaries. Each element raises a different interpretive question: how outcomes were defined, how missing observations were handled, whether multiple testing was considered, and what the adverse-event counts represent. The trial is statistically instructive because it demonstrates how those features affect confidence in conclusions even when randomization and blinding are reported. Careful reading separates what the record states from what remains unknown.
19. 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.
Several trial-specific limitations constrain interpretation. The registry describes a treatment duration of 84 days, so the recorded outcomes concern the study period and do not establish longer-term patterns. The primary endpoint applies LOCF to missing observations, but the registry does not report the extent or timing of missing primary data, or the results of sensitivity analyses using other assumptions.
The primary sponsor analyses are identified as mixed models, but their model specification, estimated group differences, and confidence intervals are not reported in the available results. The recalculated estimates are unadjusted and use approximated standard deviations for the primary outcome. Because the registry identifies a discrepancy, the sponsor’s own analysis takes precedence, while the recalculation should be treated as a supplementary summary-statistic analysis.
The record does not report the original sample-size justification or detailed design assumptions. Planning illustrations based on observed effects cannot reveal the trial’s intended target effect or its original design rationale. The analysis populations are described at a high level, but detailed rules for inclusion in each individual analysis are not reported. The registry also does not describe multiplicity handling across the numerous outcomes and analyses.
The secondary outcomes use different measures and time summaries from the primary endpoint, and only some secondary results are detailed in the record. Their interpretation is further limited by the absence of reported multiplicity procedures. Safety summaries give counts of affected participants and selected event terms, but do not provide enough detail to assess timing, seriousness criteria, relatedness, or recurrence for each event. These limitations do not negate the observations; they define what can and cannot be concluded from the registry record.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: The Safety and Efficacy of the Buprenorphine Transdermal System (BTDS) in Subjects With Chronic Back Pain. — NCT00315445.
- Registry record last updated 2012-09-03; status last verified 2012-08.
- Results first posted 2011-08-10.
- 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.
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23. Record Summary
NCT00315445 is a completed phase 3 randomized, double-blind, parallel-group study of buprenorphine transdermal therapy, oxycodone/acetaminophen, and placebo in subjects with chronic back pain. Enrollment was 134, and the registry describes an 84-day treatment period. The primary endpoint was mean change from baseline in average pain ratings over days 21–84 using LOCF.
The posted primary group means were -1.01 for placebo, -1.82 for OXY/APAP, and -1.92 for BTDS. Sponsor-reported mixed-model p-values were 0.062 for placebo versus OXY/APAP and 0.035 for placebo versus BTDS. Unadjusted recalculations give intervals that include zero; due to the reported discrepancy, the sponsor analysis takes precedence. Secondary outcomes and safety counts add descriptive context, with interpretation limited by missing analysis details, LOCF, and unreported multiplicity procedures.