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 Psychosocial Pain Management to Improve Opioid Use Disorder Treatment Outcomes (NCT04433975), a randomized na study. The primary outcome is Retention on Buprenorphine Treatment According to TimeLine Follow-Back - 3-months.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT04433975 |
| Phase | NA |
| Condition | Opioid-use Disorder, Medication Assisted Treatment, Chronic Pain |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Single |
| Enrollment | 200 |
| Arms in the primary outcome | 2 |
| Lead sponsor | University of Michigan |
| Results posted | Yes |
2. Clinical Question
Population
The registry describes people with chronic pain who had recently begun buprenorphine treatment for opioid-use disorder. The study was intended to examine whether participants could benefit from programs addressing pain and medication management. The enrollment was 200 participants.
Intervention
Psychosocial Pain Management (PPMI) consisted of eight individual telephone or video therapy sessions with a research study therapist. The sessions were based on Cognitive Behavioral Therapy.
Comparator
Enhanced Usual Care (EUC) consisted of two individual telephone educational sessions with a research study therapist. Both interventions were behavioral.
Primary question
The primary outcome was the average number of days participants remained on buprenorphine before stopping it for 7 or more days in a row. It was assessed using calendar recall at 3-month follow-up. The statistical comparison asks whether the average number of days differed between PPMI and EUC over that period. It does not, by itself, answer whether either program changes pain, substance use, or longer-term treatment outcomes.
3. Trial Design
The registry describes a randomized, parallel-group trial with single masking. Participants were assigned to Psychosocial Pain Management (PPMI) or Enhanced Usual Care (EUC). The record does not identify who was masked, so the masking description cannot establish whether participants, therapists, outcome assessors, or another group were unaware of assignment.
The study enrolled 200 participants: 98 in PPMI and 102 in EUC for the primary outcome. PPMI involved eight individual telephone or video therapy sessions based on Cognitive Behavioral Therapy. EUC involved two individual telephone educational sessions. Both were delivered by a research study therapist. The registry’s brief description frames the research around pain and medication-management education and strategies for people with chronic pain who had recently begun buprenorphine treatment.
The study status is completed. The registry lists a start date of 2020-08-14 and a primary completion date of 2024-05-23. The phase is listed as NA. The record does not report how randomization was generated, whether allocation was concealed, or whether any treatment-adherence requirements were used. Those details are not reported in the registry record and should not be inferred from the randomized design alone.
The primary endpoint was retention on buprenorphine measured at 3 months. Other outcomes listed include retention at 12 months, changes in pain intensity and pain-related functioning, and days abstinent from substance use. The registry lists eight outcome measures in total. These outcomes span different domains and follow-up periods, so their interpretation depends on the outcome definition and the amount of data available for each measure.
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.
Completed Baseline and Randomized
| Stage | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| STARTED | 98 | 102 |
| COMPLETED | 98 | 102 |
| NOT COMPLETED | 0 | 0 |
1-month Follow Up
| Stage | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| STARTED | 98 | 102 |
| Completed Interview | 81 | 82 |
| COMPLETED | 76 | 76 |
| NOT COMPLETED | 22 | 26 |
Reasons for not completing this period:
| Reason | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| Withdrawal by Subject | 1 | 1 |
| Lost to Follow-up | 21 | 25 |
3-month Follow Up
| Stage | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| STARTED | 97 | 101 |
| Completed Interview | 78 | 84 |
| COMPLETED | 74 | 77 |
| NOT COMPLETED | 23 | 24 |
Reasons for not completing this period:
| Reason | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| Lost to Follow-up | 20 | 24 |
| Death | 1 | 0 |
| Withdrawal by Subject | 2 | 0 |
6-month Follow Up
| Stage | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| STARTED | 94 | 101 |
| Completed Interview | 72 | 74 |
| COMPLETED | 70 | 72 |
| NOT COMPLETED | 24 | 29 |
Reasons for not completing this period:
| Reason | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|
| Lost to Follow-up | 23 | 28 |
| Withdrawal by Subject | 1 | 1 |
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 | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) | Total |
|---|---|---|---|---|
| Participants analysed | 98 | 102 | 200 | |
| Age, Continuous | years | 42.37 (SD 10.79) | 44.68 (SD 10.78) | 43.55 (SD 10.82) |
| Sex: Female, Male: Female | Participants | 57 | 58 | 115 |
| Sex: Female, Male: Male | Participants | 41 | 44 | 85 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 8 | 4 | 12 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 88 | 97 | 185 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 2 | 1 | 3 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Asian | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 12 | 8 | 20 |
| Race (NIH/OMB): White | Participants | 75 | 90 | 165 |
| Race (NIH/OMB): More than one race | Participants | 3 | 1 | 4 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 8 | 3 | 11 |
| Region of Enrollment: United States | participants | 98 | 102 | 200 |
| Military Status | Participants | 2 | 5 | 7 |
| Brief Pain Inventory (BPI) Score | units on a scale | 4.7 (SD 2.2) | 4.8 (SD 2.4) | 4.8 (SD 2.3) |
| Percent days abstinent | percent | 51.3 (SD 33.2) | 50.9 (SD 34.0) | 51.1 (SD 33.6) |
| Numeric Rating Scale (NRS-I) Score | units on a scale | 7.43 (SD 1.28) | 7.55 (SD 1.26) | 7.49 (SD 1.28) |
| Rapid Opioid Dependence Screen (RODS) | units on a scale | 6.22 (SD 1.36) | 6.04 (SD 1.52) | 6.13 (SD 1.44) |
| Severity of Opioid Use Disorder: Mild | Participants | 8 | 13 | 21 |
| Severity of Opioid Use Disorder: Moderate | Participants | 11 | 14 | 25 |
| Severity of Opioid Use Disorder: Severe | Participants | 79 | 75 | 154 |
6. Primary Endpoint
The registry lists the primary outcome as Retention on Buprenorphine Treatment According to TimeLine Follow-Back - 3-months, measured over 3-months post enrollment.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | days |
| Endpoint classification | Continuous Endpoint |
The primary endpoint measures time on buprenorphine, in days, before a participant stopped taking the medication for 7 or more days in a row. The registry says this was assessed with the TimeLine Follow-Back (TLFB), a calendar recall method, at 3 months after enrollment. The reported summary is the mean number of days participants remained on treatment before meeting the stopping definition.
This endpoint is used to represent short-term treatment retention. In general, a retention measure can capture whether participants continue taking a medication over a defined period, rather than only whether they report a symptom or behavior at a single visit. Its meaning depends on how discontinuation is defined and how information is collected. Here, a stop of 7 or more consecutive days is the stated threshold, and the information came from calendar recall at follow-up. The registry does not describe any additional confirmation method.
The mean provides a group-level summary: it averages the recorded days across participants with outcome data. It does not show the distribution of individual retention times or establish why someone stopped treatment. Nor does the endpoint alone describe pain intensity, pain-related functioning, substance use, or retention after the 3-month assessment. Those are separate outcomes in the registry.
7. Results Posted in the Registry
- Psychosocial Pain Management (PPMI): mean 81.10 versus 75.40 on control; difference 5.70 (95% CI -2.49 to 13.89), standardized effect d = 0.19; z-test p = 0.172.
Mean difference: Psychosocial Pain Management (PPMI)
95% CI: -2.49 to 13.89
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 |
|---|---|---|---|---|
| Retention on Buprenorphine Treatment According to TimeLine Follow-Back - 12 Months | Continuous Endpoint | Mean difference | 15.60 (-23.83 to 55.03) | 1,310 per arm |
| Average Change in Self-reported Level of Pain Intensity on the Numerical Rating Scale for Pain Intensity (NRS-I) at 3-month Follow up (Compared to Baseline) | Continuous Endpoint | Mean difference | 0.40 (-0.18 to 0.98) | 334 per arm |
| Average Change in Self-Reported Level of Pain Related Functioning on the Brief Pain Inventory - Short Form (BPI) at 3-month Follow up (Compared to Baseline) | Continuous Endpoint | Mean difference | 0.50 (-0.19 to 1.19) | 291 per arm |
Retention on Buprenorphine Treatment According to TimeLine Follow-Back - 12 Months
- 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 deviations.
- Result:
- Psychosocial Pain Management (PPMI): mean 252.10 versus 236.50 on control; difference 15.60 (95% CI -23.83 to 55.03), standardized effect d = 0.11; z-test p = 0.438.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Psychosocial Pain Management (PPMI) and the control. The interval gives the range of effects that remain compatible with the data.
Average Change in Self-reported Level of Pain Intensity on the Numerical Rating Scale for Pain Intensity (NRS-I) at 3-month Follow up (Compared to Baseline)
- 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 deviations.
- Result:
- Psychosocial Pain Management (PPMI): mean -0.70 versus -1.10 on control; difference 0.40 (95% CI -0.18 to 0.98), standardized effect d = 0.22; z-test p = 0.178.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Psychosocial Pain Management (PPMI) and the control. The interval gives the range of effects that remain compatible with the data.
Average Change in Self-Reported Level of Pain Related Functioning on the Brief Pain Inventory - Short Form (BPI) at 3-month Follow up (Compared to Baseline)
- 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 deviations.
- Result:
- Psychosocial Pain Management (PPMI): mean -0.30 versus -0.80 on control; difference 0.50 (95% CI -0.19 to 1.19), standardized effect d = 0.23; z-test p = 0.154.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Psychosocial Pain Management (PPMI) and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes extend the research question beyond 3-month retention. They include retention on buprenorphine at 12 months, pain intensity and pain-related functioning at 3 and 12 months, and percent days abstinent from substance use at 3 and 12 months. The registry lists seven secondary outcomes. Numerical summaries and unadjusted comparisons are posted for 12-month retention and for the two pain measures at 3 months; the record does not report numerical results for the other listed secondary outcomes.
The available secondary comparisons do not present a single consistent pattern that can be treated as a confirmatory result across every outcome. Their outcomes differ in scale, follow-up, and participant counts, and they are not interchangeable with the primary endpoint. They provide context about related areas of interest, but they do not redefine the primary result, which concerns mean days retained on buprenorphine at 3 months.
In general, secondary outcomes are often useful for describing broader patterns and generating questions for later research. Their interpretation depends on whether they were prespecified, how many outcomes were examined, how missing observations were handled, and whether adjustments for multiple testing were planned. The registry record does not report a multiplicity procedure or detailed analysis plan. Consequently, unadjusted secondary comparisons carry less weight as confirmatory evidence than a clearly prespecified primary analysis, especially when several outcomes and follow-up periods are considered.
Different denominators across outcome measures also matter. A secondary result based on fewer participants may have different precision from the primary result. The record does not explain why the available sample differs by outcome, so those differences should not be attributed to a particular cause. In combination, the secondary listings indicate the scope of measurement, while the posted estimates should be interpreted individually and cautiously rather than combined into a single overall conclusion.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Retention on Buprenorphine Treatment According to TimeLine Follow-Back - 12 Months
- Average Change in Self-reported Level of Pain Intensity on the Numerical Rating Scale for Pain Intensity (NRS-I) at 3-month Follow up (Compared to Baseline)
- Average Change in Self-Reported Level of Pain Related Functioning on the Brief Pain Inventory - Short Form (BPI) at 3-month Follow up (Compared to Baseline)
- Percent Days Abstinent From Substance Use on the TimeLine Follow-Back - 3-months
- Average Change in Self-reported Level of Pain Intensity on the Numerical Rating Scale for Pain Intensity (NRS-I) at 12-month Follow up (Compared to Baseline)
- Average Change in Self-Reported Level of Pain Related Functioning on the Brief Pain Inventory - Short Form (BPI) at 12-month Follow up (Compared to Baseline)
- Percent Days Abstinent From Substance Use on the TimeLine Follow-Back - 12 Months
9. Statistical Interpretation
For the primary outcome, the PPMI group had a reported mean of 81.1 days, compared with 75.4 days for EUC. The unadjusted mean difference, expressed as PPMI minus EUC, is 5.7 days. Its 95% confidence interval is -2.487 to 13.89 days, and the unadjusted p-value is 0.172.
The observed group means therefore differ in the positive direction, but the interval is compatible with a range of underlying differences that includes a negative difference as well as a positive one. The estimate is not precise enough to distinguish clearly between those possibilities. The p-value is a measure of how compatible the observed data are with a specified no-difference model under the calculation used; it is not the probability that the treatment effect is zero, and it does not measure clinical importance.
The record reports means and standard deviations: 81.1 days with a standard deviation of 26.6 for PPMI, and 75.4 days with a standard deviation of 32.3 for EUC. The standard deviations describe variation among participants within each group. They are distinct from the uncertainty around the difference between group means, which is represented by the confidence interval.
The comparison is an unadjusted calculation from the posted group summaries. The registry record does not report a formal analysis plan, covariate adjustment, or the method used for an inferential analysis. It also does not report an analysis population definition. The result should therefore be read as a straightforward comparison of the posted summaries, rather than as evidence about any unreported adjusted or model-based analysis.
The same caution applies to the other outcomes. Some secondary comparisons have estimates and confidence intervals that also include values on either side of no difference. They cover different outcomes and follow-up periods, so they do not change the definition or interpretation of the primary endpoint. The presence of several outcomes also raises questions about multiplicity: when many outcomes are examined, chance findings become more plausible unless an appropriate analysis strategy is specified. Such a strategy is not reported in the registry record.
These results describe the recorded groups and the endpoint as defined. They do not establish the cause of individual outcomes, and they should not be translated into a recommendation about treatment. The registry record does not report a sponsor-authored inferential analysis alongside the posted summaries; the numerical comparison is an unadjusted recalculation from those summaries. No discrepancy is flagged between the recalculation and a sponsor analysis.
10. Statistical Methods Explained
The primary outcome is continuous: it is a count of days summarized by a group mean and standard deviation. A mean difference is a natural way to express how the group averages compare. The comparison is PPMI minus EUC, so a positive estimate means the posted PPMI mean is higher, while a negative estimate would mean it is lower. This direction describes the arithmetic contrast and does not, by itself, establish a meaningful or causal effect.
What does a standard deviation describe?
In general, a standard deviation describes how spread out individual observations are around their group mean. It is not the same as a confidence interval for a mean or for a difference. The posted standard deviations for the primary outcome are 26.6 days in PPMI and 32.3 days in EUC. These indicate variation in participant outcomes within each group, while the confidence interval for the mean difference describes uncertainty in the estimated contrast.
In general, the standard error of a mean reflects the precision of that estimated mean and depends on both the variability of observations and the number of observations. A difference between two independent group means has uncertainty contributed by both groups. The posted primary comparison uses 98 participants in PPMI and 102 in EUC. The record does not report the detailed statistical procedure used by the investigators, so the recalculated comparison should not be mistaken for a documented sponsor model.
How should the p-value be read?
In general, a p-value evaluates how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It is not a measure of the size of a difference, the probability that the null hypothesis is true, or the probability that a result occurred by chance. The posted unadjusted p-value for the primary mean difference is 0.172. It should be interpreted alongside the estimated difference and confidence interval, not as a standalone decision rule.
The word “unadjusted” matters because no correction for examining multiple outcomes is reflected in this p-value. The record lists several outcomes, but it does not report a multiplicity strategy or an analysis plan describing which outcomes would be emphasized. General statistical practice treats isolated unadjusted results cautiously when multiple comparisons are possible, particularly when the comparisons are not all independent or when the primary and secondary outcomes have different roles.
What does the confidence interval add?
In general, a confidence interval displays a range of effect estimates compatible with the observed data under the chosen method and its assumptions. It conveys both the direction and the precision of the estimated contrast. For the primary result, the interval extends from -2.487 to 13.89 days. Because it includes zero, it includes no mean difference as one possibility, as well as differences in either direction. The interval does not give the probability that the true effect lies within its particular endpoints.
The registry provides no standard errors or confidence limits for the group means themselves. It does provide the group standard deviations and the comparison interval. The comparison statistics are straightforward unadjusted calculations from the posted summaries. The record does not identify whether the investigators used an alternative model, how they handled deviations from statistical assumptions, or whether they planned a transformation or other outcome-specific procedure.
Why can outcome distributions matter?
In general, methods that compare means rely on assumptions about the sampling distribution of the estimate. Very skewed outcomes, influential observations, or unequal variability can affect how well a simple approximation describes uncertainty. The record gives means and standard deviations but does not provide participant-level data, distributional plots, or diagnostics. It is therefore not possible to assess those features from the registry summaries alone. This is a limitation of the available aggregate information, not evidence that any assumption was violated.
Retention is described as days before a participant stopped medication for at least 7 consecutive days, assessed at a 3-month follow-up. The registry reports the endpoint as a mean and standard deviation, not as a time-to-event analysis. The statistical comparison should therefore be read according to the posted continuous summary, without assuming that a survival model or censoring method was used. The record does not report such a model or its assumptions.
General statistical interpretation also distinguishes a difference in group averages from a difference for every participant. Group means can conceal variation in individual responses. Without participant-level results, subgroup summaries, or a reported distribution, the posted means cannot show whether outcomes were similar across participants or concentrated in a smaller part of the group.
11. Confidence Intervals and Precision
The primary mean difference is 5.7 days, with a 95% confidence interval from -2.487 to 13.89 days. The interval is wide enough to include a negative difference, no difference, and a positive difference. Thus the point estimate gives one summary of the observed contrast, while the interval communicates that the direction and size remain uncertain. It does not prove that the groups are equivalent, nor does it establish that a particular value inside the interval is likely.
In general, a confidence interval is constructed by a statistical procedure that has a stated long-run coverage property when its assumptions hold. It is not a range containing a fixed percentage probability for the true effect after the data have been observed. Its width reflects the amount of information and variability, together with the method used. The registry does not report the investigators’ interval-estimation method, so the posted interval should be interpreted as the available numerical precision rather than as a complete account of the analysis.
The group standard deviations are 26.6 days for PPMI and 32.3 days for EUC. These values describe participant-level spread, not uncertainty in the mean difference. The 95% interval is the more direct summary of uncertainty about the contrast. Its endpoints are on the days scale, matching the endpoint’s unit.
Precision is also outcome-specific. Secondary outcomes have different numbers of participants with posted data and different measures, so their precision cannot be inferred from the primary comparison. A narrow or wide interval should be considered in relation to the measure and its scale, and an interval crossing zero should not be treated as evidence that all potentially important differences have been ruled out.
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 | 425 | 569 |
| 75% of the observed effect | 755 | 1,011 |
| 50% of the observed effect | 1,699 | 2,274 |
The planning illustrations for these continuous outcomes are stated as participants per arm, not total events. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each illustration uses the stated fraction of the observed effect as the effect to detect. These are planning assumptions for the illustrations; the registry record does not report the trial’s original sample-size justification or design assumptions.
The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed for an 80% chance of detecting the specified effect under those assumptions, if that effect were the true effect and the assumptions held. The 90% column gives the corresponding planning quantity for a 90% chance. Power is conditional on a particular effect size and statistical setup; it is not a property of the observed result alone.
For the primary outcome, planning for 100% of the observed effect gives 425 participants per arm for 80% power and 569 participants per arm for 90% power. Planning for 75% of the observed effect gives 755 participants per arm for 80% power and 1,011 participants per arm for 90% power. Planning for 50% of the observed effect gives 1,699 participants per arm for 80% power and 2,274 participants per arm for 90% power. Smaller effects require more participants because they are harder to distinguish from sampling variation under the same assumptions.
These are prospective planning illustrations based on the observed effect, not observed power. They do not establish that the completed trial was designed around these figures, and they should not be used to infer the original investigators’ rationale. Planning based on an observed effect can be particularly uncertain when that estimate itself is imprecise.
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 = 5.700; pooled standard deviation σ = 29.645.
- n = 2 × (1.96 + 0.842)2 × 29.6452 / 5.7002 = 424.6, rounded up to 425 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 <- 5.69999999999999 # observed difference in means
sigma <- 29.6448344930649 # 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(4433975)
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 = 425 (80% power), 569 (90% power)
75% of observed effect: n per arm = 755 (80% power), 1,011 (90% power)
50% of observed effect: n per arm = 1,699 (80% power), 2,274 (90% power)
power.t.test: 425.6
Simulated power at n = 425 per arm: 0.800 (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. Multiplicity, Missing Data and Analysis Populations
The registry lists one primary outcome and several secondary outcomes across multiple domains and follow-up periods. When researchers test many outcomes, the chance of at least one apparently unusual result can rise, even if there is no underlying effect for any outcome. In general, a prespecified hierarchy, adjustment method, or other multiplicity strategy can help define how results should be interpreted. Such a strategy is not reported in the registry record. The posted p-values for the comparisons are unadjusted, so they should not be read as multiplicity-controlled evidence.
The record also does not report a statistical analysis plan, outcome hierarchy beyond the primary designation, or details about interim analyses. The absence of a report is not evidence that a procedure was or was not used; it means those details cannot be evaluated from the registry record. The number of reported analyses is listed as zero, and no secondary analyses are attached to the listed outcomes in the registry information used for these summaries. The displayed unadjusted comparisons should therefore be distinguished from any formal analysis that may have occurred outside the posted record.
Missing-data handling is another unresolved issue. The primary outcome has 98 participants in PPMI and 102 in EUC, while some secondary outcomes have smaller posted group counts. The record does not explain the reasons for those differences, describe how missing observations were handled, or state whether imputation was used. No analysis population definition, such as an intention-to-treat or per-protocol population, is reported. It is not possible to infer from the counts alone whether missingness reflects nonresponse, outcome eligibility, data quality, or another reason.
In general, conclusions can depend on whether missing outcomes are related to treatment assignment or to participants’ likely outcomes. Without a description of missingness and analysis methods, readers cannot assess that possibility or compare alternative assumptions. This limitation is relevant to the primary result and to the secondary outcomes, whose participant counts vary. It does not establish that bias occurred; it identifies information needed to judge the robustness of the estimates.
15. 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 |
|---|---|---|---|
| Psychosocial Pain Management (PPMI) | 20 | 98 | 20.4% |
| Enhanced Usual Care (EUC) | 16 | 102 | 15.7% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Psychosocial Pain Management (PPMI) | 1 of 98 |
| Enhanced Usual Care (EUC) | 1 of 102 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Psychosocial Pain Management (PPMI) | 10 of 98 |
| Enhanced Usual Care (EUC) | 7 of 102 |
Most frequent serious adverse event terms
| Event term | Organ system | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|---|
| Hospitalization - general medical | General disorders | 16 of 98 | 13 of 102 |
| Hospitalization - psych | Psychiatric disorders | 4 of 98 | 4 of 102 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Psychosocial Pain Management (PPMI) | Enhanced Usual Care (EUC) |
|---|---|---|---|
| Residential Substance Use Treatment | General disorders | 2 of 98 | 5 of 102 |
| Detox | General disorders | 1 of 98 | 4 of 102 |
| Emergency Medical Visit | General disorders | 3 of 98 | 0 of 102 |
| Injury - Fall | General disorders | 3 of 98 | 0 of 102 |
| Car Accident | General disorders | 1 of 98 | 0 of 102 |
Serious events with the highest arm-level rate: hospitalization - general medical (16.3%), hospitalization - psych (4.1%).
The registry reports serious adverse events affecting 20 of 98 participants in PPMI and 16 of 102 in EUC. Other adverse events are reported for 10 of 98 participants in PPMI and 7 of 102 in EUC. One death is reported in each group. These figures describe the counts in the registry record; they do not by themselves establish that an event was caused by an intervention.
The most frequent serious-event terms listed are “Hospitalization - general medical” at 16.3% and “Hospitalization - psych” at 4.1%. The record does not specify the denominator for these term percentages in the information, so they should be read as listed event-term frequencies rather than assigned to a particular arm or interpreted as participant-level risks. Event terms may also not represent mutually exclusive participants.
In general, adverse-event counts require context about definitions, observation time, severity, relatedness, and how events were collected. The registry record does not provide further detail on those aspects. The counts are therefore descriptive safety information, not a causal comparison or an individual assessment.
16. What the Result Does, and Does Not, Mean
The primary result is a comparison of average days retained on buprenorphine at the 3-month assessment. The observed mean was 81.1 days in PPMI and 75.4 days in EUC, with an unadjusted mean difference of 5.7 days. The 95% confidence interval, -2.487 to 13.89 days, includes values on both sides of zero. The posted summaries therefore leave uncertainty about the direction and magnitude of the difference.
This result does not show that every participant had an outcome close to the group mean. It does not explain why participants stopped or continued medication, and it does not describe the full distribution of retention times. The endpoint uses a particular definition of discontinuation and a calendar recall method at follow-up. Other definitions or measurement methods are not reported in the registry record.
The result also does not answer every question raised by the study. Pain intensity, pain-related functioning, longer-term retention, and substance-use abstinence are distinct outcomes. Some secondary numerical summaries are posted, while the registry does not report numerical results for all listed secondary outcomes. The presence of outcomes in the registry is not itself evidence of a difference between groups.
In general, a randomized comparison can help estimate a difference between assigned groups when the design and analysis are appropriate, but a registry summary alone does not resolve all questions about adherence, missing data, analysis populations, or outcome ascertainment. Those details are not reported in the registry record. The posted result should be interpreted as a statistical description of the available aggregate data, not as a definitive explanation of participant experience or a basis for medical advice.
The planning illustrations likewise do not establish the trial’s original target sample size or its achieved probability of detecting an effect. They apply stated planning assumptions to the observed estimate. Overall, the record offers a numerical comparison and several related outcome listings, while leaving important design and analysis details unreported.
17. Why This Trial Matters Statistically
This trial is statistically informative because its primary outcome is a measurable duration, reported as a mean and standard deviation, while the research question concerns retention over a defined follow-up period. The registry gives a clear operational definition: stopping buprenorphine for 7 or more days in a row, assessed by calendar recall at 3 months. Clear outcome definitions are essential because the meaning of a statistical estimate depends on what was measured.
The comparison also illustrates why an estimate should be read together with its uncertainty. A mean difference of 5.7 days is a point estimate, but its confidence interval extends from -2.487 to 13.89 days. Those values convey more than a binary interpretation of the unadjusted p-value. They show that the data summarized in the record are compatible with a range of possible group differences.
Several statistical questions remain important for interpretation. The registry does not report the original sample-size justification, an analysis plan, missing-data methods, or a multiplicity procedure. The secondary outcomes span several measures and time points, and participant counts vary across them. These features make transparent reporting of prespecification and analysis methods particularly valuable. They help readers distinguish confirmatory tests from exploratory comparisons and judge how robust results may be to analytic choices.
The planning illustrations demonstrate how required sample sizes depend on the effect chosen for planning: a smaller target effect requires more participants under the stated assumptions. They are not a substitute for the trial’s own design rationale, which is not reported. Together, the trial and its registry record provide a useful example of separating observed group summaries, uncertainty, planning assumptions, and unanswered methodological questions.
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 leaves several trial-specific questions unresolved. Although the study is described as single-masked, it does not say who was masked. It also does not report the randomization procedure or allocation concealment. The interventions differed in the number and format of sessions, but adherence to sessions and treatment fidelity are not described in the record.
The primary endpoint depends on calendar recall at the 3-month follow-up. The record does not describe how complete the recall information was, whether it was corroborated, or how missing information was handled. The primary outcome counts are 98 in PPMI and 102 in EUC, while some secondary outcomes have different counts. Reasons for those differences and the definition of each analysis population are not reported in the registry record.
The record does not report the original sample-size calculation, a statistical analysis plan, covariate adjustment, interim analyses, or a multiplicity strategy. Therefore, the posted unadjusted comparisons cannot establish whether they match the investigators’ prespecified inferential approach. The confidence interval and p-value are useful summaries of the unadjusted comparison, but the available aggregate data do not allow evaluation of distributional assumptions or alternative models.
The reported secondary outcomes cover several measures and follow-up times, yet numerical results are not reported for every listed outcome. The adverse-event summary also does not provide further detail about event relatedness, observation time, or the denominator for the listed serious-event term percentages. These gaps constrain interpretation; they should not be treated as proof that any specific bias, analysis choice, or safety issue occurred.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Psychosocial Pain Management to Improve Opioid Use Disorder Treatment Outcomes — NCT04433975.
- Registry record last updated 2025-07-09; status last verified 2025-06.
- Results first posted 2025-07-09.
- 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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22. Record Summary
The completed randomized parallel-group trial enrolled 200 participants with chronic pain who had recently begun buprenorphine treatment. It compared eight individual Cognitive Behavioral Therapy-based telephone or video sessions in PPMI with two individual telephone educational sessions in EUC. The registry lists single masking but does not identify who was masked.
The primary outcome was mean days retained on buprenorphine before stopping for 7 or more consecutive days, assessed by calendar recall at 3 months. The posted means were 81.1 days for PPMI and 75.4 days for EUC. The unadjusted mean difference was 5.7 days, with a 95% confidence interval from -2.487 to 13.89 days and an unadjusted p-value of 0.172.
The record lists secondary outcomes across retention, pain, and substance-use measures. It does not report a formal analysis plan, missing-data methods, multiplicity strategy, or original sample-size justification. The primary comparison is therefore best read as an unadjusted summary with uncertainty, alongside methodological details that remain unreported.