Efficacy of Computer Delivered Community Reinforcement Approach (CRA) (Bup II): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy of Computer Delivered Community Reinforcement Approach (CRA) (Bup II) (NCT00929253), a randomized na study. The primary outcome is Abstinence.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, parallel-group study with no masking. It lists the study as completed and identifies Virginia Polytechnic Institute and State University as the sponsor. The study title is Efficacy of Computer Delivered Community Reinforcement Approach (CRA) (Bup II). The official title refers to Efficacy of Computer Delivered CRA (Bup II) Grant No. R01DA012997-10. The study start is listed as 2007-09 and primary completion as 2010-04.

The two reported arms share Suboxone and contingency management, with computer-delivered therapy distinguishing the intervention arm. The arm titled Computer Delivered CRA + CM + Suboxone has a reported outcome sample size of 91.0. The comparator, CM + Suboxone, has a reported outcome sample size of 79.0. Those are the group sizes attached to the posted outcome; the registry record does not describe how many participants were included in any particular analysis beyond those entries.

The study summary says it was designed to examine combined buprenorphine and voucher incentives to promote abstinence from illicit opiate use, with or without computer-delivered therapy, during treatment of opioid dependence. The primary outcome was the longest documented continuous abstinence period from opioids and cocaine, summarized as a mean and standard deviation. The record lists one outcome measure and no posted analysis entries. It does not report the original allocation sequence, how allocation was concealed, the planned analysis population, or any blinding of participants or study staff. Randomized allocation is reported, but those further design details are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Abstinence, measured over 12 weeks.

The primary endpoint, titled Abstinence, records days of continuous abstinence. Its definition is the longest documented period of continuous abstinence from opioids and cocaine, assessed over 12 weeks. This is a continuous outcome: each participant’s recorded value can take different numerical values, and the arm-level result is summarized using a mean and standard deviation.

A longest-period measure captures the most sustained documented interval meeting the outcome definition during the stated timeframe. It is distinct from a count of every abstinent day or from the proportion of participants meeting a binary abstinence criterion. The registry record does not report the rules used to establish the start and end of an abstinent interval, how missing or unverified observations were handled, or whether additional definitions were used. Those details are important for understanding exactly how the endpoint was constructed.

For this comparison, the endpoint allows the average duration of the longest documented abstinence period to be contrasted between the two treatment arms. The posted means are 55.0 days for Computer Delivered CRA + CM + Suboxone and 49.5 days for CM + Suboxone. The registry’s summary measure is useful for comparing group averages, but it does not show the full distribution of individual outcomes or how many participants had any particular duration.

7. Results Posted in the Registry

• CM + Suboxone: mean 49.50 versus 55.00 on control; difference -5.50 (95% CI -14.13 to 3.13), standardized effect d = -0.19; z-test p = 0.212.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous and is summarized by a mean and standard deviation in each arm. A mean is the arithmetic average of the recorded outcome values within a group. It gives a compact description of the group’s central level, but it does not show how values are distributed or whether a small number of unusually high or low values influence the average. The standard deviation describes the spread of values around that group mean. The reported standard deviations are 26.2 days and 30.6 days, respectively.

The comparison is expressed as a mean difference. The posted estimate is -5.5 days for CM + Suboxone relative to Computer Delivered CRA + CM + Suboxone. A negative estimate means the comparator’s reported mean is lower under this stated orientation. Reversing the order of the arms would reverse the sign, without changing the underlying contrast. The estimate is unadjusted, so it represents a direct comparison of the posted group summaries rather than an estimate adjusted for baseline variables.

A confidence interval describes a range of values compatible with the data under the statistical procedure used, with uncertainty reflected in the interval. It is not a range containing a known fixed proportion of individual participants’ outcomes, and it is not a guarantee that the true effect lies inside it. The reported interval extends from -14.13 to 3.132 days. Because zero is included, the data are compatible with no mean difference under this interval procedure. The interval also allows differences favoring either arm, so the point estimate alone should not be treated as a definitive direction.

The unadjusted p-value is 0.212. In general, a p-value describes how unusual data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the model assumptions were true. It is not the probability that the null hypothesis is true, the probability that the finding is due to chance, or a measure of the size or importance of an effect. A p-value must be interpreted alongside the estimate, interval, outcome definition, and design. The record does not state a trial-specific analysis plan or provide further detail on the test used.

The comparison also reports a pooled standard deviation of 28.33 and a standardized effect estimate of -0.194. In general, a standardized effect expresses a difference relative to a measure of outcome spread, which can help describe the magnitude on a scale that is not in the original outcome units. It does not replace the mean difference in days, and it does not convey uncertainty on its own. The posted record does not provide a confidence interval for this standardized estimate.

Randomized allocation can support a comparison between assigned groups, but its interpretation depends on implementation and follow-up. The registry record reports randomization and a parallel design, but details of sequence generation and allocation concealment are not reported in the registry record. Masking is listed as none. The record also does not report whether the analysis followed assigned groups, how deviations from assigned treatment were handled, or how missing outcome measurements were treated. These omissions limit assessment of possible bias and the population represented by the estimate.

No posted analysis entries are listed, even though outcome summaries and a comparison are present. The record therefore does not describe model diagnostics, any adjustments, or whether other analytic approaches were considered. There is one listed outcome measure and no posted secondary outcomes, but this alone does not establish that no other outcomes or analyses were collected. Details on multiplicity procedures are not reported in the registry record.

General statistical context is useful when interpreting an unadjusted comparison of group means. Such a comparison summarizes the observed contrast but may be affected by chance imbalance in characteristics, measurement variation, or incomplete follow-up. Randomization is intended to balance prognostic factors across groups on average, while the registry record does not provide baseline characteristics with which to assess the groups’ observed comparability. The analysis should therefore be read as the posted estimate for the reported endpoint, not as a fully documented adjusted causal estimate.

10. Confidence Intervals and Precision

The reported confidence interval for the mean difference is -14.13 to 3.132 days, with the comparison oriented as CM + Suboxone relative to Computer Delivered CRA + CM + Suboxone. The interval spans zero. It therefore includes values consistent with no average difference, as well as negative and positive differences. The point estimate of -5.5 days is only one value within that range and should not be interpreted without the interval.

In general, a confidence interval conveys uncertainty in an estimated quantity. A narrower interval indicates greater precision for that quantity under the method used, while a wider interval leaves more possible values compatible with the data. The interval allows a range of possible mean differences, so the exact size and direction of the underlying contrast are not pinned down precisely by this estimate. The interval is expressed in days, making its values interpretable on the outcome’s original scale.

The group standard deviations are 26.2 days and 30.6 days. They describe variation among outcome values, not uncertainty in the group means themselves. The reported standard errors are 2.747 and 3.443. Standard errors quantify sampling uncertainty in an estimate under statistical assumptions; they are not measures of the spread of participant outcomes. The registry record does not give further details on the procedures used to derive the uncertainty estimates.

The unadjusted p-value is 0.212. It addresses evidence against a specified null hypothesis under a statistical model, whereas the confidence interval communicates a range of effect values. Neither alone establishes equivalence or the absence of an effect. The record does not report a prespecified equivalence margin or non-inferiority framework, so the interval should not be read as an equivalence assessment.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect, rather than a report of the trial’s original design assumptions. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. The trial’s own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants per arm for a hypothetical study designed to have an 80% chance of detecting the specified effect under the stated assumptions, if that effect and the model assumptions are correct. The 90% power column gives the corresponding per-arm planning number for a higher target probability of detecting that effect. These are design targets for hypothetical future studies, not descriptions of the probability that the completed study detected an effect.

The table gives planning figures for detecting 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For example, the figures for 100% are 417 participants per arm for 80% power and 558 participants per arm for 90% power. For 75%, they are 741 and 992 participants per arm; for 50%, they are 1,666 and 2,230 participants per arm. Smaller effects require more participants under these assumptions because they are harder to distinguish from sampling variation.

These figures are not observed power. They are planning illustrations tied to the observed effect estimate, which itself is uncertain. The table and curve should be read as conditional planning aids, not as evidence that the trial was adequately or inadequately powered according to its original protocol.

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 = -5.500; pooled standard deviation σ = 28.328.
2. n = 2 × (1.96 + 0.842)² × 28.328² / -5.500² = 416.4, rounded up to 417 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 <- -5.5                      # observed difference in means
sigma <- 28.3279770847529                     # 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(929253)
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 = 417 (80% power), 558 (90% power)
 75% of observed effect: n per arm = 741 (80% power), 992 (90% power)
 50% of observed effect: n per arm = 1,666 (80% power), 2,230 (90% power)
power.t.test: 417.4 
Simulated power at n = 417 per arm: 0.803 (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 record lists one outcome measure, Abstinence, as primary, and reports no posted secondary outcomes. It also lists no analysis entries. This gives a limited picture of the analyses available in the registry record; it does not establish that the study collected no other outcomes or conducted no additional analyses. The registry record does not report a multiplicity plan, such as whether any adjustment was intended for multiple endpoints, time points, or comparisons.

In general, multiplicity matters when several statistical hypotheses are tested. The more comparisons considered, the greater the chance that at least one result may appear notable by chance alone if each is interpreted separately. Whether that issue applies, and how it should be handled, depends on the complete prespecified analysis plan and the family of tests. Those details are not reported in the registry record, so the unadjusted p-value should be understood as the posted comparison rather than as evidence of any particular multiplicity strategy.

The record does not report missing-outcome counts, reasons for missingness, imputation methods, or sensitivity analyses. It also does not report the analysis population, such as whether analyses were based on assignment, treatment received, or participants with complete outcome data. Consequently, the available result cannot establish how incomplete observations or treatment deviations were handled.

These omissions affect interpretation because missingness and analysis-population choices can influence the estimate and its uncertainty. No particular pattern of missing data or analysis procedure should be assumed. Further detail on the protocol and statistical analysis plan is not reported in the registry record.

14. Safety Results

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

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The serious adverse event figures list 0 affected participants in the Computer Delivered CRA + CM + Suboxone arm, with 91 at risk, and 0 affected participants in the CM + Suboxone arm, with 79 at risk. These are counts of participants affected by serious adverse events as entered in the registry record. They should not be interpreted as a comprehensive description of all safety outcomes or as proof that no serious events occurred outside the reported record.

The registry also lists other adverse events affecting 57 participants in the computer-delivered arm and 55 participants in the comparator arm. These are separate entries from the serious adverse event counts. The record does not provide event terms for serious adverse events, and no top serious-event terms are listed. Death counts are not reported in the registry record. Further details such as event definitions, timing, severity grading, relatedness assessments, and methods of collection are not reported in the registry record.

These entries are descriptive counts. They do not by themselves support a comparative safety conclusion, because the record does not provide a detailed safety analysis or context for individual events.

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

The result describes one measured outcome: the mean of the longest documented continuous abstinence period from opioids and cocaine during 12 weeks. The reported mean is 55.0 days in the computer-delivered CRA, contingency management, and Suboxone arm, and 49.5 days in the contingency management and Suboxone arm. The estimated difference, oriented as comparator relative to intervention, is -5.5 days. The confidence interval runs from -14.13 to 3.132 days, and the unadjusted p-value is 0.212.

These statistics do not establish that the arms are equivalent, and they do not establish that one regimen is better. The interval includes zero and allows differences in both directions. The estimate concerns group averages, not the experience of any individual participant. The endpoint is a longest-period measure and does not capture every aspect of substance use, treatment participation, or longer-term outcomes.

The trial record describes a randomized comparison, but it does not provide details on allocation procedures, participant characteristics, missing data, treatment adherence, or analysis populations. It also does not report a statistical analysis plan or an equivalence margin. Those omissions mean the result should be interpreted within the scope of the reported comparison and outcome, rather than as a broad conclusion about treatment.

The record includes adverse-event counts, but not the event-level detail needed to characterize safety fully. The primary endpoint and the adverse-event entries answer different questions; neither substitutes for the other. The posted data therefore support a statistical description of the reported outcome and its uncertainty, while leaving important questions about analysis methods, completeness, and wider relevance unresolved.

16. Why This Trial Matters Statistically

This trial is statistically informative as a comparison of an added behavioral component within treatment arms that both include Suboxone and contingency management. The posted result is not a comparison of medication versus no medication or vouchers versus no vouchers. The contrast concerns computer-delivered therapy added to the shared components, making the stated treatment difference important for interpreting the mean difference.

The outcome also illustrates why an estimate and its uncertainty should be read together. The point estimate favors a higher mean in the computer-delivered arm under the reported contrast, but the confidence interval extends across zero and allows estimates on either side. Reporting the mean difference in days gives a direct scale-based interpretation, while the interval communicates uncertainty about its magnitude and direction.

The record also highlights the distinction between a completed trial’s observed result and planning calculations based on that result. The sample-size illustrations depend on an uncertain observed effect and explicit assumptions. They are not a retrospective measure of trial performance, and they do not recover the study’s original design rationale, which is not reported in the registry record.

Finally, the registry entry shows why documentation is part of statistical interpretation. Randomization and the primary outcome are identified, but details on analysis populations, missing data, multiplicity, and the statistical plan are absent. Recognizing these gaps helps readers distinguish what the result describes from what cannot be assessed using the registry record alone.

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 outcome is defined as the longest documented continuous abstinence period from opioids and cocaine over 12 weeks. The registry record does not report how abstinence was documented, how the continuous interval was determined, or how observations that could not be verified were treated. The endpoint therefore cannot be evaluated in detail from the definition alone.

The record reports group means, standard deviations, and an unadjusted comparison, but does not provide baseline characteristics, individual outcome distributions, or adjusted analyses. The outcome sample sizes are 91.0 and 79.0, but the registry record does not explain whether these represent all randomized participants, participants with available endpoint data, or another analysis population. Enrollment is listed as 170, and no further accounting of participant flow is reported.

Randomized allocation is reported, but the method for generating and concealing allocation is not reported in the registry record. Masking is listed as none. The record does not describe treatment adherence, intervention fidelity, crossover, or other deviations from assigned care. These details may matter when interpreting the comparison.

The computer-delivered therapy arm description is truncated, limiting the available description of the intervention content. The record does not report the study’s original sample-size assumptions, a statistical analysis plan, missing-data methods, or multiplicity procedures. No secondary outcomes are posted, and no analysis entries are listed. Safety information is also limited: event terms and death counts are not reported in the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Efficacy of Computer Delivered Community Reinforcement Approach (CRA) (Bup II) — NCT00929253.
• Registry record last updated 2022-05-27; status last verified 2022-05.
• Results first posted 2022-05-27.
• 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

NCT00929253 is listed as a completed, randomized, parallel-group study with no masking. It compares Computer Delivered CRA + CM + Suboxone with CM + Suboxone. The registry lists Opiate Addiction as the condition, enrollment of 170, and Virginia Polytechnic Institute and State University as sponsor. The study start is 2007-09 and primary completion is 2010-04.

The primary endpoint is Abstinence, measured in days over 12 weeks and defined as the longest documented continuous abstinence period from opioids and cocaine. The reported means are 55.0 days and 49.5 days; the mean difference is -5.5 days for the comparator relative to the computer-delivered arm. The confidence interval is -14.13 to 3.132 days, and the unadjusted p-value is 0.212. The registry record does not report detailed analysis methods, missing-data procedures, or the original sample-size plan.