A Sequenced Behavioral and Medication Intervention for Cocaine Dependence: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Sequenced Behavioral and Medication Intervention for Cocaine Dependence (NCT01986075), a randomized phase 1, phase 2 study. The primary outcome is Those Achieving Three Consecutive Weeks of Cocaine Abstinence at the End of the Trial..

2. Clinical Question

3. Trial Design

The registry describes NCT01986075, “A Sequenced Behavioral and Medication Intervention for Cocaine Dependence,” as a completed randomized trial with quadruple masking and a sequential model. It lists Phase 1 and Phase 2 and an enrollment of 145. The study began in 2014-01, and primary completion was recorded as 2021-01. These record-level details describe the trial’s registration, but do not by themselves establish which participants contributed to each posted outcome.

The strategy began with computer-assisted behavioral intervention. The registry summary says medication would be combined with behavioral treatment for individuals who did not respond to behavioral intervention alone. The posted primary comparison is between computer-assisted CBT plus MAS-ER and computer-assisted CBT plus placebo. The registry also lists a non-randomized CBT plus CM group in the safety information. It does not provide a primary-outcome result for that group in the posted comparison.

Randomization indicates that assignment to the compared treatment groups was intended to use chance. Quadruple masking indicates the registry’s masking classification, but it does not identify the parties masked or explain how masking was maintained. The record does not report the randomization procedure, allocation concealment details, or the point in the sequence at which participants entered the randomized comparison.

The listed primary outcome is binary: participants either met the abstinence criterion or did not. The arm counts are 7 participants in the MAS-ER group and 5 in the placebo group, with the respective posted group sizes of 45 and 41. The record does not report a detailed participant-flow account linking the trial’s enrollment figure to these outcome denominators. Nor does it report the trial’s original sample-size justification or the full statistical analysis plan.

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: Of the 145 participants enrolled, 21 participants were designated as treatment responders during the first month of the psychosocial intervention and were not randomized. An additional 38 individuals were lost to follow-up or not eligible to be randomized prior to completing the first month of the intervention. Eighty-six participants continued to use cocaine through the first month of treatment and were randomized to receive either MAS-XR or Placebo at the beginning of treatment week 5.

Initial CBT + CM (Pre-randomization)

Randomized Intervention

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 Those Achieving Three Consecutive Weeks of Cocaine Abstinence at the End of the Trial., measured over weeks 12-14 of trial.

The primary endpoint was the count of participants achieving at least three consecutive weeks of cocaine abstinence at the end of the trial. The stated timeframe was weeks 12-14. The registry describes the outcome as a yes-or-no indicator based on self-reported abstinence confirmed by urine toxicology. Thus, the endpoint combines a report of abstinence with an objective toxicology confirmation and requires abstinence to persist for a consecutive period, rather than recording only a single point-in-time report.

A binary endpoint makes the treatment groups comparable in terms of the proportion meeting a clearly stated criterion. The clinical question represented by this measure is whether participants reached the specified abstinence threshold during the final weeks, not how much cocaine they used, how long abstinence lasted beyond the required interval, or whether they maintained abstinence after the trial. Those other outcomes are not reported in the registry record.

The outcome is listed as a count of participants, while the comparison expresses the difference in the proportions meeting the criterion. In the posted arms, 7 of 45 participants in the MAS-ER group and 5 of 41 in the placebo group met the endpoint. These counts describe the recorded outcome; by themselves they do not establish why a participant met or did not meet the criterion. The registry does not report the handling of missing urine samples or missing self-reports, so the endpoint’s treatment of such cases cannot be determined from the record.

7. Results Posted in the Registry

• Computer-assisted CBT Plus Mixed-Amphetamine Salts- Extended Release (MAS-ER): 15.6% (7/45) versus 12.2% (5/41) on control; risk difference 3.4 percentage points (95% CI -11.2 to 17.9), risk ratio 1.28 (0.44–3.71); unadjusted two-proportion z-test p = 0.653.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary: each participant either achieved the stated abstinence criterion or did not. For a binary outcome, a group proportion describes the share meeting the criterion. The registry reports 7 of 45 in the MAS-ER group and 5 of 41 in the placebo group, with corresponding proportions of 0.156 and 0.122. Those proportions are the basis for expressing the comparison as a risk difference, risk ratio, or odds ratio. These measures answer related but different questions, so they should not be treated as interchangeable.

What does the risk difference express?

The risk difference subtracts the comparator group’s event proportion from the intervention group’s event proportion. A positive value means the observed proportion was higher in the intervention group; a negative value means it was lower. The posted estimate is 0.034. Unlike a relative measure, it describes the contrast on the proportion scale. The confidence interval runs from -0.112 to 0.179, spanning both directions. This interval indicates that the point estimate is imprecise and that the posted data do not rule out differences that would matter in either direction. No clinical threshold for an important difference is reported in the registry record.

How do relative measures differ?

The risk ratio compares the event proportions as a ratio. The posted estimate is 1.276, with an interval from 0.439 to 3.707. A ratio of one represents equal proportions; values on either side represent relative differences in opposite directions. The odds ratio compares the odds of the event rather than the proportions themselves. Its posted estimate is 1.326, with an interval from 0.386 to 4.56. An odds ratio is not the same quantity as a risk ratio. When an event is not rare, the numerical values of these relative measures can differ appreciably, so interpretation should name which measure is being discussed.

What does the p-value tell the reader?

The unadjusted p-value is 0.653. A p-value describes how unusual data at least as incompatible with a specified null model would be, assuming that model and the analysis assumptions hold. It is not the probability that the null model is true, and it does not measure the size or clinical importance of a treatment effect. It also does not establish that the groups are equivalent. The registry does not report a prespecified equivalence margin or a noninferiority margin.

“Unadjusted” means that the posted p-value is not described as accounting for covariates or other adjustments. The registry lists no analyses, and the analysis plan is not reported in the registry record. Consequently, it is not possible to determine from the record whether this comparison was prespecified in its posted form, whether additional planned models existed, or whether the p-value corresponds to the primary planned test.

Why do the counts and estimates differ in what they convey?

The counts show how many participants met the endpoint in each posted group. The proportions place those counts in the context of the group denominators. The effect estimates describe the between-group contrast, while the confidence intervals describe uncertainty around those estimates. Each representation contributes different information. A small difference between event counts cannot be interpreted without the denominators, and a point estimate should not be interpreted without its interval.

The registry labels the outcome as a participant count, but the comparison reports proportion-based effect measures. This is appropriate to the binary endpoint: the clinical question is about the chance or proportion of meeting the criterion, not simply which group has the larger raw count. Differences in group sizes mean raw counts alone are especially insufficient for comparing the groups.

What does uncertainty mean for this estimate?

A confidence interval is a range generated by a statistical procedure that, under its assumptions, has a stated long-run coverage property. For an individual study, it conveys the precision of the estimate and the range of effects compatible with the data and method. It is not a guarantee that the true value lies in the particular interval, nor is it a list of equally likely values. Here, the risk-difference interval includes values below and above no difference, and the relative-effect intervals also include their no-difference values. The intervals are wide, so the estimates do not sharply distinguish among possible effect sizes.

The comparison is unadjusted in the posted summary. The record does not describe covariate adjustment, clustering, stratification, the exact confidence-interval method, or checks of model assumptions. It does not report the handling of missing endpoint data or the analysis population. These omissions limit assessment of how the estimates were produced and whether the method matched the trial’s planned analysis. They should not be filled in by assuming a particular protocol or statistical procedure.

10. Confidence Intervals and Precision

The risk-difference estimate is 0.034, and its 95% confidence interval extends from -0.112 to 0.179. The interval crosses no difference and spans estimates favoring either group. The data therefore do not pin down the size or direction of the between-group difference with high precision. The point estimate is only one value within a much broader range of estimates compatible with the reported analysis.

The relative measures tell a similar story of uncertainty. The risk ratio is 1.276, with a 95% confidence interval from 0.439 to 3.707. The odds ratio is 1.326, with a 95% confidence interval from 0.386 to 4.56. Each interval includes its no-relative-difference value and accommodates effects in opposing directions. The risk ratio and odds ratio use different scales, but both indicate that the comparison is not precise enough to isolate a single direction or magnitude.

Confidence intervals describe uncertainty under the analysis method; they do not resolve limitations in the underlying record. The registry does not report missing-data handling, the analysis population, or the exact interval method. Nor does it report a threshold for a clinically important difference. Without those details, statistical precision cannot be translated into a judgment about practical importance. The 0.653 unadjusted p-value is consistent with the broad uncertainty reflected by the intervals, but it does not replace them or prove equivalence.

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 participants across arms. They are planning illustrations based on the observed effect, not the trial’s original design calculations. The registry’s planning assumptions specify a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect. The original trial’s own sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions. The 90% power column gives the per-arm number for a design with a 90% chance under those same assumptions. These are design targets conditional on the assumed effect and statistical model, not guarantees about the result of a future study. Smaller effects require more participants to detect, which is why planning for a smaller fraction of the observed effect produces larger required group sizes.

The listed scenarios use the observed effect as a reference and then consider smaller fractions of that effect. Their figures should not be read as observed enrollment needs, a reconstruction of the trial protocol, or evidence that the trial was designed with these assumptions. They are not observed power. Power is a prospective planning quantity for a specified design and effect; it is not a measure of how persuasive the completed trial’s result is. The uncertainty in the posted effect also matters: planning from an observed estimate can be unstable, particularly when the estimate is imprecise.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.122; treatment proportion p₁ = 0.156; average p̄ = 0.139.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4889 = 0.9582.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4883 = 0.4110.
4. n = (0.9582 + 0.4110)² / (0.0336)² = 1,660.0, rounded up to 1,661 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
p0 <- 0.121951219512195                          # control proportion
p1 <- 0.155555555555556                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1986075)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 1,661 (80% power), 2,222 (90% power)
 75% of observed effect: n per arm = 2,877 (80% power), 3,851 (90% power)
 50% of observed effect: n per arm = 6,303 (80% power), 8,437 (90% power)
power.prop.test: 1660 
Simulated power at n = 1,661 per arm: 0.798 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The registry lists one outcome measure and zero posted secondary outcomes. It also lists zero analyses. These entries do not establish that the trial had no additional outcomes, planned tests, or analyses; they indicate what is recorded in the registry record. The full statistical analysis plan, including any hierarchy of outcomes or tests, is not reported in the registry record.

Multiplicity arises when several outcomes, timepoints, subgroups, or statistical comparisons are tested. Repeated testing can increase the chance of at least one apparently notable result unless the plan addresses that issue. The record does not report whether multiplicity adjustments were planned or used, nor whether the primary comparison was selected from a larger set of analyses. It would therefore be inappropriate to assume either that adjustment was required and omitted or that the reported comparison was the only analysis conducted.

Missing-data methods are also not reported. The endpoint depends on self-report and urine toxicology confirmation, but the record does not explain how unavailable samples, missing reports, or incomplete follow-up were classified. It does not say whether imputation, a complete-case approach, or another method was used. The posted group denominators are available, but the record does not provide enough participant-flow information to determine how they relate to all enrolled participants.

The analysis population is not reported in the registry record. It is not stated whether the posted comparison used an intention-to-treat population, a per-protocol population, or another definition. The record does not report the timing or conduct of interim analyses, and no inference about their presence or absence can be made. These details matter because choices about analysis populations, missing outcomes, and repeated testing can affect both the estimate and its uncertainty. They remain unreported rather than inferable from the p-value or endpoint counts.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: inpatient rehabilitation stay (2.4%), dehydration (2.2%), hernia (1.7%), atrial fibrillation (1.7%), gi issue (1.7%).

The safety record reports serious adverse events among 1 participant in the MAS-ER group and 1 participant in the placebo group. It lists 45 and 41 participants at risk in those groups, respectively. The non-randomized CBT plus CM group has 4 participants with serious adverse events among 59 at risk. The record reports zero deaths in each of the three listed groups. These are group-specific registry counts; the non-randomized group should not be treated as part of the randomized medication comparison.

The registry also lists serious-event terms with percentages: inpatient rehabilitation stay, 2.4%; dehydration, 2.2%; hernia, 1.7%; atrial fibrillation, 1.7%; and GI issue, 1.7%. The record does not map these terms to particular treatment groups or explain whether participants could contribute more than one event term. They should not be interpreted as comparative rates between MAS-ER and placebo.

These summaries describe reported safety events, not a complete assessment of risk. The registry does not provide event timing, duration, severity beyond the serious classification, relatedness to treatment, or a detailed event-level account. The listed counts alone do not establish causation or allow a full comparison of safety profiles.

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

The posted result is an uncertain comparison of a specific binary outcome: at least three consecutive weeks of toxicology-confirmed self-reported abstinence during weeks 12-14. The MAS-ER group had 7 participants meeting this criterion among 45, and the placebo group had 5 among 41. The estimated risk difference is 0.034, but its confidence interval extends from -0.112 to 0.179. The comparison therefore does not establish a clear direction or precise size of a difference.

The result does not demonstrate equivalence. A non-significant p-value, such as the posted 0.653, is not a test showing that effects are the same. Equivalence requires a prespecified margin and an analysis designed to assess whether the uncertainty falls within that margin; neither is reported in the registry record. The broad confidence interval also leaves a range of possible differences unresolved.

The posted comparison does not answer every question raised by the sequential strategy. The study summary describes medication being added for people who do not respond to initial behavioral intervention, but the registry does not report the initial response classification or a separate primary-outcome estimate for that subgroup. Nor do the posted figures establish outcomes beyond the trial’s specified final weeks. Other measures of cocaine use, longer follow-up, or broader treatment effects are not reported in the registry record.

Interpretation is also limited by absent analysis details. The registry does not report missing-data handling, the analysis population, or the original statistical plan. These gaps do not invalidate the posted counts, but they constrain how fully the comparison can be assessed. The most defensible reading is descriptive: the record reports the group counts and an imprecise estimated difference, with uncertainty that includes effects in either direction. The data do not support a stronger conclusion about treatment efficacy, equivalence, or the overall strategy.

16. Why This Trial Matters Statistically

This trial raises a statistical question about evaluating a sequence of care rather than a single treatment offered in isolation. The registry summary describes behavioral intervention first and medication for people who do not respond. That structure makes clear definitions of response, assignment, and analysis population important: an estimate for a medication comparison among nonresponders addresses a narrower question than an estimate for the full sequence. The posted record does not provide enough detail to connect the primary comparison to that full decision pathway.

The endpoint also illustrates the distinction between a clinically framed outcome and a statistical contrast. The criterion requires consecutive abstinence over the final weeks, confirmed by urine toxicology and self-report. The posted analysis then summarizes the proportion meeting that threshold. This can make group comparison straightforward, but it does not capture every dimension of use or persistence outside the stated timeframe.

Finally, the result illustrates why effect estimates and uncertainty should be read together. The point estimate is positive on the risk-difference scale, while its interval includes a range in both directions. Reporting the estimate alone would overstate how settled the comparison is; focusing only on the p-value would discard information about possible effect sizes. The interval and the registry’s missing analysis details are central to understanding what can and cannot be concluded from the posted data.

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 registry record leaves several trial-specific questions unresolved. Although the study summary describes a sequence beginning with behavioral intervention, it does not report how initial nonresponse was defined, how many participants met that definition, or whether the posted randomized groups consist only of those nonresponders. The primary hypothesis concerns nonresponders, but the posted result does not provide a subgroup-specific description that allows this connection to be verified.

The arm descriptions are incomplete. The MAS-ER description ends during the medication-taking instruction, and the placebo description also ends before its complete instructions. Details beyond the recorded titration and dosing information are not reported in the registry record. The record lists quadruple masking but does not name the masked parties or describe masking procedures.

The primary endpoint combines self-report and urine toxicology, but the registry does not report how missing tests or reports were handled, the timing of individual assessments, or the rule for determining consecutive abstinence in incomplete records. It also does not report the analysis population, participant flow for the primary comparison, or the original sample-size rationale. The enrollment figure is not accompanied by enough information to explain how participants progressed through the sequential design and into the posted outcome denominators.

Only one outcome measure is listed, with no secondary outcomes or analyses posted. The full protocol and statistical analysis plan are not reported in the registry record, so details about multiplicity, interim analyses, adjustment, and planned sensitivity analyses remain unknown. These limitations concern the information available in the record; they should not be taken as evidence that a specific procedure was or was not used.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Sequenced Behavioral and Medication Intervention for Cocaine Dependence — NCT01986075.
• Registry record last updated 2022-01-25; status last verified 2022-01.
• Results first posted 2022-01-25.
• 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

NCT01986075 is recorded as a completed randomized, quadruple-masked, sequential Phase 1 and Phase 2 study of computer-assisted behavioral intervention and medication for cocaine dependence. The registry lists enrollment of 145, a start in 2014-01, and primary completion in 2021-01. The posted primary endpoint is at least three consecutive weeks of toxicology-confirmed self-reported abstinence during weeks 12-14.

The primary comparison reports 7 of 45 participants meeting the endpoint with computer-assisted CBT plus MAS-ER and 5 of 41 with computer-assisted CBT plus placebo. The risk difference is 0.034, with a 95% confidence interval from -0.112 to 0.179; the unadjusted p-value is 0.653. The estimate is imprecise and does not establish a clear direction of difference. The record does not report the original sample-size assumptions, full analysis plan, missing-data approach, or analysis population.