Effectiveness of Contingency Management in the Treatment of Crack Addiction in Brazil: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effectiveness of Contingency Management in the Treatment of Crack Addiction in Brazil (NCT03345394), a randomized na study. The primary outcome is Pattern of Crack Cocaine Use.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, single-blind, parallel-group controlled trial, listed as completed. Enrollment was 98. The posted arm summaries report 48 participants in Standard Treatment and 50 in Contingency Management. The record lists the phase as NA. The sponsor was Federal University of São Paulo.

Both groups were offered 12 weeks of treatment at the Unidade Recomeço Helvétia treatment program. One group received standard treatment, while the other received standard treatment associated with Contingency Management. This design addresses the added treatment package, not the isolated effect of Contingency Management separated from the standard program.

The primary outcome was the pattern of crack cocaine use, measured as the percentage of negative cocaine urine samples submitted during the 12 weeks of treatment. The primary population is described as all enrolled participants analyzed on an intention-to-treat basis. Treatment retention, measured in weeks over a 12-week timeframe, was the posted secondary outcome.

The registry record gives a start date of 2017-12-01 and a primary completion date of 2020-12-01. It does not identify which people were blinded, describe how allocation was generated or concealed, or provide further details about recruitment, follow-up, or treatment delivery. Those design details are not reported in the registry record, so the labels randomized and single-blind cannot answer those more specific methodological questions.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: all enrolled participants were analyzed (intention to treat)

5. Baseline Characteristics

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

Population: all participants enrolled in the study were analyzed (intention to treat)

6. Primary Endpoint

The registry lists the primary outcome as Pattern of Crack Cocaine Use, measured over 12 weeks.

The primary endpoint is the percentage of negative crack cocaine urine samples submitted during 12 weeks of treatment. In practical terms, it summarizes the pattern of submitted samples classified as negative for cocaine over the treatment period. The registry record reports this measure as a mean with standard deviation, rather than as a time-to-event outcome or a binary status at a single visit.

Urine samples provide an objective measure of cocaine detection at the times samples are collected. Using the percentage of negative samples can describe repeated observations across treatment, rather than relying only on a participant’s report or a single measurement. It is therefore relevant to the stated trial question about crack cocaine use during treatment. This general rationale does not establish how samples were scheduled, how unsubmitted samples were handled, or how the laboratory procedures worked; those details are not reported in the registry record.

The measure has a specific scope: it concerns submitted urine samples during the 12-week treatment period. It does not, on its own, describe use outside the observation period, longer-term outcomes, or every aspect of recovery. Interpretation also depends on how many samples each participant submitted and how missing samples were treated in the analysis, details that are not reported in the registry record.

7. Results Posted in the Registry

• Contingency Management: mean 40.70 versus 14.30 on control; difference 26.40 (95% CI 24.33 to 28.47), standardized effect d = 5.03; z-test p = <0.001.

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.

Treatment Retention

• 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:
  • Contingency Management: mean 7.00 versus 3.40 on control; difference 3.60 (95% CI 1.62 to 5.58), standardized effect d = 0.72; z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Contingency Management than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The registry record posts one secondary endpoint: treatment retention. Its direction is consistent with the primary outcome’s direction, in that the Contingency Management group has a higher mean on the posted measure. That broad alignment may be useful context because retention and the percentage of negative urine samples describe related but distinct aspects of the treatment period.

Retention is not interchangeable with the primary measure. A participant can remain in treatment without every submitted sample being negative, and the percentage of negative samples does not directly measure how long someone remained in treatment. The endpoints therefore offer different perspectives on the treatment experience; neither one alone explains the pathway that produced the other.

The secondary result does not independently confirm the primary result. It is one secondary outcome, and the registry record does not report a multiplicity adjustment, a prespecified hierarchy among outcomes, or an analysis plan. When outcomes are considered without adjustment for multiple testing, their inferential evidence is less secure than a single prespecified primary test would be under a documented plan. The unadjusted secondary finding is best viewed as supportive and descriptive rather than decisive.

The registry record also does not report how retention was defined operationally, how early departures were handled, or whether missing outcome data affected the analysis. Such details matter because retention can be summarized in different ways, and the interpretation depends on the actual measurement and analysis. The posted result provides a group-level comparison, but does not establish why the groups differed or whether the pattern would persist beyond the treatment period.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Treatment Retention

9. Statistical Interpretation

10. Statistical Methods Explained

The posted outcomes are continuous measures summarized by their means and standard deviations. The primary outcome is a percentage, while treatment retention is reported in weeks. A mean describes the average recorded value within an arm. A standard deviation describes the spread of individual observations around that arm’s mean; it is not the same as a confidence interval and does not express uncertainty about the mean in the same way.

What does a mean difference represent?

For each outcome, the unadjusted comparison is the Contingency Management group mean minus the Standard Treatment group mean. For the primary measure, the estimated mean difference is 26.4 percentage points. For retention, the estimated mean difference is 3.6 weeks. A difference between group means is an estimate of the contrast in these trial summaries. It is not an adjusted estimate, and it does not account for participant or treatment characteristics beyond the posted summaries.

As a general statistical explanation, an unadjusted comparison treats the groups’ outcome summaries as the basis for inference without incorporating covariates or other model adjustments. Random assignment is intended to make groups comparable on average, but it does not guarantee that every realized group is balanced or that outcome data are complete. Because participant-level data and details of the allocation procedure are not reported in the registry record, the calculations cannot assess those features.

How should the p-values be read?

The posted p-values are unadjusted and are reported as p < 0.001 for both outcomes. In general, a p-value describes how incompatible the observed data, or more extreme data, would be with a specified null model if that model and the analysis assumptions held. It is not the chance that the null hypothesis is true, nor a measure of the size or importance of a difference. The registry record lists no reported analyses, so these unadjusted calculations should not be mistaken for a documented trial analysis plan.

When many outcomes or analyses are examined, the chance of obtaining small p-values can increase if no allowance is made for multiple testing. The registry record identifies one primary outcome and one secondary outcome, but does not report a multiplicity strategy or a full analysis plan. The secondary result should therefore be read as supportive descriptive evidence, not as a result confirmed under a stated family-wise testing procedure.

What does a confidence interval add?

The recalculated intervals express uncertainty around each unadjusted mean difference. The primary interval runs from 24.33 to 28.47 percentage points, and the retention interval runs from 1.62 to 5.58 weeks. In general, a confidence interval is produced by a procedure designed to capture the true parameter at its stated rate across repeated samples when the model assumptions are met. It gives a range of estimates compatible with the data and calculation, rather than a guarantee that the true value lies in that particular interval.

The intervals are recalculated from the posted arm summaries. The registry record does not report sponsor inferential analyses or confidence intervals. No discrepancy is flagged. The intervals should still be interpreted in light of the unreported details about the outcome distributions, missing observations, and analysis methods. A narrow interval under a calculation does not address biases or design limitations that the calculation does not model.

Why do assumptions matter?

As a general point, inference from means often relies on assumptions about independence, sampling variation, and the adequacy of the method for the outcome distribution. Urine results are measured repeatedly during treatment, and observations from the same participant may be related. The registry record does not say how the repeated measurements were handled when producing each participant’s percentage, nor does it describe a participant-level model. Therefore the summary-based recalculations cannot show whether within-person dependence or other features of the data were addressed in the original analysis.

The primary measure is bounded as a percentage, and treatment retention is measured over a defined treatment period. General methods for continuous outcomes can be affected by skewness, clustering, or unequal variability. Those considerations do not establish that a particular assumption was violated in this trial; the required distributional and participant-level information is not reported in the registry record.

The posted standard deviations are 4.6 and 5.8 for the primary outcome, and 4.8 and 5.2 for retention, in Standard Treatment and Contingency Management respectively. The recalculation uses the arm means, standard deviations, and group sizes posted for each outcome. It is an unadjusted summary-statistic calculation, not a reconstruction of an undocumented original statistical model. It cannot account for details that are absent from the registry record.

11. Confidence Intervals and Precision

The primary mean difference is 26.4 percentage points, with a recalculated 95% confidence interval from 24.33 to 28.47. The interval lies above zero under the stated unadjusted calculation, and its endpoints indicate the range of mean differences compatible with the posted summary data and calculation. The interval does not include uncertainty from possible missing-data mechanisms, measurement procedures, or analysis choices that are not represented in the calculation.

For treatment retention, the recalculated mean difference is 3.6 weeks, with a 95% confidence interval from 1.62 to 5.58. As with the primary outcome, this is an unadjusted interval calculated from posted group summaries. Its width conveys sampling uncertainty under the calculation’s assumptions; it is not a measure of the importance of the outcome or the likelihood that the result will be replicated in another setting.

Confidence intervals are useful because they show both the estimated contrast and the range of values consistent with the data under a specified method. In general, narrower intervals indicate greater statistical precision under that method, while wider intervals indicate more uncertainty. Precision is not the same as validity: an interval can be precise and still fail to account for bias, missing data, dependence among repeated measurements, or limited generalizability.

The registry record does not report sponsor-produced confidence intervals, and the intervals described are recalculated from the posted means, standard deviations, and arm sizes. No discrepancy is flagged. Their interpretation is consequently tied to those summary data and the unadjusted calculation, rather than to a documented adjusted analysis.

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.

The planning illustrations give participants per arm for 80% power and participants per arm for 90% power. These are not total trial enrollment figures and are not counts of observed outcomes or events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each illustration uses the stated fraction of the observed effect as the effect to detect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

The 80% power column represents a planning target for the chance of detecting an effect of the specified size under the calculation assumptions, if that effect and those assumptions held. The 90% power column uses a higher target chance of detection, which generally requires more participants for the same effect. These are prospective planning quantities, not a measure of the probability that the trial’s result is true.

For the primary outcome, the illustrations range from 1 participant per arm when planning for 100% of the observed effect to 3 participants per arm for 50% of the observed effect at 80% power. At 90% power, the corresponding figures range from 1 to 4 participants per arm. For treatment retention, the corresponding planning figures range from 31 to 122 participants per arm at 80% power and from 41 to 163 participants per arm at 90% power. Smaller effects require more participants in these calculations; this is why planning for a fraction of the observed effect raises the required sample size.

These illustrations are based on the observed estimates, which may not represent the effect in a future study. In particular, a planning result based on a large observed effect can produce very small illustrative sample sizes and should not be read as evidence that a small trial would reliably reproduce the result. This is not observed power: it is a planning exercise based on stated assumptions, not a retrospective measure of what the completed trial had a chance to detect.

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 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 = 26.400; pooled standard deviation σ = 5.247.
2. n = 2 × (1.96 + 0.842)² × 5.247² / 26.400² = 0.6, rounded up to 1 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 <- 26.4                      # observed difference in means
sigma <- 5.24690384893796                     # 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(3345394)
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 = 1 (80% power), 1 (90% power)
 75% of observed effect: n per arm = 2 (80% power), 2 (90% power)
 50% of observed effect: n per arm = 3 (80% power), 4 (90% power)
power.t.test: 2.1 
Simulated power at n = 1 per arm: NA (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 record identifies Pattern of Crack Cocaine Use as the primary outcome and Treatment Retention as a secondary outcome. It reports no analyses in the analysis listing and does not describe a statistical analysis plan, a testing hierarchy, or a method for controlling multiplicity. The p-values discussed for the posted outcomes are unadjusted. Without a reported plan, it is not possible to determine whether additional outcomes, time points, subgroup comparisons, or analyses were considered when the trial was conducted.

Multiplicity matters because repeated statistical testing can increase the chance of finding at least one apparently strong result even when no underlying differences exist. This general concern does not mean that the posted results are false; it means that an unadjusted secondary result should carry less inferential weight when the family of planned or performed tests is unknown. The primary outcome is more central to the stated question, but its analysis methods are also not fully documented in the registry record.

The primary outcome description says all enrolled participants were analyzed on an intention-to-treat basis. That statement identifies the intended analysis population, but the registry record does not explain how missing urine samples or other missing measurements were handled. It also does not report how missing retention information, withdrawal, or incomplete follow-up was addressed. The listed arm sizes for outcome summaries do not by themselves reveal whether every enrolled participant contributed complete data to each measure.

Allocation is described as randomized, but the record does not report the sequence-generation method or allocation concealment. Masking is described as single, without saying who was masked or whether masking was maintained. These omissions limit assessment of potential bias. The record also does not report interim analyses, protocol deviations, or a prespecified sample-size justification. Those matters should be treated as unreported in the registry record, not inferred from the posted results.

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

The posted data show higher group means for the primary percentage of negative urine samples and for treatment retention in the Contingency Management group than in the Standard Treatment group during the 12-week treatment period. The unadjusted recalculated comparisons are statistically separated from zero under the summary-statistic calculations described. These findings characterize the trial’s posted outcome summaries; they do not establish that the intervention will produce the same results for every participant or in every treatment setting.

The trial evaluated Contingency Management as an addition to standard treatment, not as a replacement for standard treatment. Any observed group contrast therefore concerns the two treatment packages as delivered in this program. The design does not isolate the behavioral component from the surrounding treatment, and the registry record does not provide enough detail to assess which features of delivery may have contributed to the pattern.

The primary endpoint concerns submitted urine samples over treatment, and retention concerns weeks in treatment. Neither outcome describes longer-term outcomes after the 12-week period, and the registry record does not post such follow-up results. The results also do not describe broader social, psychiatric, or other health outcomes mentioned in the trial’s background. A statistical comparison of these endpoints should not be extended to outcomes that were not reported.

Statistical significance is not the same as clinical importance. The registry record does not state a threshold for a clinically meaningful change, and the posted summaries cannot determine how participants experienced the differences. Uncertainty about missing data, outcome procedures, analysis choices, and generalizability also remains. The results may inform understanding of this trial, but they should not be used as individual medical advice or as a guarantee of outcomes in other circumstances.

16. Why This Trial Matters Statistically

This trial is statistically notable for comparing two behavioral treatment approaches in a defined program setting: standard treatment alone and standard treatment associated with Contingency Management. Because the primary endpoint is based on submitted urine samples across treatment, it addresses observed patterns during the treatment period rather than a single endpoint measurement. The retention outcome adds a separate view of engagement in care.

For biostatistical interpretation, the record illustrates why effect estimates, uncertainty, and design information all matter. The posted group means and recalculated mean differences describe the scale and direction of the observed contrasts. Confidence intervals show uncertainty under an unadjusted calculation, while the p-values alone do not convey effect size or establish broad applicability. The planning illustrations also show how assumptions about the effect to detect influence planning quantities, and why calculations based on an observed effect should not be confused with the original trial design.

The registry record leaves important analytical questions unanswered, including missing-data handling, the detailed analysis plan, and multiplicity. These are not minor technicalities: they shape how confidently a reader can interpret the inferential results and how readily the findings can be compared with future studies. The distinction between the posted descriptive summaries and the recalculated unadjusted inference is especially important when the sponsor’s original analyses are not listed.

The record can therefore be useful as a focused example of interpreting continuous outcomes from a randomized trial while preserving uncertainty about methods and applicability. Its statistical meaning depends not only on the size of the group contrasts, but also on how the endpoints were collected, analyzed, and situated within the trial’s broader design.

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 trial’s setting is specific: treatment was offered through the Unidade Recomeço Helvétia program in the Crackland region of Brazil. The registry record does not report participant demographics, eligibility criteria, or detailed clinical characteristics. That limits assessment of how closely the enrolled participants resemble people receiving care in other settings.

The intervention group received standard treatment associated with Contingency Management, so the comparison does not isolate the effects of Contingency Management from other components of the program. Details of the behavioral intervention, treatment fidelity, and differences in contact or delivery between groups are not reported. The single-blind designation is also not elaborated: the record does not identify who was masked or how masking was maintained.

The primary outcome is based on submitted urine samples, but sample schedules, laboratory procedures, and the handling of unsubmitted samples are not described. The record states that all enrolled participants were analyzed for the primary outcome on an intention-to-treat basis, yet does not explain the approach to missing measurements. The way treatment retention was defined and measured is also not detailed.

The registry record does not report a complete analysis plan, a multiplicity strategy, or sponsor-reported analyses. The inferential comparisons discussed are unadjusted recalculations from summary statistics. No adverse events or deaths are listed as occurring in either group, but the record also lists zero participants at risk for the adverse-event categories. These fields do not support a broad safety conclusion. Finally, the posted outcomes cover the 12-week treatment period, with no longer-term outcome results reported in the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effectiveness of Contingency Management in the Treatment of Crack Addiction in Brazil — NCT03345394.
• Registry record last updated 2021-04-08; status last verified 2021-03.
• Results first posted 2021-04-08.
• 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

NCT03345394 is a completed randomized, single-blind, parallel trial sponsored by Federal University of São Paulo. The registry record lists enrollment of 98 and compares 12 weeks of standard treatment with standard treatment associated with Contingency Management at the Unidade Recomeço Helvétia treatment program. The phase is listed as NA.

The primary outcome is the percentage of negative cocaine urine samples submitted during 12 weeks of treatment, analyzed as a mean with standard deviation. Treatment retention, measured in weeks over 12 weeks, is the posted secondary outcome. The primary population is described as all enrolled participants analyzed on an intention-to-treat basis.

Posted arm summaries favor the Contingency Management group on both measures, and the unadjusted recalculations show confidence intervals above zero for the mean differences. The registry record does not report a detailed statistical analysis plan, missing-data methods, or multiplicity procedures. Interpretation should therefore retain the distinction between the observed summaries and the limits of the documented methods.