Brief Intervention for Justice-Involved Substance Users: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Brief Intervention for Justice-Involved Substance Users (NCT03308877), a randomized na study. The primary outcome is Percent Days Abstinent.

2. Clinical Question

The central statistical contrast is the difference in the average percentage of days abstinent between the randomized arms. The posted arm means are 44.0 for BMI and 42.0 for Standard Care. The unadjusted comparison estimates a mean difference of 2.0 in favor of BMI on the endpoint scale, but its confidence interval extends in both directions around no difference. These are descriptive and inferential results for the participants included in the endpoint analysis; they do not establish what happened for participants without a recorded 6-month endpoint.

The registry describes the broader trial as studying ways of helping justice-involved people change to healthier behavior and lists substance use and violence as conditions. The primary outcome presented in the record is specifically abstinence from alcohol or drugs. No primary endpoint about violence is identified in the posted outcome details. The clinical question addressed by this result is therefore focused on a behavioral measure of abstinent days, rather than every behavior or condition named in the trial record.

3. Trial Design

This was a randomized, parallel-group behavioral trial comparing Brief Motivational Intervention (BMI) with Standard Care (SC). The registry lists triple masking. It does not describe which parties were masked, how randomization was generated or implemented, or what procedures were used to preserve masking, so those design details are not reported in the registry record. The trial is listed as completed, with enrollment of 132. Its recorded start date is 2018-02-01 and its primary completion date is 2023-08-01.

The sponsor was the University of Rochester. The phase is listed as NA, and no further explanation of that designation is reported. Both interventions are classified as behavioral. Although the arm names are given, the arm descriptions are empty in the registry record; the specific activities, duration, and delivery of BMI and Standard Care are therefore not reported. The general trial summary describes a study of ways to support healthier behavior among justice-involved people, but it does not provide detailed eligibility criteria or recruitment procedures.

The primary endpoint analysis is described for those who completed 6-month follow-up. The BMI arm has 38 participants in the posted endpoint summary, and the Standard Care arm has 34. These are the endpoint-analysis group sizes, not a description of every participant enrolled. The record does not explain the difference between enrollment and these analysis counts, describe missing outcome data, or specify how participants without a completed follow-up were handled. It also does not report the trial's original sample-size justification, planned analysis population, interim analyses, or detailed statistical plan. Those omissions limit how fully the observed summaries can be connected to the initial design.

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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Those who completed 6-month follow-up

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 Percent Days Abstinent, measured over 6 months.

The primary endpoint is Percent Days Abstinent at 6 months. It measures the percentage of days on which participants did not use alcohol or drugs, among those who completed the 6-month follow-up. The registry describes the outcome as a mean with standard deviation. The BMI arm's mean is 44.0, with a standard deviation of 42.0; the Standard Care arm's mean is 42.0, with a standard deviation of 41.0.

As a continuous measure, the endpoint summarizes abstinence across days rather than classifying each participant only as abstinent or not abstinent. In general, a measure of the percentage of abstinent days can represent variation in behavior across participants and capture changes that a single yes-or-no status may miss. That is a general reason such an outcome can be useful; the registry record does not report a separate rationale for choosing it, nor does it specify additional details about how days or use were assessed.

The endpoint is limited to alcohol and drug use as described in the outcome definition. It should not be read as measuring violence, overall health, or every aspect of behavior change. The follow-up time is 6 months, and the stated analysis population consists of follow-up completers. The record does not report whether this endpoint was collected at other times or how observations from participants who did not complete follow-up were treated.

7. Results Posted in the Registry

• Brief Motivational Intervention (BMI): mean 44.00 versus 42.00 on control; difference 2.00 (95% CI -17.19 to 21.19), standardized effect d = 0.05; z-test p = 0.838.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous measure, and the registry reports a mean and standard deviation for each arm. The BMI mean is 44.0 among 38 participants; the Standard Care mean is 42.0 among 34 participants. The corresponding standard deviations are 42.0 and 41.0. In general, the mean describes the center of a set of measurements, while the standard deviation describes how spread out individual measurements are around that mean. A large standard deviation indicates substantial participant-to-participant variation, not uncertainty about the mean by itself.

What does a mean difference represent?

A mean difference compares the average outcome in one group with the average in another, using the outcome's original scale. The posted comparison is BMI relative to Standard Care and gives an estimate of 2.0. Its sign indicates the direction of the difference under that ordering. Because the outcome is a percentage of days abstinent, the estimate is expressed on the endpoint scale. The registry does not provide further detail on whether the comparison was adjusted for any baseline or other variables; the recalculation is explicitly unadjusted.

In general, an unadjusted comparison uses the group summaries without accounting for additional covariates. A regression model can estimate a comparison while incorporating variables into the model, but the precise meaning of its coefficient depends on the outcome, predictors, coding, and model specification. Although linear regression entries appear in the registry, those details are not reported sufficiently to identify their relationship to the unadjusted mean difference. It would therefore be inappropriate to assume which variables were included or to describe the regression coefficients as adjusted treatment effects.

How should the standard error and interval be understood?

A standard error describes the sampling uncertainty of an estimate under a statistical model. The recalculation reports standard errors of 7.031 for the Standard Care mean and 6.813 for the BMI mean. In general, the standard error is not the same as the standard deviation: the standard deviation describes variation among individual outcomes, whereas the standard error concerns uncertainty in an estimated quantity. An interval around a mean difference combines an estimate with uncertainty to show a range of values compatible with the data and the method used. The posted mean-difference interval is -17.19 to 21.19. The confidence level for that recalculated interval is not stated in the comparison details, so no level should be inferred from the registry record.

For the sponsor's regression entry with B .063, the record explicitly labels the interval as 95%, with limits .007 and .156. In general, a 95% confidence procedure is designed so that, across repeated uses under its assumptions, intervals would cover the target parameter at the stated rate. It is not a probability statement about a fixed parameter after observing one interval. The registry does not identify the parameter and model details well enough to interpret B as the same target as the mean difference.

What does a p-value test?

In general, a p-value assesses how unusual data at least as extreme as those observed would be if a specified null model were true. Its interpretation depends on the hypothesis, model, and analysis choices. The recalculated unadjusted p-value is 0.838. The registry also posts regression p-values of .07, .02, and <.01, but does not provide enough details to establish that they test the same hypothesis. A p-value does not measure the size or importance of a difference, and it does not account for unreported analyses or missing outcomes.

Random assignment is generally intended to make treatment groups comparable in expectation, but it does not guarantee identical group composition in a particular trial. The registry identifies the allocation as randomized, but the randomization procedure and any stratification or blocking are not reported. The recalculated comparison is based on the observed endpoint summaries; it should not be mistaken for a complete description of the original analysis plan.

Why can variability matter?

When individual outcomes vary substantially, the group means may be estimated with less precision. General statistical methods can account for variability under stated assumptions; the recalculation reports a pooled standard deviation of 41.53. Over-dispersion is a general concern when observed variability exceeds what a chosen model expects: standard errors and intervals may then be too small if the model does not accommodate that extra variability. The registry record does not report a specific over-dispersion assessment or a model choice addressing it, so it is not possible to say that over-dispersion occurred in this trial.

Finally, the endpoint analysis is described for follow-up completers. General complete-case analyses can be biased if completion is related to outcome or treatment in ways not accounted for by the analysis. The record does not report the extent or reasons for missing follow-up, or methods used to address missingness. Consequently, the available mean comparison describes the analyzed participants and cannot, by itself, resolve how missing data might affect interpretation.

10. Confidence Intervals and Precision

The unadjusted mean difference is 2.0, and its posted interval extends from -17.19 to 21.19. The interval includes zero, the value representing no difference in means. It also includes values in either direction: the BMI mean could be lower or higher than the Standard Care mean within the range of estimates compatible with this calculation. The interval is wide relative to the point estimate, so the estimate is not precise enough to pin down a narrow range of differences.

In general, a confidence interval communicates uncertainty about an estimate under the method's assumptions. It is more informative than a point estimate alone because it shows both the direction and range of plausible values. It does not mean that every value in the interval is equally likely, and it does not include uncertainty from design or data issues that the method does not account for. The confidence level for the recalculated mean-difference interval is not stated in the registry record, and the result should not be assigned a level that is not reported.

The arm-level standard deviations, 42.0 and 41.0, indicate considerable variability in the endpoint. The group sizes in the primary summary are 38 for BMI and 34 for Standard Care. In general, variability and the amount of information available both affect the precision of a mean comparison. The posted interval is consistent with substantial uncertainty about the underlying mean difference. It does not establish equivalence, nor does the interval alone determine whether a difference would be important for participants.

The sponsor's regression entry has a separately reported 95% confidence interval, from .007 to .156, for B .063. Because the registry does not give enough information to identify that coefficient's outcome and estimand, its precision cannot be directly compared with the unadjusted mean-difference interval. The discrepancy flag also means that the sponsor's own analysis takes precedence over the recalculation when interpreting the trial's reported analysis.

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 and are not the trial's original design assumptions. The registry record does not report the original sample-size justification or the assumptions used when the trial was planned.

The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row uses a stated fraction of the observed effect as the effect to detect. For planning for 100% of the observed effect, the figures are 6,770 participants per arm for 80% power and 9,062 participants per arm for 90% power. For planning for 75% of the observed effect, they are 12,035 participants per arm for 80% power and 16,111 participants per arm for 90% power. For planning for 50% of the observed effect, they are 27,077 participants per arm for 80% power and 36,248 participants per arm for 90% power.

In general, power is the chance that a study will detect an effect of a specified size under the assumptions used for planning, if that effect is present. The 80% and 90% columns therefore describe different design targets: the higher target aims for a greater chance of detecting the stated effect, and requires more participants under these assumptions. Smaller effects are harder to distinguish from random variation and need more participants. These figures are planning illustrations, not observed power.

Because the illustrations are anchored to the observed effect, they should not be read as a recommendation or as evidence that the original trial was designed to detect those effects. The record does not provide the original target effect, planned enrollment rationale, or the relationship between these illustrations and the trial's enrollment.

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 = 2.000; pooled standard deviation σ = 41.532.
2. n = 2 × (1.96 + 0.842)² × 41.532² / 2.000² = 6,769.2, rounded up to 6,770 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 <- 2                      # observed difference in means
sigma <- 41.5315714676369                     # 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(3308877)
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 = 6,770 (80% power), 9,062 (90% power)
 75% of observed effect: n per arm = 12,035 (80% power), 16,111 (90% power)
 50% of observed effect: n per arm = 27,077 (80% power), 36,248 (90% power)
power.t.test: 6770.1 
Simulated power at n = 6,770 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.

13. Analyses Reported by the Sponsor

The posted arm summaries allow a simple unadjusted recalculation of the mean difference: 2.0, with an interval from -17.19 to 21.19 and p-value 0.838. The registry separately lists linear regression analyses, including entries with p-values .07 and .02, and an entry with B .063, a 95% confidence interval from .007 to .156, and p <.01.

The registry flags a discrepancy between the sponsor's analysis and the recalculation. The sponsor's own analysis takes precedence; the recalculation is not a replacement for it. The regression entries do not identify enough details about their outcomes, covariates, model specifications, or target parameters to determine exactly why the results differ or whether they address the same estimand as the raw mean comparison. The model details and a reconciliation are not reported in the registry record.

Accordingly, the unadjusted result is best treated as a transparent, summary-statistic comparison. It can help readers understand the scale and uncertainty of the observed group means, but it cannot be used to override or reconstruct the sponsor's model-based findings.

14. Multiplicity, Missing Data and Analysis Populations

The registry identifies Percent Days Abstinent at 6 months as the primary endpoint. It also records 3 outcome measures and 5 analyses, while the count of posted secondary outcomes is 0. The available analysis entries include three linear regression results: two p-values, .07 and .02, and a coefficient B .063 with a 95% confidence interval from .007 to .156 and p <.01. The record does not link each analysis clearly to an outcome, hypothesis, or model specification.

Multiplicity arises in general when researchers conduct multiple statistical tests or examine several outcomes, time points, subgroups, or model specifications. If many tests are considered, the chance of at least one apparently noteworthy result can increase unless the analysis plan addresses that issue. The registry record does not report a multiplicity adjustment, a hierarchy among tests, or a prespecified strategy for interpreting the analyses. It is therefore not possible to determine from the record whether these regression analyses were planned as confirmatory tests, exploratory analyses, or whether any adjustment was used.

The primary endpoint population is described as participants who completed 6-month follow-up. The record does not report the number of enrolled participants with missing primary outcomes, the reasons for missingness, or whether missing values were addressed through imputation or another method. It also does not state whether the endpoint analysis followed an intention-to-treat population or another prespecified analysis population. In general, restricting an analysis to participants with observed follow-up can affect the comparison if follow-up completion is related to treatment or outcome. Without details about missingness and analysis populations, that possibility cannot be assessed.

The registry identifies randomized allocation, but does not report the planned primary statistical model, its covariates, assumptions, or handling of deviations from the assigned intervention. Nor does it report interim analyses or stopping rules. These omissions do not establish that such procedures were absent; they mean they are not reported in the registry record. They limit the ability to distinguish prespecified analyses from additional analyses and to assess how multiplicity and missing data may affect the reported evidence.

15. 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 0% reporting threshold.

Most frequent non-serious adverse event terms

The posted safety counts list 70 participants at risk for serious adverse events in the BMI group and 62 in Standard Care. Serious adverse events are recorded for 0 participants in each group, and deaths are recorded for 0 in each group. The counts for other adverse events are 19 in BMI and 15 in Standard Care, among 70 and 62 participants at risk, respectively.

These are counts, not rates, and the registry does not describe the event terms or provide a breakdown of the other adverse events. The serious-event listing has no serious adverse event terms. Zero recorded serious events in these groups means none are listed in the posted results; it does not establish that an intervention is free of risk or that an event could not occur. The record does not report event severity beyond the serious-versus-other grouping, timing, relatedness assessments, or details of how events were collected.

Safety counts should be interpreted alongside the population at risk and the trial's follow-up and reporting procedures. The registry does not provide enough information to compare event rates over equivalent exposure periods or to determine whether the groups differed in event duration or ascertainment. The counts describe the posted safety record and should not be treated as a complete characterization of safety.

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

The primary endpoint results describe mean Percent Days Abstinent at 6 months among participants who completed follow-up. BMI has a posted mean of 44.0 and Standard Care a mean of 42.0. The unadjusted mean difference is 2.0, while the interval from -17.19 to 21.19 includes both no difference and differences in either direction. The p-value of 0.838 likewise does not provide strong evidence against a zero difference under the assumptions of that unadjusted comparison.

This does not prove that the groups are equivalent or that there is no difference. The interval is broad, and the registry's discrepancy flag indicates that the sponsor's own analysis takes precedence over the recalculation. The regression results cannot be interpreted as estimates of the same endpoint contrast without additional model information. The record does not report enough analysis detail to reconcile those results.

The endpoint is a measure of alcohol- and drug-abstinent days, not a direct measure of every behavior or condition listed in the trial record. It also applies to follow-up completers; missing-outcome handling and the analysis population are not reported. These limits mean the posted endpoint summary should not be generalized automatically to participants without recorded follow-up or to outcomes not represented by this measure.

In general, statistical evidence addresses uncertainty about a particular estimate under particular assumptions. It does not by itself establish clinical importance, explain the mechanism of an intervention, or show how a result applies to people outside the analyzed population. The registry record does not report a threshold for a clinically important difference, detailed intervention content, or sufficient information about the sponsor's regression models to support those broader conclusions. The results are best read as an imprecise comparison of the posted completer means, considered alongside rather than in place of the sponsor's analysis.

17. Why This Trial Matters Statistically

This trial illustrates an important distinction in clinical statistics: a small difference between group means is not the same as a precise estimate. The posted means, 44.0 for BMI and 42.0 for Standard Care, yield an unadjusted mean difference of 2.0. Yet the interval from -17.19 to 21.19 spans values in both directions, so the point estimate alone would give an incomplete account of the uncertainty. Reading the estimate together with its interval helps avoid treating a single observed difference as a settled result.

The record also makes clear why estimands and model details matter. A simple comparison from arm summaries and a regression coefficient can have different meanings if they address different outcomes, use different covariates, or rely on different populations. Here, the registry flags a discrepancy and supplies only limited details for the regression entries. The sponsor's own analysis therefore takes precedence, while the recalculation serves as a descriptive cross-check rather than a replacement.

Follow-up completion, multiplicity, and safety reporting are also part of interpreting evidence. The primary outcome applies to those who completed 6-month follow-up, while missing-data procedures are not reported. Several analysis entries appear, but the record does not state how multiple tests were handled. Safety counts are posted, but event detail is limited. These are not reasons to assume a particular bias or problem; they identify what the available registry information cannot resolve.

Statistically, the study is a useful example of how randomization, outcome summaries, uncertainty, sponsor analyses, and missing reporting details each contribute to interpretation. None should be reduced to a single p-value or mean difference.

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 endpoint summary is restricted to participants who completed 6-month follow-up, and the registry does not report how missing primary outcomes were handled. The endpoint-analysis counts are 38 for BMI and 34 for Standard Care, whereas enrollment is listed as 132; the record does not explain the relationship between enrollment and the analysis counts. This prevents a clear assessment of follow-up completeness or the effect of missing data.

The intervention arm descriptions are empty. The record identifies BMI and Standard Care as behavioral interventions but does not detail their content, duration, delivery, or adherence. Eligibility criteria and recruitment details are also not reported in the registry record, limiting assessment of who the analyzed participants represent. The population is described broadly as justice-involved people with substance use, but further characteristics are not available in the registry entries.

The registry reports multiple linear regression entries but does not give enough information to identify their outcome measures, covariates, model specifications, or relationship to the primary endpoint comparison. It flags a discrepancy between the sponsor analysis and the unadjusted recalculation without explaining the source. The sponsor's own analysis takes precedence, but its interpretation is limited by the absence of model details. The original sample-size justification, analysis plan, multiplicity approach, interim analyses, and analysis population are not reported.

The safety information gives group counts for serious and other adverse events and deaths, but does not provide event terms, severity details beyond the broad categories, relatedness, timing, or collection methods. These limitations constrain interpretation of both benefit-related outcomes and safety. They describe gaps in the registry record and do not establish that the trial failed to collect information that is not posted.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Brief Intervention for Justice-Involved Substance Users — NCT03308877.
• Registry record last updated 2025-03-18; status last verified 2025-03.
• Results first posted 2025-03-18.
• 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.

22. Record Summary

NCT03308877 is a completed randomized, triple-masked, parallel-group behavioral trial sponsored by the University of Rochester. It enrolled 132 participants and compared Brief Motivational Intervention with Standard Care. The record lists substance use and violence as conditions; the phase is NA. The recorded start date is 2018-02-01 and primary completion date is 2023-08-01.

The primary endpoint is mean Percent Days Abstinent at 6 months among follow-up completers. The posted means are 44.0 for BMI and 42.0 for Standard Care. An unadjusted recalculation estimates a mean difference of 2.0, with an interval from -17.19 to 21.19 and p-value 0.838. The registry also posts linear regression results and flags a discrepancy; the sponsor's own analysis takes precedence.

The record does not report sufficient detail about the regression models, missing-data handling, multiplicity, original sample-size rationale, or intervention content to resolve these limitations. Safety counts include 0 serious adverse events and 0 deaths in each arm, with other adverse events recorded for 19 BMI participants and 15 Standard Care participants.