Preventing Opioid Overdose Mortality in the United States: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Preventing Opioid Overdose Mortality in the United States (NCT03924505), a randomized na study. The primary outcome is Naloxone Coverage (Consistency).

2. Clinical Question

3. Trial Design

This was a randomized, unmasked, parallel-group trial. The registry lists an enrollment of 105 and describes the study as involving syringe services programs throughout the United States. The study status is completed; the recorded start date is 2019-09-03 and the primary completion date is 2022-03-14. The sponsor was RTI International. The phase is listed as not applicable.

The two arms were Organize and Mobilize for Implementation Effectiveness and Dissemination of Best Practice Recommendations. The first approach was based on Implementation Sustainment Facilitation and included discrete strategies from the Addiction Technology Transfer Center. The second arm was to receive best practice recommendations for implementing overdose education and naloxone distribution within SSPs. The registry record does not give a complete description of the first arm, so its specific activities and delivery cannot be fully characterized.

The primary outcome was assessed at 3 months. Its stated measure was the mean number of SSP participants receiving naloxone per total number of SSP participants. The registry lists outcome-summary sample sizes of 45 and 49 for the two arms. Those figures are reported in the outcome summaries; the record does not explain their relationship to the enrollment figure of 105. The analysis populations and reasons for any difference are not reported in the registry record.

The registry identifies randomization and parallel allocation but does not report the allocation procedure, concealment, or whether any program-level features were used to stratify assignment. Masking is listed as none. The original trial’s sample-size justification, planned statistical analysis details, and any interim analyses 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.

Population: Our trial enrolled syringe services programs and randomized them to two arms. This was a study of organizations, not individuals.

6. Primary Endpoint

The registry lists the primary outcome as Naloxone Coverage (Consistency), measured over 3 months.

The primary endpoint, Naloxone Coverage (Consistency), was assessed at 3 months. It is defined as the mean number of syringe services program participants receiving naloxone per total number of SSP participants, with the unit described as a proportion of participants. In practical terms, the endpoint concerns how consistently naloxone was reaching people served by a program, as represented by the stated numerator and denominator.

This kind of implementation outcome can describe whether a program is putting a recommended service into practice. It is distinct from a direct clinical outcome such as overdose events or deaths: the registry’s primary endpoint measures naloxone coverage, not mortality. The trial’s title refers to preventing opioid overdose mortality, but the posted primary outcome does not itself quantify whether mortality changed.

The record reports an arm mean and standard deviation for this continuous measure. It does not give further operational details about the timing or collection of the participant counts, how missing program data were handled, or whether the measure was transformed for the regression analysis. Those details are not reported in the registry record, and should not be assumed from the endpoint name alone.

7. Results Posted in the Registry

• Dissemination of Best Practice Recommendations: mean 0.40 versus 0.90 on control; difference -0.50 (95% CI -0.92 to -0.08), standardized effect d = -0.50; z-test p = 0.019.

8. Statistical Interpretation

9. Statistical Methods Explained

The trial is described as randomized, unmasked, and parallel-group. Randomization is intended, in general, to make treatment groups comparable on average by assigning units through a chance process. The registry does not describe the assignment sequence, concealment, or any stratification factors, so those features cannot be assessed from the record. The unit receiving the implementation strategy was the syringe services program, while the outcome is framed using participants served by those programs. Details about how that relationship was handled in statistical analyses are not reported.

What does the arm summary represent?

The primary endpoint is described as a continuous measure, and the reported arm values are means with standard deviations. A mean gives the average of observed values on the measure; a standard deviation describes their spread around the mean. The posted means are 0.9 and 0.4, and the standard deviations are 1.4 and 0.3, respectively. The registry does not explain whether the values were transformed, whether they summarize program-level proportions directly, or how observations with missing components were treated.

The unadjusted recalculation compares the two posted arm means. The reported mean difference of -0.5 is expressed as the dissemination arm relative to the Organize and Mobilize arm. A negative value therefore indicates that the posted mean in the dissemination arm is lower on this comparison scale. This is a summary-statistic comparison; it is not an adjusted regression estimate and does not account for factors beyond the posted summaries.

What does the sponsor’s regression estimate represent?

The registry reports that the sponsor used negative binomial regression and expressed its result as an incidence rate ratio. In general, a rate ratio compares rates between groups, with the interpretation depending on which group is in the numerator and which is the reference. The registry reports an incidence rate ratio of 2.15, a 95% confidence interval of 1.42 to 2.35, and p < 0.01. It does not identify the contrast coding or provide a fuller model specification. The direction and exact substantive meaning of the ratio should therefore not be inferred beyond the information stated in the record.

In general, negative binomial regression can be useful for count data when observations are more variable than a basic count model would allow. This extra variability is often called over-dispersion. Allowing for it can produce uncertainty estimates better suited to such data than a model that assumes variability follows a more restrictive pattern. That is a general explanation of the method; the registry does not report whether over-dispersion was assessed or how the model was specified for this endpoint.

The difference between the regression result and the recalculated mean difference is not, by itself, evidence of an error. The estimates use different statistical forms: a rate ratio from a regression and a difference between unadjusted arm means. Their outcome definitions, adjustments, and reference coding may differ. The registry does not provide enough model detail to map one estimate exactly onto the other. The registry record does not flag a discrepancy.

How should the p-values be read?

A p-value summarizes how incompatible the observed result is with a specified null hypothesis under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. The unadjusted recalculation has p = 0.019; the sponsor’s regression result has p < 0.01. These values belong to different analyses, so they should not be treated as competing versions of one identical test.

The registry record does not report whether the sponsor’s result was adjusted for covariates, whether standard errors accounted for the program-level design, or what inferential assumptions were used beyond the named regression method. It also does not report the complete statistical analysis plan, handling of missing observations, or analysis populations. These omissions limit independent evaluation of model fit, precision, and reproducibility. The reported values can be described as posted, but the missing methods should not be filled in by assumption.

10. Confidence Intervals and Precision

Confidence intervals express uncertainty around an estimate under the assumptions of the analysis. They indicate a range of values that are more or less compatible with the data and model; they are not a guarantee that the true value lies in the interval. Precision depends on the width of the interval, while interpretation also depends on the estimate’s scale and the analysis design.

For the sponsor’s negative binomial regression, the incidence rate ratio is 2.15 with a 95% confidence interval from 1.42 to 2.35. The interval does not include the null value of 1 for a ratio, and the registry reports p < 0.01. This describes the model-based estimate as posted. Because the contrast coding and model details are not reported, the interval should not be used to infer an unstated direction or a more specific adjusted effect.

The unadjusted recalculation reports a mean difference of -0.5, with an interval entirely below zero and p = 0.019. The confidence level for that recalculated interval is not specified in the registry record. It is based on posted summary statistics and is not the same quantity as the regression interval. The distinct scales and methods matter when judging whether the two results are comparable.

The outcome summaries also show different standard deviations across arms: 1.4 and 0.3. In general, greater variability can make an estimate less precise, while the amount of information, the analysis method, and the data structure also affect uncertainty. The registry does not report enough detail about missingness, program-level dependence, or regression specification to assess how those features influenced the posted intervals.

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 sample-size display is a planning illustration based on the observed effect, not the trial’s original design calculation. Its entries are participants per arm for 80% power and participants per arm for 90% power, not total event counts. The columns describe different target probabilities of detecting the stated effect under the planning assumptions: 80% power means the calculation targets an 80% chance of detecting that effect if the assumptions hold, while 90% power targets a higher chance. These are planning quantities, not a description of what the completed trial achieved.

The listed 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 as a stated fraction of the observed effect. The rows describe planning for 100%, 75%, and 50% of the observed effect. Smaller target effects require more participants because they are harder to distinguish from random variation under the same assumptions. The displayed values are participants per arm for 80% power and participants per arm for 90% power.

This is not observed power. It is a prospective illustration calculated from the observed effect, not a measure of the trial’s achieved ability to detect an effect. The registry record does not report the original sample-size justification or its planning assumptions. The illustration should therefore not be used as evidence that the trial was designed around these assumptions or that its completed analyses had the displayed power.

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 = -0.500; pooled standard deviation σ = 0.992.
2. n = 2 × (1.96 + 0.842)² × 0.992² / -0.500² = 61.8, rounded up to 62 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 <- -0.5                      # observed difference in means
sigma <- 0.992143047189747                     # 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(3924505)
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 = 62 (80% power), 83 (90% power)
 75% of observed effect: n per arm = 110 (80% power), 148 (90% power)
 50% of observed effect: n per arm = 248 (80% power), 331 (90% power)
power.t.test: 62.8 
Simulated power at n = 62 per arm: 0.790 (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 sponsor’s own posted analysis is a negative binomial regression with an incidence rate ratio of 2.15, a 95% confidence interval from 1.42 to 2.35, and p < 0.01. The registry does not flag a discrepancy. This result is distinct from the unadjusted recalculation, which compares arm means and reports a mean difference of -0.5 with p = 0.019.

The two analyses use different scales and methods: one reports a regression-based rate ratio, while the other is a simple comparison of the posted continuous-measure summaries. The record does not provide sufficient detail about the regression outcome, contrast coding, covariates, or model specification to reproduce or fully reconcile the sponsor’s estimate. Accordingly, the recalculation should be read as a separate, unadjusted summary-statistic analysis rather than a replacement for the sponsor’s regression result.

The sponsor’s estimate is the registry’s reported model-based analysis. Its interpretation remains constrained by the missing specification details, especially the direction of the contrast and how the stated proportion outcome was represented in the negative binomial model. The posted result can be reported as recorded without assigning an unreported reference group or implying that the analyses estimate precisely the same quantity.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 3 outcome measures and 3 analyses, but no secondary results are posted. It does not identify the full set of outcomes or analyses, distinguish all planned from exploratory analyses, or report whether any adjustment for multiple comparisons was used. When several outcomes or analyses are examined, the chance of at least one apparently unusual result can increase; methods to address that issue depend on the analysis plan. Whether such methods were used in this trial is not reported in the registry record.

The registry does not describe missing-data frequency, reasons for missingness, imputation, or sensitivity analyses. It also does not state which analysis population was used, such as whether analyses followed all randomized programs or a subset with available outcome data. The outcome summaries list sample sizes of 45 and 49, while the trial enrollment is recorded as 105; the registry does not explain the relationship between these figures. They should not be reconciled by assumption.

The record identifies the trial as randomized but does not report details of allocation concealment, analysis by assigned group, or handling of program-level clustering. These design and analysis details can affect interpretation of standard errors and confidence intervals. The registry also does not provide the full statistical analysis plan, model diagnostics, or information about interim analyses. These items are not reported in the registry record, so their presence or absence in the conduct of the trial cannot be established from the posted information.

Because the primary endpoint concerns participants within SSPs, it is important to know how within-program observations and program-level assignment were represented in the analysis. The registry does not specify that structure for the regression result. This is a general design consideration, not a claim that the analysis failed to account for it. Together, the unreported multiplicity, missing-data, population, and model details limit a complete assessment of the statistical analysis.

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.

The registry reports serious adverse events, other adverse events, and deaths separately by arm. For Organize and Mobilize for Implementation Effectiveness, the safety record lists 51 at risk for serious adverse events and 51 at risk for other adverse events; each event count is 0, and deaths are 0. For Dissemination of Best Practice Recommendations, the corresponding at-risk figures are also 51 and 51, with 0 serious adverse events, 0 other adverse events, and 0 deaths.

These are the event figures recorded in the registry. Zero recorded events means none were reported in these categories for the listed groups; it does not establish that no event occurred outside the recorded reporting or observation process. The registry does not provide further detail about event definitions, collection procedures, or the relationship between the safety at-risk counts and the outcome-summary sample sizes. No serious adverse event terms are listed.

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

The posted results show higher mean naloxone coverage consistency in the Organize and Mobilize for Implementation Effectiveness arm than in the Dissemination of Best Practice Recommendations arm: the reported means are 0.9 and 0.4, respectively. The unadjusted recalculation expresses the comparison as a mean difference of -0.5 for dissemination relative to Organize and Mobilize, with p = 0.019. Separately, the sponsor reports a negative binomial regression incidence rate ratio of 2.15, with a 95% confidence interval from 1.42 to 2.35 and p < 0.01. The coding and reference group for that ratio are not stated.

These results concern an implementation measure at 3 months. They do not directly measure opioid overdose mortality, and the registry does not post a mortality estimate. The trial title and rationale refer to preventing overdose mortality, but the primary endpoint described in the record is naloxone coverage consistency within SSPs. The posted outcome therefore cannot be treated as a direct estimate of deaths prevented.

The results also do not establish which elements of the implementation approaches account for the observed arm summaries. The record does not fully describe the first intervention, the regression specification, or the handling of missing data and analysis populations. The reported estimates should be interpreted within those limits and on their stated scales, without treating the unadjusted mean difference and regression rate ratio as identical quantities.

Statistical results alone do not establish clinical or operational importance. The record does not provide a threshold for a meaningful difference in the coverage measure or additional context that would define such a threshold. The posted values describe the observed data and model-based analysis, not a recommendation for how any program should act.

17. Why This Trial Matters Statistically

This trial addresses a question about implementation rather than a direct comparison of clinical treatments. Its primary outcome asks whether naloxone distribution was reaching participants in syringe services programs consistently. That distinction matters statistically: implementation measures can describe adoption or coverage, while clinical outcomes such as overdose events and mortality require their own data and analyses.

The record presents two kinds of estimates: arm-level means and a sponsor-reported negative binomial regression result. Keeping their scales separate is essential. A mean difference describes an absolute contrast between summaries, whereas an incidence rate ratio is a relative measure from a regression model. Without the regression contrast coding and fuller specification, the ratio cannot be aligned precisely with the unadjusted arm comparison.

The registry also illustrates why uncertainty and reporting detail matter. The sponsor’s regression interval and the recalculated interval describe uncertainty for different analyses. Information about outcome construction, missing data, analysis populations, and program-level structure would help readers assess how the model relates to the trial design. Those details are not reported in the registry record.

Finally, an implementation outcome should not be conflated with a downstream health outcome. The study’s stated goal concerns improving naloxone implementation and access, but the posted primary measure is coverage consistency. Interpreting the outcome at that level avoids claiming a mortality result that the record does not report.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record leaves important trial-specific details unresolved. It describes the trial as involving 105 SSPs, but the outcome summaries list sample sizes of 45 and 49. The reason for this difference and the analysis populations are not reported. The measure is described as a proportion, while the sponsor’s reported analysis uses negative binomial regression and an incidence rate ratio; the record does not explain how the outcome was represented in that model.

The intervention description for Organize and Mobilize for Implementation Effectiveness is incomplete in the registry record. The delivery, duration, and implementation fidelity of the strategies are not fully described. The comparator is described as receiving best practice recommendations, but the record does not explain how those recommendations were delivered. These gaps limit interpretation of what the contrast entailed in practice.

The regression’s reference group, covariates, exposure definition, and model diagnostics are not reported. Nor does the registry detail missing-data handling, multiplicity procedures, allocation concealment, or analysis by assigned group. It does not report program characteristics that would help readers judge how broadly the results apply. These are limits on what can be concluded from this record, not evidence that particular procedures were or were not used.

The primary endpoint is a measure of naloxone coverage at 3 months, not a direct measure of overdose mortality. The registry does not post a mortality result or report a threshold for a meaningful change in the coverage measure. Consequently, the posted statistical estimates cannot establish a mortality effect or the operational importance of the observed differences.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Preventing Opioid Overdose Mortality in the United States — NCT03924505.
• Registry record last updated 2024-12-12; status last verified 2024-12.
• Results first posted 2024-12-12.
• 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

NCT03924505, titled “Preventing Opioid Overdose Mortality in the United States,” is recorded as a completed, randomized, unmasked, parallel-group trial sponsored by RTI International. The registry describes enrollment of 105 and a study involving syringe services programs throughout the United States. Its recorded start date is 2019-09-03, and its primary completion date is 2022-03-14.

The comparison was between Organize and Mobilize for Implementation Effectiveness and Dissemination of Best Practice Recommendations. The primary endpoint was Naloxone Coverage (Consistency), assessed at 3 months and defined using the number of SSP participants receiving naloxone relative to the total number of SSP participants.

The posted arm means were 0.9 and 0.4. The unadjusted recalculation reports a mean difference of -0.5 for dissemination relative to Organize and Mobilize. The sponsor’s reported negative binomial regression gives an incidence rate ratio of 2.15, with a 95% confidence interval from 1.42 to 2.35 and p < 0.01. Important details about the model, missing data, and analysis populations are not reported in the registry record.