ALK21-003: Study of Medisorb® Naltrexone (VIVITROL®) in Alcohol-Dependent Adults: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for ALK21-003: Study of Medisorb® Naltrexone (VIVITROL®) in Alcohol-Dependent Adults (NCT01218958), a randomized phase 3 study. The primary outcome is Percentage of Heavy Drinking Days Over the Treatment Period.

2. Clinical Question

The study was designed to examine drinking outcomes in adults with alcohol dependence under a randomized, placebo-controlled design. Participants reported drinking through the validated Timeline Follow-Back method. A heavy drinking day was defined as at least 5 drinks for men and at least 4 drinks for women. The primary efficacy analysis used the intent-to-treat population as defined in the registry record, with the last post-baseline observation carried forward.

The posted outcome summaries give median percentages of heavy drinking days and interquartile ranges for the two active-dose groups and pooled placebo groups. The reported inferential analyses compare each dose with pooled placebo using recurrent-event Cox models. The registry record does not explain how the two outcome descriptions relate analytically, nor does it report a direct statistical comparison between the active doses. The interpretation therefore needs to keep the descriptive endpoint summaries separate from the sponsor's reported hazard-ratio analyses.

3. Trial Design

This was a completed Phase 3, multicenter, randomized, quadruple-masked, parallel-group study. The registry lists enrollment as 624 and describes four assigned groups: Medisorb naltrexone 190 mg, Medisorb naltrexone 380 mg, placebo matching the 190 mg dose, and placebo matching the 380 mg dose. The randomization ratio was 2:2:1:1. For the posted efficacy comparisons, the two placebo groups are pooled.

Study drug was administered by intramuscular injection every 4 weeks, for a total of 6 injections. The recorded study start was 2002-02, and primary completion was 2003-09. The registry identifies alcohol dependence as the condition and reports the study as completed. It describes the study as double-blind in the brief summary and quadruple-masked in the design details; the record does not further define which roles were masked.

The primary endpoint covered baseline through Week 24 (168 days). Drinking was assessed using participant self-reports collected with a validated Timeline Follow-Back calendar. The primary efficacy population was the intent-to-treat population, defined in the record as all randomized participants who received at least one injection. The last post-baseline observation carried forward was used for each participant in that population.

The registry reports two dose-versus-pooled-placebo analyses using Andersen-Gill recurrent-event Cox models. It also lists a secondary outcome concerning participants reporting at least one treatment-emergent adverse event. The posted results include serious and other adverse-event counts by group. The registry record does not report further details about allocation concealment, the masking procedures, protocol deviations, adherence, or the original statistical design assumptions. Those details should not be inferred from the general design description.

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: A dynamic randomization was implemented to optimize balancing treatment assignment for 4 prespecified factors: gender, subject's baseline goal of abstinence (ie, yes/no), presence of abstinence prior to randomization, and study site.

Overall Study

Analysis population for the primary outcome, as defined in the registry: The last post-baseline observation carried forward (LOCF) of each participant in the intent-to-treat population (all randomized participants who received at least 1 injection of study drug) were utilized for the primary efficacy analysis.

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 Percentage of Heavy Drinking Days Over the Treatment Period, measured over Baseline through Week 24 (168 days).

The primary endpoint was the percentage of heavy drinking days over baseline through Week 24 (168 days). A heavy drinking day was defined as a day with at least 5 drinks for men or at least 4 drinks for women. Participants recorded the number of days on which they drank and the amount consumed each day using the validated Timeline Follow-Back method. The endpoint therefore summarizes the frequency of days meeting the study's heavy-drinking definition across the treatment period.

The posted group summaries use medians and interquartile ranges. The median is a measure of the middle of the observed distribution; the interquartile range describes the spread of the middle half of observations. These summaries can be useful when participant outcomes are skewed or contain a wide range of values, because the median is less influenced by extreme observations than the mean. This is a general statistical explanation, not a claim about the observed distribution beyond the reported summaries.

Assessing heavy drinking days provides a defined way to describe drinking patterns over time, rather than relying only on whether any drinking occurred. The registry also reports recurrent-event Cox hazard ratios, which are a separate model-based result. Those hazard ratios should not be read as the median percentage of heavy drinking days or as a direct conversion of that percentage. The registry record does not provide a detailed explanation reconciling the endpoint summary with the recurrent-event analysis.

7. Results Posted in the Registry

• Medisorb Naltrexone 380 mg vs Placebo Groups (Pooled): hazard ratio 0.75 (95% CI 0.60–0.94), reported p = 0.025 (as reported in the registry).
• Medisorb Naltrexone 190 mg vs Placebo Groups (Pooled): hazard ratio 0.83 (95% CI 0.68–1.02), reported p = 0.074 (as reported in the registry).

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports medians and interquartile ranges for the primary endpoint, together with hazard ratios from Andersen-Gill recurrent-event Cox analyses. These methods answer different descriptive and inferential questions. A median locates the middle of a distribution of participant-level percentages. An interquartile range describes variability across those percentages. A hazard ratio from a recurrent-event model compares event rates over follow-up according to the model. It is not another way of writing the median, and the two types of result should not be substituted for one another.

What does the median describe?

The median is the central value after observations are ordered. It is less sensitive than a mean to unusually high or low observations. The interquartile range marks the central portion of the distribution and conveys how much participant outcomes vary. These are general explanations of the statistics. In this study, the posted median percentages and interquartile ranges summarize heavy drinking days over the treatment period for each efficacy group. A median alone does not describe every participant's result, and overlapping interquartile ranges are not a formal test of a group difference.

What does an Andersen-Gill model do?

An Andersen-Gill recurrent-event Cox model is a time-to-event approach adapted to outcomes where events can occur repeatedly for the same participant. General recurrent-event methods use the timing and recurrence of events rather than treating every participant as having only a single possible event. A Cox-model hazard ratio compares the modeled event rate between groups over the observed follow-up, conditional on the model's structure. In general, a hazard ratio below 1 indicates a lower estimated rate for the numerator group relative to the reference group; a hazard ratio above 1 indicates a higher estimated rate. The registry labels the reported estimates as hazard ratios and identifies the pooled placebo groups as the comparator.

Repeated events from the same participant may be statistically related rather than independent. A model for recurrent events is intended to account for the repeated-event structure; treating each event as if it came from a different independent person can make uncertainty estimates unreliable. Over-dispersion is a general concern when event counts vary more than a simple model expects. Methods that account for recurrent events and within-person dependence can help represent that variability. The registry record names the Andersen-Gill method but does not report additional model details, diagnostics, covariate adjustment, or the exact handling of within-participant dependence. No further model assumptions should be attributed to the trial without that information.

How should the confidence interval and p-value be read?

A confidence interval describes a range of values compatible with the data and the statistical model at the stated confidence level. It gives information about precision as well as direction. For a hazard ratio, a confidence interval that includes 1 is compatible with no relative difference under the model at that confidence level; an interval that excludes 1 is not. The p-value measures how unusual results at least as discrepant as the observed result would be under a specified null model, assuming the model and analysis are appropriate. It is not the probability that the null hypothesis is true, and it does not measure clinical importance.

For the 380 mg comparison, the reported 95% confidence interval is 0.600 to 0.940 and p = 0.025. For the 190 mg comparison, it is 0.677 to 1.018 and p = 0.074. These are the sponsor's reported results. The distinctions between interval inclusion of 1 and the reported p-values describe statistical evidence under the respective analyses, not certainty about a treatment effect.

What does the LOCF approach mean?

The primary efficacy analysis used the last post-baseline observation carried forward for each participant in the intent-to-treat population. In general, LOCF fills a missing later outcome with the participant's last available post-baseline outcome. This preserves an outcome value for analysis but makes an assumption that the earlier value is a suitable stand-in for the unobserved later value. That assumption may not hold if outcomes change after the last measurement, and LOCF does not automatically remove bias from missing data. The registry record does not report missingness patterns, sensitivity analyses, or a comparison with other missing-data methods.

Because each participant's last recorded value may occur at a different time, LOCF can also mean that the analyzed value does not represent the same observed follow-up point for everyone. That is a general property of the approach, not evidence about the timing of missing observations in this trial. The record identifies the procedure but does not give the number of observations carried forward or explain how discontinuation was handled beyond the stated analysis population.

What does pooling the placebo groups mean?

The study assigned participants to two active doses and two dose-matched placebo groups. The posted hazard-ratio comparisons use pooled placebo groups. Pooling combines the placebo groups for those reported comparisons, rather than presenting each placebo group separately. The registry record does not give a separate efficacy estimate for each placebo group or explain additional pooling assumptions. It also does not report a direct test comparing the 190 mg and 380 mg groups.

The outcome summaries and model results should be kept in their stated forms: group medians and interquartile ranges for the endpoint, and sponsor-reported hazard ratios with confidence intervals and p-values for recurrent events. General statistical interpretation can clarify what those measures represent, but it cannot fill in unreported analysis choices or establish that assumptions were met.

10. Confidence Intervals and Precision

The confidence intervals indicate how precisely the recurrent-event hazard ratios were estimated under the sponsor's models. For 380 mg versus pooled placebo, the reported hazard ratio is 0.751 and the 95% confidence interval is 0.600 to 0.940. The interval lies below 1, so the reported estimate is compatible with a lower modeled recurrent-event rate in the 380 mg group than in pooled placebo, under the analysis. The interval nevertheless spans a range of possible relative effects; it is not a single known value.

For 190 mg versus pooled placebo, the hazard ratio is 0.830 and the 95% confidence interval is 0.677 to 1.018. This interval includes 1 and is wider across values on both sides of that reference point. It therefore leaves uncertainty about the direction of the relative rate under the model. The corresponding p-value is 0.074. The distinction between the two reported comparisons should not be interpreted as a formal finding that the doses differ from each other, because no direct dose-versus-dose result is reported.

Confidence intervals are not guarantees that the true value lies within the interval. In general, they reflect the uncertainty arising from sampling and the stated model, and narrower intervals indicate greater precision than wider intervals. They do not capture every source of uncertainty, including unreported analytic choices, missing-data assumptions, or limitations in how participants and outcomes were measured.

The registry gives interquartile ranges for the median endpoint summaries but does not report confidence intervals for those medians or for a difference in medians. The descriptive ranges show substantial spread in the participant-level percentages, but they are not confidence intervals for a treatment contrast. The registry record does not report a confidence interval for the primary endpoint comparison itself, so its precision cannot be evaluated from a direct effect interval in the posted results.

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 illustrations based on the observed hazard-ratio effects, not the trial's original design calculations. For these time-to-event comparisons, the entries are total events, not participants per arm. For the 380 mg comparison, planning for 100% of the observed effect requires 383 total events for 80% power and 513 for 90% power. Planning for 75% of the observed effect requires 681 total events for 80% power and 912 for 90% power. Planning for 50% of the observed effect requires 1,532 total events for 80% power and 2,051 for 90% power.

For the 190 mg comparison, planning for 100% of the observed effect requires 905 total events for 80% power and 1,211 for 90% power. Planning for 75% of the observed effect requires 1,608 total events for 80% power and 2,153 for 90% power. Planning for 50% of the observed effect requires 3,618 total events for 80% power and 4,843 for 90% power.

The illustrations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The 80% power column means the planned event count is calculated to give an 80% chance of statistical significance under those assumptions if the specified effect is true; the 90% column uses a higher target chance. Smaller effects require more events to distinguish from the null under the same assumptions. These figures are not observed power, and they do not establish the trial's original design rationale.

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

d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.

Worked calculation for this trial

1. Hazard ratio HR = 0.751, so ln(HR) = -0.2863.
2. d = 4 × (1.96 + 0.842)² / [ln(0.751)]² = 382.9, rounded up to 383 events in total 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
hr <- 0.751                              # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6))   # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))

# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(1218958)
d    <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z  <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))

Output from running the code

100% of observed effect: events = 383 (80% power), 513 (90% power)
 75% of observed effect: events = 681 (80% power), 912 (90% power)
 50% of observed effect: events = 1,532 (80% power), 2,051 (90% power)
Simulated power with 383 events: 0.801 (20000 replicates)

The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.

13. Analyses Reported by the Sponsor

The registry's reported analyses are the sponsor's own analyses and take precedence over any simple recalculation based on posted summary statistics. The reported method is an Andersen-Gill recurrent-event Cox analysis for both dose comparisons. The 380 mg comparison has a reported hazard ratio of 0.751, a 95% confidence interval of 0.600 to 0.940, and p = 0.025. The 190 mg comparison has a reported hazard ratio of 0.830, a 95% confidence interval of 0.677 to 1.018, and p = 0.074.

These are the estimates to use when describing the trial's inferential results. The posted group medians and interquartile ranges are descriptive summaries of the primary endpoint; they are not enough to reproduce the recurrent-event model or its uncertainty. A simple recalculation from summary statistics, if presented, would be unadjusted and would not replace the sponsor's model-based analysis. The registry record does not report additional details that would permit a fuller reconstruction of the model or an assessment of every analytic decision.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports two dose-versus-pooled-placebo comparisons for the primary efficacy results. It does not report whether the two tests were handled with a multiplicity adjustment, whether one comparison was designated primary over the other, or what testing sequence was planned. The original multiplicity strategy is therefore not reported in the registry record. The p-values should be read as the reported values for their respective analyses, without assuming a family-wise error adjustment or a prespecified hierarchy.

The record identifies the primary endpoint and the intent-to-treat population used for its efficacy analysis. That population consists of randomized participants who received at least one injection, and the last post-baseline observation carried forward was used. The record does not report the amount of missing outcome data, when missing observations occurred, or whether missingness differed across groups. It also does not report sensitivity analyses using other missing-data assumptions. As a result, the effect of missing data on the estimates cannot be evaluated from the registry information.

The registry record does not report interim analyses, stopping rules, or the full statistical analysis plan. It also does not state whether the analyses were adjusted for baseline variables or other covariates. These omissions do not establish that such procedures were absent; they mean they are not reported in the registry record. The record's definition of the efficacy population is narrower than all randomized participants because receipt of at least one injection is required. The number excluded by that definition and the reasons are not reported.

The record lists a secondary outcome of participants reporting at least one treatment-emergent adverse event, but it does not provide enough information in the listed outcome description to evaluate its analysis plan or multiplicity handling. No additional claims about the prespecified status of individual secondary comparisons should be inferred. These gaps limit assessment of how the reported analyses relate to all planned outcomes and comparisons.

15. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: alcoholism (3.3%), interstitial pneumonia (0.5%), myocardial infarction (0.5%), gastrointestinal haemorrhage nos (0.5%), perirectal abscess (0.5%).

The serious adverse-event figures are reported as affected participants and participants at risk in each group. The registry lists 10 of 210 for Medisorb naltrexone 190 mg, 11 of 205 for Medisorb naltrexone 380 mg, and 15 of 209 for pooled placebo groups. These are group-specific counts; the denominators differ from the efficacy analysis counts, and the record does not explain the difference in analysis populations in the posted safety summary.

The registry also lists counts for other adverse events: 190 of 210 in the 190 mg group, 187 of 205 in the 380 mg group, and 181 of 209 in pooled placebo groups. These figures are distinct from the serious adverse-event counts. They should be read as the posted group-level counts, not as a comparison adjusted for exposure or participant characteristics.

The most frequently listed serious-event terms include Alcoholism (3.3%), and Interstitial pneumonia, Myocardial infarction, Gastrointestinal haemorrhage NOS, Perirectal abscess, and Chest tightness (each 0.5%). These listings do not establish causation. Deaths are not reported in the registry record. The figures do not, by themselves, describe event timing, duration, severity beyond the serious classification, or individual participants' full safety histories.

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

The registry record presents lower median percentages of heavy drinking days in both active-dose groups than in pooled placebo groups: 10.23 for the 380 mg group, 14.75 for the 190 mg group, and 19.77 for pooled placebo. It also reports a recurrent-event hazard ratio of 0.751 for 380 mg versus pooled placebo, with a 95% confidence interval that excludes 1 and p = 0.025. For 190 mg versus pooled placebo, the reported hazard ratio is 0.830, with a 95% confidence interval that includes 1 and p = 0.074.

These statistics describe the registry's posted results; they should not be turned into a general claim that a treatment works or does not work. The model-based hazard ratios are not percentages of heavy drinking days, and the medians are not estimates of an adjusted relative event rate. The trial does not report a direct statistical comparison between the active doses, so the two dose estimates cannot be used as proof that one dose is different from the other.

Statistical significance is not a measure of clinical importance, and a result that does not meet a significance threshold does not demonstrate equivalence. The confidence intervals express uncertainty under the reported models, while the endpoint summaries show the distributional spread through interquartile ranges. The registry does not report a confidence interval for a direct difference in the primary endpoint medians.

The findings apply to the enrolled study population and the recorded study procedures. The record identifies adults with alcohol dependence, a 24-week endpoint period, a specified definition of heavy drinking, and an efficacy population requiring at least one injection. It does not provide enough information to determine how results might apply to populations or circumstances not represented in this trial. Missing-data details, the original sample-size justification, and the multiplicity strategy are not reported in the registry record.

17. Why This Trial Matters Statistically

This trial illustrates why clinical results need to be read according to the type of statistic reported. The primary endpoint is a percentage of heavy drinking days, summarized using medians and interquartile ranges. The inferential comparisons are recurrent-event Cox hazard ratios. Although both concern drinking outcomes, they are not interchangeable measures. Clear interpretation requires identifying what each statistic summarizes and what comparison it supports.

It also shows how a result can have different levels of certainty across comparisons. The 380 mg hazard-ratio confidence interval is below 1, whereas the 190 mg interval includes 1. That distinction describes uncertainty under the reported models, but it does not establish a difference between the doses. A direct dose comparison would be needed to support that specific question, and none is reported in the registry record.

The efficacy population and missing-data procedure also matter. The analysis includes randomized participants who received at least one injection and uses LOCF for the last post-baseline observation. Readers need these details to understand whose outcomes are represented and how unavailable later measurements were handled. Without missingness information or sensitivity analyses, the robustness of the results to the LOCF assumption cannot be assessed.

Finally, planning illustrations based on observed effects are not the same as the trial's original design rationale or observed power. Distinguishing those concepts prevents post hoc planning calculations from being mistaken for evidence about why the study was designed as it was. The registry record offers useful statistical results, while leaving important details about multiplicity, original assumptions, and analytic sensitivity unreported.

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 primary efficacy analysis used last observation carried forward, but the registry record does not report how much data were missing, why observations were missing, or whether missingness differed across groups. It does not report sensitivity analyses under alternative assumptions. Because LOCF assumes that an earlier observation can stand in for an unavailable later outcome, the impact of that choice cannot be assessed from the posted record alone.

The registry reports median endpoint summaries but does not provide confidence intervals for those medians or a direct effect estimate and interval for the primary endpoint comparison. The recurrent-event hazard ratios offer model-based comparisons, but the record does not explain in detail how those analyses correspond to the percentage endpoint. It also does not report model diagnostics, covariate adjustment, or additional recurrent-event model specifications.

The two dose comparisons use pooled placebo groups. Separate placebo-group efficacy estimates and a direct comparison between active doses are not reported. The record also does not report a multiplicity strategy, the original sample-size justification, interim analyses, or the full analysis plan. These details limit assessment of the prespecification and robustness of the reported findings.

The safety summary provides group-level affected counts and selected serious-event terms, but the registry record does not report event timing, exposure-adjusted rates, or deaths. The record also does not explain why the safety denominators differ from the primary efficacy group counts. These are limitations of what is reported, rather than evidence that a particular procedure or analysis was not performed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: ALK21-003: Study of Medisorb® Naltrexone (VIVITROL®) in Alcohol-Dependent Adults — NCT01218958.
• Registry record last updated 2017-07-11; status last verified 2017-06.
• Results first posted 2010-12-07.
• 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

The registry describes a completed, randomized, quadruple-masked, parallel-group Phase 3 study in adults with alcohol dependence. It reports enrollment of 624 and assignment to Medisorb naltrexone 190 mg, Medisorb naltrexone 380 mg, or one of two matching placebo groups. Injections were given every 4 weeks for a total of 6 injections.

The primary endpoint was the percentage of heavy drinking days from baseline through Week 24 (168 days), assessed by Timeline Follow-Back self-report. The posted medians were 14.75 for 190 mg, 10.23 for 380 mg, and 19.77 for pooled placebo groups. Sponsor-reported recurrent-event hazard ratios versus pooled placebo were 0.830 for 190 mg and 0.751 for 380 mg.

The registry also posts adverse-event counts and selected serious-event terms. It does not report the original sample-size justification, multiplicity strategy, interim analyses, or detailed missing-data sensitivity analyses.