Ketamine for Reduction of Alcoholic Relapse: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Ketamine for Reduction of Alcoholic Relapse (NCT02649231), a randomized phase 2 study. The primary outcome is Relapse Rates.

2. Clinical Question

The clinical question concerns relapse after detoxification among people with alcohol dependence: how do six-month relapse counts differ across combinations of ketamine or placebo and psychological therapy or alcohol education? The registry describes a randomized, quadruple-masked, parallel-group Phase II trial with four groups. The primary outcome is relapse status at six months, assessed using a timeline follow-back measure of drinking.

This is not a single two-group comparison of ketamine against placebo under one shared behavioral condition. The four combinations vary both the drug assignment and the behavioral support. The registry also reports an overall odds ratio across the four groups, but does not describe its method or specify the contrast represented by that estimate. Therefore, it should be read as the sponsor’s posted overall analysis, not as a directly interchangeable estimate of any one pairwise comparison.

3. Trial Design

The registry identifies NCT02649231 as a completed Phase II randomized, quadruple-masked, parallel-group trial. Enrollment was 96. The recorded start was 2016-10, and primary completion was 2020-02. University College, London is listed as the sponsor. The registry’s official title describes a multisite trial of ketamine for alcohol dependence.

Four groups combine two drug assignments with two forms of behavioral support: ketamine with psychological therapy, ketamine with alcohol education, placebo with psychological therapy, and placebo with simple alcohol education. The registry summary describes three treatment sessions and assessments at 3 and 6 months. The primary endpoints were planned as percentage of days abstinent and relapse rates at 6 months; secondary endpoints included depressive symptoms, craving, and quality of life. The posted outcome analyzed is relapse status at 6 months, recorded as a participant count.

The group counts in the posted relapse analysis are 21.0, 22.0, 21.0, and 23.0, respectively. These are not the same as the overall enrollment figure. The registry explains that only participants with a minimum of 159 days of completed drinking self-report data were included in the main analysis of alcohol relapse status. It says this criterion accounts for a difference between the overall number analyzed and the flow diagram, but the explanation in the record is truncated. Further details about the flow of participants into this outcome analysis are not reported in the registry record.

The registry record does not report the original sample-size justification, the planned statistical model for the primary endpoint, or the intended handling of the four-group structure in that model. It also does not describe allocation concealment or the specific roles included in quadruple masking. Those details should not be inferred from the trial title or the posted results.

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: To explain discrepancies between overall number of participants analysed and the flow diagram: Only participants with a minimum of 159 days of completed drinking self-report data were included in the main analysis of alcohol relapse status as this was the shortest duration of time before any participant completed the 6 month (23-25 week) follow up in the study. Reporting time was capped at 180 days.

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 Relapse Rates, measured over 6 months.

The posted primary outcome is relapse rates at 6 months, expressed as the number of participants with an event. The registry describes the assessment as timeline follow-back. This approach uses participants’ reported drinking history over time to classify relapse status. The record’s analysis-population note says that participants needed at least 159 days of completed drinking self-report data to be included in the main relapse analysis.

A binary event count is useful because it expresses how many participants in each group met the recorded relapse criterion during the outcome period. It can support comparisons of event risk between groups. Unlike a measure of the amount or frequency of drinking, the posted count does not describe the pattern of drinking among participants who were not classified as having relapsed, nor does it convey the timing of relapse within the six-month period. The registry separately mentions percentage of days abstinent as a primary endpoint in the trial summary, but that outcome is not part of the posted analysis being interpreted.

General statistical context: a binary endpoint simplifies a complex clinical course into an event/no-event classification. Its interpretation depends on how the event was defined and how complete outcome data were handled. The relapse definition’s detailed operational criteria, beyond the timeline follow-back description, are not reported in the registry record.

7. Results Posted in the Registry

• Ketamine+Psychological Therapy: 61.9% (13/21) versus 66.7% (14/21) on control; risk difference -4.8 percentage points (95% CI -33.7 to 24.2), risk ratio 0.93 (0.59–1.46); unadjusted two-proportion z-test p = 0.747.
• Ketamine+Education: 68.2% (15/22) versus 66.7% (14/21) on control; risk difference 1.5 percentage points (95% CI -26.5 to 29.5), risk ratio 1.02 (0.67–1.55); unadjusted two-proportion z-test p = 0.916.
• Placebo+Education: 78.3% (18/23) versus 66.7% (14/21) on control; risk difference 11.6 percentage points (95% CI -14.7 to 37.9), risk ratio 1.17 (0.81–1.70); unadjusted two-proportion z-test p = 0.388.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted outcome is binary: each analyzed participant is counted as having or not having a relapse event by the six-month assessment. The recalculated pairwise results compare each group with placebo plus psychological therapy. These are unadjusted comparisons derived from the event counts and analyzed group sizes. They do not adjust for other participant characteristics or account for a model beyond the posted summary counts.

What does a risk difference describe?

A risk difference expresses the difference in event proportions between two groups. A value below zero means the event proportion is lower in the first group in the comparison’s stated orientation; a value above zero means it is higher. The registry’s recalculated risk-difference intervals for all three pairwise comparisons extend across zero. That means the data are compatible with no difference and also with differences in either direction. The intervals are broad, reflecting substantial uncertainty in these small group comparisons. The exact recalculated risk-difference estimates are not repeated because their posted precision exceeds the permitted three decimal places.

How should the p-values be read?

The unadjusted p-values are 0.747, 0.916, and 0.388 for the three comparisons, in the order. General statistical context: a p-value measures how unusual data at least this discrepant from a specified null model would be if that model were true. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. These p-values do not provide evidence of a clear separation in the pairwise comparisons, but they also cannot show that the groups are equivalent. The record does not report a multiplicity adjustment for these recalculations.

Why consider an odds ratio as well?

An odds ratio compares the odds of an event between groups. An odds ratio of 1 corresponds to equal odds under the stated comparison. Values below or above 1 indicate lower or higher odds in the numerator group, respectively, depending on the comparison’s orientation. The sponsor reports an odds ratio of 0.7 and a 95% confidence interval from 0.28 to 1.75. Since the interval includes 1, it is compatible with no odds difference and with effects in either direction. The registry does not state the precise contrast or method for this overall result, so it cannot be treated as another name for one of the three unadjusted pairwise comparisons.

General statistical context: odds and risks are different quantities. When events are common, an odds ratio should not be interpreted as though it were a risk ratio or a risk difference. This distinction matters for the posted data because relapse events were recorded in substantial portions of each analyzed group. The risk-difference comparisons and the sponsor’s odds-ratio result therefore use different effect scales as well as potentially different analysis structures.

What does the group structure imply?

The four arms combine ketamine or placebo with psychological therapy or alcohol education. Comparisons that hold the behavioral support constant can help describe the drug-assignment contrast within that support setting; comparisons that hold the drug assignment constant can describe the behavioral-support contrast. The recalculated pairwise comparisons use placebo plus psychological therapy as their common reference, so they do not isolate a single component across all four groups. The registry does not report a factorial model or a planned interaction analysis. No claim about a drug-by-support interaction can therefore be drawn from the listed pairwise estimates alone.

General statistical context: in a factorial design, an interaction asks whether the effect associated with one factor differs according to the level of another factor. It is not established merely by observing that one pairwise comparison differs from another. Estimating an interaction generally requires a model or contrast designed for that question. The model and contrasts planned for this trial are not reported in the registry record.

Why can over-dispersion matter?

General statistical context: for count outcomes, over-dispersion means that observed variability exceeds what a chosen count model expects. It can make standard errors too small if the model assumes less variability than the data contain. Over-dispersion is not the relevant main issue for the posted relapse endpoint as analyzed here, because the registry reports participants with a binary event rather than a repeated event count or a rate. The record does not report a count model for relapse, and no such model should be assumed.

The analysis population also matters. The registry states that inclusion in the main relapse analysis required at least 159 days of completed drinking self-report data. This rule may affect which participants contribute to the outcome, but the record does not provide enough detail to assess the impact of missing reports or compare included and excluded participants. The group counts describe the analyzed participants under that rule; they should not be read as the full randomized enrollment.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an effect estimate. The recalculated risk-difference confidence intervals are broad and each spans zero. Thus, the estimates do not pin down a single direction or a narrow range of plausible differences. The event counts and analyzed group sizes are modest, so a small number of participants can materially affect the observed proportions. This helps explain why the comparisons remain uncertain even when the point estimates differ.

General statistical context: a confidence interval is a range of values generated by a method that, over repeated studies under its assumptions, would cover the true parameter at the stated rate. It is not a guarantee that the true effect lies within the interval for this particular study. A 95% confidence interval also does not mean there is a 95% probability that the parameter is within the observed limits. The sponsor’s reported 95% confidence interval for the odds ratio, 0.28 to 1.75, is wide and includes 1, indicating that the posted overall estimate is also imprecise.

The recalculated pairwise intervals and the sponsor’s interval answer different statistical questions unless their contrasts and methods coincide. The registry does not explain the sponsor analysis sufficiently to establish that they do. Precision should therefore be assessed within each analysis rather than by treating the estimates as interchangeable. The registry record does not report confidence intervals for every outcome named in the trial summary, and no results for secondary endpoints are posted.

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 planning figures are illustrations based on the observed effect, not the trial’s original design calculations. For these binary-outcome comparisons, the reported values are participants per arm. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect used for planning is a stated fraction of the observed effect. These assumptions describe the illustration only; the trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the number of participants per arm that the planning calculation indicates would be needed to have an 80% chance of detecting the effect used in that row, under the stated assumptions. The 90% power column uses a higher target chance of detecting that effect and therefore calls for more participants per arm. For example, planning for 100% of the observed effect gives different figures from planning for 75% or 50% of that effect. Across the displayed planning scenarios, smaller effects require more participants per arm.

These calculations are not observed power. They are prospective planning illustrations, not a measure of whether the completed trial had adequate power after results were known. They also depend on the observed effect, which can be unstable in small groups, and do not replace a design-specific calculation using the trial’s intended model, outcome definition, and analysis population. The record does not report those original design details.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.667; treatment proportion p₁ = 0.619; average p̄ = 0.643.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6776 = 1.3281.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6768 = 0.5696.
4. n = (1.3281 + 0.5696)² / (-0.0476)² = 1,588.2, rounded up to 1,589 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
p0 <- 0.666666666666667                          # control proportion
p1 <- 0.619047619047619                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(2649231)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 1,589 (80% power), 2,126 (90% power)
 75% of observed effect: n per arm = 2,804 (80% power), 3,752 (90% power)
 50% of observed effect: n per arm = 6,259 (80% power), 8,378 (90% power)
power.prop.test: 1588.2 
Simulated power at n = 1,589 per arm: 0.800 (20000 replicates)

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

13. Analyses Reported by the Sponsor

The registry’s sponsor-reported analysis gives an odds ratio of 0.7, with a 95% confidence interval from 0.28 to 1.75, for an analysis involving all four groups. It does not state the method, identify a comparison reference, or explain how the four arms were combined or contrasted. No p-value is posted for this result. Those omissions limit how specifically the estimate can be interpreted.

The recalculated estimates are unadjusted pairwise comparisons of each group against placebo plus psychological therapy, using the posted event counts and analyzed group sizes. They are not a reproduction of the sponsor’s overall analysis. The sponsor estimate uses an odds-ratio scale, while the recalculated comparisons are expressed as risk differences, and the underlying contrasts may differ. A direct numerical match should not be expected without the sponsor’s method and contrast.

The sponsor’s interval includes 1, the odds-ratio value associated with no difference. The recalculated pairwise risk-difference intervals also include zero. These features point to substantial uncertainty in both presentations, but they do not establish that the analyses answer the same question. The registry does not report enough detail to reconcile the two analyses further.

14. Multiplicity, Missing Data and Analysis Populations

There are four treatment combinations and three recalculated pairwise comparisons against placebo plus psychological therapy. Testing several contrasts can increase the chance of at least one apparently notable result when all null hypotheses are true. General statistical context: multiplicity procedures address this issue by adjusting inference across a defined family of tests or by specifying a hierarchy of hypotheses. The recalculated p-values are explicitly unadjusted. The registry does not report whether or how the sponsor’s analysis accounted for multiple comparisons.

The registry summary names two primary endpoints: percentage of days abstinent and relapse rates at 6 months. The posted outcome analysis concerns relapse. The record does not report a hierarchy between the primary endpoints, a multiplicity strategy for them, or a prespecified approach to the several treatment comparisons. It also does not report results for secondary endpoints in the posted record. Without the planned testing framework, the relationship between the analyses and any overall type I error control cannot be assessed.

The analysis population for relapse was restricted to participants with a minimum of 159 days of completed drinking self-report data. The registry notes that this criterion explains a difference between the overall number analyzed and the flow diagram, but the available explanation is truncated. The number and characteristics of participants who did not meet the data-completion requirement, and the handling of missing reports within eligible participants, are not reported in the registry record.

General statistical context: complete-case analyses can be biased if missingness is related to relapse or differs between groups. The direction and magnitude of any such bias depend on why data are missing and how the analysis handles them. The posted information does not support a judgment about whether the missing-data process was ignorable. It also does not report whether analyses were intention-to-treat, per-protocol, or based on another defined population. The counts should consequently be interpreted as applying to the recorded analysis population rather than assumed to represent every randomized participant.

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 4% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: abdominal pain (4.3%), kidney infection (4.3%), brain hemorrhage (4.0%), alcohol intoxication (4.0%), skull fracture (4.0%).

The serious adverse event figures are reported separately from the relapse outcome. The registry lists 24 participants at risk in ketamine plus psychological therapy, 24 in ketamine plus education, 23 in placebo plus psychological therapy, and 25 in placebo plus education. Serious adverse events affected 0, 0, 2, and 1 participants in those groups, respectively. Deaths are recorded as 0 in each group.

For other adverse events, the registry lists 13, 17, 16, and 17 affected participants in those same groups. These figures are counts of affected participants, not event rates or a comparison adjusted for differences between groups. The record also lists abdominal pain and kidney infection at 4.3%, and brain hemorrhage, alcohol intoxication, and skull fracture at 4.0%, among the top serious adverse event terms. The registry excerpt does not state the group attribution for those terms.

These safety counts should be read descriptively. The registry does not provide enough detail about event definitions, timing, severity grading, relatedness assessments, or statistical comparisons to support causal conclusions about treatment assignment. Counts of zero serious events in a group do not establish that no risk exists.

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

The registry results describe six-month relapse status among participants who met the stated drinking self-report data requirement. The observed counts are 13 of 21.0 for ketamine plus psychological therapy, 15 of 22.0 for ketamine plus education, 14 of 21.0 for placebo plus psychological therapy, and 18 of 23.0 for placebo plus education. The unadjusted comparisons with placebo plus psychological therapy are imprecise, and their risk-difference confidence intervals include no difference.

The sponsor’s overall odds-ratio estimate is also imprecise: its 95% confidence interval includes the no-difference value. Because the sponsor’s method and contrast are not reported, that estimate cannot be used to resolve the pairwise comparisons or to identify which treatment component might account for the observed pattern. The results do not establish equivalence among groups, nor do they show that a particular combination is superior.

The endpoint captures relapse classification, not every aspect of alcohol use or recovery. The registry summary also names abstinent days and several secondary outcomes, but those results are not reported in the available record. The follow-up period described for the primary outcome is six months, so the posted counts do not characterize later outcomes.

These are findings about recorded outcomes in this trial and its analysis population. They should not be interpreted as medical advice or as proof that a treatment works or does not work. Further interpretation would require details that are not reported in the registry record, including the full analysis plan, the precise sponsor contrast, handling of missing data, and results for the other planned outcomes.

17. Why This Trial Matters Statistically

This trial is statistically informative because its four groups combine a drug assignment with two types of behavioral support. That structure raises questions beyond a simple ketamine-versus-placebo comparison: estimates may depend on which support condition is considered, and an interaction could be relevant. The registry does not report a model or planned interaction analysis, so the structure of the trial and the structure of the available inference cannot be assumed to be the same.

The example also shows why event counts, effect estimates, and uncertainty should be read together. A difference in observed counts does not by itself establish a reliable group difference. The recalculated confidence intervals span zero, and the sponsor’s odds-ratio interval spans the no-difference value. The small analyzed group sizes leave substantial uncertainty around the comparisons.

Finally, the record’s analysis-population note matters. Eligibility for the main relapse analysis depended on completing at least 159 days of drinking self-report data. Enrollment and outcome-analysis counts therefore refer to different populations. Transparent reporting of the outcome definition, analysis population, missing-data handling, model, and multiplicity plan would help readers judge how closely a result answers the original clinical question. Several of those details are not reported in the registry record.

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.

Several trial-specific limitations constrain interpretation. First, the four groups vary both drug assignment and behavioral support. The recalculated comparisons use placebo plus psychological therapy as the common reference, and do not provide a single pooled estimate of ketamine versus placebo across support conditions. The registry does not report a factorial model or an interaction analysis.

Second, the analyzed group sizes for relapse are 21.0, 22.0, 21.0, and 23.0. The registry says that the main analysis included participants with at least 159 days of completed drinking self-report data, but the available explanation of the difference between the analysis count and the flow diagram is incomplete. Details on excluded participants and missing-data methods are not reported.

Third, the sponsor’s overall odds ratio is reported without its method, precise contrast, or p-value. It is therefore difficult to relate that estimate to the pairwise recalculations. The registry also does not report the original sample-size justification, planned analysis model, multiplicity strategy, or a hierarchy for the two named primary endpoints.

Finally, although the trial summary mentions percentage of days abstinent and secondary psychological and biological outcomes, the posted analysis contains no secondary outcome results. The relapse measure is described as timeline follow-back, but detailed event criteria and information about the timing of relapse are not reported. These gaps limit assessment of robustness, generalizability, and the intended interpretation of the full trial.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Ketamine for Reduction of Alcoholic Relapse — NCT02649231.
• Registry record last updated 2021-10-05; status last verified 2021-09.
• Results first posted 2021-09-09.
• 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

NCT02649231 is a completed randomized, quadruple-masked, parallel-group Phase II trial of ketamine and behavioral support for alcohol dependence. Enrollment was 96. Four groups combined ketamine or placebo with psychological therapy or alcohol education. The registry identifies six-month relapse rates as a primary endpoint and describes timeline follow-back assessment.

The posted relapse analysis includes groups of 21.0, 22.0, 21.0, and 23.0 participants, with event counts of 13, 15, 14, and 18. Unadjusted comparisons against placebo plus psychological therapy are imprecise. The sponsor reports an overall odds ratio of 0.7 with a 95% confidence interval from 0.28 to 1.75, but the method and contrast are not described. The registry’s analysis-population note requires at least 159 days of completed drinking self-report data. Original design assumptions, detailed missing-data methods, and secondary outcome results are not reported in the registry record.