Ketamine for the Rapid Treatment of Major Depressive Disorder and Alcohol Use Disorder: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Ketamine for the Rapid Treatment of Major Depressive Disorder and Alcohol Use Disorder (NCT02461927), a randomized phase 1, phase 2 study. The primary outcome is Number of Participants With 50% or Greater Improvement in MADRS Scores From Baseline.

2. Clinical Question

3. Trial Design

The registry describes a randomized, quadruple-masked, parallel-group trial, listed as Phase 1 and Phase 2, with 65 participants enrolled. The study is marked completed. Its stated conditions are major depressive disorder and alcohol use disorder, and the sponsor is the VA Office of Research and Development. The recorded study start is 2015-01-01, and primary completion is dated 2023-10-30.

The brief description outlines two stages. First, an open-label trial was planned to include 5 patients with both conditions. Its purpose was to assess safety and efficacy of repeated ketamine treatment: 0.5 mg/kg once a week for 4 weeks, followed by a 4-week follow-up. The description says the randomized stage would proceed after review of the safety and efficacy information from this initial stage.

The second stage was described as an 8-week randomized, double-blind, placebo-controlled trial intended to include 60 patients. Three groups are listed: ketamine plus naltrexone, ketamine plus placebo, and psychoactive placebo midazolam plus placebo. The ketamine-containing arms used the same planned infusion schedule. Naltrexone or its placebo was planned as a monthly intramuscular injection, for a total of 2 injections. The brief description also refers to a 4-week follow-up and a 4-month follow-up session.

The reported primary endpoint was assessed on Day 21, after the fourth infusion, at 240 minutes. The registry does not report the original statistical analysis plan, the rationale for the planned enrollment, or how the staged open-label and randomized results were combined, if they were combined.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: Subjects who completed the outcome measure on Day 21 (after 4th infusion, 240 minutes)

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: Subjects receiving at least one infusion were analyzed

6. Primary Endpoint

The registry lists the primary outcome as Number of Participants With 50% or Greater Improvement in MADRS Scores From Baseline, measured over Day 21 (after 4th infusion, 240 minutes).

The primary endpoint counts participants whose MADRS score improved by 50% or greater from baseline. MADRS is the named rating scale used to assess depressive symptom severity. The registry defines this response at the end-of-treatment time point: Day 21, after the fourth infusion, at 240 minutes. The outcome is binary for each participant: the person either met the stated response threshold or did not.

A response threshold is useful because it turns a continuous symptom score into a clinically interpretable category for comparing groups. A group count alone, however, does not show the full range of score changes. People who narrowly miss the threshold and people whose scores change very little are both counted as nonresponders under this definition, while variation in the amount of improvement among responders is not represented. The registry does not post a continuous MADRS outcome among its secondary results.

The reported endpoint population consists of subjects who completed the measure at the specified time. The displayed counts are 15 of 16 for ketamine plus naltrexone, 9 of 11 for ketamine plus placebo, and 13 of 15 for psychoactive placebo plus placebo. These are the arm-level counts used for the posted endpoint. The registry record does not explain why the analysis counts are smaller than the overall enrollment or how participants without a Day 21 measure were handled.

7. Results Posted in the Registry

• Ketamine + Naltrexone: 93.8% (15/16) versus 81.8% (9/11) on control; risk difference 11.9 percentage points (95% CI -13.8 to 37.6), risk ratio 1.15 (0.84–1.56); unadjusted two-proportion z-test p = 0.332.
• Placebo (Psychoactive Placebo Midazolam) + Placebo: 86.7% (13/15) versus 81.8% (9/11) on control; risk difference 4.8 percentage points (95% CI -23.7 to 33.4), risk ratio 1.06 (0.75–1.49); unadjusted two-proportion z-test p = 0.735.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: each participant is counted as having or not having a 50% or greater improvement in MADRS from baseline at the stated time point. For a binary endpoint, a group response proportion is based on the number of participants meeting the definition and the number included in that group’s endpoint analysis. The registry reports counts rather than a continuous summary of MADRS scores. The counts are 15 of 16, 9 of 11, and 13 of 15 for the three arms, respectively.

The comparison measure is a risk difference. In general, a risk difference subtracts one group’s event proportion from another group’s event proportion. Here, the event is meeting the response definition. A value above zero means the first-named arm had a higher observed response proportion than the ketamine-plus-placebo reference arm; a value below zero means it had a lower observed response proportion. This direction describes the estimate, not a causal conclusion independent of the study design and analysis limitations.

The estimated risk difference for ketamine plus naltrexone versus ketamine plus placebo was 0.119. Its 95% confidence interval was -0.138 to 0.376. The estimate for psychoactive placebo plus placebo versus ketamine plus placebo was 0.049, with a 95% confidence interval from -0.237 to 0.334. These are absolute differences on the response-proportion scale. The registry also reports risk ratios and odds ratios, but the risk difference is a direct way to express the absolute contrast in the observed proportions.

In general, a confidence interval describes a range of estimates compatible with the data under the interval’s statistical assumptions. It does not mean that every value in the interval is equally likely, and it is not a range containing a fixed fraction of individual participant outcomes. Both posted intervals include zero, the value representing no difference in response proportions. Their widths also indicate that the estimated contrasts are uncertain. The registry record does not identify the method used to construct these intervals, so no particular interval procedure should be assumed.

The p-values reported for the comparisons are unadjusted: 0.332 for ketamine plus naltrexone versus ketamine plus placebo, and 0.735 for psychoactive placebo plus placebo versus ketamine plus placebo. In general, a p-value evaluates how compatible the observed data are with a specified null hypothesis under the statistical model used. It is not the probability that the null hypothesis is true, and it does not quantify the size or clinical importance of an effect. The registry does not report a multiplicity adjustment or a complete inferential plan. The p-values should therefore be read as the posted unadjusted results, not as evidence that every planned comparison was accounted for.

The comparison groups were randomized according to the registry description, which can support causal interpretation when allocation, follow-up, and analysis are appropriately implemented. The registry reports quadruple masking and a parallel model, but does not give details of who was masked, how randomization was generated, or whether masking was maintained. Those implementation details are not reported in the registry record. The primary analysis population is described as participants who completed the Day 21 outcome measure. The record does not say whether the analysis followed an intention-to-treat principle or how missing endpoint values were treated.

General statistical point: small group counts make estimates sensitive to the outcomes of individual participants. With binary outcomes, a small change in the number of responders can change the observed proportions and their uncertainty. This is one reason to interpret the point estimates alongside the confidence intervals rather than focusing on the estimates alone. No alternative modeling approach, baseline adjustment, or sensitivity analysis is posted.

The record lists no posted analysis entries, and it reports no posted secondary outcome results. This means the primary endpoint comparisons can be described, but the registry does not supply enough statistical detail to reconstruct a complete analysis strategy. The original protocol’s sample-size justification, planned handling of interim reviews, statistical methods, missing-data procedures, and multiplicity strategy are not reported in the registry record. General explanations of statistical concepts do not fill those gaps or establish which methods were actually used.

10. Confidence Intervals and Precision

The confidence intervals are central to judging how precisely the group contrasts are estimated. For ketamine plus naltrexone versus ketamine plus placebo, the estimated risk difference is 0.119, and the 95% confidence interval extends from -0.138 to 0.376. For psychoactive placebo plus placebo versus ketamine plus placebo, the estimated risk difference is 0.049, and the interval extends from -0.237 to 0.334. Both intervals include zero, so the posted estimates are compatible with no difference as well as with differences in either direction.

The intervals are broad, and the analyzed groups are small: the relevant arm counts are 16 and 11 for the first comparison, and 15 and 11 for the second. Broad intervals mean the data do not pin down the size or direction of the contrast precisely. The point estimate is only one location within that range; it should not be presented as though it were known exactly.

In general, a 95% confidence interval is a property of a statistical procedure across repeated samples under its assumptions. It is not a guarantee that the true effect lies within a particular computed interval. The registry record does not state the interval-construction method, so the interpretation should remain at this general level. The posted results also do not report adjusted confidence intervals or a prespecified threshold for a meaningful difference.

These precision limits matter in both directions. The estimates do not establish a difference, but the intervals also do not establish that the groups are equivalent or that meaningful differences are excluded. The available endpoint counts and uncertainty intervals support a cautious reading: the observed contrasts are uncertain, and a more precise estimate would require more information than these results provide.

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 figures are planning illustrations based on the observed effect, not the trial’s original design calculations. They are given as participants per arm for 80% power and participants per arm for 90% power. They are not total event counts. The stated planning 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 the stated fraction of the observed effect.

For the ketamine-plus-naltrexone comparison, planning for 100% of the observed effect gives 118 participants per arm for 80% power and 157 participants per arm for 90% power. Planning for 75% of the observed effect gives 231 participants per arm for 80% power and 309 participants per arm for 90% power. Planning for 50% of the observed effect gives 568 participants per arm for 80% power and 759 participants per arm for 90% power.

For the psychoactive-placebo-plus-placebo comparison, planning for 100% of the observed effect gives 886 participants per arm for 80% power and 1,185 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,624 participants per arm for 80% power and 2,173 participants per arm for 90% power. Planning for 50% of the observed effect gives 3,763 participants per arm for 80% power and 5,037 participants per arm for 90% power.

In plain terms, the 80% column describes the number per group estimated to give an 80% chance of detecting the specified effect under the stated assumptions; the 90% column uses a higher target chance. Smaller effects need more participants because they are harder to distinguish from sampling variation. These figures are not observed power and do not show what power the completed trial achieved. The registry record does not report the original sample-size justification or its design assumptions.

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 = 0.818; treatment proportion p₁ = 0.938; average p̄ = 0.878.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4631 = 0.9077.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4554 = 0.3832.
4. n = (0.9077 + 0.3832)² / (0.1193)² = 117.1, rounded up to 118 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 <- 0.818181818181818                          # control proportion
p1 <- 0.9375                          # 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(2461927)
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 = 118 (80% power), 157 (90% power)
 75% of observed effect: n per arm = 231 (80% power), 309 (90% power)
 50% of observed effect: n per arm = 568 (80% power), 759 (90% power)
power.prop.test: 117.1 
Simulated power at n = 118 per arm: 0.819 (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. Multiplicity, Missing Data and Analysis Populations

The registry posts two primary-outcome comparisons, each against ketamine plus placebo, and gives unadjusted p-values. It does not report a multiplicity adjustment or a prespecified hierarchy for interpreting multiple comparisons. When several hypotheses are tested, the chance of at least one apparently notable result can increase; in general, multiplicity procedures are used to control or otherwise address that issue. The registry record does not specify whether such procedures were planned or used, so the posted p-values should be interpreted as unadjusted.

The analysis population is described as subjects who completed the outcome measure on Day 21. This identifies a completer-based endpoint population, but the record does not say how many enrolled participants lacked the outcome or why. It does not report whether missing values were imputed, excluded, or handled in another way, nor does it provide sensitivity analyses for missing data. The arm-level outcome counts are therefore best understood as the participants reported for the endpoint, not as an analysis of every enrolled participant.

The registry does not state whether the primary analysis was intention-to-treat, per-protocol, or another defined population. It also does not provide a detailed account of deviations from the planned treatment schedule, treatment discontinuations, or exclusions from analysis. These details affect how an observed difference can be interpreted, particularly when the primary outcome population is defined by completion of a specific follow-up measure.

No analysis entries are posted, and no secondary outcome results are posted. The absence of those results does not establish that no other analyses were planned or conducted; it means they are not reported in the registry record. The original statistical analysis plan, interim-analysis procedures, missing-data approach, and multiplicity strategy are not reported in the registry record. Consequently, the available results support a description of the posted comparisons, but not a full audit of the planned and completed analysis process.

14. 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 non-serious adverse event terms

The registry reports serious adverse event figures by safety group. The number at risk is 20 for ketamine plus naltrexone, 19 for ketamine plus placebo, and 19 for psychoactive placebo plus placebo. The number affected by a serious adverse event is 0 in each group. Deaths are also reported as 0 in each group. No serious adverse event terms are listed among the top serious terms.

These are counts, not rates calculated for a common follow-up duration. They do not describe the timing, duration, or clinical details of individual events, and the registry does not provide a narrative accounting of serious events. A zero count in these posted groups means no affected participants are recorded in the serious adverse event count; it does not establish that a treatment is free of risk or that an event could not occur in another population or setting.

For other adverse events, the number affected is 14 of 20 in the ketamine-plus-naltrexone group, 11 of 19 in the ketamine-plus-placebo group, and 14 of 19 in the psychoactive-placebo-plus-placebo group. These counts are distinct from the serious adverse event counts. The registry does not list the individual other-event terms in the registry record reported for this analysis, so the counts alone cannot describe event type or severity. Safety interpretation should remain limited to the posted group counts and their stated denominators.

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

The primary endpoint captures whether a participant crossed a defined threshold for improvement in depressive symptoms at a specific time: Day 21, after the fourth infusion, at 240 minutes. The registry reports response counts in all three groups and unadjusted comparisons of each of two arms with ketamine plus placebo. Those comparisons yield positive point estimates, but both confidence intervals include zero and are broad. The posted data therefore do not determine the direction or size of the group differences with precision.

This result does not establish that the groups are equivalent. A failure to show a clear difference is not the same as evidence that two treatments have identical effects; the intervals still include a range of possible contrasts. Nor do the counts by themselves establish that any particular treatment caused the observed responses. Randomization is a design strength described in the registry, but details of allocation implementation, missing-data handling, and the analysis population are not reported.

The primary endpoint is about depression response, not alcohol use. Although alcohol use disorder is part of the study population and the trial description identifies both conditions as targets, no secondary outcome results are posted. The Day 21 endpoint also does not describe whether responses persisted through the follow-up period. The record mentions follow-up sessions, but no later efficacy results are included in the posted results.

The safety counts are also limited. No serious adverse events or deaths are recorded in the reported group counts, while other adverse events affected participants in each group. Those counts do not convey the types or timing of other events, and they should not be treated as a comprehensive comparison of safety without further detail. Taken together, the registry results describe a narrow endpoint and a limited set of posted safety counts. They do not answer every question about efficacy, durability, alcohol-related outcomes, or safety.

16. Why This Trial Matters Statistically

This trial raises a statistical question involving three groups, a binary response endpoint, and a staged study description. The posted primary results make the distinction between an observed group pattern and a precise comparison especially important. Response counts are high in each endpoint group, but the analysis groups are small and the confidence intervals around the contrasts are broad. The point estimates alone would give an incomplete picture of how much uncertainty remains.

The endpoint also illustrates the tradeoff involved in dichotomizing a continuous measure. A 50% or greater MADRS improvement is easy to describe as a response, but it compresses a range of score changes into two categories. It does not show how far participants’ scores changed or what happened to those who did not cross the threshold. The registry’s primary result is therefore informative about the stated response definition, while leaving other aspects of symptom change unreported.

Interpretation also depends on the analysis population and the handling of missing data. The endpoint is defined among participants who completed the Day 21 measure, but the record does not explain the difference between the planned enrollment and the arm-level analysis counts. Without a reported missing-data procedure or analysis-plan details, readers cannot assess whether the posted comparisons represent all randomized participants or a selected subset.

Finally, the study description refers to an open-label stage before the randomized trial, while the posted efficacy comparisons concern randomized groups. Clear reporting of which participants contributed to each analysis, how the stages were handled, and which comparisons were prespecified would help readers assess the evidence. The record’s limited analysis details make those questions salient. These are general statistical concerns about precision, outcome definition, and analysis transparency, rather than conclusions about the clinical value of any group.

17. Limitations

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

The registry describes an initial open-label group of 5 patients followed by a planned randomized stage of 60 patients, while the primary endpoint counts are reported for 16, 11, and 15 participants across the three groups. The record does not explain how these stages relate to the posted endpoint counts, whether any open-label participants contributed to the randomized comparisons, or why the arm-level counts are smaller than the enrollment figures. This limits the ability to reconstruct the analysis population.

The primary endpoint is measured at a single stated time point, Day 21 after the fourth infusion at 240 minutes. The registry record does not post later efficacy outcomes, continuous MADRS results, or secondary outcome results. Although a 4-week follow-up and a 4-month follow-up session are described, results from those follow-ups are not reported in the registry record.

The posted comparisons use ketamine plus placebo as the reference group. A direct comparison between ketamine plus naltrexone and psychoactive placebo plus placebo is not reported. The registry also does not describe adjustment for baseline characteristics, the method used to calculate confidence intervals, missing-data handling, or multiplicity procedures. These missing details constrain interpretation of the inferential results.

The safety information is limited to group counts. The registry does not provide individual event terms for the other adverse events in the registry record, or a description of event timing and duration. The trial is marked completed, but the record does not provide a detailed account of adherence, treatment discontinuations, or protocol deviations. These limitations do not negate the posted counts; they define what can and cannot be concluded from them.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Ketamine for the Rapid Treatment of Major Depressive Disorder and Alcohol Use Disorder — NCT02461927.
• Registry record last updated 2025-04-10; status last verified 2025-04.
• Results first posted 2025-04-10.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes a completed, randomized, quadruple-masked, parallel-group study of ketamine, naltrexone, and placebo in participants with major depressive disorder and alcohol use disorder. The study is listed as Phase 1 and Phase 2, with 65 enrolled participants. The primary endpoint is the number of participants with a 50% or greater improvement in MADRS from baseline at Day 21, after the fourth infusion, at 240 minutes.

For the two reported comparisons against ketamine plus placebo, the risk-difference estimates are 0.119 and 0.049. Their 95% confidence intervals include zero, and the posted p-values are unadjusted. The registry also reports serious adverse event counts of 0 and death counts of 0 in each group, with other adverse events recorded in all groups. Detailed statistical planning, missing-data procedures, and secondary efficacy results are not reported in the registry record.