Combined Pharmacotherapy for Cannabis Dependency: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Combined Pharmacotherapy for Cannabis Dependency (NCT01020019), a randomized phase 2, phase 3 study. The primary outcome is 21 Days of Consecutive Abstinence as Measured by the Time-line Followback..

2. Clinical Question

The clinical question is framed around whether the combination is associated with a different count of participants meeting the abstinence endpoint during the study. The outcome is binary at the participant level: each participant either met the stated consecutive-abstinence criterion or did not, as represented in the posted counts. This result does not, by itself, describe every aspect of cannabis use or withdrawal, and the registry record contains no posted secondary outcome results for those topics.

The study title identifies it as a randomized, double-blind, placebo-controlled study of lofexidine and dronabinol for marijuana dependence. The record describes a parallel-arm study and quadruple masking. These design features are relevant to how the comparison was organized, but the registry does not report the identities of the parties covered by quadruple masking or further details about how the treatment groups were managed.

3. Trial Design

The registry describes a randomized, parallel-group study with quadruple masking and lists its phase as Phase 2 and Phase 3. The official title calls it a randomized, double-blind, placebo-controlled study. One arm received lofexidine and dronabinol; the other received placebo. The combination-arm description specifies 1.8mg/day of lofexidine and 60 mg/day of dronabinol. The placebo description says lofexidine-matched placebo and dronabinol placebo.

The registry records an enrollment of 156. For the primary endpoint, it posts 61 participants in the placebo arm and 61 in the combination arm. Those endpoint counts are the basis for the comparison. The record does not include a participant-flow account explaining how the enrollment relates to the number represented in the primary outcome, so the difference between those totals cannot be attributed to any particular reason from this record alone.

The study is listed as completed. Its recorded start is 2010-01, and its primary completion is 2014-09. The sponsor is New York State Psychiatric Institute. These administrative details establish what study the registry record describes; they do not supply additional information about conduct or results.

The primary measure is 21 days of consecutive abstinence, measured by the Time-line Followback. Its timeframe is described as reported daily for 12 weeks or for the duration of study participation. The registry lists one outcome measure and does not post secondary outcome results. It also records zero analyses. Consequently, the record does not give a detailed statistical analysis plan, analysis population, or explanation of how missing daily reports or other incomplete outcome information were handled. Those omissions limit how fully the posted arm counts can be interpreted.

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: The study included a one-week placebo lead-in phase. Participants were randomized at the end of the placebo lead-in phase and those who reported marijuana use less than once a week during the lead-in phase were considered placebo responders and were not randomized. A total of 34 participants discontinued prior to randomization for various reasons.

Overall Study

Reasons for not completing this period:

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 21 Days of Consecutive Abstinence as Measured by the Time-line Followback., measured over reported daily for 12 weeks/ or study participation.

The primary endpoint counts participants who achieved 21 days of consecutive abstinence, as measured by the Time-line Followback. The registry describes the outcome in terms of participants, so the posted values are counts rather than continuous measurements of the amount of cannabis used. The timeframe says the measure was reported daily for 12 weeks or for the duration of study participation.

A consecutive-abstinence endpoint captures whether a participant met a defined stretch of abstinence, rather than summarizing all use across the full study period. In general, this kind of binary endpoint can make a clinical question straightforward to state: how many participants met the criterion in each group? It does not show the length or pattern of abstinence among participants who did not meet the full criterion, nor does it provide a complete account of use or withdrawal. Those outcomes would require their own reported measures.

The posted outcome is 18 participants in the placebo arm and 17 in the lofexidine-and-dronabinol arm, with 61 participants listed in each arm. The registry does not supply further endpoint details such as rules for incomplete daily reports or how the abstinence criterion was applied when information was missing. The endpoint therefore supports a comparison of the posted counts, while leaving those operational details unreported in the registry record.

7. Results Posted in the Registry

• Lofexidine and Dronabinol: 27.9% (17/61) versus 29.5% (18/61) on control; risk difference -1.6 percentage points (95% CI -17.7 to 14.4), risk ratio 0.94 (0.54–1.65); unadjusted two-proportion z-test p = 0.841.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: participants are counted according to whether they achieved the stated 21 days of consecutive abstinence. The registry posts the number meeting the endpoint and the number in each arm. For this outcome, it lists 18 of 61 participants in the placebo arm and 17 of 61 in the combination arm. The comparison is expressed as a risk difference, which describes the difference between the proportions meeting the endpoint in the two groups. The direction depends on which arm is subtracted from which; the registry comparison treats the combination arm relative to placebo.

What does a risk difference describe?

As a general statistical explanation, a risk difference is an absolute contrast between two event proportions. It answers how far apart the observed event rates are on the original proportion scale, rather than expressing one group’s rate as a multiple of the other. A value near zero corresponds to little separation on that scale. The posted interval for this comparison includes zero, so it does not exclude no difference. It also covers values in both directions, which means the data are compatible with the combination arm having a lower or higher event proportion than placebo within the interval’s range.

How should the p-value be read?

The comparison reports an unadjusted p-value of 0.841. In general, a p-value is calculated under a null hypothesis and a statistical model. It indicates how unusual data at least as discrepant as those observed would be under that model; it is not a measure of the probability that the null hypothesis is correct. A large p-value is not proof that two treatments have identical effects. Interpretation also depends on the study design, analysis choices, data completeness, and precision of the estimate.

The registry record lists zero analyses. The comparison is an unadjusted recalculation from the posted summary statistics, and no discrepancy is flagged between that recalculation and the record. There is no sponsor analysis posted in the record to describe alongside it. The record does not report the test procedure, model details, covariate adjustment, or other analysis specifications, so those should not be inferred.

Why does the confidence interval matter?

As a general explanation, a confidence interval expresses uncertainty about an estimate under a statistical procedure. It identifies a range of effect values that are compatible with the data and the method used, subject to the assumptions of that method. It does not guarantee that the true effect lies in the particular interval, and it is not a range of outcomes expected for individual participants. Here, the interval crosses zero and spans effects in both directions. This conveys more than the p-value alone: the counts are consistent with a range of possible differences, not merely with a single point estimate.

What is not specified?

The registry does not report the trial’s original sample-size justification, the statistical analysis plan, or the analysis population. It does not say whether the primary comparison was intended to include all randomized participants, only participants with endpoint data, or another defined group. The record also does not describe how incomplete daily reports, missed visits, or other missing endpoint information were addressed. These details matter because outcome definitions and missing-data rules can affect which participants contribute to an estimate and how uncertainty is represented.

In general, randomization is intended to support a fair comparison by allocating participants to groups without choosing treatment based on their expected outcomes. Masking is intended to limit the influence of knowledge about group assignment. The registry identifies the study as randomized and quadruple-masked, but it does not describe the randomization procedure or identify the parties included in the masking. The design labels therefore provide useful context without establishing that every possible source of bias was prevented.

The result is a comparison of a binary abstinence measure at the participant level. It does not describe the detailed timing of abstinence, the distribution of cannabis use among participants who did not meet the endpoint, or withdrawal outcomes. Those subjects would require other measures, and the record posts no secondary results. Statistical interpretation should remain within the scope of the endpoint and data that are actually recorded.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an effect estimate. The primary comparison is based on 61 participants in each arm, with 18 meeting the abstinence endpoint in placebo and 17 in the combination arm. The posted confidence interval for the risk difference includes zero and extends in both directions. This means the data do not determine the direction of the underlying difference precisely. The interval limits are not repeated because the main interpretive point is that the range includes no difference as well as possible effects on either side.

As a general statistical explanation, a confidence interval reflects both the observed estimate and the uncertainty associated with the data and method. A narrow interval would constrain plausible effect values more tightly; a wide interval leaves more possibilities open. An interval including zero does not show that the true difference is zero. It indicates that zero is among the values compatible with the estimate and its uncertainty under the method used.

The unadjusted p-value is 0.841, but a p-value alone does not convey the full range of effect sizes compatible with the data. The interval and the group counts are important for understanding how much information the comparison provides. The small separation between the posted counts should not be mistaken for a precise estimate of equivalence, especially when the uncertainty range includes effects in both directions.

The record’s enrollment total is 156, but the primary outcome is shown for 61 participants per arm. Since participant flow and missing-outcome handling are not reported in the registry record, the source of this difference cannot be assessed. The reported endpoint sample, rather than the enrollment total alone, is relevant to the precision of this specific comparison.

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 a record of the trial’s original design calculation. Because the primary outcome is binary and the planning entries are participant counts, the figures are participants per arm, not total events. The stated 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 to the stated fraction of the observed effect. The trial’s own original sample-size assumptions are not reported in the registry record.

The column for 80% power gives the planned number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions, if that effect and the assumptions apply. The 90% power column gives the corresponding planning count for a 90% chance. These are hypothetical design quantities, not probabilities that the present trial’s result is correct.

For planning at 100% of the observed effect, the display gives 11,949 participants per arm for 80% power and 15,996 for 90% power. For planning at 75% of the observed effect, it gives 21,334 per arm for 80% power and 28,559 for 90% power. For planning at 50% of the observed effect, it gives 48,203 per arm for 80% power and 64,530 for 90% power. The pattern illustrates a general principle: smaller effects are harder to distinguish from random variation and therefore require more participants under otherwise fixed assumptions. These figures are not observed power.

The record describes the calculation as a normal-approximation planning illustration and provides no account of the assumptions used when the trial was originally designed. The curve and table should therefore be read as aids for considering hypothetical future sample sizes under the stated assumptions, not as a retrospective judgment about whether the completed study was adequately designed.

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 = 0.295; treatment proportion p₁ = 0.279; average p̄ = 0.287.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6397 = 1.2537.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6396 = 0.5383.
4. n = (1.2537 + 0.5383)² / (-0.0164)² = 11,948.7, rounded up to 11,949 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 <- 0.295081967213115                          # control proportion
p1 <- 0.278688524590164                          # 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(1020019)
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 = 11,949 (80% power), 15,996 (90% power)
 75% of observed effect: n per arm = 21,334 (80% power), 28,559 (90% power)
 50% of observed effect: n per arm = 48,203 (80% power), 64,530 (90% power)
power.prop.test: 11948.7 
Simulated power at n = 11,949 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. Multiplicity, Missing Data and Analysis Populations

The registry record posts one outcome measure, the primary endpoint of 21 days of consecutive abstinence, and zero secondary outcome results. It also records zero analyses. The study summary mentions abstinence, cannabis use, and withdrawal as aims, but the record does not provide posted results for cannabis use or withdrawal as secondary outcomes. No multiplicity procedure or plan for interpreting a family of outcomes is reported in the registry record.

As a general statistical point, multiplicity arises when several outcomes, comparisons, time points, or analyses are tested. Considering many tests can increase the chance of at least one apparently unusual result, so a prespecified approach to multiplicity can matter. Here, the limited set of posted results does not establish what outcomes or analyses were planned beyond what is shown. It would be inappropriate to assume that no additional outcomes were measured merely because they are not posted, or to assume a particular adjustment was used.

The record does not report an analysis population. It therefore does not specify whether the primary comparison includes every randomized participant, only participants with an observed endpoint, or another group. It also does not describe participant exclusions, protocol deviations, or how treatment assignment was used in analysis. The posted arm counts can be reported as they appear, but the population to which they correspond cannot be characterized more specifically.

Missing-data handling is also not reported in the registry record. The endpoint timeframe includes daily reporting, but the record does not state how missing reports were treated, how a consecutive-abstinence period was classified when information was incomplete, or whether any imputation or sensitivity analyses were performed. In general, such choices can influence both the estimated outcome and its uncertainty. Without the relevant details, readers cannot evaluate how robust the posted comparison is to alternative handling of incomplete data.

The registry does not provide an interim-analysis plan, stopping rules, or a detailed statistical analysis plan. Their presence or absence should not be inferred. The analysis information is therefore insufficient to reconstruct all the decisions behind the result or to determine whether other planned comparisons were conducted but not posted.

14. 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 0% 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 (1.6%), detoxification (1.6%).

The serious adverse event figures list 1 affected participant among 61 at risk in the placebo group and 1 among 61 at risk in the lofexidine-and-dronabinol group. The registry identifies abdominal pain and detoxification among the top serious event terms, each shown as 1.6%. The record does not assign those terms to a particular arm in the information, so they should not be attributed to one group.

The registry separately lists other, non-serious adverse event counts: 46 among 61 at risk in placebo and 47 among 61 at risk in the combination arm. These are a different category from serious adverse events and should not be combined with the serious-event figures. The death counts are not reported in the registry record.

As a general statistical point, these counts are descriptive safety information. They do not establish that an event was caused by the assigned treatment, and the record does not give enough detail to assess event severity, timing, duration, or relatedness. The figures should be read as the posted counts, not as a complete characterization of safety.

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

The posted primary outcome shows 18 participants meeting the 21-day consecutive-abstinence criterion in the placebo arm and 17 in the lofexidine-and-dronabinol arm, with 61 participants listed per arm. The unadjusted comparison reports p=0.841, and the confidence interval for the risk difference includes zero while spanning values in both directions. Together, these results describe little separation in the observed counts and substantial uncertainty about the direction and size of any underlying difference.

This finding does not establish that the treatments have identical effects. A failure to show a clear difference in this comparison is not the same as a formal demonstration of equivalence or non-inferiority; the registry does not report such a design or analysis. Nor does the result establish that either treatment is beneficial or ineffective. It is a statistical description of the posted endpoint in this study, not medical advice or a treatment recommendation.

The result is limited to the recorded measure of 21 consecutive days of abstinence. It does not answer every question named in the study summary, including changes in cannabis use more broadly or withdrawal, for which no secondary results are posted. It also does not describe long-term outcomes beyond the timeframe stated for the endpoint.

Interpretation is further bounded by missing information. Although enrollment is recorded as 156, the primary outcome lists 61 participants in each arm. The registry does not explain participant flow, define the analysis population, or describe missing-data handling. It also does not post a detailed analysis plan. These gaps prevent a fuller assessment of how the outcome counts relate to all enrolled participants and how sensitive the comparison might be to analysis choices.

The most defensible reading is therefore narrow: the registry reports similar counts for the primary abstinence endpoint across the two listed arms, with an unadjusted comparison that does not show clear statistical separation and an interval that leaves a wide range of possible effects open. The posted information alone cannot settle broader questions about treatment effects, other outcomes, or the reliability of unreported analyses.

16. Why This Trial Matters Statistically

This trial is statistically informative because it puts a concrete binary outcome beside an explicit comparison: the number of participants achieving 21 consecutive days of abstinence in each arm. The counts are easy to understand, but the comparison also illustrates why counts alone are not enough. The uncertainty interval includes zero and extends to both sides, so the apparent closeness of the counts cannot be treated as proof that the underlying effects are identical.

The case also highlights the difference between a nonsignificant comparison and evidence of equivalence. The unadjusted p-value is 0.841, but that value does not establish that any true difference is absent. A confidence interval and the scope of the design are needed to understand what effects remain compatible with the data. The posted interval leaves direction uncertain, reinforcing the need to discuss precision rather than treating a single test result as a final answer.

Another useful lesson is the distinction between enrollment and the endpoint sample shown in the results. The registry records enrollment of 156 but lists 61 participants per arm for the primary outcome. Without participant flow or missing-data information, readers cannot determine why those quantities differ. Transparent reporting of analysis populations and outcome completeness is important for interpreting both estimates and their precision.

Finally, the sample-size display shows how planning counts can change when the target effect changes. Under its stated assumptions, planning for a smaller fraction of the observed effect requires more participants per arm. These figures are illustrations rather than the original design rationale, which is not reported. Together, the result and its reporting gaps make this trial a useful example of separating observed counts, statistical uncertainty, planning calculations, and conclusions that the registry does not support.

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 primary outcome results list 61 participants in each arm, while the registry records total enrollment of 156. The record does not report a participant-flow account or explain why the outcome counts differ from enrollment. It is not possible to identify from the registry whether this reflects missing outcome data, exclusions, a defined analysis population, or another reason.

The registry does not describe how the daily Time-line Followback reports were used to determine consecutive abstinence, how incomplete reports were handled, or whether any sensitivity analyses were conducted. These omissions matter for an endpoint that depends on a consecutive period of reported abstinence. The registry also does not state the analysis population, so the posted counts cannot be confidently described as an intention-to-treat or other specific analysis.

Although the trial is identified as randomized and quadruple-masked, the registry does not report the randomization procedure or identify who was masked. The record does not provide an analysis plan, the original sample-size justification, interim-analysis information, or details of any adjustment for multiple outcomes. It lists zero analyses and posts no secondary outcome results, leaving the broader aims of cannabis-use reduction and withdrawal unaddressed in the available results.

The primary comparison is an unadjusted recalculation from the posted summary statistics. No discrepancy is flagged, but the registry does not provide a separate sponsor analysis or enough methodological detail to reconstruct a complete analysis. The safety record is also limited: it gives event counts and selected serious-event terms, but not further information on timing, duration, relatedness, or arm-specific attribution of those terms. These limitations concern what can be learned from the registry record and should not be filled in by assumption.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Combined Pharmacotherapy for Cannabis Dependency — NCT01020019.
• Registry record last updated 2019-04-24; status last verified 2019-04.
• Results first posted 2016-05-11.
• 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 describes a completed, randomized, parallel, quadruple-masked study of lofexidine and dronabinol for cannabis dependence, with placebo as comparator. It lists Phase 2 and Phase 3, enrollment of 156, a start date of 2010-01, and primary completion in 2014-09. The sponsor is New York State Psychiatric Institute.

The primary outcome is the number of participants achieving 21 days of consecutive abstinence measured by the Time-line Followback. The posted counts are 18 of 61 in placebo and 17 of 61 in the combination arm. The unadjusted comparison has p=0.841, and the confidence interval spans zero and effects in both directions.

The record lists one outcome measure, zero analyses, and no secondary outcome results. It does not report the original sample-size justification, participant flow, analysis population, or missing-data procedures. The available results support a narrow description of the posted abstinence counts, with uncertainty and reporting gaps that limit broader conclusions.