Effects of Vaporized Marijuana on Neuropathic Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effects of Vaporized Marijuana on Neuropathic Pain (NCT01037088), a randomized phase 1, phase 2 study. The primary outcome is Participants With 30% or Greater Reduction in Pain Intensity.

2. Clinical Question

The posted results report this endpoint for the mild-dose, low-dose and placebo-cannabis groups. They also report comparisons of each cannabis dose with placebo, including risk differences, confidence intervals and unadjusted p-values. These results describe the recorded outcomes; they do not by themselves establish why any group differences occurred or how well those estimates apply beyond this trial.

3. Trial Design

The trial is listed as randomized, triple-masked and crossover, with phase I and phase II designations. The University of California, Davis is named as sponsor. Enrollment was 44, and the record lists the study as completed. The recorded start was 2009-12, with primary completion in 2012-11.

The intervention descriptions include mild-dose cannabis, low-dose cannabis and cannabis. The arm descriptions identify the mild dose as 3.53% THC by weight, the low dose as 1.29% THC by weight and the placebo as placebo marijuana. The primary endpoint results are reported for mild-dose cannabis, low-dose cannabis and placebo cannabis.

A crossover design means that participants receive study conditions in a sequence rather than being assigned to just one condition for the entire study. As a general statistical point, outcomes from the same participant can be related across conditions. Analyses of crossover data may therefore need to account for within-participant dependence and for the sequence or timing of exposures. The registry record does not report the treatment sequence, washout arrangements, or whether the primary comparison model accounted for these features.

The primary outcome timeframe is baseline to six hours. Pain intensity was assessed before administration and hourly for six hours. A secondary outcome concerns visual analogue scale pain-intensity scores at baseline and up to five hours following administration. The registry lists two outcome measures and five analyses, but the analysis methods and the full set of analysis details are not reported in the registry record.

The registry record does not report the original sample-size justification, the planned analysis population, or detailed masking procedures. Those omissions limit what can be inferred about how the study was designed to address repeated exposures and how its final analyses were selected.

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: Twenty subjects did not receive study medication: 9 withdrew for various reasons and 11 were disqualified following a medical evaluation with subsequent disclosure of exclusionary criteria on a physical exam or laboratory finding.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: This was a cross over study. Ten of the 38 subjects who were exposed to placebo had a 30% reduction in pain intensity as compared to 21 of the 37 exposed to the low dose and 22 of the 36 receiving the medium dose of cannabis.

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 Participants With 30% or Greater Reduction in Pain Intensity, measured over baseline to six hours.

The primary endpoint is the percentage of participants with a 30% or greater reduction in pain intensity from baseline to six hours. Pain intensity was recorded using a 100-mm visual analogue scale, anchored at 0 for no pain and 100 for worst possible pain. Participants reported current pain before administration of vaporized cannabis or placebo and hourly thereafter for six hours.

This endpoint turns a continuous pain-intensity measure into a binary outcome: a participant either met the stated reduction threshold or did not. As a general statistical point, a binary endpoint can make it easier to describe the proportion of participants reaching a prespecified level of change and to compare those proportions between groups. It also discards information about the size and pattern of changes that do not cross the threshold.

The endpoint therefore answers a focused question about the share of participants meeting the threshold during the stated timeframe. It does not describe every change in pain intensity, nor does it convey the full course of hourly scores. The registry lists a secondary outcome for pain-intensity scores at baseline and up to five hours after administration; those scores address change over time differently from the primary threshold outcome.

The endpoint is reported with group percentages and confidence intervals. The primary outcome description states that 10 of 38 placebo-exposed participants, 21 of 37 low-dose-exposed participants and 22 of 36 mild-dose-exposed participants had a 30% reduction in pain intensity. The comparison results use the threshold outcome to contrast each cannabis dose with placebo.

7. Results Posted in the Registry

• Mild Dose Cannabis: 61.1% (22/36) versus 26.3% (10/38) on control; risk difference 34.8 percentage points (95% CI 13.6 to 56.0), risk ratio 2.32 (1.28–4.20); unadjusted two-proportion z-test p = 0.003.
• Low Dose Cannabis: 56.8% (21/37) versus 26.3% (10/38) on control; risk difference 30.4 percentage points (95% CI 9.2 to 51.7), risk ratio 2.16 (1.18–3.94); unadjusted two-proportion z-test p = 0.007.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary because each participant is classified according to whether the stated reduction threshold was reached. The arm results report the number meeting the threshold, the denominator assessed in that exposure group, the percentage, and a 95% confidence interval. The comparison results report risk differences for each cannabis dose versus placebo, along with confidence intervals and unadjusted p-values.

As a general statistical point, a risk difference is an absolute contrast between proportions. It describes how far apart the observed event proportions are on the probability scale. A positive risk difference in these comparisons corresponds to a higher observed proportion meeting the endpoint in the cannabis exposure group than in the placebo group. The posted estimates are 0.348 for mild-dose cannabis versus placebo and 0.304 for low-dose cannabis versus placebo. The comparison intervals and group intervals represent different quantities: the former concern a contrast, while the latter concern a single group's percentage.

As a general statistical point, a confidence interval describes the range of values compatible with the data and the method used to construct the interval. Under repeated use of the same method in comparable studies, intervals would vary from sample to sample; the stated confidence level refers to the long-run coverage of that procedure, not to a probability assigned to the fixed underlying value after observing the data. Wider intervals generally indicate less precision than narrower intervals, all else equal. The registry reports 95% confidence intervals for the group percentages and the dose-versus-placebo contrasts.

The comparison p-values are unadjusted. As a general statistical point, a p-value measures how unusual data at least as incompatible with a specified null model would be if that model held, under the assumptions of the test. It is not the probability that the null model is true. Nor does a small p-value show that an estimate is precise, clinically important, or free of bias. The registry reports p-values of 0.003 for mild-dose cannabis versus placebo and 0.007 for low-dose cannabis versus placebo.

The design is randomized, triple-masked and crossover. As a general statistical point, randomization can reduce systematic differences between assigned conditions, while masking can limit some forms of expectation-related influence. In a crossover study, participants receive multiple conditions, so observations may be correlated within participant. A suitable analysis may need to reflect that dependence. The registry record does not report the statistical model, how within-participant correlation was handled, or whether treatment sequence or period effects were considered. It also does not report washout details or an analysis of carryover.

The primary assessment began before administration and continued hourly for six hours. The binary endpoint summarizes whether a participant crossed the stated reduction threshold over the baseline-to-six-hour timeframe. It does not preserve the full continuous trajectory of pain scores. The registry also lists a secondary visual analogue scale outcome for baseline and up to five hours following administration. The record reports two outcome measures and five analyses, but does not provide a complete account of how the outcomes were modeled or how the analyses relate to one another.

The arm percentages are based on the reported exposed-participant denominators: 36 for mild-dose cannabis, 37 for low-dose cannabis and 38 for placebo cannabis. The primary outcome description gives corresponding threshold counts of 22, 21 and 10. Because the study is crossover, those denominators should not automatically be interpreted as mutually exclusive sets of participants. The registry record does not report the number of participants contributing to every analysis or the handling of missing observations.

As a general statistical point, over-dispersion occurs when the observed variability is greater than a model assumes. It can make standard errors too small if the extra variability is ignored. The posted primary endpoint is binary, but the registry record does not report a model specification or an assessment of over-dispersion. The record also does not report covariate adjustment, the exact test used for the comparisons, or any interim analysis plan.

Overall, the displayed estimates allow a descriptive reading of the observed proportions and the posted comparisons. The missing analysis details limit assessment of whether uncertainty estimates fully reflect the crossover structure, missingness, multiplicity or other design features. Those details are not reported in the registry record and cannot be inferred from the outcome counts alone.

10. Confidence Intervals and Precision

The arm-level 95% confidence intervals are 45.0% to 75.0% for mild-dose cannabis, 41.0% to 71.0% for low-dose cannabis and 15.0% to 42.0% for placebo cannabis. Each interval describes uncertainty around its group's percentage of participants meeting the threshold. The intervals span a range of plausible values rather than identifying a single precisely known percentage.

The posted estimates are 61.0% for mild-dose cannabis, 57.0% for low-dose cannabis and 26.0% for placebo cannabis. The reported interval widths indicate that the group percentages are not known without uncertainty. As a general statistical point, confidence intervals are useful because they pair an estimate with information about its precision; they do not eliminate uncertainty or account for sources of bias that the analysis did not address.

The comparison results also include confidence intervals for the risk differences. Those are intervals for the between-group contrasts, not for either group's percentage by itself. The registry record reports them, but the crossover analysis details are not available, so the method used to obtain those intervals and its handling of within-participant dependence are not reported in the registry record.

Precision is affected by the amount of information in the data and by the analysis method. The outcome denominators are 36, 37 and 38 across the exposure groups, and trial enrollment was 44. In a crossover trial, the number of exposure records is not necessarily the same as the number of distinct participants. Without fuller information about observations, missingness and the model, the intervals should be read as the posted precision estimates rather than as a full assessment of every source of uncertainty.

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 estimates are participants per arm, not total event counts. They are illustrations based on the observed effect, not the trial's original design justification. The registry record does not report the trial's own sample-size assumptions or justification.

The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. For planning for 100% of the observed mild-dose contrast, the estimates are 31 participants per arm for 80% power and 41 participants per arm for 90% power. At 75% of that observed effect, the estimates are 54 and 72 participants per arm; at 50%, they are 117 and 156 participants per arm. For the low-dose contrast, the corresponding estimates are 40 and 53 participants per arm at 100%, 70 and 93 at 75%, and 151 and 202 at 50%.

In plain language, the 80% power column gives the estimated number of participants per arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect is the true one. The 90% power column gives the corresponding estimate for a design with a 90% chance. These are planning probabilities under a statistical model, not guarantees about a future study. The estimates increase as the assumed effect gets smaller, because smaller differences are harder to distinguish from random variation.

This is not observed power. It is a planning illustration based on the observed contrasts, not a measure of what the completed trial achieved. The estimates do not establish that the original trial was designed around these 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 = 0.263; treatment proportion p₁ = 0.611; average p̄ = 0.437.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7015 = 1.3749.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6569 = 0.5529.
4. n = (1.3749 + 0.5529)² / (0.3480)² = 30.7, rounded up to 31 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 <- 0.263157894736842                          # control proportion
p1 <- 0.611111111111111                          # 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(1037088)
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 = 31 (80% power), 41 (90% power)
 75% of observed effect: n per arm = 54 (80% power), 72 (90% power)
 50% of observed effect: n per arm = 117 (80% power), 156 (90% power)
power.prop.test: 30.7 
Simulated power at n = 31 per arm: 0.815 (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 reports two dose-versus-placebo comparisons for the primary endpoint and gives unadjusted p-values. It does not report whether an adjustment for multiple testing was planned or applied. When several comparisons are considered, the chance of at least one apparently notable result can increase; as a general statistical point, multiplicity procedures are used in some analyses to control that risk. Without a reported plan, the posted p-values should be read as unadjusted.

The registry record identifies a randomized, triple-masked crossover study but does not report the analysis population definition, the primary statistical model, or whether the analysis followed an intention-to-treat principle. It also does not report how participants with incomplete observations were handled. The difference between trial enrollment and the exposure-specific denominators cannot by itself establish why those denominators differ.

Missing data can affect estimates when the availability of outcomes is related to participants' outcomes or study experiences. As a general statistical point, complete-case analyses and methods that model or impute missing values rely on different assumptions. The registry record does not report the amount, pattern or handling of missing primary outcome data, so the impact of missingness cannot be assessed from the record.

The crossover structure raises further analysis questions. The registry record does not report the order in which conditions were received, whether period effects were evaluated, or whether carryover was considered. It also does not state how repeated observations from a participant were handled in the comparisons. These omissions matter when judging whether the uncertainty estimates and p-values reflect the design.

The record lists two outcome measures and five analyses, but does not describe a prespecified multiplicity strategy, an interim analysis plan, or the relationship between all analyses. Those details are not reported in the registry record. As a result, the posted endpoint and comparison results can be described, but the broader analysis-selection context remains unclear.

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 5% reporting threshold.

The serious adverse event figures report 0 affected participants among 36 at risk in the mild-dose cannabis group, 0 among 37 at risk in the low-dose cannabis group, and 0 among 38 at risk in the placebo cannabis group. These are the counts recorded for serious adverse events affecting participants in the respective exposure groups.

A zero count in these groups means that no serious adverse event was recorded as affecting a participant in the posted results. It does not establish that an event is impossible or that the study can rule out uncommon harms. As a general statistical point, estimates based on limited numbers of participants can leave substantial uncertainty about events that were not observed.

The registry lists no deaths as a numeric result for these groups; death counts are not reported in the registry record. The other adverse event figures also list 0 affected participants in each group, but this does not provide detail on event types, timing, severity below the serious category, or duration. The record does not include a list of serious adverse event terms. These results describe the recorded safety counts and should not be interpreted as a comprehensive safety assessment.

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

The primary endpoint results show that the reported proportion meeting the 30% pain-reduction threshold was 61.0% for mild-dose cannabis, 57.0% for low-dose cannabis and 26.0% for placebo cannabis. The comparison estimates favor a higher observed threshold-response proportion in each cannabis exposure group than in the placebo group. The unadjusted p-values are 0.003 and 0.007 for the mild-dose and low-dose comparisons, respectively.

Those statistics describe the posted data, not a definitive account of what would occur in every setting or for every participant. The endpoint is a thresholded measure over baseline to six hours. It does not summarize the full hourly pattern of pain scores or establish effects beyond the recorded timeframe. The registry lists a secondary pain-intensity score outcome extending to five hours, but the primary results alone do not describe that outcome.

The design is a randomized, triple-masked crossover trial, which is relevant to interpretation. However, details of treatment sequence, washout, model choice and within-participant handling are not reported in the registry record. These gaps prevent a complete assessment of how the comparison estimates account for the crossover design. The record also does not report multiplicity adjustment, missing-data methods or the original sample-size justification.

The confidence intervals communicate uncertainty around the group percentages and contrasts. They should be considered alongside the point estimates rather than as proof of a single underlying value. The p-values likewise do not measure clinical importance or remove uncertainty, and they are reported without a stated multiplicity adjustment.

The serious adverse event results record 0 affected participants in each exposure group, but those counts do not demonstrate that serious events cannot occur. Death counts are not reported in the registry record. Taken together, the findings are a description of a specific completed trial and its posted outcomes. They do not support individualized medical advice, nor do they establish conclusions beyond the measured endpoint, timeframe and analysis details available in the registry.

16. Why This Trial Matters Statistically

This trial illustrates why study design and analysis context matter as much as a headline percentage. The endpoint is binary, based on whether a participant reached a specified reduction in pain intensity, while the underlying pain measure is continuous and assessed repeatedly over time. The threshold makes group proportions easy to interpret, but it compresses changes of different sizes into the same outcome category.

The crossover design makes the comparison especially important to read with care. Participants can contribute outcomes under multiple conditions, so the observations may not be independent in the way they would be in a parallel-group trial. The registry identifies the design but does not report the statistical model or how within-participant dependence was addressed. That missing information limits assessment of the comparison's uncertainty.

The record also presents absolute risk differences as well as group percentages. As a general statistical point, absolute contrasts communicate the size of a difference on the outcome scale, while p-values address compatibility with a null model under test assumptions. Neither quantity replaces the other. The confidence intervals add a precision perspective, and the unadjusted p-values should not be mistaken for multiplicity-adjusted results.

The planning estimates make another useful statistical distinction: sample-size planning depends on an assumed effect. Smaller assumed effects require more participants per arm under the listed assumptions. These planning illustrations are not observed power and do not reveal the trial's original design rationale.

Finally, the adverse event counts demonstrate the difference between an observed zero and proof of no risk. Together, these features make the trial a useful example of how endpoint definitions, crossover analysis, uncertainty, multiplicity and safety reporting shape the interpretation of clinical results.

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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The registry record does not report the statistical model used for the primary comparisons, how repeated observations within participants were handled, or how the crossover sequence was incorporated. Treatment order, period effects and washout arrangements are also not reported. These details are relevant to judging whether the reported uncertainty estimates appropriately reflect the study design.

The record does not report how missing observations were handled, how the analysis population was defined, or whether all enrolled participants contributed to each outcome analysis. Enrollment was 44, while the primary outcome denominators are 36 for mild-dose cannabis, 37 for low-dose cannabis and 38 for placebo cannabis. The record does not explain the differences between these counts.

The primary endpoint reduces a continuous pain-intensity measure to whether a participant reached a 30% reduction threshold. This supports interpretation of the proportion meeting that threshold, but it does not show the distribution of individual changes or the complete hourly trajectory. The registry lists a secondary pain-intensity score outcome, but the full secondary results are not included in the registry record for this analysis.

The record reports two dose-versus-placebo comparisons and unadjusted p-values, but does not report a multiplicity plan or whether the comparisons were prespecified. The original sample-size justification and the trial's design assumptions are also not reported in the registry record. The planning illustrations based on observed effects cannot fill that gap.

The serious adverse event counts record zero affected participants in each group, but the registry does not give serious event terms, and death counts are not reported. The listed counts alone do not provide detail on the range, timing or duration of adverse events. These limitations restrict the conclusions that can be drawn from the posted record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effects of Vaporized Marijuana on Neuropathic Pain — NCT01037088.
• Registry record last updated 2018-01-31; status last verified 2017-10.
• Results first posted 2013-04-09.
• 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.

21. Record Summary

The registry record describes a completed randomized, triple-masked, phase I and phase II crossover trial sponsored by the University of California, Davis. Enrollment was 44. The recorded study start was 2009-12, and primary completion was 2012-11.

The trial compared mild-dose cannabis, low-dose cannabis and placebo cannabis for a primary endpoint of 30% or greater reduction in pain intensity from baseline to six hours. The reported threshold-response percentages were 61.0%, 57.0% and 26.0%, respectively. The posted comparisons report unadjusted p-values of 0.003 for mild-dose cannabis versus placebo and 0.007 for low-dose cannabis versus placebo.

For serious adverse events, the record lists 0 affected participants in each exposure group. Death counts are not reported in the registry record. Details of the crossover analysis, missing-data handling, multiplicity strategy and original sample-size justification are not reported in the registry record.