Virtual Reality Treatment for Adults With Chronic Back Pain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Virtual Reality Treatment for Adults With Chronic Back Pain (NCT04468074), a randomized na study. The primary outcome is Change in Pain Intensity and Interference..

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group study, with virtual reality therapy compared against a no-intervention Standard of Care group. The planned allocation ratio was 1:1. Enrollment was 72. The record lists the study as completed, with a start date of 2020-06-09 and primary completion on 2021-04-13. The phase is listed as not applicable.

The sequence described in the registry began with an online eligibility questionnaire, consent and a two-week baseline period during which participants completed daily pain surveys. Participants then completed an MRI scan and were randomized. The Therapy Group received education about chronic pain, sessions to personalize the virtual reality experience and training in use of the equipment. The treatment period lasted 8 weeks, followed by a two-week follow-up period with daily pain surveys. The Standard of Care group was asked to maintain its pain treatment regimes and report changes.

Both groups were scheduled for a second MRI approximately 8 weeks after the first. The registry also describes self-reported clinical outcomes and behavioral measures at several points around baseline, during the study and after the therapy period. The posted primary outcome compares pre-treatment and post-treatment change at 8 weeks.

The primary outcome summaries include 30 participants in each group. The adverse-event record gives 31 participants at risk in the Therapy Group and 30 in the Standard of Care group. The record does not explain the relationship between the enrollment figure and these outcome and safety denominators, or describe participant flow, exclusions or reasons for unavailable data. Details of the masking procedure, including who was masked, are not reported in the registry record.

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: Of 1,346 applicants, 270 met inclusion criteria. Of these, 72 were enrolled in the study; however, 11 withdrew before start / randomization. 61 participants started the study (completed randomization). After a 2-week baseline period, participants were randomized into the Experimental and No Intervention Groups.

Overall Study

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 Change in Pain Intensity and Interference., measured over Change from pre-treatment to post-treatment = 8 weeks..

The primary endpoint is change in pain intensity and interference, measured using the Brief Pain Inventory-short form (BPI-SF). The instrument is described as a scale from 0 to 10, where 0 means no pain and 10 means the worst pain imaginable. The timeframe is change from pre-treatment to post-treatment at 8 weeks.

A change score describes how the recorded outcome differs between the specified measurement occasions. Comparing the average change between randomized groups focuses on whether the groups followed different trajectories over the treatment period, rather than simply comparing their post-treatment scores. This can be useful when the research question concerns change during treatment. However, the registry record does not report the protocol's rationale for selecting this endpoint or its analysis details beyond the posted outcome description.

The Therapy Group's posted mean change was -1.5, with a standard deviation of 1.7; the Standard of Care group's mean change was -0.5, with a standard deviation of 1.3. Given the scale's direction, a negative change corresponds to a lower score at follow-up than at the earlier measurement. These group averages do not show the distribution of individual responses. The registry gives the outcome unit as units on a scale, and does not provide a minimally important difference for interpreting the size of a change.

7. Results Posted in the Registry

• Therapy Group: mean -1.50 versus -0.50 on control; difference -1.00 (95% CI -1.77 to -0.23), standardized effect d = -0.66; z-test p = 0.010.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Change in Quality of Life.

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Therapy Group: mean 3.68 versus 0.89 on control; difference 2.79 (95% CI 0.69 to 4.89), standardized effect d = 0.67; z-test p = 0.009.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Therapy Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Change in Back Pain Disability.

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Therapy Group: mean -4.22 versus -0.37 on control; difference -3.85 (95% CI -6.59 to -1.11), standardized effect d = -0.71; z-test p = 0.006.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Therapy Group than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The two posted secondary outcomes cover quality of life and back pain disability. Their group comparisons follow the same broad direction of separation as the primary result: the posted summaries show a larger change in the Therapy Group than in the Standard of Care group. The registry reports a superiority analysis for each. These outcomes add information about different aspects of participants' reported experience, but they are not substitutes for the primary endpoint.

The secondary results are relevant as supporting context because they address outcomes related to, but distinct from, pain intensity and interference. Agreement in direction across outcomes can make the overall pattern more coherent. It does not establish that all aspects of health changed in the same way, nor does it show that the secondary measures were independent of one another. The registry record does not report a threshold for clinically important change for either secondary outcome.

The registry lists 25 outcome measures and 3 analyses, while 2 secondary outcomes are posted in the results. When several outcomes are examined, the chance of at least one apparently unusual result can increase if each is assessed without accounting for the full set of comparisons. Unadjusted secondary p-values therefore carry less weight than results from a clearly prespecified analysis with a stated multiplicity strategy. The registry does not report whether secondary outcomes were prespecified in a hierarchy, whether adjustments were made, or how the 25 outcome measures relate to the posted analyses.

For these reasons, the secondary findings are best treated as supportive and exploratory in the absence of a reported multiplicity plan. They can inform interpretation of the primary outcome, but they do not independently settle the primary statistical question or establish broader effects beyond the measures and timeframes recorded.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Change in Quality of Life.
• Change in Back Pain Disability.

9. Statistical Interpretation

10. Statistical Methods Explained

The trial used random allocation to compare a therapy group with a standard-of-care group. Randomization is intended to make baseline characteristics comparable on average, although chance differences can remain, particularly in a study with a limited number of participants. A parallel-group design means that participants were assigned to one group rather than crossing between treatments. The registry lists single masking, but does not identify who was masked or explain how masking was maintained.

What does a mean change represent?

The BPI-SF outcome is continuous: it is recorded on a numeric scale, and the posted summaries describe the mean change and standard deviation in each group. The mean is the arithmetic average of participants' changes. The standard deviation describes how spread out individual values are around that average. A group mean can summarize a distribution, but it does not show whether all participants changed similarly or whether the average was influenced by a range of responses.

A mean difference compares the group averages. The unadjusted re-calculation uses the posted means and sample sizes, without fitting the sponsor's mixed model. It is therefore a straightforward comparison of summary statistics, not a reconstruction of all the trial's repeated measurements or other possible covariates. The posted re-calculated mean difference is -1.0. Its negative sign reflects the subtraction order used in that calculation. The sponsor's reported net mean difference is 1, and the registry does not state its sign convention.

What does the confidence interval convey?

A confidence interval expresses uncertainty around an estimated effect. Its width reflects how precisely the effect is estimated under the method used. A narrower interval indicates greater statistical precision; a wider interval indicates that a broader range of values remains compatible with the data and assumptions. The interval does not mean that the true value is distributed uniformly within its endpoints, nor does it capture every source of uncertainty, such as measurement limitations or unreported analysis decisions.

The re-calculated interval runs from -1.766 to -0.234. It is based on an unadjusted comparison of the posted group summaries. The registry does not give the confidence level for that re-calculation, and the sponsor's mixed-model analysis has no confidence interval posted. The re-calculated interval should not be treated as the model-based interval for the sponsor analysis.

How should p-values be read?

A p-value measures how incompatible the observed data, or more extreme data, are with a specified statistical null model. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The unadjusted re-calculation reports p = 0.01, while the sponsor's mixed-model result reports p = 0.014. They come from different analyses, so small differences between them are not unexpected and should not be read as a direct disagreement about the same calculation.

Statistical significance alone does not establish practical importance. Interpreting the size of a change also requires context about the scale, participant experience, measurement properties and clinically meaningful thresholds. The registry does not report a threshold for an important BPI-SF change.

Why might a mixed model be used?

Mixed models are general statistical methods that can represent repeated measurements from the same participant and account for the fact that observations from one person tend to be related. They can also estimate group differences over time, depending on the model specification. The sponsor identifies its method as Mixed Models Analysis. The model formula, covariance structure, included time points, covariates, estimation approach and missing-data assumptions are not reported in the registry record, so the model cannot be reproduced from the record.

Over-dispersion is a concern mainly for outcomes whose variability exceeds what a chosen probability model expects, such as some count data. The primary endpoint is a continuous scale outcome summarized by means and standard deviations. The record does not report an over-dispersion assessment, and there is no basis for claiming that it affected this analysis. More generally, appropriate modeling depends on the outcome's distribution and the design, and the registry's brief method label is not enough to assess every modeling choice.

Why does analysis population matter?

The analysis population specifies which randomized participants contribute to a result and how their data are handled. Different choices can produce different estimates, especially when outcome data are missing or participants do not follow the assigned regimen. The outcome summaries show 30 participants per group, but the record does not state whether this is an intention-to-treat, per-protocol or another analysis population. It also does not describe imputation, likelihood-based handling of missing outcomes, or sensitivity analyses.

In general, these details matter because missingness can be related to participants' outcomes or experiences. A method's ability to use incomplete records depends on assumptions about why values are missing. Those assumptions and the diagnostic or sensitivity work used to examine them are not reported in the registry record. The numerical re-calculation necessarily uses only the posted summary statistics and cannot recover participant-level information.

11. Confidence Intervals and Precision

The unadjusted mean difference is -1.0, with a confidence interval from -1.766 to -0.234. This interval shows that the estimated group difference is not a single perfectly known quantity. Values across the interval represent a range of estimates compatible with the posted summaries and the calculation's assumptions. The interval does not include zero, but this fact should be interpreted together with its unadjusted nature and the absence of a reported confidence interval for the sponsor's mixed-model analysis.

Precision is different from clinical importance. The interval describes statistical uncertainty in the estimated difference; it does not say whether a difference of a particular size matters to participants. The registry does not report a minimally important difference for the BPI-SF outcome. The scale ranges from 0 to 10, but that range alone does not define what size of change is meaningful.

The interval also does not describe how individual participants' changes were distributed. The standard deviations were 1.7 in the Therapy Group and 1.3 in the Standard of Care group. Those measures indicate variation around the group means, but they do not show the full distribution, identify subgroups, or establish how many participants improved or worsened.

The interval is a simple unadjusted re-calculation using the posted summary statistics. The sponsor's mixed-model point estimate is 1, with p = 0.014, but no interval is reported for that model result. The registry record does not explain the difference in sign conventions or supply the model details needed to derive a comparable interval. For that reason, the interval should be kept attached to the unadjusted estimate rather than presented as uncertainty around the sponsor's model-based estimate.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect, not the original trial's design calculation. The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect. The original trial's own sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed for an 80% chance of detecting the specified effect under those assumptions, if that effect and the statistical model assumptions were correct. The 90% column expresses the corresponding planning target for a 90% chance. These are design-planning concepts, not guarantees about what a future study will find.

The rows consider planning for 100%, 75% and 50% of the observed effect. Planning for a smaller effect requires more participants per arm, because a smaller group difference is harder to distinguish from random variation. For example, the primary-outcome illustration gives 36 participants per arm for 80% power when planning for 100% of the observed effect, and 144 participants per arm when planning for 50% of that effect. The 90% figures for those scenarios are 49 and 193 participants per arm, respectively.

These are not observed power calculations. They are prospective illustrations based on the observed effect and stated assumptions. They should not be interpreted as evidence that the completed trial had a particular probability of detecting its true effect. The registry does not report the original rationale for enrollment of 72 or whether the actual design used assumptions like those in the illustration.

13. 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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -1.000; pooled standard deviation σ = 1.513.
2. n = 2 × (1.96 + 0.842)² × 1.513² / -1.000² = 35.9, rounded up to 36 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
delta <- -1                      # observed difference in means
sigma <- 1.51327459504216                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(4468074)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 36 (80% power), 49 (90% power)
 75% of observed effect: n per arm = 64 (80% power), 86 (90% power)
 50% of observed effect: n per arm = 144 (80% power), 193 (90% power)
power.t.test: 36.9 
Simulated power at n = 36 per arm: 0.790 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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.

14. Analyses Reported by the Sponsor

The sponsor reports a Mixed Models Analysis for the primary outcome, with a net mean difference of 1 and p = 0.014. This is the registry's model-based analysis. Its confidence interval is not reported. The unadjusted re-calculation from the posted group summaries gives a mean difference of -1.0, a confidence interval from -1.766 to -0.234, and p = 0.01.

The estimates have equal absolute values but opposite signs. The registry does not explain the sign convention for the sponsor's net difference, so the sign difference cannot be interpreted as a substantive disagreement without further information. The posted arm means show changes of -1.5 and -0.5, while the simple re-calculation orders the comparison as Therapy Group relative to Standard of Care. The sponsor's model specification and contrast coding are not reported.

The two p-values are close but arise from different methods. The re-calculation is unadjusted and based only on summary statistics; the sponsor analysis is described as a mixed model. Because the registry record marks no discrepancy, the posted sponsor result remains the principal reported analysis, while the simple calculation is a transparent comparison from the group summaries. Neither result supplies the missing model details or an interval for the sponsor estimate.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study evaluates multiple outcomes, time points, contrasts or analyses. If each comparison is assessed separately without adjustment, the overall chance of at least one false-positive result may be higher than the chance attached to an individual test. Statistical plans can address this through prespecified outcome hierarchies, adjusted testing procedures or a clear distinction between confirmatory and exploratory analyses. The registry record does not report a multiplicity strategy for this trial.

The record lists 25 outcome measures and 3 analyses, and it posts a primary outcome and 2 secondary outcomes in the reported results. It does not explain how those measures map onto the analyses, which tests were planned as confirmatory, or whether the reported secondary p-values were adjusted. The unadjusted secondary results should therefore be interpreted cautiously. The registry record also does not report whether interim analyses were planned or conducted.

Missing-data handling is another important source of uncertainty. The enrollment figure is 72, while the primary outcome summaries list 30 participants per group. The record does not describe participant flow, the amount or pattern of missing outcome data, reasons for missingness, exclusions, or the analysis population. It does not state whether the analysis followed intention-to-treat principles, whether participants were analyzed as randomized, or whether imputation or other missing-data methods were used.

The sponsor's method is labeled Mixed Models Analysis, but the model specification and missing-data assumptions are not reported. Mixed models can use available repeated observations under particular assumptions, but the method label alone does not establish how missing data were handled or whether those assumptions were appropriate. No sensitivity analyses addressing missingness are reported in the registry record. These omissions limit independent assessment of how robust the estimates are to incomplete data and analysis choices.

16. 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 5% reporting threshold.

The registry reports zero serious adverse events among 31 participants at risk in the Therapy Group and zero among 30 participants at risk in the Standard of Care group. It also reports zero other adverse events in each group and zero deaths in each group. These are the recorded event counts and denominators for the safety information.

A zero count means that no event of the listed type was recorded in the relevant group during the registry's reported observation period. It does not establish that an event is impossible, nor does it establish that the groups have identical safety profiles. The figures are descriptive and do not provide a precise estimate of the frequency of uncommon events. The record does not provide further detail about event definitions, event collection procedures, severity classifications beyond serious versus other, or the duration of safety follow-up. The absence of reported events should therefore be read as a statement about the posted record, not as a general guarantee of safety.

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

The primary outcome summaries show a larger average decrease in BPI-SF pain intensity and interference in the Therapy Group than in the Standard of Care group over the 8-week timeframe. The unadjusted comparison estimates the mean difference as -1.0, with a confidence interval from -1.766 to -0.234. The sponsor's mixed-model analysis reports a net mean difference of 1 and p = 0.014, without a confidence interval. The record does not explain the different sign conventions.

These findings concern group averages on a specific self-reported scale at a specified time. They do not imply that every participant experienced a decrease, and they do not describe how long any change lasted beyond the reported measurement period. The registry does not provide a clinically important difference threshold, so the statistical estimates alone cannot establish the practical importance of the observed change.

The randomized comparison is the design feature that allows the study to assess differences between assigned groups, but the interpretation is constrained by what is not reported. The analysis population, participant flow, handling of missing outcomes, detailed mixed-model specification and multiplicity plan are not reported in the registry record. The outcome summaries include 30 participants per group, and the relationship of those denominators to enrollment of 72 is not explained.

The secondary outcomes show a broadly similar direction of change, but their unadjusted status and the absence of a reported multiplicity plan mean they should be viewed as supportive rather than definitive. The safety record reports no serious or other adverse events and no deaths in either group among those listed at risk; this does not rule out unrecorded or uncommon events.

Overall, the posted results quantify a between-group difference in average change during the trial's measured period. They do not establish an individual's likely response, clinical importance, durability, or broader effects beyond the outcomes and follow-up described.

18. Why This Trial Matters Statistically

This trial is statistically informative because it combines random assignment with a continuous, patient-reported primary outcome. The comparison focuses on change from pre-treatment to post-treatment, and the registry supplies both group means and measures of spread. These summaries make it possible to distinguish the estimated average difference from the variability among participants.

The comparison also illustrates why an estimate should be read alongside its uncertainty and analysis method. The simple re-calculation gives a mean difference of -1.0 and an interval from -1.766 to -0.234, while the sponsor reports a mixed-model net difference of 1 and p = 0.014. Understanding their different signs requires the model's contrast convention, which is not reported. The case therefore shows how a result can be difficult to compare across analyses when coding and model details are absent.

The trial also highlights the value of transparent reporting. Enrollment was 72, but the primary outcome summaries include 30 participants per group. Without participant flow and analysis-population details, readers cannot determine how the outcome denominators relate to enrollment or assess the implications of missing data. Likewise, several outcomes are listed, but the multiplicity plan is not reported, limiting the weight that can be placed on secondary p-values.

Finally, the planning illustrations demonstrate that sample-size requirements depend on the effect a future study aims to detect: a smaller target effect calls for more participants per arm under the stated assumptions. Those illustrations are distinct from the original design rationale, which is not reported. Together, these features make the study a useful example of how randomized comparisons, uncertainty, planning assumptions and reporting completeness all contribute to statistical interpretation.

19. 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 limitations specific to this trial affect interpretation of the posted results. The registry does not explain the participant flow from enrollment of 72 to the primary outcome summaries of 30 participants per group. It also does not state the analysis population, reasons for missing or excluded observations, or how missing data were handled. These gaps make it difficult to assess whether the outcome estimates represent all randomized participants or a subset.

The sponsor reports a mixed-model result, but the model specification, included measurements, covariates, contrast coding and assumptions are not reported. The sponsor's estimate has no confidence interval in the record. The unadjusted calculation provides an interval, but it is not a replacement for uncertainty around the mixed-model estimate. The registry also does not explain why the sponsor's estimate is positive while the simple comparison is negative.

The record lists many outcome measures and analyses but does not report a multiplicity strategy, confirmatory hierarchy or interim-analysis plan. This is especially relevant when interpreting secondary results. The masking description is limited to single masking, without identifying the masked parties or explaining how the procedure was implemented. The registry does not report a clinical-importance threshold for the primary or secondary scales, limiting interpretation of the magnitude in practical terms.

The outcome is self-reported and concerns change over the stated 8-week period. Longer-term effects are not established by these posted primary results. The record also does not provide detailed eligibility characteristics, baseline group summaries or a full account of concurrent treatments. These are reporting limitations; they do not establish that any particular bias occurred.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Virtual Reality Treatment for Adults With Chronic Back Pain — NCT04468074.
• Registry record last updated 2022-06-23; status last verified 2022-05.
• Results first posted 2022-06-23.
• 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.

23. Record Summary

The registry record describes a completed, randomized, single-masked, parallel-group study of virtual reality therapy for adults with chronic back pain, compared with a no-intervention Standard of Care group. Enrollment was 72, and the planned allocation was 1:1. The primary endpoint was change in BPI-SF pain intensity and interference from pre-treatment to post-treatment at 8 weeks.

The posted outcome summaries include 30 participants per group. The mean changes were -1.5 for the Therapy Group and -0.5 for the Standard of Care group. The unadjusted re-calculation gives a mean difference of -1.0, with a confidence interval from -1.766 to -0.234 and p = 0.01. The sponsor's mixed-model result reports a net mean difference of 1 and p = 0.014.

Two secondary outcomes are posted. Safety information reports zero serious adverse events, zero other adverse events and zero deaths in each group. Participant flow, analysis-population details, missing-data methods, model specifications and multiplicity procedures are not reported in the registry record.