Biological Signatures, Probiotic Among Those With mTBI and PTSD: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Biological Signatures, Probiotic Among Those With mTBI and PTSD (NCT02723344), a randomized phase 1 study. The primary outcome is C-Reactive Protein Change.

2. Clinical Question

3. Trial Design

The registry describes a randomized, quadruple-masked, parallel-group phase 1 trial. It lists an enrollment of 75 and a completed status. The study start date is 2016-08-01, and the primary completion date is 2019-05-31. The sponsor is the VA Office of Research and Development.

The intervention was L. reuteri, identified in the record as DSM 17938. The comparator was sunflower and medium chain triglyceride oils. The registry’s stated focus was the biological signature and safety of an immunomodulatory probiotic intervention for Veterans with co-occurring mTBI and PTSD. Its summary describes interest in inflammatory processes and in measures involving gut microbiota, gut permeability, and peripheral inflammation.

The primary outcome was change in CRP from baseline to approximately 10 weeks. It is a continuous measure reported as a mean with standard deviation. The posted group summaries include 14 participants in the placebo arm and 10 in the L. reuteri arm for this outcome. These outcome-specific counts are not the same as the overall enrollment figure. The registry notes that plasma was unavailable to run CRP for one participant in the placebo group and two participants in the L. reuteri group.

Randomization is intended to allocate participants to study groups by chance, while masking is intended to limit the influence of knowledge of assignment. The registry record does not report the detailed allocation procedure, the identities of the masked parties, or the original sample-size justification. These details should not be inferred from the design labels.

4. Participant Flow and Accounting

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

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: A sufficient amount of plasma was not available to run CRP on 1 participant in the placebo group and 2 participants in the L reuteri group.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: Prior to randomization

6. Primary Endpoint

The registry lists the primary outcome as C-Reactive Protein Change, measured over Baseline and approximately 10 weeks.

The primary endpoint is mean change in C-reactive protein (CRP), measured in mg/L, from baseline to approximately 10 weeks. CRP is a blood biomarker used as an indicator related to inflammation. In this trial, it represents a biological signature rather than a direct measure of PTSD or mTBI symptoms, functioning, or quality of life. The registry’s summary frames the study around investigating inflammatory signatures in people with co-occurring mTBI and PTSD.

Change from baseline expresses how the measure differs at follow-up relative to its starting value. A group mean summarizes the average change among participants with available CRP results; the standard deviation describes variability among those individual changes. A comparison of group means estimates the difference in average change between the intervention and placebo groups.

As a general statistical point, selecting a biomarker can help describe a biological process of interest, but a change in a biomarker does not automatically establish a change in symptoms or other clinical outcomes. The registry lists Tumor Necrosis Factor Change as a secondary outcome, but the primary endpoint is CRP change. The record does not report further detail about the CRP assay or the precise follow-up visit schedule beyond “approximately 10 weeks.”

7. Results Posted in the Registry

• L Reuteri: mean -0.62 versus 0.11 on control; difference -0.74 (95% CI -1.67 to 0.19), standardized effect d = -0.64; z-test p = 0.119.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each participant has a CRP change value, and the posted results summarize those values using means and standard deviations. A mean describes the average change in a group. A standard deviation describes how spread out individual changes are around that group mean. These answer different questions: the mean concerns the average direction and size of change, while the standard deviation concerns participant-to-participant variation.

What does the mean difference represent?

The unadjusted mean difference compares the two group means by subtracting the placebo mean from the L. reuteri mean. The posted means are 0.113 mg/L for placebo and -0.625 mg/L for L. reuteri, and the recalculated difference is -0.738 mg/L. A negative value means that the intervention group’s average change is lower than the placebo group’s average change on the recorded scale. It does not, on its own, describe symptom benefit or establish why the groups differed.

This recalculation uses the posted summary statistics and is unadjusted. It is not necessarily identical to an analysis using participant-level data, covariate adjustment, or a different statistical estimand. The registry record does not report an adjusted mean-difference estimate for this endpoint.

Why report variability?

The standard deviations are 1.2 mg/L in the placebo group and 1.1 mg/L in the L. reuteri group. They describe spread in observed CRP changes rather than uncertainty in the group means. General statistical explanation: when participant outcomes vary substantially, an average may be less precisely estimated unless there is enough information to characterize that variation. The standard deviations also help readers assess how the group averages sit within the observed variability.

What does a confidence interval add?

A confidence interval gives a range of estimates compatible with the observed data under the assumptions of the calculation. General statistical explanation: a wider interval indicates less precision, while an interval that includes zero for a difference does not rule out no difference at the confidence level used. The recalculated interval has a lower endpoint of -1.665 mg/L and extends to a positive upper endpoint, so it includes zero. The registry does not report an interval for its Wilcoxon analysis.

What does the Wilcoxon analysis test?

The registry reports a Wilcoxon rank-sum analysis for the two groups, with p-value .056. General statistical explanation: a rank-sum procedure orders observations and compares their ranks across groups. It is not the same calculation as a test of the difference between means, and its result need not match a mean-based analysis. The registry record does not report the rank-based effect estimate, its confidence interval, or additional details about how that analysis was implemented.

How should a p-value be read?

General statistical explanation: a p-value describes how unusual data at least as incompatible with a specified null model would be if that model and the test assumptions held. It does not give the probability that a treatment has an effect, and it does not measure the size or importance of a difference. The unadjusted recalculated p-value is 0.119; the registry’s rank-sum p-value is .056. They come from different analyses and should not be conflated.

Why can over-dispersion matter?

General statistical explanation: over-dispersion refers to more variability in outcomes than a statistical model expects. When a model understates variability, standard errors can be too small and intervals can appear more precise than warranted. The posted endpoint is continuous and is summarized with standard deviations; the registry record does not report a model-based analysis or a finding of over-dispersion. This concept is therefore relevant as a general reminder about matching methods to data, not as a claimed feature of this trial.

10. Confidence Intervals and Precision

The unadjusted mean-difference estimate is -0.738 mg/L. Its recalculated confidence interval has a lower endpoint of -1.665 mg/L and an upper endpoint above zero. The interval therefore includes zero and allows both negative and positive values for the difference. This range conveys substantial uncertainty about the direction and size of the mean difference; the estimate alone should not be treated as precise.

General statistical explanation: a confidence interval reflects both the observed data and the assumptions used to calculate it. It is not a guarantee that the true value lies within the interval, nor does it show the range of individual participant outcomes. The standard deviations of 1.2 mg/L for placebo and 1.1 mg/L for L. reuteri describe variation in participant changes; they are not confidence limits for the mean difference.

The primary outcome summaries are based on 14 participants in the placebo group and 10 in the L. reuteri group. The registry notes that plasma was not available for CRP testing for one participant in the placebo group and two participants in the L. reuteri group. The record does not report a missing-data method or whether the posted analysis used any adjustment for missing results.

The rank-sum analysis has a reported p-value of .056, but no effect estimate or confidence interval is reported for that analysis. A p-value alone does not show the range of effects compatible with the data. Taken together, the mean-difference estimate, its interval, outcome-specific group counts, and the distinct rank-based result should be considered as complementary information rather than as interchangeable summaries.

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 figures are participants per arm, not total events. They are illustrations based on the observed mean difference, not the original trial’s design calculation. The 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. The registry record does not report the trial’s own original sample-size assumptions or justification.

The 80% power column gives the illustrative 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 were correct. The 90% power column gives the corresponding per-arm planning figure for 90% power. These are design-planning concepts, not guarantees about a future study’s result.

Planning for 100% of the observed effect gives 39 participants per arm for 80% power and 52 for 90% power. Planning for 75% of the observed effect gives 69 participants per arm for 80% power and 93 for 90% power. Planning for 50% of the observed effect gives 156 participants per arm for 80% power and 208 for 90% power. A smaller effect requires more participants to detect under the same assumptions.

The accompanying curve represents this planning relationship across the stated effect fractions. These are planning illustrations, not observed power: observed data cannot establish the probability that the completed trial had to detect its own result.

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

Worked calculation for this trial

1. Observed difference Δ = -0.738; pooled standard deviation σ = 1.160.
2. n = 2 × (1.96 + 0.842)² × 1.160² / -0.738² = 38.8, rounded up to 39 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 <- -0.738                      # observed difference in means
sigma <- 1.16013322119017                     # 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(2723344)
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 = 39 (80% power), 52 (90% power)
 75% of observed effect: n per arm = 69 (80% power), 93 (90% power)
 50% of observed effect: n per arm = 156 (80% power), 208 (90% power)
power.t.test: 39.8 
Simulated power at n = 39 per arm: 0.788 (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.

13. Analyses Reported by the Sponsor

The registry’s own reported analysis is a Wilcoxon rank-sum test, with p-value .056. The mean-difference estimate of -0.738 mg/L, its confidence interval, and the unadjusted p-value of 0.119 are recalculations from the posted summary statistics. The recalculation compares group means; the reported Wilcoxon procedure compares ranks. They address the data using different statistical methods, so their p-values need not match.

The registry record does not report an effect estimate or confidence interval for the rank-sum analysis. That limits direct comparison of the size and precision of the sponsor-reported result with the recalculated mean difference. The registry record does not identify a discrepancy between the reported and recalculated analyses. The sponsor’s reported analysis should therefore be described on its own terms, while the recalculation is treated as a separate, unadjusted summary-statistic analysis.

Neither p-value should be interpreted as a probability that the intervention is beneficial or as a measure of clinical importance. The primary endpoint is a biomarker, and the record does not report a clinical-importance threshold for its change.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 8 outcome measures and 3 analyses, and one secondary outcome is posted: Tumor Necrosis Factor Change. The primary endpoint discussed is CRP change. Testing multiple outcomes or analyses can raise a multiplicity question: when many hypotheses are examined, the chance of at least one apparently unusual result can increase. General statistical explanation: methods such as prespecified outcome hierarchies or adjustments can address this issue, but the appropriate approach depends on the study’s design and analysis plan.

The registry record does not report whether multiplicity adjustments were planned or applied, how the primary outcome was prioritized relative to other outcomes, or whether the posted analyses were prespecified. It also does not report the detailed protocol or statistical analysis plan. The reported p-values should therefore be interpreted as the results of their stated analyses, without assuming a particular multiplicity strategy.

The record notes that plasma was unavailable for CRP testing for one participant in the placebo group and two participants in the L. reuteri group. It does not report how missing CRP values were handled analytically, whether additional outcome data were missing, or whether any imputation or sensitivity analysis was performed. The endpoint-specific summaries cover 14 placebo participants and 10 L. reuteri participants; the record does not describe the analysis population in further detail.

Although the trial is described as randomized, the registry record does not state whether the primary analysis followed an intention-to-treat principle, used another analysis population, or adjusted for baseline values or other covariates. It does not report interim analyses, stopping rules, or the original sample-size justification. These omissions do not establish that such procedures were absent; they mean that they are not reported in the registry record. Readers should avoid inferring unreported analysis decisions from the group summaries or the design description.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The registry lists zero serious adverse events in the placebo group, with 15 participants at risk, and zero serious adverse events in the L. reuteri group, with 16 participants at risk. It also lists zero other adverse events affecting participants in the placebo group, with 15 at risk, and zero in the L. reuteri group, with 16 at risk. Deaths are listed as zero in each group. No serious adverse-event terms are listed.

These figures describe what is recorded in the registry’s adverse-event results. They should not be expanded into a claim that no symptoms or health events occurred, because the displayed categories are serious adverse events and other adverse events affecting participants. The registry record does not report additional details about event definitions, collection procedures, observation time for safety, or the severity of events outside those categories.

The at-risk counts in the safety results differ from the outcome-specific CRP counts. Safety and biomarker results can have different denominators, and one should not treat either set of counts as interchangeable with the overall enrollment. Zero recorded events in these categories is a descriptive finding, not proof that an intervention is free of risk.

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

The primary result describes a comparison of mean CRP change from baseline to approximately 10 weeks in a randomized study of Veterans with co-occurring mTBI and PTSD. The posted mean changes were 0.113 mg/L for placebo and -0.625 mg/L for L. reuteri. The unadjusted mean difference was -0.738 mg/L, with a recalculated interval that includes zero. The registry separately reports a Wilcoxon rank-sum p-value of .056.

These statistics do not establish a difference between groups, and they do not establish that the groups are equivalent. The interval permits a range of possible mean differences, while the rank-based p-value comes from a distinct analysis. The CRP endpoint is a biomarker of inflammation, not a direct measure of PTSD or mTBI symptoms. The registry record does not report a threshold for interpreting the size of CRP change as clinically important.

The findings also do not establish an effect on other biological measures, symptoms, or longer-term outcomes. The registry identifies Tumor Necrosis Factor Change as a secondary outcome, but results for that outcome are not included in the registry record for this result. The registry summary discusses gut microbiota, gut permeability, and peripheral inflammatory biomarkers as areas of interest; the primary result is specifically CRP change.

General statistical explanation: a randomized design supports a comparative question, but an observed result remains subject to uncertainty from sampling variation and the analysis choices used. Here, CRP results were available for fewer participants than the registry’s overall enrollment, and the registry notes unavailable plasma for some participants. Missing-data handling and the primary analysis population are not reported in the registry record. The result is best understood as an imprecise estimate of a biomarker difference, not as a definitive account of clinical benefit or harm.

17. Why This Trial Matters Statistically

This trial illustrates why the statistical interpretation of a clinical study depends on the endpoint, the analysis method, and the precision of the estimate—not on a single p-value. The primary measure is CRP change, a continuous biomarker. Its group means and standard deviations describe average change and variability, while the mean difference gives a direct estimate of the contrast between the groups.

The registry also reports a rank-sum analysis. Because a rank-based test and a mean-based comparison do not summarize the data in the same way, their p-values answer related but distinct questions. Placing the reported p-value of .056 beside the recalculated mean difference and p-value of 0.119 makes the distinction between analysis methods important to the interpretation. Neither statistic should be treated as a measure of clinical importance.

The confidence interval is equally important: the recalculated interval crosses zero, so the posted summaries do not pin down the direction of the mean difference. This demonstrates how an estimated effect and its uncertainty should be read together. The safety results also require scope: zero events are recorded in the listed serious and other adverse-event categories, but that is not the same as proving there is no risk.

Finally, the registry’s documented missing CRP samples and unreported details about missing-data handling, multiplicity, and analysis populations limit how much can be concluded from summary results. These are practical issues in interpreting small early-phase studies, where a biomarker signal may be of interest but does not by itself answer a clinical question about symptoms or patient experience.

18. Limitations

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

The primary outcome summaries are based on 14 placebo participants and 10 L. reuteri participants. The registry notes unavailable plasma for CRP testing for one participant in the placebo group and two participants in the L. reuteri group. The reason those samples were unavailable is not reported in the registry record, nor is the method used to handle missing CRP results.

The recalculated mean difference is unadjusted and based on posted summary statistics. The registry’s own result is from a Wilcoxon rank-sum analysis, for which no effect estimate or confidence interval is reported. These distinct summaries do not provide a single shared estimate with complete precision information. The registry record does not report whether baseline CRP, other covariates, or an alternative analysis population was used in the sponsor’s analysis.

The primary outcome is a biomarker rather than a direct clinical outcome, and no clinically important threshold for CRP change is reported in the registry record. Results for the listed secondary outcome, Tumor Necrosis Factor Change, are not included in the registry record for this analysis. The record lists multiple outcomes and analyses but does not report a multiplicity strategy.

The overall enrollment is 75, but the registry record does not provide the trial’s original sample-size justification or enough information to explain the difference between enrollment and the endpoint-specific counts. Detailed recruitment criteria, baseline characteristics, allocation procedures, masking roles, protocol deviations, and the analysis plan are not reported in the registry record. These omissions constrain assessment of generalizability and analytic choices. They should be treated as limits on what can be concluded from the registry record, not as evidence that any particular procedure was or was not used.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Biological Signatures, Probiotic Among Those With mTBI and PTSD — NCT02723344.
• Registry record last updated 2020-08-18; status last verified 2020-08.
• Results first posted 2020-07-28.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT02723344 is a completed, randomized, quadruple-masked, parallel-group phase 1 trial sponsored by the VA Office of Research and Development. The registry lists an enrollment of 75, a start date of 2016-08-01, and a primary completion date of 2019-05-31. The study concerns Veterans with co-occurring mTBI and PTSD and compares L. reuteri with sunflower and medium chain triglyceride oils.

The primary endpoint is mean CRP change in mg/L from baseline to approximately 10 weeks. Posted means are 0.113 mg/L for placebo and -0.625 mg/L for L. reuteri. The unadjusted recalculated mean difference is -0.738 mg/L, with an interval that includes zero; the registry reports a Wilcoxon rank-sum p-value of .056. CRP plasma was unavailable for some participants, and the record does not report the missing-data method, multiplicity approach, or original sample-size justification.