The Effect of Chronic Nitrate Supplementation on Acute Mountain Sickness and Exercise Performance in Hypoxia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effect of Chronic Nitrate Supplementation on Acute Mountain Sickness and Exercise Performance in Hypoxia (NCT03101904), a randomized na study. The primary outcome is Acute Mountain Sickness (AMS-C) as Assessed by the Environmental Symptoms Questionnaire..

2. Clinical Question

3. Trial Design

The trial is registered as randomized, triple-masked, and crossover, with an enrollment of 23. A crossover design gives participants different study conditions in sequence, so each participant can contribute information under more than one condition. The registry lists the sequences as nitrate followed by placebo and placebo followed by nitrate. Random allocation describes how participants were assigned to sequence; masking describes concealment of treatment identity, although which parties were masked is not reported in the registry record.

The arm descriptions specify a daily nitrate-rich beetroot shot for six days and describe a minimum ten-day washout before the next condition. The placebo condition is a nitrate-depleted beetroot shot. The full details of both sequences are not completely stated in the registry record, so the complete period-by-period regimen cannot be reconstructed from it. The record identifies the intervention type as dietary supplementation and the study condition as hypoxia.

The primary outcome was assessed on the fifth day of supplementation during a six-hour exposure to hypoxia. Its posted treatment-group summaries each include 20 participants. The secondary outcome was time to exhaustion at 80% of hypoxic V̇O2max reserve, measured on the sixth day; its posted summaries each include 15 participants. Safety risk-group denominators are 23 for nitrate and 20 for placebo. These outcome-specific counts do not all match the overall enrollment. The reasons for the differing numbers, including missing outcomes or exclusions, are not reported in the registry record.

The trial status is completed. The registry gives a start of 2016-02 and a primary completion date of 2017-01-09. The trial's original sample-size justification, planned statistical model, and planned handling of sequence or period effects 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: 1. Participants completed a baseline demographics visit including the following assessments: * Age * Height * Body mass * Blood pressure * Haemoglobin * Normoxic VO2max (maximal exercise) test 2. Participants then completed a minimum 48 h wash out 3. Participants completed a hypoxic VO2max test at 14.1% O2

First Intervention (6 Days)

Wash Out (10 Days)

Reasons for not completing this period:

Second Intervention (6 Days)

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: Analysis population is different from overall number because it does not include the 3 participants that did not complete the study.

6. Primary Endpoint

The registry lists the primary outcome as Acute Mountain Sickness (AMS-C) as Assessed by the Environmental Symptoms Questionnaire., measured over Measured on the fifth day of supplementation with a six-hour exposure to hypoxia.

The primary endpoint is the Acute Cerebral Mountain Sickness score, abbreviated AMS-C, calculated from the 11-item Environmental Symptoms Questionnaire. Participants rate each item from zero to five; the ratings are multiplied by their factorial loadings and summed. The registry states that the resulting scale has a minimum value of 0 and a maximum value of 5, with higher scores indicating worse symptoms.

The measure is used to quantify acute mountain sickness symptoms during hypoxia. It is a continuous score, so the registry reports group means and standard errors, and the comparison is expressed as a mean difference. The primary measurement was taken on the fifth day of supplementation during a six-hour exposure to hypoxia. The posted means are 0.36 for nitrate and 0.21 for placebo, with 20 participants in each outcome group. These summaries describe the observed score distributions; they do not by themselves establish whether a difference is clinically important. The registry record does not report a threshold for a meaningful difference or a clinical interpretation rule beyond the scale's direction.

7. Results Posted in the Registry

• Nitrate: mean 0.36 versus 0.21 on control; difference 0.15 (95% CI -0.04 to 0.34), standardized effect d = 0.48; z-test p = 0.128.

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.

Hypoxic Exercise Performance as Assessed by Time to Exhaustion at 80% of Hypoxic V̇O2max Reserve.

• 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:
  • Nitrate: mean 666.00 versus 656.00 on control; difference 10.00 (95% CI -129.78 to 149.78), standardized effect d = 0.05; z-test p = 0.888.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Nitrate and the control. The interval gives the range of effects that remain compatible with the data.

The registry posts one secondary endpoint: time to exhaustion during hypoxic exercise. Its estimate is a mean difference of 10.0 seconds, and its confidence interval ranges from -129.8 to 149.8 seconds. The interval includes zero and leaves considerable uncertainty about the direction and magnitude of a difference. This result does not provide a clear complementary signal to the primary symptom outcome.

Only one secondary endpoint is listed, so the posted results do not allow a broad assessment of whether different secondary measures tell a consistent story. The secondary measurement is related to the trial's exercise-performance aim, while the primary AMS-C score addresses symptoms. They measure distinct outcomes and use different units, so agreement or disagreement between their estimates would not by itself establish a common treatment effect.

Secondary findings generally carry less weight than a prespecified primary result because they may be less central to the study question and may be more vulnerable to selective emphasis or multiple testing. The registry lists no reported analyses and does not report a multiplicity plan, so it is not possible to determine how the secondary result fit into the original analysis strategy. Its unadjusted p-value should not be treated as an independent confirmation or as a definitive null finding.

The secondary outcome summaries include 15 participants per condition, fewer than the primary outcome summaries. The registry does not explain the difference in outcome counts or report how missing observations were handled. That limits interpretation of the secondary result, especially when considering whether it can be directly compared with the primary endpoint. Taken together, the secondary result adds context about the exercise-performance question but does not settle the uncertainty in the primary result.

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

• Hypoxic Exercise Performance as Assessed by Time to Exhaustion at 80% of Hypoxic V̇O2max Reserve.

9. Statistical Interpretation

10. Statistical Methods Explained

The outcome is continuous, and the registry reports means with standard errors for the primary endpoint. The comparison is a mean difference: the nitrate mean minus the placebo mean. The reported estimate is 0.15. A positive value means the observed mean score was higher in the nitrate condition than in the placebo condition; for AMS-C, higher scores indicate worse symptoms. This direction describes the scale, not a medical conclusion.

What does a standard error describe?

A standard error describes the uncertainty in an estimated mean due to sampling variability. It is not the spread of individual scores. The primary outcome standard errors are 0.09 for nitrate and 0.04 for placebo. In contrast, the secondary outcome is reported with standard deviations, which describe the spread of participant values around the mean. Its standard deviations are 206.0 seconds for nitrate and 184.0 seconds for placebo. Standard errors and standard deviations answer different questions and should not be interchanged.

How should the confidence interval be read?

A confidence interval gives a range of values that are reasonably compatible with the data under the method used to calculate it. The primary mean-difference interval runs from -0.043 to 0.343. The interval crosses zero, the value corresponding to no mean difference. This means the posted estimate does not distinguish clearly between a lower mean under nitrate, no difference, or a higher mean under nitrate. The interval does not assign a probability to a particular true value, and it does not indicate whether any value is clinically important.

What does the p-value add?

The unadjusted p-value for the primary comparison is 0.128. In general, a p-value measures how unusual data at least as discrepant as those observed would be under a specified null model. It is not the probability that the null hypothesis is true, nor is it a measure of treatment importance. Because the registry lists no reported analysis and does not describe the model behind a sponsor analysis, this p-value should be interpreted as an unadjusted summary rather than as a complete account of the trial's planned inference.

The secondary unadjusted p-value is 0.888. It accompanies an estimate and interval that also remain compatible with no mean difference. A high p-value is not evidence that the conditions are identical. It can reflect an estimate near zero, substantial variability, limited information, or a combination of these. The registry results alone do not identify which factor most accounts for the uncertainty.

Why does crossover structure matter?

In a crossover trial, outcomes from the same participant under different conditions are related. A paired analysis can use that within-participant relationship and may differ from a comparison that treats the condition summaries as independent groups. Period and sequence can also matter if outcomes vary over time or if the order of conditions affects measurements. The registry identifies the design as crossover and provides treatment sequences, but it does not report the analysis model, participant-level paired data, or adjustments for period, sequence, or carryover. The comparisons presented from group summaries are therefore unadjusted re-calculations, not a substitute for a documented crossover analysis.

Standard errors in the primary summaries and standard deviations in the secondary summaries are the reported dispersion measures. The mean differences and confidence intervals are useful for seeing the direction and precision of the posted comparisons, but their assumptions may not reflect the original design. The registry record does not report details such as transformations, outlier handling, missing-data methods, or the population used for the original efficacy analysis.

What is over-dispersion?

In general, over-dispersion occurs when observed variability exceeds what a statistical model assumes. When that happens, standard errors can be too small if the extra variation is ignored, making intervals too narrow and tests too optimistic. The posted continuous outcomes use mean-based summaries; the record does not report a model or an over-dispersion assessment. This concept is relevant as a general modeling issue, but there is no basis in the registry record to state that over-dispersion occurred in this trial.

Multiplicity is another general concern when several outcomes or analyses are examined. Testing multiple hypotheses can increase the chance that at least one result appears notable by chance. The registry posts one secondary outcome and no reported analysis list. It does not report a multiplicity strategy or clarify whether additional analyses were conducted. The unadjusted results should therefore be read with that uncertainty in mind, without assuming an adjustment was or was not used in the original work.

11. Confidence Intervals and Precision

Precision is reflected in the width of a confidence interval: narrower intervals indicate a more constrained range of estimates, while wider intervals leave more uncertainty. The primary mean-difference estimate is 0.15, with a 95% confidence interval from -0.043 to 0.343. The interval includes zero and extends in both directions from the point estimate. As a result, the posted primary data do not pin down the direction or size of the underlying mean difference with high precision.

The primary endpoint means are reported with standard errors of 0.09 for nitrate and 0.04 for placebo, and each condition has 20 outcome observations. Those standard errors describe uncertainty around the group means, not the range of individual participant scores. A crossover analysis could use the within-participant relationship between condition measurements, but the registry does not provide the paired data or the model details needed to assess how that would change precision.

For the secondary endpoint, the mean difference is 10.0 seconds and the 95% confidence interval ranges from -129.8 to 149.8 seconds. This wide interval permits substantially different underlying differences, including values on either side of zero. The secondary summaries include 15 participants per condition and use standard deviations rather than standard errors. The interval is more informative about uncertainty than the point estimate alone, but it does not determine clinical importance.

Confidence intervals quantify sampling uncertainty under their calculation method; they do not account automatically for every design limitation, missing outcome, or analysis choice. The registry does not report the original inferential model, missing-data approach, or a clinically important difference threshold. Precision should therefore be understood in relation to the posted summaries, rather than as a complete account of all uncertainty in the trial.

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 sample-size figures are planning illustrations based on the observed effect, not the trial's own original design calculation. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers detecting a stated fraction of the observed effect: 100% of the observed effect, 75% of the observed effect, or 50% of the observed effect. For these continuous outcomes, the displayed figures are participants per arm, not total event counts.

The 80% power column gives the planned number of participants per arm for an illustrative design with an 80% chance of detecting the specified effect under the listed assumptions, if that effect is real and the assumptions hold. The 90% power column gives the corresponding per-arm planning count for a design with a 90% chance under those same assumptions. These columns are prospective planning quantities; they do not describe the probability that the completed trial's findings are correct.

The rows illustrate that planning for a smaller effect requires more participants per arm. For the primary outcome, the 100% row lists 68 participants per arm for 80% power and 91 for 90% power; the 50% row lists 271 and 363, respectively. For the secondary outcome, the corresponding 100% row lists 5,989 and 8,017 participants per arm, while the 50% row lists 23,953 and 32,066. The secondary planning figures are especially sensitive to the small observed mean difference relative to its variability.

These figures are not observed power. They are hypothetical planning calculations using the observed effect as an input. Since an observed effect can be unstable, particularly in a small study, the illustrations should not be treated as evidence that the trial was adequately or inadequately designed. The original sample-size assumptions and justification are not reported in the registry record.

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 = 0.150; pooled standard deviation σ = 0.311.
2. n = 2 × (1.96 + 0.842)² × 0.311² / 0.150² = 67.7, rounded up to 68 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 <- 0.15                      # observed difference in means
sigma <- 0.311448230047949                     # 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(3101904)
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 = 68 (80% power), 91 (90% power)
 75% of observed effect: n per arm = 121 (80% power), 162 (90% power)
 50% of observed effect: n per arm = 271 (80% power), 363 (90% power)
power.t.test: 68.6 
Simulated power at n = 68 per arm: 0.798 (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. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary endpoint and one secondary endpoint. It does not report a multiplicity adjustment or a hierarchy for interpreting outcomes. In general, when several outcomes or analyses are examined, the chance of a nominally notable result can rise unless the analysis plan accounts for that process. This is a reason to treat unadjusted secondary findings cautiously, not evidence that a particular adjustment was omitted in the actual study.

The registry record lists no reported analyses. It also does not report a prespecified statistical analysis plan, the exact model used, the definition of the analysis population, or whether analyses were intention-to-treat, per-protocol, or based on another population. The primary and secondary summaries have different participant counts, but the reasons for those differences are not reported in the registry record.

Missing-data methods are not reported in the registry record. It is not stated whether any outcome measurements were missing, how any missing values were handled, or whether sensitivity analyses were conducted. In a crossover trial, interpretation can also depend on the availability of paired observations and on treatment sequence and period. The registry does not report how those issues were handled, whether washout adequacy was assessed, or whether carryover was considered in the analysis.

The record identifies the trial as triple-masked, but does not say which roles were masked or how masking was maintained and assessed. It does not describe interim analyses, stopping rules, covariate adjustment, model diagnostics, or subgroup analyses. The absence of these details in the registry record is not proof that they were absent from the complete study documentation. It means the posted record cannot establish how they were planned or applied.

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.

Most frequent non-serious adverse event terms

The serious adverse event figures show zero affected participants in both recorded groups, and the death count is zero in both. The risk-group denominators are 23 for nitrate and 20 for placebo. For other adverse events, one participant is recorded as affected in the nitrate group, with none in the placebo group. The record does not provide a serious-event term because no serious events are listed.

These counts describe the registry safety entries, not a complete characterization of all possible harms. The denominator difference between groups and the crossover design mean the entries should not automatically be interpreted as independent parallel-group rates. The registry does not report event descriptions for the one other adverse event, its timing, severity, or relationship to supplementation. It also does not report whether there were additional safety assessments beyond the posted entries. With the recorded counts alone, the frequency and nature of adverse effects remain limited in detail.

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

The posted primary result is a mean AMS-C difference of 0.15, with a 95% confidence interval from -0.043 to 0.343. The point estimate places the mean score higher under nitrate than placebo, and the scale defines higher scores as worse symptoms. However, the interval includes zero and spans values in both directions. The record therefore does not establish a precise difference in the primary outcome.

The secondary exercise-performance estimate is also uncertain: its mean difference is 10.0 seconds, with a 95% confidence interval from -129.8 to 149.8 seconds. The estimate alone should not be used to claim that one condition improved or reduced performance. Neither result establishes that the conditions are equivalent. Demonstrating equivalence would require an appropriate design and a prespecified equivalence margin, neither of which is reported in the registry record.

These data do not answer whether a difference is clinically important. The registry gives the AMS-C score range and direction but does not report a threshold for a meaningful change. It also does not report a clinical interpretation threshold for the exercise outcome. Statistical uncertainty and clinical importance are separate questions: a numerical difference can be statistically uncertain, and a statistically clear difference would still need a clinical context.

The posted summaries are limited by their outcome-specific participant counts, the absence of a reported analysis model, and the lack of detail on missing outcomes and crossover handling. The registry's enrollment of 23 does not mean that every outcome summary contains 23 observations. Since the original statistical plan and analysis populations are not reported, these results should be read as registry summaries rather than as a full assessment of the trial's intended inference.

Accordingly, the result is evidence about the estimates and uncertainty recorded for this trial, not a general conclusion about beetroot supplementation in other populations or settings. It does not establish a benefit, lack of benefit, safety, or harm. The record is most informative as a small crossover study with imprecise posted outcome comparisons and limited statistical documentation.

17. Why This Trial Matters Statistically

This trial is statistically instructive because it combines a crossover design with continuous outcomes and registry-posted group summaries. In a crossover study, the same participant can contribute measurements under different conditions. That structure creates paired information, which may be important for estimating a treatment contrast. Group means and dispersion summaries do not preserve the participant-level pairing needed to assess that contribution directly.

The primary result also illustrates why estimates and confidence intervals are more informative than a p-value alone. The point estimate has a direction, but its interval includes zero and covers a range of possible differences. The unadjusted p-value does not show whether an effect is clinically meaningful and does not resolve the uncertainty in the interval.

Differences in outcome counts are another important feature. The primary summaries include 20 participants per condition, the secondary summaries include 15 per condition, and safety denominators differ by group. Without an account of missing outcomes or analysis populations, readers cannot tell why these counts differ or how that may affect inference.

Finally, the planning illustrations show how strongly sample-size requirements depend on the assumed effect. Smaller target effects require more participants per arm in the stated planning framework. These are not the trial's original design assumptions, which are not reported in the registry record, and they do not determine whether the study was successful. The case highlights the need to distinguish planning calculations, observed estimates, and prespecified trial analyses.

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.

Several limitations are specific to interpreting this registry record. The trial is identified as a randomized, triple-masked crossover study, but the identities of masked parties and the statistical handling of the crossover structure are not reported. The record gives treatment sequence labels and describes a washout, but does not fully document the complete regimen for both periods or report whether period, sequence, or carryover effects were assessed.

The primary outcome summaries include 20 participants per condition, while overall enrollment is 23. The secondary summaries include 15 per condition, and safety denominators are 23 for nitrate and 20 for placebo. The reasons for these different counts, the presence or extent of missing outcomes, and the handling of incomplete crossover data are not reported in the registry record.

No reported analyses are listed. The registry does not identify the original analysis population, model, covariates, missing-data methods, multiplicity strategy, interim analyses, or sample-size justification. As a result, the unadjusted comparisons cannot be confirmed as reproductions of the trial's prespecified analysis. The record also provides no clinical importance threshold for either outcome.

The study is registered for hypoxia, with outcomes measured during a specified hypoxia exposure and exercise test. The results therefore address those recorded settings and measures; the registry does not establish how well they generalize beyond them. The small outcome counts and wide intervals leave substantial uncertainty, particularly for the secondary outcome. These limitations constrain what can be inferred from the posted data without implying that unreported methods were necessarily absent from the complete study records.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: The Effect of Chronic Nitrate Supplementation on Acute Mountain Sickness and Exercise Performance in Hypoxia — NCT03101904.
• Registry record last updated 2025-02-26; status last verified 2025-02.
• Results first posted 2025-02-26.
• 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

NCT03101904 is a completed randomized, triple-masked crossover trial sponsored by Bangor University, with enrollment of 23. It compared nitrate-rich beetroot juice with nitrate-depleted beetroot placebo in the context of hypoxia. The primary endpoint was AMS-C score measured on the fifth day during a six-hour hypoxia exposure. The secondary endpoint was time to exhaustion during hypoxic exercise, measured on the sixth day.

The primary mean difference was 0.15, with a 95% confidence interval from -0.043 to 0.343 and an unadjusted p-value of 0.128. The secondary mean difference was 10.0 seconds, with a 95% confidence interval from -129.8 to 149.8 seconds and an unadjusted p-value of 0.888. Both intervals include zero. The registry lists no reported analyses and does not report the original statistical plan, missing-data methods, or sample-size justification. The posted outcomes therefore offer uncertain estimates rather than a definitive conclusion about the treatment conditions.