Prevention of Altitude Illness With Non-steroidal Anti-inflammatory Study (PAINS): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Prevention of Altitude Illness With Non-steroidal Anti-inflammatory Study (PAINS) (NCT01171794), a randomized phase 3 study. The primary outcome is Acute Mountain Sickness.

2. Clinical Question

3. Trial Design

This was a Phase 3, randomized, triple-masked, parallel-group study sponsored by Stanford University. Participants were assigned to ibuprofen or placebo. In the registry’s arm descriptions, ibuprofen was listed as 600mg three times daily, and the placebo was described as visually identical. The parallel design means the two groups were followed as separate arms rather than participants crossing between treatments. The registry record does not identify which parties were included in the triple masking.

The study concerned altitude illness in healthy adults who indicated interest in participating, learning about altitude illness, and hiking Barcroft Peak. The registry summary says researchers hoped to enroll about 100 participants; the recorded enrollment was 89. Enrollment and the analyzed outcome counts are distinct figures: the primary outcome lists 44 participants in the ibuprofen arm and 42 in the placebo arm. The record does not explain the difference between total enrollment and those outcome denominators.

The primary outcome was acute mountain sickness over 2 days. Its definition used Lake Louise Criteria scores, ranging from 0 to 15, with higher scores representing more severe symptoms. A score of 3 or greater and the presence of a headache together constituted a positive diagnosis. The primary outcome population is described as participants meeting all inclusion criteria. Details of the inclusion criteria are not reported in the registry record.

The study status is completed. The record lists two outcome measures, but it does not post secondary results. It lists zero analyses, and the original statistical plan, sample-size justification, allocation concealment procedures, and interim analysis plans are not reported in the registry record. The record also does not provide enough detail to reconstruct how participants moved from enrollment through analysis.

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

Analysis population for the primary outcome, as defined in the registry: Participants meeting all inclusion criteria were analyzed

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: Participants meeting all inclusion criteria were analyzed

6. Primary Endpoint

The registry lists the primary outcome as Acute Mountain Sickness, measured over 2 days.

The primary endpoint counts participants who met the registry definition of acute mountain sickness during 2 days. The definition combines a symptom score with a specific symptom requirement: Lake Louise Criteria scores range from 0 to 15, and a score of 3 or greater was considered a positive diagnosis only when headache was also present. The scale is described as assigning higher scores to more severe symptoms.

A binary endpoint reduces each participant’s outcome to whether the diagnostic threshold was met or not met. This makes it possible to compare the number of participants with an event in the ibuprofen and placebo arms. The posted results give both the number meeting the endpoint and the number of participants in each arm. The outcome is not a continuous measure of symptom severity, so these counts do not describe how far participants’ scores were above or below the threshold, or how severe symptoms were among those who met it.

Using a stated diagnostic definition helps make clear what the event count represents. It also means interpretation depends on the chosen score threshold and headache requirement. The registry record does not report additional validation details or explain why this threshold was selected. The endpoint addresses acute mountain sickness under this particular definition and timeframe; it does not by itself address other forms of altitude illness or outcomes beyond the stated 2 days.

7. Results Posted in the Registry

• Ibuprofen: 43.2% (19/44) versus 61.9% (26/42) on control; risk difference -18.7 percentage points (95% CI -39.5 to 2.0), risk ratio 0.70 (0.46–1.05); unadjusted two-proportion z-test p = 0.082.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: each participant either met the acute mountain sickness definition or did not. For this type of endpoint, the observed event count is interpreted in relation to the number of participants in the arm. The ibuprofen arm reports 19 events among 44 participants, and the placebo arm reports 26 among 42 participants. Comparing counts without their denominators can be misleading when arm sizes differ, so a comparative measure such as a risk difference expresses the contrast in event proportions.

What does the risk difference describe?

A risk difference subtracts one arm’s event proportion from the other’s. In the posted unadjusted recalculation, the comparison is framed as ibuprofen relative to placebo, and the estimate is negative. A negative value in that framing corresponds to a lower observed event proportion in the ibuprofen arm. It is a description of the sample contrast, not by itself proof of a treatment effect. The registry record does not report an adjusted analysis, so the recalculated comparison should be understood as unadjusted.

How should the p-value be read?

The unadjusted p-value is 0.082. In general, a p-value measures how compatible the observed data are with a specified null hypothesis under a statistical model. Smaller values indicate data less compatible with that null model, but a p-value does not measure effect size, clinical importance, or the probability that the null hypothesis is true. The value does not by itself answer whether the effect is large enough to matter. The record does not report the planned analysis method or its decision threshold, so the p-value should be read as a statistical summary of the posted comparison rather than confirmation of the original protocol’s analysis.

Why consider confidence intervals?

A confidence interval gives a range of values consistent with the data under the calculation method. It communicates precision and includes information about uncertainty that a single point estimate does not. The interval for this comparison spans the no-difference value and possible effects on either side. This means the data do not pin down a single direction with high precision. A confidence interval is not a guarantee that the true value lies in that particular interval, and its interpretation depends on the underlying method and assumptions.

What does a binary outcome leave out?

The diagnostic threshold turns a symptom score into an event count. That makes the primary comparison straightforward to describe, but it discards detail about scores and symptom severity. Two participants counted as events may have different scores, and participants who do not meet the threshold may still have symptoms. The record reports the scoring range, the higher-score meaning, and the event rule, but it does not post individual scores or a separate analysis of severity.

What can be said about the analysis population?

The primary outcome description says participants meeting all inclusion criteria were analyzed. That is the extent of the population information in the registry record. It does not specify whether the analysis followed randomized assignment regardless of adherence, how participants with missing outcome data were handled, or whether any participants were excluded after randomization. The record also lists zero analyses, so it does not provide a detailed sponsor analysis or enough information to establish that the recalculation matches a prespecified plan.

Why can over-dispersion matter in other settings?

General statistical explanation: over-dispersion occurs when observed variability exceeds what a statistical model assumes. It can lead to uncertainty estimates that are too narrow if the model is not adapted. The posted endpoint is a participant-level binary count, and the registry record does not report an over-dispersion analysis or identify this as a concern. No claim about over-dispersion in this trial is warranted from the available record. The general concept matters when choosing methods for outcomes whose variability may not match a model’s assumptions.

The comparison shown is a simple unadjusted recalculation from the posted summary counts. Other choices—such as adjustment for baseline characteristics, alternate models, or different missing-data assumptions—could produce different estimates, but the registry record does not report such analyses. Accordingly, the numerical comparison is best read alongside the counts, confidence interval, and limitations of the record rather than as a complete statistical analysis.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate the comparative effect. The posted confidence interval for the risk difference includes the no-difference value and extends to both negative and positive values. In plain terms, the observed data do not rule out no difference, and they also allow a range of possible effects in either direction. The interval therefore gives a more cautious account than the point estimate alone.

The width of a confidence interval reflects both the amount of information in the data and the variability expected under the analysis. Here, the primary outcome denominators are 44 in the ibuprofen arm and 42 in the placebo arm. The event counts are 19 and 26, respectively. These counts provide the basis for the posted comparison, but the record does not include additional participant-level information that could clarify how much the estimate might shift under adjustment or alternative assumptions.

A confidence interval is not an equivalence test. Since the interval includes no difference, the results do not establish that the arms are the same; nor does the interval establish a benefit in either direction. The p-value of 0.082 is consistent with the interval’s indication of uncertainty, but neither summary should be interpreted as a probability that a particular treatment effect is true.

The registry record does not state the confidence level or the method used for the original trial analysis. The interval belongs to the unadjusted recalculation of the posted summary data. It is therefore useful for understanding the precision of that comparison, while not resolving uncertainty about the planned analysis, missing data, or the wider population to which the result may apply.

11. Planning a Similar Trial: Sample Size

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

The sample-size planning figures are participants per arm, not total events. They are illustrations computed from the observed effect, rather than a report of the trial’s original design calculation. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set in turn to 100%, 75%, or 50% of the observed effect.

For planning for 100% of the observed effect, the estimates are 111 participants per arm for 80% power and 148 participants per arm for 90% power. For planning for 75% of the observed effect, the estimates are 196 participants per arm for 80% power and 262 participants per arm for 90% power. For planning for 50% of the observed effect, the estimates are 438 participants per arm for 80% power and 585 participants per arm for 90% power.

In general, 80% power means that a study designed under the stated assumptions would have an 80% chance of detecting the specified effect if that effect were the true one. The 90% column uses the corresponding 90% chance. These are planning concepts, not guarantees about a particular study’s result. The figures are not observed power.

The sample-size curve should be read as a visual representation of the same relationship: planning to detect a smaller effect requires more participants. The calculations depend on the observed effect used as their starting point, so they are not independent evidence that the effect is reliable. The registry’s original sample-size assumptions and justification are not reported in the registry record.

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 = 0.619; treatment proportion p₁ = 0.432; average p̄ = 0.525.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7062 = 1.3841.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6937 = 0.5838.
4. n = (1.3841 + 0.5838)² / (-0.1872)² = 110.5, rounded up to 111 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 <- 0.619047619047619                          # control proportion
p1 <- 0.431818181818182                          # 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(1171794)
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 = 111 (80% power), 148 (90% power)
 75% of observed effect: n per arm = 196 (80% power), 262 (90% power)
 50% of observed effect: n per arm = 438 (80% power), 585 (90% power)
power.prop.test: 110.5 
Simulated power at n = 111 per arm: 0.803 (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 lists two outcome measures, but it posts no secondary outcome results. It also lists zero analyses. The available information therefore does not show how many outcomes or comparisons were included in a planned statistical testing strategy, whether any outcomes were designated as secondary in a detailed protocol, or whether any adjustment for multiple comparisons was planned or performed.

Multiplicity arises when several hypotheses are tested. In general, conducting more tests creates more opportunities for a result to appear statistically notable by chance. Methods to address this can include prespecifying a primary outcome, adjusting thresholds, or organizing tests in a hierarchy. These are general methods; the registry record does not state which, if any, were used in this study. The single posted primary comparison should not be taken as proof that no other analyses occurred, nor should unposted analyses be assumed.

The primary outcome population is described as participants meeting all inclusion criteria. This does not specify the handling of participants who were randomized but did not meet those criteria, nor whether every randomized participant had an available outcome. The outcome denominators are 44 for ibuprofen and 42 for placebo, while total enrollment is 89. The record does not explain the relationship among these figures or identify reasons for any participants not appearing in the primary outcome counts.

Missing-data methods are not reported in the registry record. It is not stated whether missing outcomes were excluded, imputed, or handled under another approach. The record also does not say whether the primary analysis was intention-to-treat, per-protocol, or another analysis population. Those details matter because exclusions and missing outcomes can affect the estimate and its uncertainty. The posted comparison is consequently best treated as an unadjusted description based on the available summary counts, not as a complete account of the trial’s multiplicity or missing-data procedures.

14. Safety Results

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

Other (non-serious) adverse events

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

The registry record reports serious adverse event figures for 47 participants at risk in the ibuprofen group and 42 participants at risk in the placebo group. It reports zero participants affected by serious adverse events in each group. The other adverse event counts are also zero in both groups, with 47 and 42 participants at risk, respectively.

These figures are counts from the safety information recorded in the registry. They do not describe event severity beyond the serious-versus-other grouping, timing, relatedness to study medication, or individual event types. The record lists no serious adverse event terms. Death counts are not reported in the registry record.

Zero recorded events in these groups should not be interpreted as proof that no adverse events could occur, or as a complete characterization of safety. The safety denominators differ from the primary outcome denominators, and the registry record does not explain the difference. It also does not provide further detail about safety monitoring or how adverse events were collected. These limitations constrain interpretation of the posted counts.

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

The registry results show that 19 participants in the ibuprofen arm and 26 in the placebo arm met the primary acute mountain sickness definition. The corresponding arm sizes were 44 and 42. The unadjusted recalculation points toward a lower observed event proportion in the ibuprofen arm, but its confidence interval includes no difference and values on either side. The p-value is 0.082. Together, these results indicate uncertainty about the magnitude and direction of the comparison.

The result does not establish that ibuprofen prevents acute mountain sickness. A numerical difference in observed event counts can arise from a treatment effect, chance variation, or other features not captured in the registry summary. The confidence interval and p-value do not resolve those possibilities. The record also does not provide a full prespecified statistical plan, adjusted analyses, or missing-data methods that would allow a broader evaluation of the result.

The outcome has a specific scope: a diagnosis based on a Lake Louise Criteria score of 3 or greater together with headache, assessed over 2 days. It does not report the full distribution of symptom scores, duration of symptoms, outcomes beyond that timeframe, or other forms of altitude illness. The result should not be extended to people or settings not described by the study, including populations with different health characteristics or different hiking circumstances.

The safety record reports no serious or other adverse events in the listed groups, but deaths are not reported and further safety details are absent. The event counts alone do not establish that either regimen is safe or unsafe. More generally, these registry data are a limited statistical record: they document the trial design and selected results, but they do not provide enough information to make definitive causal or broader clinical claims.

16. Why This Trial Matters Statistically

This trial is statistically informative because it illustrates the distinction between a visible difference in observed counts and a precise estimate of a treatment contrast. The ibuprofen arm had fewer participants meeting the primary endpoint than the placebo arm, but the comparison’s confidence interval includes no difference and extends in both directions. Reading the event counts together with the interval avoids treating the direction of the point estimate as a settled conclusion.

It also illustrates why denominators matter. The event counts are reported alongside arm sizes, and the arms are not the same size. A comparative estimate based on event proportions is more informative than comparing raw counts alone. At the same time, a summary estimate cannot repair the limitations of missing details about analysis populations, outcome availability, or prespecified methods.

The planning illustrations show how sample-size requirements depend on the effect a future study aims to detect. Under the stated planning assumptions, smaller target effects require more participants per arm. Because those figures are based on the observed effect, they should be viewed as conditional planning examples rather than as independent evidence about the effect’s reliability or as a description of the original trial design.

Finally, the registry record demonstrates the importance of reporting the analysis plan, participant flow, missing-data handling, and secondary outcomes. Without those details, readers can describe the posted comparison but cannot fully assess whether it follows the intended analysis or how robust it is to alternative choices. The statistical lesson is not simply to look for a threshold-crossing p-value; it is to assess effect direction, uncertainty, design, and reporting completeness together.

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.

Several limitations are specific to the available record. The enrolled sample was 89, while the primary outcome is reported for 44 participants in the ibuprofen arm and 42 in the placebo arm. The registry does not explain why the enrollment and outcome denominators differ, whether all randomized participants contributed outcome data, or whether any were excluded. The primary outcome population is described only as participants meeting all inclusion criteria.

The record does not report participant characteristics, detailed eligibility criteria, the original statistical analysis plan, or the original sample-size justification. It lists zero analyses and does not post secondary results, although it records two outcome measures. There is no reported account of multiplicity control, interim analyses, adjustment for baseline variables, or missing-data handling. The unadjusted recalculation therefore cannot be assumed to represent the trial’s planned analysis.

The primary endpoint is based on a score threshold plus headache over 2 days. It provides an event count but not the distribution of symptom scores, the severity of symptoms within each group, or outcomes beyond that period. The registry record does not provide enough detail to assess how broadly the result applies to other populations, locations, or patterns of altitude exposure.

The safety figures report zero serious and zero other adverse events in the listed groups, but death counts are not reported in the registry record. The record does not provide event-level details, relatedness, or additional information about monitoring. These gaps limit conclusions about safety as well as efficacy. Taken together, the posted information supports a cautious description of the observed counts and their uncertainty, rather than a definitive conclusion.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Prevention of Altitude Illness With Non-steroidal Anti-inflammatory Study (PAINS) — NCT01171794.
• Registry record last updated 2018-12-13; status last verified 2018-11.
• Results first posted 2017-04-20.
• 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 completed study was a Phase 3, randomized, triple-masked, parallel-group comparison of ibuprofen and visually identical placebo, sponsored by Stanford University. The registry summary described healthy adults interested in hiking Barcroft Peak and stated that researchers hoped to enroll about 100 participants; recorded enrollment was 89.

The primary outcome was acute mountain sickness over 2 days, defined by a Lake Louise Criteria score of 3 or greater with headache. The posted counts were 19 of 44 participants in the ibuprofen arm and 26 of 42 in the placebo arm. The unadjusted recalculation has a confidence interval that includes no difference, and its p-value is 0.082.

The record also lists zero serious and zero other adverse events in the groups at risk, while death counts are not reported in the registry record. Secondary results, analysis details, missing-data methods, and the original sample-size justification are not reported in the registry record.