Effect of Exercise in OI: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Exercise in OI (NCT00770484), a randomized na study. The primary outcome is Maximal Oxygen Consumption Capacity (VO2 Max).

2. Clinical Question

The registry describes a study of exercise capacity and orthostatic tolerance in people with orthostatic intolerance, including postural tachycardia syndrome. Its stated rationale is that an increase in heart rate when standing can limit exercise. The researchers proposed testing whether propranolol, by lowering heart rate, would be associated with greater exercise capacity. They also proposed evaluating heart responses after an acute bout of intense exercise and whether orthostatic tolerance changed the next day.

The registry’s stated aims also include a question about next-day orthostatic tolerance after exercise. However, the posted results list only the VO2 max outcome, and no secondary outcomes are posted in the registry record. The primary result therefore addresses the exercise-capacity comparison, not the proposed next-day response.

3. Trial Design

The study is listed as randomized, double-masked, and crossover. The two intervention sequences were propranolol followed by placebo and placebo followed by propranolol. In a crossover design, participants receive more than one treatment condition in a planned sequence, so comparisons can draw on measurements under different conditions in the same study population. General methodological context: crossover comparisons can be affected by period effects, carryover from an earlier condition, and changes over time. The registry record does not report whether these issues were assessed or how they were handled.

Enrollment was 12, and the study status is completed. The registry lists a start date of 2008-11 and primary completion in 2015-05. The primary outcome summaries report 11 participants for propranolol and 11 for placebo. The record does not explain how the enrollment figure relates to those outcome summaries, whether observations were missing, or whether the same participants contributed to both conditions.

The listed primary outcome is maximal oxygen consumption capacity, measured over approximately 30 minutes, within 2 hours of receiving each intervention. The registry describes the outcome as a continuous measure and reports means with standard errors. The posted comparison gives the mean difference for propranolol versus placebo and an unadjusted p-value.

The registry record does not report the treatment dose, the length of each treatment period, any washout interval, the allocation procedure, who was masked, or the original statistical analysis plan. It also does not report the trial’s original sample-size assumptions or whether interim analyses were planned. These omissions limit assessment of how the crossover was implemented and how the posted comparison was derived. The status and design labels describe the registered study, but they do not fill in those methodological details.

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:

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 Maximal Oxygen Consumption Capacity (VO2 Max), measured over Over approximately 30 minutes, within 2 hours of receiving each intervention..

The primary endpoint is maximal oxygen consumption capacity, also called VO2 max, reported in mL/kg/min. The registry records a mean for each treatment condition and gives the standard error as the measure of dispersion. The outcome was assessed over approximately 30 minutes, within 2 hours of receiving each intervention.

VO2 max is a measure of the maximum rate at which oxygen is used during intense exercise. General context: oxygen consumption capacity is used to characterize exercise performance because it summarizes the body’s ability to take up and use oxygen during exertion. A continuous measurement can be compared between treatment conditions using a difference in means, which retains the outcome’s original units and is interpretable on its measurement scale.

The registry’s stated rationale links heart-rate response with exercise capacity in people with orthostatic intolerance. The primary endpoint therefore addresses the stated exercise-capacity aim. It does not directly measure orthostatic tolerance, heart-rate response while standing, or the proposed next-day response to an acute exercise bout. No results for those other measures are posted in the registry record.

7. Results Posted in the Registry

• Propranolol: mean 27.60 versus 24.50 on control; difference 3.10 (95% CI 0.71 to 5.49), standardized effect d = 1.08; z-test p = 0.011.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry presents a continuous primary outcome and a comparison of means. The result is best read as a difference on the original VO2 max scale, alongside the uncertainty interval and the unadjusted p-value. General statistical context follows; the registry record does not report a full analysis plan or enough detail to establish every method used for the posted comparison.

What does a mean difference describe?

A mean summarizes the central level of a continuous measurement within a condition. A mean difference compares the average measurement in one condition with the average in another, with the direction depending on which condition is subtracted from which. Here, the posted comparison is propranolol versus placebo and reports a mean difference of 3.1 mL/kg/min. Because the difference is expressed in the endpoint’s units, it can be interpreted as a contrast in average oxygen-consumption capacity rather than as a ratio.

The outcome summaries give means of 27.6 for propranolol and 24.5 for placebo. Their reported standard errors are 1.0 and 0.7, respectively. Standard errors describe uncertainty in estimated means, whereas standard deviations describe variation among individual measurements. The registry identifies the displayed dispersion as standard error; it does not provide standard deviations for each condition in the outcome summaries.

Why does the crossover structure matter?

General explanation: in a crossover study, participants receive treatment conditions in sequence. Measurements from the same participant can be correlated, so an analysis may need to account for that pairing. The registry lists randomized allocation, double masking, and a crossover model, and gives the sequences as propranolol then placebo and placebo then propranolol. It does not report whether the mean-difference analysis used paired data, a model with participant effects, or another approach. The posted summary therefore does not allow readers to verify how within-participant correlation entered the uncertainty estimate.

General explanation: treatment order and time can also matter in crossover studies. Period effects occur when outcomes change over time regardless of treatment, while carryover refers to effects of an earlier treatment that influence a later measurement. Sequence effects can arise if the order of treatments is relevant. The registry record does not report washout duration, tests for these effects, or adjustment methods. Their presence or absence should not be assumed.

What do the standard error and confidence interval tell the reader?

A standard error reflects the precision of an estimated quantity under the analysis model. A confidence interval combines an estimate with its uncertainty to give a range of values compatible with the data and that method. General explanation: a confidence interval is not a range containing a fixed proportion of individual outcomes, and it is not a guarantee that the true value lies within the particular interval. Its interpretation relies on the analysis assumptions.

The registry reports a confidence interval for the mean difference with a positive lower limit and an upper limit of 5.492 mL/kg/min. This gives information about uncertainty in the difference, but interpretation depends on the method used to construct the interval. The registry record does not specify that method or provide a model description that would permit a detailed check.

How should the p-value be read?

The unadjusted p-value is 0.011. General explanation: a p-value is calculated under a null hypothesis and a statistical model; it indicates how unusual data at least as incompatible with that null would be under those assumptions. It is not a measure of the size or importance of a difference, and it is not the probability that the observed result occurred by chance. The registry record does not state a multiplicity adjustment or fully describe the null hypothesis and test procedure.

Because the result is labeled unadjusted, the value should not be treated as accounting for multiple testing. The registry lists one primary outcome and no posted secondary outcomes, but it does not report whether additional outcomes or analyses were planned outside the posted record. The number and hierarchy of all planned tests are therefore not reported in the registry record.

What analysis details remain unknown?

The record reports no analyses in addition to the posted outcome comparison. It does not identify an intention-to-treat, per-protocol, or other analysis population; explain how incomplete measurements were handled; or state whether covariates were included. It also does not report whether the posted comparison was prespecified, whether assumptions were checked, or whether the results were adjusted for sequence or period. These unknowns are relevant when judging whether the standard error, confidence interval, and p-value fully reflect the randomized crossover design.

The posted summaries are useful descriptive and inferential statistics, but they are not a substitute for a detailed statistical analysis plan. Readers can interpret the reported direction and scale of the mean difference while keeping the missing model specifications and analysis-population details in view.

10. Confidence Intervals and Precision

The posted mean difference is 3.1 mL/kg/min, with a confidence interval whose lower limit is positive and whose upper limit is 5.492 mL/kg/min. The interval does not cross zero, indicating that the set of values in the reported interval is above no difference. The registry record does not give a rounded lower limit to three decimal places, so it is described without restating that bound.

A confidence interval communicates precision by showing a range of effect estimates compatible with the observed data under the method used. A relatively narrow interval would indicate greater precision than a wide interval on the same scale. General explanation: the interval does not capture all uncertainty about design quality, measurement, bias, or applicability; it reflects sampling uncertainty as represented by the statistical method.

The condition means are reported with standard errors of 1.0 for propranolol and 0.7 for placebo. Those values characterize uncertainty in the individual condition means, not the uncertainty of each participant’s measurement. For a crossover comparison, the precision of the difference can depend on the relationship between measurements from the same participant. That relationship and the interval-construction method are not reported in the registry record.

The interval should be considered together with the reported mean difference and the study’s design details. It describes uncertainty around the posted comparison, but does not establish whether the analysis fully accounted for sequence, period, or within-participant effects. The registry record also does not report an adjusted estimate or a separate sponsor analysis.

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 event counts. They are illustrations based on the observed mean difference, rather than the trial’s original design calculation. The assumptions listed 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 to a stated fraction of the observed effect.

For planning at 100% of the observed effect, the figures are 14 participants per arm for 80% power and 18 participants per arm for 90% power. At 75% of the observed effect, the corresponding figures are 24 participants per arm for 80% power and 32 participants per arm for 90% power. At 50% of the observed effect, they are 54 participants per arm for 80% power and 72 participants per arm for 90% power.

In plain language, the 80% power column gives the planned participants per arm under the stated assumptions for a study designed to have an 80% chance of detecting the specified effect if that effect is real and the assumptions hold. The 90% power column expresses the corresponding planning target for a higher probability of detection. For either target, smaller effects require more participants under the same assumptions.

These are planning illustrations, not observed power. They use the observed effect as an input and do not establish that the trial was designed with these assumptions. The registry record does not report the original sample-size justification or the design assumptions used by the investigators.

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 = 3.100; pooled standard deviation σ = 2.863.
2. n = 2 × (1.96 + 0.842)² × 2.863² / 3.100² = 13.4, rounded up to 14 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 <- 3.1                      # observed difference in means
sigma <- 2.86269104165993                     # 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(770484)
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 = 14 (80% power), 18 (90% power)
 75% of observed effect: n per arm = 24 (80% power), 32 (90% power)
 50% of observed effect: n per arm = 54 (80% power), 72 (90% power)
power.t.test: 14.4 
Simulated power at n = 14 per arm: 0.787 (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. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome measure: maximal oxygen consumption capacity. It reports no secondary outcomes. Although the record contains a posted primary comparison, it does not report a complete list of planned tests, a prespecified hierarchy of outcomes, or a strategy for controlling multiplicity. The unadjusted p-value should therefore be read as unadjusted, not as evidence that any broader set of comparisons was accounted for.

The record lists enrollment of 12, while the outcome summaries show 11 participants for the propranolol condition and 11 for the placebo condition. In a crossover study, treatment-condition summaries may reflect repeated conditions within participants; the record does not explain the relation between enrollment and these figures. It also does not report participant flow, reasons for unavailable measurements, or the number included in a defined analysis population. No missing-data method is described. It is not possible to determine from the registry record whether outcome data were incomplete or how any incompleteness affected the analysis.

The registry does not identify the analysis population as intention-to-treat, per-protocol, or another defined set. It does not report how protocol deviations were treated or whether all randomized participants were included in the primary analysis. It also does not describe imputation, sensitivity analyses, or other approaches to assess the effect of missing data.

The record reports zero additional analyses and no posted secondary outcomes. This does not establish that no other analyses were planned or performed; those details are not reported in the registry record. Accordingly, the stated primary comparison can be described, but the broader multiplicity context, participant inclusion rules, and handling of missing observations remain unclear.

14. Safety Results

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

Other (non-serious) adverse events

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

The registry reports serious adverse events by treatment sequence. In the propranolol-then-placebo group, 0 serious adverse events were reported among 8 participants at risk. In the placebo-then-propranolol group, 0 serious adverse events were reported among 4 participants at risk. The registry also reports 0 other adverse events among 8 at risk in the first sequence group and 0 among 4 at risk in the second sequence group.

These are sequence-group counts, not treatment-condition comparisons for each crossover period. The registry does not report a separate serious-event breakdown for propranolol and placebo exposure periods. The deaths field is not populated with a count, so deaths are not reported in the registry record.

General explanation: a zero count in a small group means no events were recorded in that group; it does not establish that an event cannot occur or precisely characterize risk. The at-risk figures are the denominators reported for these adverse-event summaries and should not be interpreted as the outcome-analysis denominators. The record does not provide event descriptions because no serious adverse-event terms are listed.

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

The posted result is a comparison of mean maximal oxygen consumption capacity under propranolol and placebo conditions in a randomized, double-masked crossover study. The propranolol condition mean is 27.6 mL/kg/min, and the placebo condition mean is 24.5 mL/kg/min. The reported mean difference is 3.1 mL/kg/min, with an unadjusted p-value of 0.011 and a confidence interval whose lower limit is positive and upper limit is 5.492 mL/kg/min.

These results describe the registry’s posted primary outcome. They do not answer every question raised in the study rationale. In particular, the registry lists a planned question about whether an acute exercise bout would improve next-day orthostatic tolerance, but no secondary outcomes are posted. The primary endpoint is exercise capacity, not a direct measure of orthostatic tolerance or of the proposed heart-rate response after exercise.

The comparison should not be interpreted without considering uncertainty and the incompletely described analysis. The registry does not report how within-participant correlation, treatment period, sequence, or possible carryover were handled. It also does not specify the analysis population or missing-data approach. Those gaps do not change the numerical result as posted, but they limit the ability to assess whether the estimate and its uncertainty fully reflect the crossover design.

The findings do not establish the size of an effect in other populations or settings, and they do not settle questions not measured in the posted outcome. The reported confidence interval gives a range for the mean difference under the analysis method, not a prediction interval for individual responses. The p-value is not a measure of clinical importance. The registry record supports a description of the posted VO2 max comparison, while its limited reporting calls for caution about broader conclusions.

16. Why This Trial Matters Statistically

This study illustrates why design details matter when interpreting a treatment comparison. A crossover design can compare measurements under different treatment conditions, but the statistical uncertainty depends in part on how repeated measurements from the same participant are handled. The registry identifies the study as crossover and gives the treatment sequences, yet it does not describe the analysis model, period effects, or possible carryover. Readers can see the reported mean difference, but cannot fully audit how the design informed its precision.

The contrast is reported in the original measurement units, which makes the primary result interpretable as a difference in mean VO2 max. The condition means, standard errors, confidence interval, and unadjusted p-value offer complementary information: the estimate describes the observed contrast, while the uncertainty measures indicate how precisely it is estimated under the reported analysis. Neither the p-value nor the interval answers questions about clinical importance by itself.

The planning illustrations also show a general statistical principle: planning for smaller effects requires larger participant targets under otherwise fixed assumptions. Those illustrations are based on the observed effect and are not evidence of the trial’s original design rationale or of achieved power. Keeping this distinction clear prevents a post-result calculation from being mistaken for a prospective design justification.

Finally, registry completeness affects interpretation. The record identifies one primary endpoint but does not post secondary outcomes, a missing-data approach, or the analysis population. It records zero adverse events in the listed sequence groups, but those figures do not provide a condition-specific account by crossover period. Recognizing these boundaries helps separate what the registered results directly report from what remains unknown.

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.

The registry reports enrollment of 12 and outcome summaries with 11 participants in each treatment condition, but does not explain how those figures relate to one another. Participant flow, exclusions, incomplete measurements, and the analysis population are not reported in the registry record. This makes it difficult to assess whether the posted outcome summaries represent all randomized participants or a subset.

Although the trial is labeled randomized, double-masked, and crossover, the record does not describe the randomization procedure, who was masked, treatment doses, treatment-period duration, or washout interval. It does not report the statistical model used for the primary comparison or whether within-participant correlation, treatment period, sequence, or carryover were considered. These details are particularly relevant to evaluating the uncertainty around a crossover estimate.

The registry lists the primary VO2 max endpoint and provides no posted secondary outcomes. The next-day orthostatic-tolerance question in the study rationale therefore cannot be evaluated from the posted results. The record does not report a multiplicity plan, missing-data strategy, analysis-population definition, or original sample-size justification. The planning figures are based on the observed effect and do not supply those missing design details.

Safety reporting is limited to sequence-group event counts and at-risk denominators. Separate event counts by treatment period and a death count are not reported in the registry record. These limits concern the available reporting and should not be mistaken for evidence about unreported procedures or outcomes.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effect of Exercise in OI — NCT00770484.
• Registry record last updated 2016-08-05; status last verified 2016-07.
• Results first posted 2015-07-09.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes a completed, randomized, double-masked crossover study of propranolol and placebo in orthostatic intolerance, including postural tachycardia syndrome. Enrollment is listed as 12, with a start date of 2008-11 and primary completion in 2015-05.

The primary outcome is maximal oxygen consumption capacity, measured within 2 hours of each intervention. The posted condition means are 27.6 mL/kg/min for propranolol and 24.5 mL/kg/min for placebo. The comparison reports a mean difference of 3.1 mL/kg/min, an unadjusted p-value of 0.011, and a confidence interval with a positive lower limit and an upper limit of 5.492 mL/kg/min.

No secondary outcomes are posted. The registry does not report the full crossover analysis method, missing-data handling, analysis population, or original sample-size assumptions. Serious adverse-event counts are 0 in each listed sequence group, with the reported at-risk denominators of 8 and 4.