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Postural Tachycardia Syndrome Phase 2, Phase 3 Continuous Endpoint NCT00685919

Peripheral Dopamine in Postural Tachycardia Syndrome: Complete Statistical Analysis

The randomized crossover trial examined kidney dopamine activity and 24-hour urinary sodium excretion in healthy participants and people with postural tachycardia syndrome. The posted results include group summaries and an unadjusted comparison for healthy participants, but no registry-reported analyses.

Trial start: 2008-05  ·  Enrollment: 32  ·  Sponsor: Vanderbilt University
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Peripheral Dopamine in Postural Tachycardia Syndrome (NCT00685919), a randomized phase 2, phase 3 study. The primary outcome is 24 Hour Urinary Sodium Excretion During Treatment Normalized to Creatinine.

32
Enrollment
Phase 2, Phase 3
4
Arms
In the primary outcome
-8.00
Mean difference
Healthy Participants Who Received Carbid
-32.51–16.51
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00685919
PhasePhase 2, Phase 3
ConditionPostural Tachycardia Syndrome, Orthostatic Intolerance
AllocationRandomized
Design modelCrossover
MaskingSingle
Enrollment32
Arms in the primary outcome4
Lead sponsorVanderbilt University
Results postedYes

2. Clinical Question

Population

Healthy participants and participants with postural tachycardia syndrome (POTS) or orthostatic intolerance. The registry lists an enrollment of 32. The outcome description notes that some data were excluded for reasons including discarded urine samples and receipt of an incorrect dose; the full exclusion description is not reported in the registry record.

Intervention

Oral carbidopa, intended to decrease kidney dopamine activity by inhibiting dopamine synthesis. One sequence specifies carbidopa 200 mg every 6 hours for 5 doses, followed by placebo every 6 hours for 5 doses.

Comparator

Placebo matching carbidopa, given in the opposite treatment sequence for participants assigned to placebo followed by carbidopa. The trial used a crossover design, so participants received both treatments in sequence.

Primary question

Does the effect of oral carbidopa on 24-hour urinary sodium excretion, normalized to creatinine, differ between participants with POTS and healthy volunteers? The registry summary describes this as a comparison of responses between those groups.

The scientific question concerns a physiological measure rather than a clinical event. Kidney dopamine activity was to be altered with carbidopa, and urinary sodium excretion was the primary measure used to assess the response. The registry’s stated null hypothesis is that carbidopa’s effect on urinary sodium excretion would not differ between people with POTS and healthy volunteers.

The posted primary outcome summaries list placebo and carbidopa treatment groups separately for healthy participants and POTS participants. However, the registry’s recalculated comparison is only for healthy participants receiving carbidopa versus placebo. It does not supply an analysis comparing treatment effects between the two populations, so the primary cross-population question cannot be answered from that comparison alone. The registry record does not report a sponsor analysis for the primary outcome.

3. Trial Design

This was a randomized, single-masked, crossover study listed as phase 2 and phase 3. The registry records enrollment of 32 and a completed status. The study start is listed as 2008-05 and primary completion as 2020-07. Vanderbilt University is named as the sponsor. The study concerned POTS and orthostatic intolerance and compared healthy volunteers with participants who had POTS.

In a crossover design, participants receive more than one treatment in sequence, rather than remaining in only one treatment group throughout the study. The arm descriptions identify a carbidopa-then-placebo sequence and a placebo-then-carbidopa sequence. For the first sequence, the registry describes carbidopa 200 mg orally every 6 hours for 5 doses, followed by placebo every 6 hours for 5 doses. The other sequence begins with matching placebo and is followed by carbidopa. The details of the second carbidopa dosing description are not reported in the registry record.

Random allocation indicates that the treatment sequence was assigned randomly. The record identifies masking as single but does not say which people were masked. It does not report a washout period, the method used to generate the allocation sequence, or procedures for concealment of allocation. These details are important to understanding how the sequences were implemented but cannot be established from the registry information.

The primary measurement was collected during approximately 24 hours of treatment, from immediately before the first dose to immediately before the fifth dose of placebo or carbidopa. Posted summaries report observations by health group and treatment. They do not provide a model accounting for the paired, within-participant nature of the crossover, sequence effects, or period effects. The statistical plan, including any prespecified approach for those issues, is 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: * Healthy Participants Group: 21 healthy controls enrolled. 3 withdrew prior to randomization. 1 screen failed. 17 healthy participants were randomized. 1 participant was withdrawn due to orthostatic symptoms during baseline testing * Postural Tachycardia Syndrome (POTS) Group: 11 POTS participants were randomized. 1 participant withdrew after the 1st dose of the intervention (placebo).

Overall Study

StageHealthy Participants-Placebo Then CarbidopaHealthy Participants-Carbidopa Then PlaceboPatients With POTS-Placebo Then CarbidopaPatients With POTS-Carbidopa Then Placebo
STARTED8983
Baseline A8983
Treatment A7983
24 hr Post-treatment A7973
Baseline B7973
Treatment B7973
24 hr Post Treatment B7973
COMPLETED7973
NOT COMPLETED1010

Reasons for not completing this period:

ReasonHealthy Participants-Placebo Then CarbidopaHealthy Participants-Carbidopa Then PlaceboPatients With POTS-Placebo Then CarbidopaPatients With POTS-Carbidopa Then Placebo
Withdrawal by Subject0010
Physician Decision1000

Analysis population for the primary outcome, as defined in the registry: No data analysis for the following: Healthy Placebo Group: * 1 subject with discarded urine sample * 1 subject who received only 50mg carbidopa (data for all arms excluded) Healthy Carbidopa Group: * 1 subject who received only 50mg carbidopa (wrong dose) POTS Placebo Group: * 1 subject with discarded urine sample * 1 subject who received only 50mg carbidopa (data for all arms excluded) POTS Carbidopa Group: * 1 subject who received only 50mg carbidopa (wrong dose)

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: * Healthy Participant Group: Data is excluded for 1 participant who was withdrawn due to orthostatic symptoms during baseline testing. * Postural Tachycardia Syndrome (POTS) Group: Data is excluded for 1 participant who was withdrawn after the 1st dose of the intervention (placebo).

CharacteristicUnitHealthy Participants-Placebo Then CarbidopaHealthy Participants-Carbidopa Then PlaceboPatients With POTS-Placebo Then CarbidopaPOTS-Carbidopa Then PlaceboTotal
Participants analysed887326
Age, Continuousyears34 (SD 11)32 (SD 10)31 (SD 10)37 (SD 3)32.8 (SD 9.5)
Sex: Female, Male: FemaleParticipants877325
Sex: Female, Male: MaleParticipants01001
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants00000
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants887326
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants00000
Race (NIH/OMB): American Indian or Alaska NativeParticipants00000
Race (NIH/OMB): AsianParticipants00000
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants00000
Race (NIH/OMB): Black or African AmericanParticipants01001
Race (NIH/OMB): WhiteParticipants877325
Race (NIH/OMB): More than one raceParticipants00000
Race (NIH/OMB): Unknown or Not ReportedParticipants00000
Region of Enrollment: United Statesparticipants887326

6. Primary Endpoint

The registry lists the primary outcome as 24 Hour Urinary Sodium Excretion During Treatment Normalized to Creatinine, measured over Immediately before the 1st dose of placebo or carbidopa to immediately before the 5th dose (approximately 24 hours).

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
UnitMilliequivalents per gram (mEq/g)
Endpoint classificationContinuous Endpoint

The primary endpoint is 24-hour urinary sodium excretion during treatment, normalized to creatinine. Urine was collected over 24 hours; volume was measured, and sodium and creatinine concentrations were analyzed. The total amounts excreted over that period were calculated, and the outcome was expressed as a sodium-to-creatinine ratio in milliequivalents per gram (mEq/g). The specified timeframe runs from immediately before the first dose to immediately before the fifth dose, approximately 24 hours.

Creatinine normalization expresses sodium excretion relative to creatinine excretion. As a general measurement concept, using a ratio can help account for differences in urine concentration or collection, but it also means the endpoint is a ratio rather than an unscaled total sodium amount. The registry describes the measurement procedure but does not report additional validation information or a rationale for choosing this endpoint over other measures.

The endpoint was selected to assess the study’s physiological question: whether changing kidney dopamine activity with carbidopa is associated with a change in urinary sodium excretion, and whether that response differs between participants with POTS and healthy volunteers. It is not itself a measure of symptoms, daily functioning, or a clinical event. The posted outcome summaries report means and standard deviations for each population-treatment group. The registry record does not report a sponsor analysis testing the stated difference in response between populations.

7. Results Posted in the Registry

Mean difference: Healthy Participants Who Received Carbidopa as Treatment A or Treatment B

-8.00

95% CI: -32.51 to 16.51

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals107121136151166180Healthy Participants Who Rece… (n=14)Healthy Participants Who Rece… (n=15)Postural Tachycardia Syndrome… (n=8)Postural Tachycardia Syndrome… (n=9)Milliequivalents per gram (mEq/g) (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Healthy Participants Who Rece…-36-25-14-2.319.0620mean difference vs control (95% CI)

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.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Systolic Blood Pressure Measured at 8 Hours After the Last Dose of Placebo or CarbidopaContinuous EndpointMean difference-2.00 (-6.56 to 2.56)161 per arm
Plasma Catecholamines (Norepinephrine) After the Last Dose of Placebo or CarbidopaContinuous EndpointMean difference31.00 (-24.70 to 86.70)99 per arm
Plasma Catecholamines (DOPA) After the Last Dose of Placebo or CarbidopaContinuous EndpointMean difference18,484 (13,666 to 23,302)3 per arm

Systolic Blood Pressure Measured at 8 Hours After the Last Dose of Placebo or Carbidopa

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Healthy Participants Who Rece…-7.29-5.17-3.06-0.941.173.29mean difference vs control (95% CI)

Plasma Catecholamines (Norepinephrine) After the Last Dose of Placebo or Carbidopa

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Healthy Participants Who Rece…-34-7.7718447096mean difference vs control (95% CI)

Plasma Catecholamines (DOPA) After the Last Dose of Placebo or Carbidopa

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Healthy Participants Who Rece…-1,8643,5428,94814,35419,76025,166mean difference vs control (95% CI)

The secondary outcomes span blood pressure, plasma catecholamines, urinary catecholamine excretion, plasma renin activity, and plasma sodium. The registry lists 7 secondary outcomes, but only 3 have posted numerical summaries in the record described: systolic blood pressure, plasma norepinephrine, and plasma DOPA. The other listed secondary outcomes do not have numerical group results in the registry record. No registry-reported analyses are listed for the secondary outcomes.

Across the outcomes with posted summaries, the groups show varied patterns rather than one uniform direction across measures. The DOPA summaries differ substantially between placebo and carbidopa groups, while the blood-pressure and norepinephrine summaries show smaller or less distinct group contrasts. These outcomes concern related physiological processes, but none substitutes for the primary urinary sodium endpoint or directly answers whether its treatment effect differs between POTS and healthy participants.

The available secondary group summaries should be treated as descriptive. The unadjusted recalculated comparisons are not sponsor-reported analyses and do not account for the crossover design. A numerical difference between group means is not by itself evidence that a treatment effect is reliable, and a result for a secondary measure does not establish the primary hypothesis.

General statistical explanation: when multiple outcomes are examined, the chance of at least one apparently unusual result can increase if each is interpreted separately without accounting for the number of comparisons. This is why prespecified outcome priorities and multiplicity procedures matter. The registry record does not report whether secondary outcomes were prespecified in a detailed analysis plan, whether adjustments for multiple testing were used, or how these outcomes were intended to support interpretation of the primary endpoint. The unadjusted secondary results therefore carry less weight than a prespecified, design-appropriate primary analysis, particularly when the primary cross-population comparison itself is not reported.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary endpoint, the posted mean was 140.0 mEq/g among healthy participants receiving placebo and 132.0 mEq/g among healthy participants receiving carbidopa. The registry’s unadjusted recalculation for this comparison gives a mean difference of -8.0 mEq/g, with a 95% confidence interval from -32.51 to 16.51 and an unadjusted p-value of 0.522. The interval includes values on either side of zero, so the posted summaries are compatible with a range of possible differences in either direction. They do not establish a precise treatment contrast.

Among participants with POTS, the posted mean was 137.0 mEq/g with placebo and 154.0 mEq/g with carbidopa. These are group summaries, not a reported inferential comparison. The registry does not provide an estimate, confidence interval, or p-value for the treatment contrast in this population, nor an analysis comparing the treatment contrasts between POTS and healthy participants. That between-population comparison is central to the stated primary question, and cannot be inferred from the healthy-participant comparison or from the separate group means alone.

The recalculated comparison is unadjusted and based on posted summary statistics. It does not incorporate the crossover pairing or any adjustment for sequence, period, or other factors. The registry has no reported analyses for the primary outcome. Consequently, the recalculated result should be read as a descriptive, unadjusted comparison, not as a substitute for a sponsor analysis of the trial’s design.

The posted group sizes for the primary endpoint are 14 and 15 for healthy participants receiving placebo and carbidopa, respectively, and 8 and 9 for participants with POTS receiving placebo and carbidopa. The primary outcome description also lists exclusions, including discarded urine and incorrect-dose cases, but the description is cut off after an additional POTS placebo exclusion begins. The complete accounting of analyzed participants and missing measurements is therefore not available in the registry record.

These summaries describe the measurements observed in the listed groups. They do not show whether carbidopa changes urinary sodium excretion in a way that differs by POTS status, because the required interaction or difference-in-treatment-effects analysis is not reported. No clinical benefit or harm should be inferred from this physiological endpoint alone.

10. Statistical Methods Explained

The registry lists the primary outcome as a continuous measure summarized by its mean and standard deviation. These statistics describe the center and spread of observed measurements. The mean is the arithmetic average; the standard deviation describes how dispersed individual values are around that average. General statistical explanation: means and standard deviations describe a sample, but do not by themselves show how uncertain a treatment comparison is or whether the design’s paired structure has been handled appropriately.

What does the recalculated comparison represent?

The healthy-participant comparison is an unadjusted difference between the posted mean for carbidopa and the posted mean for placebo. Its estimate is -8.0 mEq/g. The associated confidence interval and p-value are recalculations from the posted summary statistics, not a registry-reported sponsor analysis. They do not account for the fact that this was a crossover study in which participants received both treatments. The record does not state how the sponsor analyzed within-participant measurements, if such an analysis was performed.

General statistical explanation: in a crossover trial, measurements from the same participant are usually related. An analysis that uses the within-person comparison can account for that pairing, while an analysis treating treatment groups as independent may not. The correlation between a participant’s measurements under the two treatments is not reported, so an appropriate paired estimate cannot be reconstructed from the posted group means and standard deviations alone. The registry record also does not report whether treatment sequence, period, or carryover was assessed.

Why does the population comparison matter?

The study summary states a null hypothesis about whether carbidopa’s effect differs between participants with POTS and healthy volunteers. Answering that question requires comparing treatment effects across the two populations, rather than only testing a treatment contrast in one population or comparing one treatment group’s mean with another group’s mean. The registry provides an unadjusted recalculation for healthy participants, but no corresponding reported inferential comparison for the POTS group and no estimate of the difference between population-specific treatment effects. Therefore, the central hypothesis is not tested in the analyses reported in the registry record.

General statistical explanation: a difference in statistical significance between two separate subgroup results is not itself evidence that the treatment effects differ. A formal interaction or direct contrast is needed to evaluate whether the treatment response varies by population. No such result is reported for this study.

How should the p-value be read?

The unadjusted p-value for the healthy-participant comparison is 0.522. General statistical explanation: a p-value describes how unusual data at least as incompatible with a specified null model would be, under the assumptions of that model. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. Here it is attached to an unadjusted recalculation, not to a reported model for the crossover design or the stated cross-population hypothesis.

Interpretation should therefore consider the estimate and confidence interval as well as the p-value. The interval from -32.51 to 16.51 is wide enough to include a range of differences in both directions. This imprecision is relevant even though the p-value is not small. The registry does not state a threshold for statistical significance in the original plan; a planning illustration elsewhere specifies a two-sided significance level of 0.05, but that does not establish the trial’s original analysis plan.

What assumptions are not documented?

The record does not report the original sample-size justification, a prespecified statistical analysis plan, interim analyses, handling of missing data, or the model used for the primary outcome. It also does not report whether outcome distributions were checked, whether transformations or covariate adjustments were used, or whether sequence and period effects were considered. Those methods cannot be inferred from the posted summary statistics.

General statistical explanation: continuous outcomes are often analyzed with methods that rely on assumptions about the distribution of errors and the relationship among observations. In crossover data, within-participant dependence is particularly relevant. A suitable model should reflect the design and the scientific contrast of interest. Without the sponsor’s analysis description or participant-level data, the recalculated unadjusted comparison cannot verify those assumptions or reproduce a design-aware analysis.

There are 8 outcome measures listed, comprising the primary outcome and secondary measures. The registry reports no analyses for the primary outcome and no reported analyses for the listed secondary outcomes. In that context, the posted arm summaries are descriptive, while the recalculated comparisons are limited, unadjusted summaries rather than evidence that the trial’s prespecified statistical objectives were met.

11. Confidence Intervals and Precision

The healthy-participant primary comparison has an estimated mean difference of -8.0 mEq/g, with a 95% confidence interval from -32.51 to 16.51. A confidence interval gives a range of values compatible with the estimate under the method’s assumptions. General statistical explanation: it communicates uncertainty in an estimate; it is not a range containing a specified proportion of individual participants’ measurements, nor does it mean there is a 95% probability that the true value lies within this particular calculated interval.

The interval includes zero and extends to differences in either direction. Its width indicates that the unadjusted comparison is not precise enough to distinguish among a range of possible treatment contrasts. The estimate is based on the posted healthy-participant summaries, with 14 participants in the placebo group and 15 in the carbidopa group. Those group sizes are modest, and the registry does not provide the paired data needed to calculate a confidence interval that explicitly accounts for the crossover structure.

The standard deviations for the primary outcome are 29.0 mEq/g for healthy participants receiving placebo and 38.0 mEq/g for healthy participants receiving carbidopa. The posted POTS group standard deviations are 30.0 mEq/g with placebo and 31.0 mEq/g with carbidopa. Variation among participants contributes to uncertainty in group comparisons, but these summaries alone do not show the within-person variability across treatments.

The confidence interval is a recalculated, unadjusted interval, not a registry-reported sponsor interval. It does not address the primary question of whether the treatment effect differs between POTS and healthy participants. No confidence interval for that cross-population contrast is reported in the registry record. Precision for the study’s central hypothesis therefore cannot be judged from the healthy-participant interval alone.

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.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect283379
75% of the observed effect504674
50% of the observed effect1,1321,516
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,0005,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Calculated for the comparison: Healthy Participants Who Received Carbidopa as Treatment A or Treatment B.

The planning figures express participants per arm for 80% power and participants per arm for 90% power. They are calculated from the observed healthy-participant effect for the primary comparison, using a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect: 100%, 75%, or 50%. These are planning illustrations based on the recalculated comparison, not the original trial’s design assumptions; those original assumptions are not reported in the registry record.

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. The 90% power column expresses the corresponding planning target for a 90% chance. These are prospective design calculations, not probabilities that the observed result is correct. The figures are participants per arm, not a total across both arms and not total events.

The listed planning estimates rise as the target effect becomes smaller: for example, the entries for planning for 75% of the observed effect are larger than those for planning for 100% of the observed effect. This is the general relationship that smaller effects require more participants to detect with a given level of power, all else held constant.

The observed-effect basis is an unadjusted estimate from a small set of posted group summaries. It may not represent the effect a future study should target, and the calculations do not incorporate the crossover design or the stated comparison between POTS and healthy participants. This is not observed power. It does not retrospectively quantify the chance that this completed study detected an effect.

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 z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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 = -8.000; pooled standard deviation σ = 33.966.
  2. n = 2 × (1.96 + 0.842)2 × 33.9662 / -8.0002 = 283.0, rounded up to 283 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 <- -8                      # observed difference in means
sigma <- 33.9656689418399                     # 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(685919)
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 = 283 (80% power), 379 (90% power)
 75% of observed effect: n per arm = 504 (80% power), 674 (90% power)
 50% of observed effect: n per arm = 1,132 (80% power), 1,516 (90% power)
power.t.test: 283.9 
Simulated power at n = 283 per arm: 0.797 (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 8 outcome measures: the primary urinary sodium-to-creatinine measure and 7 secondary outcomes. It records no analyses for the primary outcome and no reported analyses for the secondary outcomes. The posted group summaries and unadjusted recalculations do not show a complete prespecified inferential analysis.

Multiplicity arises when several outcomes or comparisons are examined. General statistical explanation: interpreting many unadjusted tests as if each were the only test can make chance findings more likely across the set. A study may address this through a prespecified hierarchy, adjustment procedure, or carefully defined exploratory interpretation. The statistical plan and any multiplicity strategy are not reported in the registry record, so it is not possible to determine how the investigators intended to control or interpret multiple comparisons.

The outcome description identifies some exclusions, including a discarded urine sample and participants who received only 50mg carbidopa or an incorrect dose. It also begins to identify an exclusion in the POTS placebo group, but the description is incomplete. The full missing-data accounting, analysis populations, reasons for every exclusion, and whether participants were analyzed according to randomized sequence are not reported in the registry record. The posted group counts consequently cannot be reconciled fully with the enrollment figure from the information available.

For a crossover study, the analysis population and handling of incomplete treatment periods can affect which within-participant comparisons are usable. The record does not say how incomplete data were handled, whether imputation was used, or whether participants with measurements from only one treatment contributed to any analysis. It also does not describe any interim analyses or a stopping rule. These omissions prevent a complete assessment of the analytic framework and the potential for selective reporting.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Healthy Participants-Placebo0170.0%
Healthy Participants-Carbidopa0170.0%
POTS Participants-Placebo0110.0%
POTS Participants-Carbidopa0110.0%

Deaths

ArmDeaths (participants affected of at risk)
Healthy Participants-Placebo0 of 17
Healthy Participants-Carbidopa0 of 17
POTS Participants-Placebo0 of 11
POTS Participants-Carbidopa0 of 11

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
Healthy Participants-Placebo1 of 17
Healthy Participants-Carbidopa1 of 17
POTS Participants-Placebo2 of 11
POTS Participants-Carbidopa0 of 11

Most frequent non-serious adverse event terms

Event termOrgan systemHealthy Participants-PlaceboHealthy Participants-CarbidopaPOTS Participants-PlaceboPOTS Participants-Carbidopa
Head rushNervous system disorders0 of 170 of 171 of 110 of 11
LightheadednessNervous system disorders0 of 171 of 170 of 110 of 11
VertigoNervous system disorders0 of 170 of 171 of 110 of 11
NauseaGastrointestinal disorders1 of 170 of 170 of 110 of 11
Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry’s serious adverse event summaries list 17 participants at risk in each healthy-participant treatment group and 11 in each POTS treatment group. No serious adverse events are recorded in any of the four listed groups, and no deaths are recorded. These counts describe the registry’s reported serious-event experience; they do not establish that the treatments are free of risk.

The record also lists other, non-serious adverse events: 1 in each healthy-participant treatment group, 2 in the POTS placebo group, and 0 in the POTS carbidopa group. The serious-event figures should be read separately from these other-event counts. Because this was a crossover study, participants could receive both treatments, and the group counts should not automatically be interpreted as independent sets of people. The registry does not give event descriptions for these other events in the registry record.

General statistical explanation: when event counts are zero or small, estimates of event frequency remain uncertain, especially in a study with relatively few participants. The registry record does not provide a detailed safety analysis, event timing, severity breakdown beyond the serious/non-serious distinction, or a formal comparison between treatments. The counts therefore describe what was recorded, not a comparative conclusion about safety.

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

The posted data show group-level summaries of urinary sodium-to-creatinine ratios and selected secondary physiological measures after placebo or carbidopa treatment. For healthy participants, the recalculated unadjusted primary comparison is -8.0 mEq/g, with a 95% confidence interval from -32.51 to 16.51 and an unadjusted p-value of 0.522. This interval indicates substantial uncertainty about the direction and size of the contrast.

The registry’s central question is whether the carbidopa response differs between POTS participants and healthy volunteers. The posted primary results do not include a reported analysis of that difference between treatment effects. Separate group means are not enough to establish whether responses differ across populations, particularly in a crossover design where observations from the same participant are related. The registry record does not report the sponsor’s analysis of this hypothesis.

These results also do not establish whether a measured difference is clinically important. The primary endpoint is a laboratory-derived ratio, and the record does not report a threshold defining a meaningful change. The measure is not a direct report of symptoms or daily functioning. The secondary outcomes likewise represent physiological measurements, and their posted summaries do not provide a basis for clinical recommendations.

General statistical explanation: absence of a precise or statistically compelling estimate is not proof that there is no effect. Conversely, a difference in a mean does not prove that a treatment effect is real, clinically important, or different between populations. Interpretation depends on design-appropriate analyses, uncertainty, prespecification, and the relevance of the measure to the study question.

The findings should therefore be understood as a limited description of posted results. The registry lists a completed randomized crossover trial and gives arm summaries, but does not report the full statistical plan, complete analysis populations, or sponsor analyses. Neither efficacy nor lack of efficacy, and neither benefit nor harm, can be concluded from the information recorded.

17. Why This Trial Matters Statistically

This trial raises a useful statistical question about how to analyze a physiological response when participants receive treatments in sequence and the scientific objective is to compare that response across two populations. The primary endpoint is measured repeatedly within the crossover framework, while the stated hypothesis concerns whether the treatment effect itself varies between POTS participants and healthy volunteers.

That objective requires more than looking at separate group means. A direct analysis should reflect the within-participant structure and estimate the contrast between population-specific treatment effects. The registry’s available recalculation addresses only an unadjusted comparison among healthy participants. It does not supply the direct comparison that corresponds to the central hypothesis. This distinction illustrates why the statistical estimand—the specific quantity a study aims to estimate—must be aligned with both the design and the research question.

The record also illustrates the importance of transparent reporting. Group summaries are useful for describing the data, but they do not reveal how missing measurements, sequence effects, period effects, or multiple outcomes were handled. Without the statistical analysis plan and an account of the analyzed population, readers cannot determine whether the posted summaries represent the intended analysis.

Finally, the planning illustration shows how sample-size requirements depend on the target effect and the assumptions used. Those figures are not evidence about the original design, nor do they resolve limitations in the available trial analysis. The broader statistical lesson is to distinguish descriptive summaries, recalculated comparisons, design-aware inference, and prospective planning calculations. Each answers a different question, and they should not be treated as interchangeable.

18. Limitations

The principal limitation for interpretation is that the registry does not report an analysis of the stated primary hypothesis: whether the carbidopa effect on urinary sodium excretion differs between POTS participants and healthy volunteers. The only recalculated primary comparison is an unadjusted healthy-participant contrast. No corresponding inferential comparison for the POTS group or direct cross-population contrast is reported.

The study used a crossover design, but the available recalculation uses posted group summaries and does not account for within-participant pairing. The registry does not report analyses of sequence, period, or carryover effects, nor does it describe a washout period. The missing participant-level paired information means that a design-aware estimate cannot be reconstructed from the summaries.

The primary outcome description is incomplete. It identifies some exclusions, including discarded urine and incorrect dosing, then ends while describing an additional POTS placebo exclusion. The registry does not provide a complete flow of participants and measurements, a full missing-data approach, or the analysis populations. The listed enrollment of 32 therefore cannot be reconciled fully with the posted outcome group counts.

The statistical analysis plan, original sample-size justification, interim analyses, and multiplicity procedures are not reported. The secondary outcomes have incomplete numerical reporting and no registry-reported analyses. The outcome is a physiological ratio, and the registry does not give a threshold for clinical importance. These limitations constrain both the precision of interpretation and the conclusions that can be drawn from the posted results.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

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22. Record Summary

NCT00685919, titled “Peripheral Dopamine in Postural Tachycardia Syndrome,” is a completed randomized, single-masked crossover study sponsored by Vanderbilt University. The registry lists phase 2 and phase 3, enrollment of 32, and study dates from 2008-05 to primary completion in 2020-07. The trial compared carbidopa and placebo in healthy participants and participants with POTS.

The primary endpoint was 24-hour urinary sodium excretion normalized to creatinine. The record posts group means and standard deviations, as well as an unadjusted recalculation for healthy participants. It does not report a sponsor analysis of the primary outcome or the stated comparison of treatment effects between populations. Several secondary outcomes are listed, but numerical summaries and analyses are not available for all of them. The original statistical plan, complete missing-data accounting, and sample-size justification are not reported in the registry record.

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