← Clinical Trials
Healthy Subjects Phase 1 Continuous Endpoint NCT00834288

A Study to Compare the Bioavailability of Two Tramadol Hydrochloride Tablet Products (50 mg and 200 mg, Respectively) at Steady-state Under Fasting Conditions: Complete Statistical Analysis

This randomized crossover study compared steady-state tramadol exposure under once-daily 200 mg and six-hourly 50 mg regimens in healthy subjects. The primary outcome was area under the plasma concentration–time curve over 24 hours on day 5.

Trial start: 2003-06  ·  Enrollment: 26  ·  Sponsor: Labopharm Inc.
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 A Study to Compare the Bioavailability of Two Tramadol Hydrochloride Tablet Products (50 mg and 200 mg, Respectively) at Steady-state Under Fasting Conditions (NCT00834288), a randomized phase 1 study. The primary outcome is Area Under the Plasma Concentration Versus Time Data Pairs at Steady State (AUCss).

26
Enrollment
Phase 1
2
Arms
In the primary outcome
408.00
Mean difference
Tramadol IR (Ultram®) 50 mg 6-hourly
-441.79–1,258
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00834288
PhasePhase 1
ConditionHealthy Subjects, Pharmacokinetics, Bioavailability
AllocationRandomized
Design modelCrossover
MaskingNone (open label)
Enrollment26
Arms in the primary outcome2
Lead sponsorLabopharm Inc.
Results postedYes

2. Clinical Question

The study asked whether the steady-state pharmacokinetic profile of a once-daily tramadol hydrochloride tablet differed from that of an immediate-release tramadol tablet taken every six hours. The primary comparison concerned total exposure over a 24-hour interval, measured by the area under the plasma concentration–time curve on day 5. Other listed measures addressed peak and minimum concentrations and features of concentration fluctuation over the same interval.

Population

Healthy subjects enrolled in a phase 1 study. The registry reports enrollment of 26 participants; it does not report further demographic or eligibility details in the record.

Intervention

Tramadol HCl OAD 200 mg, given as one tablet daily at 07:30 in the described dosing schedule.

Comparator

Tramadol IR (Ultram®) 50 mg, given every six hours at 07:30, 13:30, 19:30 and 01:30 in the described dosing schedule.

Primary question

How did the 24-hour steady-state area under the plasma concentration–time curve for the two regimens compare on day 5?

This is a pharmacokinetic comparison, not a comparison of clinical symptoms or treatment outcomes. The registry describes the study as randomized and crossover, with no masking. In a crossover design, participants receive more than one study regimen, allowing measurements under different regimens to be compared within participants. The posted outcome summaries do not give sequence-specific results or the within-participant correlation needed to reconstruct a paired comparison. The record also does not report a prespecified bioequivalence margin or a formal decision criterion. The question answered by the posted primary result is therefore a comparison of average exposure, with uncertainty, rather than a formal demonstration of equivalence.

3. Trial Design

This completed phase 1 study was randomized, unmasked and used a crossover model. It enrolled 26 healthy subjects. The study dates recorded are 2003-06 for start and 2003-08 for primary completion. The sponsor named in the record is Labopharm Inc. The record describes the study as a comparison of pharmacokinetic profiles at steady state under fasting conditions.

The two regimens differed in both tablet formulation and dosing frequency. The test regimen was Tramadol HCl OAD 200 mg once daily. The reference regimen was Tramadol HCl 50 mg immediate release every six hours, identified as Ultram®. The brief description gives administration times of 07:30 for the once-daily tablet and 07:30, 13:30, 19:30 and 01:30 for the immediate-release tablets. The comparison therefore concerns the regimens as administered, not tablet strength in isolation.

The primary outcome was AUCss, the area under the plasma concentration–time data pairs over 24 hours at steady state on day 5. The registry notes that AUCss is also known as AUCtau. Secondary outcomes listed include maximum and minimum plasma concentration at steady state, time to peak exposure, percentage peak-trough fluctuation, percentage swing, half-value duration and plateau time. Numerical results are posted for only some secondary measures; numerical results for the other listed measures are not reported in the registry record.

The registry does not report the randomization sequence, washout interval, period structure, handling of period or sequence effects, or details of the fasting procedure. It also does not report the original statistical analysis plan, the intended sample-size justification, or whether any interim analyses were planned. These omissions matter when interpreting a crossover study because analysis can depend on the timing and order of treatment periods and the relationship between repeated measurements from the same participant.

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.

Treatment Phase I

StageTest (Tramadol HCl OAD 200 mg) FirstReference (Trazodone IR (Desyrel®) 100 mg 8-hourly) First
STARTED1313
COMPLETED1313
NOT COMPLETED00

Treatment Phase II

StageTest (Tramadol HCl OAD 200 mg) FirstReference (Trazodone IR (Desyrel®) 100 mg 8-hourly) First
STARTED1313
COMPLETED1313
NOT COMPLETED00

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.

CharacteristicUnitTest (Tramadol HCl OAD 200 mg) FirstReference (Tramadol IR (Ultram®) 50 mg 6-hourly) FirstTotal
Participants analysed131326
Age, Categorical: <=18 yearsParticipants000.0
Age, Categorical: Between 18 and 65 yearsParticipants131326.0
Age, Categorical: >=65 yearsParticipants000.0
Sex: Female, Male: FemaleParticipants224.0
Sex: Female, Male: MaleParticipants111122.0

6. Primary Endpoint

The registry lists the primary outcome as Area Under the Plasma Concentration Versus Time Data Pairs at Steady State (AUCss), measured over 24 hours (day 5).

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitng*h/mL
Endpoint classificationContinuous Endpoint

The primary endpoint, AUCss, measures the area under the plasma concentration–time profile across 24 hours at steady state on day 5. The registry describes this as AUCtau as well. In general, area under a concentration–time curve represents cumulative systemic exposure across the specified interval: it reflects both the concentrations measured and how those concentrations change over time.

This measure is useful in a pharmacokinetic comparison because the regimens use different dosing schedules. Looking across a full 24-hour interval captures exposure over the entire stated dosing period rather than focusing only on a single concentration measurement. It provides a way to compare overall exposure under once-daily dosing with exposure under repeated immediate-release dosing. It does not, by itself, describe the shape of the concentration profile. Peak, minimum and fluctuation measures address other aspects of that profile.

The posted outcome is a continuous measure reported as a mean and standard deviation for each regimen. The mean describes the average AUCss in the reported group; the standard deviation describes how much individual measurements varied around that mean. A comparison of means is informative about average exposure, but it does not establish that the full distributions are alike or that individual participants had similar profiles under both regimens.

For the primary result, the registry comparison expresses the mean difference as the immediate-release regimen minus the once-daily regimen. The reported interval around that difference includes values on either side of zero. The registry record does not report a prespecified equivalence margin, acceptance limits, or a formal bioequivalence analysis. Consequently, the endpoint supports a descriptive comparison of average steady-state exposure and its precision, but the posted result alone should not be read as a formal conclusion of equivalence or non-equivalence.

7. Results Posted in the Registry

Mean difference: Tramadol IR (Ultram®) 50 mg 6-hourly

408.00

95% CI: -441.79 to 1,258

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals5,3205,7036,0876,4716,8547,238Tramadol HCl OAD 200 mg (n=26)Tramadol IR (Ultram®) 50 mg 6… (n=26)ng*h/mL (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Tramadol IR (Ultram®) 50 mg 6…-578-1832116059991,394mean 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
Maximum Plasma Concentration at Steady State(Cmax,ss)Continuous EndpointMean difference78.00 (31.34 to 124.66)20 per arm
Minimum Plasma Concentration at Steady State(Cmin,ss)Continuous EndpointMean difference33.00 (2.25 to 63.75)47 per arm
Percentage Peak-trough Fluctuation (% PTF)Continuous EndpointMean difference14.20 (3.33 to 25.07)32 per arm

Maximum Plasma Concentration at Steady State(Cmax,ss)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Tramadol IR (Ultram®) 50 mg 6…-9.97194877106135mean difference vs control (95% CI)

Minimum Plasma Concentration at Steady State(Cmin,ss)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Tramadol IR (Ultram®) 50 mg 6…-5.109.6924395469mean difference vs control (95% CI)

Percentage Peak-trough Fluctuation (% PTF)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Tramadol IR (Ultram®) 50 mg 6…-2.013.819.63152127mean difference vs control (95% CI)

The secondary measures add information about the concentration profile beyond total exposure. The registry lists peak and minimum steady-state concentration, time to peak exposure, peak-trough fluctuation, percentage swing, half-value duration and plateau time. Numerical comparison results are posted for some of these measures, but numerical results for the other listed outcomes are not reported in the registry record.

Across the secondary outcomes with numerical comparisons posted, the reported mean values are directionally higher for the immediate-release regimen. This broad pattern complements the primary exposure comparison by indicating that the profiles differed in measures of concentration and fluctuation as well as in the overall area measure. It should not be read as a single coherent or definitive finding: each outcome captures a different feature, and the primary result remains imprecise.

Secondary results generally carry less evidential weight than a prespecified primary result. Multiple outcomes create more opportunities for nominally small p-values, even when each comparison is evaluated separately. The posted secondary p-values are unadjusted, and the registry record does not report a multiplicity strategy, a hierarchy among secondary outcomes, or a prespecified rule for interpreting them together. Their estimates and confidence intervals can still be informative descriptively, but nominal p-values should not be treated as confirmatory evidence without accounting for the family of analyses and the analysis plan.

The secondary comparisons also share limitations with the primary comparison. The record does not provide participant-level paired results or a detailed crossover model, and it does not report how missing measurements were handled. In addition, an observed direction across several measures does not establish why profiles differ or what the differences mean clinically. The secondary results are best viewed as supporting descriptive context for the pharmacokinetic profile, rather than as a replacement for the primary endpoint or as proof of a clinical benefit or harm.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For AUCss, the reported mean was 5991.0 ng*h/mL for Tramadol HCl OAD 200 mg and 6399.0 ng*h/mL for Tramadol IR (Ultram®) 50 mg 6-hourly. Each treatment condition has a reported sample size of 26. The posted mean difference is 408.0 ng*h/mL, defined in the comparison as immediate release minus once daily. Its 95% confidence interval runs from -441.8 to 1258.0 ng*h/mL, and the unadjusted p-value is 0.347.

The estimate is positive, so the observed average was higher under the immediate-release regimen in these posted summaries. The interval is wide enough to include zero and values in either direction. The result therefore does not clearly distinguish a positive difference from no difference or a difference in the opposite direction. The p-value is consistent with that uncertainty; it is not a measure of the probability that the regimens are equivalent, nor does it establish that they are the same.

The observed means are close relative to the spread reported within each treatment condition, but that visual or descriptive comparison is not a formal equivalence test. Equivalence requires a prespecified range of differences considered acceptably small and an analysis showing that the confidence interval lies within that range. Such a margin and decision rule are not reported in the registry record. The result should therefore be described as an imprecise estimate of the difference in mean AUCss, rather than as proof of equivalence.

The registry labels the study as crossover, but the posted summaries do not provide the paired participant-level data or a reported crossover-model analysis. The comparison is therefore interpreted as the posted summary-statistic comparison, not as an independently reconstructed paired analysis. The registry lists no reported analyses for the outcomes. There is no sponsor-reported analysis in the record against which the posted comparison could be checked, and the record does not explain how treatment period, sequence or within-participant correlation were handled.

The secondary results show a consistent direction among the measures with numerical comparisons posted: the immediate-release regimen has higher reported means for the listed concentration and fluctuation measures. These are secondary comparisons, and their p-values are unadjusted. They should not be treated as independent confirmation of a primary conclusion, especially when several outcomes are considered and no multiplicity procedure is reported. In addition, several listed secondary outcomes lack numerical results in the registry record.

Overall, the posted data describe average pharmacokinetic measurements for the two regimens in a small healthy-subject crossover study. They do not establish a clinical effect, and they do not establish formal bioequivalence. The primary estimate is compatible with more than one interpretation because its confidence interval spans zero and is broad. Its meaning depends on the question of interest and on criteria that are not reported in the registry record.

10. Statistical Methods Explained

The outcomes are continuous pharmacokinetic measures. For each treatment condition, the registry reports a mean and standard deviation. A mean gives the average observed value; a standard deviation describes the dispersion of individual values around that average. These summaries are useful for understanding the scale and variability of an outcome, but they do not show the full distribution, outliers, or how each participant’s response changed between regimens.

What does a mean difference describe?

A mean difference compares the two reported averages. For the primary endpoint, the comparison is defined as the immediate-release mean minus the once-daily mean. A positive estimate therefore indicates a higher reported average under immediate release, while a negative estimate would indicate a higher reported average under once-daily dosing. The estimate is expressed in the endpoint’s units, ng*h/mL. Its sign describes direction, not whether the size is clinically or pharmacologically important.

The registry comparison includes a confidence interval around the mean difference. In general, a confidence interval describes the range of estimates compatible with the observed data and the statistical procedure used, under its assumptions. It communicates uncertainty more directly than a point estimate alone. If the interval includes zero, the data do not clearly resolve the direction of the difference at the conventional two-sided level associated with the reported interval. That does not prove no difference. It also does not answer whether differences are small enough to satisfy a separately defined equivalence criterion.

What does the p-value add?

The unadjusted p-value is a measure of how unusual data at least as inconsistent with a null difference would be under the null hypothesis and the analysis assumptions. It is not the probability that the null hypothesis is true, and it does not measure the probability that the observed result will replicate. A p-value should be read together with the estimate, its confidence interval, the study design and the analysis plan. The posted p-values are described as unadjusted; the registry record does not report a multiplicity adjustment.

For the primary comparison, the estimate is 408.0 ng*h/mL, with a 95% confidence interval from -441.8 to 1258.0 ng*h/mL and an unadjusted p-value of 0.347. The interval’s inclusion of zero is central to interpretation: it leaves uncertainty about both the presence and direction of an average difference. The p-value does not turn that uncertainty into evidence of equivalence.

Why does the crossover design matter?

In general, a crossover design exposes participants to more than one regimen and can use within-participant comparisons. Measurements from the same person are often related. If the analysis uses that relationship appropriately, the precision of a treatment contrast can differ from a comparison treating the two conditions as unrelated groups. Period and sequence can also matter if responses change over time or depend on treatment order. These are general features of crossover analysis, not claims about the analysis used in this trial.

The registry labels this study as crossover and randomized, but it does not report the treatment sequence, washout interval, period-specific outcome summaries, paired differences, within-participant correlation, or a model accounting for period or sequence. The comparison information does include pooled variability and other summary-based quantities, but those do not substitute for a reported crossover analysis or participant-level paired data. It is therefore appropriate to interpret the comparison as the posted summary-statistic result and not to infer details of an unreported model.

The reported means and standard deviations describe each treatment condition, with 26 observations reported for each. In a crossover study, the same participants may contribute observations under multiple conditions; the registry’s arm-level counts do not by themselves describe how many complete paired records entered a particular analysis. The record does not report analysis-population definitions or missing-data handling, so the exact relationship between enrollment and analyzed observations is not fully specified.

How should standardized effects be understood?

A standardized effect expresses a mean difference relative to a measure of variability. In general, standardization can make effect magnitudes easier to compare across outcomes measured on different scales. It does not make outcomes clinically interchangeable, and it depends on how variability is defined. The posted comparison includes standardized-effect information, but the registry does not report a clinical threshold that would make a particular standardized value important. Interpretation should therefore remain anchored to the endpoint units and its confidence interval.

For the primary endpoint, the registry reports a pooled standard deviation of 1563.0 and a standardized difference of 0.261. These figures describe the posted summary comparison; they do not establish a clinical or regulatory threshold. The record does not explain whether the pooled variability represents the most appropriate variance for a crossover contrast. A within-participant standard deviation would require information about the paired measurements that is not reported.

What does the planning illustration represent?

The sample-size illustrations are based on the observed effect and assumptions stated for the illustration: a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and detection of the stated fraction of the observed effect. The primary outcome planning entries are expressed as participants per arm. These calculations are planning scenarios, not a reconstruction of the study’s original design. The registry does not report the original sample-size justification or its assumptions.

For general interpretation, smaller effects are harder to distinguish from random variation when other assumptions are unchanged, and planning for smaller effects therefore requires more participants. The 80% and 90% columns describe the planned probability of rejecting a null difference under the illustration’s assumptions if the specified effect were the true effect. They do not describe the probability that the trial’s result is correct. Because the illustration uses the observed effect as its starting point, it is not observed power and does not provide a retrospective test of whether the completed study was adequate.

All of these methods depend on assumptions about the outcome distribution, variance, allocation and analysis. The registry record does not report diagnostic checks, transformation choices, covariate adjustment, handling of outliers, or a detailed statistical analysis plan. Those choices cannot be inferred from the numerical summaries alone. The posted estimates are best read as a limited summary of the comparison, with uncertainty made explicit by the confidence interval.

11. Confidence Intervals and Precision

The primary mean difference is 408.0 ng*h/mL, with a 95% confidence interval from -441.8 to 1258.0 ng*h/mL. This interval is the key description of precision: it gives a range of values compatible with the observed comparison under the procedure’s assumptions. It includes zero, so the posted result does not resolve whether the mean difference is positive or negative. It also includes values meaningfully away from zero in either direction, leaving substantial uncertainty about the size of any difference.

The interval is more informative than the point estimate alone. The estimate of 408.0 is one value derived from the data, while the interval indicates that the true average contrast is not pinned down precisely by this sample and analysis. The interval should not be read as a range containing every participant’s response, nor as a probability statement about the specific true value. It pertains to uncertainty in the estimated mean difference under the assumptions of the statistical procedure.

Each treatment condition has 26 observations reported, and the standard deviations are 1330.0 for once-daily dosing and 1766.0 for immediate-release dosing. Those values indicate variability in individual AUCss measurements. The registry comparison does not provide paired participant-level results or a confidence interval from a described crossover model. Since within-participant association can affect precision in a crossover design, the record does not allow readers to assess how the posted interval relates to a paired analysis.

Precision and equivalence are distinct. A narrow interval lying within a prespecified equivalence margin could support an equivalence conclusion under an appropriate analysis. Here, no equivalence margin is reported, and the primary interval includes zero while extending in both directions. The posted result is therefore uncertain about the average difference; it is not evidence that the regimens are identical. The registry record does not report an equivalence decision or a formal bioequivalence assessment.

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 effect231309
75% of the observed effect410549
50% of the observed effect9221,235
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%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: Tramadol IR (Ultram®) 50 mg 6-hourly.

The planning illustrations give participants per arm for these continuous-outcome scenarios, not total event counts. Their assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect equal to the stated fraction of the observed effect. The registry record does not report the assumptions used for the study’s original design or its original sample-size justification.

The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect, if that effect were true and the assumptions held. The 90% column expresses the corresponding planning target for a 90% chance. These are planning probabilities under a stated hypothetical scenario; they do not indicate the probability that the observed result is correct, nor do they tell whether a particular treatment effect is important.

The rows consider planning for 100% of the observed effect, 75% of the observed effect and 50% of the observed effect. For the primary outcome, those scenarios correspond to 231, 410 and 922 participants per arm for 80% power, and 309, 549 and 1,235 participants per arm for 90% power. The smaller-effect scenarios require more participants because smaller differences are harder to distinguish from random variation when the other assumptions remain fixed.

These figures are illustrative rather than a record of how the trial was designed. They use the observed effect as a reference, which can be unstable in a small study. They do not account for any unreported crossover-specific design features or analysis choices. The figures are not observed power; observed power is not a useful substitute for interpreting the estimate and confidence interval. Precision should be judged from the uncertainty around the posted result, while a future design should be based on a justified target effect and an appropriate design analysis.

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 = 408.000; pooled standard deviation σ = 1563.275.
  2. n = 2 × (1.96 + 0.842)2 × 1563.2752 / 408.0002 = 230.5, rounded up to 231 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 <- 408                      # observed difference in means
sigma <- 1563.2747679151                     # 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(834288)
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 = 231 (80% power), 309 (90% power)
 75% of observed effect: n per arm = 410 (80% power), 549 (90% power)
 50% of observed effect: n per arm = 922 (80% power), 1,235 (90% power)
power.t.test: 231.4 
Simulated power at n = 231 per arm: 0.801 (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

Multiplicity arises when several outcomes or comparisons are tested. Even when each test uses the same nominal threshold, evaluating multiple results increases the chance that at least one appears unusual by chance alone. This is why a statistical plan may specify a primary endpoint, order secondary outcomes, adjust significance levels, or treat secondary findings as exploratory. The registry record identifies a primary endpoint and lists secondary measures, but it does not report a multiplicity adjustment, testing hierarchy, or other strategy for controlling the interpretation of multiple results.

The posted secondary p-values are unadjusted. They can be read as outcome-specific summaries under their own assumptions, but they should not be interpreted as if only one comparison had been considered. The primary result also needs to be interpreted in the context of the stated design and available analysis information. The registry lists no reported analyses for the outcomes, and it does not report a full statistical analysis plan. Thus, it is not possible to determine whether the posted comparisons reflect a prespecified analysis or how the investigators intended to handle multiple endpoints.

The record does not report missing-data handling, analysis populations, exclusions, or the number of participants with complete measurements for each outcome. Enrollment is 26, and each treatment condition has 26 observations reported in the posted summaries, but those figures do not reveal whether every enrolled participant contributed every measurement or how incomplete records were treated. A participant flow account and outcome-specific missingness details are not reported in the registry record.

Because this is a crossover study, the analysis population and completeness of paired observations are especially relevant. A participant may have measurements under one regimen but not another, and a paired comparison may require both. The record does not say whether the estimates were based on complete pairs, how any incomplete periods were handled, or whether period or sequence effects were considered. No assumptions about these decisions should be inferred from the summary statistics.

These reporting gaps limit reproducibility and make it difficult to assess whether the analysis matches the design. They do not establish that a particular method was or was not used; the relevant details are simply not reported in the registry record. The appropriate interpretation is to treat the posted outcomes as descriptive and to give unadjusted secondary results less weight than a fully specified confirmatory analysis.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Tramadol HCl OAD 200 mg0260.0%
Tramadol IR (Ultram®) 50 mg 6-hourly0260.0%

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Tramadol HCl OAD 200 mg12 of 26
Tramadol IR (Ultram®) 50 mg 6-hourly10 of 26

Most frequent non-serious adverse event terms

Event termOrgan systemTramadol HCl OAD 200 mgTramadol IR (Ultram®) 50 mg 6-hourly
HeadacheGeneral disorders5 of 263 of 26
ConstipationGastrointestinal disorders4 of 263 of 26
NauseaGastrointestinal disorders3 of 261 of 26
VomitingGastrointestinal disorders3 of 261 of 26
Dry mouthGeneral disorders2 of 260 of 26
ALT elevated/raisedBlood and lymphatic system disorders0 of 262 of 26
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 reports zero participants with serious adverse events in each treatment condition: 0 of 26 for Tramadol HCl OAD 200 mg and 0 of 26 for Tramadol IR (Ultram®) 50 mg 6-hourly. These are counts among the participants at risk as recorded for each regimen. No serious adverse event terms are listed in the record.

A zero count in a group of this size means that no serious adverse events were recorded in the posted results for that group; it does not show that the risk is zero or rule out events that could occur less commonly. The record does not report deaths in the safety summaries, so mortality figures are not reported in the registry record.

Other adverse events are reported separately from serious adverse events. The registry lists 12 participants affected in the once-daily group and 10 in the immediate-release group for that broader category. Those counts should not be confused with serious events, and they do not by themselves identify event type, severity or treatment relationship. The registry record does not provide enough detail in these summaries to draw conclusions about comparative safety. These counts describe the posted safety results and are not medical advice.

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

The posted results answer a limited statistical question: how the average steady-state pharmacokinetic measures compared between two tramadol regimens in this randomized crossover study of healthy subjects. For the primary 24-hour AUCss outcome, the estimated mean difference favors a higher average under immediate-release dosing, but the confidence interval includes zero and spans values in both directions. The result is therefore uncertain about the direction and size of the average difference.

That uncertainty is not the same as proof that the regimens are equivalent. A formal equivalence assessment needs a prespecified acceptable range and an analysis designed to test whether the uncertainty interval falls within that range. The registry record does not report those criteria or a formal bioequivalence analysis. A non-significant unadjusted p-value likewise does not establish sameness. It indicates that the posted comparison does not provide a clear distinction from a zero difference under its assumptions.

Nor does the primary endpoint describe every feature of drug exposure. AUCss summarizes exposure over the specified interval, while peak, minimum and fluctuation measures describe aspects of the concentration profile. The available secondary results provide some additional profile information, but several listed outcomes do not have numerical results in the registry record. Unadjusted secondary findings are less conclusive when multiple outcomes are considered without a reported multiplicity plan.

The study concerns pharmacokinetics in healthy subjects, not clinical efficacy or patient outcomes. It does not establish whether either regimen improves symptoms, changes clinical outcomes, or is preferable for any individual. The posted averages also cannot show how similar or different responses were within particular participants. Although the design is crossover, the record does not report the paired analysis details needed to assess that comparison fully.

The most defensible reading is that the registry reports mean exposure and concentration-profile summaries from a small phase 1 study, with substantial uncertainty around the primary mean difference and incomplete reporting of analysis methods. The estimates can inform understanding of the measured pharmacokinetic profiles, but they should not be extended to claims about clinical effectiveness, safety beyond the posted event counts, or formal bioequivalence.

17. Why This Trial Matters Statistically

This trial is statistically useful because it illustrates the difference between a point estimate and a conclusion. The AUCss estimate is positive, but its confidence interval covers zero and extends in both directions. Reporting the estimate with its interval makes the uncertainty visible; focusing only on the direction of the means or the p-value would give an incomplete account.

The crossover design also highlights why design information matters to interpretation. In general, crossover studies can use within-participant comparisons, but the precision and validity of those comparisons depend on treatment order, period structure, paired data and an appropriate analysis. The registry identifies the study as crossover but does not report several details needed to assess those features. A design label alone is not enough to reconstruct how the data were analyzed.

The study also shows why a pharmacokinetic comparison should not automatically be called an equivalence study. Similar-looking averages and a p-value that does not distinguish a difference are not substitutes for prespecified equivalence limits and a formal analysis. Those criteria are not reported in the registry record. The statistical question supported by the posted result is narrower: what mean difference was estimated, and how uncertain is that estimate?

Finally, the secondary measures illustrate the role of multiplicity. Several aspects of the concentration profile were measured, but the registry does not report an adjustment or hierarchy for interpreting the set of outcomes. A pattern across secondary summaries can be scientifically interesting while still carrying less weight than a prespecified, fully reported analysis. Distinguishing descriptive evidence from confirmatory inference is important when reading multiple outcomes.

18. Limitations

The primary limitation is incomplete reporting of the analysis. Although the study is described as randomized and crossover, the registry does not report the sequence allocation, washout interval, period-specific results, paired differences, or the model used to account for repeated measurements. Those details are important because observations from the same participant may be related, and period or sequence effects may influence a crossover comparison.

The record also does not report the original sample-size justification, statistical analysis plan, missing-data procedures, analysis populations, or whether interim analyses were planned. The posted planning illustrations are not evidence of the original design assumptions. Without outcome-specific completeness information, the reported counts do not show whether every enrolled participant contributed a complete set of measurements.

There is no reported equivalence margin or formal bioequivalence decision rule. This limits what can be concluded from the primary confidence interval, even though the study’s stated purpose concerns comparative bioavailability. The registry also lists secondary outcomes for which numerical results are not reported, and it does not describe a multiplicity strategy for the outcomes with posted comparisons.

The participants were healthy subjects, and the endpoint was pharmacokinetic exposure over a specified interval. The results therefore do not directly establish clinical outcomes in patients. The posted safety counts are also limited summaries and do not provide detailed event descriptions or establish comparative safety. These limitations concern the scope and reporting of the registry record; they do not establish that omitted procedures were not performed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

22. Record Summary

The registry describes a completed, randomized, unmasked phase 1 crossover study sponsored by Labopharm Inc. It enrolled 26 healthy subjects and compared Tramadol HCl OAD 200 mg once daily with Tramadol IR (Ultram®) 50 mg every six hours under fasting conditions. The primary outcome was mean AUCss over 24 hours on day 5.

The posted primary comparison gives a mean difference of 408.0 ng*h/mL for immediate release minus once daily, with a 95% confidence interval from -441.8 to 1258.0 ng*h/mL and an unadjusted p-value of 0.347. The estimate is uncertain and does not establish equivalence. Some secondary numerical comparisons and safety counts are posted, but the registry record does not report several analysis details needed to assess the crossover analysis, multiplicity, missing data or formal bioequivalence criteria.

Clinical Biostats