Alprazolam Extended-Release 3mg Tablets Bioequivalence Study Under Fasting Conditions: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Alprazolam Extended-Release 3mg Tablets Bioequivalence Study Under Fasting Conditions (NCT00829426), a randomized phase 1 study. The primary outcome is Cmax - Maximum Observed Concentration.

2. Clinical Question

3. Trial Design

This was a randomized, phase 1, open-label crossover study in healthy subjects. The registry describes two treatment sequences: test alprazolam followed by reference Xanax XR®, and reference Xanax XR® followed by test alprazolam. Each product was described as a single oral dose of one 3 mg extended-release tablet under fasting conditions. Blood samples for the primary endpoint were collected over a 72 hour period.

A crossover design compares treatments within participants across periods, rather than assigning each participant to only one treatment throughout the study. Randomizing the sequence can help distribute period order across treatment sequences. These are general features of crossover studies; the registry record does not describe the specific randomization procedure, washout duration, or other operational details. The record lists masking as none, so the study was not masked according to the registry.

The record lists enrollment as 32 and status as completed. For the primary analysis, it states that data from all subjects who completed the study were included. The arm summaries each report 31 observations. The record does not explain the difference between the enrollment figure and the arm summaries, or report reasons for any participants not represented in those summaries. It also does not describe the study’s original sample-size rationale or the full analysis protocol. The sponsor was Teva Pharmaceuticals USA.

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.

First Intervention

Washout: 7 Days

Reasons for not completing this period:

Second Intervention

Analysis population for the primary outcome, as defined in the registry: Data from all subjects who completed the study were included in the statistical analysis.

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 Cmax - Maximum Observed Concentration, measured over Blood samples collected over 72 hour period.

The primary endpoint was Cmax, the maximum observed concentration of alprazolam in blood after dosing. It is a continuous measure reported in ng/mL. In general, concentration measurements describe drug exposure over time; Cmax focuses on the highest observed concentration in the sampling period. It is used in relative bioavailability comparisons because it reflects the peak concentration reached after a dose, alongside other measures that may characterize exposure over time.

The registry describes the primary outcome as a mean with standard deviation and states that bioequivalence was based on Cmax. Blood samples were collected over a 72 hour period. The arm summaries report mean Cmax values of 24.33 ng/mL for alprazolam and 23.62 ng/mL for Xanax®, with standard deviations of 5.37 and 4.29, respectively. These summaries describe the observed concentrations in the analysis data; they are not, by themselves, a complete account of the sponsor’s bioequivalence analysis.

For a crossover study, the within-participant pattern across treatments can be important to estimating a treatment comparison. The registry record does not give participant-level concentrations or explain how the primary analysis accounted for the crossover structure. The posted sponsor analysis instead reports a geometric test/reference ratio, while the simple recalculation uses the posted arm means. Those are different statistical summaries and should not be treated as interchangeable.

7. Results Posted in the Registry

• Xanax®: mean 23.62 versus 24.33 on control; difference -0.71 (95% CI -3.13 to 1.71), standardized effect d = -0.15; z-test p = 0.565.

8. Statistical Interpretation

9. Statistical Methods Explained

Several statistical ideas help distinguish the posted results. The primary measure, Cmax, is continuous: it can take values across a numerical scale. The arm summaries use means and standard deviations. A mean describes the central level of the observed measurements, while a standard deviation describes how spread out those measurements are around the mean. The reported standard deviations are not confidence intervals and do not directly express uncertainty about the treatment comparison.

What does the mean difference describe?

The recalculated comparison uses the posted arithmetic means to express the difference in Cmax on its original scale. Its estimate is -0.71 ng/mL, comparing Xanax® with alprazolam. A value of zero would mean no difference between the two displayed means. Values below or above zero indicate direction on this subtraction scale. The reported 95% confidence interval runs from -3.13 to 1.71, and the unadjusted p-value is 0.565. These are simple, unadjusted recalculations from the posted summary statistics, not a reproduction of the sponsor’s reported analysis.

In general, a p-value measures how compatible the observed data are with a specified null model, under the assumptions of the test. It is not the probability that the null hypothesis is true, nor a measure of the size or clinical importance of an effect. The p-value is identified as unadjusted. The registry record does not report a multiplicity adjustment or the detailed test specification for this recalculation.

Why is the ratio a different estimand?

The sponsor-reported measure is a geometric test/reference ratio multiplied by 100. A ratio describes relative rather than absolute separation. A ratio scale is often useful for exposure measures when the comparison is naturally interpreted multiplicatively. A value around 100 on this multiplied scale represents a ratio around one before multiplication. The posted estimate is 102.56, with a 90% confidence interval from 98.74 to 106.52. This is not the same measure as a difference of arithmetic means, and the two estimates should not be directly substituted for one another.

In general, geometric summaries are associated with analyses of values on a logarithmic scale and subsequent expression of the comparison as a ratio. However, the registry record does not identify the sponsor’s analysis method, transformation, model, or any covariates. It is therefore not possible to verify those details from the posted record, or to assert that a particular standard model was used.

What does a crossover design change?

In general, a crossover comparison can use information about how each participant’s response changes between treatments. The relationship between measurements from the same participant can affect the uncertainty of a treatment comparison. The registry identifies a crossover design and gives the treatment sequence descriptions, but does not report participant-level paired results, the within-participant correlation, or the model used to account for period and sequence. The simple recalculation is based on posted group summary statistics and should not be mistaken for a full analysis of the crossover data.

The arm-level standard deviations describe dispersion in each treatment summary. They do not reveal how closely paired measurements within participants move together. Without that paired information and the sponsor’s method, an independent reconstruction of the sponsor’s crossover analysis is not possible from the registry record. The posted recalculation is useful as a transparent, unadjusted comparison of available summaries, but it has a narrower interpretation than the sponsor’s own reported ratio analysis.

How should confidence intervals be read?

In general, a confidence interval gives a range of estimates compatible with the data and the method used to calculate it. It captures uncertainty in an estimate rather than the spread of individual observations. The 95% interval attached to the recalculated mean difference and the 90% interval attached to the sponsor-reported ratio have different confidence levels and apply to different estimands. They should not be compared as if they were intervals for the same quantity.

A confidence interval’s interpretation also depends on the analysis assumptions. The registry does not report enough detail to assess the sponsor’s complete model or the handling of the crossover structure. The recalculated interval is explicitly unadjusted. Neither interval supplies an unstated acceptance margin for bioequivalence. When margins and a prespecified decision rule are absent, the interval can be described numerically, but a formal equivalence conclusion cannot be independently reconstructed from the registry record.

What do the planning calculations mean?

The sample-size figures are planning illustrations calculated from the observed effect, not from the trial’s own design assumptions. They use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the planning effect is the stated fraction of the observed effect. The figures describe participants per arm for 80% power or participants per arm for 90% power under those assumptions. They are not a report of the trial’s achieved power. As a general principle, aiming to detect a smaller effect requires more participants when other planning assumptions are held constant.

These calculations do not establish what sample size was considered adequate when the study was designed. The original design assumptions, including any prespecified target effect or sample-size justification, are not reported in the registry record. They also do not replace a crossover-specific sample-size calculation, since the planning assumptions listed for this illustration specify equal allocation between two arms and do not describe use of within-participant variation.

10. Confidence Intervals and Precision

Precision concerns how much uncertainty surrounds an estimate. The recalculated mean difference is -0.71 ng/mL, and its 95% confidence interval extends from -3.13 to 1.71. Because the interval includes zero and values on both sides of zero, the estimate does not pin down the direction of the mean difference with high precision. The interval also indicates that a range of mean differences is compatible with this unadjusted calculation; it is not a range containing every participant’s observed Cmax.

The sponsor-reported geometric test/reference ratio multiplied by 100 is 102.56, with a 90% confidence interval from 98.74 to 106.52. That interval concerns the ratio-scale estimate and uses a different confidence level from the mean-difference interval. Its width reflects uncertainty under the sponsor’s reported analysis, but the analysis method is not reported in the registry record. The interval should not be interpreted against a threshold unless the relevant margin and decision rule are known.

Both summaries are based on the posted analysis data, but the registry’s crossover record does not include the paired participant-level results or sufficient methodological detail to reproduce the sponsor’s model. The arm means and standard deviations alone do not show the degree of within-participant association. Accordingly, the recalculated interval provides a limited, unadjusted view of precision, while the sponsor’s interval is the posted result for a different estimand. Neither interval should be treated as a measure of individual response variability.

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 apply to a continuous outcome, rather than a time-to-event endpoint. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to a stated fraction of the observed effect. The figures are planning illustrations and are not observed power.

The 80% power column gives the planning number of participants per arm under which the calculation targets an 80% chance of detecting the specified effect, if the assumptions and effect are appropriate. The 90% power column uses a higher target chance of detection and therefore gives a separate planning requirement. These are prospective planning interpretations, not descriptions of what happened in this completed trial.

The rows scale the assumed effect to 100%, 75%, or 50% of the observed effect. For the 100% row, the figures are 736 participants per arm for 80% power and 985 participants per arm for 90% power. For 75% of the observed effect, they are 1,308 and 1,751 participants per arm. For 50% of the observed effect, they are 2,943 and 3,939 participants per arm. The pattern illustrates a general planning principle: smaller effects require more participants to detect under otherwise unchanged assumptions.

The calculation is based on the observed effect and a simplified normal approximation. It does not report the original target or assumptions for this study, and it should not be read as evidence that the trial had a particular probability of detecting an effect. The trial’s own design justification and original sample-size assumptions are not reported in the registry record.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -0.710; pooled standard deviation σ = 4.860.
2. n = 2 × (1.96 + 0.842)² × 4.860² / -0.710² = 735.5, rounded up to 736 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.709999999999997                      # observed difference in means
sigma <- 4.86009259171057                     # 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(829426)
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 = 736 (80% power), 985 (90% power)
 75% of observed effect: n per arm = 1,308 (80% power), 1,751 (90% power)
 50% of observed effect: n per arm = 2,943 (80% power), 3,939 (90% power)
power.t.test: 736.5 
Simulated power at n = 736 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.

13. Analyses Reported by the Sponsor

The registry’s sponsor-reported analysis gives a geometric test/reference ratio multiplied by 100 of 102.56, with a 90% confidence interval from 98.74 to 106.52. It identifies the measure as a legacy non-inferiority-or-equivalence analysis, but does not report the method, decision margins, or p-value. The posted ratio is the sponsor’s analysis and should be kept distinct from the simple recalculation based on arithmetic means.

The recalculation compares the arm means and reports an unadjusted mean difference of -0.71 ng/mL, with a 95% confidence interval from -3.13 to 1.71 and an unadjusted p-value of 0.565. It uses a different scale and a different summary statistic from the sponsor’s geometric ratio. Because the registry does not give enough detail to reproduce the sponsor’s analysis, the recalculation is not a substitute for it and should not be treated as an independent confirmation of the sponsor’s method or conclusion.

No discrepancy is flagged between the posted results and the recalculation. Nonetheless, the two results address related but distinct estimands. The registry record does not provide the equivalence margins or analysis details needed to independently determine how the sponsor applied its stated analysis category.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists three outcome measures and three analyses. The primary outcome is Cmax, and the endpoint description states that bioequivalence was based on Cmax. The record does not provide the other outcome details in the information reported for this analysis, and it lists no secondary outcomes as posted. The existence of multiple measures and analyses makes it important to know whether and how the analysis plan addressed multiple comparisons, but the registry record does not report a multiplicity strategy.

Multiplicity refers generally to the increased chance of a false-positive finding when multiple statistical hypotheses are examined. Methods such as prespecifying a primary endpoint or adjusting significance levels can address particular multiplicity concerns, but the registry does not state whether any such procedure was planned or used. The unadjusted p-value for the recalculated comparison should therefore be understood as unadjusted; no adjustment can be inferred from the registry information.

The primary analysis population is described as data from all subjects who completed the study. The record does not provide a more detailed definition of the analysis set, a participant flow account, or reasons why the arm summaries report 31 observations when enrollment is listed as 32. It does not explain whether all completed participants had complete measurements for every outcome, or how incomplete or unusable measurements were handled.

Missing-data procedures, imputation, sensitivity analyses, and rules for excluding observations are not reported in the registry record. The record also does not report interim analyses or a detailed statistical analysis plan. These omissions do not establish that such procedures were absent; they mean that they cannot be characterized from the registry record. The crossover design makes information about period-specific completion and paired observations potentially relevant, but those details are not reported.

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

The posted data describe Cmax after a single dose of test alprazolam extended-release tablets and reference Xanax XR® tablets under fasting conditions in healthy subjects. The arm means are close in numerical value, and the unadjusted mean-difference estimate is -0.71 ng/mL. Its 95% confidence interval spans -3.13 to 1.71, while the unadjusted p-value is 0.565. These results describe the observed summaries and the uncertainty from that recalculation; they do not prove that the products are identical.

The sponsor’s analysis reports a geometric test/reference ratio multiplied by 100 of 102.56 and a 90% confidence interval from 98.74 to 106.52. The registry record describes this as an analysis related to non-inferiority or equivalence, but does not report the method or decision margins. A formal conclusion under an equivalence framework depends on the prespecified margins and analysis rules. Without those details, the ratio and its interval can be reported but cannot be independently converted into a definitive equivalence judgment.

The results are limited to the endpoint and setting described. Cmax is a peak concentration measure; it does not fully summarize every feature of concentration over time. The study involved a single oral dose, fasting conditions, and healthy subjects. It does not, on the information reported, establish results for other populations, dosing conditions, formulations, or outcomes.

The recalculated comparison is based on group summary statistics and is not a reconstruction of the sponsor’s crossover analysis. The record does not provide the full statistical model, paired data, or enough details to assess every analysis assumption. Its absence should not be interpreted as evidence of a particular result. The numerical findings are best read as the posted endpoint summaries and analysis estimates, with the limits of their reporting kept in view.

16. Why This Trial Matters Statistically

This study illustrates why statistical interpretation depends on the estimand, not just the numerical proximity of two results. The recalculated arithmetic mean difference is on the original Cmax scale, whereas the sponsor-reported geometric test/reference ratio is on a relative scale. Both concern the same primary endpoint, but they are not interchangeable summaries. An analyst must identify which comparison is being interpreted before drawing conclusions from its estimate or interval.

The crossover design also highlights the importance of the relationship between measurements from the same participant. In general, paired treatment data can provide information that is not visible in separate arm means and standard deviations. The registry identifies the sequence structure but does not report the paired data or detailed model. That makes it possible to describe the posted results, while limiting the extent to which an outside reader can reproduce the sponsor’s analysis.

Equivalence questions require more than a non-significant difference test. The sponsor-reported ratio is accompanied by a 90% confidence interval, but the registry record does not state the applicable equivalence margins or analysis method. This example therefore shows why a ratio estimate, its interval, the prespecified margins, and the statistical model all matter when interpreting an equivalence-oriented analysis.

Finally, planning calculations based on an observed effect have a distinct role from the original sample-size justification. They illustrate how required participants per arm change as the target effect is made smaller under stated assumptions. They do not reveal the study’s original design rationale or its probability of detecting an effect. Keeping descriptive results, sponsor analysis, recalculation, and planning illustrations separate supports a more precise reading of the record.

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 record does not report the sponsor’s statistical method for the geometric ratio, the model terms, or how the crossover structure was handled. It also does not provide paired participant-level measurements or the within-participant variation needed to reproduce a detailed crossover comparison. Consequently, the simple unadjusted recalculation cannot verify or replace the sponsor’s analysis.

The record does not give the bioequivalence margins or a complete decision rule. Although it identifies the sponsor-reported analysis as related to non-inferiority or equivalence and posts a 90% confidence interval, those details are not sufficient to independently judge the result against a formal criterion. The record also does not report an analysis plan or explain how the multiple listed measures and analyses were handled.

Enrollment is listed as 32, while the arm summaries each report 31 observations and the primary analysis description refers to subjects who completed the study. The reason for this difference, participant flow, and handling of missing or incomplete measurements are not reported in the registry record. There is no basis in the posted information to infer why observations differ or whether the same subjects contributed to each summary.

The outcome described is Cmax, measured from blood samples collected over a 72 hour period. The record does not detail the sampling schedule, assay procedures, washout duration, or other operational methods that could be relevant to interpreting a crossover bioavailability study. The results are also tied to healthy subjects, a single dose, and fasting conditions. These limits define the scope of what can be concluded from the posted information; they do not establish that unreported procedures were or were not conducted.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Alprazolam Extended-Release 3mg Tablets Bioequivalence Study Under Fasting Conditions — NCT00829426.
• Registry record last updated 2024-09-19; status last verified 2024-08.
• Results first posted 2009-07-21.
• 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

NCT00829426 is a completed phase 1 randomized crossover study sponsored by Teva Pharmaceuticals USA. It compared a 3 mg alprazolam extended-release tablet with a 3 mg Xanax XR® tablet under fasting conditions in healthy subjects. The registry lists enrollment as 32 and describes opposite treatment sequences, with no masking.

The primary endpoint was Cmax, reported as a mean and standard deviation, with blood samples collected over a 72 hour period. The arm summaries report means of 24.33 ng/mL for alprazolam and 23.62 ng/mL for Xanax®. A simple unadjusted recalculation gives a mean difference of -0.71 ng/mL, with a 95% confidence interval from -3.13 to 1.71 and an unadjusted p-value of 0.565. The sponsor-reported geometric test/reference ratio multiplied by 100 is 102.56, with a 90% confidence interval from 98.74 to 106.52.

The registry record does not report the sponsor’s detailed analysis method, equivalence margins, or the original sample-size rationale. The posted summaries therefore support a description of the reported estimates, but not a reconstruction of every design or analysis decision.