Efficacy and Tolerability of an Intra-Nasal Testosterone Product: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy and Tolerability of an Intra-Nasal Testosterone Product (NCT00975650), a randomized phase 2 study. The primary outcome is Serum Testosterone Ln-Cmax.

2. Clinical Question

3. Trial Design

This was a phase 2, randomized, open-label crossover trial sponsored by Acerus Pharmaceuticals Corporation. The registry lists hypogonadism as the condition and 57 participants as the enrollment. The study status is completed. Its listed start was 2009-08 and its primary completion was 2010-05.

The crossover design means participants received more than one treatment over the course of the study, rather than remaining in a single parallel group. The record lists four treatment sequences, each including the three Nasobol® doses and the Androderm® comparator in a different order. This design allows treatment experiences to be compared within a participant, although the posted summary results are presented by treatment and do not report the method used to account for the crossover structure.

Each Nasobol® regimen was administered twice daily for 7 days: 8.0 mg, 11.0 mg, or 14.0 mg, each described as 2 syringes. The positive-control regimen was a 5.0 mg Androderm® patch once daily for 7 days. The trial was not masked. Details of any washout periods, sequence-generation procedures, allocation concealment, or protocol deviations are not reported in the registry record.

The endpoint population is not simply described as everyone enrolled. For each treatment, it includes participants who completed that treatment and had sufficient plasma concentration data to calculate the pharmacokinetic parameter. The counts used for the endpoint differ by treatment. Reasons for those differences and the handling of missing observations are 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.

Period 1

Period 2

Period 3

Period 4

Analysis population for the primary outcome, as defined in the registry: Number of participants includes participants who completed the corresponding treatment and had sufficient plasma concentration data to calculate the PK parameter.

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 Serum Testosterone Ln-Cmax, measured over 0.0 (trough), 0.50, 1.0, 1.5, 2.0, 3.0, 6.0, 9.0, 10.0, 10.5, 11.0, 11.5, 12.0, 13.0, 16.0, 19.0, 22.0, and 24.0 hours..

The primary endpoint is titled Serum Testosterone Ln-Cmax. Cmax is a pharmacokinetic measure of the maximum concentration observed after administration; the registry labels this endpoint Ln-Cmax and reports its unit as ng/dL. The results are presented as means and standard deviations for each treatment. The registry lists measurements at 0.0 (trough), 0.50, 1.0, 1.5, 2.0, 3.0, 6.0, 9.0, 10.0, 10.5, 11.0, 11.5, 12.0, 13.0, 16.0, 19.0, 22.0, and 24.0 hours.

In general, pharmacokinetic profiles describe how drug concentrations change over time. A maximum-concentration measure can characterize the peak exposure observed after a regimen, while the listed sampling times indicate when concentration measurements were scheduled. Such measures are useful for comparing exposure patterns, but they are not direct measures of symptoms, daily functioning, or other clinical outcomes.

The endpoint description says the primary objective was to establish a pharmacokinetic profile after Nasobol® or Androderm® treatment. The registry identifies the endpoint as a mean of a continuous measure. It does not report a clinical threshold for interpreting Ln-Cmax or specify how a difference in the endpoint relates to patient experience.

7. Results Posted in the Registry

• Treatment B: mean 6.41 versus 6.25 on control; difference 0.16 (95% CI 0.02 to 0.30), standardized effect d = 0.44; z-test p = 0.022.
• Treatment C: mean 6.54 versus 6.25 on control; difference 0.29 (95% CI 0.15 to 0.43), standardized effect d = 0.79; z-test p = <0.001.
• Treatment D: mean 6.36 versus 6.25 on control; difference 0.11 (95% CI -0.03 to 0.25), standardized effect d = 0.30; z-test p = 0.126.

8. Statistical Interpretation

9. Statistical Methods Explained

The endpoint is continuous and is reported as a mean with standard deviation. A mean describes the center of the observed endpoint values. A standard deviation describes how dispersed those values are around the mean. These summaries make it possible to compare treatment-level averages while also seeing the amount of variability among the observations. The reported endpoint is Serum Testosterone Ln-Cmax; the registry gives its unit as ng/dL.

What does a mean difference represent?

A mean difference is the estimate of how far one treatment's posted mean is from the reference treatment's mean, on the endpoint scale. The comparisons use Treatment A, the 8.0 mg Nasobol® regimen, as the reference. Treatment B, Treatment C, and Treatment D are each compared with it. The estimated differences are 0.16, 0.29, and 0.11, respectively. These are estimates from the posted results; they are not measures of clinical importance unless a meaningful clinical threshold is defined. No such threshold is reported in the registry record.

How should a confidence interval be read?

In general, a confidence interval communicates the uncertainty around an estimated effect under the assumptions of the method used to calculate it. A narrower interval indicates greater precision than a wider interval on the same scale. The posted intervals are 0.023 to 0.297 for Treatment B versus Treatment A, 0.150 to 0.430 for Treatment C versus Treatment A, and -0.031 to 0.251 for Treatment D versus Treatment A. The interval for Treatment D includes zero, while the other two do not. This describes the intervals; it does not establish clinical importance or correct for the number of comparisons.

What do the p-values add?

A p-value describes how compatible the observed data are with a specified null hypothesis under the statistical model. Smaller p-values indicate less compatibility with that null model, but they do not measure the size or importance of an effect. The posted values are unadjusted: p = 0.022 for Treatment B, p < 0.001 for Treatment C, and p = 0.126 for Treatment D. The registry record does not report a multiplicity procedure. The p-values should not be interpreted as if an adjustment for multiple comparisons had been applied.

Why does the crossover design matter?

In general, crossover data involve repeated treatment observations from the same participant. Those observations may be correlated, so analyses often account for participant-level pairing as well as treatment period and sequence. The registry lists a randomized crossover design and four treatment sequences, but a detailed statistical model or explanation of how the comparisons account for the repeated observations is not reported in the registry record. The posted comparison estimates therefore should be read with that reporting limitation in mind. Details on washout, carryover assessment, period effects, and sequence effects are also not reported in the registry record.

The population for each treatment result is defined as participants who completed that treatment and had sufficient plasma concentration data to calculate the pharmacokinetic parameter. That definition indicates an endpoint-specific analysis population. It does not describe how missing or unusable concentration data were handled beyond that criterion, nor whether any other analysis population was used. No separately listed analysis records are reported, and the registry record does not provide a fuller model specification, covariate adjustment plan, or missing-data analysis.

10. Confidence Intervals and Precision

The confidence intervals quantify uncertainty around the three posted mean differences. Treatment B versus Treatment A has an estimate of 0.16 and an interval from 0.023 to 0.297. Treatment C versus Treatment A has an estimate of 0.29 and an interval from 0.150 to 0.430. Treatment D versus Treatment A has an estimate of 0.11 and an interval from -0.031 to 0.251. The Treatment C interval is entirely above zero, as is the Treatment B interval; the Treatment D interval extends across zero.

In general, confidence intervals describe a range of effect values compatible with the observed data and the method's assumptions. They help show precision more directly than a point estimate alone. The uncertainty in these results should also be considered in light of the treatment-specific endpoint counts: 52 for Treatment A, 55 for Treatment B, 52 for Treatment C, and 54 for Treatment D. These counts represent participants completing the corresponding treatment with sufficient plasma concentration data.

The registry record does not report how its interval calculations accounted for the crossover structure, nor does it report a clinical threshold against which the interval widths could be judged. The intervals are therefore useful for describing statistical precision around the posted endpoint differences, but not for deciding whether a difference is meaningful to patients. They are also unadjusted for multiplicity according to the posted comparison labels.

11. Planning a Similar Trial: Sample Size

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

The sample-size figures are planning illustrations, not the trial's original design calculations. They are participants per arm for 80% power and participants per arm for 90% power, using equal allocation between two arms. The planning assumptions are a two-sided significance level of 0.05 and a normal approximation. Each planning scenario targets a stated fraction of the observed effect: the full observed effect, 75% of the observed effect, or 50% of the observed effect. These are hypothetical planning targets, not observed treatment outcomes.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed to detect the chosen effect with 80% power under those assumptions. The 90% power column gives the corresponding number per arm for 90% power. In general, higher power requires more participants when the other assumptions stay the same. A smaller effect is harder to distinguish from random variation, so planning for a smaller effect requires more participants.

For example, the posted illustration for the Treatment B comparison lists 80 participants per arm for 80% power and 107 per arm for 90% power when planning for 100% of the observed effect. Planning for 50% of that observed effect lists 318 per arm for 80% power and 426 per arm for 90% power. The other comparison scenarios are listed with their corresponding per-arm estimates in the sample-size display. The original trial's sample-size justification and design assumptions are not reported in the registry record. These figures are not observed power.

The trial used a crossover design, while the displayed planning assumptions describe equal allocation between two arms and do not state a crossover-specific model. The estimates should therefore be read only under the stated planning framework, not as a reconstruction of the trial's own design.

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 = 0.160; pooled standard deviation σ = 0.360.
2. n = 2 × (1.96 + 0.842)² × 0.360² / 0.160² = 79.4, rounded up to 80 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 <- 0.16                      # observed difference in means
sigma <- 0.359853144649711                     # 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(975650)
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 = 80 (80% power), 107 (90% power)
 75% of observed effect: n per arm = 142 (80% power), 189 (90% power)
 50% of observed effect: n per arm = 318 (80% power), 426 (90% power)
power.t.test: 80.4 
Simulated power at n = 80 per arm: 0.796 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The posted results include three comparisons against Treatment A: Treatment B, Treatment C, and Treatment D. Each comparison has an unadjusted p-value. The registry record does not report a procedure for controlling multiplicity, such as an adjustment across those comparisons, and the values should not be read as multiplicity-adjusted results. When several comparisons are examined, the chance of at least one apparently notable result can increase; this is a general statistical consideration, not a finding about this trial.

Missing-data reporting is limited. The primary endpoint population is defined as participants who completed the corresponding treatment and had sufficient plasma concentration data to calculate the pharmacokinetic parameter. Treatment-specific endpoint counts are 52, 55, 52, and 54. Reasons for the differences among counts, the amount or pattern of missing concentration data, and any imputation or sensitivity analysis are not reported in the registry record.

The registry record does not describe a separate intention-to-treat analysis, a per-protocol analysis, or other named analysis populations. It does not report how participants with incomplete treatment periods were handled, or whether analyses included all randomized participants. The definition of the endpoint population should therefore be kept distinct from the enrollment of 57 participants.

Although the study is randomized and crossover, details of the statistical model are not reported in the registry record. In particular, there is no posted explanation of adjustment for participant-level repeated measures, treatment period, sequence, or carryover. These details matter in general because crossover outcomes from the same participant are related and treatment order can be relevant to interpretation. The record does not permit a reader to determine which, if any, of these features were incorporated into the reported comparisons.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event figures show zero serious adverse events in each treatment group. The numbers at risk were 57 for Treatment A, 56 for Treatment B, 54 for Treatment C, and 55 for Treatment D. No deaths were reported in any group. No serious adverse event terms are listed.

For other adverse events, the registry reports 5 affected participants among 57 at risk for Treatment A, 6 among 56 for Treatment B, 0 among 54 for Treatment C, and 6 among 55 for Treatment D. These are counts of participants reported as affected, not event rates calculated. The registry does not state in these figures whether events were considered related to treatment, and the numbers alone do not establish causation or support a comparative safety conclusion.

These safety counts are distinct from the endpoint populations used for the pharmacokinetic summaries. The registry record does not provide further detail on event definitions, ascertainment, timing, severity of non-serious events, or missing safety observations.

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

The posted data describe mean Serum Testosterone Ln-Cmax values after the three Nasobol® regimens and the Androderm® patch regimen. The reported means are 6.25 for the 8.0 mg Nasobol® treatment, 6.41 for the 11.0 mg treatment, 6.54 for the 14.0 mg treatment, and 6.36 for the 5.0 mg Androderm® treatment. The posted comparisons estimate differences from Treatment A, with confidence intervals and unadjusted p-values.

Those statistics answer a limited question about a pharmacokinetic endpoint. They do not directly describe symptoms, functioning, quality of life, or other clinical outcomes. The registry record does not define a threshold for a clinically meaningful difference in Ln-Cmax, so statistical separation from zero cannot by itself establish clinical importance. Nor can the endpoint results alone establish a treatment's overall benefit or harm.

The trial is described as randomized and crossover, but its posted summary comparisons do not report how repeated observations, treatment order, or periods were handled. The treatment-specific endpoint populations also differ, and reasons for the differences are not reported. These reporting gaps limit how fully the estimates can be assessed. The unadjusted p-values further mean that the record does not document control for the set of comparisons.

The safety figures report no serious adverse events or deaths in the listed groups, with some other adverse events reported. They do not establish that events were caused by, or unrelated to, a particular treatment. In general, event counts from a trial should be considered alongside the way events were collected and the amount of follow-up; further details are not reported in the registry record.

Overall, the posted results are evidence about the recorded pharmacokinetic measure in the endpoint populations. They are not a complete account of clinical effectiveness, tolerability, or comparative safety, and the registry record does not provide the information needed to make those broader judgments.

16. Why This Trial Matters Statistically

This trial illustrates why a pharmacokinetic endpoint and a clinical outcome should be distinguished. The endpoint captures a feature of serum testosterone concentration after treatment. It can support comparisons of exposure patterns, but it does not directly measure how participants feel or function. Statistical differences in a concentration-based measure do not automatically imply a difference that matters clinically.

The crossover design also highlights the importance of transparent analysis reporting. In general, repeated treatment observations from the same participant can be more informative than unrelated observations, but they require methods that reflect their dependence and the order in which treatments were received. The registry lists randomized treatment sequences but does not report the model used for the posted comparisons. That distinction is central when interpreting estimates from a crossover trial.

The results offer estimates with confidence intervals rather than only point values, allowing readers to consider uncertainty. The intervals differ in whether they include zero, and the p-values are explicitly unadjusted. Together, those details reinforce that statistical inference depends on both the estimates and the analysis context, including how multiple comparisons are handled.

Finally, the endpoint population counts are specific to treatment completion and sufficient concentration data. Reporting such definitions helps readers distinguish the analyzed observations from overall enrollment, while the absence of detail about missing observations limits further assessment. These are broadly important reporting issues for clinical researchers evaluating pharmacokinetic studies.

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 gives a brief objective and treatment-level endpoint summaries, but does not report the full protocol or detailed analysis plan. In particular, the trial's original sample-size justification, its original design assumptions, and any interim analyses are not reported in the registry record.

Although the study is randomized and crossover, the method used for the reported comparisons is not described. Washout periods, handling of potential carryover, adjustment for period or sequence, and use of within-participant pairing are not reported in the registry record. These omissions make it difficult to judge how well the summary comparisons reflect the crossover design.

The endpoint population requires treatment completion and sufficient plasma concentration data. Treatment-specific counts are reported, but reasons for differences in those counts, missing-data patterns, and sensitivity analyses are not reported in the registry record. The registry also does not report a clinical threshold for interpreting the endpoint differences.

The comparisons are labeled unadjusted, and a multiplicity procedure is not reported. The record also does not provide detailed safety-event definitions, attribution, or follow-up context beyond the posted counts. These limitations do not invalidate the posted summaries, but they constrain what can be concluded from them.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Efficacy and Tolerability of an Intra-Nasal Testosterone Product — NCT00975650.
• Registry record last updated 2018-08-13; status last verified 2018-08.
• Results first posted 2018-08-13.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The completed phase 2 study was a randomized, open-label crossover trial sponsored by Acerus Pharmaceuticals Corporation. It enrolled 57 men with hypogonadism and compared Nasobol® at 8.0 mg, 11.0 mg, and 14.0 mg with a 5.0 mg Androderm® patch. Each treatment period is described as 7 days.

The primary endpoint was Serum Testosterone Ln-Cmax, reported as a mean and standard deviation. The posted results include treatment-specific endpoint counts, three unadjusted mean-difference comparisons, confidence intervals, and p-values. Serious adverse events and deaths were reported as zero in each group. Further details about the crossover analysis, missing data, multiplicity handling, and original sample-size planning are not reported in the registry record.