Efficacy Study of Travoprost APS Versus TRAVATAN: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Efficacy Study of Travoprost APS Versus TRAVATAN (NCT00848536), a randomized phase 3 study. The primary outcome is Mean Intraocular Pressure at 9:00 am.

2. Clinical Question

This is a comparison of a continuous measurement, reported in mmHg, rather than a count of clinical events. The posted group estimates are least-squares means, with standard errors as their dispersion measures. The separate recalculation uses posted summary statistics to express the difference and its uncertainty. Those estimates should be interpreted in light of the analysis population and the absence of a reported margin for the registry’s non-inferiority or equivalence analysis.

3. Trial Design

The registry describes a randomized, double-masked, parallel-group Phase 3 study sponsored by Alcon Research. The study compared TRAVATAN APS with TRAVATAN in patients with open-angle glaucoma or ocular hypertension. The record lists enrollment of 371 and a completed status. The recorded study start is 2009-03, and primary completion is recorded as 2010-01.

Both arms used one drop once daily in the evening for 3 months. The interventions were travoprost 0.004% eye drops, with POLYQUAD preservative for TRAVATAN APS and BAK preservative for TRAVATAN. Randomization and double masking are stated in the registry, but additional details about how allocation was generated or concealed, and how masking was maintained, are not reported in the registry record.

The primary outcome was measured at 3 months, at 9:00 am. The endpoint analysis population was per-protocol, rather than all randomized participants: a patient had to receive study medication and satisfy the specified pre-randomization and protocol criteria at that time point to be evaluable. The posted endpoint estimates include 172 participants in each arm. The registry record does not explain the difference between enrollment and the per-protocol analysis population, or provide a participant flow account in the registry record reported for this analysis.

Although the analysis is described as non-inferiority or equivalence, the registry record does not report the margin, the original design assumptions, or the statistical method used for the sponsor’s analysis. These omissions matter because the numerical difference alone cannot establish whether a prespecified non-inferiority or equivalence criterion was met. The recalculated comparison is an unadjusted calculation from posted summary statistics, not a replacement for the trial’s own analysis.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Per-Protocol. Patients who received study medication, satisfied pre-randomization criteria and satisfied protocol criteria at the specific time point were considered evaluable for PP 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 Mean Intraocular Pressure at 9:00 am, measured over 3 months (measured at 9:00 am).

The primary endpoint is mean intraocular pressure at 9:00 am, measured at 3 months, in mmHg. Intraocular pressure is a continuous measurement, so the endpoint describes a group average rather than the number of participants with an event. The registry reports least-squares means and standard errors for the per-protocol population.

For each participant, two consecutive measurements were taken for each eye using a Goldmann applanation tonometer. The description says measurements for an individual subject were preferably performed by the same operator using the same tonometer. The mean intraocular pressure for the patient’s worse eye at baseline was used in the primary endpoint analysis; if both eyes were equal, the right eye was selected. Individual eye measurements were rounded up to the next whole number when the value was ≥ 0.5 mmHg.

Comparing a group mean is one way to summarize a continuous pressure measure across treatment groups. It can make an overall difference easier to interpret than listing individual measurements, but it does not describe every participant’s outcome or variation in response. The reported standard errors convey uncertainty around the estimated group means; they are not standard deviations of individual measurements. The record’s use of a non-inferiority or equivalence analysis also makes the prespecified margin important, but that margin is not reported in the registry record.

7. Results Posted in the Registry

• TRAVATAN: mean 18.10 versus 17.90 on control; difference 0.20 (95% CI -0.49 to 0.89), standardized effect d = 0.06; z-test p = 0.572.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous: it is a group mean of intraocular pressure in mmHg. The registry reports least-squares means, which are model-based means in many trial analyses, but the exact model used for these posted estimates is not reported in the registry record. The accompanying standard errors quantify uncertainty in the estimated group means. They do not describe the spread of individual patients’ pressure measurements.

What does the mean difference represent?

A mean difference compares the average outcome in one group with the average in another. Its direction depends on which group is subtracted from which. In the recalculation, the comparison is expressed as TRAVATAN minus TRAVATAN APS, giving 0.2 mmHg. The sponsor’s reported mean difference is -0.2, reflecting the opposite direction of subtraction in the posted result. A sign change alone does not indicate disagreement about the magnitude of the comparison; the group order must be considered when reading a difference.

General statistical explanation: a confidence interval describes a range of values compatible with the data under the method’s assumptions. It communicates uncertainty around an estimate, rather than a guarantee that the true value lies in that particular interval. A confidence interval containing zero indicates that a zero difference is compatible with the data under that calculation. It does not prove that the groups are equivalent. Equivalence and non-inferiority require a prespecified margin and an analysis that evaluates the estimate against that margin.

What does the recalculation add?

The recalculated estimate is an unadjusted comparison based on posted group summary statistics. It uses the group means and standard errors to derive a comparison and its uncertainty. The pooled standard deviation used in that calculation is approximate, as indicated in the registry entries. This is a useful way to examine the numerical relationship between the posted summaries, but it is not a reconstruction of the sponsor’s full analysis. The registry does not report the sponsor’s method, so details such as model specification, covariate adjustment, or any other analysis choices cannot be assessed from the record.

The recalculated p-value is unadjusted and is 0.572. General statistical explanation: a p-value measures how unusual data at least as discrepant as those observed would be under a specified null hypothesis and statistical model. It is not the probability that the null hypothesis is true, and a value that does not cross a conventional threshold is not proof of no effect. For a non-inferiority or equivalence question, a p-value for a conventional difference test is not a substitute for comparing an appropriate confidence interval with the prespecified margin.

Why can over-dispersion matter?

General statistical explanation: over-dispersion occurs when observations vary more than a statistical model assumes. If a model underestimates variability, its standard errors can be too small and its confidence intervals too narrow; if it accounts for extra variability, uncertainty estimates may be wider. This is especially relevant to count outcomes, where variation can exceed the assumptions of simple count models. The primary outcome in this trial is a continuous mean, and the registry entries do not report an over-dispersion assessment or a model requiring one. The concept is general and should not be taken as a claim that over-dispersion occurred in this study.

What does the analysis population imply?

The primary endpoint is reported for a per-protocol population. That population includes patients who received medication and satisfied the stated pre-randomization and protocol criteria at the time point. General statistical explanation: a per-protocol analysis can focus on outcomes among participants meeting protocol-defined conditions, while an intention-to-treat analysis retains participants according to randomized assignment. These approaches answer related but not identical questions and can be affected differently by exclusions, adherence, and missing measurements. The registry entries do not provide an intention-to-treat estimate or explain the impact of exclusions on the reported endpoint.

There are also measurement details relevant to the result. Two consecutive readings were taken for each eye; the worse eye at baseline was selected, with the right eye chosen when baseline values were equal. Readings were rounded up to the next whole number if the value was ≥ 0.5 mmHg. Those rules help define the endpoint, but the registry record does not report the distribution of measurements or the consequences of rounding for the estimates.

Finally, the sponsor’s analysis is explicitly identified as non-inferiority or equivalence, but its method and margin are not reported. General statistical explanation: a non-inferiority analysis asks whether an estimate rules out a disadvantage larger than a specified margin; an equivalence analysis asks whether the uncertainty interval is contained within prespecified limits on both sides. Without the margin and decision criteria, neither conclusion can be independently judged from the numerical result alone. The recalculation is therefore descriptive and complementary, not a substitute for the sponsor’s stated analysis.

10. Confidence Intervals and Precision

The posted group means are 17.9 mmHg for TRAVATAN APS and 18.1 mmHg for TRAVATAN, each with a standard error of 0.25. The standard error reflects precision of the estimated mean, not the range of individual measurements. The unadjusted recalculated difference is 0.2 mmHg, with a 95% confidence interval from -0.493 to 0.893. This interval includes zero and spans values in both directions, so the recalculation does not narrowly pin down the direction of the difference.

General statistical explanation: a confidence interval gives an estimate together with a range of values compatible with the data and the calculation’s assumptions. A wider interval indicates less precision than a narrower interval on the same scale. Whether an interval is sufficiently precise for a non-inferiority or equivalence conclusion depends on the prespecified margin. That margin is not reported in the registry record, so the interval cannot be judged against the trial’s stated decision threshold.

The sponsor’s posted 95% confidence interval is -0.9 to 0.5 for its reported mean difference in final values. It is directionally reversed relative to the recalculated TRAVATAN-minus-TRAVATAN-APS contrast, and is consistent with the opposite group order. The two intervals come from different reporting approaches: the recalculated interval is an unadjusted derivation from summaries, whereas the sponsor’s analysis is described as a non-inferiority or equivalence analysis. The registry does not report enough method detail to compare their construction fully.

Precision is specific to the analyzed endpoint, time point, and population. These estimates concern the 9:00 am measurement at 3 months in the per-protocol population. They do not establish the precision of other outcomes or time points. Further information on missing measurements, protocol exclusions, and analysis methods is not reported in the registry record.

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 based on the observed effect, not the trial’s original design assumptions. The listed values are participants per arm for 80% power and participants per arm for 90% power; they are not total event counts. The calculation assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses an effect to detect equal to the stated fraction of the observed effect.

For planning for 100% of the observed effect, the illustration gives 4,219 participants per arm for 80% power and 5,648 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 7,501 participants per arm for 80% power and 10,041 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 16,876 participants per arm for 80% power and 22,591 participants per arm for 90% power.

In plain terms, 80% power is the probability a planned study would detect the specified effect under the calculation’s assumptions if that effect were present; the 90% column applies a higher target probability. Smaller effects are harder to detect and require more participants, as illustrated by the increasing figures across the stated effect fractions. These values are not observed power. They are illustrations derived from the observed effect, not evidence about the design choices made for this trial. The trial’s 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 = 0.200; pooled standard deviation σ = 3.279.
2. n = 2 × (1.96 + 0.842)² × 3.279² / 0.200² = 4,218.8, rounded up to 4,219 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 <- 0.200000000000003                      # observed difference in means
sigma <- 3.278719262151                     # 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(848536)
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 = 4,219 (80% power), 5,648 (90% power)
 75% of observed effect: n per arm = 7,501 (80% power), 10,041 (90% power)
 50% of observed effect: n per arm = 16,876 (80% power), 22,591 (90% power)
power.t.test: 4219.7 
Simulated power at n = 4,219 per arm: 0.797 (20000 replicates)

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

13. Analyses Reported by the Sponsor

The sponsor’s posted analysis reports a mean difference in final values of -0.2, with a 95% confidence interval from -0.9 to 0.5. It is identified in the registry as a non-inferiority or equivalence analysis. The registry does not report a p-value or the analysis method for this result. The non-inferiority or equivalence margin and decision rule are also not reported in the registry record.

The unadjusted recalculation gives a difference of 0.2 for TRAVATAN minus TRAVATAN APS, with a 95% confidence interval from -0.493 to 0.893 and p = 0.572. Its direction is reversed from the sponsor’s reported difference, consistent with comparing the groups in the opposite order. It is derived from posted group summaries and uses an approximate pooled standard deviation, so it should not be treated as the sponsor’s analysis.

The two results are broadly similar in indicating a small estimated difference, but their intervals are not identical and their methods are not established as the same. The sponsor’s own analysis is the trial’s primary reported analysis. The recalculation is an unadjusted cross-check of the displayed summary statistics and cannot establish whether the sponsor’s non-inferiority or equivalence criterion was satisfied without the missing margin and method details.

14. Multiplicity, Missing Data and Analysis Populations

The registry entries identify three outcome measures and three analyses, but do not provide secondary outcome results for this analysis. The primary endpoint is mean intraocular pressure at 9:00 am at 3 months. No multiplicity adjustment or plan for controlling error across outcomes or analyses is reported in the registry record. It is therefore not possible to determine whether the sponsor adjusted for multiple comparisons or how the primary endpoint was positioned among other planned analyses.

The recalculated p-value of 0.572 is unadjusted. It should be understood as a calculation for the posted comparison, not as an adjustment for other endpoints, time points, or analyses. The sponsor’s result is designated as non-inferiority or equivalence, but the statistical method and margin are not reported. The registry record also does not report interim analyses or a statistical analysis plan, so none should be assumed.

The primary analysis population is per-protocol. The record defines evaluable patients as those who received study medication, met pre-randomization criteria, and met protocol criteria at the specific time point. The posted endpoint estimates include 172 participants in each arm. The registry entries do not report how many participants were excluded from this population, the reasons for any exclusions, or whether an intention-to-treat analysis was conducted.

Missing endpoint data and their handling are also not described in the registry record for this analysis. The registry record does not report imputation methods, sensitivity analyses, or assumptions about missingness. These details matter because exclusions and missing measurements can influence the population represented by a per-protocol estimate. Without them, the robustness of the posted estimate to missing data or analysis-population choices cannot be evaluated.

These are limits on what can be concluded from the registry record, not evidence that particular analyses or procedures were absent from the full study. The record does not report them.

15. Safety Results

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

Other (non-serious) adverse events

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

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: abdominal mass (0.5%), chest pain (0.5%), pneumonia (0.5%).

The serious adverse event figures are reported separately from the per-protocol efficacy estimates. The registry lists 1 serious adverse event among 185 participants at risk in the TRAVATAN APS group and 2 among 186 at risk in the TRAVATAN group. These are the counts and denominators reported for serious adverse events; the registry entries do not provide a statistical comparison or an assessment of causality.

The listed top serious adverse event terms are abdominal mass, chest pain, and pneumonia, each reported as 0.5%. The registry entries do not specify a group association for those terms. Deaths are not reported in the registry record.

The registry also lists other adverse events affecting 32 participants at risk of 185 for TRAVATAN APS and 35 at risk of 186 for TRAVATAN. These figures should not be conflated with the serious adverse event counts. The record details do not provide details about event severity beyond the serious versus other categories, timing, duration, relatedness, or how events were collected. These descriptive counts alone do not establish whether a treatment caused an event or whether the groups differ reliably in safety.

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

The posted results describe mean intraocular pressure at 9:00 am after 3 months in the per-protocol population. The least-squares means are 17.9 mmHg for TRAVATAN APS and 18.1 mmHg for TRAVATAN. The unadjusted recalculation estimates the TRAVATAN-minus-TRAVATAN-APS difference as 0.2 mmHg, with a 95% confidence interval from -0.493 to 0.893 and p = 0.572. The sponsor reports a difference in final values of -0.2, with a 95% confidence interval from -0.9 to 0.5, in an analysis identified as non-inferiority or equivalence.

These results do not, by themselves, establish that the treatments are equivalent or non-inferior. Such a conclusion depends on the prespecified margin and the sponsor’s analysis method. Neither the margin nor the method is reported in the registry record. The recalculated confidence interval includes zero, but a conventional test that does not detect a difference is not a demonstration of equivalence.

The findings also do not describe all participants or every outcome. The primary endpoint analysis is per-protocol, and the record does not report an intention-to-treat estimate, secondary results, or details of missing-data handling. The result pertains to the specified 3-month, 9:00 am measurement and should not be extended to unreported times or outcomes.

General statistical explanation: statistical estimates summarize observed data under assumptions; they do not alone establish clinical importance. Judging importance requires relevant clinical context and, for a non-inferiority or equivalence claim, a defensible margin. Those details are not reported in the registry record. The appropriate reading is therefore descriptive: the posted group means and the two reported difference estimates are close in magnitude, with uncertainty that should be interpreted alongside the missing analysis details.

17. Why This Trial Matters Statistically

This trial illustrates why the label attached to a statistical question matters. A standard comparison asks about evidence of a difference; non-inferiority and equivalence analyses instead require prespecified margins and decision rules. The registry identifies the sponsor’s analysis as non-inferiority or equivalence, yet does not report the margin or method. Without those details, readers can describe the estimate and interval but cannot verify the claim against its intended criterion.

It also shows why the direction of a mean difference must be checked. The recalculated comparison is TRAVATAN minus TRAVATAN APS, while the sponsor reports -0.2. Opposite signs can arise from reversing the order of the groups, rather than from conflicting magnitudes. Reading the group means alongside the contrast helps make that orientation clear.

The per-protocol analysis population is another important part of the statistical interpretation. It focuses on participants meeting specified criteria at the endpoint time point, and is not interchangeable with an analysis of all randomized participants. Since the registry entries do not report an intention-to-treat analysis or explain exclusions and missing data, the population represented by the posted result deserves explicit attention.

Finally, the planning illustration demonstrates how sample-size requirements depend on the effect targeted. Smaller fractions of the observed effect correspond to larger planning figures. These are illustrative calculations and not the original trial design or observed power. Taken together, the record offers useful numerical estimates, while also showing how analysis population, contrast direction, precision, and reporting detail shape what a reader can responsibly infer.

18. 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 non-inferiority or equivalence margin, the sponsor’s statistical method, or the decision rule. This prevents independent evaluation of whether the sponsor’s analysis met its stated criterion. The sponsor’s confidence interval is reported, but no p-value or further model detail is given.

The recalculation is unadjusted and based on posted summary statistics, with an approximate pooled standard deviation. It is not a reproduction of the sponsor’s analysis. Its p-value is unadjusted, and the registry entries do not report how multiplicity across outcomes or analyses was handled.

The primary endpoint uses a per-protocol population. The registry entries do not explain participant flow into that population, exclusions, missing endpoint data, or whether an intention-to-treat analysis was performed. This limits assessment of how the analysis population may affect interpretation. The registry also does not report secondary outcome results, despite identifying three outcome measures and three analyses.

The endpoint concerns one measurement time and one assessment time point: mean intraocular pressure at 9:00 am after 3 months. The record’s measurement and eye-selection rules are described, but the distribution of measurements and the impact of rounding are not. Details about the original sample-size justification and interim analyses are not reported in the registry record. The planning figures are derived from the observed effect and should not be mistaken for original design assumptions.

Safety information is limited to the listed event counts and terms. Further detail on event timing, relatedness, and ascertainment is not reported in the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Efficacy Study of Travoprost APS Versus TRAVATAN — NCT00848536.
• Registry record last updated 2012-04-06; status last verified 2012-04.
• Results first posted 2011-03-08.
• 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.

22. Record Summary

The registry describes a completed randomized, double-masked, parallel-group Phase 3 study sponsored by Alcon Research, comparing TRAVATAN APS with TRAVATAN in patients with open-angle glaucoma or ocular hypertension. Enrollment is reported as 371. The recorded study start is 2009-03, with primary completion in 2010-01.

The primary endpoint was mean intraocular pressure at 9:00 am after 3 months, analyzed in a per-protocol population. The posted least-squares means were 17.9 mmHg for TRAVATAN APS and 18.1 mmHg for TRAVATAN. The sponsor reported a mean difference in final values of -0.2 with a 95% confidence interval from -0.9 to 0.5, and the registry classifies the analysis as non-inferiority or equivalence.

The registry does not report the margin or method needed to assess that classification independently. The unadjusted recalculation is a supplementary comparison, not a replacement for the sponsor’s result.