Comparing Effects of Two Fixed Combinations Ophthalmic Solutions on Ocular Blood Flow: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Comparing Effects of Two Fixed Combinations Ophthalmic Solutions on Ocular Blood Flow (NCT00811850), a randomized phase 4 study. The primary outcome is Retrobulbar Blood Flow (Peak Systolic Velocity) as Measured by Color Doppler Imaging in the Nasal Short Posterior Ciliary Artery.

2. Clinical Question

3. Trial Design

This was a Phase 4, randomized, double-masked crossover study listed as completed. Its title concerns the effects of two fixed-combination ophthalmic solutions on ocular blood flow. The registry reports 15 enrolled participants and describes an intent-to-treat population consisting of all patients who started the study after randomization.

In a crossover design, participants receive more than one treatment in a sequence, so each participant may contribute measurements under different treatment conditions. This can allow a comparison that accounts for within-participant measurements, but it also means that the order of treatments and the time between them can matter. The registry summary describes a 10 week evaluation and a 3 week washout period between treatments. It lists two weeks of dosing for each treatment, with one drop taken 2 times a day approximately 12 hours apart. The registry does not report the treatment sequence or explain how the scheduled treatment periods fit together with the stated evaluation timeframe.

The interventions were Combigan® and Cosopt®. Both include timolol maleate; the other listed ingredient differs. The primary outcome was peak systolic velocity measured by color Doppler imaging in the nasal short posterior ciliary artery at 1 Month. Although the record identifies this as a crossover trial, it does not report how the outcome analysis handled paired observations, treatment order, period effects, or possible carryover effects. Those details are important for interpreting a crossover comparison and 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.

Treatment Period 1: Combigan® or Cosopt®

Treatment Period 2: Wash Out

Treatment Period 3: Combigan® or Cosopt®

Analysis population for the primary outcome, as defined in the registry: Intent-to-treat population, which consisted of all patients that started the study (randomized)

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 Retrobulbar Blood Flow (Peak Systolic Velocity) as Measured by Color Doppler Imaging in the Nasal Short Posterior Ciliary Artery, measured over 1 Month.

The primary endpoint was peak systolic velocity of retrobulbar blood flow in the nasal short posterior ciliary artery, measured by color Doppler imaging. The unit was centimeters per second (cm/s), and results were reported as means with standard deviations. The specified timeframe was 1 Month after treatment.

The registry describes color Doppler imaging as a high-resolution ultrasound system that visualizes blood flow through a vessel. Peak systolic velocity is the maximum blood-flow speed within a vessel at systole, the point of maximum pressure exerted in a blood vessel. In general, measuring a velocity in a named artery provides a quantitative description of blood movement at that location. It is a physiological measurement, rather than a direct measure of how participants feel or function.

As a general measurement consideration, an endpoint can be useful for comparing treatments when it is defined consistently and measured in the same way across treatment conditions. The registry identifies the artery, imaging method, velocity measure, unit, and timeframe. It does not report additional measurement procedures, such as repeatability assessments or how image readings were standardized. The result therefore describes the recorded peak systolic velocity, but the registry record alone does not establish how that physiological measure relates to other outcomes.

7. Results Posted in the Registry

• Cosopt®: mean 8.02 versus 8.61 on control; difference -0.59 (95% CI -2.32 to 1.14), standardized effect d = -0.24; z-test p = 0.505.

8. Statistical Interpretation

9. Statistical Methods Explained

Several statistical ideas help interpret a comparison of means. The endpoint is continuous: peak systolic velocity is measured on a numerical scale, and the registry reports a mean and standard deviation for each treatment. The mean describes the center of the observed values. The standard deviation describes how much individual measurements vary around that center. A standard deviation is not a confidence interval for the mean, and it does not show the range of all observed values.

What does the mean difference represent?

The comparison is expressed as Cosopt® minus Combigan®. The posted means are 8.02 cm/s for Cosopt® and 8.61 cm/s for Combigan®, and the unadjusted recalculated difference is -0.59 cm/s. A negative value under this subtraction order means that the Cosopt® mean is lower in the posted summaries. The subtraction order matters: reversing it would reverse the sign, without changing the underlying contrast. The number describes the difference between the posted means; it does not on its own describe the difference expected for every participant.

In a crossover trial, the same participant may be measured under each treatment. A paired analysis can use the within-participant difference, while an independent-groups analysis treats the treatment summaries as if they came from separate groups. These approaches can have different standard errors because they use different information about the relationship between measurements from the same person. The registry identifies a crossover model but does not report a paired analysis, the within-participant correlation, or a model for period and sequence. The displayed recalculation is unadjusted from the posted summary statistics, so it should not be confused with a reported crossover model.

How should the p-value be read?

The unadjusted p-value is 0.505. In general, a p-value evaluates how unusual data at least as incompatible with a null model would be if that model and the calculation assumptions held. It does not give the probability that a treatment has no effect, nor does it measure whether an effect is important. A larger p-value does not establish equivalence or prove that the treatments are the same. It indicates that the calculation does not provide strong evidence against its null model. The registry does not report a prespecified threshold or a sponsor analysis for this endpoint.

The interpretation also depends on the method used to calculate the p-value. For this comparison it is an unadjusted recalculation from posted summary statistics, rather than an analysis reported in the registry. Since the design is crossover, methods that account for pairing and treatment period could yield a different estimate of uncertainty. The record does not provide enough detail to reproduce such an analysis.

What does a confidence interval add?

The 95% confidence interval for the unadjusted mean difference runs from -2.323 to 1.143 cm/s. In general, a confidence interval gives a range of values compatible with the observed data under the calculation method. Its width conveys precision: a narrower interval indicates more precision, while a wider interval leaves more uncertainty about the size and direction of the contrast. Here the interval includes zero, as well as negative and positive values. That makes the estimate inconclusive about the direction of the difference under this calculation. The interval is not a guarantee that the true effect lies within its bounds, and it does not account for analysis features absent from the recalculation.

Why do design details matter?

Randomization helps reduce systematic differences in treatment assignment, and masking can reduce some forms of bias in treatment delivery or assessment. In a crossover design, the treatment sequence, time period, and washout may also be relevant. A washout is intended to create a period between treatments; whether it is adequate for a particular treatment effect depends on information not reported in the registry record. The registry states that the trial was randomized and double-masked and describes a 3 week washout. It does not report how sequence or period effects were assessed, or whether the analysis tested for carryover.

The stated intent-to-treat population includes patients who started the study after randomization. This describes who was intended for the primary analysis, but it does not provide a complete account of missing outcome data or protocol deviations. The record does not report a missing-data method, the number of measurements available at each treatment period, or how any incomplete crossover records were handled. These details matter because an analysis of only available measurements may differ from a planned analysis that handles missingness explicitly.

Finally, an endpoint can be statistically analyzed without establishing that its difference is clinically important. The registry does not provide a threshold for a meaningful change in peak systolic velocity. The estimate and interval should therefore be interpreted as statistical descriptions of this physiological outcome, not as a direct statement about patient benefit or harm.

10. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an estimated treatment difference. The unadjusted recalculated mean difference was -0.59 cm/s, with a 95% confidence interval from -2.323 to 1.143 cm/s. The interval extends on both sides of zero. Thus, under this calculation, the data do not narrowly identify a direction for the contrast. The interval also allows differences larger in magnitude than the point estimate, so the estimated value should not be treated as exact.

In general, a confidence interval combines the estimated effect with its uncertainty. A narrower interval indicates a more precise estimate; a wider interval indicates more uncertainty. The interval is wide enough to include a negative difference, no difference, and a positive difference. It communicates uncertainty more fully than the point estimate alone. It is not a range of individual participant measurements, and it does not state that every value inside it is equally likely.

These limits apply to the unadjusted recalculation from posted summary statistics. The trial is described as a crossover study, but the registry record does not report a paired treatment analysis or other model that accounts for the design. The interval therefore should not be read as a sponsor-reported crossover confidence interval. Missing-measurement handling and details needed to evaluate within-participant variability are also not reported in the registry record. The confidence interval expresses precision under its calculation, not certainty about every feature of the trial.

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 events. The planning illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It is based on the observed effect, with the planning target set at the stated fraction of that effect. The trial's own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the planned number of participants per arm under those assumptions for a design with an 80% chance of detecting the specified effect if that effect is real. The 90% power column gives the corresponding per-arm planning number for a 90% chance under the same assumptions. These are design calculations, not a measure of what the completed trial achieved. This is not observed power.

For planning based on 100% of the observed effect, the figures are 265 participants per arm for 80% power and 355 participants per arm for 90% power. Planning for 75% of the observed effect gives 471 participants per arm for 80% power and 630 participants per arm for 90% power. Planning for 50% of the observed effect gives 1,058 participants per arm for 80% power and 1,417 participants per arm for 90% power.

The pattern reflects a general statistical principle: smaller effects are harder to distinguish from random variation, so detecting them with the same power generally requires more participants. These figures are illustrations based on the observed effect and specified assumptions. They should not be interpreted as the trial's actual planned enrollment, a retrospective assessment of power, or a recommendation for a future study. The registry does not report its original sample-size assumptions.

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 = -0.590; pooled standard deviation σ = 2.422.
2. n = 2 × (1.96 + 0.842)² × 2.422² / -0.590² = 264.5, rounded up to 265 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 <- -0.59                      # observed difference in means
sigma <- 2.42167297544487                     # 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(811850)
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 = 265 (80% power), 355 (90% power)
 75% of observed effect: n per arm = 471 (80% power), 630 (90% power)
 50% of observed effect: n per arm = 1,058 (80% power), 1,417 (90% power)
power.t.test: 265.4 
Simulated power at n = 265 per arm: 0.803 (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 registry lists eight outcome measures, but it posts no secondary outcome results. It also lists zero analyses. The primary endpoint is identified as peak systolic velocity of retrobulbar blood flow in the nasal short posterior ciliary artery. The registry does not report a full statistical analysis plan, including whether other outcomes or analyses were prespecified.

Multiplicity arises when several statistical questions are examined. In general, making many comparisons can increase the chance of at least one apparently unusual result, so a trial may specify how to account for multiple testing. The registry record does not report whether multiplicity was considered or adjusted for. With no secondary results posted, it is not possible to assess the results of those measures or how they relate to the primary endpoint.

The primary population is described as intent-to-treat, comprising all patients who started the study after randomization. The registry does not report a participant flow account, missing outcome counts by treatment period, or a missing-data method. It is therefore unclear from the record how incomplete measurements, withdrawals, or deviations from the treatment sequence were handled. Although the outcome summaries list 15 observations for each treatment, that information does not establish that every randomized participant contributed a complete paired set of measurements.

The crossover structure also raises analysis questions that are not answered in the registry record. The record does not report the treatment sequence, whether period effects were modeled, how within-participant dependence was handled, or whether carryover was assessed. These are not details that can be reconstructed from the group means and standard deviations alone. The posted unadjusted recalculation should consequently be distinguished from a complete analysis of the crossover trial.

14. 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.

The registry reports serious adverse event figures separately for Combigan® and Cosopt®. Each treatment listing has 15 participants at risk and zero serious adverse events. The record also lists zero other adverse events for each treatment group. These are the posted counts for the adverse-event categories and group summaries; they do not provide event details, timing, or an analysis comparing safety between treatments.

The deaths field is not populated for either group. Deaths are therefore not reported in the registry record, rather than being established as zero by the posted figures. The absence of reported serious adverse events in these summaries should be read within the context of the recorded groups and trial, not as proof that no risk exists. The registry does not give further information about how adverse events were collected, classified, or assessed for relationship to treatment.

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

The posted results describe peak systolic velocity at the stated artery and timeframe. Combigan® had a mean of 8.61 cm/s, with a standard deviation of 2.33; Cosopt® had a mean of 8.02 cm/s, with a standard deviation of 2.51. The unadjusted recalculated difference, defined as Cosopt® minus Combigan®, was -0.59 cm/s. Its 95% confidence interval ranged from -2.323 to 1.143 cm/s, and the unadjusted p-value was 0.505.

Those values do not establish that the treatments are equivalent. A confidence interval that includes zero is compatible with no difference under the calculation, but it also includes differences in either direction. Nor do the values establish a clinically important difference: the registry record does not specify a threshold for a meaningful change in this measure. The result is an estimate with considerable uncertainty, not a definitive statement about the comparative effect.

The endpoint is a physiological measure of blood-flow velocity obtained by color Doppler imaging. It does not directly report symptoms, visual function, quality of life, or other clinical outcomes. The record lists eight outcome measures but posts no secondary results, so those other measures cannot be assessed from the registry record.

The comparison is also limited by the analysis information available. The trial is identified as randomized, double-masked, and crossover, but no sponsor analysis is posted for the primary outcome. The recalculated comparison uses summary statistics and does not account explicitly for the crossover pairing. Missing-data handling and treatment-sequence details are not reported. Accordingly, the figures support a cautious description of the posted endpoint summaries, not a broad claim about treatment benefit, lack of benefit, or safety.

16. Why This Trial Matters Statistically

This trial is statistically notable because it combines a crossover design with a continuous physiological endpoint. A crossover can make within-participant comparisons possible, which may help account for stable differences between participants. At the same time, the analysis needs to reflect the repeated measurements and the treatment sequence. The registry identifies the crossover model, but does not report the paired analysis or how period and carryover effects were handled. That gap makes it important to distinguish the unadjusted recalculation from a trial-specific crossover analysis.

The posted treatment means are relatively close, but the uncertainty around their recalculated contrast is broad. The confidence interval includes zero and values on both sides of zero. This illustrates why an estimate and its precision should be read together: the point estimate alone does not reveal how much uncertainty remains. The unadjusted p-value is also not a measure of clinical importance and cannot resolve the design and analysis questions left unanswered by the registry record.

The planning illustration highlights how assumptions about the effect to detect influence enrollment needs. Smaller target effects require larger planned numbers to attain the same power under the stated assumptions. Those calculations are separate from the trial's original design justification, which is not reported. They also do not tell whether the completed trial had adequate power for its intended analysis.

Finally, the record distinguishes a defined primary measurement from a full clinical interpretation. Peak systolic velocity describes blood flow at a specified vessel, measured by a specified imaging method. The registry does not supply a threshold for clinical relevance, secondary outcome results, or detailed safety assessment methods. The statistical record therefore supports careful interpretation of the measured endpoint while leaving important questions about analysis and broader meaning open.

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 is brief relative to the questions raised by this design. It describes a crossover trial, a 3 week washout, a 10 week evaluation, and two weeks of dosing per treatment, but does not explain the treatment sequence or how these schedule elements relate. It does not report whether potential period or carryover effects were assessed. These details matter because the outcome under one treatment may depend on the order and timing of treatment periods.

The posted comparison is an unadjusted recalculation from group summary statistics. No sponsor analysis is listed, and the record does not report a paired analysis that uses within-participant differences. The means and standard deviations alone do not provide the information needed to reproduce a crossover model. The reported confidence interval and p-value should therefore be interpreted as applying to the recalculation, rather than assumed to represent a complete trial-specific analysis.

The registry describes the intent-to-treat population as all patients who started the study after randomization. It does not report participant flow, missing measurements by treatment period, reasons for missingness, or how incomplete data were handled. The outcome summaries list 15 observations for each treatment, but do not establish that all observations form complete paired records.

The record also does not report a sample-size justification or the trial's original design assumptions. It lists eight outcome measures but no secondary results, and no analysis details sufficient to assess multiplicity. The primary endpoint is a physiological measure, and no threshold for clinically meaningful change is stated. Safety information is limited to posted adverse-event counts; details of collection and assessment are not reported. These limitations constrain both the precision and scope of conclusions that can be drawn from the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Comparing Effects of Two Fixed Combinations Ophthalmic Solutions on Ocular Blood Flow — NCT00811850.
• Registry record last updated 2019-04-24; status last verified 2019-04.
• Results first posted 2012-08-01.
• 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

NCT00811850 is a completed Phase 4 randomized, double-masked crossover trial comparing Combigan® with Cosopt® for ocular blood flow in participants with glaucoma. The registry records 15 enrolled participants and describes the intent-to-treat population as patients who started the study after randomization.

The primary endpoint was peak systolic velocity of retrobulbar blood flow in the nasal short posterior ciliary artery, measured by color Doppler imaging at 1 Month. The posted means were 8.61 cm/s for Combigan® and 8.02 cm/s for Cosopt®. The unadjusted recalculated mean difference was -0.59 cm/s, with a 95% confidence interval from -2.323 to 1.143 cm/s and an unadjusted p-value of 0.505.

The registry does not report a sponsor analysis of the primary endpoint, crossover-specific analysis details, missing-data methods, or secondary outcome results. The reported summaries therefore allow a limited descriptive comparison but do not resolve the uncertainty around the treatment contrast.