Vivid Vision, Inc.
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VVP Power Analysis Calculator

Calculate sample size and power for the Vivid Vision Perimetry (VVP) visual function endpoint used in AMD, glaucoma, and IRD clinical trials

VVP Configuration

sessions
number
presentations
seconds
dB, for 4 stimuli presentations
days
days

Study Parameters

Bundle MS SD
σε,MS 0.00 dB
Bundle 1-Loc SD
σε,1-Loc 0.00 dB
# of Bundles 0
Total Test Stimuli 0
Est. Session Time 0:00
Est. Bundle Time 0:00
dB
%
p-value
dB difference
participants per group

Results

Power vs Sample Size Per Group

0%20%40%60%80%100%02040608010080%Sample Size: 1Sample Size Per GroupPower (%)Single LocationMean Sensitivity
Sample Size 1 patients
Power 80.0%
Effect Size 0.20 dB/360d
Significance α = 0.05
Bundle MS SD
σε,MS 0.00 dB
Bundle 1-Loc SD
σε,1-Loc 0.00 dB
Time Points 0
Cum. Bundle 1-Loc SD 0.00 dB
Total Sample 2 patients
Test Type Two-sample t-test (df=0)

Overview

The VVP (Vivid Vision Perimetry) Power Analysis Calculator is a specialized tool for designing clinical studies that measure visual field progression over time. It implements the formal statistical model above and provides power calculations for both progression studies (longitudinal) and comparative studies (cross-sectional), accounting for the unique characteristics of visual field testing and repeated measurements.

Study Design Types

1. RCT Design (Comparative Studies)

  • Purpose: Compare differences between two independent groups
  • Design: Cross-sectional comparison between groups (e.g., treatment vs. control)
  • Analysis: Two-sample t-test following the formal model
  • Test Statistic: t = (Ȳ₂ - Ȳ₁) / √(2σ²total/n)
  • Degrees of Freedom: df = 2n - 2
  • Considerations: Accounts for both measurement error and population variability

2. Patient Progression

  • Purpose: Detect progression or change over time within the same patient or group
  • Design: Longitudinal study with multiple measurement time points
  • Analysis: Linear mixed model to estimate rate of change (slope)
  • Benefits: Gains statistical power from multiple time points and correlation between measurements
  • Repeated Measures: SE reduction factor accounts for number of measurements and correlation

Analysis Types

Mean Sensitivity (MS)

  • Definition: Average sensitivity across all tested locations in the visual field
  • Standard Error: SEMS = SElocation / √(number of locations)
  • Advantages: Lower measurement error due to averaging; more stable and reliable; better for global changes
  • Use Case: Recommended for studies focusing on overall visual field function

Single Location (1-Loc)

  • Definition: Sensitivity measurement at one specific visual field location
  • Standard Error: Uses the base measurement error without location averaging
  • Advantages: Can detect localized changes; relevant for specific visual field regions
  • Disadvantages: Higher measurement error, requires larger sample sizes

Calculated Metrics

  • Bundle Mean Sensitivity SE: Session SE ÷ √(locations × presentations × sessions_per_bundle)
  • Bundle Single Location SE: Session SE ÷ √(presentations × sessions_per_bundle)
  • Number of Bundles: floor(study_duration ÷ days_between_bundles) + 1
  • Effective Standard Errors: Account for repeated measures benefits
  • Degrees of Freedom (RCT): 2n - 2 for two-group comparison
  • Time Estimates: Session and bundle duration for feasibility assessment

Statistical Methods

RCT Design (Comparative Studies)

  • Test Type: Two-sample t-test with equal variances
  • Test Statistic: t = (Ȳ₂ - Ȳ₁) / √(2σ²total/n)
  • Variance Components: σ²total = σ²measurement + σ²population
  • Distribution: t-distribution with df = 2n - 2
  • Power Calculation: Uses non-central t-distribution approximation
  • Sample Size: Iterative refinement using t-distribution critical values

Progression Studies

  • Model: Linear mixed model with compound symmetry correlation
  • Repeated Measures: For n equally spaced measurements with correlation ρ
  • SE Reduction Factor: Accounts for multiple time points and correlation
  • Power Calculations: Uses normal distribution with adjusted standard errors

Example Use Cases

Glaucoma Progression Study

  • Goal: Detect 1 dB/year (0.25dB in 3 mo.) progression with 85% power
  • Design: 3 month study, measurements before, during, and after
  • Analysis: Mean sensitivity (more stable for global changes)
  • Expected Result: ~12 patients needed per arm

Treatment Efficacy Trial (RCT)

  • Goal: Compare 0.2 dB difference between groups with 80% power
  • Design: Comparative study using t-test
  • Analysis: Mean sensitivity for global assessment
  • Expected Result: ~27 patients per group

Key Assumptions

Statistical

  • Normal distribution of measurements
  • Independence between subjects
  • Equal variances between groups (RCT)
  • Linear progression over time
  • Constant measurement variance
  • Compound symmetry correlation
  • Population variability (σ²β) estimated from similar populations

Practical

  • Patient compliance with visits
  • Consistent testing conditions
  • No learning effects
  • Equipment stability
  • No missing data
  • Random assignment (RCT)

Formal Model Specification

For patient i in treatment group j, the observed change in sensitivity is:

Yij = μj + βi + γj + εi

Where:

  • Yij = Observed change for patient i in group j
  • μj = True mean change for treatment group j (μ₁ for controls, μ₂ for treatment)
  • βi ~ N(0, σ²β) = Patient-specific deviation from group mean (inter-subject variability)
  • γj ~ N(0, σ²γ) = Variability in treatment effect across patients (assumed 0 for power analysis)
  • εi ~ N(0, σ²ε) = Measurement error in estimating patient i's change

Model for Power Analysis

Yij = μj + βi + εi

Both measurement error and population variability contribute to observed variance

Hypotheses

H₀: μtreatment - μcontrol = 0

H₁: μtreatment - μcontrol ≠ 0

Test Statistic (Two-Sample t-test)

t = (Ȳ₂ - Ȳ₁) / √(2σ²total/n)

where σ²total = σ²measurement + σ²population, n₁ = n₂ = n (equal group sizes), and df = 2n - 2

Variance Components

Measurement error for change: σ²ε = 2 × σ²measurement

(measuring change requires two measurements, variance adds)

Total variance: σ²total = σ²ε + σ²β

(both measurement error and population variability contribute)

σ²ε (measurement): Can be reduced via more sessions, presentations, or locations

σ²β (population): Cannot be reduced; inherent to the patient population

Key Parameters - VVP Configuration

Sessions per Bundle
  • Definition: Number of individual testing sessions combined into one measurement bundle
  • Typical Range: 1-20 sessions
  • Impact: More sessions per bundle reduce measurement error by √(sessions)
  • Trade-off: More sessions = better precision but longer testing time
Days Between Bundles (Progression Studies Only)
  • Definition: Time interval between measurement bundles
  • Typical Range: 30-180 days
  • Impact: Shorter intervals = more time points = better slope estimation
  • Considerations: Must balance statistical power with practical constraints
Study Duration (Progression Studies Only)
  • Definition: Total duration of the study in days
  • Impact: Longer studies allow detection of smaller effect sizes
  • Calculation: Determines number of bundles = floor(duration/interval) + 1
Locations per Session per Eye
  • Definition: Number of visual field locations tested in each session
  • Typical Values: 24 (central), 52 (standard), 76 (extended)
  • Impact: More locations improve mean sensitivity precision by √(locations)

Key Parameters - Testing & Statistical

Stimulus Presentations per Location
  • Definition: Number of stimulus presentations at each visual field location
  • Typical Range: 1-6 presentations
  • Standard: Often 3-4 presentations for reliability
  • Impact: More presentations reduce measurement error by √(presentations)
Single Location Standard Error
  • Definition: Measurement precision for one location with 4 stimulus presentations (single timepoint)
  • Typical Values: 3-8 dB depending on patient population and testing conditions
  • Note: This is the baseline measurement error that gets adjusted for actual testing parameters
  • For change measurements: σ²ε = 2 × σ²single measurement
Population Standard Deviation (σβ)
  • Definition: Inter-subject variability in rates of progression or treatment response
  • Nature: Inherent variability between patients that cannot be reduced through improved testing
  • Impact: Sets a floor on detectable effect sizes regardless of measurement precision
Statistical Power
  • Definition: Probability of detecting a true effect when it exists (1 - β)
  • Standard Values: 80% or 90%
  • Interpretation: 80% power means 80% chance of detecting the effect if it truly exists
Significance Level (α)
  • Definition: Probability of Type I error (false positive)
  • Standard Values: 0.05 (5%) or 0.01 (1%)
  • Interpretation: 5% chance of detecting an effect when none exists
Effect Size Types
Progression Studies:
  • Entire Study: Total effect size detectable over the complete study duration
  • Per Year: Annual rate of progression (dB/year)
  • Per Bundle: Effect size between consecutive measurement bundles
Comparative Studies:
  • Between Groups: Difference in means between two independent groups
  • Uses two-sample t-test from formal model

Limitations & Best Practices

Model Limitations

  • Linear assumption may not capture non-linear patterns
  • Constant correlation assumption
  • No ceiling/floor effects considered
  • Perfect compliance assumed
  • Equal group sizes assumed for RCT
  • Normal approximation for non-central t-distribution
  • Requires accurate population variance estimate

Best Practices

  • Validate measurement precision in pilot studies
  • Use conservative SE estimates
  • Ensure population variance input reflects your patient population
  • Understand that reducing measurement error alone may not substantially improve power if population variance dominates
  • Consider cost vs. power trade-offs
  • Plan for interim analysis in long studies
  • Account for multiple comparisons if applicable
  • Document deviations from model assumptions

This calculator is provided as-is and without warranty of any kind. It is intended for informational purposes only and should not be considered as professional advice.