Getting Started with SQUIRE

Introduction

SQUIRE (Statistical Quality-Assured Integrated Response Estimation) provides a structured workflow for biological parameter estimation that combines statistical validation with systematic testing of constraint configurations.

Basic Usage

Here’s a simple example using synthetic germination data:

# Generate example data
set.seed(123)
germination_data <- data.frame(
  time = rep(0:7, times = 12),
  treatment = rep(c("Control", "Inhibitor", "Promoter"), each = 32),
  replicate = rep(rep(1:4, each = 8), times = 3),
  response = c(
    # Control: normal germination
    rnorm(32, mean = rep(seq(0, 80, length.out = 8), 4), sd = 3),
    # Inhibitor: reduced germination
    rnorm(32, mean = rep(seq(0, 60, length.out = 8), 4), sd = 3),
    # Promoter: enhanced germination
    rnorm(32, mean = rep(seq(0, 95, length.out = 8), 4), sd = 3)
  )
)

# Run SQUIRE analysis
results <- SQUIRE(
  data = germination_data,
  treatments = c("Control", "Inhibitor", "Promoter"),
  control_treatment = "Control",
  verbose = FALSE
)

# Check results
if (results$optimization_performed) {
  print("Optimization was performed. Parameter estimates:")
  print(results$parameters$parameter_matrix)
} else {
  print(paste("Optimization not performed:", results$validation_results$reason))
}

Understanding the Workflow

SQUIRE follows a three-step process:

Step 1: Statistical Validation

Tests for significant treatment effects using ANOVA
Calculates effect sizes
Only proceeds if effects are statistically significant

Step 2: Constraint Configuration Testing

Systematically tests combinations of:
- T: Log-scale constraints
- P: Positive domain constraints
- E: Euclidean (unconstrained) parameters
Selects the configuration that best fits the data

Step 3: Geometry-Aware Optimization

Applies the selected constraints during optimization
Uses GALAHAD for trust-region methods
Returns parameter estimates for each treatment

Interpreting Results

The results include:

optimization_performed: Whether optimization proceeded (based on validation)
validation_results: Statistical test results and p-values
parameters: Matrix of optimized parameters for each treatment
galahad_settings: The constraint configuration used

Applications

SQUIRE is designed for:

Germination studies
Growth curve analysis
Enzyme kinetics
RT-QuIC kinetic analysis
Dose-response studies

Any time-series biological data with treatment comparisons can benefit from SQUIRE’s systematic approach to parameter estimation.