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MCDA Clinical Threshold-Based Normalization

mcda-value-functions.Rmd

Overview

This package provides three MCDA visualization functions that implement clinical threshold-based normalization:

  1. create_mcda_barplot_comparison(): Shows normalized values for Placebo and Drug side-by-side with their difference
  2. create_mcda_walkthrough(): Shows the complete MCDA calculation from normalized differences through weighted scores
  3. create_mcda_waterfall(): Shows cumulative contribution of each criterion to the total benefit-risk score

All functions use fixed clinical scales (global scales) rather than treatment-relative normalization (local scales), as recommended by FDA/EMA best practices and the PROTECT framework.

The Normalization Approach

Value Function

For each criterion, we apply a linear value function based on clinical thresholds:

For “increasing” direction (higher is better):

v(x) = 100 * (x - min) / (max - min)

For “decreasing” direction (lower is better):

v(x) = 100 * (max - x) / (max - min)

Where min and max are clinically meaningful thresholds, not observed treatment values.

Key Steps

  1. Normalize actual values separately
    • Apply value function to drug’s actual values → Drug normalized (0-100)
    • Apply value function to placebo’s actual values → Placebo normalized (0-100)
  2. Compute normalized differences
    • Normalized difference = Drug normalized - Placebo normalized
    • Positive = Drug performs better than Placebo
    • Negative = Drug performs worse than Placebo
  3. Apply weights and aggregate
    • Weighted contribution = Normalized difference × Weight
    • Total benefit-risk score = Sum of weighted contributions

Defining Clinical Scales

Each criterion requires three parameters:

clinical_scales <- list(
  `Criterion Name` = list(
    min = 0,                  # Lower threshold
    max = 100,                # Upper threshold
    direction = "increasing"  # "increasing" or "decreasing"
  )
)

Direction: - "increasing": Higher raw values are better (e.g., efficacy) - "decreasing": Lower raw values are better (e.g., adverse events)

Thresholds should be based on clinical guidelines, Minimum Clinically Important Difference (MCID), or regulatory precedents.

Example

Prepare Data 

mcda_data <- prepare_mcda_data(effects_table)

Define Clinical Scales 

clinical_scales <- list(
  `Benefit 1` = list(min = 0, max = 1, direction = "increasing"),
  `Benefit 2` = list(min = 0, max = 100, direction = "decreasing"),
  `Benefit 3` = list(min = 0, max = 100, direction = "increasing"),
  `Risk 1` = list(min = 0, max = 0.5, direction = "decreasing"),
  `Risk 2` = list(min = 0, max = 0.3, direction = "decreasing")
)

Define Weights 

weights <- c(
  `Benefit 1` = 0.30,
  `Benefit 2` = 0.20,
  `Benefit 3` = 0.10,
  `Risk 1` = 0.30,
  `Risk 2` = 0.10
)

Create Visualizations

Comparison Plot: Shows normalized values and their difference

barplot_comparison <- create_mcda_barplot_comparison(
  data = mcda_data,
  study = "Study 1",
  benefit_criteria = c("Benefit 1", "Benefit 2", "Benefit 3"),
  risk_criteria = c("Risk 1", "Risk 2"),
  comparison_drug = "Drug A",
  clinical_scales = clinical_scales
)

This shows 3 columns for each criterion: - Normalized Placebo (0-100 scale) - Normalized Drug (0-100 scale) - Normalized Difference (Drug - Placebo)

Walkthrough Plot: Shows complete MCDA calculation

barplot_walkthrough <- create_mcda_walkthrough(
  data = mcda_data,
  study = "Study 1",
  benefit_criteria = c("Benefit 1", "Benefit 2", "Benefit 3"),
  risk_criteria = c("Risk 1", "Risk 2"),
  comparison_drug = "Drug A",
  weights = weights,
  clinical_scales = clinical_scales
)

Waterfall Plot: Shows cumulative contributions

# Show all active treatments compared to their study-specific comparators
waterfall_all <- create_mcda_waterfall(
  data = mcda_data,
  comparator_name = "Placebo",
  benefit_criteria = c("Benefit 1", "Benefit 2", "Benefit 3"),
  risk_criteria = c("Risk 1", "Risk 2"),
  weights = weights,
  clinical_scales = clinical_scales
)

# Or analyze a single study
waterfall_study1 <- create_mcda_waterfall(
  data = mcda_data,
  study = "Study 1",
  comparator_name = "Placebo",
  benefit_criteria = c("Benefit 1", "Benefit 2", "Benefit 3"),
  risk_criteria = c("Risk 1", "Risk 2"),
  weights = weights,
  clinical_scales = clinical_scales
)

Interpreting the Walkthrough Output

The plot shows 3 panels representing the MCDA calculation steps:

Panel 1: Normalized Difference - Shows: (Drug normalized - Placebo normalized) - Positive values = Drug performs better than Placebo - Negative values = Drug performs worse than Placebo - Scale is symmetric around zero

Panel 2: Weight - Shows: Relative importance (must sum to 100%) - Each criterion’s contribution to final score

Panel 3: Benefit-Risk - Shows: Normalized Difference × Weight - Weighted contribution for each criterion - Total score = Sum of all contributions - Positive total = Drug has better overall benefit-risk profile - Negative total = Placebo has better overall benefit-risk profile

Interpreting the Waterfall Output

The waterfall chart shows how criteria cumulatively contribute to the total benefit-risk score:

Bar Segments - Each colored segment represents one criterion’s weighted contribution - Blue segments = Benefits (positive contribution) - Red segments = Risks (negative contribution) - Gray bar = Total score (cumulative sum)

Dotted Connector Lines - Connect the end of one bar to the start of the next - Show cumulative progression toward total score

Interpretation - Segments extending right = Favorable contributions - Segments extending left = Unfavorable contributions - The Total bar shows the net benefit-risk balance - Positive total = Drug favored over comparator - Negative total = Comparator favored over drug

When showing all studies, each facet panel displays one active treatment compared to its study-specific comparator, allowing visual comparison across multiple drugs.

Understanding Negative Normalized Values

Example: Drug has 19% adverse events, Placebo has 3% adverse events

# Clinical scale: min=0%, max=50%, direction="decreasing"

# Step 1: Normalize separately
Drug_normalized = 100 * (50-19) / 50 = 62
Placebo_normalized = 100 * (50-3) / 50 = 94

# Step 2: Compute difference
Normalized_difference = 62 - 94 = -32  # Drug performs worse

The -32 indicates Drug has worse safety than Placebo (higher AE rate)

Key Points

Setting Thresholds: - Base on clinical guidelines, MCID, or regulatory precedents - Do NOT use observed min/max from your data - Document rationale

Validation: - Check face validity (does it make clinical sense?) - Perform sensitivity analysis on weights - Ensure stakeholder acceptance

References

  • Mussen F, et al. (2007). Pharmacoepidemiol Drug Saf, 16 Suppl 1:S2-15
  • PROTECT Benefit-Risk Framework (2012)
  • Thokala P, et al. (2016). Value in Health, 19(1):1-13
  • FDA Benefit-Risk Assessment Framework (2013)
  • EMA Benefit-Risk Methodology Project (2011)

For detailed implementation reference: dev/references/MCDA_Value_Function_Implementation.md