stc-methodology

STC Methodology

Comprehensive methodological guidance for conducting rigorous Simulated Treatment Comparisons following NICE DSU TSD 18.

When to Use This Skill

• Deciding between STC and MAIC
• Selecting effect modifiers for STC model
• Understanding the covariate centering approach
• Implementing Bayesian STC
• Reviewing STC code or results

Fundamental Concept

Outcome Regression vs Propensity Weighting

STC Approach:

• Fit outcome regression model in IPD
• Include treatment and treatment-covariate interactions
• Predict treatment effect at external population covariate values
• Model-based adjustment for population differences

MAIC Approach:

• Reweight IPD to match external population
• Analyze weighted data as if from external population
• Design-based adjustment

Key Equation (Binary Outcome)

logit(P(Y=1)) = β₀ + β_trt × Treatment + β_X × X + β_trt:X × Treatment × X

Where:
- β_trt: Treatment effect when X = 0
- β_X: Effect of covariate X on outcome
- β_trt:X: Treatment-covariate interaction (effect modification)

For anchored STC:
1. Center X on external population mean: X_centered = X - X_external
2. Fit model with centered X
3. β_trt now represents treatment effect at external population values

Assumptions

Conditional Constancy of Relative Effects

Same as MAIC:

• Relative treatment effect is constant across populations after adjusting for effect modifiers
• Requires all effect modifiers included in model

Model Specification

Additional assumption vs MAIC:

• Outcome model must be correctly specified
• Includes functional form of covariate effects
• Includes correct interactions

Trade-off:
├── If model correct → STC more efficient than MAIC
├── If model wrong → STC may be biased
└── MAIC doesn't require outcome model specification

Effect Modifier Selection

What is an Effect Modifier?

A covariate that interacts with treatment effect:

• Treatment effect differs at different covariate values
• Shows significant treatment × covariate interaction
• Has biological plausibility for interaction

Selection Strategy

Effect Modifier Identification:
├── 1. Clinical/Biological Rationale
│   - Published literature on effect modification
│   - Mechanism of action considerations
│   - Expert clinical input
│
├── 2. Statistical Evidence (from IPD)
│   - Interaction terms in regression
│   - Subgroup analyses
│   - Use α = 0.10 (underpowered for interactions)
│
├── 3. Availability in AgD
│   - Must have summary statistics
│   - Means for continuous, proportions for binary
│
└── 4. Imbalance Between Populations
    - Focus on covariates that differ
    - Balanced covariates less important

Using identify_effect_modifiers()

em_result <- identify_effect_modifiers(
  data = ipd_data,
  outcome_var = "response",
  treatment_var = "treatment",
  candidate_covariates = c("age", "sex", "biomarker", "stage"),
  alpha = 0.10
)

# Returns:
# - Interaction p-values
# - Interaction coefficients
# - Recommended effect modifiers

Covariate Centering

Why Center Covariates?

Without centering (X = raw values):
- β_trt = treatment effect when ALL covariates = 0
- This may be meaningless (e.g., age = 0)

With centering (X_centered = X - X_external):
- β_trt = treatment effect when X = X_external
- This is the effect in external trial population
- Exactly what we need for ITC

Centering Process

# For continuous covariate
age_centered <- age - agd_mean_age

# For binary covariate
male_centered <- male - agd_prop_male

# Result: mean of centered covariate = (IPD mean - AgD mean)
# When evaluated at X_centered = 0, we get AgD population

Including vs Excluding Main Effects

With interactions:

# Model: Y ~ treatment + X_centered + treatment:X_centered
# β_trt: effect at X = X_external
# β_trt:X: how effect changes with X

Main effects typically included even if not "significant":

• Required for proper interpretation of interactions
• Follows statistical best practice
• Model hierarchically well-formulated

Anchored vs Unanchored STC

Anchored STC

Setup:
- IPD trial: A vs Common (C)
- AgD trial: B vs Common (C)

Steps:
1. Center covariates on AgD population
2. Fit: logit(Y) ~ Treatment + X_centered + Treatment:X_centered
3. Extract β_A (A vs C at AgD population)
4. Calculate d_BC from AgD (B vs C)
5. Indirect: d_AB = β_A - d_BC

Unanchored STC

Setup:
- IPD trial: Treatment A only (or A vs something)
- AgD: Single-arm Treatment B

Caution: Same issues as unanchored MAIC
- Must adjust for ALL prognostic factors
- Assumes absolute effects transportable
- Strong assumptions - use as sensitivity only

STC vs MAIC Comparison

Theoretical Comparison

Aspect	STC	MAIC
Method	Outcome regression	Propensity weighting
Efficiency	Higher (if model correct)	Lower (ESS reduction)
Model dependence	Higher	Lower
Continuous covariates	Natural	May need categorization
Extrapolation	Possible (with caution)	Limited to overlap
Diagnostic	Model fit, residuals	ESS, weight distribution

When to Prefer STC

• Model specification confidence is high
• Continuous covariates to adjust for
• Want to leverage regression framework
• MAIC gives very low ESS
• Interested in Bayesian framework

When to Prefer MAIC

• Uncertain about outcome model
• Want design-based approach
• Good overlap in covariate distributions
• Acceptable ESS achieved

Best Practice: Both as Sensitivity

# Run both methods
stc_result <- anchored_stc_binary(...)
maic_result <- maic_anchored(...)

# Compare results
# If similar: increased confidence
# If different: investigate why

Bayesian STC

Advantages

• Natural uncertainty quantification
• Prior information incorporation
• Posterior predictive checks
• Sensitivity to prior specification

Prior Selection

# Treatment effect prior
prior_normal(0, 10)  # Weakly informative

# Covariate effects
prior_normal(0, 5)

# Interactions (typically smaller)
prior_normal(0, 2)

# Sensitivity analysis with different priors

Implementation

bayes_result <- bayesian_anchored_stc_binary(
  ipd_data = ipd,
  agd_data = agd,
  outcome_var = "response",
  treatment_var = "treatment",
  covariates = c("age", "sex"),
  priors = list(
    treatment = prior_normal(0, 10),
    covariates = prior_normal(0, 5),
    interactions = prior_normal(0, 2)
  ),
  n_iter = 10000,
  n_warmup = 2000,
  seed = 12345
)

Reporting Requirements

Methods

• Justification for STC (vs MAIC, vs nothing)
• Effect modifier selection process
• Covariates included with rationale
• Model specification (link function, interactions)
• Centering approach explained
• Frequentist vs Bayesian justification
• Prior specification (if Bayesian)

Results

• Model coefficients with CIs
• Treatment effect at external population
• Comparison with unadjusted estimate
• Model diagnostics
• Sensitivity analyses (including vs MAIC)

Common Pitfalls

1. Forgetting to Center Covariates

• Treatment coefficient won't have correct interpretation
• Will estimate effect at covariate = 0, not external population

2. Omitting Interactions

• Defeats purpose of STC
• Must include treatment × covariate interactions

3. Including Too Many Covariates

• Model overfitting
• Unstable estimates
• Focus on effect modifiers only

4. Ignoring Model Diagnostics

• Check residuals
• Assess model fit
• Validate assumptions (linearity, etc.)

5. Not Comparing to MAIC

• Both methods should give similar answers
• Differences indicate model issues
• Always run as sensitivity

Quick Reference Code

library(stc)

# 1. Identify effect modifiers
em <- identify_effect_modifiers(
  data = ipd,
  outcome_var = "response",
  treatment_var = "treatment",
  candidate_covariates = c("age", "sex", "biomarker"),
  alpha = 0.10
)

# 2. Run anchored STC (frequentist)
result <- anchored_stc_binary(
  ipd_data = ipd,
  agd_data = list(
    n_total_A = 150, n_total_C = 150,
    n_events_A = 45, n_events_C = 60,
    covariates = list(
      age = list(mean = 62),
      sex = list(prop = 0.55)
    )
  ),
  outcome_var = "response",
  treatment_var = "treatment",
  covariates = c("age", "sex"),
  reference_arm = "A",
  include_interactions = TRUE,
  robust_se = TRUE
)

# 3. View results
print(result)
summary(result)

# 4. Access specific effects
result$treatment_effect_BC  # Indirect comparison
result$treatment_effect_AB  # Direct from IPD
result$treatment_effect_AC  # From AgD

# 5. Bayesian sensitivity
bayes_result <- bayesian_anchored_stc_binary(
  ...,
  priors = list(
    treatment = prior_normal(0, 10)
  )
)

Resources

• NICE DSU TSD 18: Population-adjusted indirect comparisons
• Phillippo et al. (2018): Methods for STC
• Ishak et al. (2015): Simulation studies
• stc package documentation