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