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() ```r 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 ```r # 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**: ```r # 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 ```r # 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 ```r # 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 ```r 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 ```r 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