QC of implementation in new API

[mattsecrest]

Equation-to-code QC checklist

EC-IPW (.ec_ipw_borrow_core() in R/ec_ipw.R)

Reference: Zhou et al. (2024b), JRSS-A

• Eq 4 — density ratio W00 = pi_S(X)(1-pi_S) / (1-pi_S(X))pi_S: rx <- (pi_SX / (1 - pi_SX)) * ((1 - pi_S) / pi_S)
• Def 1, Eq 6 — mu_hat_11: mu1 <- colSums(potential[S==1 & A==1,]) / sum(S*A/w11)
• Def 1, Eq 6 — mu_hat_10: mu10 <- colSums(potential[S==1 & A==0,]) / sum(S*(1-A)/w10)
• Def 1, Eq 6 — mu_hat_00: mu00 <- colSums(potential[S==0,]) / sum((1-S)*w00)
• Eq 11 — optimal weight: w_opt <- num / (num + denom)
• Def 1 — ATE: tau <- mu1 - ((1-borrow_weight)*mu10 + borrow_weight*mu00)

Sandwich variance (.ec_ipw_sandwich())

• Theorem 3, Eq 12 — bread matrix blocks A11, A22, A33, A34, A44
• Theorem 3, Eq 12 — influence functions Psi_1 through Psi_4
• Eq 13 — sandwich: A_inv %*% B %*% t(A_inv)

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EC-AIPW (.ec_aipw_core() in R/ec_aipw.R)

Reference: Zhou et al. (2024b), JRSS-A

• Theorem 2 — outcome model on controls: lm(..., data=df[A==0,])
• Theorem 2 — residuals Y-tilde = Y - mu(X): Yr <- Y - Y0
• Def 2, Eq 7 — mu_hat_11 through mu_hat_00 (same as IPW but on residuals)
• Eq 11 — optimal weight (same formula as IPW)
• Def 2 — ATE on residuals

Sandwich variance (.ec_aipw_sandwich())

• Theorem 4, Eq 15 — bread: extends IPW with outcome model Jacobian blocks (Phi1_gamma, Phi2_gamma, Phi3_gamma)
• Theorem 4, Eq 15 — bread: outcome model Hessian (Y0_gamma)
• Theorem 4, Eq 15 — meat: adds Psi_5 for outcome model params
• Eq 16 — sandwich with augmented blocks

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DID-EC-IPW (.did_ec_ipw_core() in R/did_ec_ipw.R)

Reference: Zhou et al. (2024a), J Biopharm Stats

• Eq 4 — PS model pi_S(X) and treatment model pi_A(X)
• Eq 4 — weights W11 = 1/pi_A, W10 = 1/(1-pi_A), W0 = density ratio
• Eq 4 — Delta_trial: treated OLE weighted mean minus RCT control pre-crossover mean
• Eq 4 — Delta_EC: EC OLE weighted mean minus EC pre-crossover mean
• Eq 4 — tau = Delta_trial - Delta_EC: mu_S1A1 - mu_S0A0 - bias

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DID-EC-AIPW (.did_ec_aipw_core() in R/did_ec_aipw.R)

Reference: Zhou et al. (2024a), J Biopharm Stats

• Eq 5 — outcome model on external controls: lm(..., data=df[S==0,])
• Eq 5 — residuals Y-tilde = Y - mu(X,S=0,A=0,t): Yr <- Y - Y0
• Eq 5 — same DID structure as IPW applied to residuals
• Eq 5 — tau = Delta_trial - Delta_EC on residuals

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DID-EC-OR (.did_ec_or_core() in R/did_ec_or.R)

Reference: Zhou et al. (2024a), J Biopharm Stats

• Eq 3 — EC outcome models: lm(outcome_formula_ext[t], data=df[S==0,])
• Eq 3 — RCT control models (pre-crossover): lm(outcome_formula_rct_ctrl[t], data=df[S==1 & A==0,])
• Eq 3 — RCT treated models (OLE): lm(outcome_formula_rct_trt[t], data=df[S==1 & A==1,])
• Eq 3 — Delta_trial = avg_S1[OLE] - mean(avg_S1[pre])
• Eq 3 — Delta_EC = avg_S0A0[OLE] - mean(avg_S0A0[pre])
• Eq 3 — tau = Delta_trial - Delta_EC

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SCM (.scm_subject_sc() + .scm_lambdacv() in R/scm.R)

Reference: Zhou et al. (2024a), J Biopharm Stats

• Eq 7 — penalized SC optimization: loss + lambda * penalty with sum(w)==1, w>=0
• Eq 7 — z_i = stacked covariates + pre-crossover outcomes (matching variables)
• Eq 8 — synthetic control prediction: X00[long_term,] %*% wt_est
• Eq 9 — ATE: Y_trt - colMeans(y_est_mat)
• Remark 4 — LOOCV lambda selection in .scm_lambdacv()

[mattsecrest]

Current plan:

Speed up vignettes (reduce SCM params)
Rewire run_analysis() to use estimate() dispatch
Delete legacy files and deprecated constructors
Equation QC as a separate issue