scripts/run_warfarin.py

"""Section 5.1 -- personalized warfarin dosing on the PharmGKB/IWPC cohort.

Paper setup (verbatim, Section 5.1 "RCB Setup"):
  "The total number of trials is set at T = 5528, with reward noise sigma_hat = 0.054
   estimated from the true optimal dosing of warfarin after scaling. To create an
   online decision-making scenario, we simulate the process across 10 random
   permutations of patient arrivals, averaging the results over these permutations.
   The exploration budget eps is varied among [0.025, 0.035, 0.045]. The minimum gap
   tau_P0 is set at 0.005. The prior variance is defined as Sigma = [0.4, 0.6, 0.8] Id,
   and the prior means are beta_{2,0} = 0.05 x Id, beta_{1,0} = beta_{3,0} = 0_d."

Full grid: 3 budgets x 3 prior variances x 10 permutations = 90 runs of T = 5528.
"""

import argparse, json, os, sys, time
import numpy as np
from sklearn.linear_model import LinearRegression

os.chdir(os.path.abspath(os.path.join(os.path.dirname(__file__), "..")))
sys.path.insert(0, os.path.join(os.path.dirname(__file__), ".."))
from rcb.core import RCB, N_eps, L_eps
from rcb.env import build_warfarin

PREV = None   # true class prevalences p_k, filled from the data


def ground_truth(X, arm, dose):
    """Appendix F.4 / Section 5.1 ground truth: scale the optimal dose into [0,1]
    (min 0, max 1); per dosage group, regress the scaled dose on the covariates to
    get beta_i; the true mean reward of a patient is x'beta_i for the *optimal* arm
    and 0 for every counterfactual arm."""
    s = (dose - dose.min()) / (dose.max() - dose.min())
    betas = []
    for i in range(3):
        m = arm == i
        lr = LinearRegression(fit_intercept=False).fit(X[m], s[m])
        betas.append(lr.coef_)
    betas = np.array(betas)
    mu_opt = np.einsum("ij,ij->i", X, betas[arm])       # x'beta_{optimal arm}
    sigma_hat = float(np.std(s))
    return betas, mu_opt, s, sigma_hat


def weighted_risk_score(correct, arm, prev):
    """Section 5.1: Score = sum_k p_k ( I(Correct|k) - I(Incorrect|k) ) = sum_k p_k (2 a_k - 1)."""
    sc = 0.0
    for k in range(3):
        m = arm == k
        a = correct[m].mean() if m.sum() else 0.0
        sc += prev[k] * (2 * a - 1)
    return sc


def effective_phi0(X):
    """Assumption 3 requires lambda_min(E[xx']) >= phi0 > 0. On the IWPC design this
    eigenvalue is exactly 0 (the dummy encoding is rank deficient), so we substitute
    the smallest *positive* eigenvalue -- the tightest value for which the assumption
    is not vacuous. This substitution is reported in the logbook."""
    ev = np.linalg.eigvalsh(X.T @ X / len(X))
    return float(ev[ev > 1e-8].min())


def run_one(X, arm, mu_opt, sigma, eps, prior_var, seed, tau_P0=0.005, rho_P0=0.95,
            C_N=None, gamma_const=4.0, phi0=None, use_empirical_EF=True,
            reward="continuous", rng_noise=None, N_override=None):
    rng = np.random.default_rng(seed)
    n, d = X.shape
    K = 3
    order = rng.permutation(n)

    beta0 = [np.zeros(d), 0.05 * np.ones(d), np.zeros(d)]     # Medium arm is prior-best
    Sigma0 = [prior_var * np.eye(d) for _ in range(K)]
    if phi0 is None:
        phi0 = effective_phi0(X)

    N = N_eps(K, d, sigma, eps, tau_P0, phi0, C=C_N) if N_override is None else float(N_override)
    L = L_eps(eps, tau_P0, rho_P0)

    algo = RCB(K, d, sigma, beta0, Sigma0, N=max(1, N), L=L, offset=0.0,
               phi0=phi0, trust_mode="linear", trust_rate=1.0,
               gamma_const=gamma_const, use_empirical_EF=use_empirical_EF, rng=rng)

    regret = np.empty(n); gains = np.empty(n); correct = np.empty(n, bool)
    rec_by_patient = np.empty(n, int)
    cum = 0.0
    for t, idx in enumerate(order):
        x = X[idx]
        rec, info = algo.recommend(x)
        rec_by_patient[idx] = rec
        gains[t] = algo.dbic_gain_expected(x, algo.rec_kernel(x, info))
        ok = rec == arm[idx]
        correct[t] = ok
        # mu(x, i) = x'beta_i for the optimal arm, 0 for counterfactuals
        cum += mu_opt[idx] - (mu_opt[idx] if ok else 0.0)
        regret[t] = cum
        if reward == "binary":
            y = 1.0 if ok else 0.0
        else:
            # y_t = mu(x_t, a_t) + eta_t, mu = x'beta_i for the optimal arm and 0
            # for counterfactual arms (Section 5.1 "Ground Truth"), eta ~ N(0, sigma^2)
            y = (mu_opt[idx] if ok else 0.0) + sigma * rng.standard_normal()
        algo.update(x, rec, y, info)

    return dict(regret=regret, gain=gains, correct=correct, order=order,
                rec_by_patient=rec_by_patient,
                Tcold=algo.Tcold if algo.Tcold else n, N=N, L=L, phi0=phi0)


def main():
    ap = argparse.ArgumentParser()
    ap.add_argument("--data", default="data/iwpc_warfarin_5528.csv")
    ap.add_argument("--out", default="outputs/warfarin.json")
    ap.add_argument("--perms", type=int, default=10)
    ap.add_argument("--C_N", type=float, default=None, required=True,
                    help="implementation constant multiplying Theorem 1's N(eps)")
    ap.add_argument("--N", type=int, default=None,
                    help="explicit per-arm cold-start size (overrides C_N * Theorem 1)")
    ap.add_argument("--reward", default="binary", choices=["binary", "continuous"],
                    help="Section 5.1 states y_t = 1{correct arm} (binary); the "
                         "'Ground Truth' paragraph instead implies y = x'beta_opt.")
    ap.add_argument("--EF", default="theory", choices=["theory", "empirical"],
                    help="source of E_{F,delta}(|T_{m-1}|) in Algorithm 2 line 10")
    ap.add_argument("--phi0", type=float, default=1.0,
                    help="Assumption 3 lambda_min(E[xx']); <=0 means use the smallest "
                         "positive eigenvalue of the empirical design")
    args = ap.parse_args()

    X, arm, dose, cols = build_warfarin(args.data)
    betas, mu_opt, s, sigma_hat = ground_truth(X, arm, dose)
    n, d = X.shape
    prev = np.bincount(arm, minlength=3) / n
    phi0 = args.phi0 if args.phi0 > 0 else effective_phi0(X)
    print(f"patients={n} features={d} sigma_hat={sigma_hat:.3f} prevalence={prev.round(3)}")
    print(f"reward={args.reward} EF={args.EF} phi0={phi0:.6g}")

    # Physician baseline: always Medium
    phys_correct = (arm == 1)
    phys_score = weighted_risk_score(phys_correct, arm, prev)
    print(f"physician weighted risk score = {phys_score:.3f}  (paper: 0.20)")

    # Offline full-information ceiling for the paper's own oracle class (per-arm
    # ridge on ALL 5528 patients). No online policy using this oracle can beat it.
    lam = 1e-2
    bh = []
    for i in range(3):
        yv = (arm == i).astype(float) if args.reward == "binary" else np.where(arm == i, mu_opt, 0.0)
        bh.append(np.linalg.solve(X.T @ X + lam * np.eye(d), X.T @ yv))
    pred = (X @ np.array(bh).T).argmax(1)
    ceil_cm = np.array([[float((pred[arm == k] == j).mean()) for j in range(3)] for k in range(3)])
    print(f"offline oracle ceiling: err={1 - (pred == arm).mean():.4f} "
          f"score={weighted_risk_score(pred == arm, arm, prev):+.4f}")

    # Theorem 1's own requirement at this scale, with C = 1 (no fudge factor).
    N_thm1 = {e: N_eps(3, d, sigma_hat, e, 0.005, phi0, C=1.0) for e in [0.025, 0.035, 0.045]}
    print("Theorem 1 required N(eps) at C=1: " +
          " ".join(f"{e}:{v:.0f}" for e, v in N_thm1.items()) + f"   (T = {n})")

    res = {"meta": dict(n=n, d=d, sigma_hat=sigma_hat, prevalence=prev.tolist(),
                        physician_score=phys_score,
                        physician_error=float(1 - phys_correct.mean()),
                        C_N=args.C_N, reward=args.reward, EF=args.EF, phi0=phi0,
                        ceiling_error=float(1 - (pred == arm).mean()),
                        ceiling_score=weighted_risk_score(pred == arm, arm, prev),
                        ceiling_confusion=ceil_cm.tolist(),
                        N_theorem1_C1={str(k): v for k, v in N_thm1.items()},
                        columns=cols), "runs": []}

    t0 = time.time()
    for eps in [0.025, 0.035, 0.045]:
        for pv in [0.4, 0.6, 0.8]:
            regs, errs, gns, scores, conf, tcolds = [], [], [], [], [], []
            for p in range(args.perms):
                r = run_one(X, arm, mu_opt, sigma_hat, eps, pv, seed=1000 * p + 7,
                            C_N=args.C_N, reward=args.reward, phi0=phi0,
                            use_empirical_EF=(args.EF == "empirical"),
                            N_override=args.N)
                regs.append(r["regret"]); gns.append(r["gain"])
                errs.append(1 - np.cumsum(r["correct"]) / np.arange(1, n + 1))
                rp = r["rec_by_patient"]
                scores.append(weighted_risk_score(rp == arm, arm, prev))
                # Table 2: rows = true dosage stratum, cols = RCB assigned dosage
                cm = np.zeros((3, 3))
                for k in range(3):
                    m = arm == k
                    for j in range(3):
                        cm[k, j] = (rp[m] == j).mean()
                conf.append(cm)
                tcolds.append(r["Tcold"])
            entry = dict(eps=eps, prior_var=pv,
                         regret_mean=float(np.mean([g[-1] for g in regs])),
                         regret_curve=np.mean(regs, 0)[::20].tolist(),
                         error_final=float(np.mean([e[-1] for e in errs])),
                         error_curve=np.mean(errs, 0)[::20].tolist(),
                         gain_curve=np.mean(gns, 0)[::20].tolist(),
                         gain_min=float(np.min(np.mean(gns, 0))),
                         frac_gain_below_negeps=float(np.mean(np.mean(gns, 0) < -eps)),
                         score=float(np.mean(scores)), score_sd=float(np.std(scores)),
                         confusion=np.mean(conf, 0).tolist(),
                         Tcold=float(np.mean(tcolds)), N=r["N"], L=r["L"])
            res["runs"].append(entry)
            print(f"eps={eps} Sigma={pv}I | N={r['N']:.1f} L={r['L']:.1f} "
                  f"Tcold={np.mean(tcolds):.0f} | err={entry['error_final']:.3f} "
                  f"score={entry['score']:.3f} regret={entry['regret_mean']:.0f} "
                  f"min-gain={entry['gain_min']:+.4f}")

    res["physician_confusion"] = [[0, 1, 0], [0, 1, 0], [0, 1, 0]]
    res["wall_clock_s"] = time.time() - t0
    os.makedirs(os.path.dirname(args.out), exist_ok=True)
    json.dump(res, open(args.out, "w"))
    print(f"wrote {args.out} in {res['wall_clock_s']:.0f}s")


if __name__ == "__main__":
    main()