#!/usr/bin/env python3
"""Fit a Cox proportional hazards model (stdlib) and check its assumptions.
Input: CSV with duration, event (1/0) and covariate columns. Numeric covariates are used as they are;
non-numeric ones are one-hot encoded with the first level (sorted) as reference.
Fitting: Newton-Raphson on the partial likelihood with Efron's method for tied event times (the default in
lifelines and R's coxph), covariates centred internally for stability, optional ridge --penalizer.
Reports:
coefficients coef, hazard ratio exp(coef), 95% CI, z, p for every covariate
fit log partial likelihood, likelihood-ratio test against the null model, Harrell's concordance
PH check Grambsch-Therneau test per covariate: correlation of scaled Schoenfeld residuals with the
rank of event time (as lifelines' proportional_hazard_test(time_transform="rank") and R's
cox.zph). p < 0.05 means the hazard ratio changes over time: stratify on the variable, add a
time interaction, or report time-specific effects
warnings events per covariate < 10 (overfitting), separation (|coef| > 10), non-convergence
Usage:
python cox_fit.py survival.csv --duration-col duration_days --event-col event --covariates plan age
python cox_fit.py data.csv --duration-col t --event-col died --covariates age sex stage --penalizer 0.1 --json
Exit codes: 0 fitted and PH holds, 1 PH violated for at least one covariate (p < --ph-alpha), 2 usage error or
no convergence.
"""
import argparse
import json
import math
import os
import random
import sys
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from _surv_io import chi2_sf, load, norm_sf, num # noqa: E402
def design(rows, covs):
cols, cats = [], {}
for c in covs:
vals = [r[c] for _, _, r in rows]
if all(num(v) is not None for v in vals):
cols.append((c, None))
else:
levels = sorted(set(vals))
if len(levels) < 2:
continue
cats[c] = levels
cols += [(c, lv) for lv in levels[1:]]
X = []
for _, _, r in rows:
X.append([float(r[c]) if lv is None else (1.0 if r[c] == lv else 0.0) for c, lv in cols])
names = [c if lv is None else f"{c}={lv}" for c, lv in cols]
return names, X, cats
def solve(A, b):
n = len(b)
M = [A[i][:] + [b[i]] for i in range(n)]
for c in range(n):
piv = max(range(c, n), key=lambda r: abs(M[r][c]))
if abs(M[piv][c]) < 1e-14:
raise ValueError("singular information matrix (collinear covariates or separation)")
M[c], M[piv] = M[piv], M[c]
for r in range(n):
if r != c:
f = M[r][c] / M[c][c]
M[r] = [x - f * y for x, y in zip(M[r], M[c])]
return [M[i][n] / M[i][i] for i in range(n)]
def inverse(A):
n = len(A)
return [list(col) for col in zip(*[solve(A, [1.0 if i == j else 0.0 for i in range(n)]) for j in range(n)])]
def efron(times, events, X, beta, pen):
"""Log partial likelihood, gradient and Hessian with Efron ties."""
n, p = len(X), len(beta)
order = sorted(range(n), key=lambda i: -times[i])
eta = [sum(b * x for b, x in zip(beta, X[i])) for i in range(n)]
w = [math.exp(min(e, 700)) for e in eta]
S0, S1, S2 = 0.0, [0.0] * p, [[0.0] * p for _ in range(p)]
ll, g, H = 0.0, [0.0] * p, [[0.0] * p for _ in range(p)]
i = 0
while i < n:
t = times[order[i]]
j = i
tied = []
while j < n and times[order[j]] == t:
k = order[j]
S0 += w[k]
for a in range(p):
S1[a] += w[k] * X[k][a]
for b in range(p):
S2[a][b] += w[k] * X[k][a] * X[k][b]
if events[k]:
tied.append(k)
j += 1
d = len(tied)
if d:
T0 = sum(w[k] for k in tied)
T1 = [sum(w[k] * X[k][a] for k in tied) for a in range(p)]
T2 = [[sum(w[k] * X[k][a] * X[k][b] for k in tied) for b in range(p)] for a in range(p)]
for k in tied:
ll += eta[k]
for a in range(p):
g[a] += X[k][a]
for l in range(d):
c = l / d
s0 = S0 - c * T0
s1 = [S1[a] - c * T1[a] for a in range(p)]
ll -= math.log(s0)
for a in range(p):
g[a] -= s1[a] / s0
for b in range(p):
H[a][b] -= (S2[a][b] - c * T2[a][b]) / s0 - s1[a] * s1[b] / (s0 * s0)
i = j
if pen:
ll -= 0.5 * pen * sum(b * b for b in beta)
for a in range(p):
g[a] -= pen * beta[a]
H[a][a] -= pen
return ll, g, H
def fit(times, events, X, pen=0.0, max_iter=50):
p = len(X[0])
beta = [0.0] * p
ll, g, H = efron(times, events, X, beta, pen)
ll0 = ll
for it in range(max_iter):
step = solve([[-v for v in row] for row in H], g)
t = 1.0
while True:
nb = [b + t * s for b, s in zip(beta, step)]
nll, ng, nH = efron(times, events, X, nb, pen)
if nll >= ll - 1e-12 or t < 1e-8:
break
t /= 2
converged = abs(nll - ll) < 1e-10
beta, ll, g, H = nb, nll, ng, nH
if converged:
return beta, ll, ll0, H, it + 1
raise ValueError("Newton-Raphson did not converge (separation or collinearity?)")
def schoenfeld(times, events, X, beta):
"""Schoenfeld residuals (x_i - risk-set weighted mean) for each event, in time order."""
n, p = len(X), len(beta)
w = [math.exp(min(sum(b * x for b, x in zip(beta, X[i])), 700)) for i in range(n)]
ev = sorted((times[i], i) for i in range(n) if events[i])
out = []
for t, i in ev:
risk = [k for k in range(n) if times[k] >= t]
s0 = sum(w[k] for k in risk)
mean = [sum(w[k] * X[k][a] for k in risk) / s0 for a in range(p)]
out.append((t, [X[i][a] - mean[a] for a in range(p)]))
return out
def ph_test(res_s, V, p):
d = len(res_s)
times = [t for t, _ in res_s]
order = sorted(range(d), key=lambda k: times[k])
rank = [0.0] * d
for r, k in enumerate(order):
rank[k] = r + 1.0
gbar = sum(rank) / d
T = [r - gbar for r in rank]
scaled = [[d * sum(res[b] * V[b][a] for b in range(p)) for a in range(p)] for _, res in res_s]
out = []
for a in range(p):
numer = sum(T[k] * scaled[k][a] for k in range(d)) ** 2
denom = d * sum(x * x for x in T) * V[a][a]
stat = numer / denom if denom > 0 else 0.0
out.append((stat, chi2_sf(stat, 1)))
return out
def concordance(times, events, risk, limit=3000):
idx = list(range(len(times)))
note = None
if len(idx) > limit:
idx = random.Random(0).sample(idx, limit)
note = f"computed on a random sample of {limit} rows"
conc = disc = tied = 0
for a in idx:
if not events[a]:
continue
for b in idx:
if times[b] > times[a]:
if risk[a] > risk[b]:
conc += 1
elif risk[a] < risk[b]:
disc += 1
else:
tied += 1
tot = conc + disc + tied
return ((conc + 0.5 * tied) / tot if tot else None), note
def main():
ap = argparse.ArgumentParser(description="Fit a Cox PH model and check proportional hazards.", epilog=__doc__,
formatter_class=argparse.RawDescriptionHelpFormatter)
ap.add_argument("csv")
ap.add_argument("--duration-col", required=True)
ap.add_argument("--event-col", required=True)
ap.add_argument("--covariates", nargs="+", required=True)
ap.add_argument("--penalizer", type=float, default=0.0)
ap.add_argument("--ph-alpha", type=float, default=0.05)
ap.add_argument("--json", action="store_true")
a = ap.parse_args()
try:
rows = load(a.csv, a.duration_col, a.event_col)
missing = [c for c in a.covariates if c not in rows[0][2]]
if missing:
raise ValueError(f"covariates not found: {', '.join(missing)}")
rows = [r for r in rows if all(r[2][c] not in ("", None) for c in a.covariates)]
names, X, cats = design(rows, a.covariates)
if not names:
raise ValueError("no usable covariates")
times = [t for t, _, _ in rows]
events = [e for _, e, _ in rows]
means = [sum(x[j] for x in X) / len(X) for j in range(len(names))]
Xc = [[x[j] - means[j] for j in range(len(names))] for x in X]
beta, ll, ll0, H, iters = fit(times, events, Xc, a.penalizer)
V = inverse([[-v for v in row] for row in H])
except (OSError, ValueError) as e:
print(f"error: {e}", file=sys.stderr)
return 2
p = len(names)
coefs = []
for j, nme in enumerate(names):
se = math.sqrt(max(V[j][j], 0.0))
z = beta[j] / se if se else 0.0
coefs.append({"covariate": nme, "coef": beta[j], "hr": math.exp(beta[j]), "se": se,
"hr_lo": math.exp(beta[j] - 1.959964 * se), "hr_hi": math.exp(beta[j] + 1.959964 * se),
"z": z, "p": 2 * norm_sf(abs(z))})
lr = 2 * (ll - ll0)
risk = [sum(b * x for b, x in zip(beta, xr)) for xr in Xc]
cidx, cnote = concordance(times, events, risk)
ph = ph_test(schoenfeld(times, events, Xc, beta), V, p)
n_events = sum(events)
res = {"n": len(rows), "events": n_events, "iterations": iters, "log_likelihood": ll,
"lr_test": {"chi2": lr, "df": p, "p": chi2_sf(lr, p)}, "concordance": cidx, "coefficients": coefs,
"ph_test": [{"covariate": nme, "stat": s, "p": pv} for nme, (s, pv) in zip(names, ph)],
"reference_levels": {c: lv[0] for c, lv in cats.items()}, "warnings": []}
if n_events / p < 10:
res["warnings"].append(f"{n_events} events for {p} covariates (< 10 per covariate): coefficients may be "
"unstable; use --penalizer or fewer covariates")
for c in coefs:
if abs(c["coef"]) > 10:
res["warnings"].append(f"{c['covariate']}: |coef| > 10 - separation or a covariate on a tiny scale")
if cnote:
res["warnings"].append(f"concordance {cnote}")
violated = [r for r in res["ph_test"] if r["p"] < a.ph_alpha]
if a.json:
print(json.dumps(res, indent=2))
else:
lines = [f"n={res['n']} events={n_events} iterations={iters} log partial likelihood {ll:.4f} "
f"LR test chi2={lr:.3f} df={p} p={res['lr_test']['p']:.4g} concordance {cidx:.3f}",
"" if not cats else "reference levels: " + ", ".join(f"{c}={lv}" for c, lv in res["reference_levels"].items()),
f"{'covariate':<22} {'coef':>8} {'HR':>7} {'95% CI':>17} {'z':>7} {'p':>9} PH p"]
for c, r in zip(coefs, res["ph_test"]):
lines.append(f"{c['covariate'][:22]:<22} {c['coef']:>8.4f} {c['hr']:>7.3f} "
f"{'[' + format(c['hr_lo'], '.3f') + ', ' + format(c['hr_hi'], '.3f') + ']':>17} "
f"{c['z']:>7.2f} {c['p']:>9.3g} {r['p']:.3g}" + (" PH VIOLATED" if r["p"] < a.ph_alpha else ""))
lines.append("")
if violated:
lines.append("PH assumption violated for: " + ", ".join(r["covariate"] for r in violated)
+ " - stratify, add covariate x time, or report time-specific effects")
else:
lines.append(f"proportional hazards: no evidence against it (all PH p >= {a.ph_alpha})")
for w in res["warnings"]:
lines.append(f"WARNING: {w}")
print("\n".join(ln for ln in lines if ln != ""))
return 1 if violated else 0
if __name__ == "__main__":
sys.exit(main())
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