#!/usr/bin/env python3
"""Kaplan-Meier survival report: curves, medians, survival at chosen times, log-rank test and RMST.
Input: CSV with a duration column (time from start to event or censoring) and an event column (1 = event
observed, 0 = censored); optional --group column.
Reports per group (and overall):
n, events, censored share
survival S(t) at --at times with 95% CIs (Greenwood variance, log(-log) transform, as in lifelines and R)
median survival time with its 95% CI (Brookmeyer-Crowley style: where the CI band crosses 0.5), or
"not reached" when fewer than half had the event
restricted mean survival time (RMST) up to --tau (default: the smallest group's largest follow-up), the
average event-free time in [0, tau], with the difference between groups
number at risk at the --at times
Across groups:
log-rank test (chi-square with k-1 df) for equal survival curves
Warnings: heavy censoring (> 70%), groups with < 10 events, curves that cross (proportional hazards is
doubtful: prefer RMST or time-specific comparisons over a single hazard ratio).
Usage:
python km_report.py survival.csv --duration-col duration_days --event-col event
python km_report.py survival.csv --duration-col duration_days --event-col event --group plan --at 90 180 365
python km_report.py data.csv --duration-col t --event-col died --group arm --tau 365 --json
Exit codes: 0 reported, 2 usage or read error.
"""
import argparse
import json
import math
import os
import sys
from collections import defaultdict
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
from _surv_io import chi2_sf, load # noqa: E402
def km(data):
"""data: list of (t, e). Returns step points [(t, S, var_greenwood_sum, n_at_risk, d)]."""
times = sorted({t for t, e in data if e == 1})
n = len(data)
by_t = defaultdict(lambda: [0, 0])
for t, e in data:
by_t[t][0 if e else 1] += 1
at_risk = n
s, gw = 1.0, 0.0
steps = []
for t in sorted(by_t):
d, c = by_t[t]
if d:
s *= 1 - d / at_risk
if at_risk > d:
gw += d / (at_risk * (at_risk - d))
steps.append((t, s, gw, at_risk, d))
at_risk -= d + c
return steps
def s_at(steps, t):
s, gw = 1.0, 0.0
for st, sv, g, _, _ in steps:
if st <= t:
s, gw = sv, g
else:
break
return s, gw
def ci_loglog(s, gw, z=1.959964):
if s <= 0 or s >= 1 or gw == 0:
return (s, s)
se = math.sqrt(gw) / abs(math.log(s))
lo = s ** math.exp(z * se)
hi = s ** math.exp(-z * se)
return lo, hi
def median(steps):
def cross(f):
for st, sv, g, _, _ in steps:
if f(sv, g) <= 0.5:
return st
return None
est = cross(lambda s, g: s)
lo = cross(lambda s, g: ci_loglog(s, g)[0])
hi = cross(lambda s, g: ci_loglog(s, g)[1])
return est, lo, hi
def rmst(steps, tau):
area, prev_t, prev_s = 0.0, 0.0, 1.0
for st, sv, _, _, _ in steps:
if st > tau:
break
area += prev_s * (st - prev_t)
prev_t, prev_s = st, sv
return area + prev_s * (tau - prev_t)
def at_risk(data, t):
return sum(1 for d, _ in data if d >= t)
def logrank(groups):
names = list(groups)
all_data = [(t, e, g) for g in names for t, e in groups[g]]
times = sorted({t for t, e, _ in all_data if e})
k = len(names)
O = [0.0] * k
E = [0.0] * k
V = [[0.0] * k for _ in range(k)]
for t in times:
n_j = [sum(1 for d, _ in groups[g] if d >= t) for g in names]
d_j = [sum(1 for d, e in groups[g] if d == t and e) for g in names]
n, d = sum(n_j), sum(d_j)
if n < 2:
continue
for i in range(k):
O[i] += d_j[i]
E[i] += d * n_j[i] / n
for j in range(k):
cov = d * (n - d) / (n * n * (n - 1)) * (n_j[i] * (n if i == j else 0) - n_j[i] * n_j[j])
V[i][j] += cov
m = k - 1
if m < 1:
return None
u = [O[i] - E[i] for i in range(m)]
A = [row[:m] for row in V[:m]]
# solve A x = u (Gauss-Jordan)
M = [A[i] + [u[i]] for i in range(m)]
for c in range(m):
piv = max(range(c, m), key=lambda r: abs(M[r][c]))
if abs(M[piv][c]) < 1e-12:
return None
M[c], M[piv] = M[piv], M[c]
for r in range(m):
if r != c:
f = M[r][c] / M[c][c]
M[r] = [a - f * b for a, b in zip(M[r], M[c])]
x = [M[i][m] / M[i][i] for i in range(m)]
chi2 = sum(ui * xi for ui, xi in zip(u, x))
return {"chi2": chi2, "df": m, "p": chi2_sf(chi2, m), "observed": dict(zip(names, O)), "expected": dict(zip(names, E))}
def report(res, at):
lines = []
for g, r in res["groups"].items():
med = r["median"]
mtxt = "not reached" if med[0] is None else (
f"{med[0]:.4g} (95% CI {med[1]:.4g} - " + ("NR" if med[2] is None else f"{med[2]:.4g}") + ")"
if med[1] is not None else f"{med[0]:.4g}")
lines.append(f"[{g}] n={r['n']} events={r['events']} censored={r['censored_share']:.0%} median survival: {mtxt} "
f"RMST({res['tau']:.4g}) = {r['rmst']:.4g}")
for t, s in zip(at, r["at"]):
lines.append(f" S({t:g}) = {s['s']:.3f} [{s['lo']:.3f}, {s['hi']:.3f}] at risk: {s['at_risk']}")
lr = res.get("logrank")
if lr:
lines.append("")
lines.append(f"log-rank test: chi2 = {lr['chi2']:.3f}, df = {lr['df']}, p = {lr['p']:.4g}")
lines.append(" observed / expected events: " + ", ".join(f"{g} {lr['observed'][g]:.0f}/{lr['expected'][g]:.1f}"
for g in lr["observed"]))
if len(res["groups"]) == 3 and "overall" in res["groups"]:
pass
diffs = res.get("rmst_diff")
if diffs:
lines.append("RMST difference vs " + diffs["reference"] + ": " +
", ".join(f"{g} {d:+.4g}" for g, d in diffs["diff"].items()))
for w in res["warnings"]:
lines.append(f"WARNING: {w}")
return "\n".join(lines)
def main():
ap = argparse.ArgumentParser(description="Kaplan-Meier survival report.", 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("--group")
ap.add_argument("--at", type=float, nargs="*", help="times at which to report S(t) (default: quartiles of follow-up)")
ap.add_argument("--tau", type=float, help="RMST horizon")
ap.add_argument("--json", action="store_true")
a = ap.parse_args()
try:
rows = load(a.csv, a.duration_col, a.event_col)
if a.group and a.group not in rows[0][2]:
raise ValueError(f"group column {a.group!r} not found")
except (OSError, ValueError) as e:
print(f"error: {e}", file=sys.stderr)
return 2
groups = defaultdict(list)
for t, e, r in rows:
groups[r[a.group] if a.group else "all"].append((t, e))
groups = dict(sorted(groups.items()))
follow = sorted(t for t, _, _ in rows)
at = a.at or [round(follow[int(q * (len(follow) - 1))], 1) for q in (0.25, 0.5, 0.75)]
tau = a.tau or min(max(t for t, _ in g) for g in groups.values())
res = {"groups": {}, "tau": tau, "warnings": []}
curves = {}
for g, data in groups.items():
steps = km(data)
curves[g] = steps
ev = sum(e for _, e in data)
r = {"n": len(data), "events": ev, "censored_share": 1 - ev / len(data), "median": median(steps),
"rmst": rmst(steps, tau), "at": []}
for t in at:
s, gw = s_at(steps, t)
lo, hi = ci_loglog(s, gw)
r["at"].append({"t": t, "s": s, "lo": lo, "hi": hi, "at_risk": at_risk(data, t)})
res["groups"][g] = r
if r["censored_share"] > 0.7:
res["warnings"].append(f"{g}: {r['censored_share']:.0%} censored - estimates beyond early times are uncertain")
if ev < 10:
res["warnings"].append(f"{g}: only {ev} events - curves and tests are unreliable")
if len(groups) > 1:
res["logrank"] = logrank(groups)
ref = next(iter(groups))
res["rmst_diff"] = {"reference": ref, "diff": {g: res["groups"][g]["rmst"] - res["groups"][ref]["rmst"]
for g in groups if g != ref}}
grid = sorted({st for steps in curves.values() for st, *_ in steps})
names = list(groups)
if len(names) == 2 and grid:
sign = [s_at(curves[names[0]], t)[0] - s_at(curves[names[1]], t)[0] for t in grid]
sig = [x for x in sign if abs(x) > 0.05]
if sig and min(sig) < 0 < max(sig):
res["warnings"].append("the survival curves cross: a single hazard ratio misrepresents the difference; "
"report RMST or survival at specific times")
print(json.dumps(res, indent=2) if a.json else report(res, at))
return 0
if __name__ == "__main__":
sys.exit(main())
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