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import os
import numpy as np
from statsmodels.duration.survfunc import (
SurvfuncRight, survdiff, plot_survfunc,
CumIncidenceRight)
from numpy.testing import assert_allclose
import pandas as pd
import pytest
# If true, the output is written to a multi-page pdf file.
pdf_output = False
try:
import matplotlib.pyplot as plt
except ImportError:
pass
def close_or_save(pdf, fig):
if pdf_output:
pdf.savefig(fig)
"""
library(survival)
ti1 = c(3, 1, 2, 3, 2, 1, 5, 3)
st1 = c(0, 1, 1, 1, 0, 0, 1, 0)
ti2 = c(1, 1, 2, 3, 7, 1, 5, 3, 9)
st2 = c(0, 1, 0, 0, 1, 0, 1, 0, 1)
ti = c(ti1, ti2)
st = c(st1, st2)
ix = c(rep(1, length(ti1)), rep(2, length(ti2)))
sd = survdiff(Surv(ti, st) ~ ix)
"""
ti1 = np.r_[3, 1, 2, 3, 2, 1, 5, 3]
st1 = np.r_[0, 1, 1, 1, 0, 0, 1, 0]
times1 = np.r_[1, 2, 3, 5]
surv_prob1 = np.r_[0.8750000, 0.7291667, 0.5468750, 0.0000000]
surv_prob_se1 = np.r_[0.1169268, 0.1649762, 0.2005800, np.nan]
n_risk1 = np.r_[8, 6, 4, 1]
n_events1 = np.r_[1., 1., 1., 1.]
ti2 = np.r_[1, 1, 2, 3, 7, 1, 5, 3, 9]
st2 = np.r_[0, 1, 0, 0, 1, 0, 1, 0, 1]
times2 = np.r_[1, 5, 7, 9]
surv_prob2 = np.r_[0.8888889, 0.5925926, 0.2962963, 0.0000000]
surv_prob_se2 = np.r_[0.1047566, 0.2518034, 0.2444320, np.nan]
n_risk2 = np.r_[9, 3, 2, 1]
n_events2 = np.r_[1., 1., 1., 1.]
cur_dir = os.path.dirname(os.path.abspath(__file__))
fp = os.path.join(cur_dir, 'results', 'bmt.csv')
bmt = pd.read_csv(fp)
def test_survfunc1():
# Test where all times have at least 1 event.
sr = SurvfuncRight(ti1, st1)
assert_allclose(sr.surv_prob, surv_prob1, atol=1e-5, rtol=1e-5)
assert_allclose(sr.surv_prob_se, surv_prob_se1, atol=1e-5, rtol=1e-5)
assert_allclose(sr.surv_times, times1)
assert_allclose(sr.n_risk, n_risk1)
assert_allclose(sr.n_events, n_events1)
def test_survfunc2():
# Test where some times have no events.
sr = SurvfuncRight(ti2, st2)
assert_allclose(sr.surv_prob, surv_prob2, atol=1e-5, rtol=1e-5)
assert_allclose(sr.surv_prob_se, surv_prob_se2, atol=1e-5, rtol=1e-5)
assert_allclose(sr.surv_times, times2)
assert_allclose(sr.n_risk, n_risk2)
assert_allclose(sr.n_events, n_events2)
def test_survdiff_basic():
# Constants taken from R, code above
ti = np.concatenate((ti1, ti2))
st = np.concatenate((st1, st2))
groups = np.ones(len(ti))
groups[0:len(ti1)] = 0
z, p = survdiff(ti, st, groups)
assert_allclose(z, 2.14673, atol=1e-4, rtol=1e-4)
assert_allclose(p, 0.14287, atol=1e-4, rtol=1e-4)
def test_simultaneous_cb():
# The exact numbers here are regression tests, but they are close
# to page 103 of Klein and Moeschberger.
df = bmt.loc[bmt["Group"] == "ALL", :]
sf = SurvfuncRight(df["T"], df["Status"])
lcb1, ucb1 = sf.simultaneous_cb(transform="log")
lcb2, ucb2 = sf.simultaneous_cb(transform="arcsin")
ti = sf.surv_times.tolist()
ix = [ti.index(x) for x in (110, 122, 129, 172)]
assert_allclose(lcb1[ix], np.r_[0.43590582, 0.42115592,
0.4035897, 0.38785927])
assert_allclose(ucb1[ix], np.r_[0.93491636, 0.89776803,
0.87922239, 0.85894181])
assert_allclose(lcb2[ix], np.r_[0.52115708, 0.48079378,
0.45595321, 0.43341115])
assert_allclose(ucb2[ix], np.r_[0.96465636, 0.92745068,
0.90885428, 0.88796708])
def test_bmt():
# All tests against SAS
# Results taken from here:
# http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_lifetest_details03.htm
# Confidence intervals for 25% percentile of the survival
# distribution (for "ALL" subjects), taken from the SAS web site
cb = {"linear": [107, 276],
"cloglog": [86, 230],
"log": [107, 332],
"asinsqrt": [104, 276],
"logit": [104, 230]}
dfa = bmt[bmt.Group == "ALL"]
cur_dir = os.path.dirname(os.path.abspath(__file__))
fp = os.path.join(cur_dir, 'results', 'bmt_results.csv')
rslt = pd.read_csv(fp)
sf = SurvfuncRight(dfa["T"].values, dfa.Status.values)
assert_allclose(sf.surv_times, rslt.t)
assert_allclose(sf.surv_prob, rslt.s, atol=1e-4, rtol=1e-4)
assert_allclose(sf.surv_prob_se, rslt.se, atol=1e-4, rtol=1e-4)
for method in "linear", "cloglog", "log", "logit", "asinsqrt":
lcb, ucb = sf.quantile_ci(0.25, method=method)
assert_allclose(cb[method], np.r_[lcb, ucb])
def test_survdiff():
# Results come from R survival and survMisc packages (survMisc is
# used for non G-rho family tests but does not seem to support
# stratification)
full_df = bmt.copy()
df = bmt[bmt.Group != "ALL"].copy()
# Not stratified
stat, p = survdiff(df["T"], df.Status, df.Group)
assert_allclose(stat, 13.44556, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="gb")
assert_allclose(stat, 15.38787, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="tw")
assert_allclose(stat, 14.98382, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="fh",
fh_p=0.5)
assert_allclose(stat, 14.46866, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, weight_type="fh",
fh_p=1)
assert_allclose(stat, 14.84500, atol=1e-4, rtol=1e-4)
# Not stratified, >2 groups
stat, p = survdiff(full_df["T"], full_df.Status, full_df.Group,
weight_type="fh", fh_p=1)
assert_allclose(stat, 15.67247, atol=1e-4, rtol=1e-4)
# 5 strata
strata = np.arange(df.shape[0]) % 5
df["strata"] = strata
stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata)
assert_allclose(stat, 11.97799, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata,
weight_type="fh", fh_p=0.5)
assert_allclose(stat, 12.6257, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata,
weight_type="fh", fh_p=1)
assert_allclose(stat, 12.73565, atol=1e-4, rtol=1e-4)
# 5 strata, >2 groups
full_strata = np.arange(full_df.shape[0]) % 5
full_df["strata"] = full_strata
stat, p = survdiff(full_df["T"], full_df.Status, full_df.Group,
strata=full_df.strata, weight_type="fh", fh_p=0.5)
assert_allclose(stat, 13.56793, atol=1e-4, rtol=1e-4)
# 8 strata
df["strata"] = np.arange(df.shape[0]) % 8
stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata)
assert_allclose(stat, 12.12631, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata,
weight_type="fh", fh_p=0.5)
assert_allclose(stat, 12.9633, atol=1e-4, rtol=1e-4)
stat, p = survdiff(df["T"], df.Status, df.Group, strata=df.strata,
weight_type="fh", fh_p=1)
assert_allclose(stat, 13.35259, atol=1e-4, rtol=1e-4)
@pytest.mark.matplotlib
def test_plot_km(close_figures):
if pdf_output:
from matplotlib.backends.backend_pdf import PdfPages
pdf = PdfPages("test_survfunc.pdf")
else:
pdf = None
sr1 = SurvfuncRight(ti1, st1)
sr2 = SurvfuncRight(ti2, st2)
fig = plot_survfunc(sr1)
close_or_save(pdf, fig)
fig = plot_survfunc(sr2)
close_or_save(pdf, fig)
fig = plot_survfunc([sr1, sr2])
close_or_save(pdf, fig)
# Plot the SAS BMT data
gb = bmt.groupby("Group")
sv = []
for g in gb:
s0 = SurvfuncRight(g[1]["T"], g[1]["Status"], title=g[0])
sv.append(s0)
fig = plot_survfunc(sv)
ax = fig.get_axes()[0]
ax.set_position([0.1, 0.1, 0.64, 0.8])
ha, lb = ax.get_legend_handles_labels()
fig.legend([ha[k] for k in (0, 2, 4)],
[lb[k] for k in (0, 2, 4)],
loc='center right')
close_or_save(pdf, fig)
# Simultaneous CB for BMT data
ii = bmt.Group == "ALL"
sf = SurvfuncRight(bmt.loc[ii, "T"], bmt.loc[ii, "Status"])
fig = sf.plot()
ax = fig.get_axes()[0]
ax.set_position([0.1, 0.1, 0.64, 0.8])
ha, lb = ax.get_legend_handles_labels()
lcb, ucb = sf.simultaneous_cb(transform="log")
plt.fill_between(sf.surv_times, lcb, ucb, color="lightgrey")
lcb, ucb = sf.simultaneous_cb(transform="arcsin")
plt.plot(sf.surv_times, lcb, color="darkgrey")
plt.plot(sf.surv_times, ucb, color="darkgrey")
plt.plot(sf.surv_times, sf.surv_prob - 2*sf.surv_prob_se, color="red")
plt.plot(sf.surv_times, sf.surv_prob + 2*sf.surv_prob_se, color="red")
plt.xlim(100, 600)
close_or_save(pdf, fig)
if pdf_output:
pdf.close()
def test_weights1():
# tm = c(1, 3, 5, 6, 7, 8, 8, 9, 3, 4, 1, 3, 2)
# st = c(1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0)
# wt = c(1, 2, 3, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1)
# library(survival)
# sf = survfit(Surv(tm, st) ~ 1, weights=wt, err='tsiatis')
tm = np.r_[1, 3, 5, 6, 7, 8, 8, 9, 3, 4, 1, 3, 2]
st = np.r_[1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]
wt = np.r_[1, 2, 3, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1]
sf = SurvfuncRight(tm, st, freq_weights=wt)
assert_allclose(sf.surv_times, np.r_[1, 3, 6, 7, 9])
assert_allclose(sf.surv_prob,
np.r_[0.875, 0.65625, 0.51041667, 0.29166667, 0.])
assert_allclose(sf.surv_prob_se,
np.r_[0.07216878, 0.13307266, 0.20591185, 0.3219071,
1.05053519])
def test_weights2():
# tm = c(1, 3, 5, 6, 7, 2, 4, 6, 8, 10)
# st = c(1, 1, 0, 1, 1, 1, 1, 0, 1, 1)
# wt = c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2)
# library(survival)
# sf =s urvfit(Surv(tm, st) ~ 1, weights=wt, err='tsiatis')
tm = np.r_[1, 3, 5, 6, 7, 2, 4, 6, 8, 10]
st = np.r_[1, 1, 0, 1, 1, 1, 1, 0, 1, 1]
wt = np.r_[1, 1, 1, 1, 1, 2, 2, 2, 2, 2]
tm0 = np.r_[1, 3, 5, 6, 7, 2, 4, 6, 8, 10, 2, 4, 6, 8, 10]
st0 = np.r_[1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]
sf0 = SurvfuncRight(tm, st, freq_weights=wt)
sf1 = SurvfuncRight(tm0, st0)
assert_allclose(sf0.surv_times, sf1.surv_times)
assert_allclose(sf0.surv_prob, sf1.surv_prob)
assert_allclose(sf0.surv_prob_se,
np.r_[0.06666667, 0.1210311, 0.14694547,
0.19524829, 0.23183377,
0.30618115, 0.46770386, 0.84778942])
def test_incidence():
# Check estimates in R:
# ftime = c(1, 1, 2, 4, 4, 4, 6, 6, 7, 8, 9, 9, 9, 1, 2, 2, 4, 4)
# fstat = c(1, 1, 1, 2, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0)
# cuminc(ftime, fstat)
#
# The standard errors agree with Stata, not with R (cmprisk
# package), which uses a different SE formula from Aalen (1978)
#
# To check with Stata:
# stset ftime failure(fstat==1)
# stcompet ci=ci, compet1(2)
ftime = np.r_[1, 1, 2, 4, 4, 4, 6, 6, 7, 8, 9, 9, 9, 1, 2, 2, 4, 4]
fstat = np.r_[1, 1, 1, 2, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ci = CumIncidenceRight(ftime, fstat)
cinc = [np.array([0.11111111, 0.17037037, 0.17037037, 0.17037037,
0.17037037, 0.17037037, 0.17037037]),
np.array([0., 0., 0.20740741, 0.20740741,
0.20740741, 0.20740741, 0.20740741]),
np.array([0., 0., 0., 0.17777778,
0.26666667, 0.26666667, 0.26666667])]
assert_allclose(cinc[0], ci.cinc[0])
assert_allclose(cinc[1], ci.cinc[1])
assert_allclose(cinc[2], ci.cinc[2])
cinc_se = [np.array([0.07407407, 0.08976251, 0.08976251, 0.08976251,
0.08976251, 0.08976251, 0.08976251]),
np.array([0., 0., 0.10610391, 0.10610391, 0.10610391,
0.10610391, 0.10610391]),
np.array([0., 0., 0., 0.11196147, 0.12787781,
0.12787781, 0.12787781])]
assert_allclose(cinc_se[0], ci.cinc_se[0])
assert_allclose(cinc_se[1], ci.cinc_se[1])
assert_allclose(cinc_se[2], ci.cinc_se[2])
# Simple check for frequency weights
weights = np.ones(len(ftime))
ciw = CumIncidenceRight(ftime, fstat, freq_weights=weights)
assert_allclose(ci.cinc[0], ciw.cinc[0])
assert_allclose(ci.cinc[1], ciw.cinc[1])
assert_allclose(ci.cinc[2], ciw.cinc[2])
def test_survfunc_entry_1():
# times = c(1, 3, 3, 5, 5, 7, 7, 8, 8, 9, 10, 10)
# status = c(1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1)
# entry = c(0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 0)
# sv = Surv(entry, times, event=status)
# sdf = survfit(coxph(sv ~ 1), type='kaplan-meier')
times = np.r_[1, 3, 3, 5, 5, 7, 7, 8, 8, 9, 10, 10]
status = np.r_[1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]
entry = np.r_[0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 0]
sf = SurvfuncRight(times, status, entry=entry)
assert_allclose(sf.n_risk, np.r_[2, 6, 9, 7, 5, 3, 2])
assert_allclose(sf.surv_times, np.r_[1, 3, 5, 7, 8, 9, 10])
assert_allclose(sf.surv_prob, np.r_[
0.5000, 0.4167, 0.3241, 0.2778, 0.2222, 0.1481, 0.0741],
atol=1e-4)
assert_allclose(sf.surv_prob_se, np.r_[
0.3536, 0.3043, 0.2436, 0.2132, 0.1776, 0.1330, 0.0846],
atol=1e-4)
def test_survfunc_entry_2():
# entry = 0 is equivalent to no entry time
times = np.r_[1, 3, 3, 5, 5, 7, 7, 8, 8, 9, 10, 10]
status = np.r_[1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1]
entry = np.r_[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
sf = SurvfuncRight(times, status, entry=entry)
sf0 = SurvfuncRight(times, status)
assert_allclose(sf.n_risk, sf0.n_risk)
assert_allclose(sf.surv_times, sf0.surv_times)
assert_allclose(sf.surv_prob, sf0.surv_prob)
assert_allclose(sf.surv_prob_se, sf0.surv_prob_se)
def test_survfunc_entry_3():
# times = c(1, 2, 5, 6, 6, 6, 6, 6, 9)
# status = c(0, 0, 1, 1, 1, 0, 1, 1, 0)
# entry = c(0, 1, 1, 2, 2, 2, 3, 4, 4)
# sv = Surv(entry, times, event=status)
# sdf = survfit(coxph(sv ~ 1), type='kaplan-meier')
times = np.r_[1, 2, 5, 6, 6, 6, 6, 6, 9]
status = np.r_[0, 0, 1, 1, 1, 0, 1, 1, 0]
entry = np.r_[0, 1, 1, 2, 2, 2, 3, 4, 4]
sf = SurvfuncRight(times, status, entry=entry)
assert_allclose(sf.n_risk, np.r_[7, 6])
assert_allclose(sf.surv_times, np.r_[5, 6])
assert_allclose(sf.surv_prob, np.r_[0.857143, 0.285714], atol=1e-5)
assert_allclose(sf.surv_prob_se, np.r_[0.13226, 0.170747], atol=1e-5)
def test_survdiff_entry_1():
# entry times = 0 is equivalent to no entry times
ti = np.r_[1, 3, 4, 2, 5, 4, 6, 7, 5, 9]
st = np.r_[1, 1, 0, 1, 1, 0, 1, 1, 0, 0]
gr = np.r_[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
entry = np.r_[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
z1, p1 = survdiff(ti, st, gr, entry=entry)
z2, p2 = survdiff(ti, st, gr)
assert_allclose(z1, z2)
assert_allclose(p1, p2)
def test_survdiff_entry_2():
# Tests against Stata:
#
# stset time, failure(status) entry(entry)
# sts test group, logrank
ti = np.r_[5, 3, 4, 2, 5, 4, 6, 7, 5, 9]
st = np.r_[1, 1, 0, 1, 1, 0, 1, 1, 0, 0]
gr = np.r_[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
entry = np.r_[1, 2, 2, 1, 3, 3, 5, 4, 2, 5]
# Check with no entry times
z, p = survdiff(ti, st, gr)
assert_allclose(z, 6.694424)
assert_allclose(p, 0.00967149)
# Check with entry times
z, p = survdiff(ti, st, gr, entry=entry)
assert_allclose(z, 3.0)
assert_allclose(p, 0.083264516)
def test_survdiff_entry_3():
# Tests against Stata:
#
# stset time, failure(status) entry(entry)
# sts test group, logrank
ti = np.r_[2, 1, 5, 8, 7, 8, 8, 9, 4, 9]
st = np.r_[1, 1, 1, 1, 1, 0, 1, 0, 0, 0]
gr = np.r_[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
entry = np.r_[1, 1, 2, 2, 3, 3, 2, 1, 2, 0]
# Check with no entry times
z, p = survdiff(ti, st, gr)
assert_allclose(z, 6.9543024)
assert_allclose(p, 0.008361789)
# Check with entry times
z, p = survdiff(ti, st, gr, entry=entry)
assert_allclose(z, 6.75082959)
assert_allclose(p, 0.00937041)
def test_incidence2():
# Check that the cumulative incidence functions for all competing
# risks sum to the complementary survival function.
np.random.seed(2423)
n = 200
time = -np.log(np.random.uniform(size=n))
status = np.random.randint(0, 3, size=n)
ii = np.argsort(time)
time = time[ii]
status = status[ii]
ci = CumIncidenceRight(time, status)
statusa = 1*(status >= 1)
sf = SurvfuncRight(time, statusa)
x = 1 - sf.surv_prob
y = (ci.cinc[0] + ci.cinc[1])[np.flatnonzero(statusa)]
assert_allclose(x, y)
def test_kernel_survfunc1():
# Regression test
n = 100
np.random.seed(3434)
x = np.random.normal(size=(n, 3))
time = np.random.uniform(size=n)
status = np.random.randint(0, 2, size=n)
result = SurvfuncRight(time, status, exog=x)
timex = np.r_[0.30721103, 0.0515439, 0.69246897, 0.16446079, 0.31308528]
sprob = np.r_[0.98948277, 0.98162275, 0.97129237, 0.96044668, 0.95030368]
assert_allclose(result.time[0:5], timex)
assert_allclose(result.surv_prob[0:5], sprob)
def test_kernel_survfunc2():
# Check that when bandwidth is very large, the kernel procedure
# agrees with standard KM. (Note: the results do not agree
# perfectly when there are tied times).
n = 100
np.random.seed(3434)
x = np.random.normal(size=(n, 3))
time = np.random.uniform(0, 10, size=n)
status = np.random.randint(0, 2, size=n)
resultkm = SurvfuncRight(time, status)
result = SurvfuncRight(time, status, exog=x, bw_factor=10000)
assert_allclose(resultkm.surv_times, result.surv_times)
assert_allclose(resultkm.surv_prob, result.surv_prob, rtol=1e-6, atol=1e-6)
@pytest.mark.smoke
def test_kernel_survfunc3():
# cases with tied times
n = 100
np.random.seed(3434)
x = np.random.normal(size=(n, 3))
time = np.random.randint(0, 10, size=n)
status = np.random.randint(0, 2, size=n)
SurvfuncRight(time, status, exog=x, bw_factor=10000)
SurvfuncRight(time, status, exog=x, bw_factor=np.r_[10000, 10000])
def test_kernel_cumincidence1():
# Check that when the bandwidth is very large, the kernel
# procedure agrees with standard cumulative incidence
# calculations. (Note: the results do not agree perfectly when
# there are tied times).
n = 100
np.random.seed(3434)
x = np.random.normal(size=(n, 3))
time = np.random.uniform(0, 10, size=n)
status = np.random.randint(0, 3, size=n)
result1 = CumIncidenceRight(time, status)
for dimred in False, True:
result2 = CumIncidenceRight(time, status, exog=x, bw_factor=10000,
dimred=dimred)
assert_allclose(result1.times, result2.times)
for k in 0, 1:
assert_allclose(result1.cinc[k], result2.cinc[k], rtol=1e-5)
@pytest.mark.smoke
def test_kernel_cumincidence2():
# cases with tied times
n = 100
np.random.seed(3434)
x = np.random.normal(size=(n, 3))
time = np.random.randint(0, 10, size=n)
status = np.random.randint(0, 3, size=n)
CumIncidenceRight(time, status, exog=x, bw_factor=10000)