from statsmodels.compat.testing import skipif

import numpy as np
from statsmodels.duration.survfunc import (
    SurvfuncRight, survdiff, plot_survfunc,
    CumIncidenceRight)
from numpy.testing import assert_allclose
from numpy.testing import dec
import pandas as pd
import os

# If true, the output is written to a multi-page pdf file.
pdf_output = False

try:
    import matplotlib.pyplot as plt
    have_matplotlib = True
except ImportError:
    have_matplotlib = False


def close_or_save(pdf, fig):
    if pdf_output:
        pdf.savefig(fig)
    else:
        plt.close(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)

    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)

    # 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)

    # 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)


@skipif(not have_matplotlib, reason='requires matplotlib')
def test_plot_km():

    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)],
               '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)


def test_kernel_survfunc3():
    # Smoke test for 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)


def test_kernel_cumincidence2():
    # Smoke tests for 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)
