Methods for Survival and Duration Analysis

statsmodels.duration implements several standard methods for working with censored data. These methods are most commonly used when the data consist of durations between an origin time point and the time at which some event of interest occurred. A typical example is a medical study in which the origin is the time at which a subject is diagnosed with some condition, and the event of interest is death (or disease progression, recovery, etc.).

Currently only right-censoring is handled. Right censoring occurs when we know that an event occurred after a given time t, but we do not know the exact event time.

Survival function estimation and inference

The statsmodels.api.SurvfuncRight class can be used to estimate a survival function using data that may be right censored. SurvfuncRight implements several inference procedures including confidence intervals for survival distribution quantiles, pointwise and simultaneous confidence bands for the survival function, and plotting procedures. The duration.survdiff function provides testing procedures for comparing survival distributions.

Here we create a SurvfuncRight object using data from the flchain study, which is available through the R datasets repository. We fit the survival distribution only for the female subjects.

In [1]: import statsmodels.api as sm

In [2]: data = sm.datasets.get_rdataset("flchain", "survival", cache=True).data
---------------------------------------------------------------------------
ConnectionRefusedError                    Traceback (most recent call last)
File /usr/lib/python3.12/urllib/request.py:1344, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
   1343 try:
-> 1344     h.request(req.get_method(), req.selector, req.data, headers,
   1345               encode_chunked=req.has_header('Transfer-encoding'))
   1346 except OSError as err: # timeout error

File /usr/lib/python3.12/http/client.py:1336, in HTTPConnection.request(self, method, url, body, headers, encode_chunked)
   1335 """Send a complete request to the server."""
-> 1336 self._send_request(method, url, body, headers, encode_chunked)

File /usr/lib/python3.12/http/client.py:1382, in HTTPConnection._send_request(self, method, url, body, headers, encode_chunked)
   1381     body = _encode(body, 'body')
-> 1382 self.endheaders(body, encode_chunked=encode_chunked)

File /usr/lib/python3.12/http/client.py:1331, in HTTPConnection.endheaders(self, message_body, encode_chunked)
   1330     raise CannotSendHeader()
-> 1331 self._send_output(message_body, encode_chunked=encode_chunked)

File /usr/lib/python3.12/http/client.py:1091, in HTTPConnection._send_output(self, message_body, encode_chunked)
   1090 del self._buffer[:]
-> 1091 self.send(msg)
   1093 if message_body is not None:
   1094 
   1095     # create a consistent interface to message_body

File /usr/lib/python3.12/http/client.py:1035, in HTTPConnection.send(self, data)
   1034 if self.auto_open:
-> 1035     self.connect()
   1036 else:

File /usr/lib/python3.12/http/client.py:1470, in HTTPSConnection.connect(self)
   1468 "Connect to a host on a given (SSL) port."
-> 1470 super().connect()
   1472 if self._tunnel_host:

File /usr/lib/python3.12/http/client.py:1001, in HTTPConnection.connect(self)
   1000 sys.audit("http.client.connect", self, self.host, self.port)
-> 1001 self.sock = self._create_connection(
   1002     (self.host,self.port), self.timeout, self.source_address)
   1003 # Might fail in OSs that don't implement TCP_NODELAY

File /usr/lib/python3.12/socket.py:852, in create_connection(address, timeout, source_address, all_errors)
    851 if not all_errors:
--> 852     raise exceptions[0]
    853 raise ExceptionGroup("create_connection failed", exceptions)

File /usr/lib/python3.12/socket.py:837, in create_connection(address, timeout, source_address, all_errors)
    836     sock.bind(source_address)
--> 837 sock.connect(sa)
    838 # Break explicitly a reference cycle

ConnectionRefusedError: [Errno 111] Connection refused

During handling of the above exception, another exception occurred:

URLError                                  Traceback (most recent call last)
Cell In[2], line 1
----> 1 data = sm.datasets.get_rdataset("flchain", "survival", cache=True).data

File /usr/lib/python3/dist-packages/statsmodels/datasets/utils.py:237, in get_rdataset(dataname, package, cache)
    234 docs_base_url = ("https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/"
    235                  "master/doc/"+package+"/rst/")
    236 cache = _get_cache(cache)
--> 237 data, from_cache = _get_data(data_base_url, dataname, cache)
    238 data = read_csv(data, index_col=0)
    239 data = _maybe_reset_index(data)

File /usr/lib/python3/dist-packages/statsmodels/datasets/utils.py:166, in _get_data(base_url, dataname, cache, extension)
    164 url = base_url + (dataname + ".%s") % extension
    165 try:
--> 166     data, from_cache = _urlopen_cached(url, cache)
    167 except HTTPError as err:
    168     if '404' in str(err):

File /usr/lib/python3/dist-packages/statsmodels/datasets/utils.py:157, in _urlopen_cached(url, cache)
    155 # not using the cache or did not find it in cache
    156 if not from_cache:
--> 157     data = urlopen(url, timeout=3).read()
    158     if cache is not None:  # then put it in the cache
    159         _cache_it(data, cache_path)

File /usr/lib/python3.12/urllib/request.py:215, in urlopen(url, data, timeout, cafile, capath, cadefault, context)
    213 else:
    214     opener = _opener
--> 215 return opener.open(url, data, timeout)

File /usr/lib/python3.12/urllib/request.py:515, in OpenerDirector.open(self, fullurl, data, timeout)
    512     req = meth(req)
    514 sys.audit('urllib.Request', req.full_url, req.data, req.headers, req.get_method())
--> 515 response = self._open(req, data)
    517 # post-process response
    518 meth_name = protocol+"_response"

File /usr/lib/python3.12/urllib/request.py:532, in OpenerDirector._open(self, req, data)
    529     return result
    531 protocol = req.type
--> 532 result = self._call_chain(self.handle_open, protocol, protocol +
    533                           '_open', req)
    534 if result:
    535     return result

File /usr/lib/python3.12/urllib/request.py:492, in OpenerDirector._call_chain(self, chain, kind, meth_name, *args)
    490 for handler in handlers:
    491     func = getattr(handler, meth_name)
--> 492     result = func(*args)
    493     if result is not None:
    494         return result

File /usr/lib/python3.12/urllib/request.py:1392, in HTTPSHandler.https_open(self, req)
   1391 def https_open(self, req):
-> 1392     return self.do_open(http.client.HTTPSConnection, req,
   1393                         context=self._context)

File /usr/lib/python3.12/urllib/request.py:1347, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
   1344         h.request(req.get_method(), req.selector, req.data, headers,
   1345                   encode_chunked=req.has_header('Transfer-encoding'))
   1346     except OSError as err: # timeout error
-> 1347         raise URLError(err)
   1348     r = h.getresponse()
   1349 except:

URLError: <urlopen error [Errno 111] Connection refused>

In [3]: df = data.loc[data.sex == "F", :]
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[3], line 1
----> 1 df = data.loc[data.sex == "F", :]

AttributeError: 'Dataset' object has no attribute 'loc'

In [4]: sf = sm.SurvfuncRight(df["futime"], df["death"])
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
File /usr/lib/python3/dist-packages/pandas/core/indexes/base.py:3791, in Index.get_loc(self, key)
   3790 try:
-> 3791     return self._engine.get_loc(casted_key)
   3792 except KeyError as err:

File /usr/lib/python3/dist-packages/pandas/_libs/index.pyx:152, in pandas._libs.index.IndexEngine.get_loc()

File /usr/lib/python3/dist-packages/pandas/_libs/index.pyx:181, in pandas._libs.index.IndexEngine.get_loc()

File pandas/_libs/hashtable_class_helper.pxi:7080, in pandas._libs.hashtable.PyObjectHashTable.get_item()

File pandas/_libs/hashtable_class_helper.pxi:7088, in pandas._libs.hashtable.PyObjectHashTable.get_item()

KeyError: 'futime'

The above exception was the direct cause of the following exception:

KeyError                                  Traceback (most recent call last)
Cell In[4], line 1
----> 1 sf = sm.SurvfuncRight(df["futime"], df["death"])

File /usr/lib/python3/dist-packages/pandas/core/frame.py:3893, in DataFrame.__getitem__(self, key)
   3891 if self.columns.nlevels > 1:
   3892     return self._getitem_multilevel(key)
-> 3893 indexer = self.columns.get_loc(key)
   3894 if is_integer(indexer):
   3895     indexer = [indexer]

File /usr/lib/python3/dist-packages/pandas/core/indexes/base.py:3798, in Index.get_loc(self, key)
   3793     if isinstance(casted_key, slice) or (
   3794         isinstance(casted_key, abc.Iterable)
   3795         and any(isinstance(x, slice) for x in casted_key)
   3796     ):
   3797         raise InvalidIndexError(key)
-> 3798     raise KeyError(key) from err
   3799 except TypeError:
   3800     # If we have a listlike key, _check_indexing_error will raise
   3801     #  InvalidIndexError. Otherwise we fall through and re-raise
   3802     #  the TypeError.
   3803     self._check_indexing_error(key)

KeyError: 'futime'

The main features of the fitted survival distribution can be seen by calling the summary method:

In [5]: sf.summary().head()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[5], line 1
----> 1 sf.summary().head()

NameError: name 'sf' is not defined

We can obtain point estimates and confidence intervals for quantiles of the survival distribution. Since only around 30% of the subjects died during this study, we can only estimate quantiles below the 0.3 probability point:

In [6]: sf.quantile(0.25)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[6], line 1
----> 1 sf.quantile(0.25)

NameError: name 'sf' is not defined

In [7]: sf.quantile_ci(0.25)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[7], line 1
----> 1 sf.quantile_ci(0.25)

NameError: name 'sf' is not defined

To plot a single survival function, call the plot method:

In [8]: sf.plot()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[8], line 1
----> 1 sf.plot()

NameError: name 'sf' is not defined
savefig/duration_survival_plot1.png

Since this is a large dataset with a lot of censoring, we may wish to not plot the censoring symbols:

In [9]: fig = sf.plot()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[9], line 1
----> 1 fig = sf.plot()

NameError: name 'sf' is not defined

In [10]: ax = fig.get_axes()[0]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[10], line 1
----> 1 ax = fig.get_axes()[0]

IndexError: list index out of range

In [11]: pt = ax.get_lines()[1]
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[11], line 1
----> 1 pt = ax.get_lines()[1]

NameError: name 'ax' is not defined

In [12]: pt.set_visible(False)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[12], line 1
----> 1 pt.set_visible(False)

NameError: name 'pt' is not defined
savefig/duration_survival_nocensor_plot.png

We can also add a 95% simultaneous confidence band to the plot. Typically these bands only plotted for central part of the distribution.

In [13]: fig = sf.plot()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[13], line 1
----> 1 fig = sf.plot()

NameError: name 'sf' is not defined

In [14]: lcb, ucb = sf.simultaneous_cb()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[14], line 1
----> 1 lcb, ucb = sf.simultaneous_cb()

NameError: name 'sf' is not defined

In [15]: ax = fig.get_axes()[0]
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[15], line 1
----> 1 ax = fig.get_axes()[0]

IndexError: list index out of range

In [16]: ax.fill_between(sf.surv_times, lcb, ucb, color='lightgrey')
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[16], line 1
----> 1 ax.fill_between(sf.surv_times, lcb, ucb, color='lightgrey')

NameError: name 'ax' is not defined

In [17]: ax.set_xlim(365, 365*10)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[17], line 1
----> 1 ax.set_xlim(365, 365*10)

NameError: name 'ax' is not defined

In [18]: ax.set_ylim(0.7, 1)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[18], line 1
----> 1 ax.set_ylim(0.7, 1)

NameError: name 'ax' is not defined

In [19]: ax.set_ylabel("Proportion alive")
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[19], line 1
----> 1 ax.set_ylabel("Proportion alive")

NameError: name 'ax' is not defined

In [20]: ax.set_xlabel("Days since enrollment")
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[20], line 1
----> 1 ax.set_xlabel("Days since enrollment")

NameError: name 'ax' is not defined
savefig/duration_survival_95ci_plot.png

Here we plot survival functions for two groups (females and males) on the same axes:

In [21]: import matplotlib.pyplot as plt

In [22]: gb = data.groupby("sex")
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[22], line 1
----> 1 gb = data.groupby("sex")

AttributeError: 'Dataset' object has no attribute 'groupby'

In [23]: ax = plt.axes()

In [24]: sexes = []

In [25]: for g in gb:
   ....:     sexes.append(g[0])
   ....:     sf = sm.SurvfuncRight(g[1]["futime"], g[1]["death"])
   ....:     sf.plot(ax)
   ....: 
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[25], line 1
----> 1 for g in gb:
      2     sexes.append(g[0])
      3     sf = sm.SurvfuncRight(g[1]["futime"], g[1]["death"])

NameError: name 'gb' is not defined

In [26]: li = ax.get_lines()

In [27]: li[1].set_visible(False)
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[27], line 1
----> 1 li[1].set_visible(False)

IndexError: list index out of range

In [28]: li[3].set_visible(False)
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[28], line 1
----> 1 li[3].set_visible(False)

IndexError: list index out of range

In [29]: plt.figlegend((li[0], li[2]), sexes, loc="center right")
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
Cell In[29], line 1
----> 1 plt.figlegend((li[0], li[2]), sexes, loc="center right")

IndexError: list index out of range

In [30]: plt.ylim(0.6, 1)
Out[30]: (0.6, 1.0)

In [31]: ax.set_ylabel("Proportion alive")
Out[31]: Text(0, 0.5, 'Proportion alive')

In [32]: ax.set_xlabel("Days since enrollment")
Out[32]: Text(0.5, 0, 'Days since enrollment')
savefig/duration_survival_bysex_plot.png

We can formally compare two survival distributions with survdiff, which implements several standard nonparametric procedures. The default procedure is the logrank test:

In [33]: stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[33], line 1
----> 1 stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex)

AttributeError: 'Dataset' object has no attribute 'futime'

Here are some of the other testing procedures implemented by survdiff:

 # Fleming-Harrington with p=1, i.e. weight by pooled survival time
In [34]: stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='fh', fh_p=1)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[34], line 1
----> 1 stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='fh', fh_p=1)

AttributeError: 'Dataset' object has no attribute 'futime'

 # Gehan-Breslow, weight by number at risk
In [35]: stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='gb')
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[35], line 1
----> 1 stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='gb')

AttributeError: 'Dataset' object has no attribute 'futime'

 # Tarone-Ware, weight by the square root of the number at risk
In [36]: stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='tw')
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[36], line 1
----> 1 stat, pv = sm.duration.survdiff(data.futime, data.death, data.sex, weight_type='tw')

AttributeError: 'Dataset' object has no attribute 'futime'

Regression methods

Proportional hazard regression models (“Cox models”) are a regression technique for censored data. They allow variation in the time to an event to be explained in terms of covariates, similar to what is done in a linear or generalized linear regression model. These models express the covariate effects in terms of “hazard ratios”, meaning the the hazard (instantaneous event rate) is multiplied by a given factor depending on the value of the covariates.

In [37]: import statsmodels.api as sm

In [38]: import statsmodels.formula.api as smf

In [39]: data = sm.datasets.get_rdataset("flchain", "survival", cache=True).data
---------------------------------------------------------------------------
ConnectionRefusedError                    Traceback (most recent call last)
File /usr/lib/python3.12/urllib/request.py:1344, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
   1343 try:
-> 1344     h.request(req.get_method(), req.selector, req.data, headers,
   1345               encode_chunked=req.has_header('Transfer-encoding'))
   1346 except OSError as err: # timeout error

File /usr/lib/python3.12/http/client.py:1336, in HTTPConnection.request(self, method, url, body, headers, encode_chunked)
   1335 """Send a complete request to the server."""
-> 1336 self._send_request(method, url, body, headers, encode_chunked)

File /usr/lib/python3.12/http/client.py:1382, in HTTPConnection._send_request(self, method, url, body, headers, encode_chunked)
   1381     body = _encode(body, 'body')
-> 1382 self.endheaders(body, encode_chunked=encode_chunked)

File /usr/lib/python3.12/http/client.py:1331, in HTTPConnection.endheaders(self, message_body, encode_chunked)
   1330     raise CannotSendHeader()
-> 1331 self._send_output(message_body, encode_chunked=encode_chunked)

File /usr/lib/python3.12/http/client.py:1091, in HTTPConnection._send_output(self, message_body, encode_chunked)
   1090 del self._buffer[:]
-> 1091 self.send(msg)
   1093 if message_body is not None:
   1094 
   1095     # create a consistent interface to message_body

File /usr/lib/python3.12/http/client.py:1035, in HTTPConnection.send(self, data)
   1034 if self.auto_open:
-> 1035     self.connect()
   1036 else:

File /usr/lib/python3.12/http/client.py:1470, in HTTPSConnection.connect(self)
   1468 "Connect to a host on a given (SSL) port."
-> 1470 super().connect()
   1472 if self._tunnel_host:

File /usr/lib/python3.12/http/client.py:1001, in HTTPConnection.connect(self)
   1000 sys.audit("http.client.connect", self, self.host, self.port)
-> 1001 self.sock = self._create_connection(
   1002     (self.host,self.port), self.timeout, self.source_address)
   1003 # Might fail in OSs that don't implement TCP_NODELAY

File /usr/lib/python3.12/socket.py:852, in create_connection(address, timeout, source_address, all_errors)
    851 if not all_errors:
--> 852     raise exceptions[0]
    853 raise ExceptionGroup("create_connection failed", exceptions)

File /usr/lib/python3.12/socket.py:837, in create_connection(address, timeout, source_address, all_errors)
    836     sock.bind(source_address)
--> 837 sock.connect(sa)
    838 # Break explicitly a reference cycle

ConnectionRefusedError: [Errno 111] Connection refused

During handling of the above exception, another exception occurred:

URLError                                  Traceback (most recent call last)
Cell In[39], line 1
----> 1 data = sm.datasets.get_rdataset("flchain", "survival", cache=True).data

File /usr/lib/python3/dist-packages/statsmodels/datasets/utils.py:237, in get_rdataset(dataname, package, cache)
    234 docs_base_url = ("https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/"
    235                  "master/doc/"+package+"/rst/")
    236 cache = _get_cache(cache)
--> 237 data, from_cache = _get_data(data_base_url, dataname, cache)
    238 data = read_csv(data, index_col=0)
    239 data = _maybe_reset_index(data)

File /usr/lib/python3/dist-packages/statsmodels/datasets/utils.py:166, in _get_data(base_url, dataname, cache, extension)
    164 url = base_url + (dataname + ".%s") % extension
    165 try:
--> 166     data, from_cache = _urlopen_cached(url, cache)
    167 except HTTPError as err:
    168     if '404' in str(err):

File /usr/lib/python3/dist-packages/statsmodels/datasets/utils.py:157, in _urlopen_cached(url, cache)
    155 # not using the cache or did not find it in cache
    156 if not from_cache:
--> 157     data = urlopen(url, timeout=3).read()
    158     if cache is not None:  # then put it in the cache
    159         _cache_it(data, cache_path)

File /usr/lib/python3.12/urllib/request.py:215, in urlopen(url, data, timeout, cafile, capath, cadefault, context)
    213 else:
    214     opener = _opener
--> 215 return opener.open(url, data, timeout)

File /usr/lib/python3.12/urllib/request.py:515, in OpenerDirector.open(self, fullurl, data, timeout)
    512     req = meth(req)
    514 sys.audit('urllib.Request', req.full_url, req.data, req.headers, req.get_method())
--> 515 response = self._open(req, data)
    517 # post-process response
    518 meth_name = protocol+"_response"

File /usr/lib/python3.12/urllib/request.py:532, in OpenerDirector._open(self, req, data)
    529     return result
    531 protocol = req.type
--> 532 result = self._call_chain(self.handle_open, protocol, protocol +
    533                           '_open', req)
    534 if result:
    535     return result

File /usr/lib/python3.12/urllib/request.py:492, in OpenerDirector._call_chain(self, chain, kind, meth_name, *args)
    490 for handler in handlers:
    491     func = getattr(handler, meth_name)
--> 492     result = func(*args)
    493     if result is not None:
    494         return result

File /usr/lib/python3.12/urllib/request.py:1392, in HTTPSHandler.https_open(self, req)
   1391 def https_open(self, req):
-> 1392     return self.do_open(http.client.HTTPSConnection, req,
   1393                         context=self._context)

File /usr/lib/python3.12/urllib/request.py:1347, in AbstractHTTPHandler.do_open(self, http_class, req, **http_conn_args)
   1344         h.request(req.get_method(), req.selector, req.data, headers,
   1345                   encode_chunked=req.has_header('Transfer-encoding'))
   1346     except OSError as err: # timeout error
-> 1347         raise URLError(err)
   1348     r = h.getresponse()
   1349 except:

URLError: <urlopen error [Errno 111] Connection refused>

In [40]: del data["chapter"]
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Cell In[40], line 1
----> 1 del data["chapter"]

KeyError: 'chapter'

In [41]: data = data.dropna()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[41], line 1
----> 1 data = data.dropna()

AttributeError: 'Dataset' object has no attribute 'dropna'

In [42]: data["lam"] = data["lambda"]
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Cell In[42], line 1
----> 1 data["lam"] = data["lambda"]

KeyError: 'lambda'

In [43]: data["female"] = (data["sex"] == "F").astype(int)
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Cell In[43], line 1
----> 1 data["female"] = (data["sex"] == "F").astype(int)

KeyError: 'sex'

In [44]: data["year"] = data["sample.yr"] - min(data["sample.yr"])
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Cell In[44], line 1
----> 1 data["year"] = data["sample.yr"] - min(data["sample.yr"])

KeyError: 'sample.yr'

In [45]: status = data["death"].values
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
Cell In[45], line 1
----> 1 status = data["death"].values

KeyError: 'death'

In [46]: mod = smf.phreg("futime ~ 0 + age + female + creatinine + np.sqrt(kappa) + np.sqrt(lam) + year + mgus", data, status=status, ties="efron")
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[46], line 1
----> 1 mod = smf.phreg("futime ~ 0 + age + female + creatinine + np.sqrt(kappa) + np.sqrt(lam) + year + mgus", data, status=status, ties="efron")

NameError: name 'status' is not defined

In [47]: rslt = mod.fit()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[47], line 1
----> 1 rslt = mod.fit()

NameError: name 'mod' is not defined

In [48]: print(rslt.summary())
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[48], line 1
----> 1 print(rslt.summary())

AttributeError: '_Bunch' object has no attribute 'summary'

See Examples for more detailed examples.

There are some notebook examples on the Wiki: Wiki notebooks for PHReg and Survival Analysis

References

References for Cox proportional hazards regression model:

T Therneau (1996). Extending the Cox model. Technical report.
http://www.mayo.edu/research/documents/biostat-58pdf/DOC-10027288

G Rodriguez (2005). Non-parametric estimation in survival models.
http://data.princeton.edu/pop509/NonParametricSurvival.pdf

B Gillespie (2006). Checking the assumptions in the Cox proportional
hazards model.
http://www.mwsug.org/proceedings/2006/stats/MWSUG-2006-SD08.pdf

Module Reference

The class for working with survival distributions is:

SurvfuncRight(time, status[, entry, title, ...])

Estimation and inference for a survival function.

The proportional hazards regression model class is:

PHReg(endog, exog[, status, entry, strata, ...])

Cox Proportional Hazards Regression Model

The proportional hazards regression result class is:

PHRegResults(model, params, cov_params[, ...])

Class to contain results of fitting a Cox proportional hazards survival model.

The primary helper class is:

rv_discrete_float(xk, pk)

A class representing a collection of discrete distributions.