<gh_stars>1-10
#Kaplan-Meier Estimator

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt
from scipy import stats
from statsmodels.iolib.table import SimpleTable

class KaplanMeier(object):

    """
    KaplanMeier(...)
        KaplanMeier(data, endog, exog=None, censoring=None)

        Create an object of class KaplanMeier for estimating
        Kaplan-Meier survival curves.

        Parameters
        ----------
        data: array_like
            An array, with observations in each row, and
            variables in the columns

        endog: index (starting at zero) of the column
            containing the endogenous variable (time)

        exog: index of the column containing the exogenous
            variable (must be catagorical). If exog = None, this
            is equivalent to a single survival curve

        censoring: index of the column containing an indicator
            of whether an observation is an event, or a censored
            observation, with 0 for censored, and 1 for an event

        Attributes
        -----------
        censorings: List of censorings associated with each unique
            time, at each value of exog

        events: List of the number of events at each unique time
            for each value of exog

        results: List of arrays containing estimates of the value
            value of the survival function and its standard error
            at each unique time, for each value of exog

        ts: List of unique times for each value of exog

        Methods
        -------
        fit: Calcuate the Kaplan-Meier estimates of the survival
            function and its standard error at each time, for each
            value of exog

        plot: Plot the survival curves using matplotlib.plyplot

        summary: Display the results of fit in a table. Gives results
            for all (including censored) times

        test_diff: Test for difference between survival curves

        Examples
        --------
        >>> import statsmodels.api as sm
        >>> import matplotlib.pyplot as plt
        >>> import numpy as np
        >>> from statsmodels.sandbox.survival2 import KaplanMeier
        >>> dta = sm.datasets.strikes.load()
        >>> dta = dta.values()[-1]
        >>> dta[range(5),:]
        array([[  7.00000000e+00,   1.13800000e-02],
               [  9.00000000e+00,   1.13800000e-02],
               [  1.30000000e+01,   1.13800000e-02],
               [  1.40000000e+01,   1.13800000e-02],
               [  2.60000000e+01,   1.13800000e-02]])
        >>> km = KaplanMeier(dta,0)
        >>> km.fit()
        >>> km.plot()

        Doing

        >>> km.summary()

        will display a table of the estimated survival and standard errors
        for each time. The first few lines are

                  Kaplan-Meier Curve
        =====================================
         Time     Survival        Std. Err
        -------------------------------------
         1.0   0.983870967742 0.0159984306572
         2.0   0.91935483871  0.0345807888235
         3.0   0.854838709677 0.0447374942184
         4.0   0.838709677419 0.0467104592871
         5.0   0.822580645161 0.0485169952543

        Doing

        >>> plt.show()

        will plot the survival curve

        Mutliple survival curves:

        >>> km2 = KaplanMeier(dta,0,exog=1)
        >>> km2.fit()

        km2 will estimate a survival curve for each value of industrial
        production, the column of dta with index one (1).

        With censoring:

        >>> censoring = np.ones_like(dta[:,0])
        >>> censoring[dta[:,0] > 80] = 0
        >>> dta = np.c_[dta,censoring]
        >>> dta[range(5),:]
        array([[  7.00000000e+00,   1.13800000e-02,   1.00000000e+00],
               [  9.00000000e+00,   1.13800000e-02,   1.00000000e+00],
               [  1.30000000e+01,   1.13800000e-02,   1.00000000e+00],
               [  1.40000000e+01,   1.13800000e-02,   1.00000000e+00],
               [  2.60000000e+01,   1.13800000e-02,   1.00000000e+00]])

        >>> km3 = KaplanMeier(dta,0,exog=1,censoring=2)
        >>> km3.fit()

        Test for difference of survival curves

        >>> log_rank = km3.test_diff([0.0645,-0.03957])

        The zeroth element of log_rank is the chi-square test statistic
        for the difference between the survival curves for exog = 0.0645
        and exog = -0.03957, the index one element is the degrees of freedom for
        the test, and the index two element is the p-value for the test

        Groups with nan names

        >>> groups = np.ones_like(dta[:,1])
        >>> groups = groups.astype('S4')
        >>> groups[dta[:,1] > 0] = 'high'
        >>> groups[dta[:,1] <= 0] = 'low'
        >>> dta = dta.astype('S4')
        >>> dta[:,1] = groups
        >>> dta[range(5),:]
        array([['7.0', 'high', '1.0'],
               ['9.0', 'high', '1.0'],
               ['13.0', 'high', '1.0'],
               ['14.0', 'high', '1.0'],
               ['26.0', 'high', '1.0']],
              dtype='|S4')
        >>> km4 = KaplanMeier(dta,0,exog=1,censoring=2)
        >>> km4.fit()

    """

    def __init__(self, data, endog, exog=None, censoring=None):
        self.exog = exog
        self.censoring = censoring
        cols = [endog]
        self.endog = 0
        if exog != None:
            cols.append(exog)
            self.exog = 1
        if censoring != None:
            cols.append(censoring)
            if exog != None:
                self.censoring = 2
            else:
                self.censoring = 1
        data = data[:,cols]
        if data.dtype == float or data.dtype == int:
            self.data = data[~np.isnan(data).any(1)]
        else:
            t = (data[:,self.endog]).astype(float)
            if exog != None:
                evec = data[:,self.exog]
                evec = evec[~np.isnan(t)]
            if censoring != None:
                cvec = (data[:,self.censoring]).astype(float)
                cvec = cvec[~np.isnan(t)]
            t = t[~np.isnan(t)]
            if censoring != None:
                t = t[~np.isnan(cvec)]
                if exog != None:
                    evec = evec[~np.isnan(cvec)]
                cvec = cvec[~np.isnan(cvec)]
            cols = [t]
            if exog != None:
                cols.append(evec)
            if censoring != None:
                cols.append(cvec)
            data = (np.array(cols)).transpose()
            self.data = data

    def fit(self):
        """
        Calculate the Kaplan-Meier estimator of the survival function
        """
        self.results = []
        self.ts = []
        self.censorings = []
        self.event = []
        if self.exog == None:
            self.fitting_proc(self.data)
        else:
            groups = np.unique(self.data[:,self.exog])
            self.groups = groups
            for g in groups:
                group = self.data[self.data[:,self.exog] == g]
                self.fitting_proc(group)

    def plot(self):
        """
        Plot the estimated survival curves. After using this method
        do

        plt.show()

        to display the plot
        """
        plt.figure()
        if self.exog == None:
            self.plotting_proc(0)
        else:
            for g in range(len(self.groups)):
                self.plotting_proc(g)
        plt.ylim(ymax=1.05)
        plt.ylabel('Survival')
        plt.xlabel('Time')

    def summary(self):
        """
        Print a set of tables containing the estimates of the survival
        function, and its standard errors
        """
        if self.exog == None:
            self.summary_proc(0)
        else:
            for g in range(len(self.groups)):
                self.summary_proc(g)

    def fitting_proc(self, group):
        """
        For internal use
        """
        t = ((group[:,self.endog]).astype(float)).astype(int)
        if self.censoring == None:
            events = np.bincount(t)
            t = np.unique(t)
            events = events[:,list(t)]
            events = events.astype(float)
            eventsSum = np.cumsum(events)
            eventsSum = np.r_[0,eventsSum]
            n = len(group) - eventsSum[:-1]
        else:
            censoring = ((group[:,self.censoring]).astype(float)).astype(int)
            reverseCensoring = -1*(censoring - 1)
            events = np.bincount(t,censoring)
            censored = np.bincount(t,reverseCensoring)
            t = np.unique(t)
            censored = censored[:,list(t)]
            censored = censored.astype(float)
            censoredSum = np.cumsum(censored)
            censoredSum = np.r_[0,censoredSum]
            events = events[:,list(t)]
            events = events.astype(float)
            eventsSum = np.cumsum(events)
            eventsSum = np.r_[0,eventsSum]
            n = len(group) - eventsSum[:-1] - censoredSum[:-1]
            (self.censorings).append(censored)
        survival = np.cumprod(1-events/n)
        var = ((survival*survival) *
               np.cumsum(events/(n*(n-events))))
        se = np.sqrt(var)
        (self.results).append(np.array([survival,se]))
        (self.ts).append(t)
        (self.event).append(events)

    def plotting_proc(self, g):
        """
        For internal use
        """
        survival = self.results[g][0]
        t = self.ts[g]
        e = (self.event)[g]
        if self.censoring != None:
            c = self.censorings[g]
            csurvival = survival[c != 0]
            ct = t[c != 0]
            if len(ct) != 0:
                plt.vlines(ct,csurvival+0.02,csurvival-0.02)
        x = np.repeat(t[e != 0], 2)
        y = np.repeat(survival[e != 0], 2)
        if self.ts[g][-1] in t[e != 0]:
            x = np.r_[0,x]
            y = np.r_[1,1,y[:-1]]
        else:
            x = np.r_[0,x,self.ts[g][-1]]
            y = np.r_[1,1,y]
        plt.plot(x,y)

    def summary_proc(self, g):
        """
        For internal use
        """
        if self.exog != None:
            myTitle = ('exog = ' + str(self.groups[g]) + '\n')
        else:
            myTitle = "Kaplan-Meier Curve"
        table = np.transpose(self.results[g])
        table = np.c_[np.transpose(self.ts[g]),table]
        table = SimpleTable(table, headers=['Time','Survival','Std. Err'],
                            title = myTitle)
        print(table)

    def test_diff(self, groups, rho=None, weight=None):

        """
        test_diff(groups, rho=0)

        Test for difference between survival curves

        Parameters
        ----------
        groups: A list of the values for exog to test for difference.
        tests the null hypothesis that the survival curves for all
        values of exog in groups are equal

        rho: compute the test statistic with weight S(t)^rho, where
        S(t) is the pooled estimate for the Kaplan-Meier survival function.
        If rho = 0, this is the logrank test, if rho = 0, this is the
        Peto and Peto modification to the Gehan-Wilcoxon test.

        weight: User specified function that accepts as its sole arguement
        an array of times, and returns an array of weights for each time
        to be used in the test

        Returns
        -------
        An array whose zeroth element is the chi-square test statistic for
        the global null hypothesis, that all survival curves are equal,
        the index one element is degrees of freedom for the test, and the
        index two element is the p-value for the test.

        Examples
        --------

        >>> import statsmodels.api as sm
        >>> import matplotlib.pyplot as plt
        >>> import numpy as np
        >>> from statsmodels.sandbox.survival2 import KaplanMeier
        >>> dta = sm.datasets.strikes.load()
        >>> dta = dta.values()[-1]
        >>> censoring = np.ones_like(dta[:,0])
        >>> censoring[dta[:,0] > 80] = 0
        >>> dta = np.c_[dta,censoring]
        >>> km = KaplanMeier(dta,0,exog=1,censoring=2)
        >>> km.fit()

        Test for difference of survival curves

        >>> log_rank = km3.test_diff([0.0645,-0.03957])

        The zeroth element of log_rank is the chi-square test statistic
        for the difference between the survival curves using the log rank test
        for exog = 0.0645 and exog = -0.03957, the index one element
        is the degrees of freedom for the test, and the index two element
        is the p-value for the test

        >>> wilcoxon = km.test_diff([0.0645,-0.03957], rho=1)

        wilcoxon is the equivalent information as log_rank, but for the
        Peto and Peto modification to the Gehan-Wilcoxon test.

        User specified weight functions

        >>> log_rank = km3.test_diff([0.0645,-0.03957], weight=np.ones_like)

        This is equivalent to the log rank test

        More than two groups

        >>> log_rank = km.test_diff([0.0645,-0.03957,0.01138])

        The test can be performed with arbitrarily many groups, so long as
        they are all in the column exog
        """
        groups = np.asarray(groups)
        if self.exog == None:
            raise ValueError("Need an exogenous variable for logrank test")

        elif (np.in1d(groups,self.groups)).all():
            data = self.data[np.in1d(self.data[:,self.exog],groups)]
            t = ((data[:,self.endog]).astype(float)).astype(int)
            tind = np.unique(t)
            NK = []
            N = []
            D = []
            Z = []
            if rho != None and weight != None:
                raise ValueError("Must use either rho or weights, not both")

            elif rho != None:
                s = KaplanMeier(data,self.endog,censoring=self.censoring)
                s.fit()
                s = (s.results[0][0]) ** (rho)
                s = np.r_[1,s[:-1]]

            elif weight != None:
                s = weight(tind)

            else:
                s = np.ones_like(tind)

            if self.censoring == None:
                for g in groups:
                    dk = np.bincount((t[data[:,self.exog] == g]))
                    d = np.bincount(t)
                    if np.max(tind) != len(dk):
                        dif = np.max(tind) - len(dk) + 1
                        dk = np.r_[dk,[0]*dif]
                    dk = dk[:,list(tind)]
                    d = d[:,list(tind)]
                    dk = dk.astype(float)
                    d = d.astype(float)
                    dkSum = np.cumsum(dk)
                    dSum = np.cumsum(d)
                    dkSum = np.r_[0,dkSum]
                    dSum = np.r_[0,dSum]
                    nk = len(data[data[:,self.exog] == g]) - dkSum[:-1]
                    n = len(data) - dSum[:-1]
                    d = d[n>1]
                    dk = dk[n>1]
                    nk = nk[n>1]
                    n = n[n>1]
                    s = s[n>1]
                    ek = (nk * d)/(n)
                    Z.append(np.sum(s * (dk - ek)))
                    NK.append(nk)
                    N.append(n)
                    D.append(d)
            else:
                for g in groups:
                    censoring = ((data[:,self.censoring]).astype(float)).astype(int)
                    reverseCensoring = -1*(censoring - 1)
                    censored = np.bincount(t,reverseCensoring)
                    ck = np.bincount((t[data[:,self.exog] == g]),
                                     reverseCensoring[data[:,self.exog] == g])
                    dk = np.bincount((t[data[:,self.exog] == g]),
                                     censoring[data[:,self.exog] == g])
                    d = np.bincount(t,censoring)
                    if np.max(tind) != len(dk):
                        dif = np.max(tind) - len(dk) + 1
                        dk = np.r_[dk,[0]*dif]
                        ck = np.r_[ck,[0]*dif]
                    dk = dk[:,list(tind)]
                    ck = ck[:,list(tind)]
                    d = d[:,list(tind)]
                    dk = dk.astype(float)
                    d = d.astype(float)
                    ck = ck.astype(float)
                    dkSum = np.cumsum(dk)
                    dSum = np.cumsum(d)
                    ck = np.cumsum(ck)
                    ck = np.r_[0,ck]
                    dkSum = np.r_[0,dkSum]
                    dSum = np.r_[0,dSum]
                    censored = censored[:,list(tind)]
                    censored = censored.astype(float)
                    censoredSum = np.cumsum(censored)
                    censoredSum = np.r_[0,censoredSum]
                    nk = (len(data[data[:,self.exog] == g]) - dkSum[:-1]
                          - ck[:-1])
                    n = len(data) - dSum[:-1] - censoredSum[:-1]
                    d = d[n>1]
                    dk = dk[n>1]
                    nk = nk[n>1]
                    n = n[n>1]
                    s = s[n>1]
                    ek = (nk * d)/(n)
                    Z.append(np.sum(s * (dk - ek)))
                    NK.append(nk)
                    N.append(n)
                    D.append(d)
            Z = np.array(Z)
            N = np.array(N)
            D = np.array(D)
            NK = np.array(NK)
            sigma = -1 * np.dot((NK/N) * ((N - D)/(N - 1)) * D
                                * np.array([(s ** 2)]*len(D))
                            ,np.transpose(NK/N))
            np.fill_diagonal(sigma, np.diagonal(np.dot((NK/N)
                                                  * ((N - D)/(N - 1)) * D
                                                       * np.array([(s ** 2)]*len(D))
                                                  ,np.transpose(1 - (NK/N)))))
            chisq = np.dot(np.transpose(Z),np.dot(la.pinv(sigma), Z))
            df = len(groups) - 1
            return np.array([chisq, df, stats.chi2.sf(chisq,df)])
        else:
            raise ValueError("groups must be in column exog")

#Kaplan-Meier Estimator

import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt
from scipy import stats
from statsmodels.iolib.table import SimpleTable

class KaplanMeier(object):

    """
    KaplanMeier(...)
        KaplanMeier(data, endog, exog=None, censoring=None)

        Create an object of class KaplanMeier for estimating
        Kaplan-Meier survival curves.

        Parameters
        ----------
        data: array_like
            An array, with observations in each row, and
            variables in the columns

        endog: index (starting at zero) of the column
            containing the endogenous variable (time)

        exog: index of the column containing the exogenous
            variable (must be catagorical). If exog = None, this
            is equivalent to a single survival curve

        censoring: index of the column containing an indicator
            of whether an observation is an event, or a censored
            observation, with 0 for censored, and 1 for an event

        Attributes
        -----------
        censorings: List of censorings associated with each unique
            time, at each value of exog

        events: List of the number of events at each unique time
            for each value of exog

        results: List of arrays containing estimates of the value
            value of the survival function and its standard error
            at each unique time, for each value of exog

        ts: List of unique times for each value of exog

        Methods
        -------
        fit: Calcuate the Kaplan-Meier estimates of the survival
            function and its standard error at each time, for each
            value of exog

        plot: Plot the survival curves using matplotlib.plyplot

        summary: Display the results of fit in a table. Gives results
            for all (including censored) times

        test_diff: Test for difference between survival curves

        Examples
        --------
        >>> import statsmodels.api as sm
        >>> import matplotlib.pyplot as plt
        >>> import numpy as np
        >>> from statsmodels.sandbox.survival2 import KaplanMeier
        >>> dta = sm.datasets.strikes.load()
        >>> dta = dta.values()[-1]
        >>> dta[range(5),:]
        array([[  7.00000000e+00,   1.13800000e-02],
               [  9.00000000e+00,   1.13800000e-02],
               [  1.30000000e+01,   1.13800000e-02],
               [  1.40000000e+01,   1.13800000e-02],
               [  2.60000000e+01,   1.13800000e-02]])
        >>> km = KaplanMeier(dta,0)
        >>> km.fit()
        >>> km.plot()

        Doing

        >>> km.summary()

        will display a table of the estimated survival and standard errors
        for each time. The first few lines are

                  Kaplan-Meier Curve
        =====================================
         Time     Survival        Std. Err
        -------------------------------------
         1.0   0.983870967742 0.0159984306572
         2.0   0.91935483871  0.0345807888235
         3.0   0.854838709677 0.0447374942184
         4.0   0.838709677419 0.0467104592871
         5.0   0.822580645161 0.0485169952543

        Doing

        >>> plt.show()

        will plot the survival curve

        Mutliple survival curves:

        >>> km2 = KaplanMeier(dta,0,exog=1)
        >>> km2.fit()

        km2 will estimate a survival curve for each value of industrial
        production, the column of dta with index one (1).

        With censoring:

        >>> censoring = np.ones_like(dta[:,0])
        >>> censoring[dta[:,0] > 80] = 0
        >>> dta = np.c_[dta,censoring]
        >>> dta[range(5),:]
        array([[  7.00000000e+00,   1.13800000e-02,   1.00000000e+00],
               [  9.00000000e+00,   1.13800000e-02,   1.00000000e+00],
               [  1.30000000e+01,   1.13800000e-02,   1.00000000e+00],
               [  1.40000000e+01,   1.13800000e-02,   1.00000000e+00],
               [  2.60000000e+01,   1.13800000e-02,   1.00000000e+00]])

        >>> km3 = KaplanMeier(dta,0,exog=1,censoring=2)
        >>> km3.fit()

        Test for difference of survival curves

        >>> log_rank = km3.test_diff([0.0645,-0.03957])

        The zeroth element of log_rank is the chi-square test statistic
        for the difference between the survival curves for exog = 0.0645
        and exog = -0.03957, the index one element is the degrees of freedom for
        the test, and the index two element is the p-value for the test

        Groups with nan names

        >>> groups = np.ones_like(dta[:,1])
        >>> groups = groups.astype('S4')
        >>> groups[dta[:,1] > 0] = 'high'
        >>> groups[dta[:,1] <= 0] = 'low'
        >>> dta = dta.astype('S4')
        >>> dta[:,1] = groups
        >>> dta[range(5),:]
        array([['7.0', 'high', '1.0'],
               ['9.0', 'high', '1.0'],
               ['13.0', 'high', '1.0'],
               ['14.0', 'high', '1.0'],
               ['26.0', 'high', '1.0']],
              dtype='|S4')
        >>> km4 = KaplanMeier(dta,0,exog=1,censoring=2)
        >>> km4.fit()

    """

    def __init__(self, data, endog, exog=None, censoring=None):
        self.exog = exog
        self.censoring = censoring
        cols = [endog]
        self.endog = 0
        if exog != None:
            cols.append(exog)
            self.exog = 1
        if censoring != None:
            cols.append(censoring)
            if exog != None:
                self.censoring = 2
            else:
                self.censoring = 1
        data = data[:,cols]
        if data.dtype == float or data.dtype == int:
            self.data = data[~np.isnan(data).any(1)]
        else:
            t = (data[:,self.endog]).astype(float)
            if exog != None:
                evec = data[:,self.exog]
                evec = evec[~np.isnan(t)]
            if censoring != None:
                cvec = (data[:,self.censoring]).astype(float)
                cvec = cvec[~np.isnan(t)]
            t = t[~np.isnan(t)]
            if censoring != None:
                t = t[~np.isnan(cvec)]
                if exog != None:
                    evec = evec[~np.isnan(cvec)]
                cvec = cvec[~np.isnan(cvec)]
            cols = [t]
            if exog != None:
                cols.append(evec)
            if censoring != None:
                cols.append(cvec)
            data = (np.array(cols)).transpose()
            self.data = data

    def fit(self):
        """
        Calculate the Kaplan-Meier estimator of the survival function
        """
        self.results = []
        self.ts = []
        self.censorings = []
        self.event = []
        if self.exog == None:
            self.fitting_proc(self.data)
        else:
            groups = np.unique(self.data[:,self.exog])
            self.groups = groups
            for g in groups:
                group = self.data[self.data[:,self.exog] == g]
                self.fitting_proc(group)

    def plot(self):
        """
        Plot the estimated survival curves. After using this method
        do

        plt.show()

        to display the plot
        """
        plt.figure()
        if self.exog == None:
            self.plotting_proc(0)
        else:
            for g in range(len(self.groups)):
                self.plotting_proc(g)
        plt.ylim(ymax=1.05)
        plt.ylabel('Survival')
        plt.xlabel('Time')

    def summary(self):
        """
        Print a set of tables containing the estimates of the survival
        function, and its standard errors
        """
        if self.exog == None:
            self.summary_proc(0)
        else:
            for g in range(len(self.groups)):
                self.summary_proc(g)

    def fitting_proc(self, group):
        """
        For internal use
        """
        t = ((group[:,self.endog]).astype(float)).astype(int)
        if self.censoring == None:
            events = np.bincount(t)
            t = np.unique(t)
            events = events[:,list(t)]
            events = events.astype(float)
            eventsSum = np.cumsum(events)
            eventsSum = np.r_[0,eventsSum]
            n = len(group) - eventsSum[:-1]
        else:
            censoring = ((group[:,self.censoring]).astype(float)).astype(int)
            reverseCensoring = -1*(censoring - 1)
            events = np.bincount(t,censoring)
            censored = np.bincount(t,reverseCensoring)
            t = np.unique(t)
            censored = censored[:,list(t)]
            censored = censored.astype(float)
            censoredSum = np.cumsum(censored)
            censoredSum = np.r_[0,censoredSum]
            events = events[:,list(t)]
            events = events.astype(float)
            eventsSum = np.cumsum(events)
            eventsSum = np.r_[0,eventsSum]
            n = len(group) - eventsSum[:-1] - censoredSum[:-1]
            (self.censorings).append(censored)
        survival = np.cumprod(1-events/n)
        var = ((survival*survival) *
               np.cumsum(events/(n*(n-events))))
        se = np.sqrt(var)
        (self.results).append(np.array([survival,se]))
        (self.ts).append(t)
        (self.event).append(events)

    def plotting_proc(self, g):
        """
        For internal use
        """
        survival = self.results[g][0]
        t = self.ts[g]
        e = (self.event)[g]
        if self.censoring != None:
            c = self.censorings[g]
            csurvival = survival[c != 0]
            ct = t[c != 0]
            if len(ct) != 0:
                plt.vlines(ct,csurvival+0.02,csurvival-0.02)
        x = np.repeat(t[e != 0], 2)
        y = np.repeat(survival[e != 0], 2)
        if self.ts[g][-1] in t[e != 0]:
            x = np.r_[0,x]
            y = np.r_[1,1,y[:-1]]
        else:
            x = np.r_[0,x,self.ts[g][-1]]
            y = np.r_[1,1,y]
        plt.plot(x,y)

    def summary_proc(self, g):
        """
        For internal use
        """
        if self.exog != None:
            myTitle = ('exog = ' + str(self.groups[g]) + '\n')
        else:
            myTitle = "Kaplan-Meier Curve"
        table = np.transpose(self.results[g])
        table = np.c_[np.transpose(self.ts[g]),table]
        table = SimpleTable(table, headers=['Time','Survival','Std. Err'],
                            title = myTitle)
        print(table)

    def test_diff(self, groups, rho=None, weight=None):

        """
        test_diff(groups, rho=0)

        Test for difference between survival curves

        Parameters
        ----------
        groups: A list of the values for exog to test for difference.
        tests the null hypothesis that the survival curves for all
        values of exog in groups are equal

        rho: compute the test statistic with weight S(t)^rho, where
        S(t) is the pooled estimate for the Kaplan-Meier survival function.
        If rho = 0, this is the logrank test, if rho = 0, this is the
        Peto and Peto modification to the Gehan-Wilcoxon test.

        weight: User specified function that accepts as its sole arguement
        an array of times, and returns an array of weights for each time
        to be used in the test

        Returns
        -------
        An array whose zeroth element is the chi-square test statistic for
        the global null hypothesis, that all survival curves are equal,
        the index one element is degrees of freedom for the test, and the
        index two element is the p-value for the test.

        Examples
        --------

        >>> import statsmodels.api as sm
        >>> import matplotlib.pyplot as plt
        >>> import numpy as np
        >>> from statsmodels.sandbox.survival2 import KaplanMeier
        >>> dta = sm.datasets.strikes.load()
        >>> dta = dta.values()[-1]
        >>> censoring = np.ones_like(dta[:,0])
        >>> censoring[dta[:,0] > 80] = 0
        >>> dta = np.c_[dta,censoring]
        >>> km = KaplanMeier(dta,0,exog=1,censoring=2)
        >>> km.fit()

        Test for difference of survival curves

        >>> log_rank = km3.test_diff([0.0645,-0.03957])

        The zeroth element of log_rank is the chi-square test statistic
        for the difference between the survival curves using the log rank test
        for exog = 0.0645 and exog = -0.03957, the index one element
        is the degrees of freedom for the test, and the index two element
        is the p-value for the test

        >>> wilcoxon = km.test_diff([0.0645,-0.03957], rho=1)

        wilcoxon is the equivalent information as log_rank, but for the
        Peto and Peto modification to the Gehan-Wilcoxon test.

        User specified weight functions

        >>> log_rank = km3.test_diff([0.0645,-0.03957], weight=np.ones_like)

        This is equivalent to the log rank test

        More than two groups

        >>> log_rank = km.test_diff([0.0645,-0.03957,0.01138])

        The test can be performed with arbitrarily many groups, so long as
        they are all in the column exog
        """
        groups = np.asarray(groups)
        if self.exog == None:
            raise ValueError("Need an exogenous variable for logrank test")

        elif (np.in1d(groups,self.groups)).all():
            data = self.data[np.in1d(self.data[:,self.exog],groups)]
            t = ((data[:,self.endog]).astype(float)).astype(int)
            tind = np.unique(t)
            NK = []
            N = []
            D = []
            Z = []
            if rho != None and weight != None:
                raise ValueError("Must use either rho or weights, not both")

            elif rho != None:
                s = KaplanMeier(data,self.endog,censoring=self.censoring)
                s.fit()
                s = (s.results[0][0]) ** (rho)
                s = np.r_[1,s[:-1]]

            elif weight != None:
                s = weight(tind)

            else:
                s = np.ones_like(tind)

            if self.censoring == None:
                for g in groups:
                    dk = np.bincount((t[data[:,self.exog] == g]))
                    d = np.bincount(t)
                    if np.max(tind) != len(dk):
                        dif = np.max(tind) - len(dk) + 1
                        dk = np.r_[dk,[0]*dif]
                    dk = dk[:,list(tind)]
                    d = d[:,list(tind)]
                    dk = dk.astype(float)
                    d = d.astype(float)
                    dkSum = np.cumsum(dk)
                    dSum = np.cumsum(d)
                    dkSum = np.r_[0,dkSum]
                    dSum = np.r_[0,dSum]
                    nk = len(data[data[:,self.exog] == g]) - dkSum[:-1]
                    n = len(data) - dSum[:-1]
                    d = d[n>1]
                    dk = dk[n>1]
                    nk = nk[n>1]
                    n = n[n>1]
                    s = s[n>1]
                    ek = (nk * d)/(n)
                    Z.append(np.sum(s * (dk - ek)))
                    NK.append(nk)
                    N.append(n)
                    D.append(d)
            else:
                for g in groups:
                    censoring = ((data[:,self.censoring]).astype(float)).astype(int)
                    reverseCensoring = -1*(censoring - 1)
                    censored = np.bincount(t,reverseCensoring)
                    ck = np.bincount((t[data[:,self.exog] == g]),
                                     reverseCensoring[data[:,self.exog] == g])
                    dk = np.bincount((t[data[:,self.exog] == g]),
                                     censoring[data[:,self.exog] == g])
                    d = np.bincount(t,censoring)
                    if np.max(tind) != len(dk):
                        dif = np.max(tind) - len(dk) + 1
                        dk = np.r_[dk,[0]*dif]
                        ck = np.r_[ck,[0]*dif]
                    dk = dk[:,list(tind)]
                    ck = ck[:,list(tind)]
                    d = d[:,list(tind)]
                    dk = dk.astype(float)
                    d = d.astype(float)
                    ck = ck.astype(float)
                    dkSum = np.cumsum(dk)
                    dSum = np.cumsum(d)
                    ck = np.cumsum(ck)
                    ck = np.r_[0,ck]
                    dkSum = np.r_[0,dkSum]
                    dSum = np.r_[0,dSum]
                    censored = censored[:,list(tind)]
                    censored = censored.astype(float)
                    censoredSum = np.cumsum(censored)
                    censoredSum = np.r_[0,censoredSum]
                    nk = (len(data[data[:,self.exog] == g]) - dkSum[:-1]
                          - ck[:-1])
                    n = len(data) - dSum[:-1] - censoredSum[:-1]
                    d = d[n>1]
                    dk = dk[n>1]
                    nk = nk[n>1]
                    n = n[n>1]
                    s = s[n>1]
                    ek = (nk * d)/(n)
                    Z.append(np.sum(s * (dk - ek)))
                    NK.append(nk)
                    N.append(n)
                    D.append(d)
            Z = np.array(Z)
            N = np.array(N)
            D = np.array(D)
            NK = np.array(NK)
            sigma = -1 * np.dot((NK/N) * ((N - D)/(N - 1)) * D
                                * np.array([(s ** 2)]*len(D))
                            ,np.transpose(NK/N))
            np.fill_diagonal(sigma, np.diagonal(np.dot((NK/N)
                                                  * ((N - D)/(N - 1)) * D
                                                       * np.array([(s ** 2)]*len(D))
                                                  ,np.transpose(1 - (NK/N)))))
            chisq = np.dot(np.transpose(Z),np.dot(la.pinv(sigma), Z))
            df = len(groups) - 1
            return np.array([chisq, df, stats.chi2.sf(chisq,df)])
        else:
            raise ValueError("groups must be in column exog")
#Kaplan-Meier Estimator KaplanMeier(...)         KaplanMeier(data, endog, exog=None, censoring=None)          Create an object of class KaplanMeier for estimating         Kaplan-Meier survival curves.          Parameters         ----------         data: array_like             An array, with observations in each row, and             variables in the columns          endog: index (starting at zero) of the column             containing the endogenous variable (time)          exog: index of the column containing the exogenous             variable (must be catagorical). If exog = None, this             is equivalent to a single survival curve          censoring: index of the column containing an indicator             of whether an observation is an event, or a censored             observation, with 0 for censored, and 1 for an event          Attributes         -----------         censorings: List of censorings associated with each unique             time, at each value of exog          events: List of the number of events at each unique time             for each value of exog          results: List of arrays containing estimates of the value             value of the survival function and its standard error             at each unique time, for each value of exog          ts: List of unique times for each value of exog          Methods         -------         fit: Calcuate the Kaplan-Meier estimates of the survival             function and its standard error at each time, for each             value of exog          plot: Plot the survival curves using matplotlib.plyplot          summary: Display the results of fit in a table. Gives results             for all (including censored) times          test_diff: Test for difference between survival curves          Examples         --------         >>> import statsmodels.api as sm         >>> import matplotlib.pyplot as plt         >>> import numpy as np         >>> from statsmodels.sandbox.survival2 import KaplanMeier         >>> dta = sm.datasets.strikes.load()         >>> dta = dta.values()[-1]         >>> dta[range(5),:]         array([[  7.00000000e+00,   1.13800000e-02],                [  9.00000000e+00,   1.13800000e-02],                [  1.30000000e+01,   1.13800000e-02],                [  1.40000000e+01,   1.13800000e-02],                [  2.60000000e+01,   1.13800000e-02]])         >>> km = KaplanMeier(dta,0)         >>> km.fit()         >>> km.plot()          Doing          >>> km.summary()          will display a table of the estimated survival and standard errors         for each time. The first few lines are                    Kaplan-Meier Curve         =====================================          Time     Survival        Std. Err         -------------------------------------          1.0   0.983870967742 0.0159984306572          2.0   0.91935483871  0.0345807888235          3.0   0.854838709677 0.0447374942184          4.0   0.838709677419 0.0467104592871          5.0   0.822580645161 0.0485169952543          Doing          >>> plt.show()          will plot the survival curve          Mutliple survival curves:          >>> km2 = KaplanMeier(dta,0,exog=1)         >>> km2.fit()          km2 will estimate a survival curve for each value of industrial         production, the column of dta with index one (1).          With censoring:          >>> censoring = np.ones_like(dta[:,0])         >>> censoring[dta[:,0] > 80] = 0         >>> dta = np.c_[dta,censoring]         >>> dta[range(5),:]         array([[  7.00000000e+00,   1.13800000e-02,   1.00000000e+00],                [  9.00000000e+00,   1.13800000e-02,   1.00000000e+00],                [  1.30000000e+01,   1.13800000e-02,   1.00000000e+00],                [  1.40000000e+01,   1.13800000e-02,   1.00000000e+00],                [  2.60000000e+01,   1.13800000e-02,   1.00000000e+00]])          >>> km3 = KaplanMeier(dta,0,exog=1,censoring=2)         >>> km3.fit()          Test for difference of survival curves          >>> log_rank = km3.test_diff([0.0645,-0.03957])          The zeroth element of log_rank is the chi-square test statistic         for the difference between the survival curves for exog = 0.0645         and exog = -0.03957, the index one element is the degrees of freedom for         the test, and the index two element is the p-value for the test          Groups with nan names          >>> groups = np.ones_like(dta[:,1])         >>> groups = groups.astype('S4')         >>> groups[dta[:,1] > 0] = 'high'         >>> groups[dta[:,1] <= 0] = 'low'         >>> dta = dta.astype('S4')         >>> dta[:,1] = groups         >>> dta[range(5),:]         array([['7.0', 'high', '1.0'],                ['9.0', 'high', '1.0'],                ['13.0', 'high', '1.0'],                ['14.0', 'high', '1.0'],                ['26.0', 'high', '1.0']],               dtype='|S4')         >>> km4 = KaplanMeier(dta,0,exog=1,censoring=2)         >>> km4.fit() Calculate the Kaplan-Meier estimator of the survival function Plot the estimated survival curves. After using this method         do          plt.show()          to display the plot Print a set of tables containing the estimates of the survival         function, and its standard errors For internal use For internal use For internal use test_diff(groups, rho=0)          Test for difference between survival curves          Parameters         ----------         groups: A list of the values for exog to test for difference.         tests the null hypothesis that the survival curves for all         values of exog in groups are equal          rho: compute the test statistic with weight S(t)^rho, where         S(t) is the pooled estimate for the Kaplan-Meier survival function.         If rho = 0, this is the logrank test, if rho = 0, this is the         Peto and Peto modification to the Gehan-Wilcoxon test.          weight: User specified function that accepts as its sole arguement         an array of times, and returns an array of weights for each time         to be used in the test          Returns         -------         An array whose zeroth element is the chi-square test statistic for         the global null hypothesis, that all survival curves are equal,         the index one element is degrees of freedom for the test, and the         index two element is the p-value for the test.          Examples         --------          >>> import statsmodels.api as sm         >>> import matplotlib.pyplot as plt         >>> import numpy as np         >>> from statsmodels.sandbox.survival2 import KaplanMeier         >>> dta = sm.datasets.strikes.load()         >>> dta = dta.values()[-1]         >>> censoring = np.ones_like(dta[:,0])         >>> censoring[dta[:,0] > 80] = 0         >>> dta = np.c_[dta,censoring]         >>> km = KaplanMeier(dta,0,exog=1,censoring=2)         >>> km.fit()          Test for difference of survival curves          >>> log_rank = km3.test_diff([0.0645,-0.03957])          The zeroth element of log_rank is the chi-square test statistic         for the difference between the survival curves using the log rank test         for exog = 0.0645 and exog = -0.03957, the index one element         is the degrees of freedom for the test, and the index two element         is the p-value for the test          >>> wilcoxon = km.test_diff([0.0645,-0.03957], rho=1)          wilcoxon is the equivalent information as log_rank, but for the         Peto and Peto modification to the Gehan-Wilcoxon test.          User specified weight functions          >>> log_rank = km3.test_diff([0.0645,-0.03957], weight=np.ones_like)          This is equivalent to the log rank test          More than two groups          >>> log_rank = km.test_diff([0.0645,-0.03957,0.01138])          The test can be performed with arbitrarily many groups, so long as         they are all in the column exog