{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Survival Analysis\n",
    "\n",
    "Author: Austin Rochford\n",
    "\n",
    "[Survival analysis](https://en.wikipedia.org/wiki/Survival_analysis) studies the distribution of the time to an event.  Its applications span many fields across medicine, biology, engineering, and social science.  This tutorial shows how to fit and analyze a Bayesian survival model in Python using PyMC3.\n",
    "\n",
    "We illustrate these concepts by analyzing a [mastectomy data set](https://vincentarelbundock.github.io/Rdatasets/doc/HSAUR/mastectomy.html) from `R`'s [HSAUR](https://cran.r-project.org/web/packages/HSAUR/index.html) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "from pymc3.distributions.timeseries import GaussianRandomWalk\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "from theano import tensor as T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(pm.get_data('mastectomy.csv'))\n",
    "df.event = df.event.astype(np.int64)\n",
    "df.metastized = (df.metastized == 'yes').astype(np.int64)\n",
    "n_patients = df.shape[0]\n",
    "patients = np.arange(n_patients)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "      <th>metastized</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>23</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>47</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>69</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time  event  metastized\n",
       "0    23      1           0\n",
       "1    47      1           0\n",
       "2    69      1           0\n",
       "3    70      0           0\n",
       "4   100      0           0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_patients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each row represents observations from a woman diagnosed with breast cancer that underwent a mastectomy.  The column `time` represents the time (in months) post-surgery that the woman was observed.  The column `event` indicates whether or not the woman died during the observation period.  The column `metastized` represents whether the cancer had [metastized](https://en.wikipedia.org/wiki/Metastatic_breast_cancer) prior to surgery.\n",
    "\n",
    "This tutorial analyzes the relationship between survival time post-mastectomy and whether or not the cancer had metastized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A crash course in survival analysis\n",
    "\n",
    "First we introduce a (very little) bit of theory.  If the random variable $T$ is the time to the event we are studying, survival analysis is primarily concerned with the survival function\n",
    "\n",
    "$$S(t) = P(T > t) = 1 - F(t),$$\n",
    "\n",
    "where $F$ is the [CDF](https://en.wikipedia.org/wiki/Cumulative_distribution_function) of $T$.  It is mathematically convenient to express the survival function in terms of the [hazard rate](https://en.wikipedia.org/wiki/Survival_analysis#Hazard_function_and_cumulative_hazard_function), $\\lambda(t)$.  The hazard rate is the instantaneous probability that the event occurs at time $t$ given that it has not yet occured.  That is,\n",
    "\n",
    "$$\\begin{align*}\n",
    "\\lambda(t)\n",
    "    & = \\lim_{\\Delta t \\to 0} \\frac{P(t < T < t + \\Delta t\\ |\\ T > t)}{\\Delta t} \\\\\n",
    "    & = \\lim_{\\Delta t \\to 0} \\frac{P(t < T < t + \\Delta t)}{\\Delta t \\cdot P(T > t)} \\\\\n",
    "    & = \\frac{1}{S(t)} \\cdot \\lim_{\\Delta t \\to 0} \\frac{S(t + \\Delta t) - S(t)}{\\Delta t}\n",
    "      = -\\frac{S'(t)}{S(t)}.\n",
    "\\end{align*}$$\n",
    "\n",
    "Solving this differential equation for the survival function shows that\n",
    "\n",
    "$$S(t) = \\exp\\left(-\\int_0^s \\lambda(s)\\ ds\\right).$$\n",
    "\n",
    "This representation of the survival function shows that the cumulative hazard function\n",
    "\n",
    "$$\\Lambda(t) = \\int_0^t \\lambda(s)\\ ds$$\n",
    "\n",
    "is an important quantity in survival analysis, since we may consicesly write $S(t) = \\exp(-\\Lambda(t)).$\n",
    "\n",
    "An important, but subtle, point in survival analysis is [censoring](https://en.wikipedia.org/wiki/Survival_analysis#Censoring).  Even though the quantity we are interested in estimating is the time between surgery and death, we do not observe the death of every subject.  At the point in time that we perform our analysis, some of our subjects will thankfully still be alive. In the case of our mastectomy study, `df.event` is one if the subject's death was observed (the observation is not censored) and is zero if the death was not observed (the observation is censored)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5909090909090909"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.event.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just over 40% of our observations are censored.  We visualize the observed durations and indicate which observations are censored below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NrfYax72RzOxfzWyZma03s/fM7E5vO7/vURTVwmtmTST9UtJ3JXWVNMrMukbz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\n/wX07nqjED5brgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13cd1e6320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "blue, _, red = sns.color_palette()[:3]\n",
    "\n",
    "ax.hlines(patients[df.event.values == 0], 0, df[df.event.values == 0].time,\n",
    "          color=blue, label='Censored')\n",
    "\n",
    "ax.hlines(patients[df.event.values == 1], 0, df[df.event.values == 1].time,\n",
    "          color=red, label='Uncensored')\n",
    "\n",
    "ax.scatter(df[df.metastized.values == 1].time, patients[df.metastized.values == 1],\n",
    "           color='k', zorder=10, label='Metastized')\n",
    "\n",
    "ax.set_xlim(left=0)\n",
    "ax.set_xlabel('Months since mastectomy')\n",
    "ax.set_yticks([])\n",
    "ax.set_ylabel('Subject')\n",
    "\n",
    "ax.set_ylim(-0.25, n_patients + 0.25)\n",
    "\n",
    "ax.legend(loc='center right');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When an observation is censored (`df.event` is zero), `df.time` is not the subject's survival time.  All we can conclude from such a censored obsevation is that the subject's true survival time exceeds `df.time`.\n",
    "\n",
    "This is enough basic surival analysis theory for the purposes of this tutorial; for a more extensive introduction, consult Aalen et al.^[Aalen, Odd, Ornulf Borgan, and Hakon Gjessing. Survival and event history analysis: a process point of view. Springer Science & Business Media, 2008.]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bayesian proportional hazards model\n",
    "\n",
    "The two most basic estimators in survial analysis are the [Kaplan-Meier estimator](https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator) of the survival function and the [Nelson-Aalen estimator](https://en.wikipedia.org/wiki/Nelson%E2%80%93Aalen_estimator) of the cumulative hazard function.  However, since we want to understand the impact of metastization on survival time, a risk regression model is more appropriate.  Perhaps the most commonly used risk regression model is [Cox's proportional hazards model](https://en.wikipedia.org/wiki/Proportional_hazards_model).  In this model, if we have covariates $\\mathbf{x}$ and regression coefficients $\\beta$, the hazard rate is modeled as\n",
    "\n",
    "$$\\lambda(t) = \\lambda_0(t) \\exp(\\mathbf{x} \\beta).$$\n",
    "\n",
    "Here $\\lambda_0(t)$ is the baseline hazard, which is independent of the covariates $\\mathbf{x}$.  In this example, the covariates are the one-dimensonal vector `df.metastized`.\n",
    "\n",
    "Unlike in many regression situations, $\\mathbf{x}$ should not include a constant term corresponding to an intercept.  If $\\mathbf{x}$ includes a constant term corresponding to an intercept, the model becomes [unidentifiable](https://en.wikipedia.org/wiki/Identifiability).  To illustrate this unidentifiability, suppose that\n",
    "\n",
    "$$\\lambda(t) = \\lambda_0(t) \\exp(\\beta_0 + \\mathbf{x} \\beta) = \\lambda_0(t) \\exp(\\beta_0) \\exp(\\mathbf{x} \\beta).$$\n",
    "\n",
    "If $\\tilde{\\beta}_0 = \\beta_0 + \\delta$ and $\\tilde{\\lambda}_0(t) = \\lambda_0(t) \\exp(-\\delta)$, then $\\lambda(t) = \\tilde{\\lambda}_0(t) \\exp(\\tilde{\\beta}_0 + \\mathbf{x} \\beta)$ as well, making the model with $\\beta_0$ unidentifiable.\n",
    "\n",
    "In order to perform Bayesian inference with the Cox model, we must specify priors on $\\beta$ and $\\lambda_0(t)$.  We place a normal prior on $\\beta$, $\\beta \\sim N(\\mu_{\\beta}, \\sigma_{\\beta}^2),$ where $\\mu_{\\beta} \\sim N(0, 10^2)$ and $\\sigma_{\\beta} \\sim U(0, 10)$.\n",
    "\n",
    "A suitable prior on $\\lambda_0(t)$ is less obvious.  We choose a semiparametric prior, where $\\lambda_0(t)$ is a piecewise constant function.  This prior requires us to partition the time range in question into intervals with endpoints $0 \\leq s_1 < s_2 < \\cdots < s_N$.  With this partition, $\\lambda_0 (t) = \\lambda_j$ if $s_j \\leq t < s_{j + 1}$.  With $\\lambda_0(t)$ constrained to have this form, all we need to do is choose priors for the $N - 1$ values $\\lambda_j$.  We use independent vague priors $\\lambda_j \\sim \\operatorname{Gamma}(10^{-2}, 10^{-2}).$  For our mastectomy example, we make each interval three months long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "interval_length = 3\n",
    "interval_bounds = np.arange(0, df.time.max() + interval_length + 1, interval_length)\n",
    "n_intervals = interval_bounds.size - 1\n",
    "intervals = np.arange(n_intervals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see how deaths and censored observations are distributed in these intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XrB8EHoyI6zLz911YkyRJqtNIpyjvFONZ7w70aZmZmQ6RKUlSF2jkBrMbgWeBwcA3gXnA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13cabc8828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(df[df.event == 1].time.values, bins=interval_bounds,\n",
    "        color=red, alpha=0.5, lw=0,\n",
    "        label='Uncensored');\n",
    "ax.hist(df[df.event == 0].time.values, bins=interval_bounds,\n",
    "        color=blue, alpha=0.5, lw=0,\n",
    "        label='Censored');\n",
    "\n",
    "ax.set_xlim(0, interval_bounds[-1]);\n",
    "ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "ax.set_yticks([0, 1, 2, 3]);\n",
    "ax.set_ylabel('Number of observations');\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the prior distributions on $\\beta$ and $\\lambda_0(t)$ chosen, we now show how the model may be fit using MCMC simulation with `pymc3`.  The key observation is that the piecewise-constant proportional hazard model is [closely related](http://data.princeton.edu/wws509/notes/c7s4.html) to a Poisson regression model.   (The models are not identical, but their likelihoods differ by a factor that depends only on the observed data and not the parameters $\\beta$ and $\\lambda_j$.  For details, see Germán Rodríguez's WWS 509 [course notes](http://data.princeton.edu/wws509/notes/c7s4.html).)\n",
    "\n",
    "We define indicator variables based on whether or the $i$-th suject died in the $j$-th interval,\n",
    "\n",
    "$$d_{i, j} = \\begin{cases}\n",
    "    1 & \\textrm{if subject } i \\textrm{ died in interval } j \\\\\n",
    "    0 & \\textrm{otherwise}\n",
    "\\end{cases}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "last_period = np.floor((df.time - 0.01) / interval_length).astype(int)\n",
    "\n",
    "death = np.zeros((n_patients, n_intervals))\n",
    "death[patients, last_period] = df.event"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also define $t_{i, j}$ to be the amount of time the $i$-th subject was at risk in the $j$-th interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "exposure = np.greater_equal.outer(df.time, interval_bounds[:-1]) * interval_length\n",
    "exposure[patients, last_period] = df.time - interval_bounds[last_period]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, denote the risk incurred by the $i$-th subject in the $j$-th interval as $\\lambda_{i, j} = \\lambda_j \\exp(\\mathbf{x}_i \\beta)$.\n",
    "\n",
    "We may approximate $d_{i, j}$ with a Possion random variable with mean $t_{i, j}\\ \\lambda_{i, j}$.  This approximation leads to the following `pymc3` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "SEED = 5078864 # from random.org"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    \n",
    "    lambda0 = pm.Gamma('lambda0', 0.01, 0.01, shape=n_intervals)\n",
    "    \n",
    "    beta = pm.Normal('beta', 0, sd=1000)\n",
    "    \n",
    "    lambda_ = pm.Deterministic('lambda_', T.outer(T.exp(beta * df.metastized), lambda0))\n",
    "    mu = pm.Deterministic('mu', exposure * lambda_)\n",
    "    \n",
    "    obs = pm.Poisson('obs', mu, observed=death)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now sample from the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_samples = 1000\n",
    "n_tune = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [15:44<00:00,  2.31it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(n_samples, tune=n_tune, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the hazard rate for subjects whose cancer has metastized is about double the rate of those whose cancer has not metastized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1879479618944364"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(trace['beta'].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Hlil3b75qJTRQ90eeKdxm357dWjT9LfUf864kqUOfO/Vq+o2KCcZqzpR3NLmUsurgLsH9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\n9v9JpbzGWSQTxQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13baaa3fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, varnames=['beta'], color='#87ceeb');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tRLIz3w/8iqSP1l/22ibAeWmu1gMnObvjl9s6ZNe5dXad3dHIbt1yW9fsVp3b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\nEv1/xRZ/iSvYby0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13b64aa240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.autocorrplot(trace, varnames=['beta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now examine the effect of metastization on both the cumulative hazard and on the survival function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "base_hazard = trace['lambda0']\n",
    "met_hazard = trace['lambda0'] * np.exp(np.atleast_2d(trace['beta']).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cum_hazard(hazard):\n",
    "    return (interval_length * hazard).cumsum(axis=-1)\n",
    "\n",
    "def survival(hazard):\n",
    "    return np.exp(-cum_hazard(hazard))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_with_hpd(x, hazard, f, ax, color=None, label=None, alpha=0.05):\n",
    "    mean = f(hazard.mean(axis=0))\n",
    "    \n",
    "    percentiles = 100 * np.array([alpha / 2., 1. - alpha / 2.])\n",
    "    hpd = np.percentile(f(hazard), percentiles, axis=0)\n",
    "    \n",
    "    ax.fill_between(x, hpd[0], hpd[1], color=color, alpha=0.25)\n",
    "    ax.step(x, mean, color=color, label=label);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WnhYuPu5Cji87k/qm7kKhKIb09sLwhaxgZMWsBov6cXZ1bOHkqqopHxpvZtTE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Fj1dCBbIfaY2Xiabxv5z5TsyrZVjxMm5+ok7mRTuC60ZEhw9g6WeHjvKCN9SnRFRES6QSEscHzk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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13baab2ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (hazard_ax, surv_ax) = plt.subplots(ncols=2, sharex=True, sharey=False, figsize=(16, 6))\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], base_hazard, cum_hazard,\n",
    "              hazard_ax, color=blue, label='Had not metastized')\n",
    "plot_with_hpd(interval_bounds[:-1], met_hazard, cum_hazard,\n",
    "              hazard_ax, color=red, label='Metastized')\n",
    "\n",
    "hazard_ax.set_xlim(0, df.time.max());\n",
    "hazard_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "hazard_ax.set_ylabel(r'Cumulative hazard $\\Lambda(t)$');\n",
    "\n",
    "hazard_ax.legend(loc=2);\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], base_hazard, survival,\n",
    "              surv_ax, color=blue)\n",
    "plot_with_hpd(interval_bounds[:-1], met_hazard, survival,\n",
    "              surv_ax, color=red)\n",
    "\n",
    "surv_ax.set_xlim(0, df.time.max());\n",
    "surv_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "surv_ax.set_ylabel('Survival function $S(t)$');\n",
    "\n",
    "fig.suptitle('Bayesian survival model');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the cumulative hazard for metastized subjects increases more rapidly initially (through about seventy months), after which it increases roughly in parallel with the baseline cumulative hazard.\n",
    "\n",
    "These plots also show the pointwise 95% high posterior density interval for each function.  One of the distinct advantages of the Bayesian model fit with `pymc3` is the inherent quantification of uncertainty in our estimates."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Time varying effects\n",
    "\n",
    "Another of the advantages of the model we have built is its flexibility.  From the plots above, we may reasonable believe that the additional hazard due to metastization varies over time; it seems plausible that cancer that has metastized increases the hazard rate immediately after the mastectomy, but that the risk due to metastization decreases over time.  We can accomodate this mechanism in our model by allowing the regression coefficients to vary over time.  In the time-varying coefficent model, if $s_j \\leq t < s_{j + 1}$, we let $\\lambda(t) = \\lambda_j \\exp(\\mathbf{x} \\beta_j).$  The sequence of regression coefficients $\\beta_1, \\beta_2, \\ldots, \\beta_{N - 1}$ form a normal random walk with $\\beta_1 \\sim N(0, 1)$, $\\beta_j\\ |\\ \\beta_{j - 1} \\sim N(\\beta_{j - 1}, 1)$.\n",
    "\n",
    "We implement this model in `pymc3` as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with pm.Model() as time_varying_model:\n",
    "    \n",
    "    lambda0 = pm.Gamma('lambda0', 0.01, 0.01, shape=n_intervals)\n",
    "    beta = GaussianRandomWalk('beta', tau=1., shape=n_intervals)\n",
    "    \n",
    "    lambda_ = pm.Deterministic('h', lambda0 * T.exp(T.outer(T.constant(df.metastized), beta)))\n",
    "    mu = pm.Deterministic('mu', exposure * lambda_)\n",
    "    \n",
    "    obs = pm.Poisson('obs', mu, observed=death)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We proceed to sample from this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 2000/2000 [26:49<00:00,  1.84it/s]\n"
     ]
    }
   ],
   "source": [
    "with time_varying_model:\n",
    "    time_varying_trace = pm.sample(n_samples, tune=n_tune, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S23Tpyd2me4gwqd4QwjmkocCtkqaY2dKCmuuUiGZ2lscddxwAt+/0oaY9R6O0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\nfuIHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13bcd2ab00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(time_varying_trace, varnames=['beta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see from the plot of $\\beta_j$ over time below that initially $\\beta_j > 0$, indicating an elevated hazard rate due to metastization, but that this risk declines as $\\beta_j < 0$ eventually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cyfr5lSyq9kuQKCZFdyzNofYozT0JXIai2m8VTa0RCRyKTMjrprU3yfFwYlSJ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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f138daf32b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "beta_hpd = np.percentile(time_varying_trace['beta'], [2.5, 97.5], axis=0)\n",
    "beta_low = beta_hpd[0]\n",
    "beta_high = beta_hpd[1]\n",
    "ax.fill_between(interval_bounds[:-1], beta_low, beta_high,\n",
    "                color=blue, alpha=0.25);\n",
    "beta_hat = time_varying_trace['beta'].mean(axis=0)\n",
    "ax.step(interval_bounds[:-1], beta_hat, color=blue);\n",
    "ax.scatter(interval_bounds[last_period[(df.event.values == 1) & (df.metastized == 1)]],\n",
    "           beta_hat[last_period[(df.event.values == 1) & (df.metastized == 1)]],\n",
    "           c=red, zorder=10, label='Died, cancer metastized');\n",
    "ax.scatter(interval_bounds[last_period[(df.event.values == 0) & (df.metastized == 1)]],\n",
    "           beta_hat[last_period[(df.event.values == 0) & (df.metastized == 1)]],\n",
    "           c=blue, zorder=10, label='Censored, cancer metastized');\n",
    "\n",
    "ax.set_xlim(0, df.time.max());\n",
    "ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "ax.set_ylabel(r'$\\beta_j$');\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients $\\beta_j$ begin declining rapidly around one hundred months post-mastectomy, which seems reasonable, given that only three of twelve subjects whose cancer had metastized lived past this point died during the study.\n",
    "\n",
    "The change in our estimate of the cumulative hazard and survival functions due to time-varying effects is also quite apparent in the following plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tv_base_hazard = time_varying_trace['lambda0']\n",
    "tv_met_hazard = time_varying_trace['lambda0'] * np.exp(np.atleast_2d(time_varying_trace['beta']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ihB06dMjMzFJSUuyCCy6w33//3bZt22bOOVu+fLmZmaWmplrz5s3t+PHjZmaW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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f138daed320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.step(interval_bounds[:-1], cum_hazard(base_hazard.mean(axis=0)),\n",
    "        color=blue, label='Had not metastized');\n",
    "ax.step(interval_bounds[:-1], cum_hazard(met_hazard.mean(axis=0)),\n",
    "        color=red, label='Metastized');\n",
    "\n",
    "ax.step(interval_bounds[:-1], cum_hazard(tv_base_hazard.mean(axis=0)),\n",
    "        color=blue, linestyle='--', label='Had not metastized (time varying effect)');\n",
    "ax.step(interval_bounds[:-1], cum_hazard(tv_met_hazard.mean(axis=0)),\n",
    "        color=red, linestyle='--', label='Metastized (time varying effect)');\n",
    "\n",
    "ax.set_xlim(0, df.time.max() - 4);\n",
    "ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "ax.set_ylim(0, 2);\n",
    "ax.set_ylabel(r'Cumulative hazard $\\Lambda(t)$');\n",
    "\n",
    "ax.legend(loc=2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Gq2U4D/yzqh4BnAR8XkSO6LHNmcAh4c9lwH8AiIgL/CBcfwRwYS/7GmOMMcYYY4wxAzYq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31ZjpLhNjs3d47EWlM46+iZo9ckuSuZGJzggX0PAHB5rs7pySoj5d5KhCuNKYbyY0wM3qpEuMuW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f138da922b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (hazard_ax, surv_ax) = plt.subplots(ncols=2, sharex=True, sharey=False, figsize=(16, 6))\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], tv_base_hazard, cum_hazard,\n",
    "              hazard_ax, color=blue, label='Had not metastized')\n",
    "plot_with_hpd(interval_bounds[:-1], tv_met_hazard, cum_hazard,\n",
    "              hazard_ax, color=red, label='Metastized')\n",
    "\n",
    "hazard_ax.set_xlim(0, df.time.max());\n",
    "hazard_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "hazard_ax.set_ylim(0, 2);\n",
    "hazard_ax.set_ylabel(r'Cumulative hazard $\\Lambda(t)$');\n",
    "\n",
    "hazard_ax.legend(loc=2);\n",
    "\n",
    "plot_with_hpd(interval_bounds[:-1], tv_base_hazard, survival,\n",
    "              surv_ax, color=blue)\n",
    "plot_with_hpd(interval_bounds[:-1], tv_met_hazard, survival,\n",
    "              surv_ax, color=red)\n",
    "\n",
    "surv_ax.set_xlim(0, df.time.max());\n",
    "surv_ax.set_xlabel('Months since mastectomy');\n",
    "\n",
    "surv_ax.set_ylabel('Survival function $S(t)$');\n",
    "\n",
    "fig.suptitle('Bayesian survival model with time varying effects');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We have really only scratched the surface of both survival analysis and the Bayesian approach to survival analysis.  More information on Bayesian survival analysis is available in Ibrahim et al. (2005).  (For example, we may want to account for individual frailty in either or original or time-varying models.)\n",
    "\n",
    "This tutorial is available as an [IPython](http://ipython.org/) notebook [here](https://gist.github.com/AustinRochford/4c6b07e51a2247d678d6).  It is adapted from a blog post that first appeared [here](http://austinrochford.com/posts/2015-10-05-bayes-survival.html)."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
