{ "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](https://pymc-devs.github.io/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": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Couldn't import dot_parser, loading of dot files will not be possible.\n" ] } ], "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", "from statsmodels import datasets\n", "from theano import tensor as T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fortunately, [`statsmodels.datasets`](http://statsmodels.sourceforge.net/0.6.0/datasets/index.html) makes it quite easy to load a number of data sets from `R`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "df = datasets.get_rdataset('mastectomy', 'HSAUR', cache=True).data\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": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "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": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "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": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.59090909090909094" ] }, "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": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "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": false }, "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": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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frrNnz2ry5MkaO3bs/57g46MqVaq4JRwAAJ6qyF3cgYGBqlGjhv7xj38oPT1dp06dUmpq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\ng1XCNm3aZI0ePdq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"text/plain": [ "" ] }, "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": false }, "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": false }, "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": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied log-transform to lambda0 and added transformed lambda0_log to model.\n" ] } ], "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" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Assigned NUTS to lambda0_log\n", "Assigned NUTS to beta\n", " [-----------------100%-----------------] 1001 of 1000 complete in 246.7 sec" ] } ], "source": [ "with model:\n", " trace_ = pm.sample(n_samples,random_seed=SEED)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "trace = trace_[100:]" ] }, { "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": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.1839971003209597" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.exp(trace['beta'].mean())" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Js216RKAnXr5+eeLLRzakWb+nMTAwYcLTx5f61W8n1W4iKZ9NNPKTlngGAL+Q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\n6NChN2z73OzsbEaPHs25c+c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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.plot_posterior(trace, varnames=['beta'], color='#87ceeb');" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "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": 20, "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": 21, "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": 22, "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": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SXV2FZVm8+uornHPOTCorK6io2JHpSyQiA5ydSJDYvp1kfV262qrqal4yPR7s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"text/plain": [ "" ] }, "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": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied log-transform to lambda0 and added transformed lambda0_log to model.\n" ] } ], "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": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Assigned NUTS to lambda0_log\n", "Assigned NUTS to beta\n", " [-----------------100%-----------------] 1001 of 1000 complete in 949.5 sec" ] } ], "source": [ "with time_varying_model:\n", " time_varying_trace_ = pm.sample(n_samples, random_seed=SEED)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "time_varying_trace = time_varying_trace_[100:]" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kLi5OGgohhLBSdUexc6cHvXvLLAqhLMXeoZg1axZ+fn5s2bIFk8mEl5cX+fn5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\nHH5DkZ+fT1ZWFn5+fmYNxdmzZ9m+fTuHDx+mV69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PyMgI8XicL7/8kmAwaLosSUIkEkmc\nWvT393P77bcbrkhSsW7dOjo6OgD4/vvvueuuuwxXJAvx3nvv0dTUBMCFCxeIxWLccssthquym04o\nclh9fT0vvPACU1NTlJeXs3btWtMlSRJqamrYu3cvHR0deL1eGhsbTZckKdiyZQtdXV089dRTAFo/\nl6qsrOTFF19k+/bt5OXlceDAAZ00zUOzPERERCRt2m6JiIhI2rShEBERkbRpQyEiIiJp04ZCRERE\n0qYNhYiIiKRNGwoRERFJmzYUIiIikrb/A5lIJ/j8g/AcAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "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": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lAABM04TX40BzXaDsuxhMc+AEKpIGMLNmejt8N2pq/Dh66by8t1VEjX66gqEw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\ncTpUHNFUBY9L5Yj8IuGCOUREVFSKIrC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"text/plain": [ "" ] }, "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": 29, "metadata": { "collapsed": false }, "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": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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urmSFERGZlVLJa+tklUSP2Hv06KH9uUOHDli6dCl8fX0lKYqIiIhKR/SIvXfv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\niMqAwS5ziZs3IP1UNAD9DVx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"text/plain": [ "" ] }, "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": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ww2SoqoYrrrgGiqKgX7/+WLr0cZx0UmcAAqWlJXjggYU4/fQzMG3aDQCASy4Z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\nScDv5cwsk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"text/plain": [ "" ] }, "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.^[Ibrahim, Joseph G., Ming‐Hui Chen, and Debajyoti Sinha. Bayesian survival analysis. John Wiley & Sons, Ltd, 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": { "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 1 }