{ "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": 2, "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", "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": {}, "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": {}, "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": [ "0.59090909090909094" ] }, "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": {}, "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": 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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"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": 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": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = 449.81: 19%|█▉ | 38808/200000 [00:06<00:37, 4245.50it/s]\n", "Convergence archived at 39100\n", "Interrupted at 39,100 [19%]: Average Loss = 756.28\n", "100%|█████████▉| 1998/2000 [01:58<00:00, 15.05it/s]/Users/fonnescj/Repos/pymc3/pymc3/step_methods/hmc/nuts.py:456: UserWarning: Chain 0 contains 52 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n", " % (self._chain_id, n_diverging))\n", "100%|██████████| 2000/2000 [01:58<00:00, 16.84it/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": [ "2.2637250704388596" ] }, "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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"text/plain": [ "" ] }, "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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"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": 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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ndxfp338AoVCIZcv+wg9+MJPt27dhGAa9e/fhzjvvxuVysXLlCg477HDq6uqw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\nFtd5NoAKIBTQkM076++G5kIpjup2c1kBkR0qOtv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/9NFHbayKasXbMw/51//M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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": 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": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using ADVI...\n", "Average Loss = 6.6709e+08: 83%|████████▎ | 166194/200000 [00:38<00:07, 4640.71it/s]\n", "Convergence archived at 166300\n", "Interrupted at 166,300 [83%]: Average Loss = 5.9183e+09\n", "100%|█████████▉| 1999/2000 [03:46<00:00, 8.92it/s]/Users/fonnescj/Repos/pymc3/pymc3/step_methods/hmc/nuts.py:456: UserWarning: Chain 0 contains 63 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n", " % (self._chain_id, n_diverging))\n", "100%|██████████| 2000/2000 [03:46<00:00, 8.83it/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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Xr+HLL7902Holh6mVJMPVhKOosqnX+fPnadq0KZ9++ilJSUk0aNCgwn02hBDC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\nm5tLvXqBHR4TQgghApHmi42NGze6/X5aWhrr1q3zczVCCCGEqGuaPEa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"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": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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qi1TGQs60kMtbyJsStrShKQqkBObiWQx0+uB16xt5pDWTTOcxMZeCUAQUAShC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\nwNdff83kyZNpaGhod31tFRYWEhERQXR0NB4eHhQXF2M0Gu+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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": 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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idhG1FW5rS0REJFEs8kRERBLFIk9ERCRRLPJEREQSxSJPREQkUSzyREREEsUi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\n/t/evcdUXf9xHH8eARMjJMUuJCsgBl6ScqfB1JV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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": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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dB+bMeYaEhHgcDgfDh99Lo0ZX8OOPOzl8+CBNmzZj9Oj7Wbt2C1On/huz2QzA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\nKQbv9reMkgRYCOdJAiyEwMpKAaxGYDbBRaQQh6K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84hOf4IYbbuCLX/wi7373u3nd614H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4Drg9/+4/Sv59+vikJ9z+std4u1REcV5NLaP29n89YDr5/Y2JwkXh4uQEQiIiID54ZCRKdPxzQ1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\nRERGBCXAIiIiIiIiM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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. (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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }