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@ppope
Created May 11, 2016 00:14
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PYMC3 Bayesian survival analysis: depiction of bug fix
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayesian Survival Analysis\n",
"\n",
"Original Author: Austin Rochford\n",
"* Adapted from [here](https://gist.github.com/AustinRochford/afe6862e622c31494b2f)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": null,
"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": "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": [],
"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": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"last_period = np.floor((df.time - 0.01) / interval_length)\n",
"\n",
"death = np.zeros((n_patients, n_intervals))\n",
"death[patients, last_period] = df.event"
]
},
{
"cell_type": "code",
"execution_count": null,
"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": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#Add small perturbation to remove zeros\n",
"exposure = exposure + 0.0000001 "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"SEED = 5078864 # from random.org"
]
},
{
"cell_type": "code",
"execution_count": 9,
"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",
"Applied interval-transform to sigma and added transformed sigma_interval to model.\n"
]
}
],
"source": [
"with pm.Model() as model:\n",
" lambda0 = pm.Gamma('lambda0', 0.01, 0.01, shape=n_intervals)\n",
" \n",
" sigma = pm.Uniform('sigma', 0., 10.)\n",
" tau = pm.Deterministic('tau', sigma**-2)\n",
" mu_beta = pm.Normal('mu_beta', 0., 10**-2)\n",
" beta = pm.Normal('beta', mu_beta, tau)\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": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_samples = 40000\n",
"burn = 20000\n",
"thin = 20"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 40000 of 40000 complete in 38.3 sec"
]
}
],
"source": [
"with model:\n",
" step = pm.Metropolis()\n",
" trace_ = pm.sample(n_samples, step, random_seed=SEED)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"trace = trace_[burn::thin]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"1.645592148084472"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.exp(trace['beta'].mean())"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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/N0vD4TPjQGWBNzGVxedjzp4YR89NEPT7bXPsFd1x3c9mQaIaT50Zpz0aZmV3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\njMkRa2AZY4wxxhhjTI78f327woAJJSy3AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f275f72af90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#pm.traceplot(trace, vars=['beta']);\n",
"pm.traceplot(trace, varnames=['beta']);"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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