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@fonnesbeck
Created November 15, 2012 18:54
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Bioassay model in PyMC
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{
"metadata": {
"name": "Bioassay Model in PyMC"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a dose-response model that aims to calculate the LD50 for a particular drug, using groups of rats given different doses of the substance."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Import PyMC and Numpy\n",
"from pymc import *\n",
"from numpy import ones, array"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our data are the doses given to each group of rats in our sample."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Samples for each dose level\n",
"n = 5*ones(4,dtype=int)\n",
"# Log-dose\n",
"dose = array([-.86,-.3,-.05,.73])\n",
"# Subjects that died in each group\n",
"y = array([0,1,3,5])"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is the probability model."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Priors on logit-linear model parameters\n",
"alpha = Normal('alpha', 0, 0.01)\n",
"beta = Normal('beta', 0, 0.01)\n",
"\n",
"# Calculate probabilities of death\n",
"theta = Lambda('theta', lambda a=alpha, b=beta, d=dose: invlogit(a + b*d))\n",
"\n",
"# Data likelihood\n",
"deaths = Binomial('deaths', n=n, p=theta, value=y, observed=True)\n",
"\n",
"# Calculate LD50\n",
"LD50 = Lambda('LD50', lambda a=alpha, b=beta: -a/b)\n",
"\n",
"# Create MCMC model\n",
"M = MCMC(locals())"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"M.sample(10000, burn=5000)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" \r",
"[****************100%******************] 10000 of 10000 complete"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"LD50.summary()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"LD50:\n",
" \n",
"\tMean SD MC Error 95% HPD interval\n",
"\t------------------------------------------------------------------\n",
"\t-0.102 0.104 0.003 [-0.311 0.104]\n",
"\t\n",
"\t\n",
"\tPosterior quantiles:\n",
"\t\n",
"\t2.5 25 50 75 97.5\n",
"\t |---------------|===============|===============|---------------|\n",
"\t-0.286 -0.165 -0.108 -0.05 0.139\n",
"\t\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Matplot.plot(LD50)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Plotting LD50\n"
]
},
{
"output_type": "display_data",
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dZ6kd7/3UOMVeWq3BlXLTYK35Xfoue2P/JfzX5Dt9raLOqHQJ0PyQh7URq+bP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\n",
"text": [
"<matplotlib.figure.Figure at 0x11185dd50>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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