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fonnesbeck/ELSO Logistic Regression (PyMC 2).ipynb

Last active August 29, 2015 14:23
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ELSO Logistic Regression (PyMC 2).ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'2.3.5'"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import pymc as pm\n",
"import pdb\n",
"\n",
"pm.__version__"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu = pd.read_csv('data/flu_organism.csv', index_col=0)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(2937, 64)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu.shape"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(1654,)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu.PatientID.unique().shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Turn into table of unique patients, with appropriate organism columns\n",
"\n",
"Create indicator for flu-only."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_only = flu.groupby('PatientID')['OrganismName'].apply(lambda s: \n",
" len([x for x in s if str(x).startswith('Influenza')])==len(s)).astype(bool)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"PatientID\n",
"001B0EC6-66F5-48C9-8516-52D2ABFE28AA False\n",
"0034181F-59AB-4B2C-A06A-A83EE1DF1A17 True\n",
"004AE387-1096-410D-A7CB-F9A9086AA385 False\n",
"0084DCF0-8E3C-4F1C-8650-BE795A57EF2F False\n",
"0084E706-90D0-4314-8C99-496171AB639D True\n",
"Name: OrganismName, dtype: bool"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_only.head()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_only.name = 'flu_only'"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu = flu.merge(pd.DataFrame(flu_only), left_on='PatientID', right_index=True)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# flu_staph_organism = flu.groupby('PatientID')['OrganismName'].apply(lambda s: \n",
"# len([x for x in s if str(x).startswith('Influenza') or \n",
"# str(x).startswith('Staphylococcus aureus')])>1).astype(bool)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# flu_staph_organism.name = 'flu_staph_org'"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# flu = flu.merge(pd.DataFrame(flu_staph_organism), left_on='PatientID', right_index=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See if there are any flu-only or flu-other individuals with an ICD9 diagnosis of S. Aureus"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_other = flu.groupby('PatientID')['OrganismName'].apply(lambda s: \n",
" len([x for x in s if str(x).startswith('Influenza') or \n",
" str(x).startswith('Other')])>1).astype(bool)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_other.name = 'flu_other'"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"flu = flu.merge(pd.DataFrame(flu_other), left_on='PatientID', right_index=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There do not appear to be cases of flu-only or flu-other via organism that have a S.Aureus diagnosis via ICD9"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(flu_other & flu.s_aureus_icd9).sum()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(flu_only & flu.s_aureus_icd9).sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Same for pneumo"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(flu_other & flu.pneumo_icd9).sum()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"PatientID \n",
"001B0EC6-66F5-48C9-8516-52D2ABFE28AA Enterococcus 1\n",
" Klebsiella pneumoniae 1\n",
"0034181F-59AB-4B2C-A06A-A83EE1DF1A17 Influenza A 1\n",
"004AE387-1096-410D-A7CB-F9A9086AA385 Influenza A 1\n",
" Pseudomonas aerugenosa 1\n",
" Candida albicans 1\n",
"0084DCF0-8E3C-4F1C-8650-BE795A57EF2F Influenza A 1\n",
" Staphylococcus aureus 1\n",
"0084E706-90D0-4314-8C99-496171AB639D Influenza B 1\n",
"00EFD11D-650A-4317-8C4F-4B7378AD7946 Other 2\n",
"0118B486-8ACE-4BFF-8ED6-753D96E6B441 Influenza A 1\n",
"011B5A5D-9967-44A7-92F9-02F82D31216D Candida albicans 2\n",
" Influenza A 1\n",
" Epstein-Barr virus (EBV) 1\n",
"01AC9644-7CDF-4E28-A5F4-FE5B7F9FA22A Streptococcus pneumoniae 1\n",
" Staphylococcus, coag neg 1\n",
" Influenza A 1\n",
" Moraxella catarrhalis (Branhamella) 1\n",
"01F84F52-92D3-403B-B8AC-21A72A4BC771 Influenza A 1\n",
"02373407-74E6-4A1E-9629-F4DCBF707B0C Influenza A 1\n",
"025D87C9-CF70-4B9A-94BE-B15EA2185472 Eschericha coli 2\n",
" Influenza A 1\n",
" Enterococcus 1\n",
"02A94D2E-768A-4ABB-86BF-C8A188D698CC Influenza A 1\n",
"02C9FF5A-A4D6-461A-A650-E3EB405D62AE Influenza A 2\n",
"02D33150-FDDB-4F12-AAAB-D6F4B8765EBF Influenza A 1\n",
"031C1231-B585-478F-A98F-35E017B788CD Other 2\n",
"035A053E-91B1-4B68-87D4-F92C675FE6E3 Other 2\n",
"03AA4AD0-1B0E-4CAD-BD76-03FE52AA580D Influenza A 1\n",
" Epstein-Barr virus (EBV) 1\n",
" ..\n",
"FC9F84B4-B2CD-4C28-B824-D5CE1AF7BEF1 Gram positive, other 2\n",
" Yeast sp. 1\n",
" Aspergillus fumigatus 1\n",
" Pseudomonas fluorescens 1\n",
" Enterococcus 1\n",
" Candida albicans 1\n",
" Stenotrophomonas maltophilia (Xanthomonas) 1\n",
" Other 1\n",
"FCBAEC19-EFA1-4A95-A98D-1D8FE65B53CE Influenza A 1\n",
"FCD795A0-9FD1-4C20-961B-04BEF1B23E96 Influenza A 1\n",
" Staphylococcus aureus 1\n",
"FCDF1967-C307-4FF1-8CF1-7AA02FE0BE47 Influenza A 1\n",
"FD2FA339-7417-4F13-811B-2E1873E529C7 Influenza A 1\n",
"FDC32D1D-0D67-4752-A2E1-72E790FCB797 Influenza A 1\n",
" Pseudomonas aerugenosa 1\n",
"FDED68D1-1DFF-4899-9CF9-797E6AE70D18 Influenza A 1\n",
"FDFF23E3-C0CB-468D-98D9-998192CA7590 Influenza A 1\n",
" Yeast sp. 1\n",
" Eschericha coli 1\n",
" Candida albicans 1\n",
"FEA94F00-083A-479C-B862-05274A9842B5 Influenza A 1\n",
" Streptococcus, group A 1\n",
" Staphylococcus aureus 1\n",
"FF0D88BF-E131-4E56-9E78-CC6B60E461FD Influenza A 1\n",
" Yeast sp. 1\n",
" Staphylococcus, coag neg 1\n",
"FF0FB831-9804-4506-AE0B-B447AB54D4D5 Hemophilus influenza 1\n",
"FF528500-5274-4225-96C2-CF1153EE3AB0 Other 1\n",
"FF6CD7E8-8956-4C15-AF6C-3033A38C48D7 Influenza A 1\n",
" Staphylococcus epidermidis 1\n",
"dtype: int64"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu.groupby('PatientID')['OrganismName'].value_counts()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create indictors for coinfection type"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"for org in flu.Type.unique():\n",
" flu[org] = (flu.Type==org).astype(int)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create data frame of unique patients"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_unique = flu.drop_duplicates(subset=['PatientID']).set_index('PatientID')"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"100"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.s_aureus_icd9.sum()"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_unique['flu_only'] = flu_only"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.34159613059250304"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.flu_only.mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Several missing values for admission to time on ECMO"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.16686819830713423"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.AdmitToTimeOnHours.isnull().mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create variables for use in analysis"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# ECMO Type\n",
"flu_unique['VA'] = flu_unique.Mode.isin(['VA', 'VV-VA'])\n",
"# Set \"Other\" type to NA (there are only a couple)\n",
"flu_unique.loc[flu_unique.Mode=='Other', 'VA'] = None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create oxygen index"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_unique['OI'] = flu_unique.FiO2 * flu_unique.MAP / flu_unique.PO2"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10dbac6a0>"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
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"ZRwkEvTArK4AAAAASUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10dbac1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"flu_unique.OI.hist(bins=20)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"covariates = ['AgeYears', 'pH', 'PO2', 'VA']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get counts of missing values"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"AgeYears 0.000000\n",
"pH 0.107618\n",
"PO2 0.091898\n",
"VA 0.010883\n",
"dtype: float64"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique[covariates].isnull().mean()"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"RU5ErkJggg==\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10dd8bc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"flu_unique[covariates].hist(bins=25);"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10dbc1e80>"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"QmCC\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10e243940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"flu_unique[flu_unique.AgeYears< 1].AgeDays.hist(bins=15)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"100"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.s_aureus_icd9.sum()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"244"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(flu_unique.flu_staph_org | flu_unique.s_aureus_icd9).sum()"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"flu_staph_org False\n",
"s_aureus_icd9 True\n",
"Name: 01AC9644-7CDF-4E28-A5F4-FE5B7F9FA22A, dtype: object"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"foo = '01AC9644-7CDF-4E28-A5F4-FE5B7F9FA22A'\n",
"flu_unique.ix[foo][['flu_staph_org', 's_aureus_icd9']]"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_unique['flu_staph'] = (flu_unique.flu_staph_org | flu_unique.s_aureus_icd9).astype(int)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"flu_unique.to_csv('Data/flu_unique.csv')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Logistic regression model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fate of each patient"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"died = (flu_unique.fate=='Died').astype(int).values"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"N_obs = len(died)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Functions for standarizing and centering"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"center = lambda x: (x - x[np.isnan(x) ^ True].mean())\n",
"standardize = lambda x: center(x) / x[np.isnan(x) ^ True].std()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['AgeYears', 'pH', 'PO2', 'VA']"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"covariates"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"AgeYears, pH, PO2, va = flu_unique[covariates].values.T\n",
"\n",
"AgeYears_center = center(AgeYears).round(1)\n",
"\n",
"# Center pH at 7.4\n",
"pH_center = pH - 7.4\n",
"\n",
"# OI_std = standardize(OI)\n",
"# PO2_std = standardize(PO2)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"no_coinfection = flu_unique.flu_only.values\n",
"with_staph = flu_unique.flu_staph.values"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"244"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.flu_staph.sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from pymc import MCMC, Normal, Poisson, Uniform, Lambda, Laplace, Exponential, Beta, HalfCauchy, Uninformative\n",
"from pymc import Bernoulli, Lognormal, observed, Matplot, deterministic, Gamma, stochastic\n",
"from pymc import AdaptiveMetropolis, normal_like, rnormal, potential, invlogit\n",
"from pymc.gp import *"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Values for missing elements, to be replaced in model\n",
"# OI_std[np.isnan(OI_std)] = 0\n",
"pH_center[np.isnan(pH_center)] = 7.111\n",
"va[np.isnan(va)] = 0.5\n",
"PO2[np.isnan(PO2)] = 20.111"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def spline(name, x, knots, smoothing, interpolation_method='linear', pred_points=10):\n",
" \"\"\" Generate PyMC objects for a spline model of age-specific rate\n",
"\n",
" Parameters\n",
" ----------\n",
" name : str\n",
" knots : array\n",
" x : array, points to interpolate to\n",
" smoothing : pymc.Node, smoothness parameter for smoothing spline\n",
" interpolation_method : str, optional, one of 'linear', 'nearest', 'zero', 'slinear', 'quadratic, 'cubic'\n",
"\n",
" Results\n",
" -------\n",
" Returns dict of PyMC objects, including 'gamma' (log of rate at\n",
" knots) and 'mu_age' (age-specific rate interpolated at all age\n",
" points)\n",
" \"\"\"\n",
" assert np.all(np.diff(knots) > 0), 'Spline knots must be strictly increasing'\n",
"\n",
" # TODO: consider changing this prior distribution to be something more familiar in linear space\n",
" gamma = [Normal('gamma_%s_%d'%(name,k), 0., 10.**-2, value=0.) for k in knots]\n",
" #gamma = [mc.Uniform('gamma_%s_%d'%(name,k), -20., 20., value=-10.) for k in knots]\n",
"\n",
" import scipy.interpolate\n",
" @deterministic(name='mu_x_%s'%name)\n",
" def mu_x(gamma=gamma, knots=knots, x=x):\n",
" mu = scipy.interpolate.interp1d(knots, np.exp(gamma), kind=interpolation_method, \n",
" bounds_error=False, fill_value=0.)\n",
" return mu(x)\n",
" \n",
" @deterministic(name='pred_%s'%name)\n",
" def pred(gamma=gamma, knots=knots):\n",
" mu = scipy.interpolate.interp1d(knots, np.exp(gamma), kind=interpolation_method, \n",
" bounds_error=False, fill_value=0.)\n",
" return mu(np.linspace(x.min(), x.max(), pred_points))\n",
"\n",
" vars = dict(gamma=gamma, mu_x=mu_x, pred=pred, x=x, knots=knots)\n",
"\n",
" if (smoothing > 0) and (smoothing < 1e10):\n",
" #print 'adding smoothing of', smoothing\n",
" @potential(name='smooth_mu_%s'%name)\n",
" def smooth_gamma(gamma=gamma, knots=knots, tau=smoothing**-2):\n",
" # the following is to include a \"noise floor\" so that level value\n",
" # zero prior does not exert undue influence on age pattern\n",
" # smoothing\n",
" # TODO: consider changing this to an offset log normal\n",
" gamma = np.clip(gamma, np.log(np.exp(gamma).mean()/10.), np.inf) # only include smoothing on values within 10x of mean\n",
"\n",
" return normal_like(np.sqrt(np.sum(np.diff(gamma)**2 / np.diff(knots))), 0, tau)\n",
" vars['smooth_gamma'] = smooth_gamma\n",
"\n",
" return vars"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"58.167999999999999"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.mean(PO2)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 500., 886., 182., 25., 16., 11., 9., 5., 5.,\n",
" 2., 3., 1., 1., 0., 3., 0., 2., 2.,\n",
" 0., 1.]),\n",
" array([ -76. , -40.85, -5.7 , 29.45, 64.6 , 99.75, 134.9 ,\n",
" 170.05, 205.2 , 240.35, 275.5 , 310.65, 345.8 , 380.95,\n",
" 416.1 , 451.25, 486.4 , 521.55, 556.7 , 591.85, 627. ]),\n",
" <a list of 20 Patch objects>)"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10e319f60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(PO2-80, bins=20)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def survival_model(age_mask, n_knots=5):\n",
"\n",
" # Imputation of missing values\n",
" p_va = Beta('p_VA', 1, 1, value=0.5)\n",
" va_masked = np.ma.masked_values(va[age_mask], value=0.5)\n",
" x_va = Bernoulli('x_va', p_va, value=va_masked, observed=True)\n",
" \n",
" mu_pH = Normal('mu_pH', 0, 0.0001, value=7)\n",
" sigma_pH = Uniform('sigma_pH', 0, 500, value=10)\n",
" tau_pH = sigma_pH**-2\n",
" pH_masked = np.ma.masked_values(pH_center[age_mask], value=7.111)\n",
" x_pH = Normal('x_pH', mu_pH, tau_pH, value=pH_masked, observed=True)\n",
" \n",
" alpha_PO2 = Exponential('alpha_PO2', 100, value=0.5)\n",
" beta_PO2 = Exponential('beta_PO2', 100, value=200)\n",
" PO2_masked = np.ma.masked_values(PO2[age_mask], value=20.111)\n",
" x_PO2 = Gamma('x_PO2', alpha_PO2, beta_PO2, value=PO2_masked, observed=True)\n",
" x_PO2_std = Lambda('x_PO2_std', lambda x=x_PO2: (x - 80)/np.std(x))\n",
"\n",
" X = [x_pH, x_PO2_std, x_va, flu_unique.flu_only.values[age_mask], flu_unique.flu_staph.values[age_mask]]\n",
" \n",
" # Intercept for survival rate\n",
" beta0 = Normal('beta0', 0.0, 0.001, value=0)\n",
" # Covariates\n",
" beta = Normal('beta', 0, 0.001, value=np.zeros(len(X)))\n",
" \n",
" odds = Lambda('odds', lambda b=beta: np.exp(b))\n",
"\n",
" if AgeYears[age_mask].max()>1:\n",
" age_knots = np.linspace(AgeYears_center[age_mask].min(), AgeYears_center[age_mask].max(), n_knots)\n",
" α_age = Exponential('α_age', 1, value=0.1)\n",
" spline_age = spline('spline_age', AgeYears_center[age_mask], age_knots, α_age)\n",
"\n",
" # Event rates\n",
" @deterministic\n",
" def π(b0=beta0, b=beta, x=X, γ=spline_age['mu_x']):\n",
" return invlogit(b0 + np.dot(np.transpose(x), b) + γ)\n",
" \n",
" else:\n",
" # Event rates\n",
" @deterministic\n",
" def π(b0=beta0, b=beta, x=X):\n",
" return invlogit(b0 + np.dot(np.transpose(x), b))\n",
" \n",
" deaths = Bernoulli('deaths', π, value=died[age_mask], observed=True)\n",
" \n",
" return locals()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Adults model"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"adult_mask = AgeYears>=18"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"M_adult = MCMC(survival_model(adult_mask))"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 100000 of 100000 complete in 332.3 sec"
]
}
],
"source": [
"M_adult.sample(100000, 90000)"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cov_labels = ['pH', 'PO2', 'VA', 'flu only', 'flu + staph']"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x1203e8860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_adult.odds, custom_labels=cov_labels, hpd=False, vline_pos=1)"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"odds:\n",
" \n",
"\tMean SD MC Error 95% HPD interval\n",
"\t------------------------------------------------------------------\n",
"\t0.086 0.038 0.003 [ 0.029 0.162]\n",
"\t0.927 0.069 0.003 [ 0.795 1.065]\n",
"\t2.825 0.588 0.036 [ 1.795 4.004]\n",
"\t1.002 0.151 0.008 [ 0.722 1.295]\n",
"\t1.069 0.22 0.012 [ 0.625 1.472]\n",
"\t\n",
"\t\n",
"\tPosterior quantiles:\n",
"\t\n",
"\t2.5 25 50 75 97.5\n",
"\t |---------------|===============|===============|---------------|\n",
"\t0.034 0.056 0.078 0.106 0.18\n",
"\t0.789 0.88 0.927 0.974 1.06\n",
"\t1.894 2.4 2.759 3.173 4.191\n",
"\t0.734 0.896 0.993 1.1 1.322\n",
"\t0.68 0.916 1.05 1.206 1.55\n",
"\t\n"
]
}
],
"source": [
"M_adult.odds.summary()"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x12026cc88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_adult.__dict__['spline_age']['pred'], \n",
" custom_labels=np.linspace(AgeYears[adult_mask].min(), AgeYears[adult_mask].max(), 10).round(1).astype(str),\n",
" xlab='Effect size', main='Age effect')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Child model"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 100000 of 100000 complete in 253.8 sec"
]
}
],
"source": [
"child_mask = (AgeYears>=1) & (AgeYears<18)\n",
"\n",
"M_child = MCMC(survival_model(child_mask))\n",
"M_child.sample(100000, 90000)"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
]
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x1203e8e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_child.odds, custom_labels=cov_labels, \n",
" hpd=False, vline_pos=1)"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
]
},
{
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"AAAASUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10df470f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_child.__dict__['spline_age']['pred'], \n",
" custom_labels=np.linspace(AgeYears[child_mask].min(), AgeYears[child_mask].max(), 10).round(1).astype(str),\n",
" xlab='Effect size', main='Age effect')"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"odds:\n",
" \n",
"\tMean SD MC Error 95% HPD interval\n",
"\t------------------------------------------------------------------\n",
"\t0.554 0.369 0.029 [ 0.068 1.244]\n",
"\t0.857 0.108 0.004 [ 0.653 1.075]\n",
"\t1.525 0.331 0.018 [ 0.888 2.138]\n",
"\t0.947 0.226 0.011 [ 0.549 1.435]\n",
"\t2.513 0.814 0.053 [ 1.173 4.082]\n",
"\t\n",
"\t\n",
"\tPosterior quantiles:\n",
"\t\n",
"\t2.5 25 50 75 97.5\n",
"\t |---------------|===============|===============|---------------|\n",
"\t0.152 0.319 0.458 0.687 1.548\n",
"\t0.653 0.784 0.855 0.927 1.078\n",
"\t0.997 1.3 1.485 1.715 2.33\n",
"\t0.57 0.788 0.922 1.077 1.476\n",
"\t1.311 1.956 2.378 2.904 4.526\n",
"\t\n"
]
}
],
"source": [
"M_child.odds.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Infant model"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 100000 of 100000 complete in 57.5 sec"
]
}
],
"source": [
"infant_mask = (AgeYears<1)\n",
"\n",
"M_infant = MCMC(survival_model(infant_mask))\n",
"M_infant.sample(100000, 90000)"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10e211390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_infant.odds, custom_labels=cov_labels, hpd=False, vline_pos=1)"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"odds:\n",
" \n",
"\tMean SD MC Error 95% HPD interval\n",
"\t------------------------------------------------------------------\n",
"\t1.344 2.017 0.134 [ 0.034 4.176]\n",
"\t1.128 0.246 0.013 [ 0.67 1.624]\n",
"\t3.313 1.821 0.133 [ 0.833 6.437]\n",
"\t1.599 0.63 0.034 [ 0.606 2.866]\n",
"\t5.411 4.469 0.333 [ 0.509 14.367]\n",
"\t\n",
"\t\n",
"\tPosterior quantiles:\n",
"\t\n",
"\t2.5 25 50 75 97.5\n",
"\t |---------------|===============|===============|---------------|\n",
"\t0.093 0.409 0.784 1.461 6.261\n",
"\t0.725 0.959 1.092 1.262 1.719\n",
"\t1.247 2.144 2.837 4.017 7.654\n",
"\t0.739 1.153 1.486 1.871 3.276\n",
"\t1.169 2.625 4.044 6.681 19.302\n",
"\t\n"
]
}
],
"source": [
"M_infant.odds.summary()"
]
}
],
"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": "3.4.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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