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fonnesbeck/ELSO Survival.ipynb

Created May 21, 2015 20:55
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ELSO Survival.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": [
"(1450, 61)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu.shape"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(922,)"
]
},
"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",
"0034181F-59AB-4B2C-A06A-A83EE1DF1A17 True\n",
"0084E706-90D0-4314-8C99-496171AB639D True\n",
"00EFD11D-650A-4317-8C4F-4B7378AD7946 False\n",
"0118B486-8ACE-4BFF-8ED6-753D96E6B441 True\n",
"014A4039-B817-4E96-9FB0-7034F341505B False\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": false
},
"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'"
]
},
{
"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": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.10845986984815618"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_staph_organism.mean()"
]
},
{
"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": 13,
"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": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_other.name = 'flu_other'"
]
},
{
"cell_type": "code",
"execution_count": 15,
"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": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(flu_other & flu.s_aureus_icd9).sum()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(flu_only & flu.s_aureus_icd9).sum()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"PatientID \n",
"0034181F-59AB-4B2C-A06A-A83EE1DF1A17 Influenza A 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",
"02C9FF5A-A4D6-461A-A650-E3EB405D62AE Influenza A 2\n",
"031C1231-B585-478F-A98F-35E017B788CD Other 2\n",
"035A053E-91B1-4B68-87D4-F92C675FE6E3 Other 2\n",
"03AA4AD0-1B0E-4CAD-BD76-03FE52AA580D Staphylococcus, coag neg 1\n",
" Epstein-Barr virus (EBV) 1\n",
" Hemophilus parainfluenzae 1\n",
" Influenza A 1\n",
" Pneumocystis carinii 1\n",
"03FA6416-FE28-484B-AC83-60A7442035BE Influenza A 1\n",
"040710D1-2D29-48F4-B14C-ABAD7F2DC3B4 Influenza A 1\n",
"04B6544B-76BD-475E-83B4-782E2387093C Influenza A 1\n",
" Candida albicans 1\n",
"04BB440E-3A59-4453-8648-72AA1FB7CE22 Influenza A 1\n",
"057101E0-8C51-441B-AA05-B52D0092D820 Influenza A 1\n",
"0630B500-DDCD-4882-B3F2-D4B6DCD0DE59 Enterovirus 1\n",
"063CA301-7E8A-47EE-B8E3-6F01E734FEB7 Other 2\n",
"06522594-1B6F-492D-B47C-D94460052212 Influenza A 1\n",
"06799A45-93D6-4AAB-AA45-02DACB2C0D27 Influenza A 1\n",
"06AAFC52-B156-41FD-83C4-B2F6FC77E70A Acinetobacter sp. 3\n",
"07233E93-332D-4766-9696-A352A852856D Candida albicans 2\n",
"07ACDC42-6DCB-48D1-8458-F31097B95330 Influenza A 1\n",
" Streptococcus pneumoniae 1\n",
"07E15E96-706B-4DA1-899B-E5A9213FC864 Influenza A 1\n",
"07E64A9C-0C5D-4D56-AB4D-BDA56B8F7E2E Other 1\n",
" Candida albicans 1\n",
"081ABE0C-3969-496A-B9DA-42536D65299E Enterovirus 1\n",
" ..\n",
"F8C7118D-C465-4065-8C7D-3DDCE71F6D28 Candida parapsilosis 1\n",
"F9BD3113-6BA4-4417-815E-F7F26B0C3E52 Influenza A 1\n",
"F9C6E182-48BA-4424-903A-47B59957F1EF Influenza A 1\n",
"F9E79DA1-74ED-4036-ABD2-BB7E24684F36 Gram negative, other 1\n",
"F9EE26A2-5A7B-4CB1-8EC4-F56AED36A623 Other 2\n",
"FAD34086-3A25-4CC2-B1EC-D69FA130446B Influenza A 1\n",
"FAE1C068-87EA-4442-9493-13B1621DAE32 Influenza B 1\n",
"FAF53806-357F-4143-AC8C-7436C6A34D66 Influenza A 1\n",
" Staphylococcus aureus 1\n",
"FB45A43B-15A3-4F3C-8166-A94B1D943600 Other 2\n",
"FB6D570C-5150-448F-A0D7-F4D23B1D3A4A Other 2\n",
"FB995686-3063-4D23-AF6B-0E69BF18A09F Influenza A 1\n",
"FBCDE028-006C-4950-AB37-E1EB88590EEB Influenza A 1\n",
"FBD37823-BF97-4418-9733-778E8A917160 Other 2\n",
"FC9F84B4-B2CD-4C28-B824-D5CE1AF7BEF1 Gram positive, other 2\n",
" Other 1\n",
" Pseudomonas fluorescens 1\n",
" Candida albicans 1\n",
" Aspergillus fumigatus 1\n",
" Yeast sp. 1\n",
" Enterococcus 1\n",
" Stenotrophomonas maltophilia (Xanthomonas) 1\n",
"FCBAEC19-EFA1-4A95-A98D-1D8FE65B53CE Influenza A 1\n",
"FCD795A0-9FD1-4C20-961B-04BEF1B23E96 Influenza A 1\n",
" Staphylococcus aureus 1\n",
"FD2FA339-7417-4F13-811B-2E1873E529C7 Influenza A 1\n",
"FDC32D1D-0D67-4752-A2E1-72E790FCB797 Influenza A 1\n",
" Pseudomonas aerugenosa 1\n",
"FF0FB831-9804-4506-AE0B-B447AB54D4D5 Hemophilus influenza 1\n",
"FF528500-5274-4225-96C2-CF1153EE3AB0 Other 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": [],
"source": [
"flu_unique['flu_only'] = flu_only"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.35791757049891543"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.flu_only.mean()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.10845986984815618"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.flu_staph.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": [
"0.13665943600867678"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.AdmitToTimeOnHours.isnull().mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we need this field to calculate event time, we will have to drop individuals with missing values from the survival analysis."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_unique = flu_unique.dropna(subset=['AdmitToTimeOnHours', 'HoursECMO'])\n",
"assert not flu_unique.AdmitToTimeOnHours.isnull().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Add time from admission to time on ECMO to get total exposure time."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"admit_through_emco = flu_unique.AdmitToTimeOnHours.add(flu_unique.HoursECMO)\n",
"flu_unique['admit_through_emco'] = admit_through_emco"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See how many have no time information from admission, and drop these"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"missing = admit_through_emco.isnull()\n",
"flu_complete = flu_unique[missing ^ True]\n",
"admit_through_emco.dropna(inplace=True)\n",
"assert not admit_through_emco.isnull().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Time to event\n",
"\n",
"Time off ECMO through to event (death or discharge). Fill with zeros for `TimeOffToDeathDateHours`, implying censoring."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"45"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_unique.TimeOffToDCDateHours.add(flu_unique.TimeOffToDeathDateHours, fill_value=0).isnull().sum()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"off_ecmo_to_event = flu_complete.TimeOffToDCDateHours.add(flu_complete.TimeOffToDeathDateHours, \n",
" fill_value=0)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"45"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"off_ecmo_to_event.isnull().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Time to event is admit throught ecmo, plus off ecmo to event times."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_complete['time_to_event'] = admit_through_emco + off_ecmo_to_event.fillna(0)\n",
"assert not flu_complete.time_to_event.isnull().sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create variables for use in analysis"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# ECMO Type\n",
"flu_complete['VA'] = flu_complete.Mode.isin(['VA', 'VV-VA'])\n",
"# Set \"Other\" type to NA (there are only a couple)\n",
"flu_complete.loc[flu_complete.Mode=='Other', 'VA'] = None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create oxygen index"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Index([ 'PatientID', 'RunNo',\n",
" 'AgeDays', 'HoursECMO',\n",
" 'SupportType', 'PrimaryDx',\n",
" 'Mode', 'Discontinuation',\n",
" 'DischargedAlive', 'DischargeLocation',\n",
" 'YearECLS', 'VentType',\n",
" 'Rate', 'FiO2',\n",
" 'PIP', 'PEEP',\n",
" 'MAP', 'HandBagging',\n",
" 'pH', 'PCO2',\n",
" 'PO2', 'HCO3',\n",
" 'SaO2', 'Venttype24',\n",
" 'Rate24', 'Fio224',\n",
" 'PIP24', 'PEEP24',\n",
" 'MAP24', 'Handbagging24',\n",
" 'SBP', 'DBP',\n",
" 'MapHemo', 'SVO2',\n",
" 'PCWP', 'SPAP',\n",
" 'DPAP', 'MPAP',\n",
" 'CI', 'Race',\n",
" 'Sex', 'AdmitToTimeOnHours',\n",
" 'TimeOffToExtubationDateHours', 'TimeOffToDeathDateHours',\n",
" 'TimeOffToDCDateHours', 'ExtubationToDCDateHours',\n",
" 'ExtubationToDeathDateHours', 'year',\n",
" 'HoursVent', 'AgeYears',\n",
" 'age_class', 'RunID',\n",
" 'OrganismNo', 'OrganismName',\n",
" 'CultureSite', 'CultureTimeIsApproximate',\n",
" 'OrganismTiming', 'Type',\n",
" 'has_flu', 'fate',\n",
" 's_aureus_icd9', 'flu_only',\n",
" 'flu_staph', 'flu_other',\n",
" 'viral', 'bacterial',\n",
" nan, 'fungal'],\n",
" dtype='object')"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu.columns"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"flu_complete['OI'] = flu_complete.FiO2 * flu_complete.MAP / flu_complete.PO2"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10a3b3390>"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x109f75828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"flu_complete.OI.hist(bins=20)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"covariates = ['AgeYears', 'pH', 'OI', 'VA']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get counts of missing values"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"AgeYears 0.000000\n",
"pH 0.073140\n",
"OI 0.407314\n",
"VA 0.016393\n",
"dtype: float64"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"flu_complete[covariates].isnull().mean()"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"YII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10a6af978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"flu_complete[covariates].hist(bins=25);"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10ab7ad68>"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10aba2e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"flu_complete[flu_complete.AgeYears< 1].AgeDays.hist(bins=15)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Survival Model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Surivival time, in days"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"obs_t = flu_complete.time_to_event.values/24."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10ac4ea58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(obs_t, bins=25);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fate of each patient"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"died = (flu_complete.fate=='Died').astype(int).values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Unique failure times"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
" 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,\n",
" 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,\n",
" 39, 40, 41, 43, 44, 45, 46, 47, 48, 50, 53, 54, 55,\n",
" 59, 61, 62, 63, 67, 68, 73, 77, 108, 121, 124, 125, 126,\n",
" 133, 142, 150, 201, 227, 235])"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"times = np.unique((flu_complete.time_to_event[flu_complete.fate=='Died'].values/24).astype(int))\n",
"times"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"N_obs = len(obs_t)\n",
"T = len(times) - 1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate risk set (the number at risk at each event time)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[1, 1, 1, ..., 0, 0, 0],\n",
" [1, 1, 1, ..., 0, 0, 0],\n",
" [1, 1, 1, ..., 0, 0, 0],\n",
" ..., \n",
" [1, 1, 1, ..., 0, 0, 0],\n",
" [1, 1, 1, ..., 0, 0, 0],\n",
" [1, 1, 1, ..., 0, 0, 0]])"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Y = np.array([[int(obs >= t) for t in times] for obs in obs_t])\n",
"Y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Counting process. Jump = 1 if $\\text{obs}_t \\in [ t_j, t_{j+1} )$"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"dN = np.array([[Y[i,j]*(times[j+1] >= obs_t[i])*died[i] for i in range(N_obs)] for j in range(T)])"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,\n",
" 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
" 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
" 0])"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Sample process for one patient\n",
"dN[:,np.random.randint(len(dN))]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Functions for standarizing and centering"
]
},
{
"cell_type": "code",
"execution_count": 52,
"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": 53,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['AgeYears', 'pH', 'OI', 'VA']"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"covariates"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"AgeYears, pH, OI, va = flu_complete[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)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Survival curves"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"CadssCXLTwAAAABJRU5ErkJggg==\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10a6b3240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from lifelines import KaplanMeierFitter\n",
"\n",
"km = KaplanMeierFitter()\n",
"km.fit(obs_t, event_observed=died)\n",
"ax = km.plot()"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"flu_only_ind = flu_complete.flu_only.values\n",
"flu_staph_ind = flu_complete.flu_staph.values\n",
"flu_other_ind = flu_complete.flu_other.values"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10af54668>"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10aee68d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"km = KaplanMeierFitter()\n",
"km.fit(obs_t[flu_staph_ind], event_observed=died[flu_staph_ind], label='flu+staph')\n",
"ax = km.plot()\n",
"\n",
"km.fit(obs_t[flu_only_ind], event_observed=died[flu_only_ind], label='flu only')\n",
"km.plot(ax=ax)\n",
"\n",
"km.fit(obs_t[flu_other_ind], event_observed=died[flu_other_ind], label='flu+other')\n",
"km.plot(ax=ax)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"age_complete = flu_complete.AgeYears.values\n",
"infant_ind = age_complete<1\n",
"kids_ind = (age_complete>=1) & (age_complete<19)\n",
"adult_ind = age_complete>=19"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10ac7f6a0>"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10adbc390>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"km = KaplanMeierFitter()\n",
"km.fit(obs_t[infant_ind], event_observed=died[infant_ind], label='infants')\n",
"ax = km.plot()\n",
"\n",
"km.fit(obs_t[kids_ind], event_observed=died[kids_ind], label='children')\n",
"km.plot(ax=ax)\n",
"\n",
"km.fit(obs_t[adult_ind], event_observed=died[adult_ind], label='adults')\n",
"km.plot(ax=ax)"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"va_ind = flu_complete.VA.astype(bool).values"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x10ad96dd8>"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10aba22e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"km = KaplanMeierFitter()\n",
"km.fit(obs_t[va_ind], event_observed=died[va_ind], label='VA')\n",
"ax = km.plot()\n",
"\n",
"km.fit(obs_t[~va_ind], event_observed=died[~va_ind], label='VV')\n",
"km.plot(ax=ax)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model"
]
},
{
"cell_type": "code",
"execution_count": 95,
"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\n",
"from pymc.gp import *"
]
},
{
"cell_type": "code",
"execution_count": 96,
"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"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"gaussian_rbf = lambda x, mu, l: np.exp(-np.abs(x - mu)**2 / l**2)"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def rbf(name, x, n=10):\n",
" \n",
" # Number of basis functions for age effect\n",
" h = np.linspace(x.min(), x.max(), n)\n",
" l = HalfCauchy('l_%s' % name, 0, 5, value=1)\n",
" \n",
" # RBF weights for all the points, for all the functions\n",
" w = Lambda('w_%s' % name, lambda l=l: np.array([gaussian_rbf(i, h, l) for i in x]))\n",
" \n",
" τ = Exponential('τ_%s' % name, 1, value=np.ones(n))\n",
"\n",
" # Coefficients\n",
" β = Normal('β_%s' % name, 0, τ, value=np.zeros(n))\n",
" \n",
" τ_rbf = Exponential('τ_rbf_%s' % name, 1, value=1)\n",
" \n",
" @stochastic(name='rbf_%s' % name)\n",
" def rbf(value=np.zeros(len(x)), β=β, w=w, τ=τ_rbf):\n",
" m = w.dot(β)\n",
" return normal_like(value, m, τ)\n",
" \n",
" @deterministic(name='rbf_eval_%s' % name)\n",
" def rbf_eval(β=β, τ=τ_rbf, l=l):\n",
" \n",
" wts = np.array([gaussian_rbf(i, h, l) for i in h])\n",
" m = wts.dot(β)\n",
" return rnormal(m, τ)\n",
" \n",
" return locals()"
]
},
{
"cell_type": "code",
"execution_count": 134,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def spline(name, x, knots, smoothing, interpolation_method='linear'):\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",
" vars = dict(gamma=gamma, mu_x=mu_x, 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": 135,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def exponential_survival_model():\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, 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, value=7.111)\n",
" x_pH = Normal('x_pH', mu_pH, tau_pH, value=pH_masked, observed=True)\n",
" \n",
"# mu_OI = Normal('mu_OI', 0, 0.0001, value=0)\n",
"# sigma_OI = Uniform('sigma_OI', 0, 500, value=10)\n",
"# tau_OI = sigma_OI**-2\n",
"# OI_masked = np.ma.masked_values(OI_std, value=0)\n",
"# x_OI = Normal('x_OI', mu_OI, tau_OI, value=OI_masked, observed=True)\n",
" \n",
" X = [x_va, flu_unique.flu_only, flu_unique.flu_staph]\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",
" age_knots = np.linspace(AgeYears_center.min(), AgeYears_center.max(), 7)\n",
" α_age = Exponential('α_age', 1, value=0.1)\n",
" spline_age = spline('spline_age', AgeYears_center, age_knots, α_age)\n",
" \n",
" pH_knots = np.linspace(pH_center.min(), pH_center.max(), 7)\n",
" α_pH = Exponential('α_pH', 1, value=0.1)\n",
" spline_pH = spline('spline_pH', pH_center, pH_knots, α_pH)\n",
" \n",
" # Survival rates\n",
" @deterministic\n",
" def lam(b0=beta0, b=beta, x=X, γ=spline_age['mu_x'], ρ=spline_pH['mu_x']):\n",
" return np.exp(b0 + np.dot(np.transpose(x), b) + γ + ρ)\n",
"\n",
" @observed\n",
" def survival(value=obs_t, lam=lam, f=died):\n",
" \"\"\"Exponential survival likelihood, accounting for censoring\"\"\"\n",
" return (f*np.log(lam) - lam*value).sum()\n",
"\n",
" return locals()"
]
},
{
"cell_type": "code",
"execution_count": 136,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"M = MCMC(exponential_survival_model())"
]
},
{
"cell_type": "code",
"execution_count": 137,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"iterations = 50000\n",
"burn = 40000"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 50000 of 50000 complete in 453.6 sec"
]
}
],
"source": [
"M.sample(iterations, burn)"
]
},
{
"cell_type": "code",
"execution_count": 139,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 50000 of 50000 complete in 445.2 sec"
]
}
],
"source": [
"M.sample(iterations, burn)"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {
"collapsed": false
},
"outputs": [
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x117c34748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M.beta, custom_labels=['VA', 'flu only', 'flu + staph'], hpd=False)"
]
},
{
"cell_type": "code",
"execution_count": 141,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"iD0AAAAASUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x10af4d470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M.__dict__['spline_pH']['gamma'], \n",
" custom_labels=np.linspace(flu_unique.pH.dropna().min(), \n",
" flu_unique.pH.dropna().max(), 7).round(1).astype(str),\n",
" xlab='Effect size', main='pH effect')"
]
},
{
"cell_type": "code",
"execution_count": 142,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x117c26518>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M.__dict__['spline_age']['gamma'], \n",
" custom_labels=np.linspace(AgeYears.min(), AgeYears.max(), 7).round(1).astype(str),\n",
" xlab='Effect size', main='Age effect')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Same model above, but with a Weibull hazard function"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def weibull_survival_model():\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, 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, value=7.111)\n",
" x_pH = Normal('x_pH', mu_pH, tau_pH, value=pH_masked, observed=True)\n",
"\n",
" X = [x_va, flu_unique.flu_only, flu_unique.flu_staph]\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",
" age_knots = np.linspace(AgeYears_center.min(), AgeYears_center.max(), 7)\n",
" α_age = Exponential('α_age', 1, value=0.1)\n",
" spline_age = spline('spline_age', AgeYears_center, age_knots, α_age)\n",
" \n",
" pH_knots = np.linspace(pH_center.min(), pH_center.max(), 7)\n",
" α_pH = Exponential('α_pH', 1, value=0.1)\n",
" spline_pH = spline('spline_pH', pH_center, pH_knots, α_pH)\n",
" \n",
" # Survival rates\n",
" @deterministic\n",
" def lam(b0=beta0, b=beta, x=X, γ=spline_age['mu_x'], ρ=spline_pH['mu_x']):\n",
" return np.exp(b0 + np.dot(np.transpose(x), b) + γ + ρ)\n",
" \n",
" α = Exponential('α', 1, value=1)\n",
"\n",
" @observed\n",
" def survival(value=obs_t, lam=lam, f=died, α=α):\n",
" # Weibull survival log-likelihood\n",
" return (f*(np.log(α) + (α-1)*np.log(value*lam) + np.log(lam)) - (lam*value)**α).sum()\n",
"\n",
" return locals()"
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"W = MCMC(weibull_survival_model())"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [ 2% ] 1159 of 50000 complete in 11.1 secHalting at iteration 1170 of 50000\n"
]
}
],
"source": [
"W.sample(50000, 40000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cox model"
]
},
{
"cell_type": "code",
"execution_count": 162,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def cox_model():\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, 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, value=7.111)\n",
" x_pH = Normal('x_pH', mu_pH, tau_pH, value=pH_masked, observed=True)\n",
"\n",
" X = [x_va, flu_unique.flu_only, flu_unique.flu_staph]\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",
" age_knots = np.linspace(AgeYears_center.min(), AgeYears_center.max(), 7)\n",
" α_age = Exponential('α_age', 1, value=0.1)\n",
" spline_age = spline('spline_age', AgeYears_center, age_knots, α_age)\n",
" \n",
" pH_knots = np.linspace(pH_center.min(), pH_center.max(), 7)\n",
" α_pH = Exponential('α_pH', 1, value=0.1)\n",
" spline_pH = spline('spline_pH', pH_center, pH_knots, α_pH)\n",
" \n",
" c = Gamma('c', .0001, .00001, value=0.1)\n",
" r = Gamma('r', .001, .0001, value=0.1)\n",
" \n",
" dL0_star = Lambda('dL0_star', lambda r=r: r*np.diff(times))\n",
" \n",
" # prior mean hazard\n",
" mu = Lambda('mu', lambda dL0_star=dL0_star, c=c: dL0_star * c)\n",
" \n",
" dL0 = Gamma('dL0', mu, c, value=np.ones(T))\n",
" \n",
" @deterministic\n",
" def Idt(b0=beta0, b=beta, x=X, dL0=dL0, γ=spline_age['mu_x'], ρ=spline_pH['mu_x']): \n",
" # Poisson trick: independent log-normal hazard increments\n",
" Xb = np.exp(b0 + np.dot(np.transpose(x), b) + γ + ρ)\n",
" return np.transpose(Y[:,:-1] * np.outer(Xb, dL0))\n",
"# return [[Y[i,j]*Xb[i] for i in range(N_obs)] for j in range(T)]\n",
"\n",
" dN_like = Poisson('dN_like', Idt, value=dN, observed=True)\n",
" \n",
" return locals()"
]
},
{
"cell_type": "code",
"execution_count": 163,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"M_cox = MCMC(cox_model())"
]
},
{
"cell_type": "code",
"execution_count": 164,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 20000 of 20000 complete in 483.4 sec"
]
}
],
"source": [
"M_cox.sample(20000, 10000)"
]
},
{
"cell_type": "code",
"execution_count": 165,
"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 0x117a32b70>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_cox.beta, custom_labels=['VA', 'flu only', 'flu + staph'], hpd=False)"
]
},
{
"cell_type": "code",
"execution_count": 166,
"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 0x10a78d320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_cox.__dict__['spline_pH']['gamma'], \n",
" custom_labels=np.linspace(flu_unique.pH.dropna().min(), \n",
" flu_unique.pH.dropna().max(), 7).round(1).astype(str),\n",
" xlab='Effect size', main='pH effect')"
]
},
{
"cell_type": "code",
"execution_count": 167,
"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 0x10ab2f400>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Matplot.summary_plot(M_cox.__dict__['spline_age']['gamma'], \n",
" custom_labels=np.linspace(AgeYears.min(), AgeYears.max(), 7).round(1).astype(str),\n",
" xlab='Effect size', main='Age effect')"
]
}
],
"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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