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fonnesbeck/Diversity.ipynb

Created January 15, 2015 20:46
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Diversity.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import pandas as pd\n",
"import numpy as np\n",
"import pylab as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Shannon-Weiner index was developed from information theory and is based on measuring uncertainty. The degree of uncertainty of predicting the species of a random sample is related to the diversity of a community. If a community is dominated by one species (low diversity), the uncertainty of prediction is low; a randomly-sampled species is most likely going to be the dominant species. However, if diversity is high, uncertainty is high.\n",
"\n",
"$$H' = \\sum_i p_i \\log(p_i)$$\n",
"\n",
"This function calculates Shannon diversity:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Shannon index\n",
"shannon = lambda x: -np.sum([p*np.log(p) for p in x/float(sum(x)) if p])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Simpson index (1949) measures the degree of concentration when individuals are classified into types. It is based on the expected outcome of two random samples from the same community:\n",
"\n",
"$$D = \\frac{N(N-1)}{\\sum_i n_i (n_i-1)}$$\n",
"\n",
"This function calculates Simpson's index of diversity:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"simpsons = lambda x: sum(x)*(sum(x)-1)/np.sum([float(n-1)*n for n in x if n])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Genus-level diversity"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>level_0</th>\n",
" <th>Taxon</th>\n",
" <th>0</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> N3s</td>\n",
" <td> Bacteria;Acidobacteria;Acidobacteria_Gp16;Gp16...</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> N3s</td>\n",
" <td> Bacteria;Acidobacteria;Acidobacteria_Gp6;Gp6;O...</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> N3s</td>\n",
" <td> Bacteria;Actinobacteria;Actinobacteria;Acidimi...</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> N3s</td>\n",
" <td> Bacteria;Actinobacteria;Actinobacteria;Acidimi...</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> N3s</td>\n",
" <td> Bacteria;Actinobacteria;Actinobacteria;Actinom...</td>\n",
" <td> 0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" level_0 Taxon 0\n",
"0 N3s Bacteria;Acidobacteria;Acidobacteria_Gp16;Gp16... 0\n",
"1 N3s Bacteria;Acidobacteria;Acidobacteria_Gp6;Gp6;O... 0\n",
"2 N3s Bacteria;Actinobacteria;Actinobacteria;Acidimi... 0\n",
"3 N3s Bacteria;Actinobacteria;Actinobacteria;Acidimi... 0\n",
"4 N3s Bacteria;Actinobacteria;Actinobacteria;Actinom... 0"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"genus_raw = pd.read_excel('OTU.xlsx', 'L5', index_col=0).unstack().reset_index()\n",
"genus_raw.head()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"taxa = genus_raw.Taxon.unique()\n",
"taxa_dict = dict(zip(taxa, range(len(taxa))))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"genus_raw.Taxon.replace(taxa_dict, inplace=True)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"genus_raw['nec'] = genus_raw.level_0.apply(lambda x: x.startswith('N'))\n",
"genus_raw['stool'] = genus_raw.level_0.apply(lambda x: x.endswith('s'))\n",
"genus_raw['patient'] = genus_raw.level_0.apply(lambda x: int(''.join([s for s in x if s.isdigit()])))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"genus_data = genus_raw.drop('level_0', axis=1)\n",
"genus_data.columns = 'taxon', 'count', 'nec', 'stool', 'patient'"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>taxon</th>\n",
" <th>count</th>\n",
" <th>nec</th>\n",
" <th>stool</th>\n",
" <th>patient</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>16425</th>\n",
" <td> 305</td>\n",
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" <tr>\n",
" <th>16426</th>\n",
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],
"text/plain": [
" taxon count nec stool patient\n",
"16425 305 0 True False 2\n",
"16426 306 0 True False 2\n",
"16427 307 0 True False 2\n",
"16428 308 0 True False 2\n",
"16429 309 0 True False 2"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"genus_data.tail()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparison of tissue diversity in NEC vs control"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.4/site-packages/pandas/tools/plotting.py:2625: FutureWarning: \n",
"The default value for 'return_type' will change to 'axes' in a future release.\n",
" To use the future behavior now, set return_type='axes'.\n",
" To keep the previous behavior and silence this warning, set return_type='dict'.\n",
" warnings.warn(msg, FutureWarning)\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x1100ae0f0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tissue_data = genus_data[genus_data.stool==False]\n",
"simpsons_tissue = tissue_data.groupby(['patient', 'nec'])['count'].aggregate(simpsons)\n",
"simpsons_tissue.unstack().rename(columns={False: 'Control', True: 'NEC'}).boxplot(grid=False)\n",
"plt.ylabel('Simpson\\'s index');"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.4/site-packages/pandas/tools/plotting.py:2625: FutureWarning: \n",
"The default value for 'return_type' will change to 'axes' in a future release.\n",
" To use the future behavior now, set return_type='axes'.\n",
" To keep the previous behavior and silence this warning, set return_type='dict'.\n",
" warnings.warn(msg, FutureWarning)\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x110371748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"shannon_tissue = tissue_data.groupby(['patient', 'nec'])['count'].aggregate(shannon)\n",
"shannon_tissue.unstack().rename(columns={False: 'Control', True: 'NEC'}).boxplot(grid=False)\n",
"plt.ylabel('Shannon index');"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.4/site-packages/pandas/tools/plotting.py:2625: FutureWarning: \n",
"The default value for 'return_type' will change to 'axes' in a future release.\n",
" To use the future behavior now, set return_type='axes'.\n",
" To keep the previous behavior and silence this warning, set return_type='dict'.\n",
" warnings.warn(msg, FutureWarning)\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x110538358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Chao 1 index\n",
"chao = lambda x: len(x) + ((x==1).sum())**2/(2 * (x==2).sum())\n",
"\n",
"chao_tissue = tissue_data.groupby(['patient', 'nec'])['count'].aggregate(chao)\n",
"chao_tissue.unstack().rename(columns={False: 'Control', True: 'NEC'}).boxplot(grid=False)\n",
"plt.ylabel('Chao index');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparison of stool diversity in NEC vs control"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.4/site-packages/pandas/tools/plotting.py:2625: FutureWarning: \n",
"The default value for 'return_type' will change to 'axes' in a future release.\n",
" To use the future behavior now, set return_type='axes'.\n",
" To keep the previous behavior and silence this warning, set return_type='dict'.\n",
" warnings.warn(msg, FutureWarning)\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x110681fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"stool_data = genus_data[genus_data.stool==True]\n",
"\n",
"simpsons_stool = stool_data.groupby(['patient', 'nec'])['count'].aggregate(simpsons)\n",
"simpsons_stool.unstack().rename(columns={False: 'Control', True: 'NEC'}).boxplot(grid=False)\n",
"plt.ylabel('Simpson\\'s index');"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.4/site-packages/pandas/tools/plotting.py:2625: FutureWarning: \n",
"The default value for 'return_type' will change to 'axes' in a future release.\n",
" To use the future behavior now, set return_type='axes'.\n",
" To keep the previous behavior and silence this warning, set return_type='dict'.\n",
" warnings.warn(msg, FutureWarning)\n"
]
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x10fece550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"shannon_stool = stool_data.groupby(['patient', 'nec'])['count'].aggregate(shannon)\n",
"shannon_stool.unstack().rename(columns={False: 'Control', True: 'NEC'}).boxplot(grid=False)\n",
"plt.ylabel('Shannon index');"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.4/site-packages/pandas/tools/plotting.py:2625: FutureWarning: \n",
"The default value for 'return_type' will change to 'axes' in a future release.\n",
" To use the future behavior now, set return_type='axes'.\n",
" To keep the previous behavior and silence this warning, set return_type='dict'.\n",
" warnings.warn(msg, FutureWarning)\n"
]
},
{
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"TeMSGIEAAAAASUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x11036e470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"chao_stool = stool_data.groupby(['patient', 'nec'])['count'].aggregate(chao)\n",
"chao_stool.unstack().rename(columns={False: 'Control', True: 'NEC'}).boxplot(grid=False)\n",
"plt.ylabel('Chao index');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Line plots of tissue vs stool diversity in NEC samples"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>stool</th>\n",
" <th>Tissue</th>\n",
" <th>Stool</th>\n",
" </tr>\n",
" <tr>\n",
" <th>patient</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1 </th>\n",
" <td> 3.186187</td>\n",
" <td> 2.501635</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2 </th>\n",
" <td> 1.145031</td>\n",
" <td> 1.240411</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3 </th>\n",
" <td> 13.310545</td>\n",
" <td> 1.860451</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4 </th>\n",
" <td> 4.025034</td>\n",
" <td> 2.144758</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5 </th>\n",
" <td> 3.065582</td>\n",
" <td> 3.627015</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7 </th>\n",
" <td> 1.052006</td>\n",
" <td> 1.123837</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8 </th>\n",
" <td> 9.209903</td>\n",
" <td> 3.456548</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9 </th>\n",
" <td> 2.006315</td>\n",
" <td> 1.995825</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td> 2.105499</td>\n",
" <td> 1.054506</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td> 2.077362</td>\n",
" <td> 3.399880</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"stool Tissue Stool\n",
"patient \n",
"1 3.186187 2.501635\n",
"2 1.145031 1.240411\n",
"3 13.310545 1.860451\n",
"4 4.025034 2.144758\n",
"5 3.065582 3.627015\n",
"7 1.052006 1.123837\n",
"8 9.209903 3.456548\n",
"9 2.006315 1.995825\n",
"10 2.105499 1.054506\n",
"11 2.077362 3.399880"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simpsons_nec = genus_data[genus_data.nec==True].groupby(['patient','stool'])['count'].aggregate(simpsons)\n",
"simpsons_nec.unstack().rename(columns={False: 'Tissue', True: 'Stool'}).dropna()"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"22"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"len(simpsons_nec)"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_bipartite(data, label):\n",
" axes = data.unstack().rename(columns={False: 'Tissue', True: 'Stool'}).dropna().T.plot(grid=False, \n",
" color='k', \n",
" style='.-',\n",
" legend=False)\n",
" axes.set_xlim(-0.1, 1.1)\n",
" axes.set_xticks([0,1])\n",
" axes.set_xticklabels(['Tissue', 'Stool'])\n",
" axes.set_ylabel(label)\n",
" axes.set_xlabel('')"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x110a6bf28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_bipartite(simpsons_nec, 'Simpson\\'s index')"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>stool</th>\n",
" <th>Tissue</th>\n",
" <th>Stool</th>\n",
" </tr>\n",
" <tr>\n",
" <th>patient</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1 </th>\n",
" <td> 1.553132</td>\n",
" <td> 1.148086</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2 </th>\n",
" <td> 0.370677</td>\n",
" <td> 0.431641</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3 </th>\n",
" <td> 3.026228</td>\n",
" <td> 1.194941</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4 </th>\n",
" <td> 1.942193</td>\n",
" <td> 0.907746</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5 </th>\n",
" <td> 1.983316</td>\n",
" <td> 1.532137</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7 </th>\n",
" <td> 0.150379</td>\n",
" <td> 0.266457</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8 </th>\n",
" <td> 2.678588</td>\n",
" <td> 1.609806</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9 </th>\n",
" <td> 0.787423</td>\n",
" <td> 1.099322</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td> 0.875270</td>\n",
" <td> 0.125509</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td> 0.988443</td>\n",
" <td> 1.674464</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"stool Tissue Stool\n",
"patient \n",
"1 1.553132 1.148086\n",
"2 0.370677 0.431641\n",
"3 3.026228 1.194941\n",
"4 1.942193 0.907746\n",
"5 1.983316 1.532137\n",
"7 0.150379 0.266457\n",
"8 2.678588 1.609806\n",
"9 0.787423 1.099322\n",
"10 0.875270 0.125509\n",
"11 0.988443 1.674464"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"shannon_nec = genus_data[genus_data.nec==True].groupby(['patient','stool'])['count'].aggregate(shannon)\n",
"shannon_nec.unstack().rename(columns={False: 'Tissue', True: 'Stool'}).dropna()"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"SUVORK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x110b5cd30>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_bipartite(shannon_nec, 'Shannon index')"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>stool</th>\n",
" <th>Tissue</th>\n",
" <th>Stool</th>\n",
" </tr>\n",
" <tr>\n",
" <th>patient</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1 </th>\n",
" <td> 324.000000</td>\n",
" <td> inf</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2 </th>\n",
" <td> 314.166667</td>\n",
" <td> 342.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3 </th>\n",
" <td> 340.250000</td>\n",
" <td> 320.285714</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4 </th>\n",
" <td> 322.500000</td>\n",
" <td> 350.500000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5 </th>\n",
" <td> 322.500000</td>\n",
" <td> 311.125000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7 </th>\n",
" <td> inf</td>\n",
" <td> 314.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8 </th>\n",
" <td> 347.785714</td>\n",
" <td> 322.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9 </th>\n",
" <td> 314.166667</td>\n",
" <td> 318.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td> 334.500000</td>\n",
" <td> 310.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td> 314.000000</td>\n",
" <td> 656.125000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"stool Tissue Stool\n",
"patient \n",
"1 324.000000 inf\n",
"2 314.166667 342.000000\n",
"3 340.250000 320.285714\n",
"4 322.500000 350.500000\n",
"5 322.500000 311.125000\n",
"7 inf 314.000000\n",
"8 347.785714 322.000000\n",
"9 314.166667 318.000000\n",
"10 334.500000 310.000000\n",
"11 314.000000 656.125000"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chao_nec = genus_data[genus_data.nec==True].groupby(['patient','stool'])['count'].aggregate(chao)\n",
"chao_nec.unstack().rename(columns={False: 'Tissue', True: 'Stool'}).dropna()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Chao was very unstable, so I am not attempting to generate a graph."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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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