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HW3_ROC
{
"cells": [
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"from scipy.stats import lognorm\n",
"from scipy.integrate import quad as integrate\n",
"from sklearn.metrics import auc\n",
"exp = np.exp\n",
"from collections import defaultdict\n",
"\n",
"pd.options.display.max_columns = 50\n",
"pd.options.display.max_rows = 30\n",
"\n",
"from ipywidgets import interact, interactive, fixed, interact_manual\n",
"import ipywidgets as widgets"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Generate two such histograms, one representing the signal for a wild-type starting clone, and one representing a desired higher-affinity clone (with higher mean MFI but same standard deviation). The two parameters to choose are the ratio of the mutant to wild-type mean MFI, and the standard deviation applied to both curves. You can explore variations in each of these parameters in the next step."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Construct an ROC curve by varying the cutoff MFI threshold for retention across the full range of values used in (1). "
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"wt_color = 'blue'\n",
"dc_color = 'orange'\n",
"size = 200\n",
"μ_1 = 1.0"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def tpr_fpr(cutoff, negative, positive, size=size):\n",
" \n",
" true_negative = sum(negative <= cutoff)\n",
" false_positive = size - true_negative\n",
" \n",
" true_positive = sum(positive >= cutoff)\n",
" false_negative = size - true_positive\n",
" \n",
" tpr = true_positive / (true_positive + false_negative)\n",
" fpr = false_positive / (true_negative + false_positive)\n",
"\n",
" return tpr, fpr"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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"model_id": "ad923cbe304b4795a527953488cfbb1a",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"interactive(children=(FloatSlider(value=0.5, description='μ_ratio', max=1.0, step=0.01), FloatSlider(value=0.2…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"@interact(μ_ratio=(0.0,1.0,0.01), σ=(0.0,1.0,0.01))\n",
"def ROC_analysis(μ_ratio=0.5, σ=0.2):\n",
" \n",
" μ_2 = μ_1 + μ_ratio # addition, because exponentiating these means multiplication. \n",
" σ_2 = σ_1 = σ\n",
"\n",
" wt_dist = lognorm(σ_1, scale=exp(μ_1))\n",
" dc_dist = lognorm(σ_2, scale=exp(μ_2))\n",
" wt = pd.Series(wt_dist.rvs(size=size))\n",
" dc = pd.Series(dc_dist.rvs(size=size))\n",
" \n",
" mn = np.min([wt.min(), dc.min()])\n",
" mx = np.max([wt.max(), dc.max()])\n",
" bins = np.linspace(mn, mx, num=50)\n",
" logbins = np.geomspace(mn, mx, num=50)\n",
" \n",
" fig = plt.figure(figsize=(10, 7), dpi=140)\n",
" grid = plt.GridSpec(2, 3, wspace=0.4, hspace=0.3)\n",
" top = plt.subplot(grid[0, 0:])\n",
" bottom_left = plt.subplot(grid[1, :2])\n",
" bottom_right = plt.subplot(grid[1, 2:])\n",
"\n",
" top.set_title('linear x', size='x-large')\n",
" wt.plot.hist(bins=bins, alpha=0.5, color=wt_color, edgecolor=wt_color, ax=top)\n",
" dc.plot.hist(bins=bins, alpha=0.5, color=dc_color, edgecolor=dc_color, ax=top)\n",
" \n",
" bottom_left.set_title('log x', size='x-large')\n",
" wt.plot.hist(bins=logbins, alpha=0.5, color=wt_color, edgecolor=wt_color, ax=bottom_left, logx=True)\n",
" dc.plot.hist(bins=logbins, alpha=0.5, color=dc_color, edgecolor=dc_color, ax=bottom_left, logx=True)\n",
"\n",
" \n",
" s = pd.concat([wt, dc]).sort_values(ignore_index=True)\n",
" assert s.is_unique\n",
"\n",
" roc = pd.DataFrame.from_records(s.apply(tpr_fpr, args=(wt, dc)), columns=['tpr', 'fpr'])\n",
" auroc = auc(roc['fpr'], roc['tpr'])\n",
"\n",
" roc.plot.line(x='fpr', y='tpr', ax=bottom_right, xlim=(0.0, 1.0), ylim=(0.0, 1.0), color='darkorange', lw=2, title='Receiver operating characteristic', label='ROC curve (area = %0.3f)' % auroc)\n",
" plt.xlabel('False Positive Rate')\n",
" plt.ylabel('True Positive Rate')\n",
" plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')\n",
" \n",
" bottom_right.set_aspect(\"equal\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3.\tAUC, or area under curve, for the ROC is used to determine how powerful an assay or discriminator is, with AUC=1 being perfect and AUC = 0.5 being random. Assess AUC as a function of a) the mutant:wild-type mean MFI ratio and b) the standard deviation. If you’re feeling ambitious, plot a topo map of AUC values on the 2-d plane for a range of these two parameters (say 1.1x to 10x for the mean ratio, and 1% to 100% for the coefficient of variance (standard deviation divided by mean)). These ranges would encompass the most likely experimental situations for flow cytometric screening of combinatorial libraries."
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"def grid_auc():\n",
"\n",
" grid_auc = defaultdict(lambda: defaultdict(None))\n",
"\n",
" for μ_ratio in np.arange(0.0,1.05,0.05):\n",
" for σ in np.arange(0.05,1.05,0.05):\n",
"\n",
" μ_2 = μ_1 + μ_ratio # addition, because exponentiating these means multiplication. \n",
" σ_2 = σ_1 = σ\n",
"\n",
" negative = lognorm(σ_1, scale=exp(μ_1))\n",
" positive = lognorm(σ_2, scale=exp(μ_2))\n",
" auc, err = integrate(lambda t: (1-positive.cdf(t)) * negative.pdf(t), np.NINF, np.inf)\n",
"\n",
" grid_auc[μ_ratio][σ] = auc\n",
"\n",
" return pd.DataFrame(grid_auc).rename_axis('σ', axis=0).rename_axis('μ_ratio', axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"aucs = grid_auc()"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"scrolled": false
},
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" {\"responsive\": true}\n",
" ).then(function(){\n",
" \n",
"var gd = document.getElementById('265a5d3f-f0f9-430c-9e9b-1996325e5284');\n",
"var x = new MutationObserver(function (mutations, observer) {{\n",
" var display = window.getComputedStyle(gd).display;\n",
" if (!display || display === 'none') {{\n",
" console.log([gd, 'removed!']);\n",
" Plotly.purge(gd);\n",
" observer.disconnect();\n",
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"\n",
"// Listen for the removal of the full notebook cells\n",
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"if (notebookContainer) {{\n",
" x.observe(notebookContainer, {childList: true});\n",
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" x.observe(outputEl, {childList: true});\n",
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" };\n",
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" </script>\n",
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import plotly.graph_objects as go\n",
"import plotly\n",
"# import chart_studio\n",
"# chart_studio.tools.set_credentials_file(username='', api_key='')\n",
"\n",
"fig = go.Figure(data=[go.Surface(z=aucs.values, x=aucs.index.values, y=aucs.columns.values)])\n",
"fig.update_layout(title='Grid AUC', width=900, height=900, autosize=False)\n",
"fig.update_layout(scene=dict(xaxis_title=aucs.columns.name, yaxis_title=aucs.index.name, zaxis_title='AUROC'))\n",
"\n",
"fig.show()\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"hide_input": false,
"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": "3.7.6"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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