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| a | b/talk/GrahamGroup.ipynb | ||
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| 1 | { |
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| 2 | "metadata": { |
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| 3 | "celltoolbar": "Slideshow", |
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| 4 | "name": "", |
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| 5 | "signature": "sha256:683ceb13e563077b8da74ca91d75c910b368c1da6290dcded253f1373c1c887b" |
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| 6 | }, |
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| 7 | "nbformat": 3, |
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| 8 | "nbformat_minor": 0, |
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| 9 | "worksheets": [ |
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| 10 | { |
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| 11 | "cells": [ |
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| 12 | { |
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| 13 | "cell_type": "heading", |
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| 14 | "level": 1, |
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| 15 | "metadata": { |
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| 16 | "slideshow": { |
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| 17 | "slide_type": "slide" |
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| 18 | } |
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| 19 | }, |
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| 20 | "source": [ |
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| 21 | "Robust Extraction of Quantitative Information from Histology Images" |
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| 22 | ] |
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| 23 | }, |
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| 24 | { |
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| 25 | "cell_type": "heading", |
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| 26 | "level": 4, |
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| 27 | "metadata": {}, |
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| 28 | "source": [ |
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| 29 | "Quentin Caudron\n", |
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| 30 | "<br /><br />\n", |
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| 31 | "\n", |
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| 32 | "Romain Garnier\n", |
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| 33 | "<br /><br />\n", |
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| 34 | "\n", |
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| 35 | "*with Bryan Grenfell and Andrea Graham*" |
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| 36 | ] |
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| 37 | }, |
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| 38 | { |
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| 39 | "cell_type": "heading", |
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| 40 | "level": 3, |
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| 41 | "metadata": { |
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| 42 | "slideshow": { |
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| 43 | "slide_type": "slide" |
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| 44 | } |
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| 45 | }, |
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| 46 | "source": [ |
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| 47 | "Outline" |
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| 48 | ] |
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| 49 | }, |
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| 50 | { |
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| 51 | "cell_type": "markdown", |
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| 52 | "metadata": {}, |
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| 53 | "source": [ |
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| 54 | "- Image processing\n", |
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| 55 | "- Extracted measures\n", |
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| 56 | "- Preliminary analysis\n", |
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| 57 | "- Future directions" |
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| 58 | ] |
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| 59 | }, |
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| 60 | { |
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| 61 | "cell_type": "markdown", |
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| 62 | "metadata": { |
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| 63 | "slideshow": { |
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| 64 | "slide_type": "skip" |
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| 65 | } |
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| 66 | }, |
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| 67 | "source": [ |
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| 68 | "4. Age as random effect <---\n", |
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| 69 | "\n", |
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| 70 | "[\"interface_hepatitis\", \"confluent_necrosis\", \"portal_inflammation\", \"ln_ap_ri\"]" |
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| 71 | ] |
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| 72 | }, |
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| 73 | { |
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| 74 | "cell_type": "code", |
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| 75 | "collapsed": false, |
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| 76 | "input": [ |
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| 77 | "def normalise(df, skip = []) :\n", |
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| 78 | "\tfor i in df.columns :\n", |
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| 79 | "\t\tif i not in skip :\n", |
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| 80 | "\t\t\tdf[i] -= df[i].mean()\n", |
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| 81 | "\t\t\tdf[i] /= df[i].std()\n", |
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| 82 | "\treturn df\n", |
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| 83 | "\n", |
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| 84 | "\n", |
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| 85 | "\n", |
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| 86 | "\n", |
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| 87 | "\n", |
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| 88 | "\n", |
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| 89 | "def rescale(df, skip = []) :\n", |
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| 90 | " for i in df.columns :\n", |
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| 91 | " if i not in skip :\n", |
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| 92 | " df[i] -= df[i].min()\n", |
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| 93 | " df[i] /= df[i].max()\n", |
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| 94 | " return df\n", |
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| 95 | "\n", |
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| 96 | "\n", |
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| 97 | "\n", |
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| 98 | "# Remove a layer from a list\n", |
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| 99 | "def delayer(m) :\n", |
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| 100 | "\tout = []\n", |
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| 101 | "\tfor i in m :\n", |
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| 102 | "\t\tif isinstance(i, list) :\n", |
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| 103 | "\t\t\tfor j in i :\n", |
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| 104 | "\t\t\t\tout.append(j)\n", |
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| 105 | "\t\telse :\n", |
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| 106 | "\t\t\tout.append(i)\n", |
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| 107 | "\treturn out\n", |
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| 108 | "\n", |
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| 109 | "\n", |
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| 110 | "\n", |
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| 111 | "\n", |
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| 112 | "\n", |
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| 113 | "\n", |
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| 114 | "\n", |
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| 115 | "# Remove all layers from a list\n", |
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| 116 | "def flatten(m) :\n", |
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| 117 | "\tout = m[:]\n", |
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| 118 | "\n", |
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| 119 | "\twhile out != delayer(out) :\n", |
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| 120 | "\t\tout = delayer(out)\n", |
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| 121 | "\n", |
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| 122 | "\treturn out\n", |
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| 123 | "\n", |
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| 124 | "\n", |
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| 125 | "\n", |
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| 126 | "\n", |
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| 127 | "\n", |
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| 128 | "\n", |
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| 129 | "\n", |
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| 130 | "\n", |
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| 131 | "# Generate all combinations of objects in a list\n", |
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| 132 | "def combinatorial(l) :\n", |
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| 133 | "\tout = []\n", |
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| 134 | "\n", |
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| 135 | "\tfor numel in range(len(l)) :\n", |
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| 136 | "\t\tfor i in itertools.combinations(l, numel+1) :\n", |
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| 137 | "\t\t\tout.append(list(i))\n", |
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| 138 | "\n", |
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| 139 | "\treturn out\n", |
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| 140 | "\n", |
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| 141 | "\n", |
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| 142 | "\n", |
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| 143 | "\n", |
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| 144 | "\n", |
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| 145 | "\n", |
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| 146 | "\n", |
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| 147 | "\n", |
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| 148 | "\n", |
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| 149 | "\n", |
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| 150 | "def pcaplot(df) :\n", |
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| 151 | "\n", |
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| 152 | "\t# PCA\n", |
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| 153 | "\tpca = decomposition.PCA(whiten = True)\n", |
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| 154 | "\tpca.fit(df)\n", |
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| 155 | "\tp1 = pca.components_[0] / np.abs(pca.components_[0]).max() * np.sqrt(2)/2\n", |
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| 156 | "\tp2 = pca.components_[1] / np.abs(pca.components_[1]).max() * np.sqrt(2)/2\n", |
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| 157 | "\n", |
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| 158 | "\t# Normalise\n", |
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| 159 | "\tnorms = np.max([np.sqrt((np.array(zip(p1, p2)[i])**2).sum()) for i in range(len(p1))])\n", |
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| 160 | "\tc = plt.Circle( (0, 0), radius = 1, alpha = 0.2)\n", |
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| 161 | "\tplt.axes(aspect = 1)\n", |
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| 162 | "\tplt.gca().add_artist(c)\n", |
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| 163 | "\n", |
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| 164 | "\tplt.scatter(p1 / norms, p2 / norms)\n", |
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| 165 | "\tplt.xlim([-1, 1])\n", |
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| 166 | "\tplt.ylim([-1, 1])\n", |
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| 167 | "\n", |
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| 168 | "\tfor i, text in enumerate(df.columns) :\n", |
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| 169 | "\t\tplt.annotate(text, xy = [p1[i], p2[i]])\n", |
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| 170 | "\n", |
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| 171 | "\tplt.tight_layout()\n", |
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| 172 | "\n", |
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| 173 | "\n", |
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| 174 | "\n", |
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| 175 | "\n", |
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| 176 | "\n", |
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| 177 | "\n", |
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| 178 | "\n", |
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| 179 | "\n", |
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| 180 | "\n", |
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| 181 | "\n", |
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| 182 | "\n", |
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| 183 | "def test_all_linear(df, y, x, return_significant = False, group = None) :\n", |
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| 184 | "\n", |
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| 185 | " # All possible combinations of independent variables\n", |
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| 186 | "\tindependent = combinatorial(x)\n", |
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| 187 | "\n", |
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| 188 | "\tfits = {}\n", |
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| 189 | "\tpval = {}\n", |
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| 190 | "\tlinmodels = {}\n", |
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| 191 | "\tqsum = {}\n", |
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| 192 | "\taic = {}\n", |
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| 193 | "\n", |
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| 194 | "\t# For all dependent variables, one at a time\n", |
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| 195 | "\tfor dependent in y :\n", |
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| 196 | "\n", |
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| 197 | "\t\tprint \"Fitting for %s.\" % dependent\n", |
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| 198 | "\n", |
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| 199 | "\t\t# For all combinations of independent variables\n", |
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| 200 | "\t\tfor covariate in independent :\n", |
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| 201 | "\n", |
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| 202 | "\t\t\t# Standard mixed model\n", |
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| 203 | "\t\t\tif group is None :\n", |
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| 204 | "\n", |
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| 205 | "\t\t\t\t# Fit a linear model\n", |
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| 206 | "\t\t\t\tsubset = delayer([covariate, dependent])\n", |
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| 207 | "\t\t\t\tdf2 = df[delayer(subset)].dropna()\n", |
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| 208 | "\t\t\t\tdf2[\"Intercept\"] = np.ones(len(df2))\n", |
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| 209 | " \n", |
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| 210 | "\t\t\t\tols = sm.GLS(endog = df2[dependent], exog = df2[delayer([covariate, \"Intercept\"])]).fit()\n", |
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| 211 | "\n", |
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| 212 | "\t\t\t\t# Save the results\n", |
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| 213 | "\t\t\t\tif (return_significant and ols.f_pvalue < 0.05) or (not return_significant) :\n", |
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| 214 | "\t\t\t\t\tlinmodels.setdefault(dependent, []).append(ols)\n", |
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| 215 | "\t\t\t\t\tfits.setdefault(dependent, []).append(ols.rsquared)\n", |
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| 216 | "\t\t\t\t\tpval.setdefault(dependent, []).append(ols.f_pvalue)\n", |
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| 217 | "\t\t\t\t\taic.setdefault(dependent, []).append(ols.aic)\n", |
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| 218 | "\n", |
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| 219 | "\n", |
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| 220 | "\t\t\t# Mixed effects model\n", |
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| 221 | "\t\t\telse :\n", |
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| 222 | "\t\t\t\tsubset = delayer([covariate, dependent, group])\n", |
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| 223 | "\t\t\t\tdf2 = df[delayer(subset)].dropna()\n", |
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| 224 | "\n", |
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| 225 | "\t\t\t\t# Fit a mixed effects model\n", |
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| 226 | "\t\t\t\tols = MixedLM(endog = df2[dependent], exog = df2[covariate], groups = df2[group]).fit()\n", |
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| 227 | "\n", |
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| 228 | "\t\t\t\t# Calculate AIC\n", |
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| 229 | "\t\t\t\tlinmodels.setdefault(dependent, []).append(ols)\n", |
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| 230 | "\t\t\t\tfits.setdefault(dependent, []).append(2 * (ols.k_fe + 1) - 2 * ols.llf)\n", |
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| 231 | "\t\t\t\tpval.setdefault(dependent, []).append(ols.pvalues)\n", |
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| 232 | "\n", |
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| 233 | "\tif group is not None :\n", |
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| 234 | "\t\tfor i in y :\n", |
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| 235 | "\t\t\tf = np.array(fits[i])\n", |
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| 236 | "\t\t\tmodels = np.array(linmodels[i])\n", |
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| 237 | "\t\t\tidx = np.where(f - f.min() <= 2)[0]\n", |
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| 238 | "\t\t\tbestmodelDoF = [j.k_fe for j in np.array(linmodels[i])[idx]]\n", |
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| 239 | "\t\t\tbestmodels = [idx[j] for j in np.where(bestmodelDoF == np.min(bestmodelDoF))[0]]\n", |
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| 240 | "\t\t\tqsum[i] = models[idx[np.where(f[bestmodels] == np.min(f[bestmodels]))]]\n", |
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| 241 | "\n", |
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| 242 | "\n", |
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| 243 | "\t\treturn linmodels, fits, pval, qsum\n", |
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| 244 | "\n", |
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| 245 | "\treturn linmodels, fits, pval, aic\n", |
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| 246 | "\n", |
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| 247 | "\t\n", |
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| 248 | "\t\t\n", |
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| 249 | "\n", |
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| 250 | "\n", |
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| 251 | "\n", |
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| 252 | "\n", |
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| 253 | "\n", |
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| 254 | "\n", |
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| 255 | "\n", |
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| 256 | "\n", |
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| 257 | "\n", |
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| 258 | "\n", |
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| 259 | "\n", |
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| 260 | "\n", |
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| 261 | "\n", |
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| 262 | "\n", |
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| 263 | "\n", |
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| 264 | "def summary(models) :\n", |
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| 265 | "\n", |
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| 266 | "\t# Generate list of everything\n", |
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| 267 | "\tr2 = np.array([m.r2 for dependent in models.keys() for m in models[dependent]])\n", |
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| 268 | "\tp = np.array([m.f_stat[\"p-value\"] for dependent in models.keys() for m in models[dependent]])\n", |
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| 269 | "\tmod = np.array([m for dependent in models.keys() for m in models[dependent]])\n", |
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| 270 | "\tdependent = np.array([dependent for dependent in models.keys() for m in models[dependent]])\n", |
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| 271 | "\n", |
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| 272 | "\t# Sort by R2\n", |
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| 273 | "\tidx = np.argsort(r2)[::-1]\n", |
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| 274 | "\n", |
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| 275 | "\t# Output string\n", |
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| 276 | "\ts = \"%d significant regressions.\\n\\n\" % len(r2)\n", |
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| 277 | "\ts += \"Ten most correlated :\\n\\n\"\n", |
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| 278 | "\n", |
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| 279 | "\t# Print a summary of the top ten correlations\n", |
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| 280 | "\tfor i in idx[:10] :\n", |
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| 281 | "\t\ts += (\"%s ~ %s\\n\" % (dependent[i], \" + \".join(mod[i].x.columns[:-1])))\n", |
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| 282 | "\t\ts += (\"R^2 = %f\\tp = %f\\n\\n\" % (r2[i], p[i]))\n", |
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| 283 | "\n", |
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| 284 | "\tprint s\n", |
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| 285 | " \n", |
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| 286 | " \n", |
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| 287 | " \n", |
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| 288 | " \n", |
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| 289 | " \n", |
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| 290 | " \n", |
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| 291 | " \n", |
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| 292 | "def rstr(y, x) :\n", |
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| 293 | " formatstr = \"%s ~ \" % y\n", |
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| 294 | " for i in x[:-1] :\n", |
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| 295 | " formatstr += str(i)\n", |
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| 296 | " formatstr += \" + \"\n", |
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| 297 | " formatstr += str(x[-1])\n", |
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| 298 | " return formatstr\n", |
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| 299 | "\n", |
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| 300 | "\n", |
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| 301 | "\n", |
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| 302 | "\n", |
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| 303 | "\n", |
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| 304 | "\n", |
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| 305 | "\n" |
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| 306 | ], |
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| 307 | "language": "python", |
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| 308 | "metadata": { |
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| 309 | "slideshow": { |
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| 310 | "slide_type": "skip" |
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| 311 | } |
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| 312 | }, |
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| 313 | "outputs": [], |
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| 314 | "prompt_number": 3 |
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| 315 | }, |
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| 316 | { |
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| 317 | "cell_type": "code", |
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| 318 | "collapsed": false, |
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| 319 | "input": [ |
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| 320 | "import numpy as np\n", |
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| 321 | "from sklearn.neighbors import KernelDensity\n", |
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| 322 | "from matplotlib import rcParams\n", |
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| 323 | "import matplotlib.pyplot as plt\n", |
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| 324 | "import seaborn\n", |
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| 325 | "import pandas as pd\n", |
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| 326 | "import itertools\n", |
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| 327 | "from sklearn import linear_model, ensemble, decomposition, cross_validation, preprocessing\n", |
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| 328 | "from statsmodels.regression.mixed_linear_model import MixedLM\n", |
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| 329 | "import statsmodels.api as sm\n", |
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| 330 | "from statsmodels.regression.linear_model import OLSResults\n", |
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| 331 | "from statsmodels.tools.tools import add_constant\n", |
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| 332 | "\n", |
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| 333 | "\n", |
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| 334 | "%matplotlib inline\n", |
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| 335 | "rcParams[\"figure.figsize\"] = (14, 8)\n", |
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| 336 | "\n", |
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| 337 | "\n", |
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| 338 | "# RAW DATA\n", |
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| 339 | "\n", |
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| 340 | "raw_physical = pd.read_csv(\"../data/physical.csv\")\n", |
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| 341 | "raw_histo = pd.read_csv(\"../data/tawfik.csv\")\n", |
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| 342 | "ent = pd.read_csv(\"../4x/results/entropy.csv\").drop([\"Unnamed: 0\"], 1)\n", |
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| 343 | "foci = pd.read_csv(\"../4x/results/foci.csv\").drop([\"Unnamed: 0\"], 1)\n", |
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| 344 | "lac = pd.read_csv(\"../4x/results/normalised_lacunarity.csv\").drop([\"Unnamed: 0\"], 1)\n", |
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| 345 | "gabor = pd.read_csv(\"../4x/results/gabor_filters.csv\").drop([\"Unnamed: 0\"], 1)\n", |
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| 346 | "ts = pd.read_csv(\"../4x/results/tissue_sinusoid_ratio.csv\").drop([\"Unnamed: 0\"], 1)\n", |
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| 347 | "\n", |
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| 348 | "raw_image = pd.merge(lac, ent,\n", |
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| 349 | "\ton=[\"Sheep\", \"Image\"]).merge(foci, \n", |
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| 350 | "\ton=[\"Sheep\", \"Image\"]).merge(gabor,\n", |
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| 351 | "\ton=[\"Sheep\", \"Image\"]).merge(ts, \n", |
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| 352 | " on=[\"Sheep\", \"Image\"])\n", |
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| 353 | "raw_image.rename(columns = {\t\"meanSize\" : \"FociSize\", \n", |
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| 354 | "\t\t\t\t\t\t\t\t\"TSRatio\" : \"TissueToSinusoid\",\n", |
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| 355 | "\t\t\t\t\t\t\t\t\"Count\" : \"FociCount\" }, inplace=True)\n", |
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| 356 | "\n", |
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| 357 | "\n", |
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| 358 | "\n", |
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| 359 | "# CLEAN DATA\n", |
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| 360 | "\n", |
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| 361 | "physcols = [\"Weight\", \"Sex\", \"AgeAtDeath\", \"Foreleg\", \"Hindleg\"]\n", |
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| 362 | "imagecols = [\"Entropy\", \"Lacunarity\", \"Inflammation\", \"Scale\", \"Directionality\", \"FociCount\", \"FociSize\", \"TissueToSinusoid\"]\n", |
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| 363 | "histcols = [\"Lobular_collapse\", \"Interface_hepatitis\", \"Confluent_necrosis\", \"Ln_ap_ri\", \"Portal_inflammation\", \"BD_hyperplasia\", \"Fibrosis\", \"TawfikTotal\", \"Mean_hep_size\", \"Min_hep_size\", \"Max_hep_size\"]\n", |
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| 364 | "\n", |
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| 365 | "\n", |
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| 366 | "\n", |
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| 367 | "\n", |
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| 368 | "\n", |
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| 369 | "# IMAGE\n", |
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| 370 | "\n", |
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| 371 | "# Set FociSize to zero if FociCount is zero\n", |
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| 372 | "# Drop stdSize\n", |
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| 373 | "image = raw_image\n", |
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| 374 | "image = image.drop(\"stdSize\", 1)\n", |
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| 375 | "image.FociSize[raw_image.FociCount == 0] = 0\n", |
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| 376 | "\n", |
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| 377 | "\n", |
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| 378 | "\n", |
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| 379 | "# HISTO\n", |
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| 380 | "\n", |
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| 381 | "histo = raw_histo\n", |
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| 382 | "histo = histo.drop([\"Vessels\", \"Vacuol\", \"Pigment\", \"Std_hep_size\"], 1)\n", |
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| 383 | "\n", |
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| 384 | "\n", |
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| 385 | "\n", |
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| 386 | "# PHYSICAL\n", |
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| 387 | "\n", |
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| 388 | "physical = raw_physical\n", |
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| 389 | "physical = physical.drop([\"CurrTag\", \"DeathDate\", \"Category\"], 1)\n", |
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| 390 | "physical\n", |
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| 391 | "\n", |
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| 392 | "\n", |
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| 393 | "\n", |
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| 394 | "\n", |
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| 395 | "# COMPLETE DATASET\n", |
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| 396 | "\n", |
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| 397 | "raw_data = pd.merge(pd.merge(image, histo, on=\"Sheep\", how=\"outer\"), physical, on=\"Sheep\", how=\"outer\")\n", |
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| 398 | "raw_data.to_csv(\"../data/tentative_complete.csv\")\n", |
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| 399 | "\n", |
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| 400 | "\n", |
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| 401 | "\n", |
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| 402 | "\n", |
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| 403 | "# AVERAGED BY SHEEP\n", |
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| 404 | "data = raw_data\n", |
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| 405 | "data[\"Inflammation\"] = data.FociCount * data.FociSize\n", |
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| 406 | "\n", |
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| 407 | "sheep = rescale(data.groupby(\"Sheep\").mean())\n", |
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| 408 | "age = rescale(data.groupby(\"AgeAtDeath\").mean())\n", |
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| 409 | "\n", |
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| 410 | "\n", |
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| 411 | "\n", |
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| 412 | "\n", |
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| 413 | "\n", |
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| 414 | "\n", |
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| 415 | "\n", |
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| 416 | "# REGRESSIONS : fixed effects, grouped by sheep\n", |
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| 417 | "\n", |
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| 418 | "df = sheep[[\"Portal_inflammation\", \"FociSize\"]].dropna()\n", |
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| 419 | "df[\"Intercept\"] = np.ones(len(df))\n", |
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| 420 | "portal_inflammation = sm.GLS(endog = df.Portal_inflammation, exog = df[[\"FociSize\", \"Intercept\"]]).fit().summary()\n", |
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| 421 | "#portal_inflammation = portal_inflammation.summary()\n", |
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| 422 | "del portal_inflammation.tables[2]\n", |
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| 423 | "\n", |
||
| 424 | "\n", |
||
| 425 | "\n", |
||
| 426 | "df = sheep[[\"BD_hyperplasia\", \"Scale\", \"Directionality\", \"FociSize\"]].dropna()\n", |
||
| 427 | "df[\"Intercept\"] = np.ones(len(df))\n", |
||
| 428 | "hyperplasia = sm.GLS(endog = df.BD_hyperplasia, exog = df[[\"FociSize\", \"Scale\", \"Directionality\", \"Intercept\"]]).fit().summary()\n", |
||
| 429 | "#hyperplasia.summary()\n", |
||
| 430 | "del hyperplasia.tables[2]\n", |
||
| 431 | "\n", |
||
| 432 | "\n", |
||
| 433 | "\n", |
||
| 434 | "\n", |
||
| 435 | "\n", |
||
| 436 | "\n", |
||
| 437 | "# REGRESSIONS : fixed effects, grouped by age\n", |
||
| 438 | "\n", |
||
| 439 | "df = age[[\"Max_hep_size\", \"Entropy\", \"Directionality\"]].dropna()\n", |
||
| 440 | "df[\"Intercept\"] = np.ones(len(df))\n", |
||
| 441 | "maxhepsize = sm.GLS(endog = df.Max_hep_size, exog = df[[\"Entropy\", \"Directionality\", \"Intercept\"]]).fit().summary()\n", |
||
| 442 | "del maxhepsize.tables[2]\n", |
||
| 443 | "\n", |
||
| 444 | "\n", |
||
| 445 | "\n", |
||
| 446 | "\n", |
||
| 447 | "df = age[[\"Lobular_collapse\", \"FociSize\"]].dropna()\n", |
||
| 448 | "df[\"Intercept\"] = np.ones(len(df))\n", |
||
| 449 | "lobular_collapse = sm.GLS(endog = df.Lobular_collapse, exog = df[[\"FociSize\", \"Intercept\"]]).fit().summary()\n", |
||
| 450 | "del lobular_collapse.tables[2]\n", |
||
| 451 | "\n", |
||
| 452 | "\n", |
||
| 453 | "df = age[[\"Interface_hepatitis\", \"Lacunarity\"]].dropna()\n", |
||
| 454 | "df[\"Intercept\"] = np.ones(len(df))\n", |
||
| 455 | "interface_hepatitis = sm.GLS(endog = df.Interface_hepatitis, exog = df[[\"Lacunarity\", \"Intercept\"]]).fit().summary()\n", |
||
| 456 | "del interface_hepatitis.tables[2]\n", |
||
| 457 | "\n", |
||
| 458 | "\n", |
||
| 459 | "df = age[[\"Fibrosis\", \"Inflammation\"]].dropna()\n", |
||
| 460 | "df[\"Intercept\"] = np.ones(len(df))\n", |
||
| 461 | "fibrosis = sm.GLS(endog = df.Fibrosis, exog = df[[\"Inflammation\", \"Intercept\"]]).fit().summary()\n", |
||
| 462 | "del fibrosis.tables[2]\n", |
||
| 463 | "\n", |
||
| 464 | "\n", |
||
| 465 | "\n", |
||
| 466 | "\n", |
||
| 467 | "# PCA\n", |
||
| 468 | "\n", |
||
| 469 | "s = sheep.dropna(subset=delayer([imagecols, histcols]))\n", |
||
| 470 | "pca = decomposition.PCA(n_components=1)\n", |
||
| 471 | "pcax = pca.fit_transform(s[imagecols])\n", |
||
| 472 | "pcay = pca.fit_transform(s[histcols])\n", |
||
| 473 | "pca = sm.GLS(endog = pcay[:, 0][:, np.newaxis], exog = add_constant(pcax)).fit().summary()\n", |
||
| 474 | "del pca.tables[2]\n", |
||
| 475 | "\n", |
||
| 476 | "\n", |
||
| 477 | "\n", |
||
| 478 | "\n", |
||
| 479 | "\n", |
||
| 480 | "# REGRESSIONS : mixed effects, intercept on age at death\n", |
||
| 481 | "\n", |
||
| 482 | "df = age[[\"Fibrosis\", \"Inflammation\"]].dropna()\n", |
||
| 483 | "df[\"Intercept\"] = np.ones(len(df))\n", |
||
| 484 | "fibrosis = sm.GLS(endog = df.Fibrosis, exog = df[[\"Inflammation\", \"Intercept\"]]).fit().summary()\n", |
||
| 485 | "del fibrosis.tables[2]" |
||
| 486 | ], |
||
| 487 | "language": "python", |
||
| 488 | "metadata": { |
||
| 489 | "slideshow": { |
||
| 490 | "slide_type": "skip" |
||
| 491 | } |
||
| 492 | }, |
||
| 493 | "outputs": [], |
||
| 494 | "prompt_number": 14 |
||
| 495 | }, |
||
| 496 | { |
||
| 497 | "cell_type": "code", |
||
| 498 | "collapsed": false, |
||
| 499 | "input": [ |
||
| 500 | "a = portal_inflammation.summary()\n", |
||
| 501 | "del a.tables[2]\n", |
||
| 502 | "a" |
||
| 503 | ], |
||
| 504 | "language": "python", |
||
| 505 | "metadata": { |
||
| 506 | "slideshow": { |
||
| 507 | "slide_type": "skip" |
||
| 508 | } |
||
| 509 | }, |
||
| 510 | "outputs": [ |
||
| 511 | { |
||
| 512 | "html": [ |
||
| 513 | "<table class=\"simpletable\">\n", |
||
| 514 | "<caption>GLS Regression Results</caption>\n", |
||
| 515 | "<tr>\n", |
||
| 516 | " <th>Dep. Variable:</th> <td>Portal_inflammation</td> <th> R-squared: </th> <td> 0.280</td>\n", |
||
| 517 | "</tr>\n", |
||
| 518 | "<tr>\n", |
||
| 519 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.273</td>\n", |
||
| 520 | "</tr>\n", |
||
| 521 | "<tr>\n", |
||
| 522 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 37.34</td>\n", |
||
| 523 | "</tr>\n", |
||
| 524 | "<tr>\n", |
||
| 525 | " <th>Date:</th> <td>Tue, 28 Oct 2014</td> <th> Prob (F-statistic):</th> <td>2.12e-08</td>\n", |
||
| 526 | "</tr>\n", |
||
| 527 | "<tr>\n", |
||
| 528 | " <th>Time:</th> <td>23:35:30</td> <th> Log-Likelihood: </th> <td> 14.996</td>\n", |
||
| 529 | "</tr>\n", |
||
| 530 | "<tr>\n", |
||
| 531 | " <th>No. Observations:</th> <td> 98</td> <th> AIC: </th> <td> -25.99</td>\n", |
||
| 532 | "</tr>\n", |
||
| 533 | "<tr>\n", |
||
| 534 | " <th>Df Residuals:</th> <td> 96</td> <th> BIC: </th> <td> -20.82</td>\n", |
||
| 535 | "</tr>\n", |
||
| 536 | "<tr>\n", |
||
| 537 | " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n", |
||
| 538 | "</tr>\n", |
||
| 539 | "<tr>\n", |
||
| 540 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 541 | "</tr>\n", |
||
| 542 | "</table>\n", |
||
| 543 | "<table class=\"simpletable\">\n", |
||
| 544 | "<tr>\n", |
||
| 545 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 546 | "</tr>\n", |
||
| 547 | "<tr>\n", |
||
| 548 | " <th>FociSize</th> <td> 0.5627</td> <td> 0.092</td> <td> 6.111</td> <td> 0.000</td> <td> 0.380 0.746</td>\n", |
||
| 549 | "</tr>\n", |
||
| 550 | "<tr>\n", |
||
| 551 | " <th>Intercept</th> <td> 0.3368</td> <td> 0.043</td> <td> 7.855</td> <td> 0.000</td> <td> 0.252 0.422</td>\n", |
||
| 552 | "</tr>\n", |
||
| 553 | "</table>" |
||
| 554 | ], |
||
| 555 | "metadata": {}, |
||
| 556 | "output_type": "pyout", |
||
| 557 | "prompt_number": 19, |
||
| 558 | "text": [ |
||
| 559 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 560 | "\"\"\"\n", |
||
| 561 | " GLS Regression Results \n", |
||
| 562 | "===============================================================================\n", |
||
| 563 | "Dep. Variable: Portal_inflammation R-squared: 0.280\n", |
||
| 564 | "Model: GLS Adj. R-squared: 0.273\n", |
||
| 565 | "Method: Least Squares F-statistic: 37.34\n", |
||
| 566 | "Date: Tue, 28 Oct 2014 Prob (F-statistic): 2.12e-08\n", |
||
| 567 | "Time: 23:35:30 Log-Likelihood: 14.996\n", |
||
| 568 | "No. Observations: 98 AIC: -25.99\n", |
||
| 569 | "Df Residuals: 96 BIC: -20.82\n", |
||
| 570 | "Df Model: 1 \n", |
||
| 571 | "Covariance Type: nonrobust \n", |
||
| 572 | "==============================================================================\n", |
||
| 573 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 574 | "------------------------------------------------------------------------------\n", |
||
| 575 | "FociSize 0.5627 0.092 6.111 0.000 0.380 0.746\n", |
||
| 576 | "Intercept 0.3368 0.043 7.855 0.000 0.252 0.422\n", |
||
| 577 | "==============================================================================\n", |
||
| 578 | "\n", |
||
| 579 | "Warnings:\n", |
||
| 580 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 581 | "\"\"\"" |
||
| 582 | ] |
||
| 583 | } |
||
| 584 | ], |
||
| 585 | "prompt_number": 19 |
||
| 586 | }, |
||
| 587 | { |
||
| 588 | "cell_type": "heading", |
||
| 589 | "level": 2, |
||
| 590 | "metadata": { |
||
| 591 | "slideshow": { |
||
| 592 | "slide_type": "slide" |
||
| 593 | } |
||
| 594 | }, |
||
| 595 | "source": [ |
||
| 596 | "Image Processing" |
||
| 597 | ] |
||
| 598 | }, |
||
| 599 | { |
||
| 600 | "cell_type": "markdown", |
||
| 601 | "metadata": { |
||
| 602 | "slideshow": { |
||
| 603 | "slide_type": "subslide" |
||
| 604 | } |
||
| 605 | }, |
||
| 606 | "source": [ |
||
| 607 | "<img src=\"figures/sheep.jpg\"></img>" |
||
| 608 | ] |
||
| 609 | }, |
||
| 610 | { |
||
| 611 | "cell_type": "markdown", |
||
| 612 | "metadata": { |
||
| 613 | "slideshow": { |
||
| 614 | "slide_type": "subslide" |
||
| 615 | } |
||
| 616 | }, |
||
| 617 | "source": [ |
||
| 618 | "<img src=\"figures/processed.jpg\"></img>" |
||
| 619 | ] |
||
| 620 | }, |
||
| 621 | { |
||
| 622 | "cell_type": "heading", |
||
| 623 | "level": 3, |
||
| 624 | "metadata": { |
||
| 625 | "slideshow": { |
||
| 626 | "slide_type": "subslide" |
||
| 627 | } |
||
| 628 | }, |
||
| 629 | "source": [ |
||
| 630 | "Extraction" |
||
| 631 | ] |
||
| 632 | }, |
||
| 633 | { |
||
| 634 | "cell_type": "markdown", |
||
| 635 | "metadata": { |
||
| 636 | "slideshow": { |
||
| 637 | "slide_type": "-" |
||
| 638 | } |
||
| 639 | }, |
||
| 640 | "source": [ |
||
| 641 | "- Automagical\n", |
||
| 642 | "- Reasonably quick" |
||
| 643 | ] |
||
| 644 | }, |
||
| 645 | { |
||
| 646 | "cell_type": "heading", |
||
| 647 | "level": 3, |
||
| 648 | "metadata": { |
||
| 649 | "slideshow": { |
||
| 650 | "slide_type": "subslide" |
||
| 651 | } |
||
| 652 | }, |
||
| 653 | "source": [ |
||
| 654 | "Robust" |
||
| 655 | ] |
||
| 656 | }, |
||
| 657 | { |
||
| 658 | "cell_type": "markdown", |
||
| 659 | "metadata": { |
||
| 660 | "slideshow": { |
||
| 661 | "slide_type": "-" |
||
| 662 | } |
||
| 663 | }, |
||
| 664 | "source": [ |
||
| 665 | "- Invariant to staining, slicing, field-related variation\n", |
||
| 666 | "- Capture intersample variation" |
||
| 667 | ] |
||
| 668 | }, |
||
| 669 | { |
||
| 670 | "cell_type": "markdown", |
||
| 671 | "metadata": { |
||
| 672 | "slideshow": { |
||
| 673 | "slide_type": "subslide" |
||
| 674 | } |
||
| 675 | }, |
||
| 676 | "source": [ |
||
| 677 | "" |
||
| 678 | ] |
||
| 679 | }, |
||
| 680 | { |
||
| 681 | "cell_type": "markdown", |
||
| 682 | "metadata": { |
||
| 683 | "slideshow": { |
||
| 684 | "slide_type": "subslide" |
||
| 685 | } |
||
| 686 | }, |
||
| 687 | "source": [ |
||
| 688 | "" |
||
| 689 | ] |
||
| 690 | }, |
||
| 691 | { |
||
| 692 | "cell_type": "markdown", |
||
| 693 | "metadata": { |
||
| 694 | "slideshow": { |
||
| 695 | "slide_type": "subslide" |
||
| 696 | } |
||
| 697 | }, |
||
| 698 | "source": [ |
||
| 699 | "" |
||
| 700 | ] |
||
| 701 | }, |
||
| 702 | { |
||
| 703 | "cell_type": "markdown", |
||
| 704 | "metadata": { |
||
| 705 | "slideshow": { |
||
| 706 | "slide_type": "subslide" |
||
| 707 | } |
||
| 708 | }, |
||
| 709 | "source": [ |
||
| 710 | "" |
||
| 711 | ] |
||
| 712 | }, |
||
| 713 | { |
||
| 714 | "cell_type": "heading", |
||
| 715 | "level": 2, |
||
| 716 | "metadata": { |
||
| 717 | "slideshow": { |
||
| 718 | "slide_type": "slide" |
||
| 719 | } |
||
| 720 | }, |
||
| 721 | "source": [ |
||
| 722 | "Structural and Textural Measures" |
||
| 723 | ] |
||
| 724 | }, |
||
| 725 | { |
||
| 726 | "cell_type": "markdown", |
||
| 727 | "metadata": { |
||
| 728 | "slideshow": { |
||
| 729 | "slide_type": "subslide" |
||
| 730 | } |
||
| 731 | }, |
||
| 732 | "source": [ |
||
| 733 | "- characteristic **scale** of sinusoid widths\n", |
||
| 734 | "- **directional** amplitude of preferred sinusoid alignment\n", |
||
| 735 | "- **tissue to sinusoid** ratio\n", |
||
| 736 | "- **count** of inflammatory foci per image\n", |
||
| 737 | "- **mean size** of inflammatory foci per image\n", |
||
| 738 | "- information **entropy** of sinusoid distribution\n", |
||
| 739 | "- **lacunarity** ( clustering ) of sinusoids" |
||
| 740 | ] |
||
| 741 | }, |
||
| 742 | { |
||
| 743 | "cell_type": "markdown", |
||
| 744 | "metadata": { |
||
| 745 | "slideshow": { |
||
| 746 | "slide_type": "subslide" |
||
| 747 | } |
||
| 748 | }, |
||
| 749 | "source": [ |
||
| 750 | "<img src=\"figures/gif.gif\"></img>" |
||
| 751 | ] |
||
| 752 | }, |
||
| 753 | { |
||
| 754 | "cell_type": "markdown", |
||
| 755 | "metadata": { |
||
| 756 | "slideshow": { |
||
| 757 | "slide_type": "subslide" |
||
| 758 | } |
||
| 759 | }, |
||
| 760 | "source": [ |
||
| 761 | "" |
||
| 762 | ] |
||
| 763 | }, |
||
| 764 | { |
||
| 765 | "cell_type": "markdown", |
||
| 766 | "metadata": { |
||
| 767 | "slideshow": { |
||
| 768 | "slide_type": "subslide" |
||
| 769 | } |
||
| 770 | }, |
||
| 771 | "source": [ |
||
| 772 | "" |
||
| 773 | ] |
||
| 774 | }, |
||
| 775 | { |
||
| 776 | "cell_type": "heading", |
||
| 777 | "level": 2, |
||
| 778 | "metadata": { |
||
| 779 | "slideshow": { |
||
| 780 | "slide_type": "slide" |
||
| 781 | } |
||
| 782 | }, |
||
| 783 | "source": [ |
||
| 784 | "Exploratory Analysis" |
||
| 785 | ] |
||
| 786 | }, |
||
| 787 | { |
||
| 788 | "cell_type": "heading", |
||
| 789 | "level": 3, |
||
| 790 | "metadata": {}, |
||
| 791 | "source": [ |
||
| 792 | "by individual" |
||
| 793 | ] |
||
| 794 | }, |
||
| 795 | { |
||
| 796 | "cell_type": "code", |
||
| 797 | "collapsed": false, |
||
| 798 | "input": [ |
||
| 799 | "portal_inflammation" |
||
| 800 | ], |
||
| 801 | "language": "python", |
||
| 802 | "metadata": { |
||
| 803 | "slideshow": { |
||
| 804 | "slide_type": "subslide" |
||
| 805 | } |
||
| 806 | }, |
||
| 807 | "outputs": [ |
||
| 808 | { |
||
| 809 | "html": [ |
||
| 810 | "<table class=\"simpletable\">\n", |
||
| 811 | "<caption>GLS Regression Results</caption>\n", |
||
| 812 | "<tr>\n", |
||
| 813 | " <th>Dep. Variable:</th> <td>Portal_inflammation</td> <th> R-squared: </th> <td> 0.280</td>\n", |
||
| 814 | "</tr>\n", |
||
| 815 | "<tr>\n", |
||
| 816 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.273</td>\n", |
||
| 817 | "</tr>\n", |
||
| 818 | "<tr>\n", |
||
| 819 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 37.34</td>\n", |
||
| 820 | "</tr>\n", |
||
| 821 | "<tr>\n", |
||
| 822 | " <th>Date:</th> <td>Tue, 28 Oct 2014</td> <th> Prob (F-statistic):</th> <td>2.12e-08</td>\n", |
||
| 823 | "</tr>\n", |
||
| 824 | "<tr>\n", |
||
| 825 | " <th>Time:</th> <td>23:40:10</td> <th> Log-Likelihood: </th> <td> 14.996</td>\n", |
||
| 826 | "</tr>\n", |
||
| 827 | "<tr>\n", |
||
| 828 | " <th>No. Observations:</th> <td> 98</td> <th> AIC: </th> <td> -25.99</td>\n", |
||
| 829 | "</tr>\n", |
||
| 830 | "<tr>\n", |
||
| 831 | " <th>Df Residuals:</th> <td> 96</td> <th> BIC: </th> <td> -20.82</td>\n", |
||
| 832 | "</tr>\n", |
||
| 833 | "<tr>\n", |
||
| 834 | " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n", |
||
| 835 | "</tr>\n", |
||
| 836 | "<tr>\n", |
||
| 837 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 838 | "</tr>\n", |
||
| 839 | "</table>\n", |
||
| 840 | "<table class=\"simpletable\">\n", |
||
| 841 | "<tr>\n", |
||
| 842 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 843 | "</tr>\n", |
||
| 844 | "<tr>\n", |
||
| 845 | " <th>FociSize</th> <td> 0.5627</td> <td> 0.092</td> <td> 6.111</td> <td> 0.000</td> <td> 0.380 0.746</td>\n", |
||
| 846 | "</tr>\n", |
||
| 847 | "<tr>\n", |
||
| 848 | " <th>Intercept</th> <td> 0.3368</td> <td> 0.043</td> <td> 7.855</td> <td> 0.000</td> <td> 0.252 0.422</td>\n", |
||
| 849 | "</tr>\n", |
||
| 850 | "</table>" |
||
| 851 | ], |
||
| 852 | "metadata": {}, |
||
| 853 | "output_type": "pyout", |
||
| 854 | "prompt_number": 29, |
||
| 855 | "text": [ |
||
| 856 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 857 | "\"\"\"\n", |
||
| 858 | " GLS Regression Results \n", |
||
| 859 | "===============================================================================\n", |
||
| 860 | "Dep. Variable: Portal_inflammation R-squared: 0.280\n", |
||
| 861 | "Model: GLS Adj. R-squared: 0.273\n", |
||
| 862 | "Method: Least Squares F-statistic: 37.34\n", |
||
| 863 | "Date: Tue, 28 Oct 2014 Prob (F-statistic): 2.12e-08\n", |
||
| 864 | "Time: 23:40:10 Log-Likelihood: 14.996\n", |
||
| 865 | "No. Observations: 98 AIC: -25.99\n", |
||
| 866 | "Df Residuals: 96 BIC: -20.82\n", |
||
| 867 | "Df Model: 1 \n", |
||
| 868 | "Covariance Type: nonrobust \n", |
||
| 869 | "==============================================================================\n", |
||
| 870 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 871 | "------------------------------------------------------------------------------\n", |
||
| 872 | "FociSize 0.5627 0.092 6.111 0.000 0.380 0.746\n", |
||
| 873 | "Intercept 0.3368 0.043 7.855 0.000 0.252 0.422\n", |
||
| 874 | "==============================================================================\n", |
||
| 875 | "\n", |
||
| 876 | "Warnings:\n", |
||
| 877 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 878 | "\"\"\"" |
||
| 879 | ] |
||
| 880 | } |
||
| 881 | ], |
||
| 882 | "prompt_number": 29 |
||
| 883 | }, |
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| 884 | { |
||
| 885 | "cell_type": "markdown", |
||
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| 888 | "slide_type": "subslide" |
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| 895 | { |
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| 896 | "cell_type": "code", |
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| 897 | "collapsed": false, |
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| 898 | "input": [ |
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| 899 | "hyperplasia" |
||
| 900 | ], |
||
| 901 | "language": "python", |
||
| 902 | "metadata": { |
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| 903 | "slideshow": { |
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| 904 | "slide_type": "subslide" |
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| 907 | "outputs": [ |
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| 908 | { |
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| 909 | "html": [ |
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| 910 | "<table class=\"simpletable\">\n", |
||
| 911 | "<caption>GLS Regression Results</caption>\n", |
||
| 912 | "<tr>\n", |
||
| 913 | " <th>Dep. Variable:</th> <td>BD_hyperplasia</td> <th> R-squared: </th> <td> 0.306</td>\n", |
||
| 914 | "</tr>\n", |
||
| 915 | "<tr>\n", |
||
| 916 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.284</td>\n", |
||
| 917 | "</tr>\n", |
||
| 918 | "<tr>\n", |
||
| 919 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 13.83</td>\n", |
||
| 920 | "</tr>\n", |
||
| 921 | "<tr>\n", |
||
| 922 | " <th>Date:</th> <td>Tue, 28 Oct 2014</td> <th> Prob (F-statistic):</th> <td>1.52e-07</td>\n", |
||
| 923 | "</tr>\n", |
||
| 924 | "<tr>\n", |
||
| 925 | " <th>Time:</th> <td>23:40:10</td> <th> Log-Likelihood: </th> <td> -3.9632</td>\n", |
||
| 926 | "</tr>\n", |
||
| 927 | "<tr>\n", |
||
| 928 | " <th>No. Observations:</th> <td> 98</td> <th> AIC: </th> <td> 15.93</td>\n", |
||
| 929 | "</tr>\n", |
||
| 930 | "<tr>\n", |
||
| 931 | " <th>Df Residuals:</th> <td> 94</td> <th> BIC: </th> <td> 26.27</td>\n", |
||
| 932 | "</tr>\n", |
||
| 933 | "<tr>\n", |
||
| 934 | " <th>Df Model:</th> <td> 3</td> <th> </th> <td> </td> \n", |
||
| 935 | "</tr>\n", |
||
| 936 | "<tr>\n", |
||
| 937 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 938 | "</tr>\n", |
||
| 939 | "</table>\n", |
||
| 940 | "<table class=\"simpletable\">\n", |
||
| 941 | "<tr>\n", |
||
| 942 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 943 | "</tr>\n", |
||
| 944 | "<tr>\n", |
||
| 945 | " <th>FociSize</th> <td> 0.6698</td> <td> 0.113</td> <td> 5.902</td> <td> 0.000</td> <td> 0.444 0.895</td>\n", |
||
| 946 | "</tr>\n", |
||
| 947 | "<tr>\n", |
||
| 948 | " <th>Scale</th> <td> 0.5811</td> <td> 0.243</td> <td> 2.394</td> <td> 0.019</td> <td> 0.099 1.063</td>\n", |
||
| 949 | "</tr>\n", |
||
| 950 | "<tr>\n", |
||
| 951 | " <th>Directionality</th> <td> -0.4419</td> <td> 0.190</td> <td> -2.330</td> <td> 0.022</td> <td> -0.819 -0.065</td>\n", |
||
| 952 | "</tr>\n", |
||
| 953 | "<tr>\n", |
||
| 954 | " <th>Intercept</th> <td> -0.0504</td> <td> 0.079</td> <td> -0.642</td> <td> 0.523</td> <td> -0.206 0.105</td>\n", |
||
| 955 | "</tr>\n", |
||
| 956 | "</table>" |
||
| 957 | ], |
||
| 958 | "metadata": {}, |
||
| 959 | "output_type": "pyout", |
||
| 960 | "prompt_number": 31, |
||
| 961 | "text": [ |
||
| 962 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 963 | "\"\"\"\n", |
||
| 964 | " GLS Regression Results \n", |
||
| 965 | "==============================================================================\n", |
||
| 966 | "Dep. Variable: BD_hyperplasia R-squared: 0.306\n", |
||
| 967 | "Model: GLS Adj. R-squared: 0.284\n", |
||
| 968 | "Method: Least Squares F-statistic: 13.83\n", |
||
| 969 | "Date: Tue, 28 Oct 2014 Prob (F-statistic): 1.52e-07\n", |
||
| 970 | "Time: 23:40:10 Log-Likelihood: -3.9632\n", |
||
| 971 | "No. Observations: 98 AIC: 15.93\n", |
||
| 972 | "Df Residuals: 94 BIC: 26.27\n", |
||
| 973 | "Df Model: 3 \n", |
||
| 974 | "Covariance Type: nonrobust \n", |
||
| 975 | "==================================================================================\n", |
||
| 976 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 977 | "----------------------------------------------------------------------------------\n", |
||
| 978 | "FociSize 0.6698 0.113 5.902 0.000 0.444 0.895\n", |
||
| 979 | "Scale 0.5811 0.243 2.394 0.019 0.099 1.063\n", |
||
| 980 | "Directionality -0.4419 0.190 -2.330 0.022 -0.819 -0.065\n", |
||
| 981 | "Intercept -0.0504 0.079 -0.642 0.523 -0.206 0.105\n", |
||
| 982 | "==================================================================================\n", |
||
| 983 | "\n", |
||
| 984 | "Warnings:\n", |
||
| 985 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 986 | "\"\"\"" |
||
| 987 | ] |
||
| 988 | } |
||
| 989 | ], |
||
| 990 | "prompt_number": 31 |
||
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| 993 | "cell_type": "markdown", |
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| 996 | "slide_type": "subslide" |
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| 1006 | "input": [ |
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| 1007 | "pca" |
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| 1008 | ], |
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| 1009 | "language": "python", |
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| 1017 | "html": [ |
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| 1018 | "<table class=\"simpletable\">\n", |
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| 1019 | "<caption>GLS Regression Results</caption>\n", |
||
| 1020 | "<tr>\n", |
||
| 1021 | " <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 0.075</td>\n", |
||
| 1022 | "</tr>\n", |
||
| 1023 | "<tr>\n", |
||
| 1024 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.065</td>\n", |
||
| 1025 | "</tr>\n", |
||
| 1026 | "<tr>\n", |
||
| 1027 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 7.723</td>\n", |
||
| 1028 | "</tr>\n", |
||
| 1029 | "<tr>\n", |
||
| 1030 | " <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.00657</td>\n", |
||
| 1031 | "</tr>\n", |
||
| 1032 | "<tr>\n", |
||
| 1033 | " <th>Time:</th> <td>14:38:47</td> <th> Log-Likelihood: </th> <td> -70.082</td>\n", |
||
| 1034 | "</tr>\n", |
||
| 1035 | "<tr>\n", |
||
| 1036 | " <th>No. Observations:</th> <td> 97</td> <th> AIC: </th> <td> 144.2</td>\n", |
||
| 1037 | "</tr>\n", |
||
| 1038 | "<tr>\n", |
||
| 1039 | " <th>Df Residuals:</th> <td> 95</td> <th> BIC: </th> <td> 149.3</td>\n", |
||
| 1040 | "</tr>\n", |
||
| 1041 | "<tr>\n", |
||
| 1042 | " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n", |
||
| 1043 | "</tr>\n", |
||
| 1044 | "<tr>\n", |
||
| 1045 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 1046 | "</tr>\n", |
||
| 1047 | "</table>\n", |
||
| 1048 | "<table class=\"simpletable\">\n", |
||
| 1049 | "<tr>\n", |
||
| 1050 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 1051 | "</tr>\n", |
||
| 1052 | "<tr>\n", |
||
| 1053 | " <th>const</th> <td>-2.949e-17</td> <td> 0.051</td> <td>-5.77e-16</td> <td> 1.000</td> <td> -0.102 0.102</td>\n", |
||
| 1054 | "</tr>\n", |
||
| 1055 | "<tr>\n", |
||
| 1056 | " <th>x1</th> <td> 0.3865</td> <td> 0.139</td> <td> 2.779</td> <td> 0.007</td> <td> 0.110 0.663</td>\n", |
||
| 1057 | "</tr>\n", |
||
| 1058 | "</table>" |
||
| 1059 | ], |
||
| 1060 | "metadata": {}, |
||
| 1061 | "output_type": "pyout", |
||
| 1062 | "prompt_number": 15, |
||
| 1063 | "text": [ |
||
| 1064 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 1065 | "\"\"\"\n", |
||
| 1066 | " GLS Regression Results \n", |
||
| 1067 | "==============================================================================\n", |
||
| 1068 | "Dep. Variable: y R-squared: 0.075\n", |
||
| 1069 | "Model: GLS Adj. R-squared: 0.065\n", |
||
| 1070 | "Method: Least Squares F-statistic: 7.723\n", |
||
| 1071 | "Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00657\n", |
||
| 1072 | "Time: 14:38:47 Log-Likelihood: -70.082\n", |
||
| 1073 | "No. Observations: 97 AIC: 144.2\n", |
||
| 1074 | "Df Residuals: 95 BIC: 149.3\n", |
||
| 1075 | "Df Model: 1 \n", |
||
| 1076 | "Covariance Type: nonrobust \n", |
||
| 1077 | "==============================================================================\n", |
||
| 1078 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 1079 | "------------------------------------------------------------------------------\n", |
||
| 1080 | "const -2.949e-17 0.051 -5.77e-16 1.000 -0.102 0.102\n", |
||
| 1081 | "x1 0.3865 0.139 2.779 0.007 0.110 0.663\n", |
||
| 1082 | "==============================================================================\n", |
||
| 1083 | "\n", |
||
| 1084 | "Warnings:\n", |
||
| 1085 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 1086 | "\"\"\"" |
||
| 1087 | ] |
||
| 1088 | } |
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| 1089 | ], |
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| 1097 | } |
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| 1100 | "" |
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| 1101 | ] |
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| 1103 | { |
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| 1104 | "cell_type": "heading", |
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| 1105 | "level": 2, |
||
| 1106 | "metadata": { |
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| 1107 | "slideshow": { |
||
| 1108 | "slide_type": "slide" |
||
| 1109 | } |
||
| 1110 | }, |
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| 1111 | "source": [ |
||
| 1112 | "Exploratory Analysis" |
||
| 1113 | ] |
||
| 1114 | }, |
||
| 1115 | { |
||
| 1116 | "cell_type": "heading", |
||
| 1117 | "level": 3, |
||
| 1118 | "metadata": {}, |
||
| 1119 | "source": [ |
||
| 1120 | "by age class" |
||
| 1121 | ] |
||
| 1122 | }, |
||
| 1123 | { |
||
| 1124 | "cell_type": "code", |
||
| 1125 | "collapsed": false, |
||
| 1126 | "input": [ |
||
| 1127 | "fibrosis" |
||
| 1128 | ], |
||
| 1129 | "language": "python", |
||
| 1130 | "metadata": { |
||
| 1131 | "slideshow": { |
||
| 1132 | "slide_type": "subslide" |
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| 1133 | } |
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| 1134 | }, |
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| 1135 | "outputs": [ |
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| 1136 | { |
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| 1137 | "html": [ |
||
| 1138 | "<table class=\"simpletable\">\n", |
||
| 1139 | "<caption>GLS Regression Results</caption>\n", |
||
| 1140 | "<tr>\n", |
||
| 1141 | " <th>Dep. Variable:</th> <td>Fibrosis</td> <th> R-squared: </th> <td> 0.800</td>\n", |
||
| 1142 | "</tr>\n", |
||
| 1143 | "<tr>\n", |
||
| 1144 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.778</td>\n", |
||
| 1145 | "</tr>\n", |
||
| 1146 | "<tr>\n", |
||
| 1147 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 36.07</td>\n", |
||
| 1148 | "</tr>\n", |
||
| 1149 | "<tr>\n", |
||
| 1150 | " <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.000201</td>\n", |
||
| 1151 | "</tr>\n", |
||
| 1152 | "<tr>\n", |
||
| 1153 | " <th>Time:</th> <td>11:13:48</td> <th> Log-Likelihood: </th> <td> 7.8003</td>\n", |
||
| 1154 | "</tr>\n", |
||
| 1155 | "<tr>\n", |
||
| 1156 | " <th>No. Observations:</th> <td> 11</td> <th> AIC: </th> <td> -11.60</td>\n", |
||
| 1157 | "</tr>\n", |
||
| 1158 | "<tr>\n", |
||
| 1159 | " <th>Df Residuals:</th> <td> 9</td> <th> BIC: </th> <td> -10.80</td>\n", |
||
| 1160 | "</tr>\n", |
||
| 1161 | "<tr>\n", |
||
| 1162 | " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n", |
||
| 1163 | "</tr>\n", |
||
| 1164 | "<tr>\n", |
||
| 1165 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 1166 | "</tr>\n", |
||
| 1167 | "</table>\n", |
||
| 1168 | "<table class=\"simpletable\">\n", |
||
| 1169 | "<tr>\n", |
||
| 1170 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 1171 | "</tr>\n", |
||
| 1172 | "<tr>\n", |
||
| 1173 | " <th>Inflammation</th> <td> 1.0159</td> <td> 0.169</td> <td> 6.006</td> <td> 0.000</td> <td> 0.633 1.399</td>\n", |
||
| 1174 | "</tr>\n", |
||
| 1175 | "<tr>\n", |
||
| 1176 | " <th>Intercept</th> <td> -0.0105</td> <td> 0.083</td> <td> -0.126</td> <td> 0.902</td> <td> -0.198 0.177</td>\n", |
||
| 1177 | "</tr>\n", |
||
| 1178 | "</table>" |
||
| 1179 | ], |
||
| 1180 | "metadata": {}, |
||
| 1181 | "output_type": "pyout", |
||
| 1182 | "prompt_number": 6, |
||
| 1183 | "text": [ |
||
| 1184 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 1185 | "\"\"\"\n", |
||
| 1186 | " GLS Regression Results \n", |
||
| 1187 | "==============================================================================\n", |
||
| 1188 | "Dep. Variable: Fibrosis R-squared: 0.800\n", |
||
| 1189 | "Model: GLS Adj. R-squared: 0.778\n", |
||
| 1190 | "Method: Least Squares F-statistic: 36.07\n", |
||
| 1191 | "Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.000201\n", |
||
| 1192 | "Time: 11:13:48 Log-Likelihood: 7.8003\n", |
||
| 1193 | "No. Observations: 11 AIC: -11.60\n", |
||
| 1194 | "Df Residuals: 9 BIC: -10.80\n", |
||
| 1195 | "Df Model: 1 \n", |
||
| 1196 | "Covariance Type: nonrobust \n", |
||
| 1197 | "================================================================================\n", |
||
| 1198 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 1199 | "--------------------------------------------------------------------------------\n", |
||
| 1200 | "Inflammation 1.0159 0.169 6.006 0.000 0.633 1.399\n", |
||
| 1201 | "Intercept -0.0105 0.083 -0.126 0.902 -0.198 0.177\n", |
||
| 1202 | "================================================================================\n", |
||
| 1203 | "\n", |
||
| 1204 | "Warnings:\n", |
||
| 1205 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 1206 | "\"\"\"" |
||
| 1207 | ] |
||
| 1208 | } |
||
| 1209 | ], |
||
| 1210 | "prompt_number": 6 |
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| 1211 | }, |
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| 1212 | { |
||
| 1213 | "cell_type": "markdown", |
||
| 1214 | "metadata": { |
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| 1215 | "slideshow": { |
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| 1216 | "slide_type": "subslide" |
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| 1217 | } |
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| 1220 | "" |
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| 1221 | ] |
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| 1222 | }, |
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| 1223 | { |
||
| 1224 | "cell_type": "code", |
||
| 1225 | "collapsed": false, |
||
| 1226 | "input": [ |
||
| 1227 | "lobular_collapse" |
||
| 1228 | ], |
||
| 1229 | "language": "python", |
||
| 1230 | "metadata": { |
||
| 1231 | "slideshow": { |
||
| 1232 | "slide_type": "subslide" |
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| 1234 | }, |
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| 1235 | "outputs": [ |
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| 1236 | { |
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| 1237 | "html": [ |
||
| 1238 | "<table class=\"simpletable\">\n", |
||
| 1239 | "<caption>GLS Regression Results</caption>\n", |
||
| 1240 | "<tr>\n", |
||
| 1241 | " <th>Dep. Variable:</th> <td>Lobular_collapse</td> <th> R-squared: </th> <td> 0.586</td>\n", |
||
| 1242 | "</tr>\n", |
||
| 1243 | "<tr>\n", |
||
| 1244 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.540</td>\n", |
||
| 1245 | "</tr>\n", |
||
| 1246 | "<tr>\n", |
||
| 1247 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 12.73</td>\n", |
||
| 1248 | "</tr>\n", |
||
| 1249 | "<tr>\n", |
||
| 1250 | " <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.00605</td>\n", |
||
| 1251 | "</tr>\n", |
||
| 1252 | "<tr>\n", |
||
| 1253 | " <th>Time:</th> <td>11:13:48</td> <th> Log-Likelihood: </th> <td> 2.2626</td>\n", |
||
| 1254 | "</tr>\n", |
||
| 1255 | "<tr>\n", |
||
| 1256 | " <th>No. Observations:</th> <td> 11</td> <th> AIC: </th> <td> -0.5252</td>\n", |
||
| 1257 | "</tr>\n", |
||
| 1258 | "<tr>\n", |
||
| 1259 | " <th>Df Residuals:</th> <td> 9</td> <th> BIC: </th> <td> 0.2706</td>\n", |
||
| 1260 | "</tr>\n", |
||
| 1261 | "<tr>\n", |
||
| 1262 | " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n", |
||
| 1263 | "</tr>\n", |
||
| 1264 | "<tr>\n", |
||
| 1265 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 1266 | "</tr>\n", |
||
| 1267 | "</table>\n", |
||
| 1268 | "<table class=\"simpletable\">\n", |
||
| 1269 | "<tr>\n", |
||
| 1270 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 1271 | "</tr>\n", |
||
| 1272 | "<tr>\n", |
||
| 1273 | " <th>FociSize</th> <td> 1.1379</td> <td> 0.319</td> <td> 3.567</td> <td> 0.006</td> <td> 0.416 1.860</td>\n", |
||
| 1274 | "</tr>\n", |
||
| 1275 | "<tr>\n", |
||
| 1276 | " <th>Intercept</th> <td> 0.0460</td> <td> 0.159</td> <td> 0.289</td> <td> 0.779</td> <td> -0.314 0.406</td>\n", |
||
| 1277 | "</tr>\n", |
||
| 1278 | "</table>" |
||
| 1279 | ], |
||
| 1280 | "metadata": {}, |
||
| 1281 | "output_type": "pyout", |
||
| 1282 | "prompt_number": 7, |
||
| 1283 | "text": [ |
||
| 1284 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 1285 | "\"\"\"\n", |
||
| 1286 | " GLS Regression Results \n", |
||
| 1287 | "==============================================================================\n", |
||
| 1288 | "Dep. Variable: Lobular_collapse R-squared: 0.586\n", |
||
| 1289 | "Model: GLS Adj. R-squared: 0.540\n", |
||
| 1290 | "Method: Least Squares F-statistic: 12.73\n", |
||
| 1291 | "Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00605\n", |
||
| 1292 | "Time: 11:13:48 Log-Likelihood: 2.2626\n", |
||
| 1293 | "No. Observations: 11 AIC: -0.5252\n", |
||
| 1294 | "Df Residuals: 9 BIC: 0.2706\n", |
||
| 1295 | "Df Model: 1 \n", |
||
| 1296 | "Covariance Type: nonrobust \n", |
||
| 1297 | "==============================================================================\n", |
||
| 1298 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 1299 | "------------------------------------------------------------------------------\n", |
||
| 1300 | "FociSize 1.1379 0.319 3.567 0.006 0.416 1.860\n", |
||
| 1301 | "Intercept 0.0460 0.159 0.289 0.779 -0.314 0.406\n", |
||
| 1302 | "==============================================================================\n", |
||
| 1303 | "\n", |
||
| 1304 | "Warnings:\n", |
||
| 1305 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 1306 | "\"\"\"" |
||
| 1307 | ] |
||
| 1308 | } |
||
| 1309 | ], |
||
| 1310 | "prompt_number": 7 |
||
| 1311 | }, |
||
| 1312 | { |
||
| 1313 | "cell_type": "markdown", |
||
| 1314 | "metadata": { |
||
| 1315 | "slideshow": { |
||
| 1316 | "slide_type": "subslide" |
||
| 1317 | } |
||
| 1318 | }, |
||
| 1319 | "source": [ |
||
| 1320 | "" |
||
| 1321 | ] |
||
| 1322 | }, |
||
| 1323 | { |
||
| 1324 | "cell_type": "code", |
||
| 1325 | "collapsed": false, |
||
| 1326 | "input": [ |
||
| 1327 | "interface_hepatitis" |
||
| 1328 | ], |
||
| 1329 | "language": "python", |
||
| 1330 | "metadata": { |
||
| 1331 | "slideshow": { |
||
| 1332 | "slide_type": "subslide" |
||
| 1333 | } |
||
| 1334 | }, |
||
| 1335 | "outputs": [ |
||
| 1336 | { |
||
| 1337 | "html": [ |
||
| 1338 | "<table class=\"simpletable\">\n", |
||
| 1339 | "<caption>GLS Regression Results</caption>\n", |
||
| 1340 | "<tr>\n", |
||
| 1341 | " <th>Dep. Variable:</th> <td>Interface_hepatitis</td> <th> R-squared: </th> <td> 0.659</td>\n", |
||
| 1342 | "</tr>\n", |
||
| 1343 | "<tr>\n", |
||
| 1344 | " <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.621</td>\n", |
||
| 1345 | "</tr>\n", |
||
| 1346 | "<tr>\n", |
||
| 1347 | " <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 17.38</td>\n", |
||
| 1348 | "</tr>\n", |
||
| 1349 | "<tr>\n", |
||
| 1350 | " <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.00242</td>\n", |
||
| 1351 | "</tr>\n", |
||
| 1352 | "<tr>\n", |
||
| 1353 | " <th>Time:</th> <td>11:13:48</td> <th> Log-Likelihood: </th> <td> 2.3063</td>\n", |
||
| 1354 | "</tr>\n", |
||
| 1355 | "<tr>\n", |
||
| 1356 | " <th>No. Observations:</th> <td> 11</td> <th> AIC: </th> <td> -0.6126</td>\n", |
||
| 1357 | "</tr>\n", |
||
| 1358 | "<tr>\n", |
||
| 1359 | " <th>Df Residuals:</th> <td> 9</td> <th> BIC: </th> <td> 0.1832</td>\n", |
||
| 1360 | "</tr>\n", |
||
| 1361 | "<tr>\n", |
||
| 1362 | " <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n", |
||
| 1363 | "</tr>\n", |
||
| 1364 | "<tr>\n", |
||
| 1365 | " <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n", |
||
| 1366 | "</tr>\n", |
||
| 1367 | "</table>\n", |
||
| 1368 | "<table class=\"simpletable\">\n", |
||
| 1369 | "<tr>\n", |
||
| 1370 | " <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n", |
||
| 1371 | "</tr>\n", |
||
| 1372 | "<tr>\n", |
||
| 1373 | " <th>Lacunarity</th> <td> -1.0224</td> <td> 0.245</td> <td> -4.168</td> <td> 0.002</td> <td> -1.577 -0.468</td>\n", |
||
| 1374 | "</tr>\n", |
||
| 1375 | "<tr>\n", |
||
| 1376 | " <th>Intercept</th> <td> 0.9504</td> <td> 0.143</td> <td> 6.669</td> <td> 0.000</td> <td> 0.628 1.273</td>\n", |
||
| 1377 | "</tr>\n", |
||
| 1378 | "</table>" |
||
| 1379 | ], |
||
| 1380 | "metadata": {}, |
||
| 1381 | "output_type": "pyout", |
||
| 1382 | "prompt_number": 8, |
||
| 1383 | "text": [ |
||
| 1384 | "<class 'statsmodels.iolib.summary.Summary'>\n", |
||
| 1385 | "\"\"\"\n", |
||
| 1386 | " GLS Regression Results \n", |
||
| 1387 | "===============================================================================\n", |
||
| 1388 | "Dep. Variable: Interface_hepatitis R-squared: 0.659\n", |
||
| 1389 | "Model: GLS Adj. R-squared: 0.621\n", |
||
| 1390 | "Method: Least Squares F-statistic: 17.38\n", |
||
| 1391 | "Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00242\n", |
||
| 1392 | "Time: 11:13:48 Log-Likelihood: 2.3063\n", |
||
| 1393 | "No. Observations: 11 AIC: -0.6126\n", |
||
| 1394 | "Df Residuals: 9 BIC: 0.1832\n", |
||
| 1395 | "Df Model: 1 \n", |
||
| 1396 | "Covariance Type: nonrobust \n", |
||
| 1397 | "==============================================================================\n", |
||
| 1398 | " coef std err t P>|t| [95.0% Conf. Int.]\n", |
||
| 1399 | "------------------------------------------------------------------------------\n", |
||
| 1400 | "Lacunarity -1.0224 0.245 -4.168 0.002 -1.577 -0.468\n", |
||
| 1401 | "Intercept 0.9504 0.143 6.669 0.000 0.628 1.273\n", |
||
| 1402 | "==============================================================================\n", |
||
| 1403 | "\n", |
||
| 1404 | "Warnings:\n", |
||
| 1405 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", |
||
| 1406 | "\"\"\"" |
||
| 1407 | ] |
||
| 1408 | } |
||
| 1409 | ], |
||
| 1410 | "prompt_number": 8 |
||
| 1411 | }, |
||
| 1412 | { |
||
| 1413 | "cell_type": "markdown", |
||
| 1414 | "metadata": { |
||
| 1415 | "slideshow": { |
||
| 1416 | "slide_type": "subslide" |
||
| 1417 | } |
||
| 1418 | }, |
||
| 1419 | "source": [ |
||
| 1420 | "" |
||
| 1421 | ] |
||
| 1422 | }, |
||
| 1423 | { |
||
| 1424 | "cell_type": "heading", |
||
| 1425 | "level": 2, |
||
| 1426 | "metadata": { |
||
| 1427 | "slideshow": { |
||
| 1428 | "slide_type": "slide" |
||
| 1429 | } |
||
| 1430 | }, |
||
| 1431 | "source": [ |
||
| 1432 | "Exploratory analysis" |
||
| 1433 | ] |
||
| 1434 | }, |
||
| 1435 | { |
||
| 1436 | "cell_type": "heading", |
||
| 1437 | "level": 3, |
||
| 1438 | "metadata": {}, |
||
| 1439 | "source": [ |
||
| 1440 | "with a random effect on age at death" |
||
| 1441 | ] |
||
| 1442 | }, |
||
| 1443 | { |
||
| 1444 | "cell_type": "markdown", |
||
| 1445 | "metadata": { |
||
| 1446 | "slideshow": { |
||
| 1447 | "slide_type": "subslide" |
||
| 1448 | } |
||
| 1449 | }, |
||
| 1450 | "source": [ |
||
| 1451 | "| Dependent variable | Models<br />AIC < 2 + AIC<sub>min</sub> | Primary explanatory variables |\n", |
||
| 1452 | "|------------------------------------------|:----------------------------------:|---------------------------------------------------------------------|\n", |
||
| 1453 | "| Ishak score | 7 | entropy, tissue-to-sinusoid, focus count, focus size |\n", |
||
| 1454 | "| Lobular collapse | 5 | entropy, lacunarity, tissue-to-sinusoid, focus count |\n", |
||
| 1455 | "| Confluent necrosis | 1 | entropy |\n", |
||
| 1456 | "| Interface hepatitis | 2 | entropy, tissue-to-sinusoid |\n", |
||
| 1457 | "| Portal inflammation | 4 | entropy, focus size, lacunarity, focus count, scale, directionality |\n", |
||
| 1458 | "| Fibrosis | 2 | entropy, lacunarity, tissue-to-sinusoid |\n", |
||
| 1459 | "| Biliary hyperplasia | 1 | focus size |\n", |
||
| 1460 | "| Necrosis, apoptosis, random inflammation | <font color=\"white\">This_is_bla</font>2<font color=\"white\">This_is_bla</font> | entropy, lacunarity |" |
||
| 1461 | ] |
||
| 1462 | }, |
||
| 1463 | { |
||
| 1464 | "cell_type": "markdown", |
||
| 1465 | "metadata": { |
||
| 1466 | "slideshow": { |
||
| 1467 | "slide_type": "subslide" |
||
| 1468 | } |
||
| 1469 | }, |
||
| 1470 | "source": [ |
||
| 1471 | "- entropy consistently explains histological measures when controlled for age\n", |
||
| 1472 | "- also important : tissue to sinusoid ratio, focus count and size, lacunarity" |
||
| 1473 | ] |
||
| 1474 | }, |
||
| 1475 | { |
||
| 1476 | "cell_type": "markdown", |
||
| 1477 | "metadata": { |
||
| 1478 | "slideshow": { |
||
| 1479 | "slide_type": "fragment" |
||
| 1480 | } |
||
| 1481 | }, |
||
| 1482 | "source": [ |
||
| 1483 | "- biological / historical reasoning for this potential cohort effect\n", |
||
| 1484 | "- interpretation of these models\n", |
||
| 1485 | "- quality of fit" |
||
| 1486 | ] |
||
| 1487 | }, |
||
| 1488 | { |
||
| 1489 | "cell_type": "heading", |
||
| 1490 | "level": 2, |
||
| 1491 | "metadata": { |
||
| 1492 | "slideshow": { |
||
| 1493 | "slide_type": "slide" |
||
| 1494 | } |
||
| 1495 | }, |
||
| 1496 | "source": [ |
||
| 1497 | "Conclusions" |
||
| 1498 | ] |
||
| 1499 | }, |
||
| 1500 | { |
||
| 1501 | "cell_type": "markdown", |
||
| 1502 | "metadata": {}, |
||
| 1503 | "source": [ |
||
| 1504 | "- our **semi-educated guess** measures may capture relevant information\n", |
||
| 1505 | "- underlying **structure** in the data needs thought\n", |
||
| 1506 | "- still no **map** from image or histological measures to condition of individual\n" |
||
| 1507 | ] |
||
| 1508 | }, |
||
| 1509 | { |
||
| 1510 | "cell_type": "heading", |
||
| 1511 | "level": 2, |
||
| 1512 | "metadata": { |
||
| 1513 | "slideshow": { |
||
| 1514 | "slide_type": "slide" |
||
| 1515 | } |
||
| 1516 | }, |
||
| 1517 | "source": [ |
||
| 1518 | "Future directions" |
||
| 1519 | ] |
||
| 1520 | }, |
||
| 1521 | { |
||
| 1522 | "cell_type": "heading", |
||
| 1523 | "level": 3, |
||
| 1524 | "metadata": { |
||
| 1525 | "slideshow": { |
||
| 1526 | "slide_type": "subslide" |
||
| 1527 | } |
||
| 1528 | }, |
||
| 1529 | "source": [ |
||
| 1530 | "Further exploration of the dataset" |
||
| 1531 | ] |
||
| 1532 | }, |
||
| 1533 | { |
||
| 1534 | "cell_type": "markdown", |
||
| 1535 | "metadata": { |
||
| 1536 | "slideshow": { |
||
| 1537 | "slide_type": "-" |
||
| 1538 | } |
||
| 1539 | }, |
||
| 1540 | "source": [ |
||
| 1541 | "- 145 sheep ( 89 females )\n", |
||
| 1542 | "- 11 age classes\n", |
||
| 1543 | "- potential redundancy in various measures" |
||
| 1544 | ] |
||
| 1545 | }, |
||
| 1546 | { |
||
| 1547 | "cell_type": "markdown", |
||
| 1548 | "metadata": { |
||
| 1549 | "slideshow": { |
||
| 1550 | "slide_type": "fragment" |
||
| 1551 | } |
||
| 1552 | }, |
||
| 1553 | "source": [ |
||
| 1554 | "- 4460 entries across 27 variables\n", |
||
| 1555 | "- 3330 with full image and histological information\n", |
||
| 1556 | "- 1196 for which **complete** information is available" |
||
| 1557 | ] |
||
| 1558 | }, |
||
| 1559 | { |
||
| 1560 | "cell_type": "heading", |
||
| 1561 | "level": 3, |
||
| 1562 | "metadata": { |
||
| 1563 | "slideshow": { |
||
| 1564 | "slide_type": "subslide" |
||
| 1565 | } |
||
| 1566 | }, |
||
| 1567 | "source": [ |
||
| 1568 | "More data" |
||
| 1569 | ] |
||
| 1570 | }, |
||
| 1571 | { |
||
| 1572 | "cell_type": "markdown", |
||
| 1573 | "metadata": {}, |
||
| 1574 | "source": [ |
||
| 1575 | "- nutritional information\n", |
||
| 1576 | "- immunity data" |
||
| 1577 | ] |
||
| 1578 | }, |
||
| 1579 | { |
||
| 1580 | "cell_type": "heading", |
||
| 1581 | "level": 3, |
||
| 1582 | "metadata": { |
||
| 1583 | "slideshow": { |
||
| 1584 | "slide_type": "subslide" |
||
| 1585 | } |
||
| 1586 | }, |
||
| 1587 | "source": [ |
||
| 1588 | "Narrow-field images" |
||
| 1589 | ] |
||
| 1590 | }, |
||
| 1591 | { |
||
| 1592 | "cell_type": "markdown", |
||
| 1593 | "metadata": {}, |
||
| 1594 | "source": [ |
||
| 1595 | "- 12536 images\n", |
||
| 1596 | "- spatial distribution of nuclei" |
||
| 1597 | ] |
||
| 1598 | }, |
||
| 1599 | { |
||
| 1600 | "cell_type": "markdown", |
||
| 1601 | "metadata": { |
||
| 1602 | "slideshow": { |
||
| 1603 | "slide_type": "subslide" |
||
| 1604 | } |
||
| 1605 | }, |
||
| 1606 | "source": [ |
||
| 1607 | "" |
||
| 1608 | ] |
||
| 1609 | }, |
||
| 1610 | { |
||
| 1611 | "cell_type": "markdown", |
||
| 1612 | "metadata": { |
||
| 1613 | "slideshow": { |
||
| 1614 | "slide_type": "subslide" |
||
| 1615 | } |
||
| 1616 | }, |
||
| 1617 | "source": [ |
||
| 1618 | "" |
||
| 1619 | ] |
||
| 1620 | }, |
||
| 1621 | { |
||
| 1622 | "cell_type": "markdown", |
||
| 1623 | "metadata": { |
||
| 1624 | "slideshow": { |
||
| 1625 | "slide_type": "subslide" |
||
| 1626 | } |
||
| 1627 | }, |
||
| 1628 | "source": [ |
||
| 1629 | "" |
||
| 1630 | ] |
||
| 1631 | }, |
||
| 1632 | { |
||
| 1633 | "cell_type": "markdown", |
||
| 1634 | "metadata": { |
||
| 1635 | "slideshow": { |
||
| 1636 | "slide_type": "subslide" |
||
| 1637 | } |
||
| 1638 | }, |
||
| 1639 | "source": [ |
||
| 1640 | "<img src=\"figures/10x.png\" width=100%></src>" |
||
| 1641 | ] |
||
| 1642 | } |
||
| 1643 | ], |
||
| 1644 | "metadata": {} |
||
| 1645 | } |
||
| 1646 | ] |
||
| 1647 | } |