Datasets
Models
Downloads: 1
1647 lines (1647 with data), 58.0 kB
{
"metadata": {
"celltoolbar": "Slideshow",
"name": "",
"signature": "sha256:683ceb13e563077b8da74ca91d75c910b368c1da6290dcded253f1373c1c887b"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Robust Extraction of Quantitative Information from Histology Images"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Quentin Caudron\n",
"<br /><br />\n",
"\n",
"Romain Garnier\n",
"<br /><br />\n",
"\n",
"*with Bryan Grenfell and Andrea Graham*"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Outline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Image processing\n",
"- Extracted measures\n",
"- Preliminary analysis\n",
"- Future directions"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"4. Age as random effect <---\n",
"\n",
"[\"interface_hepatitis\", \"confluent_necrosis\", \"portal_inflammation\", \"ln_ap_ri\"]"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def normalise(df, skip = []) :\n",
"\tfor i in df.columns :\n",
"\t\tif i not in skip :\n",
"\t\t\tdf[i] -= df[i].mean()\n",
"\t\t\tdf[i] /= df[i].std()\n",
"\treturn df\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"def rescale(df, skip = []) :\n",
" for i in df.columns :\n",
" if i not in skip :\n",
" df[i] -= df[i].min()\n",
" df[i] /= df[i].max()\n",
" return df\n",
"\n",
"\n",
"\n",
"# Remove a layer from a list\n",
"def delayer(m) :\n",
"\tout = []\n",
"\tfor i in m :\n",
"\t\tif isinstance(i, list) :\n",
"\t\t\tfor j in i :\n",
"\t\t\t\tout.append(j)\n",
"\t\telse :\n",
"\t\t\tout.append(i)\n",
"\treturn out\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"# Remove all layers from a list\n",
"def flatten(m) :\n",
"\tout = m[:]\n",
"\n",
"\twhile out != delayer(out) :\n",
"\t\tout = delayer(out)\n",
"\n",
"\treturn out\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"# Generate all combinations of objects in a list\n",
"def combinatorial(l) :\n",
"\tout = []\n",
"\n",
"\tfor numel in range(len(l)) :\n",
"\t\tfor i in itertools.combinations(l, numel+1) :\n",
"\t\t\tout.append(list(i))\n",
"\n",
"\treturn out\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"def pcaplot(df) :\n",
"\n",
"\t# PCA\n",
"\tpca = decomposition.PCA(whiten = True)\n",
"\tpca.fit(df)\n",
"\tp1 = pca.components_[0] / np.abs(pca.components_[0]).max() * np.sqrt(2)/2\n",
"\tp2 = pca.components_[1] / np.abs(pca.components_[1]).max() * np.sqrt(2)/2\n",
"\n",
"\t# Normalise\n",
"\tnorms = np.max([np.sqrt((np.array(zip(p1, p2)[i])**2).sum()) for i in range(len(p1))])\n",
"\tc = plt.Circle( (0, 0), radius = 1, alpha = 0.2)\n",
"\tplt.axes(aspect = 1)\n",
"\tplt.gca().add_artist(c)\n",
"\n",
"\tplt.scatter(p1 / norms, p2 / norms)\n",
"\tplt.xlim([-1, 1])\n",
"\tplt.ylim([-1, 1])\n",
"\n",
"\tfor i, text in enumerate(df.columns) :\n",
"\t\tplt.annotate(text, xy = [p1[i], p2[i]])\n",
"\n",
"\tplt.tight_layout()\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"def test_all_linear(df, y, x, return_significant = False, group = None) :\n",
"\n",
" # All possible combinations of independent variables\n",
"\tindependent = combinatorial(x)\n",
"\n",
"\tfits = {}\n",
"\tpval = {}\n",
"\tlinmodels = {}\n",
"\tqsum = {}\n",
"\taic = {}\n",
"\n",
"\t# For all dependent variables, one at a time\n",
"\tfor dependent in y :\n",
"\n",
"\t\tprint \"Fitting for %s.\" % dependent\n",
"\n",
"\t\t# For all combinations of independent variables\n",
"\t\tfor covariate in independent :\n",
"\n",
"\t\t\t# Standard mixed model\n",
"\t\t\tif group is None :\n",
"\n",
"\t\t\t\t# Fit a linear model\n",
"\t\t\t\tsubset = delayer([covariate, dependent])\n",
"\t\t\t\tdf2 = df[delayer(subset)].dropna()\n",
"\t\t\t\tdf2[\"Intercept\"] = np.ones(len(df2))\n",
" \n",
"\t\t\t\tols = sm.GLS(endog = df2[dependent], exog = df2[delayer([covariate, \"Intercept\"])]).fit()\n",
"\n",
"\t\t\t\t# Save the results\n",
"\t\t\t\tif (return_significant and ols.f_pvalue < 0.05) or (not return_significant) :\n",
"\t\t\t\t\tlinmodels.setdefault(dependent, []).append(ols)\n",
"\t\t\t\t\tfits.setdefault(dependent, []).append(ols.rsquared)\n",
"\t\t\t\t\tpval.setdefault(dependent, []).append(ols.f_pvalue)\n",
"\t\t\t\t\taic.setdefault(dependent, []).append(ols.aic)\n",
"\n",
"\n",
"\t\t\t# Mixed effects model\n",
"\t\t\telse :\n",
"\t\t\t\tsubset = delayer([covariate, dependent, group])\n",
"\t\t\t\tdf2 = df[delayer(subset)].dropna()\n",
"\n",
"\t\t\t\t# Fit a mixed effects model\n",
"\t\t\t\tols = MixedLM(endog = df2[dependent], exog = df2[covariate], groups = df2[group]).fit()\n",
"\n",
"\t\t\t\t# Calculate AIC\n",
"\t\t\t\tlinmodels.setdefault(dependent, []).append(ols)\n",
"\t\t\t\tfits.setdefault(dependent, []).append(2 * (ols.k_fe + 1) - 2 * ols.llf)\n",
"\t\t\t\tpval.setdefault(dependent, []).append(ols.pvalues)\n",
"\n",
"\tif group is not None :\n",
"\t\tfor i in y :\n",
"\t\t\tf = np.array(fits[i])\n",
"\t\t\tmodels = np.array(linmodels[i])\n",
"\t\t\tidx = np.where(f - f.min() <= 2)[0]\n",
"\t\t\tbestmodelDoF = [j.k_fe for j in np.array(linmodels[i])[idx]]\n",
"\t\t\tbestmodels = [idx[j] for j in np.where(bestmodelDoF == np.min(bestmodelDoF))[0]]\n",
"\t\t\tqsum[i] = models[idx[np.where(f[bestmodels] == np.min(f[bestmodels]))]]\n",
"\n",
"\n",
"\t\treturn linmodels, fits, pval, qsum\n",
"\n",
"\treturn linmodels, fits, pval, aic\n",
"\n",
"\t\n",
"\t\t\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"def summary(models) :\n",
"\n",
"\t# Generate list of everything\n",
"\tr2 = np.array([m.r2 for dependent in models.keys() for m in models[dependent]])\n",
"\tp = np.array([m.f_stat[\"p-value\"] for dependent in models.keys() for m in models[dependent]])\n",
"\tmod = np.array([m for dependent in models.keys() for m in models[dependent]])\n",
"\tdependent = np.array([dependent for dependent in models.keys() for m in models[dependent]])\n",
"\n",
"\t# Sort by R2\n",
"\tidx = np.argsort(r2)[::-1]\n",
"\n",
"\t# Output string\n",
"\ts = \"%d significant regressions.\\n\\n\" % len(r2)\n",
"\ts += \"Ten most correlated :\\n\\n\"\n",
"\n",
"\t# Print a summary of the top ten correlations\n",
"\tfor i in idx[:10] :\n",
"\t\ts += (\"%s ~ %s\\n\" % (dependent[i], \" + \".join(mod[i].x.columns[:-1])))\n",
"\t\ts += (\"R^2 = %f\\tp = %f\\n\\n\" % (r2[i], p[i]))\n",
"\n",
"\tprint s\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
"def rstr(y, x) :\n",
" formatstr = \"%s ~ \" % y\n",
" for i in x[:-1] :\n",
" formatstr += str(i)\n",
" formatstr += \" + \"\n",
" formatstr += str(x[-1])\n",
" return formatstr\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"from sklearn.neighbors import KernelDensity\n",
"from matplotlib import rcParams\n",
"import matplotlib.pyplot as plt\n",
"import seaborn\n",
"import pandas as pd\n",
"import itertools\n",
"from sklearn import linear_model, ensemble, decomposition, cross_validation, preprocessing\n",
"from statsmodels.regression.mixed_linear_model import MixedLM\n",
"import statsmodels.api as sm\n",
"from statsmodels.regression.linear_model import OLSResults\n",
"from statsmodels.tools.tools import add_constant\n",
"\n",
"\n",
"%matplotlib inline\n",
"rcParams[\"figure.figsize\"] = (14, 8)\n",
"\n",
"\n",
"# RAW DATA\n",
"\n",
"raw_physical = pd.read_csv(\"../data/physical.csv\")\n",
"raw_histo = pd.read_csv(\"../data/tawfik.csv\")\n",
"ent = pd.read_csv(\"../4x/results/entropy.csv\").drop([\"Unnamed: 0\"], 1)\n",
"foci = pd.read_csv(\"../4x/results/foci.csv\").drop([\"Unnamed: 0\"], 1)\n",
"lac = pd.read_csv(\"../4x/results/normalised_lacunarity.csv\").drop([\"Unnamed: 0\"], 1)\n",
"gabor = pd.read_csv(\"../4x/results/gabor_filters.csv\").drop([\"Unnamed: 0\"], 1)\n",
"ts = pd.read_csv(\"../4x/results/tissue_sinusoid_ratio.csv\").drop([\"Unnamed: 0\"], 1)\n",
"\n",
"raw_image = pd.merge(lac, ent,\n",
"\ton=[\"Sheep\", \"Image\"]).merge(foci, \n",
"\ton=[\"Sheep\", \"Image\"]).merge(gabor,\n",
"\ton=[\"Sheep\", \"Image\"]).merge(ts, \n",
" on=[\"Sheep\", \"Image\"])\n",
"raw_image.rename(columns = {\t\"meanSize\" : \"FociSize\", \n",
"\t\t\t\t\t\t\t\t\"TSRatio\" : \"TissueToSinusoid\",\n",
"\t\t\t\t\t\t\t\t\"Count\" : \"FociCount\" }, inplace=True)\n",
"\n",
"\n",
"\n",
"# CLEAN DATA\n",
"\n",
"physcols = [\"Weight\", \"Sex\", \"AgeAtDeath\", \"Foreleg\", \"Hindleg\"]\n",
"imagecols = [\"Entropy\", \"Lacunarity\", \"Inflammation\", \"Scale\", \"Directionality\", \"FociCount\", \"FociSize\", \"TissueToSinusoid\"]\n",
"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",
"\n",
"\n",
"\n",
"\n",
"\n",
"# IMAGE\n",
"\n",
"# Set FociSize to zero if FociCount is zero\n",
"# Drop stdSize\n",
"image = raw_image\n",
"image = image.drop(\"stdSize\", 1)\n",
"image.FociSize[raw_image.FociCount == 0] = 0\n",
"\n",
"\n",
"\n",
"# HISTO\n",
"\n",
"histo = raw_histo\n",
"histo = histo.drop([\"Vessels\", \"Vacuol\", \"Pigment\", \"Std_hep_size\"], 1)\n",
"\n",
"\n",
"\n",
"# PHYSICAL\n",
"\n",
"physical = raw_physical\n",
"physical = physical.drop([\"CurrTag\", \"DeathDate\", \"Category\"], 1)\n",
"physical\n",
"\n",
"\n",
"\n",
"\n",
"# COMPLETE DATASET\n",
"\n",
"raw_data = pd.merge(pd.merge(image, histo, on=\"Sheep\", how=\"outer\"), physical, on=\"Sheep\", how=\"outer\")\n",
"raw_data.to_csv(\"../data/tentative_complete.csv\")\n",
"\n",
"\n",
"\n",
"\n",
"# AVERAGED BY SHEEP\n",
"data = raw_data\n",
"data[\"Inflammation\"] = data.FociCount * data.FociSize\n",
"\n",
"sheep = rescale(data.groupby(\"Sheep\").mean())\n",
"age = rescale(data.groupby(\"AgeAtDeath\").mean())\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"# REGRESSIONS : fixed effects, grouped by sheep\n",
"\n",
"df = sheep[[\"Portal_inflammation\", \"FociSize\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"portal_inflammation = sm.GLS(endog = df.Portal_inflammation, exog = df[[\"FociSize\", \"Intercept\"]]).fit().summary()\n",
"#portal_inflammation = portal_inflammation.summary()\n",
"del portal_inflammation.tables[2]\n",
"\n",
"\n",
"\n",
"df = sheep[[\"BD_hyperplasia\", \"Scale\", \"Directionality\", \"FociSize\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"hyperplasia = sm.GLS(endog = df.BD_hyperplasia, exog = df[[\"FociSize\", \"Scale\", \"Directionality\", \"Intercept\"]]).fit().summary()\n",
"#hyperplasia.summary()\n",
"del hyperplasia.tables[2]\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"# REGRESSIONS : fixed effects, grouped by age\n",
"\n",
"df = age[[\"Max_hep_size\", \"Entropy\", \"Directionality\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"maxhepsize = sm.GLS(endog = df.Max_hep_size, exog = df[[\"Entropy\", \"Directionality\", \"Intercept\"]]).fit().summary()\n",
"del maxhepsize.tables[2]\n",
"\n",
"\n",
"\n",
"\n",
"df = age[[\"Lobular_collapse\", \"FociSize\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"lobular_collapse = sm.GLS(endog = df.Lobular_collapse, exog = df[[\"FociSize\", \"Intercept\"]]).fit().summary()\n",
"del lobular_collapse.tables[2]\n",
"\n",
"\n",
"df = age[[\"Interface_hepatitis\", \"Lacunarity\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"interface_hepatitis = sm.GLS(endog = df.Interface_hepatitis, exog = df[[\"Lacunarity\", \"Intercept\"]]).fit().summary()\n",
"del interface_hepatitis.tables[2]\n",
"\n",
"\n",
"df = age[[\"Fibrosis\", \"Inflammation\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"fibrosis = sm.GLS(endog = df.Fibrosis, exog = df[[\"Inflammation\", \"Intercept\"]]).fit().summary()\n",
"del fibrosis.tables[2]\n",
"\n",
"\n",
"\n",
"\n",
"# PCA\n",
"\n",
"s = sheep.dropna(subset=delayer([imagecols, histcols]))\n",
"pca = decomposition.PCA(n_components=1)\n",
"pcax = pca.fit_transform(s[imagecols])\n",
"pcay = pca.fit_transform(s[histcols])\n",
"pca = sm.GLS(endog = pcay[:, 0][:, np.newaxis], exog = add_constant(pcax)).fit().summary()\n",
"del pca.tables[2]\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"# REGRESSIONS : mixed effects, intercept on age at death\n",
"\n",
"df = age[[\"Fibrosis\", \"Inflammation\"]].dropna()\n",
"df[\"Intercept\"] = np.ones(len(df))\n",
"fibrosis = sm.GLS(endog = df.Fibrosis, exog = df[[\"Inflammation\", \"Intercept\"]]).fit().summary()\n",
"del fibrosis.tables[2]"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a = portal_inflammation.summary()\n",
"del a.tables[2]\n",
"a"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Portal_inflammation</td> <th> R-squared: </th> <td> 0.280</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.273</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 37.34</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Tue, 28 Oct 2014</td> <th> Prob (F-statistic):</th> <td>2.12e-08</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>23:35:30</td> <th> Log-Likelihood: </th> <td> 14.996</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 98</td> <th> AIC: </th> <td> -25.99</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 96</td> <th> BIC: </th> <td> -20.82</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 19,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"===============================================================================\n",
"Dep. Variable: Portal_inflammation R-squared: 0.280\n",
"Model: GLS Adj. R-squared: 0.273\n",
"Method: Least Squares F-statistic: 37.34\n",
"Date: Tue, 28 Oct 2014 Prob (F-statistic): 2.12e-08\n",
"Time: 23:35:30 Log-Likelihood: 14.996\n",
"No. Observations: 98 AIC: -25.99\n",
"Df Residuals: 96 BIC: -20.82\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"FociSize 0.5627 0.092 6.111 0.000 0.380 0.746\n",
"Intercept 0.3368 0.043 7.855 0.000 0.252 0.422\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Image Processing"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img src=\"figures/sheep.jpg\"></img>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img src=\"figures/processed.jpg\"></img>"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Extraction"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"- Automagical\n",
"- Reasonably quick"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Robust"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"- Invariant to staining, slicing, field-related variation\n",
"- Capture intersample variation"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Structural and Textural Measures"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- characteristic **scale** of sinusoid widths\n",
"- **directional** amplitude of preferred sinusoid alignment\n",
"- **tissue to sinusoid** ratio\n",
"- **count** of inflammatory foci per image\n",
"- **mean size** of inflammatory foci per image\n",
"- information **entropy** of sinusoid distribution\n",
"- **lacunarity** ( clustering ) of sinusoids"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img src=\"figures/gif.gif\"></img>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Exploratory Analysis"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"by individual"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"portal_inflammation"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Portal_inflammation</td> <th> R-squared: </th> <td> 0.280</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.273</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 37.34</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Tue, 28 Oct 2014</td> <th> Prob (F-statistic):</th> <td>2.12e-08</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>23:40:10</td> <th> Log-Likelihood: </th> <td> 14.996</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 98</td> <th> AIC: </th> <td> -25.99</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 96</td> <th> BIC: </th> <td> -20.82</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 29,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"===============================================================================\n",
"Dep. Variable: Portal_inflammation R-squared: 0.280\n",
"Model: GLS Adj. R-squared: 0.273\n",
"Method: Least Squares F-statistic: 37.34\n",
"Date: Tue, 28 Oct 2014 Prob (F-statistic): 2.12e-08\n",
"Time: 23:40:10 Log-Likelihood: 14.996\n",
"No. Observations: 98 AIC: -25.99\n",
"Df Residuals: 96 BIC: -20.82\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"FociSize 0.5627 0.092 6.111 0.000 0.380 0.746\n",
"Intercept 0.3368 0.043 7.855 0.000 0.252 0.422\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 29
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"hyperplasia"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>BD_hyperplasia</td> <th> R-squared: </th> <td> 0.306</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.284</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 13.83</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Tue, 28 Oct 2014</td> <th> Prob (F-statistic):</th> <td>1.52e-07</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>23:40:10</td> <th> Log-Likelihood: </th> <td> -3.9632</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 98</td> <th> AIC: </th> <td> 15.93</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 94</td> <th> BIC: </th> <td> 26.27</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 3</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 31,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: BD_hyperplasia R-squared: 0.306\n",
"Model: GLS Adj. R-squared: 0.284\n",
"Method: Least Squares F-statistic: 13.83\n",
"Date: Tue, 28 Oct 2014 Prob (F-statistic): 1.52e-07\n",
"Time: 23:40:10 Log-Likelihood: -3.9632\n",
"No. Observations: 98 AIC: 15.93\n",
"Df Residuals: 94 BIC: 26.27\n",
"Df Model: 3 \n",
"Covariance Type: nonrobust \n",
"==================================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"----------------------------------------------------------------------------------\n",
"FociSize 0.6698 0.113 5.902 0.000 0.444 0.895\n",
"Scale 0.5811 0.243 2.394 0.019 0.099 1.063\n",
"Directionality -0.4419 0.190 -2.330 0.022 -0.819 -0.065\n",
"Intercept -0.0504 0.079 -0.642 0.523 -0.206 0.105\n",
"==================================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 31
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pca"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 0.075</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.065</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 7.723</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.00657</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>14:38:47</td> <th> Log-Likelihood: </th> <td> -70.082</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 97</td> <th> AIC: </th> <td> 144.2</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 95</td> <th> BIC: </th> <td> 149.3</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.075\n",
"Model: GLS Adj. R-squared: 0.065\n",
"Method: Least Squares F-statistic: 7.723\n",
"Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00657\n",
"Time: 14:38:47 Log-Likelihood: -70.082\n",
"No. Observations: 97 AIC: 144.2\n",
"Df Residuals: 95 BIC: 149.3\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"const -2.949e-17 0.051 -5.77e-16 1.000 -0.102 0.102\n",
"x1 0.3865 0.139 2.779 0.007 0.110 0.663\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Exploratory Analysis"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"by age class"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fibrosis"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Fibrosis</td> <th> R-squared: </th> <td> 0.800</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.778</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 36.07</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.000201</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>11:13:48</td> <th> Log-Likelihood: </th> <td> 7.8003</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 11</td> <th> AIC: </th> <td> -11.60</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 9</td> <th> BIC: </th> <td> -10.80</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Fibrosis R-squared: 0.800\n",
"Model: GLS Adj. R-squared: 0.778\n",
"Method: Least Squares F-statistic: 36.07\n",
"Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.000201\n",
"Time: 11:13:48 Log-Likelihood: 7.8003\n",
"No. Observations: 11 AIC: -11.60\n",
"Df Residuals: 9 BIC: -10.80\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"================================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"--------------------------------------------------------------------------------\n",
"Inflammation 1.0159 0.169 6.006 0.000 0.633 1.399\n",
"Intercept -0.0105 0.083 -0.126 0.902 -0.198 0.177\n",
"================================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"lobular_collapse"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Lobular_collapse</td> <th> R-squared: </th> <td> 0.586</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.540</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 12.73</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.00605</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>11:13:48</td> <th> Log-Likelihood: </th> <td> 2.2626</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 11</td> <th> AIC: </th> <td> -0.5252</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 9</td> <th> BIC: </th> <td> 0.2706</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Lobular_collapse R-squared: 0.586\n",
"Model: GLS Adj. R-squared: 0.540\n",
"Method: Least Squares F-statistic: 12.73\n",
"Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00605\n",
"Time: 11:13:48 Log-Likelihood: 2.2626\n",
"No. Observations: 11 AIC: -0.5252\n",
"Df Residuals: 9 BIC: 0.2706\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"FociSize 1.1379 0.319 3.567 0.006 0.416 1.860\n",
"Intercept 0.0460 0.159 0.289 0.779 -0.314 0.406\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"interface_hepatitis"
],
"language": "python",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"html": [
"<table class=\"simpletable\">\n",
"<caption>GLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Interface_hepatitis</td> <th> R-squared: </th> <td> 0.659</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLS</td> <th> Adj. R-squared: </th> <td> 0.621</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 17.38</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Wed, 29 Oct 2014</td> <th> Prob (F-statistic):</th> <td>0.00242</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>11:13:48</td> <th> Log-Likelihood: </th> <td> 2.3063</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 11</td> <th> AIC: </th> <td> -0.6126</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 9</td> <th> BIC: </th> <td> 0.1832</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"<tr>\n",
" <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",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" GLS Regression Results \n",
"===============================================================================\n",
"Dep. Variable: Interface_hepatitis R-squared: 0.659\n",
"Model: GLS Adj. R-squared: 0.621\n",
"Method: Least Squares F-statistic: 17.38\n",
"Date: Wed, 29 Oct 2014 Prob (F-statistic): 0.00242\n",
"Time: 11:13:48 Log-Likelihood: 2.3063\n",
"No. Observations: 11 AIC: -0.6126\n",
"Df Residuals: 9 BIC: 0.1832\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"Lacunarity -1.0224 0.245 -4.168 0.002 -1.577 -0.468\n",
"Intercept 0.9504 0.143 6.669 0.000 0.628 1.273\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Exploratory analysis"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"with a random effect on age at death"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"| Dependent variable | Models<br />AIC < 2 + AIC<sub>min</sub> | Primary explanatory variables |\n",
"|------------------------------------------|:----------------------------------:|---------------------------------------------------------------------|\n",
"| Ishak score | 7 | entropy, tissue-to-sinusoid, focus count, focus size |\n",
"| Lobular collapse | 5 | entropy, lacunarity, tissue-to-sinusoid, focus count |\n",
"| Confluent necrosis | 1 | entropy |\n",
"| Interface hepatitis | 2 | entropy, tissue-to-sinusoid |\n",
"| Portal inflammation | 4 | entropy, focus size, lacunarity, focus count, scale, directionality |\n",
"| Fibrosis | 2 | entropy, lacunarity, tissue-to-sinusoid |\n",
"| Biliary hyperplasia | 1 | focus size |\n",
"| Necrosis, apoptosis, random inflammation | <font color=\"white\">This_is_bla</font>2<font color=\"white\">This_is_bla</font> | entropy, lacunarity |"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"- entropy consistently explains histological measures when controlled for age\n",
"- also important : tissue to sinusoid ratio, focus count and size, lacunarity"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- biological / historical reasoning for this potential cohort effect\n",
"- interpretation of these models\n",
"- quality of fit"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Conclusions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- our **semi-educated guess** measures may capture relevant information\n",
"- underlying **structure** in the data needs thought\n",
"- still no **map** from image or histological measures to condition of individual\n"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Future directions"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Further exploration of the dataset"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"- 145 sheep ( 89 females )\n",
"- 11 age classes\n",
"- potential redundancy in various measures"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- 4460 entries across 27 variables\n",
"- 3330 with full image and histological information\n",
"- 1196 for which **complete** information is available"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"More data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- nutritional information\n",
"- immunity data"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Narrow-field images"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 12536 images\n",
"- spatial distribution of nuclei"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img src=\"figures/10x.png\" width=100%></src>"
]
}
],
"metadata": {}
}
]
}