dhimmel/hetionet-v1.0-metaedge-xswap-stats.tsv

## xswap-prior-probability.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analytical derivation of the prior XSwap probability of a hetnet edge\n",
    "\n",
    "+ Lizee prior proposed [here](https://think-lab.github.io/d/194/#2) with further discussion [here](https://think-lab.github.io/d/201/#2).\n",
    "+ Chung-Lu and Kloster priors proposed [here](https://github.com/greenelab/hetmech/issues/134#issuecomment-419133600).\n",
    "\n",
    "Created an environment for this notebook with:\n",
    "\n",
    "```\n",
    "conda create --name=r --channel=conda-forge \\\n",
    "  r-base r-dplyr r-ggplot2 r-readr r-irkernel r-boot r-rcurl r-tidyr\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load magrittr pipe\n",
    "`%>%` = dplyr::`%>%`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`curl` package not installed, falling back to using `url()`\n",
      "Parsed with column specification:\n",
      "cols(\n",
      "  compound_treats = col_integer(),\n",
      "  disease_treats = col_integer(),\n",
      "  prior_perm = col_double(),\n",
      "  prior_perm_stderr = col_double(),\n",
      "  n_treatments = col_integer(),\n",
      "  n_possible = col_integer()\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "url = 'https://github.com/dhimmel/learn/raw/0aae784e83cfaa00d1269f17a3bd3a6c6fdc3a0a/prior/data/degree-prior.tsv'\n",
    "degree_prior_df = readr::read_tsv(url) %>%\n",
    "  dplyr::mutate(xswap_prior = prior_perm) %>%\n",
    "  dplyr::mutate(logit_xswap_prior = boot::logit(xswap_prior)) %>%\n",
    "  dplyr::mutate(Lizee = compound_treats * disease_treats / sum(n_possible)) %>%\n",
    "  dplyr::mutate(`Chung-Lu` = compound_treats * disease_treats / sum(n_treatments)) %>%\n",
    "  dplyr::mutate(Kloster = compound_treats * disease_treats /\n",
    "    (sum(n_treatments) + (compound_treats - 1) * (disease_treats - 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>compound_treats</th><th scope=col>disease_treats</th><th scope=col>prior_perm</th><th scope=col>prior_perm_stderr</th><th scope=col>n_treatments</th><th scope=col>n_possible</th><th scope=col>xswap_prior</th><th scope=col>logit_xswap_prior</th><th scope=col>Lizee</th><th scope=col>Chung-Lu</th><th scope=col>Kloster</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1           </td><td>1           </td><td>0.00116183  </td><td>5.44733e-07 </td><td>5           </td><td>3612        </td><td>0.00116183  </td><td>-6.756596   </td><td>3.355817e-05</td><td>0.001324503 </td><td>0.001324503 </td></tr>\n",
       "\t<tr><td>1           </td><td>2           </td><td>0.00234128  </td><td>1.29275e-06 </td><td>3           </td><td>1290        </td><td>0.00234128  </td><td>-6.054713   </td><td>6.711635e-05</td><td>0.002649007 </td><td>0.002649007 </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " compound\\_treats & disease\\_treats & prior\\_perm & prior\\_perm\\_stderr & n\\_treatments & n\\_possible & xswap\\_prior & logit\\_xswap\\_prior & Lizee & Chung-Lu & Kloster\\\\\n",
       "\\hline\n",
       "\t 1            & 1            & 0.00116183   & 5.44733e-07  & 5            & 3612         & 0.00116183   & -6.756596    & 3.355817e-05 & 0.001324503  & 0.001324503 \\\\\n",
       "\t 1            & 2            & 0.00234128   & 1.29275e-06  & 3            & 1290         & 0.00234128   & -6.054713    & 6.711635e-05 & 0.002649007  & 0.002649007 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "compound_treats | disease_treats | prior_perm | prior_perm_stderr | n_treatments | n_possible | xswap_prior | logit_xswap_prior | Lizee | Chung-Lu | Kloster | \n",
       "|---|---|\n",
       "| 1            | 1            | 0.00116183   | 5.44733e-07  | 5            | 3612         | 0.00116183   | -6.756596    | 3.355817e-05 | 0.001324503  | 0.001324503  | \n",
       "| 1            | 2            | 0.00234128   | 1.29275e-06  | 3            | 1290         | 0.00234128   | -6.054713    | 6.711635e-05 | 0.002649007  | 0.002649007  | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  compound_treats disease_treats prior_perm prior_perm_stderr n_treatments\n",
       "1 1               1              0.00116183 5.44733e-07       5           \n",
       "2 1               2              0.00234128 1.29275e-06       3           \n",
       "  n_possible xswap_prior logit_xswap_prior Lizee        Chung-Lu    Kloster    \n",
       "1 3612       0.00116183  -6.756596         3.355817e-05 0.001324503 0.001324503\n",
       "2 1290       0.00234128  -6.054713         6.711635e-05 0.002649007 0.002649007"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree_prior_df %>% head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in qlogis(p):\n",
      "“NaNs produced”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>compound_treats</th><th scope=col>disease_treats</th><th scope=col>prior_perm</th><th scope=col>prior_perm_stderr</th><th scope=col>n_treatments</th><th scope=col>n_possible</th><th scope=col>xswap_prior</th><th scope=col>logit_xswap_prior</th><th scope=col>method</th><th scope=col>prior</th><th scope=col>logit_prior</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1           </td><td>1           </td><td>0.00116183  </td><td>5.44733e-07 </td><td>5           </td><td>3612        </td><td>0.00116183  </td><td>-6.756596   </td><td>Lizee       </td><td>3.355817e-05</td><td>-10.302197  </td></tr>\n",
       "\t<tr><td>1           </td><td>2           </td><td>0.00234128  </td><td>1.29275e-06 </td><td>3           </td><td>1290        </td><td>0.00234128  </td><td>-6.054713   </td><td>Lizee       </td><td>6.711635e-05</td><td> -9.609016  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " compound\\_treats & disease\\_treats & prior\\_perm & prior\\_perm\\_stderr & n\\_treatments & n\\_possible & xswap\\_prior & logit\\_xswap\\_prior & method & prior & logit\\_prior\\\\\n",
       "\\hline\n",
       "\t 1            & 1            & 0.00116183   & 5.44733e-07  & 5            & 3612         & 0.00116183   & -6.756596    & Lizee        & 3.355817e-05 & -10.302197  \\\\\n",
       "\t 1            & 2            & 0.00234128   & 1.29275e-06  & 3            & 1290         & 0.00234128   & -6.054713    & Lizee        & 6.711635e-05 &  -9.609016  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "compound_treats | disease_treats | prior_perm | prior_perm_stderr | n_treatments | n_possible | xswap_prior | logit_xswap_prior | method | prior | logit_prior | \n",
       "|---|---|\n",
       "| 1            | 1            | 0.00116183   | 5.44733e-07  | 5            | 3612         | 0.00116183   | -6.756596    | Lizee        | 3.355817e-05 | -10.302197   | \n",
       "| 1            | 2            | 0.00234128   | 1.29275e-06  | 3            | 1290         | 0.00234128   | -6.054713    | Lizee        | 6.711635e-05 |  -9.609016   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  compound_treats disease_treats prior_perm prior_perm_stderr n_treatments\n",
       "1 1               1              0.00116183 5.44733e-07       5           \n",
       "2 1               2              0.00234128 1.29275e-06       3           \n",
       "  n_possible xswap_prior logit_xswap_prior method prior        logit_prior\n",
       "1 3612       0.00116183  -6.756596         Lizee  3.355817e-05 -10.302197 \n",
       "2 1290       0.00234128  -6.054713         Lizee  6.711635e-05  -9.609016 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "long_df = degree_prior_df %>%\n",
    "  tidyr::gather(key = 'method', value = 'prior', Lizee:Kloster) %>%\n",
    "  dplyr::mutate(logit_prior = boot::logit(prior))\n",
    "long_df %>% head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>compound_treats</th><th scope=col>disease_treats</th><th scope=col>prior_perm</th><th scope=col>prior_perm_stderr</th><th scope=col>n_treatments</th><th scope=col>n_possible</th><th scope=col>xswap_prior</th><th scope=col>logit_xswap_prior</th><th scope=col>method</th><th scope=col>prior</th><th scope=col>logit_prior</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>12         </td><td>68         </td><td>0.669943   </td><td>0.000544807</td><td>1          </td><td>1          </td><td>0.669943   </td><td>0.7079273  </td><td>Chung-Lu   </td><td>1.080795   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>13         </td><td>68         </td><td>0.693760   </td><td>0.000534029</td><td>1          </td><td>1          </td><td>0.693760   </td><td>0.8177570  </td><td>Chung-Lu   </td><td>1.170861   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>14         </td><td>68         </td><td>0.714649   </td><td>0.000523197</td><td>0          </td><td>1          </td><td>0.714649   </td><td>0.9180715  </td><td>Chung-Lu   </td><td>1.260927   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>15         </td><td>51         </td><td>0.659217   </td><td>0.000549139</td><td>1          </td><td>1          </td><td>0.659217   </td><td>0.6598069  </td><td>Chung-Lu   </td><td>1.013245   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>15         </td><td>68         </td><td>0.734184   </td><td>0.000511826</td><td>1          </td><td>1          </td><td>0.734184   </td><td>1.0159553  </td><td>Chung-Lu   </td><td>1.350993   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>17         </td><td>51         </td><td>0.698313   </td><td>0.000531781</td><td>0          </td><td>1          </td><td>0.698313   </td><td>0.8392774  </td><td>Chung-Lu   </td><td>1.148344   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>17         </td><td>68         </td><td>0.768551   </td><td>0.000488645</td><td>0          </td><td>1          </td><td>0.768551   </td><td>1.2001474  </td><td>Chung-Lu   </td><td>1.531126   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>19         </td><td>51         </td><td>0.733662   </td><td>0.000512146</td><td>0          </td><td>1          </td><td>0.733662   </td><td>1.0132823  </td><td>Chung-Lu   </td><td>1.283444   </td><td>NaN        </td></tr>\n",
       "\t<tr><td>19         </td><td>68         </td><td>0.795997   </td><td>0.000466878</td><td>1          </td><td>1          </td><td>0.795997   </td><td>1.3614607  </td><td>Chung-Lu   </td><td>1.711258   </td><td>NaN        </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " compound\\_treats & disease\\_treats & prior\\_perm & prior\\_perm\\_stderr & n\\_treatments & n\\_possible & xswap\\_prior & logit\\_xswap\\_prior & method & prior & logit\\_prior\\\\\n",
       "\\hline\n",
       "\t 12          & 68          & 0.669943    & 0.000544807 & 1           & 1           & 0.669943    & 0.7079273   & Chung-Lu    & 1.080795    & NaN        \\\\\n",
       "\t 13          & 68          & 0.693760    & 0.000534029 & 1           & 1           & 0.693760    & 0.8177570   & Chung-Lu    & 1.170861    & NaN        \\\\\n",
       "\t 14          & 68          & 0.714649    & 0.000523197 & 0           & 1           & 0.714649    & 0.9180715   & Chung-Lu    & 1.260927    & NaN        \\\\\n",
       "\t 15          & 51          & 0.659217    & 0.000549139 & 1           & 1           & 0.659217    & 0.6598069   & Chung-Lu    & 1.013245    & NaN        \\\\\n",
       "\t 15          & 68          & 0.734184    & 0.000511826 & 1           & 1           & 0.734184    & 1.0159553   & Chung-Lu    & 1.350993    & NaN        \\\\\n",
       "\t 17          & 51          & 0.698313    & 0.000531781 & 0           & 1           & 0.698313    & 0.8392774   & Chung-Lu    & 1.148344    & NaN        \\\\\n",
       "\t 17          & 68          & 0.768551    & 0.000488645 & 0           & 1           & 0.768551    & 1.2001474   & Chung-Lu    & 1.531126    & NaN        \\\\\n",
       "\t 19          & 51          & 0.733662    & 0.000512146 & 0           & 1           & 0.733662    & 1.0132823   & Chung-Lu    & 1.283444    & NaN        \\\\\n",
       "\t 19          & 68          & 0.795997    & 0.000466878 & 1           & 1           & 0.795997    & 1.3614607   & Chung-Lu    & 1.711258    & NaN        \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "compound_treats | disease_treats | prior_perm | prior_perm_stderr | n_treatments | n_possible | xswap_prior | logit_xswap_prior | method | prior | logit_prior | \n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 12          | 68          | 0.669943    | 0.000544807 | 1           | 1           | 0.669943    | 0.7079273   | Chung-Lu    | 1.080795    | NaN         | \n",
       "| 13          | 68          | 0.693760    | 0.000534029 | 1           | 1           | 0.693760    | 0.8177570   | Chung-Lu    | 1.170861    | NaN         | \n",
       "| 14          | 68          | 0.714649    | 0.000523197 | 0           | 1           | 0.714649    | 0.9180715   | Chung-Lu    | 1.260927    | NaN         | \n",
       "| 15          | 51          | 0.659217    | 0.000549139 | 1           | 1           | 0.659217    | 0.6598069   | Chung-Lu    | 1.013245    | NaN         | \n",
       "| 15          | 68          | 0.734184    | 0.000511826 | 1           | 1           | 0.734184    | 1.0159553   | Chung-Lu    | 1.350993    | NaN         | \n",
       "| 17          | 51          | 0.698313    | 0.000531781 | 0           | 1           | 0.698313    | 0.8392774   | Chung-Lu    | 1.148344    | NaN         | \n",
       "| 17          | 68          | 0.768551    | 0.000488645 | 0           | 1           | 0.768551    | 1.2001474   | Chung-Lu    | 1.531126    | NaN         | \n",
       "| 19          | 51          | 0.733662    | 0.000512146 | 0           | 1           | 0.733662    | 1.0132823   | Chung-Lu    | 1.283444    | NaN         | \n",
       "| 19          | 68          | 0.795997    | 0.000466878 | 1           | 1           | 0.795997    | 1.3614607   | Chung-Lu    | 1.711258    | NaN         | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  compound_treats disease_treats prior_perm prior_perm_stderr n_treatments\n",
       "1 12              68             0.669943   0.000544807       1           \n",
       "2 13              68             0.693760   0.000534029       1           \n",
       "3 14              68             0.714649   0.000523197       0           \n",
       "4 15              51             0.659217   0.000549139       1           \n",
       "5 15              68             0.734184   0.000511826       1           \n",
       "6 17              51             0.698313   0.000531781       0           \n",
       "7 17              68             0.768551   0.000488645       0           \n",
       "8 19              51             0.733662   0.000512146       0           \n",
       "9 19              68             0.795997   0.000466878       1           \n",
       "  n_possible xswap_prior logit_xswap_prior method   prior    logit_prior\n",
       "1 1          0.669943    0.7079273         Chung-Lu 1.080795 NaN        \n",
       "2 1          0.693760    0.8177570         Chung-Lu 1.170861 NaN        \n",
       "3 1          0.714649    0.9180715         Chung-Lu 1.260927 NaN        \n",
       "4 1          0.659217    0.6598069         Chung-Lu 1.013245 NaN        \n",
       "5 1          0.734184    1.0159553         Chung-Lu 1.350993 NaN        \n",
       "6 1          0.698313    0.8392774         Chung-Lu 1.148344 NaN        \n",
       "7 1          0.768551    1.2001474         Chung-Lu 1.531126 NaN        \n",
       "8 1          0.733662    1.0132823         Chung-Lu 1.283444 NaN        \n",
       "9 1          0.795997    1.3614607         Chung-Lu 1.711258 NaN        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# NaNs produced when probabilities greater than 1 for example with Chung-Lu\n",
    "long_df %>% dplyr::filter(is.na(logit_prior))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Removed 9 rows containing missing values (geom_point).”"
     ]
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Removed 9 rows containing missing values (geom_point).”"
     ]
    },
    {
     "data": {
      "image/png": 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shPABh0eJJta2urXq8XiUS4SSMWi6VS6e9+9zufzzdt2rRUx5jJEkpUli5dilf3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\nvmLFioyMjLS0tFWrVl28ePH06dOxCpKHmpub+/b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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "source": "R display func"
    }
   ],
   "source": [
    "width = 9\n",
    "height = 2.5\n",
    "options(repr.plot.width=width, repr.plot.height=height)\n",
    "gg_scatter = long_df %>%\n",
    "  dplyr::mutate(method = factor(method, levels=c('Lizee', 'Chung-Lu', 'Kloster'))) %>%\n",
    "  ggplot2::ggplot(ggplot2::aes(logit_prior, logit_xswap_prior)) +\n",
    "  ggplot2::geom_abline(slope=1, color='pink', linetype='dashed') +\n",
    "  ggplot2::geom_point(alpha = 0.1, shape = 16) +\n",
    "#   ggplot2::geom_linerange(ggplot2::aes(\n",
    "#     ymin=boot::logit(xswap_prior - 2*prior_perm_stderr),\n",
    "#     ymax=boot::logit(xswap_prior + 2*prior_perm_stderr)\n",
    "#   )) +\n",
    "  ggplot2::theme_bw() +\n",
    "  ggplot2::coord_fixed() +\n",
    "  ggplot2::facet_grid(. ~ method) +\n",
    "  ggplot2::xlab('Logit of the Analytic Prob') +\n",
    "  ggplot2::ylab('Logit of the Empiric XSwap Prob')\n",
    "\n",
    "gg_scatter\n",
    "ggplot2::ggsave('estimated-xswap-priors.png', gg_scatter, dpi = 300, width = width, height = height)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>compound_treats</th><th scope=col>disease_treats</th><th scope=col>prior_perm</th><th scope=col>prior_perm_stderr</th><th scope=col>n_treatments</th><th scope=col>n_possible</th><th scope=col>xswap_prior</th><th scope=col>logit_xswap_prior</th><th scope=col>Lizee</th><th scope=col>Chung-Lu</th><th scope=col>Kloster</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>19         </td><td>68         </td><td>0.795997   </td><td>0.000466878</td><td>1          </td><td>1          </td><td>0.795997   </td><td>1.3614607  </td><td>0.04335716 </td><td>1.7112583  </td><td>0.6588475  </td></tr>\n",
       "\t<tr><td>17         </td><td>68         </td><td>0.768551   </td><td>0.000488645</td><td>0          </td><td>1          </td><td>0.768551   </td><td>1.2001474  </td><td>0.03879325 </td><td>1.5311258  </td><td>0.6327313  </td></tr>\n",
       "\t<tr><td>15         </td><td>68         </td><td>0.734184   </td><td>0.000511826</td><td>1          </td><td>1          </td><td>0.734184   </td><td>1.0159553  </td><td>0.03422934 </td><td>1.3509934  </td><td>0.6024808  </td></tr>\n",
       "\t<tr><td>19         </td><td>51         </td><td>0.733662   </td><td>0.000512146</td><td>0          </td><td>1          </td><td>0.733662   </td><td>1.0132823  </td><td>0.03251787 </td><td>1.2834437  </td><td>0.5854985  </td></tr>\n",
       "\t<tr><td>14         </td><td>68         </td><td>0.714649   </td><td>0.000523197</td><td>0          </td><td>1          </td><td>0.714649   </td><td>0.9180715  </td><td>0.03194738 </td><td>1.2609272  </td><td>0.5854859  </td></tr>\n",
       "\t<tr><td>17         </td><td>51         </td><td>0.698313   </td><td>0.000531781</td><td>0          </td><td>1          </td><td>0.698313   </td><td>0.8392774  </td><td>0.02909494 </td><td>1.1483444  </td><td>0.5575563  </td></tr>\n",
       "\t<tr><td>13         </td><td>68         </td><td>0.693760   </td><td>0.000534029</td><td>1          </td><td>1          </td><td>0.693760   </td><td>0.8177570  </td><td>0.02966543 </td><td>1.1708609  </td><td>0.5670301  </td></tr>\n",
       "\t<tr><td>12         </td><td>68         </td><td>0.669943   </td><td>0.000544807</td><td>1          </td><td>1          </td><td>0.669943   </td><td>0.7079273  </td><td>0.02738347 </td><td>1.0807947  </td><td>0.5469169  </td></tr>\n",
       "\t<tr><td>15         </td><td>51         </td><td>0.659217   </td><td>0.000549139</td><td>1          </td><td>1          </td><td>0.659217   </td><td>0.6598069  </td><td>0.02567200 </td><td>1.0132450  </td><td>0.5257732  </td></tr>\n",
       "\t<tr><td>19         </td><td>37         </td><td>0.652270   </td><td>0.000551778</td><td>1          </td><td>1          </td><td>0.652270   </td><td>0.6290323  </td><td>0.02359140 </td><td>0.9311258  </td><td>0.5010691  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllll}\n",
       " compound\\_treats & disease\\_treats & prior\\_perm & prior\\_perm\\_stderr & n\\_treatments & n\\_possible & xswap\\_prior & logit\\_xswap\\_prior & Lizee & Chung-Lu & Kloster\\\\\n",
       "\\hline\n",
       "\t 19          & 68          & 0.795997    & 0.000466878 & 1           & 1           & 0.795997    & 1.3614607   & 0.04335716  & 1.7112583   & 0.6588475  \\\\\n",
       "\t 17          & 68          & 0.768551    & 0.000488645 & 0           & 1           & 0.768551    & 1.2001474   & 0.03879325  & 1.5311258   & 0.6327313  \\\\\n",
       "\t 15          & 68          & 0.734184    & 0.000511826 & 1           & 1           & 0.734184    & 1.0159553   & 0.03422934  & 1.3509934   & 0.6024808  \\\\\n",
       "\t 19          & 51          & 0.733662    & 0.000512146 & 0           & 1           & 0.733662    & 1.0132823   & 0.03251787  & 1.2834437   & 0.5854985  \\\\\n",
       "\t 14          & 68          & 0.714649    & 0.000523197 & 0           & 1           & 0.714649    & 0.9180715   & 0.03194738  & 1.2609272   & 0.5854859  \\\\\n",
       "\t 17          & 51          & 0.698313    & 0.000531781 & 0           & 1           & 0.698313    & 0.8392774   & 0.02909494  & 1.1483444   & 0.5575563  \\\\\n",
       "\t 13          & 68          & 0.693760    & 0.000534029 & 1           & 1           & 0.693760    & 0.8177570   & 0.02966543  & 1.1708609   & 0.5670301  \\\\\n",
       "\t 12          & 68          & 0.669943    & 0.000544807 & 1           & 1           & 0.669943    & 0.7079273   & 0.02738347  & 1.0807947   & 0.5469169  \\\\\n",
       "\t 15          & 51          & 0.659217    & 0.000549139 & 1           & 1           & 0.659217    & 0.6598069   & 0.02567200  & 1.0132450   & 0.5257732  \\\\\n",
       "\t 19          & 37          & 0.652270    & 0.000551778 & 1           & 1           & 0.652270    & 0.6290323   & 0.02359140  & 0.9311258   & 0.5010691  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "compound_treats | disease_treats | prior_perm | prior_perm_stderr | n_treatments | n_possible | xswap_prior | logit_xswap_prior | Lizee | Chung-Lu | Kloster | \n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 19          | 68          | 0.795997    | 0.000466878 | 1           | 1           | 0.795997    | 1.3614607   | 0.04335716  | 1.7112583   | 0.6588475   | \n",
       "| 17          | 68          | 0.768551    | 0.000488645 | 0           | 1           | 0.768551    | 1.2001474   | 0.03879325  | 1.5311258   | 0.6327313   | \n",
       "| 15          | 68          | 0.734184    | 0.000511826 | 1           | 1           | 0.734184    | 1.0159553   | 0.03422934  | 1.3509934   | 0.6024808   | \n",
       "| 19          | 51          | 0.733662    | 0.000512146 | 0           | 1           | 0.733662    | 1.0132823   | 0.03251787  | 1.2834437   | 0.5854985   | \n",
       "| 14          | 68          | 0.714649    | 0.000523197 | 0           | 1           | 0.714649    | 0.9180715   | 0.03194738  | 1.2609272   | 0.5854859   | \n",
       "| 17          | 51          | 0.698313    | 0.000531781 | 0           | 1           | 0.698313    | 0.8392774   | 0.02909494  | 1.1483444   | 0.5575563   | \n",
       "| 13          | 68          | 0.693760    | 0.000534029 | 1           | 1           | 0.693760    | 0.8177570   | 0.02966543  | 1.1708609   | 0.5670301   | \n",
       "| 12          | 68          | 0.669943    | 0.000544807 | 1           | 1           | 0.669943    | 0.7079273   | 0.02738347  | 1.0807947   | 0.5469169   | \n",
       "| 15          | 51          | 0.659217    | 0.000549139 | 1           | 1           | 0.659217    | 0.6598069   | 0.02567200  | 1.0132450   | 0.5257732   | \n",
       "| 19          | 37          | 0.652270    | 0.000551778 | 1           | 1           | 0.652270    | 0.6290323   | 0.02359140  | 0.9311258   | 0.5010691   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "   compound_treats disease_treats prior_perm prior_perm_stderr n_treatments\n",
       "1  19              68             0.795997   0.000466878       1           \n",
       "2  17              68             0.768551   0.000488645       0           \n",
       "3  15              68             0.734184   0.000511826       1           \n",
       "4  19              51             0.733662   0.000512146       0           \n",
       "5  14              68             0.714649   0.000523197       0           \n",
       "6  17              51             0.698313   0.000531781       0           \n",
       "7  13              68             0.693760   0.000534029       1           \n",
       "8  12              68             0.669943   0.000544807       1           \n",
       "9  15              51             0.659217   0.000549139       1           \n",
       "10 19              37             0.652270   0.000551778       1           \n",
       "   n_possible xswap_prior logit_xswap_prior Lizee      Chung-Lu  Kloster  \n",
       "1  1          0.795997    1.3614607         0.04335716 1.7112583 0.6588475\n",
       "2  1          0.768551    1.2001474         0.03879325 1.5311258 0.6327313\n",
       "3  1          0.734184    1.0159553         0.03422934 1.3509934 0.6024808\n",
       "4  1          0.733662    1.0132823         0.03251787 1.2834437 0.5854985\n",
       "5  1          0.714649    0.9180715         0.03194738 1.2609272 0.5854859\n",
       "6  1          0.698313    0.8392774         0.02909494 1.1483444 0.5575563\n",
       "7  1          0.693760    0.8177570         0.02966543 1.1708609 0.5670301\n",
       "8  1          0.669943    0.7079273         0.02738347 1.0807947 0.5469169\n",
       "9  1          0.659217    0.6598069         0.02567200 1.0132450 0.5257732\n",
       "10 1          0.652270    0.6290323         0.02359140 0.9311258 0.5010691"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Top 10 degree-pairs with the highest XSwap prior\n",
    "degree_prior_df %>%\n",
    "  dplyr::arrange(desc(xswap_prior)) %>%\n",
    "  head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "R version 3.4.1 (2017-06-30)\n",
       "Platform: x86_64-pc-linux-gnu (64-bit)\n",
       "Running under: Ubuntu 18.04.1 LTS\n",
       "\n",
       "Matrix products: default\n",
       "BLAS: /home/dhimmel/anaconda3/envs/r35/lib/R/lib/libRblas.so\n",
       "LAPACK: /home/dhimmel/anaconda3/envs/r35/lib/R/lib/libRlapack.so\n",
       "\n",
       "locale:\n",
       " [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              \n",
       " [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    \n",
       " [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   \n",
       " [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 \n",
       " [9] LC_ADDRESS=C               LC_TELEPHONE=C            \n",
       "[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       \n",
       "\n",
       "attached base packages:\n",
       "[1] stats     graphics  grDevices utils     datasets  methods   base     \n",
       "\n",
       "other attached packages:\n",
       "[1] bindrcpp_0.2.2\n",
       "\n",
       "loaded via a namespace (and not attached):\n",
       " [1] Rcpp_0.12.17     plyr_1.8.4       pillar_1.3.0     compiler_3.4.1  \n",
       " [5] bindr_0.1.1      base64enc_0.1-3  tools_3.4.1      boot_1.3-19     \n",
       " [9] digest_0.6.16    uuid_0.1-2       jsonlite_1.5     evaluate_0.11   \n",
       "[13] tibble_1.4.2     gtable_0.2.0     pkgconfig_2.0.2  rlang_0.2.1     \n",
       "[17] IRdisplay_0.4.4  IRkernel_0.8.12  repr_0.15.0      dplyr_0.7.6     \n",
       "[21] stringr_1.3.1    hms_0.4.2        grid_3.4.1       tidyselect_0.2.4\n",
       "[25] glue_1.3.0       R6_2.2.2         pbdZMQ_0.3-2     reshape2_1.4.3  \n",
       "[29] purrr_0.2.5      readr_1.1.1      tidyr_0.8.1      ggplot2_3.0.0   \n",
       "[33] magrittr_1.5     scales_1.0.0     htmltools_0.3.6  assertthat_0.2.0\n",
       "[37] colorspace_1.3-2 labeling_0.3     stringi_1.2.4    lazyeval_0.2.1  \n",
       "[41] munsell_0.5.0    crayon_1.3.4    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sessionInfo()"
   ]
  }
 ],
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