MSM Test Notebook 1 - Markov Models.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9c7aee46",
   "metadata": {},
   "source": [
    "## Testing the MSM Package\n",
    "\n",
    "Building a first multi-state model using the supplied \"cav\" data.\n",
    "\n",
    "The \"cav\" data, comes with the msm library, and comes from Sharples et al. (2003) study of the progression of coronary allograft vasculopathy (CAV) - a post-transplant deterioration of the arterial walls.\n",
    "\n",
    "Dataset has 2816 state observations, defined as:\n",
    "\n",
    "- state 1: No CAV\n",
    "- state 2: Mild / Moderate CAV\n",
    "- state 3: Severe CAV\n",
    "- state 4: Death\n",
    "\n",
    "**This code and markup / explanations are taken from Jackson, C. H. (2011) Multi-State Models for Panel Data: The msm Package for R *Journal of Statistical Software* 38(8).**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1b770469",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“package ‘msm’ was built under R version 3.6.3”"
     ]
    }
   ],
   "source": [
    "library(\"msm\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "953d677f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>PTNUM</th><th scope=col>age</th><th scope=col>years</th><th scope=col>dage</th><th scope=col>sex</th><th scope=col>pdiag</th><th scope=col>cumrej</th><th scope=col>state</th><th scope=col>firstobs</th><th scope=col>statemax</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>100002  </td><td>52.49589</td><td>0.000000</td><td>21      </td><td>0       </td><td>IHD     </td><td>0       </td><td>1       </td><td>1       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>2</th><td>100002  </td><td>53.49863</td><td>1.002740</td><td>21      </td><td>0       </td><td>IHD     </td><td>2       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>3</th><td>100002  </td><td>54.49863</td><td>2.002740</td><td>21      </td><td>0       </td><td>IHD     </td><td>2       </td><td>2       </td><td>0       </td><td>2       </td></tr>\n",
       "\t<tr><th scope=row>4</th><td>100002  </td><td>55.58904</td><td>3.093151</td><td>21      </td><td>0       </td><td>IHD     </td><td>2       </td><td>2       </td><td>0       </td><td>2       </td></tr>\n",
       "\t<tr><th scope=row>5</th><td>100002  </td><td>56.49589</td><td>4.000000</td><td>21      </td><td>0       </td><td>IHD     </td><td>3       </td><td>2       </td><td>0       </td><td>2       </td></tr>\n",
       "\t<tr><th scope=row>6</th><td>100002  </td><td>57.49315</td><td>4.997260</td><td>21      </td><td>0       </td><td>IHD     </td><td>3       </td><td>3       </td><td>0       </td><td>3       </td></tr>\n",
       "\t<tr><th scope=row>7</th><td>100002  </td><td>58.35068</td><td>5.854795</td><td>21      </td><td>0       </td><td>IHD     </td><td>3       </td><td>4       </td><td>0       </td><td>4       </td></tr>\n",
       "\t<tr><th scope=row>8</th><td>100003  </td><td>29.50685</td><td>0.000000</td><td>17      </td><td>0       </td><td>IHD     </td><td>0       </td><td>1       </td><td>1       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>9</th><td>100003  </td><td>30.69589</td><td>1.189041</td><td>17      </td><td>0       </td><td>IHD     </td><td>1       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>10</th><td>100003  </td><td>31.51507</td><td>2.008219</td><td>17      </td><td>0       </td><td>IHD     </td><td>1       </td><td>3       </td><td>0       </td><td>3       </td></tr>\n",
       "\t<tr><th scope=row>11</th><td>100003  </td><td>32.49863</td><td>2.991781</td><td>17      </td><td>0       </td><td>IHD     </td><td>2       </td><td>4       </td><td>0       </td><td>4       </td></tr>\n",
       "\t<tr><th scope=row>12</th><td>100004  </td><td>35.89589</td><td>0.000000</td><td>16      </td><td>0       </td><td>IDC     </td><td>0       </td><td>1       </td><td>1       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>13</th><td>100004  </td><td>36.89863</td><td>1.002740</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>14</th><td>100004  </td><td>37.90685</td><td>2.010959</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>15</th><td>100004  </td><td>38.90685</td><td>3.010959</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>16</th><td>100004  </td><td>39.90411</td><td>4.008219</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>17</th><td>100004  </td><td>40.88767</td><td>4.991781</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>18</th><td>100004  </td><td>41.91781</td><td>6.021918</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>2       </td><td>0       </td><td>2       </td></tr>\n",
       "\t<tr><th scope=row>19</th><td>100004  </td><td>42.91507</td><td>7.019178</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>3       </td><td>0       </td><td>3       </td></tr>\n",
       "\t<tr><th scope=row>20</th><td>100004  </td><td>43.91233</td><td>8.016438</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>3       </td><td>0       </td><td>3       </td></tr>\n",
       "\t<tr><th scope=row>21</th><td>100004  </td><td>44.79726</td><td>8.901370</td><td>16      </td><td>0       </td><td>IDC     </td><td>2       </td><td>4       </td><td>0       </td><td>4       </td></tr>\n",
       "\t<tr><th scope=row>22</th><td>100006  </td><td>23.62192</td><td>0.000000</td><td>22      </td><td>0       </td><td>IDC     </td><td>0       </td><td>1       </td><td>1       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>23</th><td>100006  </td><td>24.63562</td><td>1.013699</td><td>22      </td><td>0       </td><td>IDC     </td><td>3       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>24</th><td>100006  </td><td>26.01644</td><td>2.394521</td><td>22      </td><td>0       </td><td>IDC     </td><td>3       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>25</th><td>100006  </td><td>26.65205</td><td>3.030137</td><td>22      </td><td>0       </td><td>IDC     </td><td>3       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>26</th><td>100006  </td><td>27.69041</td><td>4.068493</td><td>22      </td><td>0       </td><td>IDC     </td><td>4       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>27</th><td>100006  </td><td>28.57534</td><td>4.953425</td><td>22      </td><td>0       </td><td>IDC     </td><td>7       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>28</th><td>100006  </td><td>29.62466</td><td>6.002740</td><td>22      </td><td>0       </td><td>IDC     </td><td>8       </td><td>1       </td><td>0       </td><td>1       </td></tr>\n",
       "\t<tr><th scope=row>29</th><td>100006  </td><td>31.62466</td><td>8.002740</td><td>22      </td><td>0       </td><td>IDC     </td><td>8       </td><td>3       </td><td>0       </td><td>3       </td></tr>\n",
       "\t<tr><th scope=row>30</th><td>100006  </td><td>31.68767</td><td>8.065753</td><td>22      </td><td>0       </td><td>IDC     </td><td>8       </td><td>4       </td><td>0       </td><td>4       </td></tr>\n",
       "\t<tr><th scope=row>...</th><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr>\n",
       "\t<tr><th scope=row>2815</th><td>100822    </td><td>31.17808  </td><td>1.95342466</td><td>17        </td><td>0         </td><td>IDC       </td><td>0         </td><td>1         </td><td>0         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2818</th><td>100824    </td><td>58.46027  </td><td>0.00000000</td><td>17        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2819</th><td>100824    </td><td>59.53973  </td><td>1.07945205</td><td>17        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>0         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2820</th><td>100828    </td><td>40.81096  </td><td>0.00000000</td><td>15        </td><td>0         </td><td>IDC       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2821</th><td>100828    </td><td>42.03562  </td><td>1.22465753</td><td>15        </td><td>0         </td><td>IDC       </td><td>0         </td><td>1         </td><td>0         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2822</th><td>100830    </td><td>57.86849  </td><td>0.00000000</td><td>44        </td><td>0         </td><td>IDC       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2823</th><td>100830    </td><td>57.96986  </td><td>0.10136986</td><td>44        </td><td>0         </td><td>IDC       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2824</th><td>100832    </td><td>35.32877  </td><td>0.00000000</td><td>58        </td><td>1         </td><td>IDC       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2825</th><td>100832    </td><td>36.08493  </td><td>0.75616438</td><td>58        </td><td>1         </td><td>IDC       </td><td>2         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2826</th><td>100833    </td><td>58.57808  </td><td>0.00000000</td><td>52        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2827</th><td>100833    </td><td>58.86849  </td><td>0.29041096</td><td>52        </td><td>0         </td><td>IHD       </td><td>2         </td><td>1         </td><td>0         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2828</th><td>100837    </td><td>32.06027  </td><td>0.00000000</td><td>41        </td><td>0         </td><td>Hyper     </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2829</th><td>100837    </td><td>32.19726  </td><td>0.13698630</td><td>41        </td><td>0         </td><td>Hyper     </td><td>0         </td><td>1         </td><td>0         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2830</th><td>100837    </td><td>32.23288  </td><td>0.17260274</td><td>41        </td><td>0         </td><td>Hyper     </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2831</th><td>100843    </td><td>54.47123  </td><td>0.00000000</td><td>51        </td><td>1         </td><td>IDC       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2832</th><td>100843    </td><td>54.74247  </td><td>0.27123288</td><td>51        </td><td>1         </td><td>IDC       </td><td>2         </td><td>1         </td><td>0         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2833</th><td>100848    </td><td>61.52603  </td><td>0.00000000</td><td>45        </td><td>0         </td><td>CVCM      </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2834</th><td>100848    </td><td>62.34795  </td><td>0.82191781</td><td>45        </td><td>0         </td><td>CVCM      </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2835</th><td>100854    </td><td>62.35342  </td><td>0.00000000</td><td>43        </td><td>1         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2836</th><td>100854    </td><td>62.54795  </td><td>0.19452055</td><td>43        </td><td>1         </td><td>IHD       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2837</th><td>100858    </td><td>56.00548  </td><td>0.00000000</td><td>27        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2838</th><td>100858    </td><td>56.02740  </td><td>0.02191781</td><td>27        </td><td>0         </td><td>IHD       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2839</th><td>100860    </td><td>50.23562  </td><td>0.00000000</td><td>48        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2840</th><td>100860    </td><td>50.29863  </td><td>0.06301370</td><td>48        </td><td>0         </td><td>IHD       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2841</th><td>100880    </td><td>61.38356  </td><td>0.00000000</td><td>31        </td><td>0         </td><td>IDC       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2842</th><td>100880    </td><td>61.44384  </td><td>0.06027397</td><td>31        </td><td>0         </td><td>IDC       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2843</th><td>100892    </td><td>55.84384  </td><td>0.00000000</td><td>54        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2844</th><td>100892    </td><td>55.86575  </td><td>0.02191781</td><td>54        </td><td>0         </td><td>IHD       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "\t<tr><th scope=row>2845</th><td>100897    </td><td>62.73973  </td><td>0.00000000</td><td>54        </td><td>0         </td><td>IHD       </td><td>0         </td><td>1         </td><td>1         </td><td>1         </td></tr>\n",
       "\t<tr><th scope=row>2846</th><td>100897    </td><td>62.78904  </td><td>0.04931507</td><td>54        </td><td>0         </td><td>IHD       </td><td>0         </td><td>4         </td><td>0         </td><td>4         </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllll}\n",
       "  & PTNUM & age & years & dage & sex & pdiag & cumrej & state & firstobs & statemax\\\\\n",
       "\\hline\n",
       "\t1 & 100002   & 52.49589 & 0.000000 & 21       & 0        & IHD      & 0        & 1        & 1        & 1       \\\\\n",
       "\t2 & 100002   & 53.49863 & 1.002740 & 21       & 0        & IHD      & 2        & 1        & 0        & 1       \\\\\n",
       "\t3 & 100002   & 54.49863 & 2.002740 & 21       & 0        & IHD      & 2        & 2        & 0        & 2       \\\\\n",
       "\t4 & 100002   & 55.58904 & 3.093151 & 21       & 0        & IHD      & 2        & 2        & 0        & 2       \\\\\n",
       "\t5 & 100002   & 56.49589 & 4.000000 & 21       & 0        & IHD      & 3        & 2        & 0        & 2       \\\\\n",
       "\t6 & 100002   & 57.49315 & 4.997260 & 21       & 0        & IHD      & 3        & 3        & 0        & 3       \\\\\n",
       "\t7 & 100002   & 58.35068 & 5.854795 & 21       & 0        & IHD      & 3        & 4        & 0        & 4       \\\\\n",
       "\t8 & 100003   & 29.50685 & 0.000000 & 17       & 0        & IHD      & 0        & 1        & 1        & 1       \\\\\n",
       "\t9 & 100003   & 30.69589 & 1.189041 & 17       & 0        & IHD      & 1        & 1        & 0        & 1       \\\\\n",
       "\t10 & 100003   & 31.51507 & 2.008219 & 17       & 0        & IHD      & 1        & 3        & 0        & 3       \\\\\n",
       "\t11 & 100003   & 32.49863 & 2.991781 & 17       & 0        & IHD      & 2        & 4        & 0        & 4       \\\\\n",
       "\t12 & 100004   & 35.89589 & 0.000000 & 16       & 0        & IDC      & 0        & 1        & 1        & 1       \\\\\n",
       "\t13 & 100004   & 36.89863 & 1.002740 & 16       & 0        & IDC      & 2        & 1        & 0        & 1       \\\\\n",
       "\t14 & 100004   & 37.90685 & 2.010959 & 16       & 0        & IDC      & 2        & 1        & 0        & 1       \\\\\n",
       "\t15 & 100004   & 38.90685 & 3.010959 & 16       & 0        & IDC      & 2        & 1        & 0        & 1       \\\\\n",
       "\t16 & 100004   & 39.90411 & 4.008219 & 16       & 0        & IDC      & 2        & 1        & 0        & 1       \\\\\n",
       "\t17 & 100004   & 40.88767 & 4.991781 & 16       & 0        & IDC      & 2        & 1        & 0        & 1       \\\\\n",
       "\t18 & 100004   & 41.91781 & 6.021918 & 16       & 0        & IDC      & 2        & 2        & 0        & 2       \\\\\n",
       "\t19 & 100004   & 42.91507 & 7.019178 & 16       & 0        & IDC      & 2        & 3        & 0        & 3       \\\\\n",
       "\t20 & 100004   & 43.91233 & 8.016438 & 16       & 0        & IDC      & 2        & 3        & 0        & 3       \\\\\n",
       "\t21 & 100004   & 44.79726 & 8.901370 & 16       & 0        & IDC      & 2        & 4        & 0        & 4       \\\\\n",
       "\t22 & 100006   & 23.62192 & 0.000000 & 22       & 0        & IDC      & 0        & 1        & 1        & 1       \\\\\n",
       "\t23 & 100006   & 24.63562 & 1.013699 & 22       & 0        & IDC      & 3        & 1        & 0        & 1       \\\\\n",
       "\t24 & 100006   & 26.01644 & 2.394521 & 22       & 0        & IDC      & 3        & 1        & 0        & 1       \\\\\n",
       "\t25 & 100006   & 26.65205 & 3.030137 & 22       & 0        & IDC      & 3        & 1        & 0        & 1       \\\\\n",
       "\t26 & 100006   & 27.69041 & 4.068493 & 22       & 0        & IDC      & 4        & 1        & 0        & 1       \\\\\n",
       "\t27 & 100006   & 28.57534 & 4.953425 & 22       & 0        & IDC      & 7        & 1        & 0        & 1       \\\\\n",
       "\t28 & 100006   & 29.62466 & 6.002740 & 22       & 0        & IDC      & 8        & 1        & 0        & 1       \\\\\n",
       "\t29 & 100006   & 31.62466 & 8.002740 & 22       & 0        & IDC      & 8        & 3        & 0        & 3       \\\\\n",
       "\t30 & 100006   & 31.68767 & 8.065753 & 22       & 0        & IDC      & 8        & 4        & 0        & 4       \\\\\n",
       "\t... & ... & ... & ... & ... & ... & ... & ... & ... & ... & ...\\\\\n",
       "\t2815 & 100822     & 31.17808   & 1.95342466 & 17         & 0          & IDC        & 0          & 1          & 0          & 1         \\\\\n",
       "\t2818 & 100824     & 58.46027   & 0.00000000 & 17         & 0          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2819 & 100824     & 59.53973   & 1.07945205 & 17         & 0          & IHD        & 0          & 1          & 0          & 1         \\\\\n",
       "\t2820 & 100828     & 40.81096   & 0.00000000 & 15         & 0          & IDC        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2821 & 100828     & 42.03562   & 1.22465753 & 15         & 0          & IDC        & 0          & 1          & 0          & 1         \\\\\n",
       "\t2822 & 100830     & 57.86849   & 0.00000000 & 44         & 0          & IDC        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2823 & 100830     & 57.96986   & 0.10136986 & 44         & 0          & IDC        & 0          & 4          & 0          & 4         \\\\\n",
       "\t2824 & 100832     & 35.32877   & 0.00000000 & 58         & 1          & IDC        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2825 & 100832     & 36.08493   & 0.75616438 & 58         & 1          & IDC        & 2          & 4          & 0          & 4         \\\\\n",
       "\t2826 & 100833     & 58.57808   & 0.00000000 & 52         & 0          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2827 & 100833     & 58.86849   & 0.29041096 & 52         & 0          & IHD        & 2          & 1          & 0          & 1         \\\\\n",
       "\t2828 & 100837     & 32.06027   & 0.00000000 & 41         & 0          & Hyper      & 0          & 1          & 1          & 1         \\\\\n",
       "\t2829 & 100837     & 32.19726   & 0.13698630 & 41         & 0          & Hyper      & 0          & 1          & 0          & 1         \\\\\n",
       "\t2830 & 100837     & 32.23288   & 0.17260274 & 41         & 0          & Hyper      & 0          & 4          & 0          & 4         \\\\\n",
       "\t2831 & 100843     & 54.47123   & 0.00000000 & 51         & 1          & IDC        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2832 & 100843     & 54.74247   & 0.27123288 & 51         & 1          & IDC        & 2          & 1          & 0          & 1         \\\\\n",
       "\t2833 & 100848     & 61.52603   & 0.00000000 & 45         & 0          & CVCM       & 0          & 1          & 1          & 1         \\\\\n",
       "\t2834 & 100848     & 62.34795   & 0.82191781 & 45         & 0          & CVCM       & 0          & 4          & 0          & 4         \\\\\n",
       "\t2835 & 100854     & 62.35342   & 0.00000000 & 43         & 1          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2836 & 100854     & 62.54795   & 0.19452055 & 43         & 1          & IHD        & 0          & 4          & 0          & 4         \\\\\n",
       "\t2837 & 100858     & 56.00548   & 0.00000000 & 27         & 0          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2838 & 100858     & 56.02740   & 0.02191781 & 27         & 0          & IHD        & 0          & 4          & 0          & 4         \\\\\n",
       "\t2839 & 100860     & 50.23562   & 0.00000000 & 48         & 0          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2840 & 100860     & 50.29863   & 0.06301370 & 48         & 0          & IHD        & 0          & 4          & 0          & 4         \\\\\n",
       "\t2841 & 100880     & 61.38356   & 0.00000000 & 31         & 0          & IDC        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2842 & 100880     & 61.44384   & 0.06027397 & 31         & 0          & IDC        & 0          & 4          & 0          & 4         \\\\\n",
       "\t2843 & 100892     & 55.84384   & 0.00000000 & 54         & 0          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2844 & 100892     & 55.86575   & 0.02191781 & 54         & 0          & IHD        & 0          & 4          & 0          & 4         \\\\\n",
       "\t2845 & 100897     & 62.73973   & 0.00000000 & 54         & 0          & IHD        & 0          & 1          & 1          & 1         \\\\\n",
       "\t2846 & 100897     & 62.78904   & 0.04931507 & 54         & 0          & IHD        & 0          & 4          & 0          & 4         \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | PTNUM | age | years | dage | sex | pdiag | cumrej | state | firstobs | statemax |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 100002   | 52.49589 | 0.000000 | 21       | 0        | IHD      | 0        | 1        | 1        | 1        |\n",
       "| 2 | 100002   | 53.49863 | 1.002740 | 21       | 0        | IHD      | 2        | 1        | 0        | 1        |\n",
       "| 3 | 100002   | 54.49863 | 2.002740 | 21       | 0        | IHD      | 2        | 2        | 0        | 2        |\n",
       "| 4 | 100002   | 55.58904 | 3.093151 | 21       | 0        | IHD      | 2        | 2        | 0        | 2        |\n",
       "| 5 | 100002   | 56.49589 | 4.000000 | 21       | 0        | IHD      | 3        | 2        | 0        | 2        |\n",
       "| 6 | 100002   | 57.49315 | 4.997260 | 21       | 0        | IHD      | 3        | 3        | 0        | 3        |\n",
       "| 7 | 100002   | 58.35068 | 5.854795 | 21       | 0        | IHD      | 3        | 4        | 0        | 4        |\n",
       "| 8 | 100003   | 29.50685 | 0.000000 | 17       | 0        | IHD      | 0        | 1        | 1        | 1        |\n",
       "| 9 | 100003   | 30.69589 | 1.189041 | 17       | 0        | IHD      | 1        | 1        | 0        | 1        |\n",
       "| 10 | 100003   | 31.51507 | 2.008219 | 17       | 0        | IHD      | 1        | 3        | 0        | 3        |\n",
       "| 11 | 100003   | 32.49863 | 2.991781 | 17       | 0        | IHD      | 2        | 4        | 0        | 4        |\n",
       "| 12 | 100004   | 35.89589 | 0.000000 | 16       | 0        | IDC      | 0        | 1        | 1        | 1        |\n",
       "| 13 | 100004   | 36.89863 | 1.002740 | 16       | 0        | IDC      | 2        | 1        | 0        | 1        |\n",
       "| 14 | 100004   | 37.90685 | 2.010959 | 16       | 0        | IDC      | 2        | 1        | 0        | 1        |\n",
       "| 15 | 100004   | 38.90685 | 3.010959 | 16       | 0        | IDC      | 2        | 1        | 0        | 1        |\n",
       "| 16 | 100004   | 39.90411 | 4.008219 | 16       | 0        | IDC      | 2        | 1        | 0        | 1        |\n",
       "| 17 | 100004   | 40.88767 | 4.991781 | 16       | 0        | IDC      | 2        | 1        | 0        | 1        |\n",
       "| 18 | 100004   | 41.91781 | 6.021918 | 16       | 0        | IDC      | 2        | 2        | 0        | 2        |\n",
       "| 19 | 100004   | 42.91507 | 7.019178 | 16       | 0        | IDC      | 2        | 3        | 0        | 3        |\n",
       "| 20 | 100004   | 43.91233 | 8.016438 | 16       | 0        | IDC      | 2        | 3        | 0        | 3        |\n",
       "| 21 | 100004   | 44.79726 | 8.901370 | 16       | 0        | IDC      | 2        | 4        | 0        | 4        |\n",
       "| 22 | 100006   | 23.62192 | 0.000000 | 22       | 0        | IDC      | 0        | 1        | 1        | 1        |\n",
       "| 23 | 100006   | 24.63562 | 1.013699 | 22       | 0        | IDC      | 3        | 1        | 0        | 1        |\n",
       "| 24 | 100006   | 26.01644 | 2.394521 | 22       | 0        | IDC      | 3        | 1        | 0        | 1        |\n",
       "| 25 | 100006   | 26.65205 | 3.030137 | 22       | 0        | IDC      | 3        | 1        | 0        | 1        |\n",
       "| 26 | 100006   | 27.69041 | 4.068493 | 22       | 0        | IDC      | 4        | 1        | 0        | 1        |\n",
       "| 27 | 100006   | 28.57534 | 4.953425 | 22       | 0        | IDC      | 7        | 1        | 0        | 1        |\n",
       "| 28 | 100006   | 29.62466 | 6.002740 | 22       | 0        | IDC      | 8        | 1        | 0        | 1        |\n",
       "| 29 | 100006   | 31.62466 | 8.002740 | 22       | 0        | IDC      | 8        | 3        | 0        | 3        |\n",
       "| 30 | 100006   | 31.68767 | 8.065753 | 22       | 0        | IDC      | 8        | 4        | 0        | 4        |\n",
       "| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |\n",
       "| 2815 | 100822     | 31.17808   | 1.95342466 | 17         | 0          | IDC        | 0          | 1          | 0          | 1          |\n",
       "| 2818 | 100824     | 58.46027   | 0.00000000 | 17         | 0          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2819 | 100824     | 59.53973   | 1.07945205 | 17         | 0          | IHD        | 0          | 1          | 0          | 1          |\n",
       "| 2820 | 100828     | 40.81096   | 0.00000000 | 15         | 0          | IDC        | 0          | 1          | 1          | 1          |\n",
       "| 2821 | 100828     | 42.03562   | 1.22465753 | 15         | 0          | IDC        | 0          | 1          | 0          | 1          |\n",
       "| 2822 | 100830     | 57.86849   | 0.00000000 | 44         | 0          | IDC        | 0          | 1          | 1          | 1          |\n",
       "| 2823 | 100830     | 57.96986   | 0.10136986 | 44         | 0          | IDC        | 0          | 4          | 0          | 4          |\n",
       "| 2824 | 100832     | 35.32877   | 0.00000000 | 58         | 1          | IDC        | 0          | 1          | 1          | 1          |\n",
       "| 2825 | 100832     | 36.08493   | 0.75616438 | 58         | 1          | IDC        | 2          | 4          | 0          | 4          |\n",
       "| 2826 | 100833     | 58.57808   | 0.00000000 | 52         | 0          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2827 | 100833     | 58.86849   | 0.29041096 | 52         | 0          | IHD        | 2          | 1          | 0          | 1          |\n",
       "| 2828 | 100837     | 32.06027   | 0.00000000 | 41         | 0          | Hyper      | 0          | 1          | 1          | 1          |\n",
       "| 2829 | 100837     | 32.19726   | 0.13698630 | 41         | 0          | Hyper      | 0          | 1          | 0          | 1          |\n",
       "| 2830 | 100837     | 32.23288   | 0.17260274 | 41         | 0          | Hyper      | 0          | 4          | 0          | 4          |\n",
       "| 2831 | 100843     | 54.47123   | 0.00000000 | 51         | 1          | IDC        | 0          | 1          | 1          | 1          |\n",
       "| 2832 | 100843     | 54.74247   | 0.27123288 | 51         | 1          | IDC        | 2          | 1          | 0          | 1          |\n",
       "| 2833 | 100848     | 61.52603   | 0.00000000 | 45         | 0          | CVCM       | 0          | 1          | 1          | 1          |\n",
       "| 2834 | 100848     | 62.34795   | 0.82191781 | 45         | 0          | CVCM       | 0          | 4          | 0          | 4          |\n",
       "| 2835 | 100854     | 62.35342   | 0.00000000 | 43         | 1          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2836 | 100854     | 62.54795   | 0.19452055 | 43         | 1          | IHD        | 0          | 4          | 0          | 4          |\n",
       "| 2837 | 100858     | 56.00548   | 0.00000000 | 27         | 0          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2838 | 100858     | 56.02740   | 0.02191781 | 27         | 0          | IHD        | 0          | 4          | 0          | 4          |\n",
       "| 2839 | 100860     | 50.23562   | 0.00000000 | 48         | 0          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2840 | 100860     | 50.29863   | 0.06301370 | 48         | 0          | IHD        | 0          | 4          | 0          | 4          |\n",
       "| 2841 | 100880     | 61.38356   | 0.00000000 | 31         | 0          | IDC        | 0          | 1          | 1          | 1          |\n",
       "| 2842 | 100880     | 61.44384   | 0.06027397 | 31         | 0          | IDC        | 0          | 4          | 0          | 4          |\n",
       "| 2843 | 100892     | 55.84384   | 0.00000000 | 54         | 0          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2844 | 100892     | 55.86575   | 0.02191781 | 54         | 0          | IHD        | 0          | 4          | 0          | 4          |\n",
       "| 2845 | 100897     | 62.73973   | 0.00000000 | 54         | 0          | IHD        | 0          | 1          | 1          | 1          |\n",
       "| 2846 | 100897     | 62.78904   | 0.04931507 | 54         | 0          | IHD        | 0          | 4          | 0          | 4          |\n",
       "\n"
      ],
      "text/plain": [
       "     PTNUM  age      years      dage sex pdiag cumrej state firstobs statemax\n",
       "1    100002 52.49589 0.000000   21   0   IHD   0      1     1        1       \n",
       "2    100002 53.49863 1.002740   21   0   IHD   2      1     0        1       \n",
       "3    100002 54.49863 2.002740   21   0   IHD   2      2     0        2       \n",
       "4    100002 55.58904 3.093151   21   0   IHD   2      2     0        2       \n",
       "5    100002 56.49589 4.000000   21   0   IHD   3      2     0        2       \n",
       "6    100002 57.49315 4.997260   21   0   IHD   3      3     0        3       \n",
       "7    100002 58.35068 5.854795   21   0   IHD   3      4     0        4       \n",
       "8    100003 29.50685 0.000000   17   0   IHD   0      1     1        1       \n",
       "9    100003 30.69589 1.189041   17   0   IHD   1      1     0        1       \n",
       "10   100003 31.51507 2.008219   17   0   IHD   1      3     0        3       \n",
       "11   100003 32.49863 2.991781   17   0   IHD   2      4     0        4       \n",
       "12   100004 35.89589 0.000000   16   0   IDC   0      1     1        1       \n",
       "13   100004 36.89863 1.002740   16   0   IDC   2      1     0        1       \n",
       "14   100004 37.90685 2.010959   16   0   IDC   2      1     0        1       \n",
       "15   100004 38.90685 3.010959   16   0   IDC   2      1     0        1       \n",
       "16   100004 39.90411 4.008219   16   0   IDC   2      1     0        1       \n",
       "17   100004 40.88767 4.991781   16   0   IDC   2      1     0        1       \n",
       "18   100004 41.91781 6.021918   16   0   IDC   2      2     0        2       \n",
       "19   100004 42.91507 7.019178   16   0   IDC   2      3     0        3       \n",
       "20   100004 43.91233 8.016438   16   0   IDC   2      3     0        3       \n",
       "21   100004 44.79726 8.901370   16   0   IDC   2      4     0        4       \n",
       "22   100006 23.62192 0.000000   22   0   IDC   0      1     1        1       \n",
       "23   100006 24.63562 1.013699   22   0   IDC   3      1     0        1       \n",
       "24   100006 26.01644 2.394521   22   0   IDC   3      1     0        1       \n",
       "25   100006 26.65205 3.030137   22   0   IDC   3      1     0        1       \n",
       "26   100006 27.69041 4.068493   22   0   IDC   4      1     0        1       \n",
       "27   100006 28.57534 4.953425   22   0   IDC   7      1     0        1       \n",
       "28   100006 29.62466 6.002740   22   0   IDC   8      1     0        1       \n",
       "29   100006 31.62466 8.002740   22   0   IDC   8      3     0        3       \n",
       "30   100006 31.68767 8.065753   22   0   IDC   8      4     0        4       \n",
       "...  ...    ...      ...        ...  ... ...   ...    ...   ...      ...     \n",
       "2815 100822 31.17808 1.95342466 17   0   IDC   0      1     0        1       \n",
       "2818 100824 58.46027 0.00000000 17   0   IHD   0      1     1        1       \n",
       "2819 100824 59.53973 1.07945205 17   0   IHD   0      1     0        1       \n",
       "2820 100828 40.81096 0.00000000 15   0   IDC   0      1     1        1       \n",
       "2821 100828 42.03562 1.22465753 15   0   IDC   0      1     0        1       \n",
       "2822 100830 57.86849 0.00000000 44   0   IDC   0      1     1        1       \n",
       "2823 100830 57.96986 0.10136986 44   0   IDC   0      4     0        4       \n",
       "2824 100832 35.32877 0.00000000 58   1   IDC   0      1     1        1       \n",
       "2825 100832 36.08493 0.75616438 58   1   IDC   2      4     0        4       \n",
       "2826 100833 58.57808 0.00000000 52   0   IHD   0      1     1        1       \n",
       "2827 100833 58.86849 0.29041096 52   0   IHD   2      1     0        1       \n",
       "2828 100837 32.06027 0.00000000 41   0   Hyper 0      1     1        1       \n",
       "2829 100837 32.19726 0.13698630 41   0   Hyper 0      1     0        1       \n",
       "2830 100837 32.23288 0.17260274 41   0   Hyper 0      4     0        4       \n",
       "2831 100843 54.47123 0.00000000 51   1   IDC   0      1     1        1       \n",
       "2832 100843 54.74247 0.27123288 51   1   IDC   2      1     0        1       \n",
       "2833 100848 61.52603 0.00000000 45   0   CVCM  0      1     1        1       \n",
       "2834 100848 62.34795 0.82191781 45   0   CVCM  0      4     0        4       \n",
       "2835 100854 62.35342 0.00000000 43   1   IHD   0      1     1        1       \n",
       "2836 100854 62.54795 0.19452055 43   1   IHD   0      4     0        4       \n",
       "2837 100858 56.00548 0.00000000 27   0   IHD   0      1     1        1       \n",
       "2838 100858 56.02740 0.02191781 27   0   IHD   0      4     0        4       \n",
       "2839 100860 50.23562 0.00000000 48   0   IHD   0      1     1        1       \n",
       "2840 100860 50.29863 0.06301370 48   0   IHD   0      4     0        4       \n",
       "2841 100880 61.38356 0.00000000 31   0   IDC   0      1     1        1       \n",
       "2842 100880 61.44384 0.06027397 31   0   IDC   0      4     0        4       \n",
       "2843 100892 55.84384 0.00000000 54   0   IHD   0      1     1        1       \n",
       "2844 100892 55.86575 0.02191781 54   0   IHD   0      4     0        4       \n",
       "2845 100897 62.73973 0.00000000 54   0   IHD   0      1     1        1       \n",
       "2846 100897 62.78904 0.04931507 54   0   IHD   0      4     0        4       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cav <- cav[!is.na(cav$pdiag),]\n",
    "cav"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a33a2406",
   "metadata": {},
   "source": [
    "## Define states and transitions allowed for model\n",
    "\n",
    "Provide initial values representing a guess that the mean period in each state before moving to the next is about two years (qrr = -0.5) and there is an equal probability of progression, recovery or death (qrr = - SUM where s ne r of qrs).  \n",
    "\n",
    "An alternative to this is to supply the option \"gen.inits=TRUE\" in the msm function call.  This sets the initial values for non-zero entries of the Q matrix (transition intensity matrix) to the maximum likelihood estimates under the assumption that transitions take place only at observation times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "46b244d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Each initial transition block must add up to -qrr (0.5) based on the assumption\n",
    "# In state 1 there are 2 possible transitions to mild/mod or death\n",
    "# In state 2 there are 3 possible transitions back to no cav, to severe, or death\n",
    "# In state 3 there are again 2 possible transitions back to mild/mod or to death\n",
    "# In state 4 there are no further transitions possible (obviously)\n",
    "\n",
    "twoway4.q <- rbind(c(0, 0.25, 0, 0.25), c(0.166, 0, 0.166, 0.166), c(0, 0.25, 0, 0.25), c(0,0,0,0))\n",
    "rownames(twoway4.q) <- colnames(twoway4.q) <- c(\"Well\", \"Mild\", \"Severe\", \"Death\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "de419ea2",
   "metadata": {},
   "outputs": [],
   "source": [
    "cav.msm <- msm(state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q, death = 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a69aea19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "msm(formula = state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q,     death = 4)\n",
       "\n",
       "Maximum likelihood estimates\n",
       "\n",
       "Transition intensities\n",
       "                Baseline                   \n",
       "Well - Well     -0.17165 (-0.19178,-0.1536)\n",
       "Well - Mild      0.12920 ( 0.11246, 0.1484)\n",
       "Well - Death     0.04245 ( 0.03400, 0.0530)\n",
       "Mild - Well      0.22643 ( 0.16852, 0.3042)\n",
       "Mild - Mild     -0.60964 (-0.71100,-0.5227)\n",
       "Mild - Severe    0.34180 ( 0.27243, 0.4288)\n",
       "Mild - Death     0.04141 ( 0.01200, 0.1429)\n",
       "Severe - Mild    0.13114 ( 0.07982, 0.2155)\n",
       "Severe - Severe -0.43572 (-0.55162,-0.3442)\n",
       "Severe - Death   0.30458 ( 0.23645, 0.3923)\n",
       "\n",
       "-2 * log-likelihood:  3944.812 \n",
       "[Note, to obtain old print format, use \"printold.msm\"]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cav.msm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bb99690",
   "metadata": {},
   "source": [
    "## Interpreting the Transition Intensities\n",
    "\n",
    "- Mean time in the Well state: 1/0.1717 = 5.824 years\n",
    "- Mean time in the Mild state: 1/0.6096 = 1.64 years\n",
    "- Mean time in the Severe state: 1/0.4357 = 2.295 years\n",
    "\n",
    "\n",
    "- From the Mild state, the likelihood of transition to Well is: 0.2264 (23%)\n",
    "- From the Mild state, the likelihood of transition to Severe is: 0.34180 (34%)\n",
    "\n",
    "\n",
    "- The odds of transition to Severe, given Mild: 0.34180 / 0.26781 (0.2264 + 0.04141) = 1.276\n",
    "- The odds of transition to Well, given Mild: 0.2264 / 0.38321 (0.34180 + 0.04141) = 0.5908\n",
    "- The odds ratio: 1.276 / 0.5908 = One is 2.16 times more likely to become Severe than Well, once Mild.\n",
    "- .23 / .34-.23 = 40.4% more likely to go Mild -> Severe, than Mild -> Well\n",
    "\n",
    "\n",
    "- The odds of Death given Severe: 0.30458 / 0.13114 = 2.323\n",
    "- The odds of Death once Severe are 2.323 to 1.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e5536a99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Well                        Mild                       \n",
       "Well   0.853041 (0.839873,0.86649) 0.089166 (0.078682,0.09982)\n",
       "Mild   0.156269 (0.119468,0.20198) 0.565856 (0.508510,0.60833)\n",
       "Severe 0.009997 (0.005865,0.01631) 0.078848 (0.048978,0.12003)\n",
       "Death  0                           0                          \n",
       "       Severe                      Death                      \n",
       "Well   0.014866 (0.011441,0.01821) 0.042927 (0.035850,0.05271)\n",
       "Mild   0.205504 (0.164755,0.24234) 0.072371 (0.053939,0.13482)\n",
       "Severe 0.660577 (0.592036,0.71401) 0.250579 (0.203278,0.30601)\n",
       "Death  0                           1.000000 (1.000000,1.00000)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the Transition Probability Matrix, P(t) over an interval of t=1 (in this case, 1 year)\n",
    "# ci = \"normal\" computes a confidence interval for P(t) by repeated sampling from the asymptotic \n",
    "# normal distribution of the maximum likelihood estimates of the log(qrs)\n",
    "# Based on a default 1000 samples, converged to within 2 significant figures\n",
    "# ci = \"boot\" will instead compute intervals using nonparametric bootstrap resampling, drawn with replacement\n",
    "# the model is refitted repeatedly to estimate the sampling uncertainty surrounding the estimates \n",
    "# more accurate, but slower\n",
    "pmatrix.msm(cav.msm, t = 1, ci = \"normal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3e32a2e",
   "metadata": {},
   "source": [
    "## Transition Probabilities\n",
    "\n",
    "- The probability of being Well 1 year from now, given Well is 85%\n",
    "- The probability of being Severe 1 year from now, given Mild is 21%\n",
    "- The probability of being Dead 1 year from now, given Severe is 25%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "72e3372c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A model with covariates: dage (age at transplant) and IHD (Ischemic Heart Disease, yes or no)\n",
    "\n",
    "ihd <- as.numeric(cav[, \"pdiag\"] == \"IHD\")\n",
    "cav.cov.msm <- msm(state ~ years, subject = PTNUM, data = cav, covariates = ~ dage + ihd, \n",
    "                   qmatrix = twoway4.q, death = 4, method = \"BFGS\", \n",
    "                   control = list(fnscale=4000, maxit=10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "390248c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$dage</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>HR</th><th scope=col>L</th><th scope=col>U</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Well - Mild</th><td>1.0192338</td><td>1.0068502</td><td>1.031770 </td></tr>\n",
       "\t<tr><th scope=row>Well - Death</th><td>1.0381550</td><td>1.0180831</td><td>1.058623 </td></tr>\n",
       "\t<tr><th scope=row>Mild - Well</th><td>0.9981551</td><td>0.9725458</td><td>1.024439 </td></tr>\n",
       "\t<tr><th scope=row>Mild - Severe</th><td>0.9856465</td><td>0.9674891</td><td>1.004145 </td></tr>\n",
       "\t<tr><th scope=row>Mild - Death</th><td>0.9319173</td><td>0.8441461</td><td>1.028815 </td></tr>\n",
       "\t<tr><th scope=row>Severe - Mild</th><td>0.9976760</td><td>0.9476897</td><td>1.050299 </td></tr>\n",
       "\t<tr><th scope=row>Severe - Death</th><td>0.9884479</td><td>0.9648268</td><td>1.012647 </td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "\t<dt>$ihd</dt>\n",
       "\t\t<dd><table>\n",
       "<thead><tr><th></th><th scope=col>HR</th><th scope=col>L</th><th scope=col>U</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Well - Mild</th><td>1.5670475</td><td>1.1810830</td><td> 2.079141</td></tr>\n",
       "\t<tr><th scope=row>Well - Death</th><td>1.3025416</td><td>0.8197953</td><td> 2.069559</td></tr>\n",
       "\t<tr><th scope=row>Mild - Well</th><td>0.9386910</td><td>0.5197290</td><td> 1.695385</td></tr>\n",
       "\t<tr><th scope=row>Mild - Severe</th><td>0.9565359</td><td>0.6115378</td><td> 1.496164</td></tr>\n",
       "\t<tr><th scope=row>Mild - Death</th><td>1.7812800</td><td>0.2270497</td><td>13.974730</td></tr>\n",
       "\t<tr><th scope=row>Severe - Mild</th><td>0.7655640</td><td>0.2701033</td><td> 2.169867</td></tr>\n",
       "\t<tr><th scope=row>Severe - Death</th><td>0.7601253</td><td>0.4576902</td><td> 1.262405</td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$dage] \\begin{tabular}{r|lll}\n",
       "  & HR & L & U\\\\\n",
       "\\hline\n",
       "\tWell - Mild & 1.0192338 & 1.0068502 & 1.031770 \\\\\n",
       "\tWell - Death & 1.0381550 & 1.0180831 & 1.058623 \\\\\n",
       "\tMild - Well & 0.9981551 & 0.9725458 & 1.024439 \\\\\n",
       "\tMild - Severe & 0.9856465 & 0.9674891 & 1.004145 \\\\\n",
       "\tMild - Death & 0.9319173 & 0.8441461 & 1.028815 \\\\\n",
       "\tSevere - Mild & 0.9976760 & 0.9476897 & 1.050299 \\\\\n",
       "\tSevere - Death & 0.9884479 & 0.9648268 & 1.012647 \\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\item[\\$ihd] \\begin{tabular}{r|lll}\n",
       "  & HR & L & U\\\\\n",
       "\\hline\n",
       "\tWell - Mild & 1.5670475 & 1.1810830 &  2.079141\\\\\n",
       "\tWell - Death & 1.3025416 & 0.8197953 &  2.069559\\\\\n",
       "\tMild - Well & 0.9386910 & 0.5197290 &  1.695385\\\\\n",
       "\tMild - Severe & 0.9565359 & 0.6115378 &  1.496164\\\\\n",
       "\tMild - Death & 1.7812800 & 0.2270497 & 13.974730\\\\\n",
       "\tSevere - Mild & 0.7655640 & 0.2701033 &  2.169867\\\\\n",
       "\tSevere - Death & 0.7601253 & 0.4576902 &  1.262405\\\\\n",
       "\\end{tabular}\n",
       "\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$dage\n",
       ":   \n",
       "| <!--/--> | HR | L | U |\n",
       "|---|---|---|---|\n",
       "| Well - Mild | 1.0192338 | 1.0068502 | 1.031770  |\n",
       "| Well - Death | 1.0381550 | 1.0180831 | 1.058623  |\n",
       "| Mild - Well | 0.9981551 | 0.9725458 | 1.024439  |\n",
       "| Mild - Severe | 0.9856465 | 0.9674891 | 1.004145  |\n",
       "| Mild - Death | 0.9319173 | 0.8441461 | 1.028815  |\n",
       "| Severe - Mild | 0.9976760 | 0.9476897 | 1.050299  |\n",
       "| Severe - Death | 0.9884479 | 0.9648268 | 1.012647  |\n",
       "\n",
       "\n",
       "$ihd\n",
       ":   \n",
       "| <!--/--> | HR | L | U |\n",
       "|---|---|---|---|\n",
       "| Well - Mild | 1.5670475 | 1.1810830 |  2.079141 |\n",
       "| Well - Death | 1.3025416 | 0.8197953 |  2.069559 |\n",
       "| Mild - Well | 0.9386910 | 0.5197290 |  1.695385 |\n",
       "| Mild - Severe | 0.9565359 | 0.6115378 |  1.496164 |\n",
       "| Mild - Death | 1.7812800 | 0.2270497 | 13.974730 |\n",
       "| Severe - Mild | 0.7655640 | 0.2701033 |  2.169867 |\n",
       "| Severe - Death | 0.7601253 | 0.4576902 |  1.262405 |\n",
       "\n",
       "\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$dage\n",
       "                      HR         L        U\n",
       "Well - Mild    1.0192338 1.0068502 1.031770\n",
       "Well - Death   1.0381550 1.0180831 1.058623\n",
       "Mild - Well    0.9981551 0.9725458 1.024439\n",
       "Mild - Severe  0.9856465 0.9674891 1.004145\n",
       "Mild - Death   0.9319173 0.8441461 1.028815\n",
       "Severe - Mild  0.9976760 0.9476897 1.050299\n",
       "Severe - Death 0.9884479 0.9648268 1.012647\n",
       "\n",
       "$ihd\n",
       "                      HR         L         U\n",
       "Well - Mild    1.5670475 1.1810830  2.079141\n",
       "Well - Death   1.3025416 0.8197953  2.069559\n",
       "Mild - Well    0.9386910 0.5197290  1.695385\n",
       "Mild - Severe  0.9565359 0.6115378  1.496164\n",
       "Mild - Death   1.7812800 0.2270497 13.974730\n",
       "Severe - Mild  0.7655640 0.2701033  2.169867\n",
       "Severe - Death 0.7601253 0.4576902  1.262405\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display hazard ratios for each covariate on each transition with 95% confidence intervals\n",
    "hazard.msm(cav.cov.msm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e2678bf",
   "metadata": {},
   "source": [
    "## Interpreting the Hazard Ratios\n",
    "\n",
    "- An initial diagnosis of IHD increases the risk of CAV onset (Well -> Mild) by 57%\n",
    "- 1 year increase in donor age is associated with a 2% increased risk of CAV onset (Well -> Mild)\n",
    "- 1 year increase in donor age is associated with a 3.8% increased risk of Death (Well -> Death)\n",
    "\n",
    "All of the other intervals cross 1, so there is a lot of variability in the impact of the covariate on the transition being examined.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dd229259",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Well                          Mild                         \n",
       "Well   -0.34343 (-0.4383457,-0.2691)  0.24638 ( 0.1822871, 0.3330)\n",
       "Mild    0.21940 ( 0.1148818, 0.4190) -0.48006 (-0.6862295,-0.3358)\n",
       "Severe 0                              0.11179 ( 0.0367642, 0.3399)\n",
       "Death  0                             0                            \n",
       "       Severe                        Death                        \n",
       "Well   0                              0.09706 ( 0.0649868, 0.1449)\n",
       "Mild    0.24821 ( 0.1584555, 0.3888)  0.01246 ( 0.0007292, 0.2128)\n",
       "Severe -0.32336 (-0.5476403,-0.1909)  0.21158 ( 0.1216081, 0.3681)\n",
       "Death  0                             0                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating the Transition Intensity Matrix for specified covariates\n",
    "# Donor age: 50, Primary Diagnosis: IHD\n",
    "# Note: Avg age donor is 30, and about half of heart transplants are due to IHD\n",
    "\n",
    "qmatrix.msm(cav.cov.msm, covariates = list(dage = 50, ihd = 1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ecdae13",
   "metadata": {},
   "source": [
    "## Comparing this patient to the average patient\n",
    "\n",
    "- Average patient's likelihood of transition from Well -> Mild 13%, for this patient it is 25%\n",
    "- Average patient's likelihood of transition from Well -> Death 4%, for this patient it is 9.7%\n",
    "- Average patient's likelihood of transition from Mild -> Severe 34%, for this patient it is 25%\n",
    "- Average patient's likelihood of transition from Mild -> Death 4%, for this patient it is 1%\n",
    "\n",
    "\n",
    "- Average patient's mean time in Well state 5.8 yrs, this patient 2.9 yrs\n",
    "- Average patient's mean time in Mild state 1.6 yrs, this patient 2.1 yrs\n",
    "- Average patient's mean time in Severe state 2.3 yrs, this patient 3.1 yrs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "efccbd7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>-2 log LR</th><th scope=col>df</th><th scope=col>p</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>cav.cov.msm</th><td>58.02736   </td><td>14         </td><td>2.59407e-07</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & -2 log LR & df & p\\\\\n",
       "\\hline\n",
       "\tcav.cov.msm & 58.02736    & 14          & 2.59407e-07\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | -2 log LR | df | p |\n",
       "|---|---|---|---|\n",
       "| cav.cov.msm | 58.02736    | 14          | 2.59407e-07 |\n",
       "\n"
      ],
      "text/plain": [
       "            -2 log LR df p          \n",
       "cav.cov.msm 58.02736  14 2.59407e-07"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Does the model with covariates fit significantly better than the one without? \n",
    "# Compare the likelihood ratio statistic to Chi-square distribution with 14 degrees of freedom\n",
    "\n",
    "lrtest.msm(cav.msm, cav.cov.msm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d0f57a6",
   "metadata": {},
   "source": [
    "The p-value is highly significant."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f345d671",
   "metadata": {},
   "source": [
    "## When Q is piecewise-constant\n",
    "\n",
    "Transition probabilities can be calculated in closed form by summing the likelihood over the unknown observed state at the times when the covariates change."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9e8a598c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>-2 log LR</th><th scope=col>df</th><th scope=col>p</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>cav.pci.msm</th><td>48.6895     </td><td>7           </td><td>2.609964e-08</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & -2 log LR & df & p\\\\\n",
       "\\hline\n",
       "\tcav.pci.msm & 48.6895      & 7            & 2.609964e-08\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | -2 log LR | df | p |\n",
       "|---|---|---|---|\n",
       "| cav.pci.msm | 48.6895      | 7            | 2.609964e-08 |\n",
       "\n"
      ],
      "text/plain": [
       "            -2 log LR df p           \n",
       "cav.pci.msm 48.6895   7  2.609964e-08"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fitting a model where all intensities change 5 years after transplantation\n",
    "# Divides data into 2 time periods: -Inf to 5 yrs, and 5 yrs to Inf\n",
    "\n",
    "cav.pci.msm <- msm(state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q, \n",
    "                   death = 4, pci = 5, method = \"BFGS\")\n",
    "\n",
    "# Is this data truly time-inhomogenous?\n",
    "lrtest.msm(cav.msm, cav.pci.msm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fde3bcab",
   "metadata": {},
   "source": [
    "It is very likely that the data is time-inhomogenous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "126de076",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>$`timeperiod[5,Inf)`</strong> = <table>\n",
       "<thead><tr><th></th><th scope=col>HR</th><th scope=col>L</th><th scope=col>U</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Well - Mild</th><td> 2.2079750 </td><td>1.6417953  </td><td>   2.969404</td></tr>\n",
       "\t<tr><th scope=row>Well - Death</th><td> 0.6717832 </td><td>0.2475004  </td><td>   1.823402</td></tr>\n",
       "\t<tr><th scope=row>Mild - Well</th><td> 0.6635648 </td><td>0.3582460  </td><td>   1.229095</td></tr>\n",
       "\t<tr><th scope=row>Mild - Severe</th><td> 0.9167601 </td><td>0.5749189  </td><td>   1.461857</td></tr>\n",
       "\t<tr><th scope=row>Mild - Death</th><td>12.9098844 </td><td>0.1402478  </td><td>1188.361304</td></tr>\n",
       "\t<tr><th scope=row>Severe - Mild</th><td> 1.4255951 </td><td>0.4754527  </td><td>   4.274498</td></tr>\n",
       "\t<tr><th scope=row>Severe - Death</th><td> 1.6829959 </td><td>0.8472465  </td><td>   3.343154</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\textbf{\\$`timeperiod{[}5,Inf)`} = \\begin{tabular}{r|lll}\n",
       "  & HR & L & U\\\\\n",
       "\\hline\n",
       "\tWell - Mild &  2.2079750  & 1.6417953   &    2.969404\\\\\n",
       "\tWell - Death &  0.6717832  & 0.2475004   &    1.823402\\\\\n",
       "\tMild - Well &  0.6635648  & 0.3582460   &    1.229095\\\\\n",
       "\tMild - Severe &  0.9167601  & 0.5749189   &    1.461857\\\\\n",
       "\tMild - Death & 12.9098844  & 0.1402478   & 1188.361304\\\\\n",
       "\tSevere - Mild &  1.4255951  & 0.4754527   &    4.274498\\\\\n",
       "\tSevere - Death &  1.6829959  & 0.8472465   &    3.343154\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "**$`timeperiod[5,Inf)`** = \n",
       "| <!--/--> | HR | L | U |\n",
       "|---|---|---|---|\n",
       "| Well - Mild |  2.2079750  | 1.6417953   |    2.969404 |\n",
       "| Well - Death |  0.6717832  | 0.2475004   |    1.823402 |\n",
       "| Mild - Well |  0.6635648  | 0.3582460   |    1.229095 |\n",
       "| Mild - Severe |  0.9167601  | 0.5749189   |    1.461857 |\n",
       "| Mild - Death | 12.9098844  | 0.1402478   | 1188.361304 |\n",
       "| Severe - Mild |  1.4255951  | 0.4754527   |    4.274498 |\n",
       "| Severe - Death |  1.6829959  | 0.8472465   |    3.343154 |\n",
       "\n"
      ],
      "text/plain": [
       "$`timeperiod[5,Inf)`\n",
       "                       HR         L           U\n",
       "Well - Mild     2.2079750 1.6417953    2.969404\n",
       "Well - Death    0.6717832 0.2475004    1.823402\n",
       "Mild - Well     0.6635648 0.3582460    1.229095\n",
       "Mild - Severe   0.9167601 0.5749189    1.461857\n",
       "Mild - Death   12.9098844 0.1402478 1188.361304\n",
       "Severe - Mild   1.4255951 0.4754527    4.274498\n",
       "Severe - Death  1.6829959 0.8472465    3.343154\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hazard.msm(cav.pci.msm)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66bde6e6",
   "metadata": {},
   "source": [
    "There is an increased onset rate of Mild CAV in the second period, but no significant impact of time on the other transitions (all HR CIs cross 1). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63411a85",
   "metadata": {},
   "source": [
    "## Dealing with Censored Patients\n",
    "\n",
    "Fitting the model where state = 99 indicates the patient is alive, but in an unknown state (other than 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c23d4f06",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in msm.check.state(qmodel$nstates, mf$\"(state)\", cmodel$censor, :\n",
      "“State vector doesn't contain observations of 99”"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "msm(formula = state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q,     death = TRUE, censor = 99, censor.states = c(1, 2, 3))\n",
       "\n",
       "Maximum likelihood estimates\n",
       "\n",
       "Transition intensities\n",
       "                Baseline                   \n",
       "Well - Well     -0.17165 (-0.19178,-0.1536)\n",
       "Well - Mild      0.12920 ( 0.11246, 0.1484)\n",
       "Well - Death     0.04245 ( 0.03400, 0.0530)\n",
       "Mild - Well      0.22643 ( 0.16852, 0.3042)\n",
       "Mild - Mild     -0.60964 (-0.71100,-0.5227)\n",
       "Mild - Severe    0.34180 ( 0.27243, 0.4288)\n",
       "Mild - Death     0.04141 ( 0.01200, 0.1429)\n",
       "Severe - Mild    0.13114 ( 0.07982, 0.2155)\n",
       "Severe - Severe -0.43572 (-0.55162,-0.3442)\n",
       "Severe - Death   0.30458 ( 0.23645, 0.3923)\n",
       "\n",
       "-2 * log-likelihood:  3944.812 \n",
       "[Note, to obtain old print format, use \"printold.msm\"]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This is how it is fitted, but there's no change in results because no patients in the toy data \n",
    "# set are censored.\n",
    "cav.msm.censored <- msm(state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q, death = TRUE, \n",
    "                       censor = 99, censor.states = c(1, 2, 3))\n",
    "\n",
    "cav.msm.censored"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "090350dc",
   "metadata": {},
   "source": [
    "## Diagnostic Plots\n",
    "\n",
    "Comparing model predictions with Kaplan-Meier curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9fb1659f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aNGjVxdXYuKis6dO6epqQlg8+bN7du3Hz58ePv27R88eLBs2TIAfHYyMULEKyAA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qxKzLRY8aOwCBgYGBgYF37ty5ceOGOLaT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\nHREREZFIsLEjIiIiEgk2dkREREQi8f+BpGAapoRKagAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “(5, 10 year change points)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow = c(2, 2))\n",
    "plot.survfit.msm(cav.msm, main = \"cav.msm: no covariates\", mark.time = FALSE)\n",
    "plot.survfit.msm(cav.cov.msm, main = \"cav.cov.msm: covariates\", mark.time = FALSE)\n",
    "plot.survfit.msm(cav.pci.msm, mark.time = FALSE)\n",
    "title(\"cav.pci.msm: time-inhomogeneous\", line = 2)\n",
    "title(\"(5 year change point)\", line = 1)\n",
    "cav.pci2.msm <- msm(state ~ years, subject = PTNUM, data = cav, qmatrix = twoway4.q, death = 4, pci = c(5, 10), \n",
    "                   method = \"BFGS\", control = list(maxit = 10000))\n",
    "plot.survfit.msm(cav.pci2.msm, mark.time = FALSE)\n",
    "title(\"cav.pci2.msm: time-inhomogeneous\", line = 2)\n",
    "title(\"(5, 10 year change points)\", line = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e3eb251",
   "metadata": {},
   "source": [
    "Up to about 10 years, the models do a reasonable job of predicting survival.  However, the second time-inhomogeneous model, fitted for intensity changes at 5 and 10 years, fits substantially better because the other models over-estimate survival after 10 years."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d5d9dab",
   "metadata": {},
   "source": [
    "## Comparing Observed and Expected Prevalence\n",
    "\n",
    "Works best when individuals are actually observed at the computed times, otherwise assumptions are made such as individuals are only observed at these times, or midpoints are assumed.\n",
    "\n",
    "The observed prevalence of a state is simply calculated as the number of individuals known to be in that state, divided by the number of individuals whose state is known at that time, which ignores the information from individuals censored at earlier times (root of Kaplan-Meier estimation :))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "52df4d72",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Need to look at how this is implemented by Gentleman et al. 1994 using prevalence.msm, and plot.prevalence.msm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eeac4ed",
   "metadata": {},
   "source": [
    "## Pearson testing\n",
    "\n",
    "Aguirre-Hernandez and Farewell (2002)\n",
    "\n",
    "Titman and Sharples (2008)\n",
    "\n",
    "Uses a Chi-square approximation even though often doesn't fit exactly.  Recommended to reduce the number of observation times, time intervals or covariate categories to improve Chi-square approximation especially with a sparse contingency table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "88c79c10",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imputing sampling times after deaths...\n",
      "Calculating replicates of test statistics for imputations...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>stat</th><th scope=col>df.lower</th><th scope=col>p.lower</th><th scope=col>df.upper</th><th scope=col>p.upper</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>166.9542    </td><td>NA          </td><td>NA          </td><td>81          </td><td>6.444851e-08</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " stat & df.lower & p.lower & df.upper & p.upper\\\\\n",
       "\\hline\n",
       "\t 166.9542     & NA           & NA           & 81           & 6.444851e-08\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| stat | df.lower | p.lower | df.upper | p.upper |\n",
       "|---|---|---|---|---|\n",
       "| 166.9542     | NA           | NA           | 81           | 6.444851e-08 |\n",
       "\n"
      ],
      "text/plain": [
       " stat     df.lower p.lower df.upper p.upper     \n",
       " 166.9542 NA       NA      81       6.444851e-08"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 <- pearson.msm(cav.msm)\n",
    "p1$test\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4956d0d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imputing sampling times after deaths...\n",
      "Calculating replicates of test statistics for imputations...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>stat</th><th scope=col>df.lower</th><th scope=col>p.lower</th><th scope=col>df.upper</th><th scope=col>p.upper</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>302.8504   </td><td>NA         </td><td>NA         </td><td>237        </td><td>0.002457122</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " stat & df.lower & p.lower & df.upper & p.upper\\\\\n",
       "\\hline\n",
       "\t 302.8504    & NA          & NA          & 237         & 0.002457122\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| stat | df.lower | p.lower | df.upper | p.upper |\n",
       "|---|---|---|---|---|\n",
       "| 302.8504    | NA          | NA          | 237         | 0.002457122 |\n",
       "\n"
      ],
      "text/plain": [
       " stat     df.lower p.lower df.upper p.upper    \n",
       " 302.8504 NA       NA      237      0.002457122"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p2 <- pearson.msm(cav.cov.msm)\n",
    "p2$test\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d06de92a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in pearson.msm(cav.pci.msm):\n",
      "“Omitting censored states not at the end of individual series”"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imputing sampling times after deaths...\n",
      "Calculating replicates of test statistics for imputations...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>stat</th><th scope=col>df.lower</th><th scope=col>p.lower</th><th scope=col>df.upper</th><th scope=col>p.upper</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>161.6173    </td><td>NA          </td><td>NA          </td><td>81          </td><td>2.647557e-07</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " stat & df.lower & p.lower & df.upper & p.upper\\\\\n",
       "\\hline\n",
       "\t 161.6173     & NA           & NA           & 81           & 2.647557e-07\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| stat | df.lower | p.lower | df.upper | p.upper |\n",
       "|---|---|---|---|---|\n",
       "| 161.6173     | NA           | NA           | 81           | 2.647557e-07 |\n",
       "\n"
      ],
      "text/plain": [
       " stat     df.lower p.lower df.upper p.upper     \n",
       " 161.6173 NA       NA      81       2.647557e-07"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p3 <- pearson.msm(cav.pci.msm)\n",
    "p3$test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9bbc7f19",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in pearson.msm(cav.pci2.msm):\n",
      "“Omitting censored states not at the end of individual series”"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imputing sampling times after deaths...\n",
      "Calculating replicates of test statistics for imputations...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>stat</th><th scope=col>df.lower</th><th scope=col>p.lower</th><th scope=col>df.upper</th><th scope=col>p.upper</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>150.2663    </td><td>NA          </td><td>NA          </td><td>81          </td><td>4.657213e-06</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " stat & df.lower & p.lower & df.upper & p.upper\\\\\n",
       "\\hline\n",
       "\t 150.2663     & NA           & NA           & 81           & 4.657213e-06\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| stat | df.lower | p.lower | df.upper | p.upper |\n",
       "|---|---|---|---|---|\n",
       "| 150.2663     | NA           | NA           | 81           | 4.657213e-06 |\n",
       "\n"
      ],
      "text/plain": [
       " stat     df.lower p.lower df.upper p.upper     \n",
       " 150.2663 NA       NA      81       4.657213e-06"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p4 <- pearson.msm(cav.pci2.msm)\n",
    "p4$test"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c40104b",
   "metadata": {},
   "source": [
    "## None of these models give an adequate fit\n",
    "\n",
    "While cav.pci2.msm fits well to survival, it discriminates less well between the states of CAV severity.  \n",
    "\n",
    "A more complex pattern of time-dependence or allowing transition intensities to depend on covariates would likely yield a better fit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dcd6daa",
   "metadata": {},
   "source": [
    "## It is also possible to calculate the influence of each individual on the MLE\n",
    "\n",
    "Using scoreresid.msm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb36a095",
   "metadata": {},
   "source": [
    "## Extensions of msm and limitations\n",
    "\n",
    "For continuously-observed processes: mstate (deWreede et al. 2010)\n",
    "\n",
    "For Random Effects models (unexplained heterogeneity in transition intensities between individuals) - calculating likelihood often intractable with a few exceptions: tracking model - random effect acts on all intensities simultaneously (Satten 1999), or a discrete random effects distribution (Cook et al 2004)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f788f1b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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