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    "<style type=\"text/css\">\n",
    ".reveal h1, h2, h0, h3, p, ul, ol {\n",
    "    font-family: \"Arial\"\n",
    "}\n",
    "</style>"
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   "source": [
    "import lifemodels as lms\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "os.chdir(\"/Users/user/Work/lifemodels/examples\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "![alt text](http://a.fsdn.com/allura/p/deday/icon \"\")  `lifemodels`\n",
    "=======\n",
    "\n",
    "What is it?\n",
    "-----------\n",
    "\n",
    "**lifemodels** is a Python package for fitting lifespan data to a number of models using MLE.  It also implements GLM (generalized linear model) for those lifespan distributions.\n",
    "\n",
    "It is the next version of **deday**. **deday** stands for *Demography Data Analyses*.  The older versions can be found [here](http://sourceforge.net/projects/deday/).\n",
    "\n",
    "**[Read the minimal example](http://nbviewer.ipython.org/github/ctzhu/lifemodels/blob/master/examples/Intro_example.ipynb)** for a simple workflow in `IPython Notebook` \n",
    "\n",
    "Where to find support?\n",
    "-------------\n",
    "\n",
    "[**Read the documentation**](https://github.com/ctzhu/lifemodels/blob/master/doc/Guide.txt) for instructions.\n",
    "\n",
    "If you use deday for published research, please contact me as `lifemodels` has not yet been published.\n",
    "To install, run `pip install git+https://github.com/ctzhu/lifemodels`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "## • Time-to-event data\n",
    "• Engineering: Reliability (MTTF)\n",
    "\n",
    "• Marketing: Attribution (web cookie expiration, time-dependent binary responce)\n",
    "\n",
    "• Biomedical science: lifespan, survivorship.\n",
    "\n",
    "## • Censor and missing data\n",
    "• Event time is $[T0, T1)$\n",
    "\n",
    "• T0==T1, or only know T0, or only know T1, ..."
   ]
  },
  {
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   "source": [
    "## • Time-dependent and Time-independent components:\n",
    "• Benjamin Gompertz & William Makeham.\n",
    "\n",
    "• [Gompertz Makeham law of mortality](https://en.wikipedia.org/wiki/Gompertz%E2%80%93Makeham_law_of_mortality):\n",
    "$H(t)=\\alpha e^{\\beta t} + C$\n",
    "\n",
    "• Example: Estimated probability of a person dying at each age, for the U.S. in 2003\n",
    "\n",
    "<table>\n",
    "  <tr>\n",
    "    <th> <img src=\"https://upload.wikimedia.org/wikipedia/commons/a/a9/Gompertz.png\" alt=\"Gompertz\" height=\"200\" width=\"200\"> </th>\n",
    "    <th> <img src=\"https://s3.amazonaws.com/nodeimages/87605343/images/87605343_0_nocrop.jpg\" alt=\"Makeham\" height=\"200\" width=\"200\"> </th>\n",
    "    <th> <img src=\"https://upload.wikimedia.org/wikipedia/en/4/4d/USGompertzCurve.svg\" alt=\"Makeham\" height=\"300\" width=\"300\"> </th>\n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "## *Basic usage*\n",
    "##  · Read the data and create a survival object using `.survt_df()` method\n",
    "### · Data taken from Clive McCay *et.al* :\n",
    "\n",
    "*The effect of retarded growth upon the length of life span and upon the ultimate body size. J Nutr. 1935;10:63–79*\n",
    "\n",
    "### · Credited with the discovery of dietray restriction (Eat less live longer)\n",
    "### · Two treatments: `Diet` and `Sex`. `III` type diet being the richest.\n",
    "### · Death events of rat recorded over ~1500 days."
   ]
  },
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     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Diet</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Time0</th>\n",
       "      <th>Time1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>II</td>\n",
       "      <td>Male</td>\n",
       "      <td>41</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>II</td>\n",
       "      <td>Female</td>\n",
       "      <td>48</td>\n",
       "      <td>48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>II</td>\n",
       "      <td>Female</td>\n",
       "      <td>62</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>I</td>\n",
       "      <td>Male</td>\n",
       "      <td>71</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>I</td>\n",
       "      <td>Female</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "  Diet     Sex  Time0  Time1\n",
       "0   II    Male     41     41\n",
       "1   II  Female     48     48\n",
       "2   II  Female     62     62\n",
       "3    I    Male     71     71\n",
       "4    I  Female     74     74"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df   = pd.read_csv('mckay.txt', sep=' ')\n",
    "df['Time1'] = df.Time0 \n",
    "#Time-to-event data, Time0 is the left bound, Time1 is the right bound.\n",
    "s_df = lms.s_models.survt_df(df)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Specify the model and create the model fit object using `.distfit_df()` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "gp2_model = lms.s_models.distfit_df(s_df, 'gp2')\n",
    "gp3_model = lms.s_models.distfit_df(s_df, 'gp3')\n",
    "wb2_model = lms.s_models.distfit_df(s_df, 'wb2')\n",
    "wb3_model = lms.s_models.distfit_df(s_df, 'wb3')\n",
    "gl4_model = lms.s_models.distfit_df(s_df, 'gl4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "## · Hazard functions of 5 models in this example are:\n",
    "\n",
    "$H(t)=C$\n",
    "\n",
    "Exponential Decay\n",
    "\n",
    "---\n",
    "\n",
    "$H(t)=(\\kappa/\\lambda)\\cdot(t/\\lambda)^{\\kappa-1}$\n",
    "\n",
    "$log(H(t))=log(\\kappa \\cdot \\lambda^{-\\kappa})+(\\kappa-1)\\cdot log(x)$\n",
    "\n",
    "Weibull model (Mortality increase with time in a power function relationship) `'wb2'`\n",
    "\n",
    "---\n",
    "\n",
    "$H(t)=\\alpha e^{\\beta t}$\n",
    "\n",
    "$log(H(t))=log(\\alpha)+ \\beta t $\n",
    "\n",
    "Gompertz model (Mortality increase with time Exponentially) `'gp2'`\n",
    "\n",
    "---\n",
    "\n",
    "$H(t)=\\alpha e^{\\beta t} - \\alpha + C$\n",
    "\n",
    "Gompertz-Makehamm model `'gp3'`\n",
    "\n",
    "---\n",
    "\n",
    "$H(t)=(\\kappa/\\lambda)\\cdot(t/\\lambda)^{\\kappa-1} + C$\n",
    "\n",
    "Weibull-Makehamm model `'wb3'`\n",
    "\n",
    "---\n",
    "\n",
    "$H(t)=\\frac{\\alpha e^{\\beta t}}{d e^{\\beta t} + 1} - \\frac{\\alpha}{d+1} + C$\n",
    "\n",
    "Gompertz-logistic model `'gl4'`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · MLE parameter estimates"
   ]
  },
  {
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   "execution_count": 4,
   "metadata": {
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    "slideshow": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>beta</th>\n",
       "      <th>c</th>\n",
       "      <th>logL</th>\n",
       "      <th>optimizer_flag</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet</th>\n",
       "      <th>Sex</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">I</th>\n",
       "      <th>Female</th>\n",
       "      <td>-10.092006</td>\n",
       "      <td>-5.256360</td>\n",
       "      <td>-9.161662</td>\n",
       "      <td>150.595193</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>-7.456580</td>\n",
       "      <td>-5.600244</td>\n",
       "      <td>-8.244084</td>\n",
       "      <td>94.532260</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">II</th>\n",
       "      <th>Female</th>\n",
       "      <td>-12.035084</td>\n",
       "      <td>-5.164614</td>\n",
       "      <td>-7.347579</td>\n",
       "      <td>166.641636</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>-11.646710</td>\n",
       "      <td>-5.201537</td>\n",
       "      <td>-7.604894</td>\n",
       "      <td>93.726082</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">III</th>\n",
       "      <th>Female</th>\n",
       "      <td>-9.134449</td>\n",
       "      <td>-5.600461</td>\n",
       "      <td>-8.840873</td>\n",
       "      <td>134.671557</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>-9.521764</td>\n",
       "      <td>-5.493469</td>\n",
       "      <td>-34.652509</td>\n",
       "      <td>103.225741</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 alpha      beta          c        logL  optimizer_flag\n",
       "Diet Sex                                                               \n",
       "I    Female -10.092006 -5.256360  -9.161662  150.595193               0\n",
       "     Male    -7.456580 -5.600244  -8.244084   94.532260               0\n",
       "II   Female -12.035084 -5.164614  -7.347579  166.641636               0\n",
       "     Male   -11.646710 -5.201537  -7.604894   93.726082               0\n",
       "III  Female  -9.134449 -5.600461  -8.840873  134.671557               0\n",
       "     Male    -9.521764 -5.493469 -34.652509  103.225741               0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp3_model.mdl_all_free"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
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    {
     "data": {
      "text/plain": [
       "array([  -9.13151133,   -5.6333212 ,   -8.08416424,  760.39933924,    0.        ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp3_model.mdl_all_cnst"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Variance of the parameter estimates\n",
    "\n",
    "It might not always be there, due to float overflow and underflow problems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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    {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>beta</th>\n",
       "      <th>c</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet</th>\n",
       "      <th>Sex</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">I</th>\n",
       "      <th>Female</th>\n",
       "      <td>1.128514</td>\n",
       "      <td>0.239391</td>\n",
       "      <td>1.227479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>1.531880</td>\n",
       "      <td>0.588591</td>\n",
       "      <td>1.769442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">II</th>\n",
       "      <th>Female</th>\n",
       "      <td>2.126095</td>\n",
       "      <td>0.317832</td>\n",
       "      <td>0.375416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>3.082429</td>\n",
       "      <td>0.486870</td>\n",
       "      <td>0.654951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">III</th>\n",
       "      <th>Female</th>\n",
       "      <td>1.616147</td>\n",
       "      <td>0.429353</td>\n",
       "      <td>1.752450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>inf</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "                alpha      beta         c\n",
       "Diet Sex                                 \n",
       "I    Female  1.128514  0.239391  1.227479\n",
       "     Male    1.531880  0.588591  1.769442\n",
       "II   Female  2.126095  0.317832  0.375416\n",
       "     Male    3.082429  0.486870  0.654951\n",
       "III  Female  1.616147  0.429353  1.752450\n",
       "     Male         NaN       NaN       inf"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp3_model.var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · log quantile function (time-to-reach-%-of-death estimate):  `.logq()` method\n",
    "\n",
    ".`logq(key, q)`, `key` is genotype-food combination here. `q` is that target % of death, default to 50%, therefore by default it returns the estimate for medium lifespan.\n",
    "\n",
    ".`logq()` method and `.logq_nc()` method are similar: the latter ignores the Makehamm term ($C$), if there is one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6.7381684156777482, 6.7561002844234102)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(gp3_model.logq(('I', 'Female')), gp3_model.logq_nc(('I', 'Female')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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     "slide_type": "fragment"
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    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>With_C</th>\n",
       "      <th>Without_C</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet</th>\n",
       "      <th>Sex</th>\n",
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       "      <th></th>\n",
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       "      <th>Male</th>\n",
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       "      <td>457.970938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">II</th>\n",
       "      <th>Female</th>\n",
       "      <td>862.616125</td>\n",
       "      <td>1138.258375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>915.955188</td>\n",
       "      <td>1104.003063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">III</th>\n",
       "      <th>Female</th>\n",
       "      <td>856.054813</td>\n",
       "      <td>868.123188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <td>918.315313</td>\n",
       "      <td>896.341313</td>\n",
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      "text/plain": [
       "                 With_C    Without_C\n",
       "Diet Sex                            \n",
       "I    Female  844.013438   859.284688\n",
       "     Male    504.323750   457.970938\n",
       "II   Female  862.616125  1138.258375\n",
       "     Male    915.955188  1104.003063\n",
       "III  Female  856.054813   868.123188\n",
       "     Male    918.315313   896.341313"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "medium_df = pd.DataFrame({'With_C'   : map(gp3_model.logq,    gp3_model.mdl_all_free.index),\n",
    "                          'Without_C': map(gp3_model.logq_nc, gp3_model.mdl_all_free.index)},\n",
    "                         index=gp3_model.mdl_all_free.index)\n",
    "np.exp(medium_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Get the estimated log mean lifespan using `.logm()` method "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6.6869775131919171, 6.7150616442887863)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(gp3_model.logm(('I', 'Female')), gp3_model.logm_nc(('I', 'Female')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## · ... and the $\\sigma^2$ for calculating the confidence interval for survival time using `.logt_var()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0018048249213575979"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gp3_model.logt_var(('I', 'Female'), 6.6869775131919171)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Plot harzard plot, survival plot and other plots using `.plot()` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10c857cd0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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i1QhGNh3JRadeFLzCg8jMcM5F3LJWak8kFCasncBjEx6jWqlq9L+xP+efcr7X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c8461d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(2, 3, figsize=(14, 8), sharex=True, sharey=True)\n",
    "axes = axes.ravel()\n",
    "for ax, key in zip(axes, gp3_model.mdl_all_free.index.tolist()):\n",
    "    gp3_model.plot(key, np.linspace(0,1400,100),ax,'hzd')\n",
    "    ax.set_ylim((-10,-2))\n",
    "    ax.set_title(key)\n",
    "plt.suptitle('log-harzard plot', fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10cf54d90>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OeBD4Bfge37VGVFrvS8UH/j/bgO/w9TTZncXznmJmefGN7Xk1E1kkwOyf4RcSqszsceBn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\nMnnjZD2AJyI+qUaRGqx5fA0/7fuJ7kuacvz8cacjiUgQSxw5ExEawed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YY0KA94CGwC1A\ne2NM2WTb5ADeB5pZa28FHvBCVkknLlf81dtx7xTmr+FL+b+flnLboMdZuDjW6Wgi4gPSOsw1e4bs\njGk6hsdnP8656HNeySQikpJW2V/njR/fUO0Jcu7c4akGbLfW7rXWRgNTgZbJtnkI+NpaewDAWqt5\nSP1YZOS/Q1YGvpibLf0WkKvELj4+9rAWKBWRa3qur2mZplQrXI3BSwZ7PI+ISGr+XHsb1W+szvur\n3nc6ijjInYanMLAvyef7E76WVBkgtzFmsTFmtTHmEU8FFOdly5CN2e1nc+riKdp+1ZaLMRedjiQi\nfujdhu8yYf0ENh3e5HQUEQkir939Gm/+9CanLp5yOoo4JMyD71MVqAdkAVYYY1ZYa3ck3zAqyZOu\nkZGRRGoKMJ+W+NeTKTwT37T9hvZft+e+L+7j6we/JmNYRkezybVxuVy43FlIxQ+onviXG7LewOv1\nXufxbx9neZflhIaEOh1JrpPqifii5LNKQnluoAHPTR3Nxx37OxdMUuXtWnLVWdqMMdWBKGtto4TP\nXwKstXZYkm36AhmttYMSPv8Y+M5a+3Wy99IsKH4uOjaaDtM7cObSGaa3na6mJwBoViVJT3E2jjoT\n69ChQgd63tHT6TjiYaon4msSh+j/fvR3ak2sxY6nd5AjYw6nY8lVODFL22qglDGmmDEmAmgHzEq2\nzUygljEm1BiTGbgT2OKpkOI7wkPD+bzN52TPkJ3W01preJuIpEmICWFM0zEMcA3g8JnDwL9XYkVE\nvOXmvDfTpHQTRq4c6XQUccBVGx5rbSzwFDAP+BWYaq3dYozpbox5PGGbrcAPwCbgZ+Aja+1v3ost\nTgoLCWPKfVPIEp6FB758gEuxl5yOJCJ+pEKBCnSq1IkX5r8AqOEREe9JOjLx1TqvMmrlKE5cOOFY\nHnGGFh6VaxYdG80DXz5AWEgYU++fSliIpx4Jk/SkISjihDOXznDLB7fwSatPcE2KTNNCpuK7VE/E\n13Wa0YkSuUowoO4Ap6PIFXi6lqjhketyMeYiLaa24IasNzCx5URCjFtr2YoP0QmKOMHlgjGu6Sxm\nAH+9tp6Br4YD8Vdj9ay4/1I9EV+3/e/t3DXhLj3L4+PU8IjPORd9jkZTGlGpQCVGNR6FMX73f11Q\n0wmKOMVaS+PPGmN33MsPUc85HUc8QPVE/MEj3zxC2Txl6V9HM7b5KicmLRC5oszhmfm2/bcs27dM\niwqKiNuMMYxqPIofGcLB0wedjiMiQaJ/7f6MXDmS0xdPOx1F0okaHvGIHBlz8H2H7/ls82dazVhE\n3FYmTxlaF32cvgv6Oh1FRIJE2bxlqVe8HmPXjHU6iqQTDWkTj9pzYg81J9RkVKNRtCnfxuk44gYN\nQRGnnbl0hrLvlWXa/dOoWbSm03HkOqieiL/YdHgTDac0ZFevXWQKz+R0HElGQ9rEMe5MHXtTzpuY\n3X42Pef05Me9P3o9k4j4v6wRWRneYDi9vu9FbFys03FEJAhULFCROwvfyfj1452OIulADY+4zd21\nMqoUrMJn933G/V/ez+9Hf/dqJhEJDO1vbU/m8MxMWD/B6SgiEoBSOofpX7s/w5cP13qCQUANj3hF\ng5INGFp/KE0+b8KRs0ecjiMiPm7JEsPIRiN5dfGrnLxw0uk4IhJgUmp47ih8B2XzlmXKpinpnkfS\nl1aKlCtyuf4tEoMG/ft1d9bK6FKlC7uO76LV1FYs6riIjGEZvRNSRPyeywVRkVVpVqYZry19jbfu\nfcvpSCISBPrV6kePOT3oWKkjoSGhTscRL1HDI1eUvLFJ62rog+8ezLa/t9F1Vlcmt56sNXpE5Ire\nqPcGt3xwC4/f9jhl8pRxOo6I+DF3LtpG3hRJroy5+GbrN9xf/v70DSjpRg2PeFWICWFSq0nUnVSX\nIT8O0SJfIvKPlE9GCtCmxIv0md+Hme1mOhNMRAKCOxdtjTG8XPtlBi0ZRJtybXRhNkCp4RG3XW0I\nW2oyh2dmZruZVBtXjQoFKtDi5hYezSUi/im1k5GLMc9Q7v2xLNy1kPol6juQTESCSbMyzXh54css\n2LWABiUbOB1HvECTFojbrrXhASiUrRBfP/g1XWd15be/fvNYJhEJPBnCMjC8wXCem/ecpqkWEY+4\n0jlMiAnhxZovMmz5sHTLI+lLDY+kmztvvJPhDYbTamorzcIkIpdJfjLSplwbcmTIwcQNEx3JIyKB\n5WoXbdvd2o5tf29j7cG16ZJH0pdJz5WFtZKxADw19yn2ndrHN22/IcSo53aaVkYXX7X6wGpaTm3J\ntqe3kTUiq9NxxA2qJ+LP3l3xLiv2r+CLB75wOkrQ83Qt0dmmpLt3Gr7D0XNHGfLjEKejiIgPu6Pw\nHdxd/G7eXP6m01FEJAh0u60bi/csZvvf252OIh6mhkfSXURoBF8+8CUfrP6ABbsWOB1HRHzYkHpD\neG/1exw4dcDpKCIS4LJGZKX7bd15Z8U7TkcRD1PDI44olK0QU+6bwiPfPKITGRFJVbGcxehWtRsD\nFg9wOoqIBIGnqz3N1F+ncuTsEaejiAep4RHH1Ctej6fueIp2X7cjJi7G6Tgi4gMS1+VJql+tfsze\nPpvNhzenex4RCS4FshbgwfIP8v6q952OIh6khkcc1a92PzKFZSLKFeV0FBHxASk1PDky5qB/7f68\nuODFdM8jIsGnVujzjFkzhrOXzjodRTxEDY9ck5ROSq5FiAlhcuvJTNwwkfk753vmTUUk4PS4vQc7\nju3Qc38i4nU7V5WhZtGafLLxE6ejiIeo4ZFr4qmGB+JvH09uPZmOMzpqzKxIEHK5ICoq/tegQf9+\nnLTORIRGMKTeEPou6EucjXMipogEkRdqvMA7K97R4scBIszpACIQ/zxPx0od6TyzM7Pbz8YYv1vG\nQUSuUWTk5YsCRkWlvN395e/nrRVvMe2XabSv0D4dkolIsHC5/r3IMmgQWO7iAnl54+uZDHjgPiej\niQeo4RG3JS8GiZKfrFyrwXcPpuaEmoxeNZped/a6/jcUkYBijGH4PcPpPLMz95W7jwxhGZyOJCIB\n4r8XXgwVfnuBd39+mwGo4fF3anjEbe5ehb1W4aHhfN7mc2qMr0G94vW4Nf+tnt2BiPi8q108qXtT\nXcrnK8/YNWN5pvoz6ZJJRIJT67KteXH+i6zYt4IaRWo4HUeug57hEZ9SKncphtYfysPTH+ZizEWn\n44hIOnPnbvHQ+kMZsmwIJy+c9HoeEQk+iXUoNCSUZ6s/y9sr3nY0j1w/NTxyTTwxhC01j1V5jGI5\nizHQNdB7OxERv1WhQAUal2rMWz+95XQUEQlASc9xulTpgmuPi13HdzmWR66fsdam386Msem5P/Ff\nR84eodLYSnz94NfcVeQup+MENGMM1lq/myVC9SS4/XHyD6p8WIVfev5CwWwFnY4jCVRPJBC9tOAl\nzkWfY1TjUU5HCRqeriW6wyM+KX+W/Lzf5H06zuiohb9Egoi7U94XzVGUTpU6MXjJYK/mERF5qtpT\nTN40mePnjzsdRa6RGh7xWfeVu4/qN1an74K+TkcRkXSSljW+Xq79Ml/+9iU7ju3wWh4RkRuz30iz\nMs0Yt26c01HkGqnhEZ82qtEoZmydgWuPy+koIuJj8mTOQ+/qvXll0StORxGRAPdc9ecYvWo00bHR\nTkeRa+BWw2OMaWSM2WqM2WaMSfVyuzHmDmNMtDFGE5aLR+TKlIsxTcfw2KzHNLRNJEC5XPHT3EdF\nxa/xlfixO3d7nq3+LEv3LmXdn+u8GVFEglyVglUonbs0X/72pdNR5BpcddICY0wIsA2oDxwEVgPt\nrLVbU9huPnAemGCtnZ7Ce+mhQLkmD09/mLyZ8zKi0QinowQcPWQsviSx2UmLD1Z/wKzfZ/H9w997\nI5KkgeqJBLLZ22Yz0DWQt0qv4e67/e6fuV9xYtKCasB2a+1ea200MBVomcJ2TwNfAUc8FU4k0chG\nI/ni1y9YsW+F01FExMd0rdqV7ce2s3j3YqejiEgAa1K6CWcuneGTJUudjiJp5E7DUxjYl+Tz/Qlf\n+4cxphDQylo7BlDLKx6XJ3MeRjQaQddvu2pBUpEAdi1rfEWERjA4cjD9FvZDV+lFxFtCTAjP3vks\nP/Ou01EkjcI89D4jgKTP9qTa9EQlGasQGRlJpDdXsBS/5XL998TngfIP8Nnmzxi6bChRkVEOpAoM\nLpcLV1qmwvJhqieB51r/CttXaM/wn4YzY+sMWpdr7dFMkjrVEwkWLlf8r0s8yu/nBtArage5KUVk\npHcXYw8W3q4l7jzDUx2IstY2Svj8JcBaa4cl2SZx+VkD5AXOAo9ba2cley+NkRW3pDaOf/+p/VT5\nsApLOi2hfL7y6R0rIGnMvQSKOdvm8OKCF9nUYxOhIaFOxwlKqicSDGpH9adytVOMbjLa6SgBy4ln\neFYDpYwxxYwxEUA74LJGxlpbIuFXceKf43kiebMj4gk3Zr+RqLpRdJ/dnTgb53QcEfEhTUo3IVfG\nXEzZNMXpKCISwKrxJFM2T9FCpH7kqg2PtTYWeAqYB/wKTLXWbjHGdDfGPJ7St3g4owQJd6em7XF7\nD6Jjoxm/bnx6RxQRH2aMYWj9oQx0DdSzfiLiNc0jC9G8THM+WvuR01HETVcd0ubRnemWsbjpalPT\nbjq8iXs+vYfNPTdTIGuB9IoVkDQERfxRSs/5JWr6eVMalWzE03c+nZ6RBNUTCR7r/1xPi6kt2NVr\nF+Gh4U7HCThODGkT8TkVC1SkY6WO9Jnfx+koIuKAKz3b+ka9NxiybAhnLp1JtzwiEly0EKl/UcMj\nPsmdGU8GRg7EtceltTdE5DKVb6jM3TfdzYiftVCxiHjPczWe492f39V0+H5AQ9rEr82LEyK5AAAc\nIUlEQVTYOoN+C/uxscdGIkIjnI7jlzQERfxF4rSwEP+c38CB8R+nNC3sjmM7qP5xdX5/6nfyZM6T\nfiGDnOqJBJM4G0e598sxrvk46hSr43ScgOLpWqKGR/yatZbm/9ec2kVr07dW36t/g/yHTlDEH13t\nOT+AnrN7kjUiK2/e+2Z6RBJUTyT4jFk9hnm75vFN22+cjhJQ9AyPSBLGGEY2GsmbP73JvpP7nI4j\nIj7k1bqvMmHDBPaf2u90FBEJUB0rd2T5H8vZcWyH01HkCtTwiN8rmbskT1d7mt4/9HY6ioikE3ee\n8yuUrRDdqnZj8JLBXs8jIsEpc3hmHr/tcT0z6OM0pE0CwoWYC9zywS2MbTqWBiUbOB3Hr2gIigSy\n4+ePU+a9Mizvspwyeco4HSfgqZ5IsHG54Obb/uSWD25hR68d5M6U2+lIAUFD2kRSkDEsIyMajqDX\n9724FHvJ6Tgi4iNyZcrF8zWe55VFrzgdRUQCkMsFBbMVpMXNLfhwzYdOx5FUqOGRgNGsTDNK5CrB\nqJWjnI4iIj6k1529WL5vOWsOrnE6iogEqOdqPMd7q9/TRVcfpSFtElC2/72dGuNrsKnnJgplK+R0\nHL+gISgSDMauGcv0LdOZ98g8XC73ngGStFM9kWCQ2hT5c3Lfy1N1OtCxckenogUMTUstchX9FvTj\nwOkDfNr6U6ej+AWdoEgwiI6NpvwH5RnbdCw/flr/qlNay7VRPZFgk3SK/B92/ECf+X3Y2GMjxvjd\nYeBT9AyPBLXEKypX8nLtl1m4eyE/7//Z63lExD+Eh4bz+t2v89LCl7DoxFZEPO/ekvdisczfNd/p\nKJKMGh7xK+40PNkyZGPYPcN4+runibNxXs8kIr7P5YLfvnqAAwfiGPzlV/9clXWnpoiIpCbp8Fhj\nDM/XeJ63V7ztWB5JmYa0iV9xZ3V1AGstNSfUpFvVbnSu0tnbsfyahqBIMFmwawFtP32CQ6/+Snho\nuNNxAo7qiQS7S7GXKD6yOHMfmkulGyo5Hcdv6RkeCTqpPRwYGXnlB49XH1hNy6kt2frUVrJnyO7d\nkH5MJygSbEpGNaBPszb0uL2H01ECjuqJCAxbNoxf//pVzxJfBzU8EtTcvcOTqNOMTtyQ9Qb+d8//\nvBXJ7+kERYLNh9+uZdC25mx/ejtZIrI4HSegqJ6IwIkLJyg5qiQbum+gSI4iTsfxS5q0QCQNhtYf\nysfrPmbnsZ1ORxERH9G9+W1E3hTJOyvecTqKiASgnBlz0rFSR0b8PMLpKJJADY/4lbSunVEwW0Ge\nr/E8feb38UoeEfFPr9d7nZErR3Lk7BGno4hIAOpdvTeTNk7i+PnjTkcR1PCIn7mWxQJ71+jN+kPr\nWbx7scfziIh/KpGrBB0qdGDwksFORxGRAFQkRxGalWnG2DVjnY4iqOGRIJAxLCNvNniTZ394lti4\nWKfjiIiPeLXuq0z9ZSrb/t52xe00dbWIuCN5rehzVx9GrRrFhZgLjuSRf6nhkaDQplwbcmbMyYT1\nE5yOIiI+Im/mvPS5qw/9Fva74nZqeETEHclrxa35b+W2grfxyYZPHMkj/1LDI0HBGMO7Dd9lgGsA\nJy+cdDqOiPiIXnf2Ys3BNSz/Y7nTUUQkAL1U6yWG/zScmLgYp6MEtTCnA4ikl6oFq9KkVBOG/DiE\nYQ2GOR1HRHxApvBMvH736zw/73lWPLYCY+JnQU2+/leiq63/JSLB5Wq1olbRWhTKVogvf/2S9hXa\np39AAbQOjwSZP0//SYUxFVjZdSUlc5d0Oo5P0LoZEuzibBzVxlXjhbteoN2t7f7zelrX/wpmqicS\nzFKrFXO3z6Xfwn5s6L7hn4sqcmVah0fkOhTMVpDnajzHiwtedDqKiPiIEBPC2/e+zUsLXtLDxSLi\ncY1LNcZgmLt9rtNRgpYaHgk6vav3Zu3Btbj2uJyOIiI+ou5NdalSsEqKCwVqCJuIuCO1WmGMoV+t\nfrz+4+voTqIz1PBI0MkUnomOhYbT+4femqZaRP4x/J7hvPXTWxw+c/iyr6vhERF3XKlW3F/+fo6f\nP86i3YvSLY/8Sw2PBKffHiBrRFYmbpjodBIR8RGl85SmU+VOvLLoFaejiEiACQ0J5eXaL/P6j687\nHSUoqeGRoGQwjGg4glcXv8qpi6ecjiMiPuLVOq/y7bZvWf/neqejiEiAaX9re/ae2MuyP5Y5HSXo\naJY2CRrJp44cOBBm0plyRQvweZf/ORnNUZpVSeRyH675kM9/+RxXR5dmVEoj1RORK/t43cd88esX\nzHtkntNRfJqna4kaHglKiVNHHjx9kIpjKgb1NNU6QRG5XGxcLLePu52Xar5E21vb/ud1l0vP9aRG\n9UTkyi7FXuLm925mSusp1Cxa0+k4PsuRaamNMY2MMVuNMduMMX1TeP0hY8zGhF/LjDEVPBVQxJsK\nZSvE8zWep8/8Pk5HEREfERoSyujGo+kzvw9nL539z+uJd4pFRNIqIjSC/rX7E7UkyukoQeWqDY8x\nJgR4D2gI3AK0N8aUTbbZLqCOtbYS8DowztNBRTwp6dXZ3jV6s+HQBs2cIiL/qFW0FrWL1WbIj0Oc\njiIifsSdCyIdK3Vkx7EdepYnHYW5sU01YLu1di+AMWYq0BLYmriBtfbnJNv/DBT2ZEgRT0va8GQM\ny8hb977Fs98/y7ru6wgLceewEJFAN/ye4VQaW4lOlTtxYHPpy54BTBQZqeFtIvIvd4a8hoeG82qd\nVxmweACLOupia3pwZ0hbYWBfks/3c+WGpivw3fWEEklvrcu2Jm/mvHy45kOno4iIjyicvTD9avXj\nqe+eom5d+8+zfwMH/vscoJodEbkWj1Z6lP2n9rNw10KnowQFj17KNsbcDXQGaqW2TVRU1D8fR0ZG\nEqn/LcQHGGMY2Wgk9T+tT7tb25Encx6nI3mNy+XCFSAPIaie/H979x4eRX3vcfz9JSGAUoKgQiGI\nVw4oCojcvAaKGlFBq+VeEEpRELD1WMOlCKnwCIXDRR7xKKUoKGqAKJzKRRACKBCxAYIICBIpoNJS\nBYtVoMmcP3YiISaQZHd2djef1/Ps8+zO7s73O7D5ZH6bmd+I14a1GcacrXNYtHMRD179oN/tRBzl\niciPZ4EtcLa/AMdXiictOY1Rq0fR4bIOFX5GSK+z5JyztJlZW2Cs4zgp7uPhgOM4zsQir7sOWASk\nOI7zaQnr0iwoEtGGLh1KnpPHzLtn+t1K2GhWJZGzW79/PT0zerJj8A5qVKmhWdrOQnkiFV3BX39L\nI9/Jp9n/NmN8h/F0/q/OXrYVdfyYpW0zcKWZNTSzBKA7sKRIU5cQGOz8sqTBjkg0SGufxqKdi3TR\nQRH5wS0Nb+GOy+/g96t/D2iwIyKhUckqMb7DeEatHkVefp7f7cS0cw54HMfJA4YA7wA7gNcdx9lp\nZg+b2UD3ZaOBWsBMM9tiZh941rGIh2pVq8XT7Z9myLIh5Dv5frcjIhFi0h2TSN+RzuZDm/1uRUQi\nWFm/ELm30b0kVklk7ra5nvQjAbrwqEgRefl5tJvdjkdbPUrf5n39bsdzOgRFpHReyXmFyRsms/nX\nm6kcV9nvdiKS8kSk7DYe2EjXhV35ZMgnVKtcze92IoIvFx4VqUjiKsXxXKfnGP7ucI5+f9TvdkQk\nQvS6thd1q9dl0oZJgC5AKiKh0a5BO1rXb82zWc/63UrM0oBHpBit6reic6POjF49utjntaMjUvGY\nGS/c8wJTNk5h15FdygERCZkJP5vApA2TOHz8sN+txCQNeERK8EzHZ1jw8QI+/PzDHz2nHR2Riqlh\nzYakJafRf3F/8tFJxiISGlfVvoq+zfry1Jqn/G4lJmnAI1KCWtVqMbHjRB75yyOaPUVEgMCXHX9f\nOogvDlTh6ZVTfpiCVl+CiEiwRt82mrd2v8W2L7f53UrM0aQFImfhOA7tX27Pz5v8nOu+G3bGhcXG\njAncP9uFxaKBTjIWKbvcr3NpOr01HwzO5JqLr/G7nYihPBEJzszNM0nfkc6avmsq9MVIQ50lGvCI\nnMOuI7u4+c83s+XhLTRIbACU7cJikU47KCLl03nsnzj405lsGrCJhLgEv9uJCMoTkeDk5efRalYr\nnrjxCXpe27PCXuhYs7SJhFnjCxvzWJvHGLx0MPqFKCIFfnvbr0iqkaRj7kUkZApmiv3dyt/xzYlv\ndLhsiGjAI1IKqTenkvt1Lgs+XgBUzG9bRORM7dsbszvPZl7OPNbkrvG7HRGJEe0atCPlihR9mRJC\nOqRNpJSyDmbR5fUu5AzK4eLzL/a7nZDRISgiwVmxdwUD/m8A2QOzuej8i/xux1fKE5HgZWbC0swj\nzKQp3/5pCWMGtAai/5zhstA5PCI+Sl2ZSu7RXNJ/ke53KyGjHRSR4KWuTGXb4W0s7bWUSlZxD55Q\nnoiEzqs5r/J4xkQOjv4rleMq+91OWOkcHhEfpbVPY/vft5O+I3YGPCISvHEdxnH85HEmvDfB71ZE\nJEb0vLYnNajPxPcn+t1K1NOAR6QMqsZX5eX7XmbosqEc+uaQ3+2IiM8KTiiuHFeZ1x98nRkfzGDV\nvlW+9iQiscHMGNf2BaZnTde1eYKkAY9IGbWu35rBNwym/5L+5Dv5frcjIj4qPINSUo0kXnvgNXpn\n9Cb361zfehKR2NEt5RIm3z6ZX775S07854Tf7UQtDXhEymHkLSM5+v1RZmTN8LsVEYkgyZcmM+Lm\nEdz/xv0cP3nc73ZEJAb0adaHK2pdweg1o/1uJWpp0gKRcvr0q09pO7sty3stp2W9ln63U246yVik\nbDIzT/9lJy0NxowJ3C+YQclxHAYsGcCR746Q0TWDuEpx/jTqA+WJiDf+8e0/aPFCC2Z3ns2dV97p\ndzue0yxtIhEkfUc6I98dSfbD2dSoUsPvdspFOygi5Td2bOBW1Mm8k6S8kkLzus2ZcueUcLflG+WJ\niHfWfraW7ou689eBf6XeT+r53Y6nNEubSATpek1XOl7ekf6L+6NfliJSICEugUVdF7F873KmbKw4\nAx4R8c5tl97GoBsG0WNRD07lnfK7naiiAY9IkKanTOfgNwd/mDay8EnMIhLbznYRwAuqXcCK3iuY\nnjWdudvmhq0nEYldo24ZRfWE6jy+4nG/W4kqGvCIBKlKfBUWdl3Is1nPsnzvcg14RCqQc131vEFi\nA5b3Wk7qqlQWfrwwLD2JSOyKqxTH/J/P55197zA7e7bf7UQNDXhEQiCpRhILfrGAPm/24TDb/W5H\nRCJIk4uasKzXMoYsHULGzgy/2xGRKJdYNZHF3RczcvVIJmes9LudqKBJC0RCoGDWpu28Rsax4Tye\nuImf8NMfZm2KZDrJWCQ8tnyxhbtevYupd06lx7U9/G7HE8oTkfBZv389KXMe4L2HV9Dipy38biek\nNEubSITrMHY8/6ybzpq+a6hVrZbf7ZyTdlBEwmfO2x8xencKI28ZyeBWg/1uJ+SUJyLh1XXsIt77\nyVDe7fMuTS5q4nc7IaNZ2kQi3C2MpONlHen0aif+deJffrcjIhFk/+amrOu3jqmbpjJ81XDynXy/\nWxKRKJOZeXpK/AVpD9DmXxNo89ztzF262+fOIpcGPCIh1j7ZmHzHZJrVaUan+Z049v0xv1sSkQhy\n+QWXs/FXG9lwYAMPpj/I8ZPH/W5JRKJIcvLpAc+YMfDm2D5M7/I0I3Z1YNuX23zuLjLF+92ASKwJ\nnLNjPH/P8wxbNoyO8zqyvNdyap9X2+fORMQPBef4AaSlFSy9kN/fupL044/SelZrFnZdyNUXXe1P\ngyIS9fq16Mf5Cedz+7zbSf9FOsmXJvvdUkTROTwiHnIchxHvjuCtXW/xds+3uaLWFX639CM65l4k\nfAq+lS1szpY5PLnqSca1H8fAlgMxi7ofxx8oT0TCKzPzzMmRVueupvvC7ozrEMiTaKVzeESiiJkx\noeMEftP2N9z055tY+9lav1sSkQjTr0U/1j60lhezX+Tu+Xfzt2N/87slEYkSRWeC7XBZB97r/x7T\nNk3j10t+zb9P/duXviKNBjwiYfDIDY8w7/55dFvYjfHrxpOXn+d3SyLig5Kmqb/6oqvZ9KtNtEtq\nx/UvXM+k9ydxMu9kWHsTkdjQqHYjsgZk8d1/vqPFCy3YfGiz3y35Toe0iYTRwW8O0iujF4Yx695Z\nXFX7Kr9b0iEoIhFm71d7eWz5Y+w6sotx7cfRrWk3Kll0fD+pPBGJLG989AZDlw2l57U9SUtOI7Fq\not8tlYoOaROJYkk1kljdZzX3Nb6PdrPb8Ye1f+Dbk9/63ZaIRJAra13J2z3fZta9s5iWNY1rZl7D\nS1tf4sR/TvjdmohEmW5Nu7Fj8A6OnzxO4+caMyNrRoXMEv2FR8Qn+4/uJ3VVKuv2r2PULaPo16If\n51U+L+x96BtZkcjlOA6rc1cz8f2JbDu8jX7N+/FQ84dofGFjv1srlvJEJHJt+WILT2U+xdYvtzK0\n9VAGXD8gYi+QHuosKdWAx8xSgGkE/iI023GcicW85lngLuBb4CHHcbYW8xoFikgRH37+IePWjeP9\nA+/zRLsnSL05Naz1tYMiEh12H9nNrOxZzN8+nzrV6/BAkwe4p9E9NKvTLGJmdlOeiES+7C+ymZ41\nncW7FpNyZQq9r+tNx8s7UjW+qt+t/SDsAx4zqwR8AvwM+BzYDHR3HGdXodfcBQxxHOduM2sDTHcc\np20x61KgSIVTdMrIkuz55x4+/sfHdGncxeuWzqAdFJHIVVx+5OXnsW7/OpbsXsJf9vyFo98f5daG\nt3Jj0o3cUO8GmtVtRs2qNf1oV3kiEuEKZ8qRfx9hwY4FzP9oPjmHc0i+NJnkhsncdMlNNKvTjCrx\nVXzr049zeFoDexzH2e84zingdaDoHlkXYC6A4zhZQKKZ1QlVk8HILLjaWwzXrAjbGM01S7uKq2pf\nReKX0XEyYUWln23VDHe94t4WVymO9pe1Z2rKVPYM3UP2wGzub3w/nx39jNRVqTSY2oD6U+oz4k8j\ngupZvFMRPvMVpWa0bWPht1543oUMajWI9f3Ws2/YPno07cGer/YwYMkAak6syXXPX0fXBV0Z9e4o\nMpZlBN23n0oz4KkPHCj0+KC77GyvOVTMa3wRbR/EaKinmrFTT8qmInweVDP66jVIbEDv63ozo9MM\nNg3YxLHhx9jQfwOn9p3yrKYEpyJ85itKzVjZxtrn1aZ70+7MvHsmOYNy+Dr1a+Z0mcN9je8jIS6B\njes3hrxmOMWHu+DYQpeYTk5OJrk0x/qIRJnMzNPfoqSlnV6enFy6w9u8lJmZGTMDK+WJxKJg86OS\nVaJhzYZUT6ge+uaKUJ6IRL7yZErV+Kq0rNeSlvVaAjA2c6x3DeJ9lpRmwHMIuKTQ4yR3WdHXNDjH\na4AzA0UkVhUNkUj62Bf9RZ5WOP2ijPJEYlEk50dRyhORyBcNmeJ1lpRm0oI4YDeBSQu+AD4AejiO\ns7PQazoBj7qTFrQFppU0aUEomxeR0IjWk4z97kFEfkx5IiKhEMosOedfeBzHyTOzIcA7nJ6WeqeZ\nPRx42nnRcZylZtbJzPYSmJa6n9eNi0jFpjwRkVBRnojEtrBeeFRERERERCScSjNLm4iIiIiISFTS\ngEdERERERGJW2AY8ZpZiZrvM7BMzSw3ROpPMbLWZ7TCz7WY2zF1+gZm9Y2a7zWyFmSUWes8IM9tj\nZjvN7I4galcys2wzWxKOmmaWaGYL3HXsMLM2XtY0s9+a2UdmlmNmr5pZQqjrmdlsMztsZjmFlpW5\nhpld7/b5iZlNK0fNP7rr3Gpmi8yshtc1Cz3332aWb2a1QlWzpHpmNtRd53YzmxDKbQwnL7LEXa8v\neRLrWeKuQ3kSgprhzpKz1VSenHO9yhPlSVA/215mSUk1Cz0Xe3niOI7nNwIDq71AQ6AysBVoHIL1\n1gWau/erE5hNrjEwEXjSXZ4KTHDvXw1sITBZw6VuT1bO2r8FXgGWuI89rQm8BPRz78cDiV7VBOoB\n+4AE9/EbQN9Q1wNuBpoDOYWWlbkGkAW0cu8vBe4sY82OQCX3/gTgGa9rusuTgOVALlDLXdYk2Jol\nbGMygYlH4t3HF4aqXjhveJQl7rp9yRNiOEvcdShPQlSzuHruck+y5CzbmIzyRHniKE/OVaO0n/sS\n6sXUvslZtjOZMORJuEKlLbCs0OPhQKoHdd5yPyC7gDrusrrAruLqAsuANuWokwSsdP+TCkLFs5pA\nDeDTYpZ7UpNAoOwHLnA/aEu8+ncl8Ismp7zb5L7m40LLuwPPl6VmkefuA+aFoyawALiWM0MlJDWL\n+Xd9A+hQzOtCto3huBGmLHHX7XmeEONZ4r5HeRLCmsXVw8MsKeHfVXlS9lrKE+VJmX+2Cz0XE/sm\nJfy7hiVPwnVIW33gQKHHB91lIWNmlxIYNW4i8IE8DOA4zpfAxSX0caicfUwFfgc4hZZ5WfMy4IiZ\nzXH/VP2imZ3nVU3HcT4H/gf4m/veY47jrPJ4GwtcXMYa9Ql8ngoE+9nqT+DbAk9rmlln4IDjONuL\nPOVVzUbArWa2yczWmFlLj+t5xfMsgbDmSUxnibs+5YmHNX3IElCelInyRHniCubzFav7JhCmPImJ\nSQvMrDqwEHjMcZzjnPnDTjGPg6l1N3DYcZytwNnm7Q9ZTQLfYlwPPOc4zvUErnU0vJgaIalpZjWB\nLgRG4fWA882sl1f1ziEcNQAws1HAKcdxXvO4TjVgJDDGyzpFxAMXOIELAj9J4BscKUa48qQiZAko\nT7zME5+yBJQnpaY8CW3NipgnMb5vAmHKk3ANeA4BlxR6nOQuC5qZxRMIk3mO4yx2Fx82szru83WB\nvxfqo0GQfdwEdDazfcBrQAczmwd86WHNgwRG3B+6jxcRCBmvtrMjsM9xnK8cx8kD3gRu9LBeYWWt\nEZLaZvYQ0AnoWWixVzWvIHA86jYzy3Xfn21mF1Pyz0qwNQ8AGQCO42wG8systof1vOJZlkDY86Qi\nZAkoTwp4UdOPLAHlSakoT5QnwdauAPsmEK48Odcxb6G4AXGcPjEwgcCJgU1CtO65wJQiyybiHvdH\n8SeWJRD4U2y5Jy1w13cbp4+T/aOXNYG1QCP3/hh3Gz3ZTqA1sB2oSuCbopeAR72oR+CHa3sw/3cE\nDhNo7fa6FEgpY80UYAdQu8jrPKtZ5LlcAt9uhKxmMds4EEhz7zcC9od6G8Nxw8MscdfvS54Qo1ni\nrkN5EsKaResVeS7kWVLCNipPSrd+5YnyJJjf2zG3b1LCdoYlT8IZLCkEZinZAwwP0TpvAvIIhNQW\nINutUwtY5dZ7B6hZ6D0j3H+0ncAdQdYvHCqe1gSaAZvdbc0gMBOKZzUJBNdOIAd4mcAMNiGtB8wH\nPgdOEDgetx+BExHLVANoSSAA9wDTy1FzD4GTILPd20yvaxZ5fh/uiYGhqFnCNsYD89z3fwjcFspt\nDOcND7LEXa9veUIMZ4m7DuVJCGoWV6/I8yHNkrNso/Lk3OtVnihPSv25L6FeTO2bnGU7w5InBSMl\nERERERGRmBMTkxaIiIiIiIgURwMeERERERGJWRrwiIiIiIhIzNKAR0REREREYpYGPCIiIiIiErM0\n4BERERERkZilAY+IiIiIiMSs/wcPguzJZZlKfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c82aad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(2, 3, figsize=(14, 8), sharex=True, sharey=True)\n",
    "axes = axes.ravel()\n",
    "for ax, key in zip(axes, gp3_model.mdl_all_free.index.tolist()):\n",
    "    gp3_model.plot(key, np.linspace(0,1400,100),ax,'sf')\n",
    "    ax.set_ylim((-0.01,1.01))\n",
    "    ax.set_title(key)\n",
    "plt.suptitle('survival plot', fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Plot multidimensional confidence regions with  `.contourf_2D()` method\n",
    "### · *AKA. Why Gompertz distribution is rarely worked on*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### · Weibull model is a well-conditionned quadratic function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10de9fa10>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TvkTx5V7bkpkqWwO7S7pa0k8k7Vi7g6RZwELbTzeqRNLrgaW2f1dVtrOkm4FF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\nFAR4T3cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c857890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax, cax) = plt.subplots(1, 2, gridspec_kw={'width_ratios':[20,1], 'wspace': 0.5})\n",
    "wb2_model.contourf_2D(('I','Female'),\n",
    "                       ax, cax,\n",
    "                      (np.linspace(-5, 5, 41),\n",
    "                       np.linspace(-4, 4, 45)))\n",
    "plt.suptitle('Weibull Model 2D Conf. Region')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### · Gompertz model is an ill-conditionned very non-quadratic function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10ee53710>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1Ye6ht2DVRe2enwcJvFYSdDPGPej6pXJBJ6kGvBP4F9t3S1rf9u+abJegG3PD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\nEWMtQRcREWMtQRcREWPt/wPc8BoBysfFpQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104667e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax, cax) = plt.subplots(1, 2, gridspec_kw={'width_ratios':[20,1], 'wspace': 0.5})\n",
    "gp2_model.contourf_2D(('I','Female'),\n",
    "                       ax, cax,\n",
    "                      (np.linspace(-5, 5, 41),\n",
    "                       np.linspace(-4, 4, 45)))\n",
    "plt.suptitle('Gompertz Model 2D Conf. Region')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### · Challenge of Gompertz model: precision lost due to overflow/underflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10f10d910>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+B/iW7V8MUS9DiBGTRGuIZQixz2gOITZRx0OI42Aa8AZJ10m6QtJrut2giOiu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\nEY2UAIuIiEZKgEVERCP9f4DjcD4zlN74AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c7fbfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax, cax) = plt.subplots(1, 2, gridspec_kw={'width_ratios':[20,1], 'wspace': 0.5})\n",
    "gp2_model.contourf_2D(('I','Female'),\n",
    "                       ax, cax,\n",
    "                      (np.linspace(-5, 5, 41),\n",
    "                       np.linspace(-4, 4, 45)),\n",
    "                      levels=np.linspace(150,5000,10))\n",
    "plt.suptitle('Gompertz Model 2D Conf. Region')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### · Gompertz-Makeham model: multidimensional optimization problem is even harder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10f70db90>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yLdfk/LvMuvHuQ28Ds6xRrZfqrm292uVEcaWtQmFmfSPpgHaPoucppQW9A0Gb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\nlyRJkiSpB/4PhDBdlNWBNaAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cf54e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2, ax3, cax) = plt.subplots(1, 4, \n",
    "                                       gridspec_kw={'width_ratios':[20,20,20,1], 'wspace': 0.5}, \n",
    "                                       figsize=(16,4))\n",
    "\n",
    "gp3_model.contourf_2D(('I','Female'),\n",
    "                      ax1, cax,\n",
    "                      (np.linspace(-5, 5, 41),\n",
    "                       np.linspace(-4, 4, 45),\n",
    "                       np.linspace(0,0,1)))\n",
    "gp3_model.contourf_2D(('I','Female'),\n",
    "                      ax2, cax,\n",
    "                      (np.linspace(-5, 5, 41),\n",
    "                       np.linspace(0,0,1),\n",
    "                       np.linspace(-4, 4, 45)))\n",
    "gp3_model.contourf_2D(('I','Female'),\n",
    "                      ax3, cax,\n",
    "                      (np.linspace(0,0,1),\n",
    "                       np.linspace(-5, 5, 41),\n",
    "                       np.linspace(-4, 4, 45)))\n",
    "plt.suptitle('Gompertz Model 3D Conf. Region')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# *Experimental Functionality*\n",
    "\n",
    "## · GLM (generalized linear models) for scale, shape, location, $\\alpha$, $\\beta$, $\\kappa$, $\\lambda$... (you name it)\n",
    "## · ... and partially fixed models too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "wb2_glm = lms.s_models.model(wb2_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · With Weibull $\\lambda$ fixed, it is a form of parametric proportional hazard model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full model\n",
      "763.455156875\n",
      "1 + Diet + Sex + Diet:Sex\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Estimate</th>\n",
       "      <th>Error</th>\n",
       "      <th>Std_Estm</th>\n",
       "      <th>p</th>\n",
       "      <th>sig_code</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>lambda</th>\n",
       "      <th>FIXED</th>\n",
       "      <td>6.798327</td>\n",
       "      <td>0.038464</td>\n",
       "      <td>176.744239</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">kappa</th>\n",
       "      <th>Intercept</th>\n",
       "      <td>1.305685</td>\n",
       "      <td>0.176284</td>\n",
       "      <td>7.406721</td>\n",
       "      <td>1.294604e-13</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]</th>\n",
       "      <td>-0.741023</td>\n",
       "      <td>0.250665</td>\n",
       "      <td>-2.956224</td>\n",
       "      <td>3.114305e-03</td>\n",
       "      <td>**</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]</th>\n",
       "      <td>-0.224766</td>\n",
       "      <td>0.253053</td>\n",
       "      <td>-0.888219</td>\n",
       "      <td>3.744232e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex[T.Male]</th>\n",
       "      <td>-0.752211</td>\n",
       "      <td>0.300749</td>\n",
       "      <td>-2.501121</td>\n",
       "      <td>1.238009e-02</td>\n",
       "      <td>*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]:Sex[T.Male]</th>\n",
       "      <td>0.860879</td>\n",
       "      <td>0.424572</td>\n",
       "      <td>2.027641</td>\n",
       "      <td>4.259694e-02</td>\n",
       "      <td>*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]:Sex[T.Male]</th>\n",
       "      <td>0.994089</td>\n",
       "      <td>0.401105</td>\n",
       "      <td>2.478376</td>\n",
       "      <td>1.319818e-02</td>\n",
       "      <td>*</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                Estimate     Error    Std_Estm             p  \\\n",
       "lambda FIXED                    6.798327  0.038464  176.744239  0.000000e+00   \n",
       "kappa  Intercept                1.305685  0.176284    7.406721  1.294604e-13   \n",
       "       Diet[T.II]              -0.741023  0.250665   -2.956224  3.114305e-03   \n",
       "       Diet[T.III]             -0.224766  0.253053   -0.888219  3.744232e-01   \n",
       "       Sex[T.Male]             -0.752211  0.300749   -2.501121  1.238009e-02   \n",
       "       Diet[T.II]:Sex[T.Male]   0.860879  0.424572    2.027641  4.259694e-02   \n",
       "       Diet[T.III]:Sex[T.Male]  0.994089  0.401105    2.478376  1.319818e-02   \n",
       "\n",
       "                               sig_code  \n",
       "lambda FIXED                        ***  \n",
       "kappa  Intercept                    ***  \n",
       "       Diet[T.II]                    **  \n",
       "       Diet[T.III]                       \n",
       "       Sex[T.Male]                    *  \n",
       "       Diet[T.II]:Sex[T.Male]         *  \n",
       "       Diet[T.III]:Sex[T.Male]        *  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wb2_glm.fit_partial_model('Diet*Sex', [0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · With Weibull $\\kappa$ fixed, it is a from of ALT (Accelerated life testing) or parametric survival regression model\n",
    "\n",
    "## · `R` does it too, let's compare the solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full model\n",
      "764.764241985\n",
      "1 + Diet + Sex + Diet:Sex\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Estimate</th>\n",
       "      <th>Error</th>\n",
       "      <th>Std_Estm</th>\n",
       "      <th>p</th>\n",
       "      <th>sig_code</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">lambda</th>\n",
       "      <th>Intercept</th>\n",
       "      <td>6.751581</td>\n",
       "      <td>0.082636</td>\n",
       "      <td>81.703078</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]</th>\n",
       "      <td>0.077556</td>\n",
       "      <td>0.115595</td>\n",
       "      <td>0.670935</td>\n",
       "      <td>5.022621e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]</th>\n",
       "      <td>0.046200</td>\n",
       "      <td>0.120943</td>\n",
       "      <td>0.382001</td>\n",
       "      <td>7.024608e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex[T.Male]</th>\n",
       "      <td>-0.424428</td>\n",
       "      <td>0.132148</td>\n",
       "      <td>-3.211772</td>\n",
       "      <td>1.319189e-03</td>\n",
       "      <td>**</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]:Sex[T.Male]</th>\n",
       "      <td>0.445991</td>\n",
       "      <td>0.188387</td>\n",
       "      <td>2.367423</td>\n",
       "      <td>1.791244e-02</td>\n",
       "      <td>*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]:Sex[T.Male]</th>\n",
       "      <td>0.472587</td>\n",
       "      <td>0.187643</td>\n",
       "      <td>2.518538</td>\n",
       "      <td>1.178431e-02</td>\n",
       "      <td>*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kappa</th>\n",
       "      <th>FIXED</th>\n",
       "      <td>0.950563</td>\n",
       "      <td>0.083379</td>\n",
       "      <td>11.400464</td>\n",
       "      <td>4.158974e-30</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                Estimate     Error   Std_Estm             p  \\\n",
       "lambda Intercept                6.751581  0.082636  81.703078  0.000000e+00   \n",
       "       Diet[T.II]               0.077556  0.115595   0.670935  5.022621e-01   \n",
       "       Diet[T.III]              0.046200  0.120943   0.382001  7.024608e-01   \n",
       "       Sex[T.Male]             -0.424428  0.132148  -3.211772  1.319189e-03   \n",
       "       Diet[T.II]:Sex[T.Male]   0.445991  0.188387   2.367423  1.791244e-02   \n",
       "       Diet[T.III]:Sex[T.Male]  0.472587  0.187643   2.518538  1.178431e-02   \n",
       "kappa  FIXED                    0.950563  0.083379  11.400464  4.158974e-30   \n",
       "\n",
       "                               sig_code  \n",
       "lambda Intercept                    ***  \n",
       "       Diet[T.II]                        \n",
       "       Diet[T.III]                       \n",
       "       Sex[T.Male]                   **  \n",
       "       Diet[T.II]:Sex[T.Male]         *  \n",
       "       Diet[T.III]:Sex[T.Male]        *  \n",
       "kappa  FIXED                        ***  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wb2_glm.fit_partial_model('Diet*Sex', [1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### *R results:*\n",
    "\n",
    "```R\n",
    "> S1 <- survreg(Surv(Time0) ~ Diet*Sex, dist='weibull', data=df)\n",
    "> summary(S1)\n",
    "```\n",
    "\n",
    "    Call:\n",
    "    survreg(formula = Surv(Time0) ~ Diet * Sex, data = df, dist = \"weibull\")\n",
    "                      Value Std. Error       z        p\n",
    "    (Intercept)      6.7515     0.0827  81.680 0.00e+00\n",
    "    DietII           0.0776     0.1156   0.671 5.02e-01\n",
    "    DietIII          0.0462     0.1211   0.382 7.03e-01\n",
    "    SexMale         -0.4243     0.1323  -3.208 1.34e-03\n",
    "    DietII:SexMale   0.4459     0.1885   2.366 1.80e-02\n",
    "    DietIII:SexMale  0.4725     0.1881   2.512 1.20e-02\n",
    "    Log(scale)      -0.9506     0.0834 -11.393 4.56e-30\n",
    "\n",
    "    Scale= 0.387 \n",
    "\n",
    "    Weibull distribution\n",
    "    Loglik(model)= -764.8   Loglik(intercept only)= -771.7\n",
    "        Chisq= 13.89 on 5 degrees of freedom, p= 0.016 \n",
    "    Number of Newton-Raphson Iterations: 7 \n",
    "    n= 106 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Model both $\\lambda$ and $\\kappa$\n",
    "## · It is an inference problem, biologists like to assign parameters with biological meanings and like to know if any treatment specifically affects one type of biological process *but* not the others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full model\n",
      "756.811302667\n",
      "1 + Diet + Sex + Diet:Sex\n"
     ]
    },
    {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>Estimate</th>\n",
       "      <th>Error</th>\n",
       "      <th>Std_Estm</th>\n",
       "      <th>p</th>\n",
       "      <th>sig_code</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">lambda</th>\n",
       "      <th>Intercept</th>\n",
       "      <td>6.779874</td>\n",
       "      <td>0.060458</td>\n",
       "      <td>112.142038</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]</th>\n",
       "      <td>-0.024163</td>\n",
       "      <td>0.139007</td>\n",
       "      <td>-0.173825</td>\n",
       "      <td>8.620029e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]</th>\n",
       "      <td>0.034694</td>\n",
       "      <td>0.100518</td>\n",
       "      <td>0.345149</td>\n",
       "      <td>7.299825e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex[T.Male]</th>\n",
       "      <td>-0.457921</td>\n",
       "      <td>0.127040</td>\n",
       "      <td>-3.604546</td>\n",
       "      <td>3.126989e-04</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]:Sex[T.Male]</th>\n",
       "      <td>0.513089</td>\n",
       "      <td>0.230077</td>\n",
       "      <td>2.230075</td>\n",
       "      <td>2.574248e-02</td>\n",
       "      <td>*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]:Sex[T.Male]</th>\n",
       "      <td>0.534661</td>\n",
       "      <td>0.162749</td>\n",
       "      <td>3.285178</td>\n",
       "      <td>1.019179e-03</td>\n",
       "      <td>**</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">kappa</th>\n",
       "      <th>Intercept</th>\n",
       "      <td>1.294548</td>\n",
       "      <td>0.177237</td>\n",
       "      <td>7.304042</td>\n",
       "      <td>2.792497e-13</td>\n",
       "      <td>***</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]</th>\n",
       "      <td>-0.743416</td>\n",
       "      <td>0.254887</td>\n",
       "      <td>-2.916650</td>\n",
       "      <td>3.538121e-03</td>\n",
       "      <td>**</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]</th>\n",
       "      <td>-0.201293</td>\n",
       "      <td>0.260995</td>\n",
       "      <td>-0.771254</td>\n",
       "      <td>4.405566e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sex[T.Male]</th>\n",
       "      <td>-0.380653</td>\n",
       "      <td>0.282381</td>\n",
       "      <td>-1.348009</td>\n",
       "      <td>1.776556e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.II]:Sex[T.Male]</th>\n",
       "      <td>0.508561</td>\n",
       "      <td>0.416936</td>\n",
       "      <td>1.219757</td>\n",
       "      <td>2.225571e-01</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Diet[T.III]:Sex[T.Male]</th>\n",
       "      <td>0.761791</td>\n",
       "      <td>0.397472</td>\n",
       "      <td>1.916591</td>\n",
       "      <td>5.528997e-02</td>\n",
       "      <td>+</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                Estimate     Error    Std_Estm             p  \\\n",
       "lambda Intercept                6.779874  0.060458  112.142038  0.000000e+00   \n",
       "       Diet[T.II]              -0.024163  0.139007   -0.173825  8.620029e-01   \n",
       "       Diet[T.III]              0.034694  0.100518    0.345149  7.299825e-01   \n",
       "       Sex[T.Male]             -0.457921  0.127040   -3.604546  3.126989e-04   \n",
       "       Diet[T.II]:Sex[T.Male]   0.513089  0.230077    2.230075  2.574248e-02   \n",
       "       Diet[T.III]:Sex[T.Male]  0.534661  0.162749    3.285178  1.019179e-03   \n",
       "kappa  Intercept                1.294548  0.177237    7.304042  2.792497e-13   \n",
       "       Diet[T.II]              -0.743416  0.254887   -2.916650  3.538121e-03   \n",
       "       Diet[T.III]             -0.201293  0.260995   -0.771254  4.405566e-01   \n",
       "       Sex[T.Male]             -0.380653  0.282381   -1.348009  1.776556e-01   \n",
       "       Diet[T.II]:Sex[T.Male]   0.508561  0.416936    1.219757  2.225571e-01   \n",
       "       Diet[T.III]:Sex[T.Male]  0.761791  0.397472    1.916591  5.528997e-02   \n",
       "\n",
       "                               sig_code  \n",
       "lambda Intercept                    ***  \n",
       "       Diet[T.II]                        \n",
       "       Diet[T.III]                       \n",
       "       Sex[T.Male]                  ***  \n",
       "       Diet[T.II]:Sex[T.Male]         *  \n",
       "       Diet[T.III]:Sex[T.Male]       **  \n",
       "kappa  Intercept                    ***  \n",
       "       Diet[T.II]                    **  \n",
       "       Diet[T.III]                       \n",
       "       Sex[T.Male]                       \n",
       "       Diet[T.II]:Sex[T.Male]            \n",
       "       Diet[T.III]:Sex[T.Male]        +  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wb2_glm.fit_partial_model('Diet*Sex', [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Notes on Implementation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · log-likelihood calculation is costy\n",
    "## · ... and I want to handle interval censored, right censored, mix censored, etc in one shot\n",
    "## · ... and in some cases I want to avoid precision lost\n",
    "## · Let's do it in `FORTRAN`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`mortdist.f90`\n",
    "\n",
    "```FORTRAN\n",
    "            subroutine lg3LLK(sx1, sx2, sy, su, ss, sc, n)\n",
    "            double precision, intent(in) :: sx1(n), sx2(n)\n",
    "            double precision, intent(out) :: sy\n",
    "            double precision :: su, ss, sc\n",
    "            integer n, i\n",
    "\n",
    "            real(kind=10) :: x1(n), x2(n)\n",
    "            real(kind=10) :: y\n",
    "            real(kind=10) :: v1, v2, u, s, c\n",
    "\n",
    "            x1= sx1\n",
    "            x2= sx2\n",
    "            u = su\n",
    "            s = ss\n",
    "            c = sc\n",
    "            y = 0.0_10\n",
    "\n",
    "            do 100 i=1, n\n",
    "                v1 = exp((u-x1(i))/s)\n",
    "                if (x1(i) == x2(i)) then\n",
    "                    y = y+log(v1)-log(1.0_10+v1) &\n",
    "                         -c*x1(i) &\n",
    "                         +log(1.0_10/s/(1.0_10+v1)+c)\n",
    "                else\n",
    "                    v2 = exp((u-x2(i))/s)\n",
    "                    y = y+log(v1/(1.0_10+v1)/exp(c*x1(i)) &\n",
    "                             -v2/(1.0_10+v2)/exp(c*x2(i)))\n",
    "                end if\n",
    "    100     continue\n",
    "            sy = dble(y)\n",
    "            end subroutine lg3LLK\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## · Grid-search (to get initial guess) is costy, calculating derivative is costy\n",
    "## · `scipy.stats` build-in continuous distributions are slow\n",
    "## · Do them in `FORTRAN` as well"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Getting CDF, PDF, SF, and H from one call to avoid calculate the same thing more than once. \n",
    "\n",
    "`mortdist_cpsh.f90` \n",
    "```FORTRAN\n",
    "            subroutine gp2_cpsh(p, x, cdf, pdf, sf, hzd, m, n)\n",
    "            double precision, intent(in) :: p(m), x(n)\n",
    "            double precision, intent(out):: cdf(n), pdf(n), sf(n), hzd(n)\n",
    "            double precision :: a, b\n",
    "            double precision :: ebx(n)\n",
    "            integer :: m, n\n",
    "            a = p(1)\n",
    "            b = p(2)\n",
    "            ebx = exp(b*x)\n",
    "            hzd = a*ebx\n",
    "            sf  = exp(-a/b*(ebx-1.0d0))\n",
    "            pdf = hzd*sf\n",
    "            cdf = 1.0d0-sf\n",
    "            end subroutine gp2_cpsh\n",
    "```"
   ]
  }
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