PYTHON_Simulating_survival_data.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulated_linear(N=1000, observe_time =10, percentcensored = 0, randomseed = 100):\n",
    "    # N - population size\n",
    "    # observe_time - total observation time, after which all survivors are right-censored \n",
    "    # percentcensored - rate of dropping out early from the observation\n",
    "    # this censoring is applied unformly from 0 to 10, so for those who had the event before dropping out, \n",
    "    # would not be censored in terms of the censoring definition, and actual drop out rate <= percentcencored\n",
    "    #randomseed - random seed for population simulation, set before applying numpy.random functions\n",
    "    \n",
    "    #check that inputs are of the right type\n",
    "    c1 = isinstance(N,int)\n",
    "    c2 = (isinstance(observe_time, float)|isinstance(observe_time, int))\n",
    "    c3 = (isinstance(percentcensored, float)|isinstance(percentcensored, int))\n",
    "    if (isinstance(percentcensored, float)|isinstance(percentcensored, int)): \n",
    "        if((percentcensored>=1)|(percentcensored<0)): \n",
    "            c3= False\n",
    "    c4 = isinstance(randomseed,int)\n",
    "        \n",
    "    if (c1&c2&c3&c4 == False): \n",
    "        c= [c1,c2,c3,c4] \n",
    "        b = [\"N\", \"observe_time\", \"percentcensored\", \"randomseed\"]\n",
    "        print (\"Error with input type:\", [b[i] for i in range(len(c)) if c[i]==False])\n",
    "        return None \n",
    "    \n",
    "    #start simulations \n",
    "    random.seed(randomseed)\n",
    "    \n",
    "    #1_ generating main features:\n",
    "    df = pd.DataFrame({\"age\": np.round(np.random.uniform(-1.73,1.73,N),1),\n",
    "                  \"bmi\": np.round(np.random.normal(0, 1,N),1),  \n",
    "                  \"hyp\": np.random.binomial(1,0.20, N),\n",
    "                  \"gender\": np.random.binomial(1,0.5, N)})\n",
    "    \n",
    "    #2_ generating event times: \n",
    "    df[\"event_time\"] = 0.01 + np.round(np.random.exponential(1/(0.1*np.exp(1.0*df.bmi + \n",
    "                                      df.hyp*0.7 + df.age*0.4)),N),2)\n",
    "    df[\"observe_time\"] = observe_time\n",
    "    \n",
    "    #3_ add censored observations with a shorter observation time (drop-outs)\n",
    "    # the time is randomly drawn uniformly from observe_time/20 to observe_time ('/20' to exclude very short observations)\n",
    "    df[\"early_censored\"]=0 #marker if an observation dropped out early (1) \n",
    "    if (percentcensored > 0):\n",
    "        #assume that nobody drops out in the first 1/20th of the observation time \n",
    "        randcentime = np.random.uniform(observe_time/20, observe_time, int(N*percentcensored))\n",
    "        cens_obs = np.random.choice(df.shape[0], int(N*percentcensored), replace = False)\n",
    "        # censored time is the end of observation in this simulation\n",
    "        df[\"cens_time\"]= np.nan\n",
    "        df.loc[cens_obs, \"cens_time\"] = randcentime\n",
    "        df.loc[~ df.index.isin(cens_obs), \"cens_time\"] = observe_time\n",
    "        \n",
    "        #change early censored to 1 for those dropped out before event and before observation end:\n",
    "        df.loc[((df[\"cens_time\"] < df[\"observe_time\"]) & \n",
    "                (df[\"cens_time\"] < df[\"event_time\"])), \"early_censored\"]=1  \n",
    "    else: \n",
    "        df[\"cens_time\"] = observe_time\n",
    "    \n",
    "    #4_ defining the outcome and time \n",
    "    # time is the first from event, censoring, or end of observation\n",
    "    df[\"time\"] = df[['event_time','cens_time','observe_time']].min(axis=1)\n",
    "    \n",
    "    # event is 1 if event happened before \"time\"\n",
    "    df.loc[df.event_time<= df.time, \"event\"] = 1\n",
    "    df.loc[df.event_time > df.time, \"event\"] = 0\n",
    "    \n",
    "    # delete redundant columns \n",
    "    df = df.drop(columns = [\"cens_time\", \"event_time\"])\n",
    "    \n",
    "    return (df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "\n",
    "def simulated_nonlinear(N=1000, observe_time =10, percentcensored = 0, randomseed = 100):\n",
    "    # N - population size\n",
    "    # observe_time - total observation time, after which all survivors are right-censored \n",
    "    # percentcensored - rate of dropping out early from the observation\n",
    "    # this censoring is applied unformly from 0 to 10, so for those who had the event before dropping out, \n",
    "    # would not be censored in terms of the censoring definition, and actual drop out rate <= percentcencored\n",
    "    #randomseed - random seed for population simulation, set before applying numpy.random functions\n",
    "    \n",
    "    #check that inputs are of the right type\n",
    "    c1 = isinstance(N,int)\n",
    "    c2 = (isinstance(observe_time, float)|isinstance(observe_time, int))\n",
    "    c3 = (isinstance(percentcensored, float)|isinstance(percentcensored, int))\n",
    "    if (isinstance(percentcensored, float)|isinstance(percentcensored, int)): \n",
    "        if((percentcensored>=1)|(percentcensored<0)): \n",
    "            c3= False\n",
    "    c4 = isinstance(randomseed,int)\n",
    "        \n",
    "    if (c1&c2&c3&c4 == False): \n",
    "        c= [c1,c2,c3,c4] \n",
    "        b = [\"N\", \"observe_time\", \"percentcensored\", \"randomseed\"]\n",
    "        print (\"Error with input type:\", [b[i] for i in range(len(c)) if c[i]==False])\n",
    "        return None \n",
    "    \n",
    "    #start simulations \n",
    "    random.seed(randomseed)\n",
    "    \n",
    "    #1_ generating main features:\n",
    "    df = pd.DataFrame({\"age\": np.round(np.random.uniform(-1.73,1.73,N),1),\n",
    "                  \"bmi\": np.round(np.random.normal(0, 1,N),1),  \n",
    "                  \"hyp\": np.random.binomial(1,0.20, N),\n",
    "                  \"gender\": np.random.binomial(1,0.5, N)})\n",
    "    \n",
    "    #2_ generating event times: \n",
    "    #BMI impact is 2 for very low and high levels, 1 for high/ low level, 0 for normal range\n",
    "    bmi_beta = np.array([2 if (np.abs(x)> 1.5) else 1 if (np.abs(x)>1) else 0 for x in df[\"bmi\"]])\n",
    "\n",
    "    #Age impact is 1 for age>=55; linear age impact is also present, but is smaller than in linear simulation\n",
    "    age_beta = np.array([1 if (x >=1) else 0 for x in df[\"age\"]])\n",
    "    \n",
    "    # simulating event time\n",
    "    df[\"event_time\"] = 0.01+ np.round(np.random.exponential(1/(0.08*np.exp(bmi_beta + \n",
    "                                      (df.hyp*0.7)+ df.age*0.2 + age_beta)),N),2)\n",
    "    df[\"observe_time\"] = observe_time\n",
    "    \n",
    "    #3_ add censored observations with a shorter observation time (drop-outs)\n",
    "    # the time is randomly drawn uniformly from observe_time/20 to observe_time ('/20' to exclude very short observations)\n",
    "    df[\"early_censored\"]=0 #marker if an observation dropped out early (1) \n",
    "    if (percentcensored > 0):\n",
    "        #assume that nobody drops out in the first 1/20th of the observation time \n",
    "        randcentime = np.random.uniform(observe_time/20, observe_time, int(N*percentcensored))\n",
    "        cens_obs = np.random.choice(df.shape[0], int(N*percentcensored), replace = False)\n",
    "        # censored time is the end of observation in this simulation\n",
    "        df[\"cens_time\"]= np.nan\n",
    "        df.loc[cens_obs, \"cens_time\"] = randcentime\n",
    "        df.loc[~ df.index.isin(cens_obs), \"cens_time\"] = observe_time\n",
    "        \n",
    "        #change early censored to 1 for those dropped out before event and before observation end:\n",
    "        df.loc[((df[\"cens_time\"] < df[\"observe_time\"]) & \n",
    "                (df[\"cens_time\"] < df[\"event_time\"])), \"early_censored\"]=1  \n",
    "    else: \n",
    "        df[\"cens_time\"] = observe_time\n",
    "    \n",
    "    #4_ defining the outcome and time \n",
    "    # time is the first from event, censoring, or end of observation\n",
    "    df[\"time\"] = df[['event_time','cens_time','observe_time']].min(axis=1)\n",
    "    \n",
    "    # event is 1 if event happened before \"time\"\n",
    "    df.loc[df.event_time<= df.time, \"event\"] = 1\n",
    "    df.loc[df.event_time > df.time, \"event\"] = 0\n",
    "    \n",
    "    # delete redundant columns \n",
    "    df = df.drop(columns = [\"cens_time\", \"event_time\"])\n",
    "    \n",
    "    return (df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulated_crossterms (N = 1000, observe_time = 10, percentcensored = 0, randomseed = 100):\n",
    "    # N - population size\n",
    "    # observe_time - total observation time, after which all survivors are right-censored \n",
    "    # percentcensored - rate of dropping out early from the observation\n",
    "    # this censoring is applied unformly from 0 to 10, so for those who had the event before dropping out, \n",
    "    # would not be censored in terms of the censoring definition, and actual drop out rate <= percentcencored\n",
    "    #randomseed - random seed for population simulation, set before applying numpy.random functions\n",
    "    \n",
    "    #check that inputs are of the right type\n",
    "    c1 = isinstance(N,int)\n",
    "    c2 = (isinstance(observe_time, float)|isinstance(observe_time, int))\n",
    "    c3 = (isinstance(percentcensored, float)|isinstance(percentcensored, int))\n",
    "    if (isinstance(percentcensored, float)|isinstance(percentcensored, int)): \n",
    "        if((percentcensored>=1)|(percentcensored<0)): \n",
    "            c3= False\n",
    "    c4 = isinstance(randomseed,int)\n",
    "    if (c1&c2&c3&c4 == False): \n",
    "        c= [c1,c2,c3,c4] \n",
    "        b = [\"N\", \"observe_time\", \"percentcensored\", \"randomseed\"]\n",
    "        print (\"Error with input type:\", [b[i] for i in range(len(c)) if c[i]==False])\n",
    "        return None \n",
    "    \n",
    "    #start simulations \n",
    "    random.seed(randomseed)\n",
    "    \n",
    "    #1_ generating main features:\n",
    "    df = pd.DataFrame({\"age\": np.round(np.random.uniform(-1.73,1.73,N),1),\n",
    "                  \"bmi\": np.round(np.random.normal(0, 1,N),1),  \n",
    "                  \"hyp\": np.random.binomial(1,0.20, N),\n",
    "                  \"gender\": np.random.binomial(1,0.5, N)})\n",
    "    \n",
    "    #2_ generating event times: \n",
    "    #BMI impact is 2 for very low and high levels, 1 for high/ low level, 0 for normal range\n",
    "    bmi_beta = np.array([2 if (np.abs(x)> 1.5) else 1 if (np.abs(x)>1) else 0 for x in df[\"bmi\"]])  \n",
    "    \n",
    "    # hypertension x age interaction\n",
    "    hyp_age_beta = np.array([2 if ((df.loc[i,\"age\"]>=1) & (df.loc[i,\"hyp\"]==1))\n",
    "                        else 1 if ((df.loc[i,\"age\"]<1)&(df.loc[i,\"hyp\"]==1)) \n",
    "                                else 0 for i in range(df.shape[0])])\n",
    "\n",
    "    # simulating event time\n",
    "    df[\"event_time\"] = 0.01 + np.round(np.random.exponential(1/(0.07*np.exp(bmi_beta + \n",
    "                                      hyp_age_beta + df[\"age\"]*0.2)),N),2)\n",
    "    \n",
    "    df[\"observe_time\"] = observe_time\n",
    "\n",
    "    #3_ add censored observations with a shorter observation time (drop-outs)\n",
    "    # the time is randomly drawn uniformly from observe_time/20 to observe_time ('/20' to exclude very short observations)\n",
    "    df[\"early_censored\"]=0 #marker if an observation dropped out early (1) \n",
    "    if (percentcensored > 0):\n",
    "        #assume that nobody drops out in the first 1/20th of the observation time \n",
    "        randcentime = np.random.uniform(observe_time/20, observe_time, int(N*percentcensored))\n",
    "        cens_obs = np.random.choice(df.shape[0], int(N*percentcensored), replace = False)\n",
    "        # censored time is the end of observation in this simulation\n",
    "        df[\"cens_time\"]= np.nan\n",
    "        df.loc[cens_obs, \"cens_time\"] = randcentime\n",
    "        df.loc[~ df.index.isin(cens_obs), \"cens_time\"] = observe_time\n",
    "        \n",
    "        #change early censored to 1 for those dropped out before event and before observation end:\n",
    "        df.loc[((df[\"cens_time\"] < df[\"observe_time\"]) & \n",
    "                (df[\"cens_time\"] < df[\"event_time\"])), \"early_censored\"]=1  \n",
    "    else: \n",
    "        df[\"cens_time\"] = observe_time\n",
    "    \n",
    "    #4_ defining the outcome and time \n",
    "    # time is the first from event, censoring, or end of observation\n",
    "    df[\"time\"] = df[['event_time','cens_time','observe_time']].min(axis=1)\n",
    "    \n",
    "    # event is 1 if event happened before \"time\"\n",
    "    df.loc[df.event_time<= df.time, \"event\"] = 1\n",
    "    df.loc[df.event_time > df.time, \"event\"] = 0\n",
    "    \n",
    "    # delete redundant columns \n",
    "    df = df.drop(columns = [\"cens_time\", \"event_time\"])\n",
    "    \n",
    "    return(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>bmi</th>\n",
       "      <th>hyp</th>\n",
       "      <th>gender</th>\n",
       "      <th>observe_time</th>\n",
       "      <th>early_censored</th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.015750</td>\n",
       "      <td>-0.004780</td>\n",
       "      <td>0.197900</td>\n",
       "      <td>0.494900</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.492183</td>\n",
       "      <td>0.485600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.996015</td>\n",
       "      <td>0.998602</td>\n",
       "      <td>0.398436</td>\n",
       "      <td>0.499999</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.840634</td>\n",
       "      <td>0.499818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1.700000</td>\n",
       "      <td>-3.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.900000</td>\n",
       "      <td>-0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.690000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.800000</td>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.700000</td>\n",
       "      <td>4.300000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                age           bmi           hyp        gender  observe_time  \\\n",
       "count  10000.000000  10000.000000  10000.000000  10000.000000       10000.0   \n",
       "mean      -0.015750     -0.004780      0.197900      0.494900           5.0   \n",
       "std        0.996015      0.998602      0.398436      0.499999           0.0   \n",
       "min       -1.700000     -3.700000      0.000000      0.000000           5.0   \n",
       "25%       -0.900000     -0.700000      0.000000      0.000000           5.0   \n",
       "50%        0.000000      0.000000      0.000000      0.000000           5.0   \n",
       "75%        0.800000      0.700000      0.000000      1.000000           5.0   \n",
       "max        1.700000      4.300000      1.000000      1.000000           5.0   \n",
       "\n",
       "       early_censored          time         event  \n",
       "count         10000.0  10000.000000  10000.000000  \n",
       "mean              0.0      3.492183      0.485600  \n",
       "std               0.0      1.840634      0.499818  \n",
       "min               0.0      0.010000      0.000000  \n",
       "25%               0.0      1.690000      0.000000  \n",
       "50%               0.0      5.000000      0.000000  \n",
       "75%               0.0      5.000000      1.000000  \n",
       "max               0.0      5.000000      1.000000  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulated_crossterms(10000, observe_time = 5, percentcensored = 0.0, randomseed = 100).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>bmi</th>\n",
       "      <th>hyp</th>\n",
       "      <th>gender</th>\n",
       "      <th>observe_time</th>\n",
       "      <th>early_censored</th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.00000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>10000.00000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.001890</td>\n",
       "      <td>-0.012520</td>\n",
       "      <td>0.19960</td>\n",
       "      <td>0.502000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.13560</td>\n",
       "      <td>3.204280</td>\n",
       "      <td>0.457800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.001368</td>\n",
       "      <td>0.995005</td>\n",
       "      <td>0.39972</td>\n",
       "      <td>0.500021</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.34238</td>\n",
       "      <td>1.837717</td>\n",
       "      <td>0.498241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1.700000</td>\n",
       "      <td>-4.500000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.900000</td>\n",
       "      <td>-0.700000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1.390000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>-0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>3.700154</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.700000</td>\n",
       "      <td>3.600000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                age           bmi          hyp        gender  observe_time  \\\n",
       "count  10000.000000  10000.000000  10000.00000  10000.000000       10000.0   \n",
       "mean      -0.001890     -0.012520      0.19960      0.502000           5.0   \n",
       "std        1.001368      0.995005      0.39972      0.500021           0.0   \n",
       "min       -1.700000     -4.500000      0.00000      0.000000           5.0   \n",
       "25%       -0.900000     -0.700000      0.00000      0.000000           5.0   \n",
       "50%       -0.000000      0.000000      0.00000      1.000000           5.0   \n",
       "75%        0.900000      0.700000      0.00000      1.000000           5.0   \n",
       "max        1.700000      3.600000      1.00000      1.000000           5.0   \n",
       "\n",
       "       early_censored          time         event  \n",
       "count     10000.00000  10000.000000  10000.000000  \n",
       "mean          0.13560      3.204280      0.457800  \n",
       "std           0.34238      1.837717      0.498241  \n",
       "min           0.00000      0.010000      0.000000  \n",
       "25%           0.00000      1.390000      0.000000  \n",
       "50%           0.00000      3.700154      0.000000  \n",
       "75%           0.00000      5.000000      1.000000  \n",
       "max           1.00000      5.000000      1.000000  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulated_crossterms(10000, observe_time = 5, percentcensored = 0.2, randomseed = 100).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>bmi</th>\n",
       "      <th>hyp</th>\n",
       "      <th>gender</th>\n",
       "      <th>observe_time</th>\n",
       "      <th>early_censored</th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "      <td>10000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.001290</td>\n",
       "      <td>-0.026420</td>\n",
       "      <td>0.199100</td>\n",
       "      <td>0.513700</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.340700</td>\n",
       "      <td>2.737741</td>\n",
       "      <td>0.406500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.998401</td>\n",
       "      <td>1.006418</td>\n",
       "      <td>0.399343</td>\n",
       "      <td>0.499837</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.473968</td>\n",
       "      <td>1.786625</td>\n",
       "      <td>0.491205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-1.700000</td>\n",
       "      <td>-3.800000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.900000</td>\n",
       "      <td>-0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.036831</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.573230</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.700000</td>\n",
       "      <td>4.600000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                age           bmi           hyp        gender  observe_time  \\\n",
       "count  10000.000000  10000.000000  10000.000000  10000.000000       10000.0   \n",
       "mean       0.001290     -0.026420      0.199100      0.513700           5.0   \n",
       "std        0.998401      1.006418      0.399343      0.499837           0.0   \n",
       "min       -1.700000     -3.800000      0.000000      0.000000           5.0   \n",
       "25%       -0.900000     -0.700000      0.000000      0.000000           5.0   \n",
       "50%        0.000000     -0.000000      0.000000      1.000000           5.0   \n",
       "75%        0.900000      0.600000      0.000000      1.000000           5.0   \n",
       "max        1.700000      4.600000      1.000000      1.000000           5.0   \n",
       "\n",
       "       early_censored          time         event  \n",
       "count    10000.000000  10000.000000  10000.000000  \n",
       "mean         0.340700      2.737741      0.406500  \n",
       "std          0.473968      1.786625      0.491205  \n",
       "min          0.000000      0.010000      0.000000  \n",
       "25%          0.000000      1.036831      0.000000  \n",
       "50%          0.000000      2.573230      0.000000  \n",
       "75%          1.000000      5.000000      1.000000  \n",
       "max          1.000000      5.000000      1.000000  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simulated_crossterms(10000, observe_time = 5, percentcensored = 0.5, randomseed = 100).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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