{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Why Causal Analysis is Needed\n",
    "In this example we will perform a quick causal analysis to estimate the _causal effect_ of smoking cessation on weight gain over a period of a decade.   \n",
    "We will compare these results to the _observed effect_, arising from simple descriptive statistics.  \n",
    "We'll then dig deeper into the data and see why such discrepancies arise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Data\n",
    "We will use data from an NHEFS observational study. \n",
    "The NHANS (National Health and Nutrition Examionation Survey) Epidemiologic Followup Study (NHEFS) is a national longitudinal study that was jointly initiated by the American National Center for Health Statistics and the American National Institute on Aging. \n",
    "The study was designed to follow up on smokers, some of whom quit smoking, and record their weight (among other measurements) for a period of 11 years: from 1971 to 1982.  \n",
    "More information about the data can be found in the [NHEFS Notebook](/notebooks/nhefs.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\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>race</th>\n",
       "      <th>sex</th>\n",
       "      <th>smokeintensity</th>\n",
       "      <th>smokeyrs</th>\n",
       "      <th>wt71</th>\n",
       "      <th>active_1</th>\n",
       "      <th>active_2</th>\n",
       "      <th>education_2</th>\n",
       "      <th>education_3</th>\n",
       "      <th>education_4</th>\n",
       "      <th>education_5</th>\n",
       "      <th>exercise_1</th>\n",
       "      <th>exercise_2</th>\n",
       "      <th>age^2</th>\n",
       "      <th>wt71^2</th>\n",
       "      <th>smokeintensity^2</th>\n",
       "      <th>smokeyrs^2</th>\n",
       "      <th>qsmk</th>\n",
       "      <th>wt82_71</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>42</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>29</td>\n",
       "      <td>79.04</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1764</td>\n",
       "      <td>6247.3216</td>\n",
       "      <td>900</td>\n",
       "      <td>841</td>\n",
       "      <td>0</td>\n",
       "      <td>-10.093960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>24</td>\n",
       "      <td>58.63</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1296</td>\n",
       "      <td>3437.4769</td>\n",
       "      <td>400</td>\n",
       "      <td>576</td>\n",
       "      <td>0</td>\n",
       "      <td>2.604970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>56</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>20</td>\n",
       "      <td>26</td>\n",
       "      <td>56.81</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3136</td>\n",
       "      <td>3227.3761</td>\n",
       "      <td>400</td>\n",
       "      <td>676</td>\n",
       "      <td>0</td>\n",
       "      <td>9.414486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>68</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>53</td>\n",
       "      <td>59.42</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4624</td>\n",
       "      <td>3530.7364</td>\n",
       "      <td>9</td>\n",
       "      <td>2809</td>\n",
       "      <td>0</td>\n",
       "      <td>4.990117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>40</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>20</td>\n",
       "      <td>19</td>\n",
       "      <td>87.09</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1600</td>\n",
       "      <td>7584.6681</td>\n",
       "      <td>400</td>\n",
       "      <td>361</td>\n",
       "      <td>0</td>\n",
       "      <td>4.989251</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age  race  sex  smokeintensity  smokeyrs   wt71  active_1  active_2  \\\n",
       "0   42     1    0              30        29  79.04         0         0   \n",
       "1   36     0    0              20        24  58.63         0         0   \n",
       "2   56     1    1              20        26  56.81         0         0   \n",
       "3   68     1    0               3        53  59.42         1         0   \n",
       "4   40     0    0              20        19  87.09         1         0   \n",
       "\n",
       "   education_2  education_3  education_4  education_5  exercise_1  exercise_2  \\\n",
       "0            0            0            0            0           0           1   \n",
       "1            1            0            0            0           0           0   \n",
       "2            1            0            0            0           0           1   \n",
       "3            0            0            0            0           0           1   \n",
       "4            1            0            0            0           1           0   \n",
       "\n",
       "   age^2     wt71^2  smokeintensity^2  smokeyrs^2  qsmk    wt82_71  \n",
       "0   1764  6247.3216               900         841     0 -10.093960  \n",
       "1   1296  3437.4769               400         576     0   2.604970  \n",
       "2   3136  3227.3761               400         676     0   9.414486  \n",
       "3   4624  3530.7364                 9        2809     0   4.990117  \n",
       "4   1600  7584.6681               400         361     0   4.989251  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from causallib.datasets import load_nhefs\n",
    "\n",
    "data = load_nhefs()\n",
    "data.X.join(data.a).join(data.y).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is already divided into three components: \n",
    " * `X`: the confounders needed to be controlled for:\n",
    "   * Demographics: such as `age`, `race`, `sex` and `education` level (how many years of schools).\n",
    "   * Smoking habits: how many years an individual has been smoking (`smokeyrs`) and how many cigarettes per day (`smokeintensity`).\n",
    "   * Well-being habits: how much active a participant is daily (`active`) and how much exercise they do in recreation (`exercise`).\n",
    "   * Weight at the start of the study (`wt71`).\n",
    " * `a`: the treatment assignment - whether an individual had quit smoking or not.\n",
    " * `y`: the outcome - how much weight the individual gained during the follow up period of a decade."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating Causal Effect\n",
    "### The Causal Model\n",
    "For this demosntation, we will follow the most simple and well known causal model: _Inverse Probability of Treatment Weighting_ (also known as IPTW or IPW).  \n",
    "This model requires estimating the propensity of each participant to stop smoking based on their individual features.   \n",
    "Modeling this $\\Pr[A=1|X]$ requires a machine learning model.  \n",
    "`causallib` allows users to plug in any arbitrary ML model they want. \n",
    "For the sake of simplicity, we will use a logistic regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from causallib.estimation import IPW\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "learner = LogisticRegression(penalty='none',  # No regularization, new in scikit-learn 0.21.*\n",
    "                             solver='lbfgs',\n",
    "                             max_iter=500)    # Increased to achieve convergence with 'lbfgs' solver\n",
    "ipw = IPW(learner)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying Causal Analysis\n",
    "Once we defined the causal model, we can move on to calculate the potential outcomes and the effect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.518555013088421"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ipw.fit(data.X, data.a)\n",
    "potential_outcomes = ipw.estimate_population_outcome(data.X, data.a, data.y)\n",
    "causal_effect = potential_outcomes[1] - potential_outcomes[0]\n",
    "causal_effect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our causal analysis concluded that, on average, smoking cessation contributed 3.5 kg (7.7 lbs) to the weight gain of people over a period of a decade.  \n",
    "Put differently, had **all** the participants stoped smoking, they would have weighed 3.5 kg more than if **all** participants had continued to smoke."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating Observed Effect\n",
    "Say you are tasked with estimating how much smoking cessation contributes to weight gain but you are not familiar with causal analysis.  \n",
    "On the face of it, it might sound simple. You simply measure the weight-gain in the people who continued smoking, you measure the weight gain in people who quit, and compare the two quantities to see how much the people who quit gained more (or less) than the people who persisted.  \n",
    "Basically you measure $\\mathbb{E}[Y|A=1] - \\mathbb{E}[Y|A=0]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.540581454955886"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observed_outcomes = data.y.groupby(data.a).mean()\n",
    "observed_effect = observed_outcomes[1] - observed_outcomes[0]\n",
    "observed_effect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So if you were to avoid causal analysis, you would estimate that smoking cessation contributes only 2.5 kg (5.5 lbs) to the weight gain, as opposed to the 3.5 kg we calculated above. This is an under-estimation of close to 30 (!) percent.  \n",
    "What can cause such a discrepancy between the descriptive-statistics calculation and the causal-based estimation?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analysis of the difference between causal and observed effect\n",
    "We saw that the observed difference due to smoking cessation is 2.5 kg, while the causal inference analysis suggested it is closer to 3.5.  \n",
    "Causal analysis, in its essence, tries to balance between the treatment and control groups before calculating the difference.  \n",
    "Weight gain can be caused by many factors. \n",
    "For example, males tend to be larger than females on average, and they gain more weight on average. What if most of the people who quit smoking were female? That would bring down the observed effect.\n",
    "Our observed analysis didn't account for the different distributions of such features between the treatment groups, and therefore the observed effect is _confounded_ and most likely \"contaminated\" with _spuriuous correlations_. \n",
    "Only when controlling for such correlations and eliminating their effect, we can claim that the differences in weight gain are truly only due to the status of smoking.\n",
    "\n",
    "What the observed difference indicates is only that people who **chose** to quit smoking were observed to gain 2.5 Kg more than people who **chose** not to quit smoking. \n",
    "\n",
    "To get a clue of how the distribution differ between the treated and the controls, we can calculate the difference in means between groups for each variables. \n",
    "We visualize these differences in a plot called Love plot (named after Dr. Thomas Love)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from causallib.evaluation import PropensityEvaluator\n",
    "\n",
    "evaluator = PropensityEvaluator(ipw)\n",
    "evaluations = evaluator.evaluate_simple(data.X, data.a, data.y, \n",
    "                                        plots=[\"covariate_balance_love\"],\n",
    "                                        metrics_to_evaluate={})\n",
    "\n",
    "fig = evaluations.plots[\"covariate_balance_love\"].get_figure()\n",
    "fig.set_size_inches(6, 6);  # set a more compact size than default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The orange triangles show the differences in averages between for each covariates _before_ applying balancing.  \n",
    "We see that `age` differs the most between the treatment groups, and we suspect it might be causing the discrepancy in results between the descriptive statistics and the causal analysis.\n",
    "\n",
    "To further investigate this, let's look at the weight-gain as a function of the age:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "ax = sns.scatterplot(data.X[\"age\"], data.y, hue=data.a, alpha=0.7)\n",
    "ax.get_figure().set_size_inches(9, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that for older age people the weight-gain decreases to the point that it is more frequently negative than positive at very high age.\n",
    "\n",
    "Let's break down the observed difference by age groups of 5 years each:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0    (40.0, 45.0]\n",
       "1    (35.0, 40.0]\n",
       "2    (55.0, 60.0]\n",
       "3    (65.0, 70.0]\n",
       "4    (35.0, 40.0]\n",
       "Name: age, dtype: category\n",
       "Categories (10, interval[float64]): [(24.999, 30.0] < (30.0, 35.0] < (35.0, 40.0] < (40.0, 45.0] ... (55.0, 60.0] < (60.0, 65.0] < (65.0, 70.0] < (70.0, 75.0]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "step_size = 5\n",
    "age_groups = range(data.X[\"age\"].min(), \n",
    "                   data.X[\"age\"].max() + step_size, \n",
    "                   step_size)\n",
    "print(list(age_groups))\n",
    "age_grouped = pd.cut(data.X[\"age\"], bins=age_groups, include_lowest=True)\n",
    "age_grouped.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we examine how the weight gain differ in each age-group:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "observed_diff_by_age = data.y.groupby([data.a, age_grouped]).mean()\n",
    "observed_diff_by_age = observed_diff_by_age.xs(1) - observed_diff_by_age.xs(0)\n",
    "observed_diff_by_age = observed_diff_by_age.rename(\"observed_effect\")\n",
    "ax = observed_diff_by_age.plot(kind=\"barh\")\n",
    "ax.set_xlabel(\"observed_effect\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see here two interseting trends:\n",
    " * The oldest age group has an observed effect much lower than the others.\n",
    " * The people between ages 40-55 have larger observed difference than the average 2.5 kg.\n",
    "It means when we do a simple average across all the treated and controls, we are mixing people with different observed effects:\n",
    "$$\n",
    "\\mathbb{E}\\left[Y|A=1,\\text{Age}\\gt70\\right] - \\mathbb{E}\\left[Y|A=0,\\text{Age}\\gt70\\right] \\ll \n",
    "\\mathbb{E}\\left[Y|A=1,\\text{Age}\\in[40,55]\\right] - \\mathbb{E}\\left[Y|A=0,\\text{Age}\\in[40,55]\\right]\n",
    "$$ \n",
    "\n",
    "This certainly has to be adjusted for. But how much? the overall effect will depend in the number of people in each age group:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "age_frequency = age_grouped.value_counts(sort=False)\n",
    "age_frequency.rename(\"counts\", inplace=True)\n",
    "ax = age_frequency.plot(kind=\"barh\")\n",
    "ax.set_xlabel(\"counts\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\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>observed_effect</th>\n",
       "      <th>counts</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>(24.999, 30.0]</th>\n",
       "      <td>2.263298</td>\n",
       "      <td>276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30.0, 35.0]</th>\n",
       "      <td>3.100541</td>\n",
       "      <td>214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(35.0, 40.0]</th>\n",
       "      <td>2.433750</td>\n",
       "      <td>177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(40.0, 45.0]</th>\n",
       "      <td>3.801950</td>\n",
       "      <td>197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(45.0, 50.0]</th>\n",
       "      <td>3.603730</td>\n",
       "      <td>234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(50.0, 55.0]</th>\n",
       "      <td>5.238368</td>\n",
       "      <td>186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(55.0, 60.0]</th>\n",
       "      <td>2.871668</td>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(60.0, 65.0]</th>\n",
       "      <td>1.402340</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(65.0, 70.0]</th>\n",
       "      <td>3.602345</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(70.0, 75.0]</th>\n",
       "      <td>-9.985035</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                observed_effect  counts\n",
       "age                                    \n",
       "(24.999, 30.0]         2.263298     276\n",
       "(30.0, 35.0]           3.100541     214\n",
       "(35.0, 40.0]           2.433750     177\n",
       "(40.0, 45.0]           3.801950     197\n",
       "(45.0, 50.0]           3.603730     234\n",
       "(50.0, 55.0]           5.238368     186\n",
       "(55.0, 60.0]           2.871668     132\n",
       "(60.0, 65.0]           1.402340      85\n",
       "(65.0, 70.0]           3.602345      53\n",
       "(70.0, 75.0]          -9.985035      12"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "by_age = observed_diff_by_age.to_frame().join(age_frequency)\n",
    "by_age"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, for the largest groups, ages 40 to 55, the observed effect is larger than the overall average observed effect (2.5kg).  \n",
    "This is somewhat similar to [Simpson's paradox](https://en.wikipedia.org/wiki/Simpson%27s_paradox): \n",
    "How come combining groups with a large effect results in a small effect?  \n",
    "\n",
    "To check this, we'll dig even deeper into the distribution of treated vs. control in each of these age groups:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\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>observed_effect</th>\n",
       "      <th>counts</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>propensity</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</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>(24.999, 30.0]</th>\n",
       "      <td>2.263298</td>\n",
       "      <td>276</td>\n",
       "      <td>228</td>\n",
       "      <td>48</td>\n",
       "      <td>0.173913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(30.0, 35.0]</th>\n",
       "      <td>3.100541</td>\n",
       "      <td>214</td>\n",
       "      <td>160</td>\n",
       "      <td>54</td>\n",
       "      <td>0.252336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(35.0, 40.0]</th>\n",
       "      <td>2.433750</td>\n",
       "      <td>177</td>\n",
       "      <td>136</td>\n",
       "      <td>41</td>\n",
       "      <td>0.231638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(40.0, 45.0]</th>\n",
       "      <td>3.801950</td>\n",
       "      <td>197</td>\n",
       "      <td>146</td>\n",
       "      <td>51</td>\n",
       "      <td>0.258883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(45.0, 50.0]</th>\n",
       "      <td>3.603730</td>\n",
       "      <td>234</td>\n",
       "      <td>181</td>\n",
       "      <td>53</td>\n",
       "      <td>0.226496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(50.0, 55.0]</th>\n",
       "      <td>5.238368</td>\n",
       "      <td>186</td>\n",
       "      <td>133</td>\n",
       "      <td>53</td>\n",
       "      <td>0.284946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(55.0, 60.0]</th>\n",
       "      <td>2.871668</td>\n",
       "      <td>132</td>\n",
       "      <td>81</td>\n",
       "      <td>51</td>\n",
       "      <td>0.386364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(60.0, 65.0]</th>\n",
       "      <td>1.402340</td>\n",
       "      <td>85</td>\n",
       "      <td>55</td>\n",
       "      <td>30</td>\n",
       "      <td>0.352941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(65.0, 70.0]</th>\n",
       "      <td>3.602345</td>\n",
       "      <td>53</td>\n",
       "      <td>38</td>\n",
       "      <td>15</td>\n",
       "      <td>0.283019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(70.0, 75.0]</th>\n",
       "      <td>-9.985035</td>\n",
       "      <td>12</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>0.583333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                observed_effect  counts    0   1  propensity\n",
       "age                                                         \n",
       "(24.999, 30.0]         2.263298     276  228  48    0.173913\n",
       "(30.0, 35.0]           3.100541     214  160  54    0.252336\n",
       "(35.0, 40.0]           2.433750     177  136  41    0.231638\n",
       "(40.0, 45.0]           3.801950     197  146  51    0.258883\n",
       "(45.0, 50.0]           3.603730     234  181  53    0.226496\n",
       "(50.0, 55.0]           5.238368     186  133  53    0.284946\n",
       "(55.0, 60.0]           2.871668     132   81  51    0.386364\n",
       "(60.0, 65.0]           1.402340      85   55  30    0.352941\n",
       "(65.0, 70.0]           3.602345      53   38  15    0.283019\n",
       "(70.0, 75.0]          -9.985035      12    5   7    0.583333"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tx_distribution_by_age = data.a.groupby(age_grouped).value_counts()\n",
    "tx_distribution_by_age = tx_distribution_by_age.unstack(\"qsmk\")\n",
    "tx_distribution_by_age[\"propensity\"] = tx_distribution_by_age[1] / tx_distribution_by_age.sum(axis=\"columns\")\n",
    "\n",
    "by_age = by_age.join(tx_distribution_by_age)\n",
    "by_age"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that each age group has different proportions between the treated and control, \n",
    "meaning, _individuals in each treatment group have different propensity to quit smoking_.\n",
    "\n",
    "We can go on and visualize the observed effect as a function of the propensity of each age group (blue dots), compared to the overall average (green line) and the effect derived from the causal analysis (orange line):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(x=\"propensity\", y=\"observed_effect\", data=by_age.reset_index(),\n",
    "                     size=\"counts\", size_norm=(20, 200))\n",
    "ax.axhline(y=causal_effect, linestyle=\"--\", color=\"C1\", label=\"causal effect\", zorder=0)\n",
    "ax.axhline(y=observed_effect, linestyle=\":\", color=\"C2\", label=\"observed effect\", zorder=0)\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that the ratios of those who quit smoking is smaller (small propensity) in the groups for which the effect is large (the top left of the plot). The groups with small effect contribute disproportionately to the observed effect.\n",
    "The overall observed effect is therefore smaller than what would have been observed if the ratios were the same across all groups. \n",
    "In fact, it would be closer to the 3.5 value that is predicted by the causal analysis.\n",
    "\n",
    "More generally, both the effect size and the prevalence of treatment changes between age groups, and age is therefore a confounder of the effect. \n",
    "Therefore, the overall population effect can only be calculated by weighting the observed group-differences by the size of each age group.  \n",
    "So if we were to average the observed effect and factoring in the size of each age group we would get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1002018883702958"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.average(by_age[\"observed_effect\"], weights=by_age[\"counts\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observed effect of 3.1 is closer to the causal effect of 3.5, than to the simple observed effect of 2.5 we originally got.  \n",
    "What we did was to take the already averaged-within-each-age-group effect and average it once more using the sizes of each group.  \n",
    "This is equivalent to providing each individual with a propensity value based only on their age group, and then applying an inverse-probability-weighting scheme to obtain a slightly-more corrected effect.  \n",
    "Let's do IPW by hand:\n",
    "#### Building an age-based IPW model by hand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.100201888370302"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Give each individual their propensity according their age group:\n",
    "individual_age_weights = age_grouped.map(by_age[\"propensity\"])\n",
    "\n",
    "# Give each individual the pobability to be in their original treatment group,\n",
    "# i.e. the treated get their propensity (=probability to be treated) \n",
    "#      and the control get 1 minus that propensity (=probability to by untreated)\n",
    "individual_age_weights = (data.a * individual_age_weights) + ((1-data.a) * (1-individual_age_weights))\n",
    "\n",
    "# We then inverse these propensity:\n",
    "individual_age_weights = 1 / individual_age_weights\n",
    "\n",
    "# We use the inversed propensities to create a weighted outcome:\n",
    "weighted_outcome = individual_age_weights * data.y\n",
    "\n",
    "# Finaly, we take the weighted average of the weighted outcome in each treatment group:\n",
    "weighted_outcome = weighted_outcome.groupby(data.a).sum() / individual_age_weights.groupby(data.a).sum()\n",
    "\n",
    "# And we can \n",
    "weighted_outcome[1] - weighted_outcome[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed we got the same effect as the weighted-average-of-averages above.\n",
    "\n",
    "However, remember we had only 10 unique propensity values, because we arbitrarily binned the age variable into 10 age groups.  \n",
    "Meanwhile, using a machine learning model allows us to model the propensity using `age` as a continuous variable.  \n",
    "Let's examine what happens when using the age continuously, by building an IPW model that uses `age` as its sole feature when modeling propensity to treat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.098787136071221"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learner = LogisticRegression(penalty='none', solver='lbfgs', max_iter=500)\n",
    "ipw = IPW(learner)\n",
    "ipw.fit(data.X[[\"age\"]], data.a)\n",
    "outcomes = ipw.estimate_population_outcome(data.X[[\"age\"]], data.a, data.y)\n",
    "outcomes[1] - outcomes[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed we got an almost identical effect, correcting only for age in our IPW model.  \n",
    "We can only assume that when correcting for more variables and eliminating more spuriuous correlations in the process, we will get to the causal effect of 3.5 kg."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary\n",
    "1. We saw that there is a discrepancy between the \"effect\" using simple descriptive statistics, and the causal effect resulting from a causal analysis.\n",
    "2. The discrepancy originated from the groups (quitting or not quitting smoking) having different distributions of charachteristics, and thus, are not comparable.\n",
    "3. We discovered that participants' age had the largest distributional shift among the treatment groups and focused on it.\n",
    "4. We saw that the observed effect differed across different age groups, and that different age groups had different number of people, suggesting a simple average mixes different effects indifferently. \n",
    "5. We demonstrated that when accounting for the number of participants in each age group, the \"effect\" shifted from the original observed-effect towards the causal-effect.\n",
    "7. We saw we get similar result when building a causal model that controls only for age (and not for all confounders)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}