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   "source": [
    "# Confounding Example: Finding causal effects from observed data\n",
    "\n",
    "Suppose you are given some data with treatment and outcome. Can you determine whether the treatment causes the outcome, or the correlation is purely due to another common cause?"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import dowhy\n",
    "from dowhy import CausalModel\n",
    "import dowhy.datasets, dowhy.plotter\n",
    "\n",
    "# Config dict to set the logging level\n",
    "import logging.config\n",
    "DEFAULT_LOGGING = {\n",
    "    'version': 1,\n",
    "    'disable_existing_loggers': False,\n",
    "    'loggers': {\n",
    "        '': {\n",
    "            'level': 'INFO',\n",
    "        },\n",
    "    }\n",
    "}\n",
    "\n",
    "logging.config.dictConfig(DEFAULT_LOGGING)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's create a mystery dataset for which we need to determine whether there is a causal effect.\n",
    "\n",
    "Creating the dataset. It is generated from either one of two models:\n",
    "* **Model 1**: Treatment does cause outcome. \n",
    "* **Model 2**: Treatment does not cause outcome. All observed correlation is due to a common cause."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "rvar = 1 if np.random.uniform() >0.5 else 0\n",
    "data_dict = dowhy.datasets.xy_dataset(10000, effect=rvar, \n",
    "                                      num_common_causes=1, \n",
    "                                      sd_error=0.2)                                               \n",
    "df = data_dict['df']                                                                                 \n",
    "print(df[[\"Treatment\", \"Outcome\", \"w0\"]].head())\n",
    "                                                                                                                                                                                                         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "dowhy.plotter.plot_treatment_outcome(df[data_dict[\"treatment_name\"]], df[data_dict[\"outcome_name\"]],\n",
    "                             df[data_dict[\"time_val\"]])                                                       "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using DoWhy to resolve the mystery: *Does Treatment cause Outcome?*\n",
    "### STEP 1: Model the problem as a causal graph\n",
    "Initializing the causal model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model= CausalModel(                                                                                                                      \n",
    "        data=df,                                                                                                                         \n",
    "        treatment=data_dict[\"treatment_name\"],                                                                                           \n",
    "        outcome=data_dict[\"outcome_name\"],                                                                                               \n",
    "        common_causes=data_dict[\"common_causes_names\"],                                                                                  \n",
    "        instruments=data_dict[\"instrument_names\"])                                                                                       \n",
    "model.view_model(layout=\"dot\")                                                                                                                                                                                                                                             "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Showing the causal model stored in the local file \"causal_model.png\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image, display\n",
    "display(Image(filename=\"causal_model.png\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP 2: Identify causal effect using properties of the formal causal graph\n",
    "Identify the causal effect using properties of the causal graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "identified_estimand = model.identify_effect(proceed_when_unidentifiable=True)\n",
    "print(identified_estimand)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### STEP 3: Estimate the causal effect\n",
    "\n",
    "Once we have identified the estimand, we can use any statistical method to estimate the causal effect. \n",
    "\n",
    "Let's use Linear Regression for simplicity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "estimate = model.estimate_effect(identified_estimand,\n",
    "        method_name=\"backdoor.linear_regression\")\n",
    "print(\"Causal Estimate is \" + str(estimate.value))\n",
    "\n",
    "# Plot Slope of line between treamtent and outcome =causal effect                                                                                                 \n",
    "dowhy.plotter.plot_causal_effect(estimate, df[data_dict[\"treatment_name\"]], df[data_dict[\"outcome_name\"]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Checking if the estimate is correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"DoWhy estimate is \" + str(estimate.value)) \n",
    "print (\"Actual true causal effect was {0}\".format(rvar))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4: Refuting the estimate\n",
    "\n",
    "We can also refute the estimate to check its robustness to assumptions (*aka* sensitivity analysis, but on steroids). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding a random common cause variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_random=model.refute_estimate(identified_estimand, estimate, method_name=\"random_common_cause\")\n",
    "print(res_random)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Replacing treatment with a random (placebo) variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_placebo=model.refute_estimate(identified_estimand, estimate,\n",
    "        method_name=\"placebo_treatment_refuter\", placebo_type=\"permute\")\n",
    "print(res_placebo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Removing a random subset of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_subset=model.refute_estimate(identified_estimand, estimate,\n",
    "        method_name=\"data_subset_refuter\", subset_fraction=0.9)\n",
    "print(res_subset)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, our causal estimator is robust to simple refutations."
   ]
  }
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