{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3971c098-f9ea-47ee-a2b8-9313078552da",
   "metadata": {},
   "source": [
    "# Zivich et al. (2025): An Introduction to Confidence Bands\n",
    "\n",
    "Zivich et al. (2025) provides an introduction to different types of confidence regions, including confidence bands. Briefly, confidence bands are an extension of confidence intervals for vectors (or multiple) parameters. The issue with standard confidence intervals, is that they only claim a single parameter at that rate. When considering coverage for *multiple* parameters, simultaneous confidence interval coverage can be far below the nominal rate. Confidence bands are a set of intervals for a set of parameters. \n",
    "\n",
    "In Zivich et al., the primary focus is on the sup-t method for computing the confidence bands. The sup-t method adjusts the overall critical value such that it provides a set of confidence regions corresponding to the $1-\\alpha$ coverage rate. See the publication for further details on the procedure. \n",
    "\n",
    "Here, we will replicate the analysis shown in the Supplementary Materials of Zivich et al. This example covers the usage of confidence bands with nuisance parameter estimation. Data comes from the AIDS Clinical Trial Group (ACTG) 175, which compared 2-drug versus 1-drug antiretroviral therapy for the prevention of disease progression among people with HIV.\n",
    "\n",
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "03cb7ba9-268b-4d0a-9602-43836adcf914",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Versions\n",
      "NumPy:        2.3.5\n",
      "SciPy:        1.16.3\n",
      "pandas:       2.3.3\n",
      "Matplotlib:   3.10.8\n",
      "Delicatessen: 4.1\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from formulaic import model_matrix\n",
    "\n",
    "import delicatessen as deli\n",
    "from delicatessen import MEstimator\n",
    "from delicatessen.estimating_equations import ee_regression\n",
    "from delicatessen.sandwich import compute_confidence_bands\n",
    "from delicatessen.utilities import inverse_logit, spline, regression_predictions\n",
    "\n",
    "print(\"Versions\")\n",
    "print(\"NumPy:       \", np.__version__)\n",
    "print(\"SciPy:       \", sp.__version__)\n",
    "print(\"pandas:      \", pd.__version__)\n",
    "print(\"Matplotlib:  \", mpl.__version__)\n",
    "print(\"Delicatessen:\", deli.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "728e7624-5a5a-49b6-937f-28fbbfa6cfd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = pd.read_csv(\"data/actg175.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94d23fac-5dc2-4004-bb27-ff00c35d957f",
   "metadata": {},
   "source": [
    "Hereafter, we will estimate each parameter using an inverse probability weighting (IPW) estimator. See the Hernan and Robins applied examples for further details. Briefly, we will estimate the probability of antiretroviral therapy type given baseline covariates. This probability is commonly referred to as the propensity score. Using the estimated propensity score, we will then construct the inverse probability of treatment weights. These weights will then be used to estimate the causal parameters of interest by either using a weighted mean or a marginal structural model.\n",
    "\n",
    "## Case Study 1: Multiple Outcomes\n",
    "\n",
    "For the first case, we are interested in the average causal effect of 2-drug versus 1-drug antiretroviral therapy on CD4 and CD8 T cell counts 20-weeks post-randomization. CD4 and CD8 are immunological markers often used to assess immune function, and CD4 is a particular important immunological marker for assessing disease progression among people with HIV.\n",
    "\n",
    "Here, we are interested in a *pair* of parameters, which we might indicate as a vector with two elements. For statistical inference, we want coverage for both parameters simultaneously. As such, reporting the confidence bands is appropriate here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b0d38ca9-5e36-4081-94ab-daa6c14ba173",
   "metadata": {},
   "outputs": [],
   "source": [
    "g_model = (\"white + male + idu + C(karnof) \"\n",
    "           \"+ age + age_rs1 + age_rs2 + age_rs3\"\n",
    "           \"+ cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3\"\n",
    "           \"+ cd8c_0wk + cd8_rs1 + cd8_rs2 + cd8_rs3\")\n",
    "Wmat = model_matrix(g_model, data=d)\n",
    "a = np.asarray(d['treat'])\n",
    "y1 = np.asarray(d['cd4_20wk'])\n",
    "y2 = np.asarray(d['cd8_20wk'])\n",
    "n = a.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0c6b5fc4-b662-4293-9224-8e7a08aba125",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estfunc(theta):\n",
    "    # Dividing up the parameters \n",
    "    psi_y, psi_z = theta[0], theta[1]\n",
    "    mu_1, mu_0 = theta[2], theta[3]\n",
    "    om_1, om_0 = theta[4], theta[5]\n",
    "    alpha = theta[6:]\n",
    "\n",
    "    # Constructing inverse probability weights\n",
    "    pi_a = inverse_logit(np.dot(Wmat, alpha))\n",
    "    ipw = a / pi_a + (1-a)/(1-pi_a)\n",
    "    ef_ps = ee_regression(theta=alpha, X=Wmat, y=a, model='logistic')\n",
    "\n",
    "    # Estimating functions for causal parameters\n",
    "    ef_psi1 = np.ones(n)*(mu_1 - mu_0) - theta[0]\n",
    "    ef_psi2 = np.ones(n)*(om_1 - om_0) - theta[1]\n",
    "    ef_mu1 = a * ipw * (y1 - mu_1)\n",
    "    ef_mu0 = (1-a) * ipw * (y1 - mu_0)\n",
    "    ef_om1 = a * ipw * (y2 - om_1)\n",
    "    ef_om0 = (1-a)* ipw * (y2 - om_0)\n",
    "\n",
    "    # Returning stacked estimating functions\n",
    "    return np.vstack([ef_psi1, ef_psi2, ef_mu1, ef_mu0, ef_om1, ef_om0, ef_ps])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5f8b8e48-3251-40a9-a879-1b573e4da5e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimating the parameters\n",
    "inits = [0., 0., 300., 300., 300., 300., ] + [0., ]*Wmat.shape[1]\n",
    "estr = MEstimator(estfunc, init=inits)\n",
    "estr.estimate()\n",
    "psi = estr.theta\n",
    "\n",
    "# Confidence intervals\n",
    "ci = estr.confidence_intervals()\n",
    "# Confidence bands\n",
    "cb = estr.confidence_bands(method='supt', subset=[0, 1], seed=10177)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aa3620db-67b9-4ff8-9269-b1dde6ccda82",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% Confidence Intervals\n",
      "[[ 43.29001011  65.81961093]\n",
      " [-29.79373499  30.18198678]] \n",
      "\n",
      "95% Confidence Bands\n",
      "[[ 41.81903109  67.29058994]\n",
      " [-33.70960677  34.09785855]]\n"
     ]
    }
   ],
   "source": [
    "print(\"95% Confidence Intervals\")\n",
    "print(ci[:2, :], '\\n')\n",
    "print(\"95% Confidence Bands\")\n",
    "print(cb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcbfad4a-0356-4bb1-8584-a451c1d5d15f",
   "metadata": {},
   "source": [
    "As shown here, the confidence bands encapsulate the confidence intervals. These wider intervals are the price we pay to have simultaneous coverage of our parameters. However, this drop in precision is important since our interest (and thus our interpretations) are for more than one parameter). This distincton between confidence regions is slightly easier to understand visually. \n",
    "\n",
    "One item to note here is that the confidence bands were only computed for a *subset* of the parameter vector (i.e., the `subset=[0,1]` argument). This is due to the our inference only being on the parameters of interest. When computing the confidence bands here, we can ignore the nuisance parameters (since we are not making inference for them)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a9426129-37a7-4423-9f7f-97b4afe3f16c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# References lines for the null\n",
    "plt.axhline(linestyle=':', color='gray')\n",
    "plt.axvline(linestyle=':', color='gray')\n",
    "\n",
    "# Plotting Implied Confidence Interval Rectangle\n",
    "plt.plot([ci[0, 0], ci[0, 0], ci[0, 1], ci[0, 1], ci[0, 0]],\n",
    "         [ci[1, 0], ci[1, 1], ci[1, 1], ci[1, 0], ci[1, 0]],\n",
    "         '--', color='red', alpha=0.3)\n",
    "# Plotting Confidence Intervals\n",
    "plt.plot([ci[0, 0], ci[0, 1]], [psi[1], psi[1]],\n",
    "         '-', color='red', label='Intervals')\n",
    "plt.plot([psi[0], psi[0]], [ci[1, 0], ci[1, 1]],\n",
    "         '-', color='red')\n",
    "\n",
    "# Plotting Confidence Bands\n",
    "plt.plot([cb[0, 0], cb[0, 0], cb[0, 1], cb[0, 1], cb[0, 0]],\n",
    "         [cb[1, 0], cb[1, 1], cb[1, 1], cb[1, 0], cb[1, 0]],\n",
    "         color='blue', label='sup-t Band')\n",
    "\n",
    "# Estimated Parameters\n",
    "plt.plot([psi[0], ], [psi[1], ], 'D', color='k', markersize=7, label=r'$\\hat{\\theta}$')\n",
    "\n",
    "# Plot Formatting\n",
    "plt.ylim([-70, 70])\n",
    "plt.ylabel(r\"Average Causal Effect - CD8, $\\psi_2$\")\n",
    "plt.xlim([-10, 80])\n",
    "plt.xlabel(r\"Average Causal Effect - CD4, $\\psi_1$\")\n",
    "plt.legend(loc='upper left', framealpha=1.)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0111b385-5581-4a9b-8e91-19873be7048c",
   "metadata": {},
   "source": [
    "Using this visualization, we can imagine the true value of the parameters as a point in this 2 dimensional Euclidean space. Therefore, our confidence regions (rectangles here) claim to include that point 95% of the times as the number of computed regions from new samples goes to infinity. The red rectangle (implied by the confidence intervals) is too small to cover the parameter at that rate. The blue rectangle, or confidence bands, do coverage the true point at that rate. \n",
    "\n",
    "## Case Study 2: Effect Measure Modification by a Binary Covariate\n",
    "\n",
    "For the second example, we are interested in studying modificiation of the effect of antiretroviral therapy on CD4 by gender. Here, we will estimate the following marginal structural model\n",
    "$$ E[Y^a_i | V; \\beta] = \\beta_0 + \\beta_1 a + \\beta_2 V_i + \\beta_3 a V_i $$\n",
    "where $V_i$ is gender. Here, interest is in the full set of $\\beta$ parameters (a vector of 4 numbers). Again, confidence bands are appropriate in this setting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "963e36e1-2d63-42f3-a813-e50b4f03def0",
   "metadata": {},
   "outputs": [],
   "source": [
    "g_model = (\"white + male + idu + C(karnof) \"\n",
    "           \"+ age + age_rs1 + age_rs2 + age_rs3\"\n",
    "           \"+ cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3\"\n",
    "           \"+ cd8c_0wk + cd8_rs1 + cd8_rs2 + cd8_rs3\")\n",
    "Wmat = model_matrix(g_model, data=d)\n",
    "msm = model_matrix(\"treat + male + treat:male\", data=d)\n",
    "a = np.asarray(d['treat'])\n",
    "y = np.asarray(d['cd4_20wk'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9a776542-d6e2-4573-8836-fbbe9d5bf06d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estfunc(theta):\n",
    "    beta = theta[:4]\n",
    "    alpha = theta[4:]\n",
    "\n",
    "    # Estimating function for propensity score\n",
    "    ef_ps = ee_regression(theta=alpha, X=Wmat, y=a, model='logistic')\n",
    "\n",
    "    # Constructing weights\n",
    "    pi_a = inverse_logit(np.dot(Wmat, alpha))\n",
    "    ipw = a / pi_a + (1-a)/(1-pi_a)\n",
    "    \n",
    "    # Estimating function for MSM\n",
    "    ef_msm = ee_regression(theta=beta, X=msm, y=y, model='linear', weights=ipw)\n",
    "\n",
    "    # Returning stacked estimating functions\n",
    "    return np.vstack([ef_msm, ef_ps])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "023925b4-2257-4943-af3a-515c3bf21c2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Estimating the parameters\n",
    "inits = [300., 0., 0., 0.] + [0., ]*Wmat.shape[1]\n",
    "estr = MEstimator(estfunc, init=inits)\n",
    "estr.estimate()\n",
    "psi = estr.theta\n",
    "\n",
    "# Confidence intervals\n",
    "ci = estr.confidence_intervals()\n",
    "# Confidence bands\n",
    "cb = estr.confidence_bands(method='supt', subset=[0, 1, 2, 3], seed=10177)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2d9195c5-3bc7-44e8-80dd-fcfd45a36c55",
   "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>Names</th>\n",
       "      <th>Intercept</th>\n",
       "      <th>treat</th>\n",
       "      <th>male</th>\n",
       "      <th>treat:male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Estimate</th>\n",
       "      <td>355.8</td>\n",
       "      <td>43.4</td>\n",
       "      <td>-27.1</td>\n",
       "      <td>13.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Interval</th>\n",
       "      <td>[327.5 384.2]</td>\n",
       "      <td>[ 8.1 78.7]</td>\n",
       "      <td>[-58.9   4.7]</td>\n",
       "      <td>[-26.5  53.6]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bands</th>\n",
       "      <td>[323.  388.7]</td>\n",
       "      <td>[ 2.4 84.3]</td>\n",
       "      <td>[-63.9   9.8]</td>\n",
       "      <td>[-32.8  59.9]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Names         Intercept        treat           male     treat:male\n",
       "Estimate          355.8         43.4          -27.1           13.5\n",
       "Interval  [327.5 384.2]  [ 8.1 78.7]  [-58.9   4.7]  [-26.5  53.6]\n",
       "Bands     [323.  388.7]  [ 2.4 84.3]  [-63.9   9.8]  [-32.8  59.9]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = pd.DataFrame()\n",
    "r['Names'] = list(msm.columns)\n",
    "r['Estimate'] = np.round(psi[:4], 1)\n",
    "r['Interval'] = [np.array2string(x) for x in np.round(ci[:4], 1)]\n",
    "r['Bands'] = [np.array2string(x) for x in np.round(cb, 1)]\n",
    "r.set_index('Names').T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a17609-ed96-44b7-b4ab-1918a85aaccf",
   "metadata": {},
   "source": [
    "Again, the bands compensate for the fact that we are interested in simultaneous inference. Additionally, we restrict the computation of the confidence bands only to the parameters of interest (the first 4 parameters of `theta`).\n",
    "\n",
    "## Case Study 3: Effect Measure Modification by a Continuous Covariate\n",
    "\n",
    "For the final example, we are interested in studying modification by *baseline* CD4 cell counts. Again, we will use a marginal structural model. However, for a continuous variable we want to model it flexibly in our model. However, flexibly modeling a continuous variable makes it challenging to interpret. Thus, we plot the conditional average causal effect over values of baseline CD4 for interpretative purposes. \n",
    "\n",
    "The first part of the code will estimate the parameters of the specified marginal strucutral model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a701e052-f2b5-4c20-9049-2a9e0d76f69b",
   "metadata": {},
   "outputs": [],
   "source": [
    "g_model = (\"white + male + idu + C(karnof) \"\n",
    "           \"+ age + age_rs1 + age_rs2 + age_rs3\"\n",
    "           \"+ cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3\"\n",
    "           \"+ cd8c_0wk + cd8_rs1 + cd8_rs2 + cd8_rs3\")\n",
    "msm = model_matrix(\"treat + cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3 \"\n",
    "                   \"+ treat:(cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3)\", data=d)\n",
    "a = np.asarray(d['treat'])\n",
    "y = np.asarray(d['cd4_20wk'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "de635e99-a0da-49f2-81b5-55ab64f11209",
   "metadata": {},
   "outputs": [],
   "source": [
    "def estfunc(theta):\n",
    "    beta = theta[:msm_size]\n",
    "    alpha = theta[msm_size:]\n",
    "\n",
    "    # Estimating function for propensity score\n",
    "    ef_ps = ee_regression(theta=alpha, X=Wmat, y=a, model='logistic')\n",
    "\n",
    "    # Constructing weights\n",
    "    pi_a = inverse_logit(np.dot(Wmat, alpha))\n",
    "    ipw = a / pi_a + (1-a)/(1-pi_a)\n",
    "    \n",
    "    # Estimating function for MSM\n",
    "    ef_msm = ee_regression(theta=beta, X=msm, y=y, model='linear', weights=ipw)\n",
    "\n",
    "    # Returning stacked estimating functions\n",
    "    return np.vstack([ef_msm, ef_ps])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b34e83e4-7873-495b-b78a-c15cd9de7363",
   "metadata": {},
   "outputs": [],
   "source": [
    "msm_size = msm.shape[1]\n",
    "inits = [300, ] + [0, ]*(msm_size - 1) + [0., ]*Wmat.shape[1]\n",
    "estr = MEstimator(estfunc, init=inits)\n",
    "estr.estimate()\n",
    "\n",
    "psi = estr.theta[:msm_size]\n",
    "v_psi = estr.variance[:msm_size, :msm_size]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c531de88-b268-4b6f-8c7f-61b41e2cbae7",
   "metadata": {},
   "source": [
    "To create the plot, we will generate some data across a range of equally spaced values between the min and max observed CD4 values. Then I will recreate the splines for this grid (same as those used to fit the model). Using those values, we will compute the predicted 20-week CD4 from the model parameters using the `regression_predictions` function. From there, we will construct the covariance matrix of the predictions. Finally, we can use all those values to compute the confidence bands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "74e344b3-3aed-4a36-b20a-e7c0f8736a7d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating grid of CD4 values for plotting\n",
    "dp = pd.DataFrame()\n",
    "dp['cd4c_0wk'] = np.linspace(np.min(d['cd4c_0wk']), np.max(d['cd4c_0wk']), 500)\n",
    "dp['cd4_0wk'] = dp['cd4c_0wk'] * np.std(d['cd4_0wk']) + np.mean(d['cd4_0wk'])\n",
    "dp[[\"cd4_rs1\", \"cd4_rs2\", \"cd4_rs3\"]] = spline(dp['cd4c_0wk'], knots=np.percentile(d['cd4c_0wk'], [5, 35, 65, 95]),\n",
    "                                               power=2)\n",
    "dp['treat'] = 1\n",
    "Xp = model_matrix(\"treat + cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3 \"\n",
    "                  \"+ treat:(cd4c_0wk + cd4_rs1 + cd4_rs2 + cd4_rs3)\", data=dp)\n",
    "xvals = np.asarray(dp['cd4_0wk'])\n",
    "\n",
    "# Generating predictions from the estimated marginal structural model parameters \n",
    "y_hat = regression_predictions(X=Xp, theta=psi, covariance=v_psi)\n",
    "y_vals = y_hat[:, 0]       # Predicted values from model\n",
    "var = y_hat[:, 1]          # Variance for predictions\n",
    "cov_p = np.dot(Xp, v_psi) @ Xp.T  # Covariance matrix for predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f74db23d-bc25-446e-b234-7df36d6240e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "cb = compute_confidence_bands(y_vals, covariance=cov_p, method='supt', seed=10177)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "93adab2d-a84f-49fb-a86d-4b36fec81f0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.grid(True, zorder=1)\n",
    "plt.fill_between(xvals, cb[:, 0], cb[:, 1], alpha=0.4, color='blue', zorder=2, label='Bands')\n",
    "plt.fill_between(xvals, y_hat[:, 2], y_hat[:, 3], alpha=0.4, color='red', zorder=2, label='Intervals')\n",
    "plt.plot(xvals, y_vals, color='k', zorder=3)\n",
    "plt.ylim([150, 700])\n",
    "plt.xlim([90, 930])\n",
    "plt.xlabel(\"Baseline CD4\")\n",
    "plt.ylabel(\"Conditional Average Causal Effect\")\n",
    "plt.legend(loc='upper left')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
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   "cell_type": "markdown",
   "id": "02e6410a-2c52-4f8b-a458-5768bc2d713f",
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    "Again, we can see the confidence intervals provide much too precise of inference when we are interested in multiple parameters (like a *function*). While confidence bands have not routinely be used, they ought to be and `delicatessen` makes them easy to compute.\n",
    "\n",
    "**NOTE**: A caveat here is that each case study should be interpreted as if it is independent of the others. If we truly were interested in each of the parameters of each case study and wanted to report them in a single paper, then we should adjust our confidence bands for simultaneous inference on all the parameters described here.\n",
    "\n",
    "## References\n",
    "\n",
    "Hammer SM, et al. (1996). \"A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter\". *New England Journal of Medicine*, 335(15), 1081-1090.\n",
    "\n",
    "Zivich PN, Cole SR, Greifer N, Montoya LM, Kosorok MR, & Edwards JK. (2025). \"Confidence Regions for Multiple Outcomes, Effect Modifiers, and Other Multiple Comparisons\". *arXiv:2510.07076*"
   ]
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