chapter15.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load packages / modules\n",
    "\n",
    "Standard library:\n",
    "- Printf for string formatting\n",
    "- Statistics for mean and std functions\n",
    "- Random for boostrap sampling\n",
    "\n",
    "External:\n",
    "- CSV.jl to load CSV files\n",
    "- DataFrames.jl for tabular data\n",
    "- CategoricalArrays.jl for working with categorical data columns and the `cut` function\n",
    "- GLM.jl for models\n",
    "- StatsBase.jl for histogram binning\n",
    "- CairoMakie.jl for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, Statistics, Random\n",
    "using CSV, DataFrames, CategoricalArrays, GLM, StatsBase, CairoMakie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "nhefs_all = DataFrame(CSV.File(\"nhefs.csv\"));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1629, 64)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(nhefs_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "for s in [:education, :exercise, :active]\n",
    "    nhefs_all[!, s] = categorical(nhefs_all[!, s])\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subset to uncensored rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "nhefs = dropmissing(nhefs_all, :wt82);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1566, 64)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(nhefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 15.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 15.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"Using the same model as in Section 13.2...\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = @formula(\n",
    "    wt82_71 ~ qsmk\n",
    "            + sex\n",
    "            + race\n",
    "            + education\n",
    "            + exercise\n",
    "            + active\n",
    "            + age + age ^ 2\n",
    "            + wt71 + wt71 ^ 2\n",
    "            + smokeintensity + smokeintensity ^ 2\n",
    "            + smokeyrs + smokeyrs ^ 2\n",
    "            + qsmk & smokeintensity\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "wt82_71 ~ 1 + qsmk + sex + race + education + exercise + active + age + :(age ^ 2) + wt71 + :(wt71 ^ 2) + smokeintensity + :(smokeintensity ^ 2) + smokeyrs + :(smokeyrs ^ 2) + qsmk & smokeintensity\n",
       "\n",
       "Coefficients:\n",
       "─────────────────────────────────────────────────────────────────────────────────────────────\n",
       "                              Coef.   Std. Error      t  Pr(>|t|)     Lower 95%     Upper 95%\n",
       "─────────────────────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)            -1.58817      4.31304      -0.37    0.7128  -10.0482       6.87186\n",
       "qsmk                    2.55959      0.809149      3.16    0.0016    0.972449     4.14674\n",
       "sex                    -1.43027      0.468958     -3.05    0.0023   -2.35013     -0.510411\n",
       "race                    0.56011      0.581889      0.96    0.3359   -0.581266     1.70148\n",
       "education: 2            0.790444     0.607         1.30    0.1930   -0.400188     1.98108\n",
       "education: 3            0.556312     0.556102      1.00    0.3173   -0.534481     1.64711\n",
       "education: 4            1.49157      0.83227       1.79    0.0733   -0.140929     3.12407\n",
       "education: 5           -0.194977     0.741369     -0.26    0.7926   -1.64917      1.25922\n",
       "exercise: 1             0.295975     0.535153      0.55    0.5803   -0.753728     1.34568\n",
       "exercise: 2             0.353913     0.558859      0.63    0.5266   -0.742289     1.45011\n",
       "active: 1              -0.947569     0.409934     -2.31    0.0209   -1.75166     -0.143483\n",
       "active: 2              -0.261378     0.684558     -0.38    0.7026   -1.60414      1.08138\n",
       "age                     0.359635     0.163319      2.20    0.0278    0.0392854    0.679985\n",
       "age ^ 2                -0.00610096   0.00172614   -3.53    0.0004   -0.00948677  -0.00271514\n",
       "wt71                    0.0455018    0.0833709     0.55    0.5853   -0.11803      0.209034\n",
       "wt71 ^ 2               -0.000965325  0.000524713  -1.84    0.0660   -0.00199455   6.38996e-5\n",
       "smokeintensity          0.0491365    0.0517254     0.95    0.3423   -0.052323     0.150596\n",
       "smokeintensity ^ 2     -0.000990651  0.000938046  -1.06    0.2911   -0.00283063   0.000849327\n",
       "smokeyrs                0.134369     0.0917122     1.47    0.1431   -0.045525     0.314262\n",
       "smokeyrs ^ 2           -0.00186643   0.00154372   -1.21    0.2268   -0.00489444   0.00116158\n",
       "qsmk & smokeintensity   0.0466628    0.0351448     1.33    0.1845   -0.0222737    0.115599\n",
       "─────────────────────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols = lm(spec, nhefs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           estimate\n",
      "alpha_1       2.56\n",
      "alpha_2       0.05"
     ]
    }
   ],
   "source": [
    "println(\"           estimate\")\n",
    "@printf \"alpha_1     %6.2f\\n\" coef(ols)[2]\n",
    "@printf \"alpha_2     %6.2f\" coef(ols)[end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To obtain the estimates of the effect of quitting smoking, we'll use a `t_test` on the fitted model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Software often provides a convenient way to calculate these, but here we'll use a more manual calculation. We create two arrays of values to represent to two situations we want to compare. We take the difference of arrays, and multiply by the coefficients above to get the estimate and mutiply with the covariance matrix to get the standard error.\n",
    "\n",
    "In the current case, here are two options for the created arrays\n",
    "1. Arrays with one value for each term in the regression. Use zeros for all terms except intercept, and terms involving `qsmk` and `smokeintensity`.\n",
    "2. Use sub-arrays for just the terms of interest and use corresponding values in the estimated coefficient and covariance matrix.\n",
    "\n",
    "We'll use the second approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First extract the values of the coefficents and covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# intercept, qsmk, smokeintensity, smokeintensity^2, qsmk * smokeintensity\n",
    "contrast_indices = [1, 2, 17, 18, 21]\n",
    "sub_coef = coef(ols)[contrast_indices]\n",
    "sub_vcov = vcov(ols)[contrast_indices, contrast_indices];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, for the 5 cigarettes/day example, we'll construct the constrast arrays and calculate the effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# intercept, qsmk, smokeintensity, smokeintensity^2, qsmk * smokeintensity\n",
    "contrast_array1 = [1, 1, 5, 25, 5]  \n",
    "contrast_array2 = [1, 0, 5, 25, 0]\n",
    "contrast_diff = contrast_array1 .- contrast_array2;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "est = sum(sub_coef .* contrast_diff)\n",
    "ste = sqrt(contrast_diff' * sub_vcov * contrast_diff);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "effect of quitting when smoking 5 cigarettes/day\n",
      "\n",
      "              estimate    95% C.I.\n",
      "qsmk effect      2.8     (1.5, 4.1)\n"
     ]
    }
   ],
   "source": [
    "lo = (est - 1.96 * ste)\n",
    "hi = (est + 1.96 * ste)\n",
    "\n",
    "println(\"effect of quitting when smoking 5 cigarettes/day\\n\")\n",
    "println(\"              estimate    95% C.I.\")\n",
    "@printf \"qsmk effect   %6.1f     (%0.1f, %0.1f)\\n\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "Now we'll do the same for 40 cigarettes/day."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# intercept, qsmk, smokeintensity, smokeintensity^2, qsmk * smokeintensity\n",
    "contrast_array1 = [1, 1, 40, 1600, 40]  \n",
    "contrast_array2 = [1, 0, 40, 1600,  0]\n",
    "contrast_diff = contrast_array1 .- contrast_array2;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "est = sum(sub_coef .* contrast_diff)\n",
    "ste = sqrt(contrast_diff' * sub_vcov * contrast_diff);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "effect of quitting when smoking 40 cigarettes/day\n",
      "\n",
      "              estimate    95% C.I.\n",
      "qsmk effect      4.4     (2.8, 6.1)\n"
     ]
    }
   ],
   "source": [
    "lo = (est - 1.96 * ste)\n",
    "hi = (est + 1.96 * ste)\n",
    "\n",
    "println(\"effect of quitting when smoking 40 cigarettes/day\\n\")\n",
    "println(\"              estimate    95% C.I.\")\n",
    "@printf \"qsmk effect   %6.1f     (%0.1f, %0.1f)\\n\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "If we don't use the product term `qsmk & smokeintensity`, we get the following model and effect estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = @formula(\n",
    "    wt82_71 ~ qsmk\n",
    "            + sex\n",
    "            + race\n",
    "            + education\n",
    "            + exercise\n",
    "            + active\n",
    "            + age + age ^ 2\n",
    "            + wt71 + wt71 ^ 2\n",
    "            + smokeintensity + smokeintensity ^ 2\n",
    "            + smokeyrs + smokeyrs ^ 2\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "wt82_71 ~ 1 + qsmk + sex + race + education + exercise + active + age + :(age ^ 2) + wt71 + :(wt71 ^ 2) + smokeintensity + :(smokeintensity ^ 2) + smokeyrs + :(smokeyrs ^ 2)\n",
       "\n",
       "Coefficients:\n",
       "──────────────────────────────────────────────────────────────────────────────────────────\n",
       "                           Coef.   Std. Error      t  Pr(>|t|)     Lower 95%     Upper 95%\n",
       "──────────────────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)         -1.65862      4.31377      -0.38    0.7007  -10.1201       6.80285\n",
       "qsmk                 3.46262      0.438454      7.90    <1e-14    2.60259      4.32265\n",
       "sex                 -1.46505      0.468341     -3.13    0.0018   -2.3837      -0.546399\n",
       "race                 0.586412     0.581695      1.01    0.3136   -0.554583     1.72741\n",
       "education: 2         0.818526     0.606782      1.35    0.1775   -0.371675     2.00873\n",
       "education: 3         0.5715       0.556121      1.03    0.3043   -0.519331     1.66233\n",
       "education: 4         1.50852      0.832378      1.81    0.0701   -0.124191     3.14123\n",
       "education: 5        -0.170826     0.741329     -0.23    0.8178   -1.62494      1.28329\n",
       "exercise: 1          0.320682     0.534962      0.60    0.5490   -0.728645     1.37001\n",
       "exercise: 2          0.362879     0.558956      0.65    0.5163   -0.733513     1.45927\n",
       "active: 1           -0.942957     0.410021     -2.30    0.0216   -1.74721     -0.138702\n",
       "active: 2           -0.258037     0.684722     -0.38    0.7063   -1.60112      1.08504\n",
       "age                  0.362662     0.163343      2.22    0.0265    0.0422649    0.68306\n",
       "age ^ 2             -0.00613773   0.00172634   -3.56    0.0004   -0.00952394  -0.00275151\n",
       "wt71                 0.0373642    0.0831658     0.45    0.6533   -0.125766     0.200494\n",
       "wt71 ^ 2            -0.000915822  0.000523516  -1.75    0.0804   -0.0019427    0.000111054\n",
       "smokeintensity       0.0651533    0.0503115     1.29    0.1955   -0.0335327    0.163839\n",
       "smokeintensity ^ 2  -0.00104679   0.000937324  -1.12    0.2643   -0.00288535   0.000791775\n",
       "smokeyrs             0.133393     0.0917319     1.45    0.1461   -0.0465389    0.313325\n",
       "smokeyrs ^ 2        -0.00182701   0.00154381   -1.18    0.2368   -0.0048552    0.00120118\n",
       "──────────────────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols = lm(spec, nhefs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           estimate   95% C.I.\n",
      "alpha_1       3.5    (2.6, 4.3)"
     ]
    }
   ],
   "source": [
    "est = coef(ols)[2]\n",
    "lo, hi = confint(ols)[2, 1], confint(ols)[2, 2]\n",
    "\n",
    "println(\"           estimate   95% C.I.\")\n",
    "@printf \"alpha_1     %5.1f    (%0.1f, %0.1f)\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 15.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 15.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To estimate propensity score, we fit a logistic model for `qsmk` conditional on $L$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = @formula(\n",
    "    qsmk ~ sex\n",
    "         + race\n",
    "         + age + age ^ 2\n",
    "         + education\n",
    "         + smokeintensity + smokeintensity ^ 2\n",
    "         + smokeyrs + smokeyrs ^ 2\n",
    "         + exercise\n",
    "         + active\n",
    "         + wt71 + wt71 ^ 2\n",
    ")\n",
    "\n",
    "model = glm(spec, nhefs_all, Binomial(), LogitLink());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then propensity is the predicted values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "propensity = predict(model, nhefs_all)\n",
    "nhefs_all.propensity = propensity;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The lowest and highest propensity scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "ranked = sort(nhefs_all[!, [:seqn, :propensity]], :propensity);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>DataFrameRow (2 columns)</p><div class=\"data-frame\"><table class=\"data-frame\"><thead><tr><th></th><th>seqn</th><th>propensity</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Union{Missing, Float64}\">Float64?</th></tr></thead><tbody><tr><th>1</th><td>22941</td><td>0.0529808</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& seqn & propensity\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 22941 & 0.0529808 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1mDataFrameRow\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m seqn  \u001b[0m\u001b[1m propensity \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Int64 \u001b[0m\u001b[90m Float64?   \u001b[0m\n",
       "─────┼───────────────────\n",
       "   1 │ 22941   0.0529808"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ranked[1, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p>DataFrameRow (2 columns)</p><div class=\"data-frame\"><table class=\"data-frame\"><thead><tr><th></th><th>seqn</th><th>propensity</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Union{Missing, Float64}\">Float64?</th></tr></thead><tbody><tr><th>1629</th><td>24949</td><td>0.793205</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& seqn & propensity\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64?\\\\\n",
       "\t\\hline\n",
       "\t1629 & 24949 & 0.793205 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1mDataFrameRow\u001b[0m\n",
       "\u001b[1m  Row \u001b[0m│\u001b[1m seqn  \u001b[0m\u001b[1m propensity \u001b[0m\n",
       "\u001b[1m      \u001b[0m│\u001b[90m Int64 \u001b[0m\u001b[90m Float64?   \u001b[0m\n",
       "──────┼───────────────────\n",
       " 1629 │ 24949    0.793205"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ranked[end, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll attempt to recreate Figure 15.1, pg 45\n",
    "\n",
    "First, we'll split the propensities based on whether the subject quit smoking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "propensity0 = propensity[nhefs_all.qsmk .== 0]\n",
    "propensity1 = propensity[nhefs_all.qsmk .== 1];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the bins are spaced every 0.05 (except at the right end), with the first bin starting at 0.025."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins = collect(0.025:0.05:0.85)\n",
    "top0 = fit(Histogram, propensity0, bins)\n",
    "top1 = fit(Histogram, propensity1, bins);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "xpos = bins[1:end-1] .+ 0.025;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure()"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = Figure(resolution=(600, 450)) \n",
    "ax = Axis(\n",
    "    fig[1, 1],\n",
    "    xlabel=\"Estimated Propensity Score\",\n",
    "    ylabel=\"No. Subjects\",\n",
    "    xticklabelsize=12,\n",
    "    yticklabelsize=12\n",
    ")\n",
    "\n",
    "barplot!(\n",
    "    ax,\n",
    "    xpos,\n",
    "    top0.weights,\n",
    "    color=:white,\n",
    "    strokecolor=:gray40,\n",
    "    strokewidth=1,\n",
    "    bar_labels=:y,\n",
    "    label_size=12,\n",
    "    label_formatter=(y -> string(Int(y)))\n",
    ")\n",
    "\n",
    "barplot!(\n",
    "    ax,\n",
    "    xpos,\n",
    "    (-1 .* top1.weights),\n",
    "    color=:gray40,\n",
    "    strokecolor=:gray40,\n",
    "    strokewidth=1,\n",
    "    bar_labels=:y,\n",
    "    label_size=12,\n",
    "    label_formatter=(y -> string(Int(-y)))\n",
    ")\n",
    "\n",
    "text!(\n",
    "    ax,\n",
    "    [\"A = 0\", \"A = 1\"],\n",
    "    position=[(0.75, 260), (0.75, -80)],\n",
    "    textsize=12,\n",
    ")\n",
    "\n",
    "ylims!(ax, -120, 300)\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  mean propensity\n",
      "    non-quitters: 0.245\n",
      "        quitters: 0.312"
     ]
    }
   ],
   "source": [
    "println(\"                  mean propensity\")\n",
    "@printf \"    non-quitters: %0.3f\\n\" mean(propensity0)\n",
    "@printf \"        quitters: %0.3f\" mean(propensity1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 15.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 15.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"only individual 22005 had an estimated $\\pi(L)$ of 0.6563\", pg 186"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>1 rows × 2 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>seqn</th><th>propensity</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Union{Missing, Float64}\">Float64?</th></tr></thead><tbody><tr><th>1</th><td>22005</td><td>0.656281</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& seqn & propensity\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 22005 & 0.656281 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m1×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m seqn  \u001b[0m\u001b[1m propensity \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Int64 \u001b[0m\u001b[90m Float64?   \u001b[0m\n",
       "─────┼───────────────────\n",
       "   1 │ 22005    0.656281"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nhefs_all[abs.(propensity .- 0.6563) .< 1e-4, [:seqn, :propensity]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the deciles and check their counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "nhefs_all.decile = cut(propensity, 10, labels=[\"$i\" for i in 1:10]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>10 rows × 2 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>decile</th><th>nrow</th></tr><tr><th></th><th title=\"Union{Missing, CategoricalValue{String, UInt32}}\">Cat…?</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>1</td><td>163</td></tr><tr><th>2</th><td>2</td><td>163</td></tr><tr><th>3</th><td>3</td><td>163</td></tr><tr><th>4</th><td>4</td><td>163</td></tr><tr><th>5</th><td>5</td><td>162</td></tr><tr><th>6</th><td>6</td><td>163</td></tr><tr><th>7</th><td>7</td><td>163</td></tr><tr><th>8</th><td>8</td><td>163</td></tr><tr><th>9</th><td>9</td><td>163</td></tr><tr><th>10</th><td>10</td><td>163</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& decile & nrow\\\\\n",
       "\t\\hline\n",
       "\t& Cat…? & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 1 & 163 \\\\\n",
       "\t2 & 2 & 163 \\\\\n",
       "\t3 & 3 & 163 \\\\\n",
       "\t4 & 4 & 163 \\\\\n",
       "\t5 & 5 & 162 \\\\\n",
       "\t6 & 6 & 163 \\\\\n",
       "\t7 & 7 & 163 \\\\\n",
       "\t8 & 8 & 163 \\\\\n",
       "\t9 & 9 & 163 \\\\\n",
       "\t10 & 10 & 163 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×2 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m decile \u001b[0m\u001b[1m nrow  \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Cat…?  \u001b[0m\u001b[90m Int64 \u001b[0m\n",
       "─────┼───────────────\n",
       "   1 │ 1         163\n",
       "   2 │ 2         163\n",
       "   3 │ 3         163\n",
       "   4 │ 4         163\n",
       "   5 │ 5         162\n",
       "   6 │ 6         163\n",
       "   7 │ 7         163\n",
       "   8 │ 8         163\n",
       "   9 │ 9         163\n",
       "  10 │ 10        163"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# count number in each decile\n",
    "combine(groupby(nhefs_all, :decile), nrow)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now create a model with interaction between `qsmk` and deciles of $\\pi(L)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "wt82_71 ~ 1 + qsmk + decile + qsmk & decile\n",
       "\n",
       "Coefficients:\n",
       "─────────────────────────────────────────────────────────────────────────────────\n",
       "                        Coef.  Std. Error      t  Pr(>|t|)  Lower 95%   Upper 95%\n",
       "─────────────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)         3.9952       0.630308   6.34    <1e-09   2.75886    5.23155\n",
       "qsmk               -0.0146537    2.38883   -0.01    0.9951  -4.70034    4.67103\n",
       "decile: 2          -1.09053      0.916364  -1.19    0.2342  -2.88797    0.706921\n",
       "decile: 3          -1.38311      0.918205  -1.51    0.1322  -3.18417    0.417948\n",
       "decile: 4          -0.520526     0.925819  -0.56    0.5740  -2.33652    1.29547\n",
       "decile: 5          -1.88542      0.942367  -2.00    0.0456  -3.73387   -0.0369653\n",
       "decile: 6          -2.15738      0.951381  -2.27    0.0235  -4.02351   -0.291246\n",
       "decile: 7          -2.43516      0.949078  -2.57    0.0104  -4.29677   -0.573541\n",
       "decile: 8          -3.71052      0.973779  -3.81    0.0001  -5.62059   -1.80045\n",
       "decile: 9          -4.89065      1.03372   -4.73    <1e-05  -6.91829   -2.86302\n",
       "decile: 10         -4.49958      1.04925   -4.29    <1e-04  -6.55768   -2.44148\n",
       "qsmk & decile: 2    4.1634       2.89744    1.44    0.1509  -1.51992    9.84672\n",
       "qsmk & decile: 3    6.55913      2.88363    2.27    0.0231   0.902887  12.2154\n",
       "qsmk & decile: 4    2.35695      2.80785    0.84    0.4014  -3.15065    7.86456\n",
       "qsmk & decile: 5    4.13402      2.75459    1.50    0.1336  -1.26911    9.53715\n",
       "qsmk & decile: 6    4.56717      2.75769    1.66    0.0979  -0.842038   9.97638\n",
       "qsmk & decile: 7    4.33055      2.77623    1.56    0.1190  -1.11502    9.77612\n",
       "qsmk & decile: 8    3.58473      2.74355    1.31    0.1915  -1.79673    8.9662\n",
       "qsmk & decile: 9    2.3155       2.70006    0.86    0.3913  -2.98066    7.61166\n",
       "qsmk & decile: 10   2.25488      2.68724    0.84    0.4015  -3.01614    7.52591\n",
       "─────────────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lm(@formula(wt82_71 ~ qsmk * decile), nhefs_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the effect estimates, we'll calculate contrasts, like we did in Program 15.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           estimate    95% C.I.\n",
      "\n",
      "decile  1     -0.0    (-4.7, 4.7)\n",
      "decile  2      4.1    ( 0.9, 7.4)\n",
      "decile  3      6.5    ( 3.4, 9.7)\n",
      "decile  4      2.3    (-0.5, 5.2)\n",
      "decile  5      4.1    ( 1.4, 6.8)\n",
      "decile  6      4.6    ( 1.9, 7.3)\n",
      "decile  7      4.3    ( 1.5, 7.1)\n",
      "decile  8      3.6    ( 0.9, 6.2)\n",
      "decile  9      2.3    (-0.2, 4.8)\n",
      "decile 10      2.2    (-0.2, 4.7)\n",
      "\n",
      "(using normal approximation)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# extract model coefficients and covariance matrix\n",
    "betas = reshape(coef(model), 20, 1)\n",
    "beta_cov = vcov(model)\n",
    "\n",
    "# create contrast arrays\n",
    "c1 = cat([1, 1], zeros(18), dims=1)    # for qsmk=1\n",
    "c2 = cat([1, 0], zeros(18), dims=1)    # for qsmk=0\n",
    "\n",
    "# loop through tests, modify c1 and c2 for each decile,\n",
    "# and print out effect estimate and confidence interval\n",
    "println(\"           estimate    95% C.I.\\n\")\n",
    "for i in 1:10\n",
    "    if i != 1\n",
    "        # set the decile number\n",
    "        c1[i + 1] = 1     # qsmk=1: set decile\n",
    "        c1[i + 10] = 1    # qsmk=1: set qsmk & decile term\n",
    "        c2[i + 1] = 1     # qsmk=0: set decile\n",
    "    end\n",
    "    \n",
    "    cdiff = reshape(c1 .- c2, 20, 1)\n",
    "\n",
    "    est = cdiff' * betas\n",
    "    ste = sqrt(cdiff' * beta_cov * cdiff)\n",
    "    lo = est - 1.96 * ste\n",
    "    hi = est + 1.96 * ste\n",
    "\n",
    "    @printf \"decile %2d    %5.1f    (%4.1f,%4.1f)\\n\" i est[1] lo[1] hi[1]\n",
    "    \n",
    "    if i != 1\n",
    "        # reset to zero\n",
    "        c1[i + 1] = 0\n",
    "        c1[i + 10] = 0\n",
    "        c2[i + 1] = 0\n",
    "    end\n",
    "end\n",
    "\n",
    "println(\"\\n(using normal approximation)\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compare the estimates above to the estimate we get from a model without interaction between `qsmk` and deciles of $\\pi(L)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "wt82_71 ~ 1 + qsmk + decile\n",
       "\n",
       "Coefficients:\n",
       "──────────────────────────────────────────────────────────────────────────\n",
       "                 Coef.  Std. Error      t  Pr(>|t|)  Lower 95%   Upper 95%\n",
       "──────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)   3.75049     0.608914   6.16    <1e-09    2.55611   4.94487\n",
       "qsmk          3.50039     0.457059   7.66    <1e-13    2.60387   4.3969\n",
       "decile: 2    -0.739116    0.861052  -0.86    0.3908   -2.42806   0.94983\n",
       "decile: 3    -0.6182      0.861203  -0.72    0.4730   -2.30744   1.07104\n",
       "decile: 4    -0.520373    0.858385  -0.61    0.5445   -2.20409   1.16334\n",
       "decile: 5    -1.47923     0.860395  -1.72    0.0858   -3.16688   0.208429\n",
       "decile: 6    -1.6312      0.866063  -1.88    0.0598   -3.32997   0.0675734\n",
       "decile: 7    -1.98525     0.868104  -2.29    0.0223   -3.68802  -0.282468\n",
       "decile: 8    -3.44471     0.874909  -3.94    <1e-04   -5.16084  -1.72858\n",
       "decile: 9    -5.15435     0.884806  -5.83    <1e-08   -6.88989  -3.41881\n",
       "decile: 10   -4.84023     0.882758  -5.48    <1e-07   -6.57175  -3.1087\n",
       "──────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lm(@formula(wt82_71 ~ qsmk + decile), nhefs_all)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         estimate   95% C.I.\n",
      "effect      3.5    (2.6, 4.4)"
     ]
    }
   ],
   "source": [
    "est = coef(model)[2]\n",
    "lo, hi = confint(model)[2, 1], confint(model)[2, 2]\n",
    "\n",
    "println(\"         estimate   95% C.I.\")\n",
    "@printf \"effect    %5.1f    (%0.1f, %0.1f)\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 15.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will do \"outcome regression $\\mathrm{E}[Y|A, C=0, p(L)]$ with the estimated propensity score $\\pi(L)$ as a continuous covariate rather than as a set of indicators\" (pg 187)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "nhefs.propensity = propensity[.! ismissing.(nhefs_all.wt82_71)];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Vector{Float64}}, GLM.DensePredChol{Float64, LinearAlgebra.CholeskyPivoted{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "wt82_71 ~ 1 + qsmk + propensity\n",
       "\n",
       "Coefficients:\n",
       "─────────────────────────────────────────────────────────────────────────\n",
       "                 Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%\n",
       "─────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)    5.59449    0.483076  11.58    <1e-29    4.64694    6.54204\n",
       "qsmk           3.5506     0.45726    7.76    <1e-13    2.65369    4.4475\n",
       "propensity   -14.8218     1.75758   -8.43    <1e-16  -18.2693   -11.3744\n",
       "─────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lm(@formula(wt82_71 ~ qsmk + propensity), nhefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the coefficient on `qsmk` we can see the effect estimate is 3.6.\n",
    "\n",
    "We'll use bootstrap to get confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "function outcome_regress_effect(data::DataFrame)\n",
    "    model = lm(@formula(wt82_71 ~ qsmk + propensity), data)\n",
    "    \n",
    "    data_qsmk_1 = copy(data)\n",
    "    data_qsmk_1.qsmk .= 1\n",
    "    \n",
    "    data_qsmk_0 = copy(data)\n",
    "    data_qsmk_0.qsmk .= 0\n",
    "    \n",
    "    mean_qsmk_1 = mean(predict(model, data_qsmk_1))\n",
    "    mean_qsmk_0 = mean(predict(model, data_qsmk_0))\n",
    "    \n",
    "    return mean_qsmk_1 - mean_qsmk_0\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "function nonparametric_bootstrap(data, func; num_samples=1000)\n",
    "    estimate = func(data)\n",
    "    \n",
    "    b_values = zeros(num_samples)\n",
    "    for i in 1:num_samples\n",
    "        rand_indices = rand(1:nrow(data), nrow(data))\n",
    "        sample_data = data[rand_indices, :]\n",
    "        b_values[i] = func(sample_data)\n",
    "    end\n",
    "\n",
    "    std_val = std(b_values)\n",
    "\n",
    "    return estimate, (estimate - 1.96 * std_val, estimate + 1.96 * std_val)\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.550595855838712, (2.59021228973868, 4.510979421938744))"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = nhefs[!, [:wt82_71, :qsmk, :propensity]]\n",
    "\n",
    "info = nonparametric_bootstrap(data, outcome_regress_effect, num_samples=2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         estimate   95% C.I.\n",
      "effect      3.6    (2.6, 4.5)"
     ]
    }
   ],
   "source": [
    "println(\"         estimate   95% C.I.\")\n",
    "@printf \"effect    %5.1f    (%0.1f, %0.1f)\" info[1] info[2][1] info[2][2]"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.6.0",
   "language": "julia",
   "name": "julia-1.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}