chapter12.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load packages / modules\n",
    "\n",
    "Standard library:\n",
    "- Printf for string formatting\n",
    "- Statistics for the mean function\n",
    "\n",
    "External:\n",
    "- CSV to load CSV files\n",
    "- DataFrames.jl for tabular data\n",
    "- CategoricalArrays.jl for working with categorical data columns\n",
    "- GLM.jl for models\n",
    "- CairoMakie.jl for plotting\n",
    "- PyCall.jl for using the Python Statsmodels package\n",
    "- Distributions.jl for PDF values of Normal distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, Statistics\n",
    "using CSV, DataFrames, CategoricalArrays, GLM, CairoMakie, PyCall, Distributions"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "Look at a couple basic details"
   ]
  },
  {
   "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": [
    {
     "data": {
      "text/plain": [
       "64-element Vector{String}:\n",
       " \"seqn\"\n",
       " \"qsmk\"\n",
       " \"death\"\n",
       " \"yrdth\"\n",
       " \"modth\"\n",
       " \"dadth\"\n",
       " \"sbp\"\n",
       " \"dbp\"\n",
       " \"sex\"\n",
       " \"age\"\n",
       " \"race\"\n",
       " \"income\"\n",
       " \"marital\"\n",
       " ⋮\n",
       " \"active\"\n",
       " \"exercise\"\n",
       " \"birthcontrol\"\n",
       " \"pregnancies\"\n",
       " \"cholesterol\"\n",
       " \"hightax82\"\n",
       " \"price71\"\n",
       " \"price82\"\n",
       " \"tax71\"\n",
       " \"tax82\"\n",
       " \"price71_82\"\n",
       " \"tax71_82\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names(nhefs_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set a few columns as categorical, so they're handled correctly by GLM models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "for s in [:education, :exercise, :active, :seqn]\n",
    "    nhefs_all[!, s] = categorical(nhefs_all[!, s])\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 12.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"We restricted the analysis to NHEFS individuals with known sex, age, race, ...\" (pg 149, margin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "restriction_cols = [\n",
    "    :sex, :age, :race, :wt82, :ht, :school, :alcoholpy, :smokeintensity\n",
    "]\n",
    "nhefs = dropmissing(nhefs_all, restriction_cols);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1566, 64)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(nhefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average weight gains in quitters and non-quitters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average weight gain\n",
      "      quitters: 4.5 kg\n",
      "  non-quitters: 2.0 kg"
     ]
    }
   ],
   "source": [
    "ave_gain_quit = mean(nhefs[nhefs.qsmk .== 1, :wt82_71])\n",
    "ave_gain_noquit = mean(nhefs[nhefs.qsmk .== 0, :wt82_71])\n",
    "\n",
    "println(\"Average weight gain\")\n",
    "@printf \"      quitters: %0.1f kg\\n\" ave_gain_quit\n",
    "@printf \"  non-quitters: %0.1f kg\" ave_gain_noquit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a simple linear model to get a confidence interval on weight difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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\n",
       "\n",
       "Coefficients:\n",
       "──────────────────────────────────────────────────────────────────────\n",
       "               Coef.  Std. Error     t  Pr(>|t|)  Lower 95%  Upper 95%\n",
       "──────────────────────────────────────────────────────────────────────\n",
       "(Intercept)  1.9845     0.228829  8.67    <1e-16    1.53565    2.43334\n",
       "qsmk         2.54058    0.45108   5.63    <1e-07    1.6558     3.42537\n",
       "──────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols = lm(@formula(wt82_71 ~ qsmk), nhefs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        estimate   95% C.I.\n",
      "difference     2.54   (1.7, 3.4)"
     ]
    }
   ],
   "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 \"difference   %6.2f   (%0.1f, %0.1f)\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add some columns to help calculate Table 12.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "nhefs.university = (nhefs.education .== 5)\n",
    "nhefs.inactive = (nhefs.active .== 2)\n",
    "nhefs.no_exercise = (nhefs.exercise .== 2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create Table 12.1 in the margin of pg 149."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "transpose_df (generic function with 1 method)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transpose method from\n",
    "# https://github.com/JuliaData/DataFrames.jl/issues/2065#issuecomment-568937464\n",
    "# https://stackoverflow.com/a/59485866\n",
    "\n",
    "function transpose_df(df::AbstractDataFrame)::DataFrame\n",
    "    DataFrame(\n",
    "        [[names(df)]; collect.(eachrow(df))], [:column; Symbol.(axes(df, 1))]\n",
    "    )\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>9 rows × 3 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>Mean baseline characteristics</th><th>A = 1</th><th>A = 0</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>Age, years</td><td>46.2</td><td>42.8</td></tr><tr><th>2</th><td>Men, %</td><td>54.6</td><td>46.6</td></tr><tr><th>3</th><td>White, %</td><td>91.1</td><td>85.4</td></tr><tr><th>4</th><td>University education, %</td><td>15.4</td><td>9.9</td></tr><tr><th>5</th><td>Weight, kg</td><td>72.4</td><td>70.3</td></tr><tr><th>6</th><td>Cigarettes/day</td><td>18.6</td><td>21.2</td></tr><tr><th>7</th><td>Years smoking</td><td>26.0</td><td>24.1</td></tr><tr><th>8</th><td>Little or no exercise, %</td><td>40.7</td><td>37.9</td></tr><tr><th>9</th><td>Inactive daily life, %</td><td>11.2</td><td>8.9</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& Mean baseline characteristics & A = 1 & A = 0\\\\\n",
       "\t\\hline\n",
       "\t& String & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & Age, years & 46.2 & 42.8 \\\\\n",
       "\t2 & Men, \\% & 54.6 & 46.6 \\\\\n",
       "\t3 & White, \\% & 91.1 & 85.4 \\\\\n",
       "\t4 & University education, \\% & 15.4 & 9.9 \\\\\n",
       "\t5 & Weight, kg & 72.4 & 70.3 \\\\\n",
       "\t6 & Cigarettes/day & 18.6 & 21.2 \\\\\n",
       "\t7 & Years smoking & 26.0 & 24.1 \\\\\n",
       "\t8 & Little or no exercise, \\% & 40.7 & 37.9 \\\\\n",
       "\t9 & Inactive daily life, \\% & 11.2 & 8.9 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m9×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m Mean baseline characteristics \u001b[0m\u001b[1m A = 1   \u001b[0m\u001b[1m A = 0   \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m String                        \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼─────────────────────────────────────────────────\n",
       "   1 │ Age, years                        46.2     42.8\n",
       "   2 │ Men, %                            54.6     46.6\n",
       "   3 │ White, %                          91.1     85.4\n",
       "   4 │ University education, %           15.4      9.9\n",
       "   5 │ Weight, kg                        72.4     70.3\n",
       "   6 │ Cigarettes/day                    18.6     21.2\n",
       "   7 │ Years smoking                     26.0     24.1\n",
       "   8 │ Little or no exercise, %          40.7     37.9\n",
       "   9 │ Inactive daily life, %            11.2      8.9"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate values\n",
    "table = combine(\n",
    "    groupby(nhefs, :qsmk),\n",
    "    :age => mean => \"Age, years\",    # i.e., take the mean of :age and call it \"Age, years\"\n",
    "    :sex => (x -> mean(100 * (x .== 0))) => \"Men, %\",\n",
    "    :race => (x -> mean(100 * (x .== 0))) => \"White, %\",\n",
    "    :university => (x -> 100 * mean(x)) => \"University education, %\",\n",
    "    :wt71 => mean => \"Weight, kg\",\n",
    "    :smokeintensity => mean => \"Cigarettes/day\",\n",
    "    :smokeyrs => mean => \"Years smoking\",\n",
    "    :no_exercise => (x -> 100 * mean(x)) => \"Little or no exercise, %\",\n",
    "    :inactive => (x -> 100 * mean(x)) => \"Inactive daily life, %\",\n",
    ")\n",
    "\n",
    "# rearrange, rename, etc\n",
    "table = table[!, Not(:qsmk)]\n",
    "table = round.(table; digits=1)\n",
    "table = transpose_df(table)\n",
    "table = rename(\n",
    "    table[!, [1, 3, 2]],\n",
    "    :1 => \"Mean baseline characteristics\",\n",
    "    :2 => \"A = 1\",\n",
    "    :3 => \"A = 0\",\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 12.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to be creating a lot of IP weights from logistic regressions so a function will help reduce the work. The following function creates the denominators of the IP weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "    logit_ip_f(spec, data, y_name=:qsmk)\n",
    "\n",
    "Create the f(y|X) part of IP weights from logistic regression\n",
    "\n",
    "# Arguments\n",
    "- `spec::FormulaTerm`: model formula\n",
    "- `data::DataFrame`: data to fit model\n",
    "- `y_name::Symbol`: name of outcome variable in `data` and `spec`\n",
    "\n",
    "# Returns\n",
    "- `Array`: IP weights\n",
    "\n",
    "\"\"\"\n",
    "function logit_ip_f(spec, data, y_name=:qsmk)\n",
    "    model = glm(spec, data, Binomial(), LogitLink())\n",
    "\n",
    "    y_vals = data[!, y_name]\n",
    "    pred_y = predict(model, data)\n",
    "    pred_y0 = pred_y[y_vals .== 0]\n",
    "    pred_y1 = pred_y[y_vals .== 1]\n",
    "\n",
    "    weights = zeros(size(data, 1))\n",
    "    weights[y_vals .== 1] = pred_y1\n",
    "    weights[y_vals .== 0] = (1 .- pred_y0)\n",
    "    weights\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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",
    "denoms = logit_ip_f(spec, nhefs)\n",
    "weights = 1 ./ denoms;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IP weights\n",
      "   min:  1.05   expected:  1.05\n",
      "   max: 16.70   expected: 16.70\n",
      "  mean:  2.00   expected:  2.00"
     ]
    }
   ],
   "source": [
    "println(\"IP weights\")\n",
    "@printf \"   min: %5.2f   expected:  1.05\\n\" minimum(weights)\n",
    "@printf \"   max: %5.2f   expected: 16.70\\n\" maximum(weights)\n",
    "@printf \"  mean: %5.2f   expected:  2.00\" mean(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAGQCAIAAAD9V4nPAAAABmJLR0QA/wD/AP+gvaeTAAATfklEQVR4nO3dXWyU953o8WfGM9gG2ww2C+IlXjvOgUWsN6D2pKQSLbAF1BdZqrIX5wgRFR/KXrWhFTrtRS6o2qSKWEXc7EVZLRdZFmlvsoLLQ8wiFekcKh02QFwOCYhxCYfU2IYxzhpswuyFt8glG178jBnj3+dzETHP//E/PzMef/HjsSdTLpcTAIgqW+0BAKCahBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0HLVHiCV/fv3v//++21tbdUeBIAZoVgsrlmzZvfu3Y//Js92CN9///1isSiEz4TR0dFcLpfP56s9CFN3+/btbDY7Z86cag/C1N25cydJktra2moPMl2KxeKTvsmzHcK2tra2tra9e/dWexAebXBwsK6ubt68edUehKm7ceNGLpdrbGys9iBMXalUSpJk/vz51R5kukyhCL5HCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoz/arT1TKR9c//ZdLA+n3+dafLVpeqE+/DwBPjRAmSZJ8NPDpgf/dl36fv1jSJIQAzxaXRgEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQjtyUJ47969np6eHTt2NDU1ZTKZYrH4+XP6+/u3b9/e3Nzc0NCwdevW3t7eSq0CQMU9WQhPnTr15ptvrl+/fs+ePf/pCePj41u2bLl48eLp06f7+vpaWlo2bNhw7dq19KsAMB2eLIQvv/xyT09Pd3d3U1PTf3rC4cOHz5w5c/Dgwba2tpaWlgMHDoyNje3bty/9KgBMhwp/j/Do0aMdHR2rVq2auNnQ0LBp06YjR46kXwWA6VDhEPb29q5YsWLykZUrV16+fHl0dDTlKgBMhwqHcGhoaP78+ZOPFAqFcrl88+bNlKsAMB1yld2uXC4/5Eia1SRJ3nrrrbfeemvykS996UudnZ0ff/zxlAeeMDAwPDY2lnKTJEn6+/s/rvk0/T6z0o0bN2pra+fOnVvtQZi6UqlUU1PT0NBQ7UGYulu3bt3/76w0PDz8Rc9i+SIVDmFzc3OpVJp8pFQqZTKZQqGQcjVJkh/+8Iff//73J5/w9ttv19TULF26NOXYLcP5OXMGUm6SJMnChQuXLl2Qfp9Zqba2tq6ubt68edUehKmrr6/P5XKNjY3VHoSpm/g0+8Dlt9lkCh+fFQ7h6tWrz549O/nIhQsX2tvb6+vrU64mSVJfX3//z/8xfS6XJEk2m/YCbyaTSbnDhGw2m36Y2Sr7B9UehKlzJ84CE3ffLL4Tp/D5vMJ/F11dXZcuXTp//vzEzZGRkePHj3d1daVfBYDpUOEQbtu2rbOzs7u7u1gsDg4O7tq1K5/P3//p+zSrADAdniyEd+/ezWQymUzmRz/6UZIk7e3tmUzmO9/5zv0T8vn8sWPHOjo61q5d29raOjAwcOLEiWXLlqVfBYDp8GTfI8zlcp9/bucDFi9efOjQoelYBYCKm7XfLwWAxyGEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEJoQAhCaEAIQmhACEVuEQvvfee5k/tnDhwskn9Pf3b9++vbm5uaGhYevWrb29vY+/CgAVNy1fEZ47d678BwMDA/ePj4+Pb9my5eLFi6dPn+7r62tpadmwYcO1a9ceZxUApsNTvTR6+PDhM2fOHDx4sK2traWl5cCBA2NjY/v27XucVQCYDk81hEePHu3o6Fi1atXEzYaGhk2bNh05cuRxVgFgOkxLCDdu3JjP55csWbJjx46rV6/eP97b27tixYrJZ65cufLy5cujo6OPXAWA6VDhENbW1r7++usnT54cGhp65513Tp48uW7duuvXr0+sDg0NzZ8/f/L5hUKhXC7fvHnzkasAMB1yld1u/fr169evn/jz5s2b33333RdffHH//v1vvPFGkiTlcvmB8ycfefhqkiRvvPHGL37xi8lHvvrVr7744otXrlxJOfb168NjY2MpN0mS5Pe///2V7Ej6fWalGzdu1NbWzp07t9qDMHWlUqmmpqahoaHagzB1t27dSpJkeHi42oNMl+Hh4aampid6kwqH8AGdnZ3PPffcqVOnJm42NzeXSqXJJ5RKpUwmUygUHrmaJMlPfvKTH//4x5NP+OUvf5nJZJYvX55yzoW3+ufMGUy5SZIkixYtWr58Qfp9ZqX6+vq6urp58+ZVexCmbt68eblcrrGxsdqDMHUTn2YfuPw2m0zh43N6Q/iA1atXnz17dvKRCxcutLe319fXP3I1SZJcLpfL/dHA2Ww2SZJMJpNysPQ73N+nUlvNPvd/tLTagzB17sRZYOLum8V34hTetel91ugHH3xw5cqVl156aeJmV1fXpUuXzp8/P3FzZGTk+PHjXV1dj7MKANOhwiHcuXPnoUOH+vr6RkZGenp6XnnllaVLl+7evXtiddu2bZ2dnd3d3cVicXBwcNeuXfl8fs+ePY+zCgDTocIh/OlPf/rrX/9648aNzc3N3/ve9772ta/95je/WbRo0cRqPp8/duxYR0fH2rVrW1tbBwYGTpw4sWzZssdZBYDpUOHvEb7wwgu/+tWvHnLC4sWLDx06NLVVAKg4rz4BQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBoQghAaEIIQGhCCEBouWoPMKtcG7597tpwyk3yNdk/W9RQkXkAeCQhrKR//L9Xizf+LeUmzXPn/K+/XleReQB4JJdGAQhNCAEITQgBCE0IAQhNCAEITQgBCE0IAQhNCAEITQgBCM1vlplx7n5W/tbf/Z/0+7zyF0v/x1da0+8DMLsJ4YxTTpL+kbH0+9y6czf9JgCznhDOWh9d//SH/3wu/T4//cv/srSpLv0+ADOTEM5apdvj/69/JP0+I76yBGY1T5YBIDQhBCA0IQQgNN8j5BH+5sSl9E9AbS3U/8+XF1dkHoDKEkIe4f8P3/5k+E7KTcrliswCUHkujQIQmhACEJoQAhCaEAIQmhACEJoQAhCaH5/gaSiXk+ufjtfezc69l+pDrrEuNzdfU6mpABIh5OkYGbv73/7pt9lsNptNdRHitfXPb//y8kpNBZDMtEuj/f3927dvb25ubmho2Lp1a29vb7UnAmCWm0FfEY6Pj2/ZsqW+vv706dONjY0/+MEPNmzYcPbs2SVLllR7NGaKno8G/v43v0u/zz9/778umJtPvw8wC8ygEB4+fPjMmTO//e1v29rakiQ5cODAsmXL9u3b9/bbb1d7NGaKu/fuVeT1Ee98du/O3XspN8lmknzNzLqmAkzBDArh0aNHOzo6Vq1aNXGzoaFh06ZNR44cEUIq7r//w+lbd8ZTbvKV1gV/+0pnReYBqmgGhbC3t3fFihWTj6xcufLIkSOjo6P19fXVmgq+yOj4vXfPXUu/z5eXF1oX+AiHqplBIRwaGlq7du3kI4VCoVwu37x5UwiZgYZvj7/53kfp9/n+uj9d8Sfz0u+z7k8XpN+kJpOZk5tt13s/u1ce+yztlfAkSWpz2Wwmk36f2edeOblz97P0+9TmarLV+AueQSEsf+6leh44snfv3p/97GeTj3z9619fu3bt736X9tkT88bu/NXKxpSbJElSm818eVHafWoymc/KdemHqc9n/3xBBd6pOdns2JI5KTfJZzOlwt1cLjdnTqqt6nOVeadqksxnSdq/5NqabPq7O0mS0eEbp24Mpd/n1IdX0m+ycG7uT774aUQjIyM1NTWP8w/TF5rrGufMlKCeHxj910/+Lf0+33qhUKh75n+M9datW0mSlEqlCu557dbYv/TdSr/Py8sa2hfUptykVCrNnz//id5kBoWwubn5gfumVCplMplCoTBxc+/evXv37p18wsTN1tbWlP/r1tbk6y+m3INHGBwcrKurmzevAl/6UC03btzI5XKNjRXI/9PU2ppsrfYMM8fEp9knTcXDtSbJV1ZXcL9UpvCuzZR/siVJsnr16g8//HDykQsXLrS3t7suCsD0mUEh7OrqunTp0vnz5ydujoyMHD9+vKurq7pTATC7zaAQbtu2rbOzs7u7u1gsDg4O7tq1K5/P79mzp9pzATCbzaAQ5vP5Y8eOdXR0rF27trW1dWBg4MSJE8uWLav2XADMZjPoyTJJkixevPjQoUPVngKAQGbQV4QA8PQJIQChCSEAoQkhAKEJIQChCSEAoQkhAKEJIQChzawfqH9SxWKxWCw+8JIUzEyjo6O5XC6f/8KX+GHmu337djabTflaWlTXnTt3kiSprU37akcz1okTJ9ra2p7oTZ7trwjXrFnzpO8w1dLX1zc0VIFX3aOKPv744+vXr1d7ClK5du3atWvXqj3FNGpra1uzZs0TvUnm8y+HC9Ph1Vdf/cY3vvHqq69WexCm7rXXXnv++edfe+21ag/C1E1cQnMhbbJn+ytCAEhJCAEITQgBCE0IAQjt2f7xCZ4h3/3ud59//vlqT0Eq3/zmNxcsWFDtKUhlw4YN1R5hxvGsUQBCc2kUgNCEEIDQhBCA0IQQgNCEkOn13nvvZf7YwoULqz0Uj3Dv3r2enp4dO3Y0NTVlMplisfjACf39/du3b29ubm5oaNi6dWtvb281xuRhHn4nemBOJoQ8DefOnSv/wcDAQLXH4RFOnTr15ptvrl+/fs+ePZ9fHR8f37Jly8WLF0+fPt3X19fS0rJhw4bZ/Xucn0UPvxMneGBOEELgQS+//HJPT093d3dTU9PnVw8fPnzmzJmDBw+2tbW1tLQcOHBgbGxs3759T39OHuLhdyKTCSHwZI4ePdrR0bFq1aqJmw0NDZs2bTpy5Eh1p4IpE0Keho0bN+bz+SVLluzYsePq1avVHodUent7V6xYMfnIypUrL1++PDo6Wq2RmBoPzAlCyPSqra19/fXXT548OTQ09M4775w8eXLdunVe3PWZNjQ0NH/+/MlHCoVCuVy+efNmtUbiSXlgTiaETK/169f//Oc/X7lyZWNj4+bNm999992rV6/u37+/2nMxdZ//vYx+U+MzxwNzMiHkqers7HzuuedOnTpV7UGYuubm5lKpNPlIqVTKZDKFQqFaI5FS8AemEAJPZvXq1R9++OHkIxcuXGhvb6+vr6/WSJCGEPJUffDBB1euXHnppZeqPQhT19XVdenSpfPnz0/cHBkZOX78eFdXV3WnIo3gD0whZHrt3Lnz0KFDfX19IyMjPT09r7zyytKlS3fv3l3tuZi6bdu2dXZ2dnd3F4vFwcHBXbt25fP5h/zUNjOQB+YfKcN0+uijj3bt2tXe3p7P55cvX75z586rV69WeygeYXx8/POfK7797W/fP+GTTz7Ztm1boVCYO3fu5s2bJ/+CEmaIh9+JHpiTeWFeAEJzaRSA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQhBCA0IQQgNCEEIDQ/h1ga0sr04GvQgAAAABJRU5ErkJggg==",
      "text/plain": [
       "FigureAxisPlot()"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist(weights, bins=20, figure=(resolution=(600, 400),))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, the main model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without clustering, weighted least squares (WLS) gives the right coefficients, but the standard error is off."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Normal{Float64}, IdentityLink}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "wt82_71 ~ 1 + qsmk\n",
       "\n",
       "Coefficients:\n",
       "───────────────────────────────────────────────────────────────────────\n",
       "               Coef.  Std. Error      z  Pr(>|z|)  Lower 95%  Upper 95%\n",
       "───────────────────────────────────────────────────────────────────────\n",
       "(Intercept)  1.77998    0.203939   8.73    <1e-17    1.38027    2.17969\n",
       "qsmk         3.44053    0.288623  11.92    <1e-32    2.87484    4.00622\n",
       "───────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wls = glm(@formula(wt82_71 ~ qsmk), nhefs, Normal(), IdentityLink(), wts=weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(The standard errors above also differ slightly from the results in Python using Statsmodels.)\n",
    "\n",
    "It doesn't seem to be possible to use clustering directly in Julia GLM models, and there doesn't seem to be an implementation of GEE in Julia. It's preferable to use native Julia packages when they exist, but when they don't, you can use PyCall.jl or RCall.jl to use packages from Python or R installations.\n",
    "\n",
    "We'll use Statsmodels for any model that uses clustering in covariance estimation. Statsmodels will need to be installed for whichever Python executable that PyCall is using. The [PyCall GitHub page](https://github.com/JuliaPy/PyCall.jl) describes how to install Python packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "sm = pyimport(\"statsmodels.api\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we'll pass X and y as separate values, instead of using \n",
    "# formula syntax\n",
    "y = nhefs.wt82_71\n",
    "X = [ones(nrow(nhefs)) nhefs.qsmk];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the full output for the statsmodels version of the model above (i.e., still without clustering)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>WLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.044</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>WLS</td>       <th>  Adj. R-squared:    </th> <td>   0.043</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   71.14</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 20 Dec 2021</td> <th>  Prob (F-statistic):</th> <td>7.47e-17</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>23:07:41</td>     <th>  Log-Likelihood:    </th> <td> -5613.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1566</td>      <th>  AIC:               </th> <td>1.123e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  1564</td>      <th>  BIC:               </th> <td>1.124e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>    1.7800</td> <td>    0.288</td> <td>    6.175</td> <td> 0.000</td> <td>    1.215</td> <td>    2.345</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.4405</td> <td>    0.408</td> <td>    8.434</td> <td> 0.000</td> <td>    2.640</td> <td>    4.241</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>209.379</td> <th>  Durbin-Watson:     </th> <td>   2.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1901.742</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.281</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.369</td>  <th>  Cond. No.          </th> <td>    2.62</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "PyObject <class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            WLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.044\n",
       "Model:                            WLS   Adj. R-squared:                  0.043\n",
       "Method:                 Least Squares   F-statistic:                     71.14\n",
       "Date:                Mon, 20 Dec 2021   Prob (F-statistic):           7.47e-17\n",
       "Time:                        23:07:41   Log-Likelihood:                -5613.4\n",
       "No. Observations:                1566   AIC:                         1.123e+04\n",
       "Df Residuals:                    1564   BIC:                         1.124e+04\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "(Intercept)     1.7800      0.288      6.175      0.000       1.215       2.345\n",
       "qsmk            3.4405      0.408      8.434      0.000       2.640       4.241\n",
       "==============================================================================\n",
       "Omnibus:                      209.379   Durbin-Watson:                   2.071\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1901.742\n",
       "Skew:                           0.281   Prob(JB):                         0.00\n",
       "Kurtosis:                       8.369   Cond. No.                         2.62\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wls = sm.WLS(y, X, weights=weights)\n",
    "res = wls.fit()\n",
    "sry = res.summary(xname=[\"(Intercept)\", \"qsmk\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "There's a lot of useful information in this output, but in these notebooks we'll focus on the middle portion, the coefficients and confidence intervals. The function below will display just that portion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "function display_coefs(sm_results; xname=nothing)\n",
    "    sm_summary = sm_results.summary(xname=xname)\n",
    "    tables = split(sm_summary.as_html(), \"</table>\\n<table\")\n",
    "    display(\"text/html\", \"<table\" * tables[2] * \"</table>\")\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>    1.7800</td> <td>    0.288</td> <td>    6.175</td> <td> 0.000</td> <td>    1.215</td> <td>    2.345</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.4405</td> <td>    0.408</td> <td>    8.434</td> <td> 0.000</td> <td>    2.640</td> <td>    4.241</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(Intercept)\", \"qsmk\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The version above, which estimates covariance without clustering, has standard errors that are too small.\n",
    "\n",
    "With clustering, GEE and WLS give the right coefficients and better standard errors. Unfortunately, Statsmodel's GEE doesn't currently work through PyCall."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "WLS with clustering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# PyCall seems to have trouble converting a categorical column\n",
    "# into a Python object\n",
    "groups = convert(Array{Int}, nhefs.seqn);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "wls = sm.WLS(y, X, weights=weights)\n",
    "res = wls.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>    1.7800</td> <td>    0.225</td> <td>    7.915</td> <td> 0.000</td> <td>    1.339</td> <td>    2.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.4405</td> <td>    0.526</td> <td>    6.543</td> <td> 0.000</td> <td>    2.410</td> <td>    4.471</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(Intercept)\", \"qsmk\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           estimate   95% C.I.\n",
      "theta_1       3.44   (2.4, 4.5)"
     ]
    }
   ],
   "source": [
    "est = res.params[2]\n",
    "conf_ints = res.conf_int(alpha=0.05)\n",
    "lo, hi = conf_ints[2, 1], conf_ints[2, 2]\n",
    "\n",
    "println(\"           estimate   95% C.I.\")\n",
    "@printf \"theta_1     %6.2f   (%0.1f, %0.1f)\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a simple check that there is no association between `sex` and `qsmk`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>2 rows × 3 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>sex</th><th>qsmk_0</th><th>qsmk_1</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>0</td><td>763.608</td><td>763.623</td></tr><tr><th>2</th><td>1</td><td>801.749</td><td>797.2</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& sex & qsmk\\_0 & qsmk\\_1\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 763.608 & 763.623 \\\\\n",
       "\t2 & 1 & 801.749 & 797.2 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m sex   \u001b[0m\u001b[1m qsmk_0  \u001b[0m\u001b[1m qsmk_1  \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼─────────────────────────\n",
       "   1 │     0  763.608  763.623\n",
       "   2 │     1  801.749  797.2"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qsmk = nhefs.qsmk\n",
    "sex = nhefs.sex\n",
    "DataFrame(\n",
    "    sex=[0, 1],\n",
    "    qsmk_0=[\n",
    "        sum(weights[(qsmk .== 0) .& (sex .== 0)]),\n",
    "        sum(weights[(qsmk .== 0) .& (sex .== 1)])\n",
    "    ],\n",
    "    qsmk_1=[\n",
    "        sum(weights[(qsmk .== 1) .& (sex .== 0)]),\n",
    "        sum(weights[(qsmk .== 1) .& (sex .== 1)])\n",
    "    ],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "subset_indices = (nhefs.race .== 0) .& (nhefs.sex .== 1)\n",
    "subset = nhefs[subset_indices, :];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now a check for positivity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# counts of qsmk x age\n",
    "age_grouped = groupby(subset[!, [:age, :qsmk]], :age)\n",
    "qsmk_1 = combine(age_grouped, :qsmk => sum).qsmk_sum\n",
    "qsmk_0 = combine(age_grouped, nrow => :count).count .- qsmk_1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "age = sort(unique(subset.age));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure()"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = Figure(resolution=(600, 400)) \n",
    "ax = Axis(fig[1, 1], xlabel=\"age\", ylabel=\"count\")\n",
    "\n",
    "line1 = lines!(ax, age, qsmk_0)\n",
    "line2 = lines!(ax, age, qsmk_1)\n",
    "\n",
    "Legend(fig[1, 2], [line1, line2], [\"non-quitters\", \"quitters\"])\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a few combinations of qsmk x age with zero counts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>10 rows × 3 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>age</th><th>qsmk_0</th><th>qsmk_1</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th><th title=\"Int64\">Int64</th></tr></thead><tbody><tr><th>1</th><td>63</td><td>3</td><td>3</td></tr><tr><th>2</th><td>64</td><td>7</td><td>1</td></tr><tr><th>3</th><td>65</td><td>3</td><td>2</td></tr><tr><th>4</th><td>66</td><td>4</td><td>0</td></tr><tr><th>5</th><td>67</td><td>2</td><td>0</td></tr><tr><th>6</th><td>69</td><td>6</td><td>2</td></tr><tr><th>7</th><td>70</td><td>2</td><td>1</td></tr><tr><th>8</th><td>71</td><td>0</td><td>1</td></tr><tr><th>9</th><td>72</td><td>2</td><td>2</td></tr><tr><th>10</th><td>74</td><td>0</td><td>1</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& age & qsmk\\_0 & qsmk\\_1\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Int64 & Int64\\\\\n",
       "\t\\hline\n",
       "\t1 & 63 & 3 & 3 \\\\\n",
       "\t2 & 64 & 7 & 1 \\\\\n",
       "\t3 & 65 & 3 & 2 \\\\\n",
       "\t4 & 66 & 4 & 0 \\\\\n",
       "\t5 & 67 & 2 & 0 \\\\\n",
       "\t6 & 69 & 6 & 2 \\\\\n",
       "\t7 & 70 & 2 & 1 \\\\\n",
       "\t8 & 71 & 0 & 1 \\\\\n",
       "\t9 & 72 & 2 & 2 \\\\\n",
       "\t10 & 74 & 0 & 1 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m age   \u001b[0m\u001b[1m qsmk_0 \u001b[0m\u001b[1m qsmk_1 \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Int64 \u001b[0m\u001b[90m Int64  \u001b[0m\u001b[90m Int64  \u001b[0m\n",
       "─────┼───────────────────────\n",
       "   1 │    63       3       3\n",
       "   2 │    64       7       1\n",
       "   3 │    65       3       2\n",
       "   4 │    66       4       0\n",
       "   5 │    67       2       0\n",
       "   6 │    69       6       2\n",
       "   7 │    70       2       1\n",
       "   8 │    71       0       1\n",
       "   9 │    72       2       2\n",
       "  10 │    74       0       1"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DataFrame(age=age, qsmk_0=qsmk_0, qsmk_1=qsmk_1)[end-9:end, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a discussion on cells with zero counts, see Fine Point 12.2, pg 155."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 12.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"The effect estimate obtained in the pseudo-population created by weights $0.5 \\, / \\, f(A|L)$\n",
    "is equal to that obtained in the pseudo-population created by weights $1 \\, / \\, f(A|L)$.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "wls = sm.WLS(y, X, weights=(0.5 .* weights))\n",
    "res = wls.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>    1.7800</td> <td>    0.225</td> <td>    7.915</td> <td> 0.000</td> <td>    1.339</td> <td>    2.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.4405</td> <td>    0.526</td> <td>    6.543</td> <td> 0.000</td> <td>    2.410</td> <td>    4.471</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(Intercept)\", \"qsmk\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"Second, we need to estimate Pr[A=1] for the numerator of the weights. We can obtain a nonparametric estimate by the ratio 403/1566 or, equivalently, by fitting a saturated logistic model for Pr[A=1] with an intercept and no covariates.\" pg 154"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "qsmk = (nhefs.qsmk .== 1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25734355044699875"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# option 1\n",
    "qsmk_mean = mean(qsmk)\n",
    "qsmk_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{GeneralizedLinearModel{GLM.GlmResp{Vector{Float64}, Binomial{Float64}, LogitLink}, GLM.DensePredChol{Float64, LinearAlgebra.Cholesky{Float64, Matrix{Float64}}}}, Matrix{Float64}}\n",
       "\n",
       "qsmk ~ 1\n",
       "\n",
       "Coefficients:\n",
       "─────────────────────────────────────────────────────────────────────────\n",
       "                Coef.  Std. Error       z  Pr(>|z|)  Lower 95%  Upper 95%\n",
       "─────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)  -1.05982   0.0578034  -18.33    <1e-74   -1.17311  -0.946529\n",
       "─────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# option 2\n",
    "# note this is using GLM.jl not Python Statsmodels\n",
    "lgt = glm(@formula(qsmk ~ 1), nhefs, Binomial(), LogitLink())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgt_pred = predict(lgt);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check for equivalence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "equivalent: true\n"
     ]
    }
   ],
   "source": [
    "equivalent = isapprox(lgt_pred, qsmk_mean .* ones(nrow(nhefs)))\n",
    "println(\"equivalent: \", equivalent)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create stabilized IP weights. Shortcut: modify the IP weights already calculated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_weights = zeros(nrow(nhefs))\n",
    "s_weights[qsmk] = mean(qsmk) * weights[qsmk]    # `qsmk` was defined a few cells ago\n",
    "s_weights[.! qsmk] = mean(1 .- qsmk) * weights[.! qsmk];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stabilized weights\n",
      " min   mean    max\n",
      "------------------\n",
      "0.33   1.00   4.30"
     ]
    }
   ],
   "source": [
    "println(\"Stabilized weights\")\n",
    "println(\" min   mean    max\")\n",
    "println(\"------------------\")\n",
    "@printf \"%04.2f   %04.2f   %04.2f\" minimum(s_weights) mean(s_weights) maximum(s_weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Refit the model from the last section, using the new weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "wls = sm.WLS(y, X, weights=s_weights)\n",
    "res = wls.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>    1.7800</td> <td>    0.225</td> <td>    7.915</td> <td> 0.000</td> <td>    1.339</td> <td>    2.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.4405</td> <td>    0.526</td> <td>    6.543</td> <td> 0.000</td> <td>    2.410</td> <td>    4.471</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(Intercept)\", \"qsmk\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           estimate   95% C.I.\n",
      "theta_1       3.44   (2.4, 4.5)"
     ]
    }
   ],
   "source": [
    "est = res.params[2]\n",
    "conf_ints = res.conf_int(alpha=0.05)\n",
    "lo, hi = conf_ints[2, 1], conf_ints[2, 2]\n",
    "\n",
    "println(\"           estimate   95% C.I.\")\n",
    "@printf \"theta_1     %6.2f   (%0.1f, %0.1f)\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimate is the same as in the previous section"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check again for no association between sex and qsmk in the the pseudo-population"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"data-frame\"><p>2 rows × 3 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>sex</th><th>qsmk_0</th><th>qsmk_1</th></tr><tr><th></th><th title=\"Int64\">Int64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>0</td><td>567.098</td><td>196.513</td></tr><tr><th>2</th><td>1</td><td>595.424</td><td>205.154</td></tr></tbody></table></div>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& sex & qsmk\\_0 & qsmk\\_1\\\\\n",
       "\t\\hline\n",
       "\t& Int64 & Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 0 & 567.098 & 196.513 \\\\\n",
       "\t2 & 1 & 595.424 & 205.154 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m2×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m sex   \u001b[0m\u001b[1m qsmk_0  \u001b[0m\u001b[1m qsmk_1  \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Int64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
       "─────┼─────────────────────────\n",
       "   1 │     0  567.098  196.513\n",
       "   2 │     1  595.424  205.154"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qsmk = nhefs.qsmk\n",
    "sex = nhefs.sex\n",
    "DataFrame(\n",
    "    sex=[0, 1],\n",
    "    qsmk_0=[\n",
    "        sum(s_weights[(qsmk .== 0) .& (sex .== 0)]),\n",
    "        sum(s_weights[(qsmk .== 0) .& (sex .== 1)])\n",
    "    ],\n",
    "    qsmk_1=[\n",
    "        sum(s_weights[(qsmk .== 1) .& (sex .== 0)]),\n",
    "        sum(s_weights[(qsmk .== 1) .& (sex .== 1)])\n",
    "    ],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 12.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subset the data to subjects that smoked 25 or fewer cigarettes per day at baseline. In this case, we can either obtain the subset from the original dataset, or we can obtain it from the reduced dataset that we've been using. I'll get it from the reduced subset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1162, 64)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from original dataset\n",
    "\n",
    "good_rows = (nhefs_all.smokeintensity .<= 25) .& .! ismissing.(nhefs_all.wt82)\n",
    "intensity25 = nhefs_all[good_rows, :]\n",
    "size(intensity25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1162, 67)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# from reduced dataset\n",
    "\n",
    "intensity25 = nhefs[nhefs.smokeintensity .<= 25, :]\n",
    "size(intensity25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the stabilized IP weights $SW^A = f(A) \\, / \\, f(A|L)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"we assumed that the density f(A|L) was normal (Gaussian) with mean $\\mu = E[A|L]$ and variance $\\sigma^2$.  We then used a linear regression model to estimate the mean $E[A|L]$ and variance of residuals $\\sigma^2$ for all combinations of values of L.\" pg 156\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = @formula(\n",
    "    smkintensity82_71 ~ 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",
    "ols = lm(spec, intensity25);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = intensity25.smkintensity82_71;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_pred = predict(ols, intensity25);   # i.e., E[A|L]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominator is the distribution, $N(\\mu, \\sigma)$, evaluated at each point of $y = A$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "mse_resid = sum((A - A_pred) .^ 2) / dof_residual(ols)  # variance\n",
    "fAL = [\n",
    "    pdf(Normal(a_pred, sqrt(mse_resid)), a)\n",
    "    for (a, a_pred) in zip(A, A_pred)\n",
    "];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"We also assumed that the density f(A) in the numerator was normal.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "FigureAxisPlot()"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist(A, bins=30, figure=(resolution=(600, 400),))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.057659208261618, 10.467830908151857)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(A), std(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_dist = Normal(mean(A), std(A))\n",
    "fA = [pdf(a_dist, a) for a in A];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then the stabilized IP weights are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "sw = fA ./ fAL;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stabilized weights\n",
      " min   mean    max\n",
      "------------------\n",
      "0.19   1.00   5.10"
     ]
    }
   ],
   "source": [
    "println(\"Stabilized weights\")\n",
    "println(\" min   mean    max\")\n",
    "println(\"------------------\")\n",
    "@printf \"%04.2f   %04.2f   %04.2f\" minimum(sw) mean(sw) maximum(sw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now fit the marginal structural model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = intensity25.wt82_71\n",
    "X = [ones(nrow(intensity25)) A A.^2]   # A = intensity25.smkintensity82_71\n",
    "groups = convert(Array{Int}, intensity25.seqn);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "wls = sm.WLS(y, X, weights=sw)\n",
    "res = wls.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>    2.0045</td> <td>    0.296</td> <td>    6.783</td> <td> 0.000</td> <td>    1.425</td> <td>    2.584</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>A</th>           <td>   -0.1090</td> <td>    0.032</td> <td>   -3.452</td> <td> 0.001</td> <td>   -0.171</td> <td>   -0.047</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>A^2</th>         <td>    0.0027</td> <td>    0.002</td> <td>    1.113</td> <td> 0.266</td> <td>   -0.002</td> <td>    0.007</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(Intercept)\", \"A\", \"A^2\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the estimate and confidence interval for \"no change\", you can read off the values in the `constant` row above (because `A` and `A^2` will be zero).\n",
    "\n",
    "To calculate the estimate and confidence interval for when smoking increases by 20 cigarettes / day we'll use the `get_prediction` method on the Python model object.\n",
    "\n",
    "There are three versions below that just modify the presentation by using extra knowledge of the underlying Python objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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>mean</th>\n",
       "      <th>mean_se</th>\n",
       "      <th>mean_ci_lower</th>\n",
       "      <th>mean_ci_upper</th>\n",
       "      <th>obs_ci_lower</th>\n",
       "      <th>obs_ci_upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.004525</td>\n",
       "      <td>0.295502</td>\n",
       "      <td>1.425351</td>\n",
       "      <td>2.583698</td>\n",
       "      <td>-13.243053</td>\n",
       "      <td>17.252103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.902723</td>\n",
       "      <td>1.310533</td>\n",
       "      <td>-1.665873</td>\n",
       "      <td>3.471320</td>\n",
       "      <td>-14.548842</td>\n",
       "      <td>16.354289</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "PyObject        mean   mean_se  mean_ci_lower  mean_ci_upper  obs_ci_lower  obs_ci_upper\n",
       "0  2.004525  0.295502       1.425351       2.583698    -13.243053     17.252103\n",
       "1  0.902723  1.310533      -1.665873       3.471320    -14.548842     16.354289"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# version 1: basic\n",
    "\n",
    "pred_inputs = [\n",
    "    1  0  0  ;    # no change in smoking intensity\n",
    "    1 20 20^2     # plus 20 cigarettes / day\n",
    "]\n",
    "pred = res.get_prediction(exog=pred_inputs)\n",
    "summary = pred.summary_frame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "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>mean</th>\n",
       "      <th>mean_ci_lower</th>\n",
       "      <th>mean_ci_upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>2.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.9</td>\n",
       "      <td>-1.7</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "PyObject    mean  mean_ci_lower  mean_ci_upper\n",
       "0   2.0            1.4            2.6\n",
       "1   0.9           -1.7            3.5"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# version 2: simplify\n",
    "\n",
    "summary = summary.round(1)\n",
    "summary = summary.__getitem__([\"mean\", \"mean_ci_lower\", \"mean_ci_upper\"])\n",
    "# Using __getitem__ is not the standard way to do this in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "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>estimate</th>\n",
       "      <th>CI lower</th>\n",
       "      <th>CI upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>no change</th>\n",
       "      <td>2.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>2.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>+20 per day</th>\n",
       "      <td>0.9</td>\n",
       "      <td>-1.7</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "PyObject              estimate  CI lower  CI upper\n",
       "no change         2.0       1.4       2.6\n",
       "+20 per day       0.9      -1.7       3.5"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# version 3: relabel the rows and columns\n",
    "\n",
    "summary.index = [\"no change\", \"+20 per day\"]\n",
    "summary.columns = [\"estimate\", \"CI lower\", \"CI upper\"]\n",
    "summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"if interested in the causal effect of quitting smoking A (1: yes, 0: no) on the risk of death D (1: yes, 0: no) by 1982, one could consider a _marginal structural logistic model_\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = nhefs.death\n",
    "X = [ones(nrow(nhefs)) nhefs.qsmk]\n",
    "groups = convert(Array{Int}, nhefs.seqn);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgt = sm.GLM(y, X, freq_weights=s_weights, family=sm.families.Binomial())\n",
    "res = lgt.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(Intercept)</th> <td>   -1.4905</td> <td>    0.079</td> <td>  -18.869</td> <td> 0.000</td> <td>   -1.645</td> <td>   -1.336</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    0.0301</td> <td>    0.157</td> <td>    0.191</td> <td> 0.848</td> <td>   -0.278</td> <td>    0.339</td>\n",
       "</tr>\n",
       "</table></table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(Intercept)\", \"qsmk\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Odd ratio is $\\exp(\\hat{\\theta}_1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           estimate   95% C.I.\n",
      "odds ratio    1.03   (0.8, 1.4)"
     ]
    }
   ],
   "source": [
    "est = exp(res.params[2])\n",
    "conf_ints = res.conf_int(alpha=0.05)\n",
    "lo = exp(conf_ints[2, 1])\n",
    "hi = exp(conf_ints[2, 2])\n",
    "\n",
    "println(\"           estimate   95% C.I.\")\n",
    "@printf \"odds ratio  %6.2f   (%0.1f, %0.1f)\" est lo hi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 12.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the numerator of the IP weights. Reuse the basic `weights` for the denominator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = @formula(qsmk ~ sex)\n",
    "numer = logit_ip_f(spec, nhefs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "sw_AV = numer .* weights;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stabilized weights\n",
      " min   mean    max\n",
      "------------------\n",
      "0.29   1.00   3.80"
     ]
    }
   ],
   "source": [
    "println(\"Stabilized weights\")\n",
    "println(\" min   mean    max\")\n",
    "println(\"------------------\")\n",
    "@printf \"%04.2f   %04.2f   %04.2f\" minimum(sw_AV) mean(sw_AV) maximum(sw_AV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = nhefs.wt82_71\n",
    "X = [ones(nrow(nhefs)) nhefs.qsmk nhefs.sex nhefs.qsmk .* nhefs.sex]\n",
    "groups = convert(Array{Int}, nhefs.seqn);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "wls = sm.WLS(y, X, weights=sw_AV)\n",
    "res = wls.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(intercept)</th> <td>    1.7844</td> <td>    0.310</td> <td>    5.752</td> <td> 0.000</td> <td>    1.176</td> <td>    2.393</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.5220</td> <td>    0.658</td> <td>    5.353</td> <td> 0.000</td> <td>    2.232</td> <td>    4.811</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sex</th>         <td>   -0.0087</td> <td>    0.449</td> <td>   -0.019</td> <td> 0.985</td> <td>   -0.890</td> <td>    0.872</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk & sex</th>  <td>   -0.1595</td> <td>    1.047</td> <td>   -0.152</td> <td> 0.879</td> <td>   -2.212</td> <td>    1.893</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(intercept)\", \"qsmk\", \"sex\", \"qsmk & sex\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last line gives the estimate $\\hat{\\theta}_2$ = -0.2 and confidence interval (-2.2, 1.9)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Section 12.6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Program 12.7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going back to the original dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1629, 64)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size(nhefs_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll add a feature to track censored individuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "nhefs_all.censored = ismissing.(nhefs_all.wt82);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the IP weights for treatment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "spec = @formula(\n",
    "    qsmk ~ 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",
    ")\n",
    "ip_denom = logit_ip_f(spec, nhefs_all);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "ip_numer = zeros(nrow(nhefs_all))\n",
    "ip_numer[nhefs_all.qsmk .== 0] .= mean(nhefs_all.qsmk .== 0)\n",
    "ip_numer[nhefs_all.qsmk .== 1] .= mean(nhefs_all.qsmk .== 1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "sw_A = ip_numer ./ ip_denom;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stabilized weights\n",
      " min   mean    max\n",
      "------------------\n",
      "0.33   1.00   4.21"
     ]
    }
   ],
   "source": [
    "println(\"Stabilized weights\")\n",
    "println(\" min   mean    max\")\n",
    "println(\"------------------\")\n",
    "@printf \"%04.2f   %04.2f   %04.2f\" minimum(sw_A) mean(sw_A) maximum(sw_A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the IP weights for censoring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "spec = @formula(\n",
    "    censored ~ 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\n",
    ")\n",
    "ip_denom = logit_ip_f(spec, nhefs_all, :censored);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = @formula(censored ~ qsmk)\n",
    "ip_numer = logit_ip_f(spec, nhefs_all, :censored);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "sw_C = ip_numer ./ ip_denom\n",
    "sw_C[nhefs_all.censored .== 1] .= 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stabilized weights\n",
      " min   mean    max\n",
      "------------------\n",
      "0.94   1.00   1.72"
     ]
    }
   ],
   "source": [
    "println(\"Stabilized weights\")\n",
    "println(\" min   mean    max\")\n",
    "println(\"------------------\")\n",
    "@printf \"%04.2f   %04.2f   %04.2f\" minimum(sw_C) mean(sw_C) maximum(sw_C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now create the combined IP weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "sw_AC = sw_A .* sw_C;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stabilized weights\n",
      " min   mean    max\n",
      "------------------\n",
      "0.35   1.00   4.09"
     ]
    }
   ],
   "source": [
    "println(\"Stabilized weights\")\n",
    "println(\" min   mean    max\")\n",
    "println(\"------------------\")\n",
    "@printf \"%04.2f   %04.2f   %04.2f\" minimum(sw_AC) mean(sw_AC) maximum(sw_AC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now model weight gain using the combined IP weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = nhefs.wt82_71\n",
    "X = [ones(nrow(nhefs)) nhefs.qsmk]\n",
    "groups = convert(Array{Int}, nhefs.seqn);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "wls = sm.WLS(y, X, weights=sw_AC[nhefs_all.censored .== 0])\n",
    "res = wls.fit(cov_type=\"cluster\", cov_kwds=Dict(\"groups\" => groups));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>(intercept)</th> <td>    1.6620</td> <td>    0.233</td> <td>    7.136</td> <td> 0.000</td> <td>    1.206</td> <td>    2.118</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>qsmk</th>        <td>    3.4965</td> <td>    0.526</td> <td>    6.648</td> <td> 0.000</td> <td>    2.466</td> <td>    4.527</td>\n",
       "</tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_coefs(res, xname=[\"(intercept)\", \"qsmk\"])"
   ]
  }
 ],
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