josef-pkt/ex_metaanalysis_short.ipynb

## ex_metaanalysis_short.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Meta-Analysis in statmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats, optimize\n",
    "\n",
    "from statsmodels.regression.linear_model import WLS\n",
    "from statsmodels.genmod.generalized_linear_model import GLM\n",
    "\n",
    "from statsmodels.stats.meta_analysis import (\n",
    "    effectsize_smd, combine_effects, _fit_tau_iterative,\n",
    "    _fit_tau_mm, _fit_tau_iter_mm)\n",
    "\n",
    "# increase line length for pandas\n",
    "pd.set_option('display.width', 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Carroll', 'Grant', 'Peck', 'Donat', 'Stewart', 'Young']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [\n",
    "[\"Carroll\", 94, 22,60,92, 20,60],\n",
    "[\"Grant\", 98, 21,65, 92,22, 65],\n",
    "[\"Peck\", 98, 28, 40,88 ,26, 40],\n",
    "[\"Donat\", 94,19, 200, 82,17, 200],\n",
    "[\"Stewart\", 98, 21,50, 88,22 , 45],\n",
    "[\"Young\", 96,21,85, 92 ,22, 85]]\n",
    "colnames = [\"study\",\"mean_t\",\"sd_t\",\"n_t\",\"mean_c\",\"sd_c\",\"n_c\"]\n",
    "rownames = [i[0] for i in data]\n",
    "dframe1 = pd.DataFrame(data, columns=colnames)\n",
    "rownames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean2, sd2, nobs2, mean1, sd1, nobs1 = np.asarray(dframe1[[\"mean_t\",\"sd_t\",\"n_t\",\"mean_c\",\"sd_c\",\"n_c\"]]).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### estimate effect size standardized mean difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "eff, var_eff = effectsize_smd(mean2, sd2, nobs2, mean1, sd1, nobs1, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using one-step chi2, DerSimonian-Laird estimate for random effects variance tau\n",
    "\n",
    "Method option for random effect `method_re=\"chi2\"` or `method_re=\"dl\"`, both names are accepted.\n",
    "This is commonly referred to as the DerSimonian-Laird method, it is based on a moment estimator based on pearson chi2 from the fixed effects estimate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        eff    sd_eff    ci_low    ci_upp      w_fe      w_re\n",
      "Carroll            0.094524  0.182680 -0.263528  0.452576  0.123868  0.157481\n",
      "Grant              0.277356  0.176279 -0.068151  0.622864  0.133026  0.162789\n",
      "Peck               0.366546  0.225573 -0.075577  0.808670  0.081239  0.126137\n",
      "Donat              0.664385  0.102748  0.462998  0.865772  0.391552  0.232875\n",
      "Stewart            0.449310  0.208160  0.041316  0.857305  0.095399  0.137981\n",
      "Young              0.185165  0.153729 -0.116144  0.486474  0.174915  0.182736\n",
      "fixed effect       0.413775  0.064294  0.248503  0.579048  1.000000       NaN\n",
      "random effect      0.356823  0.105345  0.086025  0.627621       NaN  1.000000\n",
      "fixed effect wls   0.413775  0.099131  0.158950  0.668601  1.000000       NaN\n",
      "random effect wls  0.356823  0.089965  0.125561  0.588085       NaN  1.000000\n"
     ]
    }
   ],
   "source": [
    "res3 = combine_effects(eff, var_eff, method_re=\"chi2\", use_t=True, row_names=rownames)\n",
    "print(res3.summary_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'chi2'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res3.method_re"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = res3.plot_forest()\n",
    "fig.set_figheight(6)\n",
    "fig.set_figwidth(6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using iterated, Paule-Mandel estimate for random effects variance tau\n",
    "\n",
    "The method commonly referred to as Paule-Mandel estimate is a method of moment estimate for the random effects variance that iterates between mean and variance estimate until convergence.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: iterated\n",
      "                        eff    sd_eff    ci_low    ci_upp      w_fe      w_re\n",
      "Carroll            0.094524  0.182680 -0.263528  0.452576  0.123868  0.152470\n",
      "Grant              0.277356  0.176279 -0.068151  0.622864  0.133026  0.159034\n",
      "Peck               0.366546  0.225573 -0.075577  0.808670  0.081239  0.115980\n",
      "Donat              0.664385  0.102748  0.462998  0.865772  0.391552  0.258380\n",
      "Stewart            0.449310  0.208160  0.041316  0.857305  0.095399  0.129329\n",
      "Young              0.185165  0.153729 -0.116144  0.486474  0.174915  0.184807\n",
      "fixed effect       0.413775  0.064294  0.287762  0.539789  1.000000       NaN\n",
      "random effect      0.365026  0.092121  0.184472  0.545579       NaN  1.000000\n",
      "fixed effect wls   0.413775  0.099131  0.219481  0.608069  1.000000       NaN\n",
      "random effect wls  0.365026  0.092121  0.184472  0.545579       NaN  1.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res4 = combine_effects(eff, var_eff, method_re=\"iterated\", use_t=False, row_names=rownames)\n",
    "res4_df = res4.summary_frame()\n",
    "print(\"method RE:\", res4.method_re)\n",
    "print(res4.summary_frame())\n",
    "fig = res4.plot_forest()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example Kacker interlaboratory mean\n",
    "\n",
    "In this example the effect size is the mean of measurments in a lab. We combine the estimates from several labs to estimate and overall average."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "eff = np.array([61.00, 61.40, 62.21, 62.30, 62.34, 62.60, 62.70,\n",
    "                62.84, 65.90])\n",
    "var_eff = np.array([0.2025, 1.2100, 0.0900, 0.2025, 0.3844, 0.5625,\n",
    "                    0.0676, 0.0225, 1.8225])\n",
    "rownames = ['PTB', 'NMi', 'NIMC', 'KRISS', 'LGC', 'NRC', 'IRMM', 'NIST', 'LNE']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: dl\n",
      "                         eff    sd_eff     ci_low     ci_upp      w_fe      w_re\n",
      "PTB                61.000000  0.450000  60.118000  61.882000  0.057436  0.123113\n",
      "NMi                61.400000  1.100000  59.244000  63.556000  0.009612  0.040314\n",
      "NIMC               62.210000  0.300000  61.622000  62.798000  0.129230  0.159749\n",
      "KRISS              62.300000  0.450000  61.418000  63.182000  0.057436  0.123113\n",
      "LGC                62.340000  0.620000  61.124800  63.555200  0.030257  0.089810\n",
      "NRC                62.600000  0.750000  61.130000  64.070000  0.020677  0.071005\n",
      "IRMM               62.700000  0.260000  62.190400  63.209600  0.172052  0.169810\n",
      "NIST               62.840000  0.150000  62.546000  63.134000  0.516920  0.194471\n",
      "LNE                65.900000  1.350000  63.254000  68.546000  0.006382  0.028615\n",
      "fixed effect       62.583397  0.107846  62.334704  62.832090  1.000000       NaN\n",
      "random effect      62.390139  0.245750  61.823439  62.956838       NaN  1.000000\n",
      "fixed effect wls   62.583397  0.189889  62.145512  63.021282  1.000000       NaN\n",
      "random effect wls  62.390139  0.294776  61.710384  63.069893       NaN  1.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res2_DL = combine_effects(eff, var_eff, method_re=\"dl\", use_t=True, row_names=rownames)\n",
    "print(\"method RE:\", res2_DL.method_re)\n",
    "print(res2_DL.summary_frame())\n",
    "fig = res2_DL.plot_forest()\n",
    "fig.set_figheight(6)\n",
    "fig.set_figwidth(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "method RE: pm\n",
      "                         eff    sd_eff     ci_low     ci_upp      w_fe      w_re\n",
      "PTB                61.000000  0.450000  60.118000  61.882000  0.057436  0.125857\n",
      "NMi                61.400000  1.100000  59.244000  63.556000  0.009612  0.059656\n",
      "NIMC               62.210000  0.300000  61.622000  62.798000  0.129230  0.143658\n",
      "KRISS              62.300000  0.450000  61.418000  63.182000  0.057436  0.125857\n",
      "LGC                62.340000  0.620000  61.124800  63.555200  0.030257  0.104850\n",
      "NRC                62.600000  0.750000  61.130000  64.070000  0.020677  0.090122\n",
      "IRMM               62.700000  0.260000  62.190400  63.209600  0.172052  0.147821\n",
      "NIST               62.840000  0.150000  62.546000  63.134000  0.516920  0.156980\n",
      "LNE                65.900000  1.350000  63.254000  68.546000  0.006382  0.045201\n",
      "fixed effect       62.583397  0.107846  62.334704  62.832090  1.000000       NaN\n",
      "random effect      62.407620  0.338030  61.628120  63.187119       NaN  1.000000\n",
      "fixed effect wls   62.583397  0.189889  62.145512  63.021282  1.000000       NaN\n",
      "random effect wls  62.407620  0.338030  61.628120  63.187120       NaN  1.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res2_PM = combine_effects(eff, var_eff, method_re=\"pm\", use_t=True, row_names=rownames)\n",
    "print(\"method RE:\", res2_PM.method_re)\n",
    "print(res2_PM.summary_frame())\n",
    "fig = res2_PM.plot_forest()\n",
    "fig.set_figheight(6)\n",
    "fig.set_figwidth(6)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}