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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Think Bayes\n",
"\n",
"This notebook presents code and exercises from Think Bayes, second edition.\n",
"\n",
"Copyright 2018 Allen B. Downey\n",
"\n",
"MIT License: https://opensource.org/licenses/MIT"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Configure Jupyter so figures appear in the notebook\n",
"%matplotlib inline\n",
"\n",
"# Configure Jupyter to display the assigned value after an assignment\n",
"%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
"\n",
"import math\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"from thinkbayes2 import Pmf, Cdf, Suite, Joint\n",
"import thinkplot"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### The August birthday problem\n",
"\n",
"This article:\n",
"\n",
"[Attention Deficit–Hyperactivity Disorder and Month of School Enrollment](https://www.nejm.org/doi/10.1056/NEJMoa1806828)\n",
"\n",
"Finds:\n",
"\n",
">The rate of claims-based ADHD diagnosis among children in states with a September 1 cutoff was 85.1 per 10,000 children (309 cases among 36,319 children; 95% confidence interval [CI], 75.6 to 94.2) among those born in August and 63.6 per 10,000 children (225 cases among 35,353 children; 95% CI, 55.4 to 71.9) among those born in September, an absolute difference of 21.5 per 10,000 children (95% CI, 8.8 to 34.0); the corresponding difference in states without the September 1 cutoff was 8.9 per 10,000 children (95% CI, −14.9 to 20.8). The rate of ADHD treatment was 52.9 per 10,000 children (192 of 36,319 children; 95% CI, 45.4 to 60.3) among those born in August and 40.4 per 10,000 children (143 of 35,353 children; 95% CI, 33.8 to 47.1) among those born in September, an absolute difference of 12.5 per 10,000 children (95% CI, 2.43 to 22.4). These differences were not observed for other month-to-month comparisons, nor were they observed in states with non-September cutoff dates for starting kindergarten. In addition, in states with a September 1 cutoff, no significant differences between August-born and September-born children were observed in rates of asthma, diabetes, or obesity.\n",
"\n",
"It includes this figure:\n",
"\n",
"![](https://www.nejm.org/na101/home/literatum/publisher/mms/journals/content/nejm/2018/nejm_2018.379.issue-22/nejmoa1806828/20181123/images/img_xlarge/nejmoa1806828_f1.jpeg)\n",
"\n",
"However, there is an error in this figure, confirmed by personal correspondence:\n",
"\n",
">The May and June [diagnoses] are reversed. May should be 317 (not 287) and June should be 287 (not 317).\n",
"\n",
"\n",
"Based on this corrected data, what can we say about the probability of diagnosis as a function of birth month?\n",
"\n",
"What can we say about the rate of misdiagnosis?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's the data from the table."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([265, 280, 307, 312, 317, 287, 320, 309, 225, 240, 232, 243])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"totals = np.array([32690, 31238, 34405, 34565, 34977, 34415, \n",
" 36577, 36319, 35353, 34405, 31285, 31617])\n",
"\n",
"diagnosed = np.array([265, 280, 307, 312, 317, 287, \n",
" 320, 309, 225, 240, 232, 243])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I'll roll the data so September comes first."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([225, 240, 232, 243, 265, 280, 307, 312, 317, 287, 320, 309])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"totals = np.roll(totals, -8)\n",
"diagnosed = np.roll(diagnosed, -8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are the diagnosis rates, which we can check against the rates in the table."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([63.6, 69.8, 74.2, 76.9, 81.1, 89.6, 89.2, 90.3, 90.6, 83.4, 87.5,\n",
" 85.1])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates = diagnosed / totals * 10000\n",
"np.round(rates, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's what the rates look like as a function of months after the September cutoff."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xs = np.arange(12)\n",
"thinkplot.plot(xs, rates)\n",
"thinkplot.decorate(xlabel='Months after cutoff',\n",
" ylabel='Diagnosis rate per 10,000')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the first 9 months, from September to May, we see what we would expect if at least some of the excess diagnoses are due to behavioral differences due to age. For each month of difference in age, we see an increase in the number of diagnoses.\n",
"\n",
"This pattern breaks down for the last three months, June, July, and August. This might be explained by random variation, but it also might be due to parental manipulation; if some parents hold back students born near the deadline, the observations for these month would include a mixture of children who are relatively old for their grade, and therefore less likely to be diagnosed.\n",
"\n",
"We could test this hypothesis by checking the actual ages of these students when they started school, rather than just looking at their months of birth.\n",
"\n",
"I'll use a beta distribution to compute the posterior credible interval for each of these rates."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import scipy.stats\n",
"\n",
"pcount = 1\n",
"res = []\n",
"for (x, d, t) in zip(xs, diagnosed, totals):\n",
" a = d + pcount\n",
" b = t-d + pcount\n",
" ci = scipy.stats.beta(a, b).ppf([0.025, 0.975])\n",
" res.append(ci * 10000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By transposing the results, we can get them into two arrays for plotting."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"low, high = np.transpose(res)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([55.88350221, 61.50636809, 65.24705555, 67.82200497, 71.91566468,\n",
" 79.7803044 , 79.8376067 , 80.83488731, 81.23383696, 74.32935962,\n",
" 78.45460029, 76.14872189])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"low"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 72.49141124, 79.12409251, 84.2928591 , 87.10526514,\n",
" 91.38514006, 100.71257892, 99.73630892, 100.8006574 ,\n",
" 101.12113503, 93.57085021, 97.56460619, 95.0639517 ])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"high"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's what the plot looks like with error bars."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"def errorbar(xs, low, high, **options):\n",
" for x, l, h in zip(xs, low, high):\n",
" plt.vlines(x, l, h, **options)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"errorbar(xs, low, high, color='gray', alpha=0.7)\n",
"thinkplot.plot(xs, rates)\n",
"thinkplot.decorate(xlabel='Months after cutoff',\n",
" ylabel='Diagnosis rate per 10,000')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It seems like the lower rates in the last 3 months are unlikely to be due to random variation, so it might be good to investigate the effect of \"red shirting\".\n",
"\n",
"But for now I will proceed with a linear logistic model. The following table shows log odds of diagnosis for each month, which I will use to lay out a grid for parameter estimation."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 -5.050653410037134\n",
"1 -4.9583180838728875\n",
"2 -4.89671332938555\n",
"3 -4.860673360075637\n",
"4 -4.806955183198423\n",
"5 -4.705597122964573\n",
"6 -4.71014626293798\n",
"7 -4.698526243285876\n",
"8 -4.694439789392316\n",
"9 -4.778391224951511\n",
"10 -4.730066749295253\n",
"11 -4.758210679745176\n"
]
}
],
"source": [
"from scipy.special import expit, logit\n",
"\n",
"for (x, d, t) in zip(xs, diagnosed, totals):\n",
" print(x, logit(d/t))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's a Suite that estimates the parameters of a logistic regression model, `b0` and `b1`."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"class August(Suite, Joint):\n",
" \n",
" def Likelihood(self, data, hypo):\n",
" x, d, t = data\n",
" b0, b1 = hypo\n",
" \n",
" p = expit(b0 + b1 * x)\n",
" like = scipy.stats.binom.pmf(d, t, p)\n",
" \n",
" return like"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The prior distributions are uniform over a grid that covers the most likely values."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"from itertools import product\n",
"\n",
"b0 = np.linspace(-4.75, -5.1, 101)\n",
"b1 = np.linspace(-0.05, 0.05, 101)\n",
"hypos = product(b0, b1)\n",
"\n",
"suite = August(hypos);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's the update."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"for data in zip(xs, diagnosed, totals):\n",
" suite.Update(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here's the posterior marginal distribution for `b0`."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-4.935267063442661\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pmf0 = suite.Marginal(0)\n",
"b0 = pmf0.Mean()\n",
"print(b0)\n",
"thinkplot.Pdf(pmf0)\n",
"\n",
"thinkplot.decorate(title='Posterior marginal distribution',\n",
" xlabel='Intercept log odds (b0)',\n",
" ylabel='Pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the posterior marginal distribution for `b1`."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.023935981894059242\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pmf1 = suite.Marginal(1)\n",
"b1 = pmf1.Mean()\n",
"print(b1)\n",
"thinkplot.Pdf(pmf1)\n",
"\n",
"thinkplot.decorate(title='Posterior marginal distribution',\n",
" xlabel='Slope log odds (b0)',\n",
" ylabel='Pdf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see what the posterior regression lines look like, superimposed on the data."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i in range(100):\n",
" b0, b1 = suite.Random()\n",
" ys = expit(b0 + b1 * xs) * 10000\n",
" thinkplot.plot(xs, ys, color='green', alpha=0.01)\n",
" \n",
"errorbar(xs, low, high, color='gray', alpha=0.7)\n",
"thinkplot.plot(xs, rates)\n",
"\n",
"thinkplot.decorate(xlabel='Months after cutoff',\n",
" ylabel='Diagnosis rate per 10,000')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Most of these regression lines fall within the credible intervals of the observed rates, so in that sense it seems like this model is not ruled out by the data.\n",
"\n",
"But it is clear that the lower rates in the last 3 months bring down the estimated slope, so we should probably treat the estimated effect size as a lower bound.\n",
"\n",
"To express the results more clearly, we can look at the posterior predictive distribution for the difference between a child born in September and one born in August:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def posterior_predictive(x):\n",
" pmf = Pmf()\n",
"\n",
" for (b0, b1), p in suite.Items():\n",
" base = expit(b0 + b1 * x) * 10000\n",
" pmf[base] += p\n",
" \n",
" return pmf"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are posterior predictive CDFs for diagnosis rates."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pmf0 = posterior_predictive(0)\n",
"thinkplot.Cdf(pmf0.MakeCdf(), label='September')\n",
"\n",
"pmf1 = posterior_predictive(11)\n",
"thinkplot.Cdf(pmf1.MakeCdf(), label='August')\n",
"\n",
"thinkplot.decorate(title='Posterior predictive distribution',\n",
" xlabel='Diagnosis rate per 10,000',\n",
" ylabel='CDF')"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"71.41299996984112"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pmf0.Mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we can compute the posterior predictive distribution for the difference."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"def posterior_predictive_diff():\n",
" pmf = Pmf()\n",
" \n",
" for (b0, b1), p in suite.Items():\n",
" p0 = expit(b0) * 10000\n",
" p1 = expit(b0 + b1 * 11) * 10000\n",
" diff = p1 - p0\n",
" pmf[diff] += p\n",
" \n",
" return pmf"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pmf_diff = posterior_predictive_diff()\n",
"thinkplot.Cdf(pmf_diff.MakeCdf())\n",
"\n",
"thinkplot.decorate(title='Posterior predictive distribution',\n",
" xlabel='11 month increase in diagnosis rate per 10,000',\n",
" ylabel='CDF')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To summarize, we can compute the mean and 95% credible interval for this difference."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"21.301302380532498"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pmf_diff.Mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": []
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(12.53483625370616, 30.001082782077376)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pmf_diff.CredibleInterval(95)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A difference of 21 diagnoses, on a base rate of 71 diagnoses, is an increase of 30% (18%, 42%)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.29828325920390386"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pmf_diff.Mean() / pmf0.Mean()"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.17552597, 0.42010674])"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pmf_diff.CredibleInterval(95) / pmf0.Mean()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
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"language": "python",
"name": "python3"
},
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"name": "ipython",
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},
"file_extension": ".py",
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"name": "python",
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},
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}
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