{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Incidence of influenza-like illness in France" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import isoweek" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data on the incidence of influenza-like illness are available from the Web site of the [Réseau Sentinelles](http://www.sentiweb.fr/). We download them as a file in CSV format, in which each line corresponds to a week in the observation period. Only the complete dataset, starting in 1984 and ending with a recent week, is available for download." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "data_url = \"http://www.sentiweb.fr/datasets/incidence-PAY-3.csv\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the documentation of the data from [the download site](https://ns.sentiweb.fr/incidence/csv-schema-v1.json):\n", "\n", "| Column name | Description |\n", "|--------------|---------------------------------------------------------------------------------------------------------------------------|\n", "| `week` | ISO8601 Yearweek number as numeric (year times 100 + week nubmer) |\n", "| `indicator` | Unique identifier of the indicator, see metadata document https://www.sentiweb.fr/meta.json |\n", "| `inc` | Estimated incidence value for the time step, in the geographic level |\n", "| `inc_low` | Lower bound of the estimated incidence 95% Confidence Interval |\n", "| `inc_up` | Upper bound of the estimated incidence 95% Confidence Interval |\n", "| `inc100` | Estimated rate incidence per 100,000 inhabitants |\n", "| `inc100_low` | Lower bound of the estimated incidence 95% Confidence Interval |\n", "| `inc100_up` | Upper bound of the estimated rate incidence 95% Confidence Interval |\n", "| `geo_insee` | Identifier of the geographic area, from INSEE https://www.insee.fr |\n", "| `geo_name` | Geographic label of the area, corresponding to INSEE code. This label is not an id and is only provided for human reading |\n", "\n", "The first line of the CSV file is a comment, which we ignore with `skip=1`." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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weekindicatorincinc_lowinc_upinc100inc100_lowinc100_upgeo_inseegeo_name
020243432822921391.035067.04232.052.0FRFrance
120243332079515392.026198.03123.039.0FRFrance
220243232318717532.028842.03527.043.0FRFrance
320243132603520267.031803.03930.048.0FRFrance
420243033639328593.044193.05543.067.0FRFrance
520242933956032592.046528.05949.069.0FRFrance
620242835434245781.062903.08168.094.0FRFrance
720242734736440234.054494.07160.082.0FRFrance
820242634421936956.051482.06655.077.0FRFrance
920242534720440300.054108.07161.081.0FRFrance
1020242434111034671.047549.06252.072.0FRFrance
1120242333587530610.041140.05446.062.0FRFrance
1220242233377228274.039270.05143.059.0FRFrance
1320242132196317556.026370.03326.040.0FRFrance
1420242032005715780.024334.03024.036.0FRFrance
1520241931537511274.019476.02317.029.0FRFrance
1620241832240917653.027165.03427.041.0FRFrance
1720241732704221410.032674.04133.049.0FRFrance
1820241632888223305.034459.04335.051.0FRFrance
1920241533022924648.035810.04537.053.0FRFrance
2020241433181326529.037097.04840.056.0FRFrance
2120241333509029607.040573.05345.061.0FRFrance
2220241234063934582.046696.06152.070.0FRFrance
2320241135026843331.057205.07565.085.0FRFrance
2420241036010752623.067591.09079.0101.0FRFrance
2520240937112162920.079322.010795.0119.0FRFrance
26202408310456694520.0114612.0157142.0172.0FRFrance
272024073138078127050.0149106.0207190.0224.0FRFrance
282024063190062177955.0202169.0285267.0303.0FRFrance
292024053216237203595.0228879.0324305.0343.0FRFrance
.................................
204819852132609619621.032571.04735.059.0FRFrance
204919852032789620885.034907.05138.064.0FRFrance
205019851934315432821.053487.07859.097.0FRFrance
205119851834055529935.051175.07455.093.0FRFrance
205219851733405324366.043740.06244.080.0FRFrance
205319851635036236451.064273.09166.0116.0FRFrance
205419851536388145538.082224.011683.0149.0FRFrance
20551985143134545114400.0154690.0244207.0281.0FRFrance
20561985133197206176080.0218332.0357319.0395.0FRFrance
20571985123245240223304.0267176.0445405.0485.0FRFrance
20581985113276205252399.0300011.0501458.0544.0FRFrance
20591985103353231326279.0380183.0640591.0689.0FRFrance
20601985093369895341109.0398681.0670618.0722.0FRFrance
20611985083389886359529.0420243.0707652.0762.0FRFrance
20621985073471852432599.0511105.0855784.0926.0FRFrance
20631985063565825518011.0613639.01026939.01113.0FRFrance
20641985053637302592795.0681809.011551074.01236.0FRFrance
20651985043424937390794.0459080.0770708.0832.0FRFrance
20661985033213901174689.0253113.0388317.0459.0FRFrance
206719850239758680949.0114223.0177147.0207.0FRFrance
206819850138548965918.0105060.0155120.0190.0FRFrance
206919845238483060602.0109058.0154110.0198.0FRFrance
2070198451310172680242.0123210.0185146.0224.0FRFrance
20711984503123680101401.0145959.0225184.0266.0FRFrance
2072198449310107381684.0120462.0184149.0219.0FRFrance
207319844837862060634.096606.0143110.0176.0FRFrance
207419844737202954274.089784.013199.0163.0FRFrance
207519844638733067686.0106974.0159123.0195.0FRFrance
20761984453135223101414.0169032.0246184.0308.0FRFrance
207719844436842220056.0116788.012537.0213.0FRFrance
\n", "

2078 rows × 10 columns

\n", "
" ], "text/plain": [ " week indicator inc inc_low inc_up inc100 inc100_low \\\n", "0 202434 3 28229 21391.0 35067.0 42 32.0 \n", "1 202433 3 20795 15392.0 26198.0 31 23.0 \n", "2 202432 3 23187 17532.0 28842.0 35 27.0 \n", "3 202431 3 26035 20267.0 31803.0 39 30.0 \n", "4 202430 3 36393 28593.0 44193.0 55 43.0 \n", "5 202429 3 39560 32592.0 46528.0 59 49.0 \n", "6 202428 3 54342 45781.0 62903.0 81 68.0 \n", "7 202427 3 47364 40234.0 54494.0 71 60.0 \n", "8 202426 3 44219 36956.0 51482.0 66 55.0 \n", "9 202425 3 47204 40300.0 54108.0 71 61.0 \n", "10 202424 3 41110 34671.0 47549.0 62 52.0 \n", "11 202423 3 35875 30610.0 41140.0 54 46.0 \n", "12 202422 3 33772 28274.0 39270.0 51 43.0 \n", "13 202421 3 21963 17556.0 26370.0 33 26.0 \n", "14 202420 3 20057 15780.0 24334.0 30 24.0 \n", "15 202419 3 15375 11274.0 19476.0 23 17.0 \n", "16 202418 3 22409 17653.0 27165.0 34 27.0 \n", "17 202417 3 27042 21410.0 32674.0 41 33.0 \n", "18 202416 3 28882 23305.0 34459.0 43 35.0 \n", "19 202415 3 30229 24648.0 35810.0 45 37.0 \n", "20 202414 3 31813 26529.0 37097.0 48 40.0 \n", "21 202413 3 35090 29607.0 40573.0 53 45.0 \n", "22 202412 3 40639 34582.0 46696.0 61 52.0 \n", "23 202411 3 50268 43331.0 57205.0 75 65.0 \n", "24 202410 3 60107 52623.0 67591.0 90 79.0 \n", "25 202409 3 71121 62920.0 79322.0 107 95.0 \n", "26 202408 3 104566 94520.0 114612.0 157 142.0 \n", "27 202407 3 138078 127050.0 149106.0 207 190.0 \n", "28 202406 3 190062 177955.0 202169.0 285 267.0 \n", "29 202405 3 216237 203595.0 228879.0 324 305.0 \n", "... ... ... ... ... ... ... ... \n", "2048 198521 3 26096 19621.0 32571.0 47 35.0 \n", "2049 198520 3 27896 20885.0 34907.0 51 38.0 \n", "2050 198519 3 43154 32821.0 53487.0 78 59.0 \n", "2051 198518 3 40555 29935.0 51175.0 74 55.0 \n", "2052 198517 3 34053 24366.0 43740.0 62 44.0 \n", "2053 198516 3 50362 36451.0 64273.0 91 66.0 \n", "2054 198515 3 63881 45538.0 82224.0 116 83.0 \n", "2055 198514 3 134545 114400.0 154690.0 244 207.0 \n", "2056 198513 3 197206 176080.0 218332.0 357 319.0 \n", "2057 198512 3 245240 223304.0 267176.0 445 405.0 \n", "2058 198511 3 276205 252399.0 300011.0 501 458.0 \n", "2059 198510 3 353231 326279.0 380183.0 640 591.0 \n", "2060 198509 3 369895 341109.0 398681.0 670 618.0 \n", "2061 198508 3 389886 359529.0 420243.0 707 652.0 \n", "2062 198507 3 471852 432599.0 511105.0 855 784.0 \n", "2063 198506 3 565825 518011.0 613639.0 1026 939.0 \n", "2064 198505 3 637302 592795.0 681809.0 1155 1074.0 \n", "2065 198504 3 424937 390794.0 459080.0 770 708.0 \n", "2066 198503 3 213901 174689.0 253113.0 388 317.0 \n", "2067 198502 3 97586 80949.0 114223.0 177 147.0 \n", "2068 198501 3 85489 65918.0 105060.0 155 120.0 \n", "2069 198452 3 84830 60602.0 109058.0 154 110.0 \n", "2070 198451 3 101726 80242.0 123210.0 185 146.0 \n", "2071 198450 3 123680 101401.0 145959.0 225 184.0 \n", "2072 198449 3 101073 81684.0 120462.0 184 149.0 \n", "2073 198448 3 78620 60634.0 96606.0 143 110.0 \n", "2074 198447 3 72029 54274.0 89784.0 131 99.0 \n", "2075 198446 3 87330 67686.0 106974.0 159 123.0 \n", "2076 198445 3 135223 101414.0 169032.0 246 184.0 \n", "2077 198444 3 68422 20056.0 116788.0 125 37.0 \n", "\n", " inc100_up geo_insee geo_name \n", "0 52.0 FR France \n", "1 39.0 FR France \n", "2 43.0 FR France \n", "3 48.0 FR France \n", "4 67.0 FR France \n", "5 69.0 FR France \n", "6 94.0 FR France \n", "7 82.0 FR France \n", "8 77.0 FR France \n", "9 81.0 FR France \n", "10 72.0 FR France \n", "11 62.0 FR France \n", "12 59.0 FR France \n", "13 40.0 FR France \n", "14 36.0 FR France \n", "15 29.0 FR France \n", "16 41.0 FR France \n", "17 49.0 FR France \n", "18 51.0 FR France \n", "19 53.0 FR France \n", "20 56.0 FR France \n", "21 61.0 FR France \n", "22 70.0 FR France \n", "23 85.0 FR France \n", "24 101.0 FR France \n", "25 119.0 FR France \n", "26 172.0 FR France \n", "27 224.0 FR France \n", "28 303.0 FR France \n", "29 343.0 FR France \n", "... ... ... ... \n", "2048 59.0 FR France \n", "2049 64.0 FR France \n", "2050 97.0 FR France \n", "2051 93.0 FR France \n", "2052 80.0 FR France \n", "2053 116.0 FR France \n", "2054 149.0 FR France \n", "2055 281.0 FR France \n", "2056 395.0 FR France \n", "2057 485.0 FR France \n", "2058 544.0 FR France \n", "2059 689.0 FR France \n", "2060 722.0 FR France \n", "2061 762.0 FR France \n", "2062 926.0 FR France \n", "2063 1113.0 FR France \n", "2064 1236.0 FR France \n", "2065 832.0 FR France \n", "2066 459.0 FR France \n", "2067 207.0 FR France \n", "2068 190.0 FR France \n", "2069 198.0 FR France \n", "2070 224.0 FR France \n", "2071 266.0 FR France \n", "2072 219.0 FR France \n", "2073 176.0 FR France \n", "2074 163.0 FR France \n", "2075 195.0 FR France \n", "2076 308.0 FR France \n", "2077 213.0 FR France \n", "\n", "[2078 rows x 10 columns]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "raw_data = pd.read_csv(data_url, skiprows=1)\n", "raw_data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Are there missing data points? Yes, week 19 of year 1989 does not have any observed values." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "raw_data[raw_data.isnull().any(axis=1)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We delete this point, which does not have big consequence for our rather simple analysis." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "data = raw_data.dropna().copy()\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our dataset uses an uncommon encoding; the week number is attached\n", "to the year number, leaving the impression of a six-digit integer.\n", "That is how Pandas interprets it.\n", "\n", "A second problem is that Pandas does not know about week numbers.\n", "It needs to be given the dates of the beginning and end of the week.\n", "We use the library `isoweek` for that.\n", "\n", "Since the conversion is a bit lengthy, we write a small Python \n", "function for doing it. Then we apply it to all points in our dataset. \n", "The results go into a new column 'period'." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def convert_week(year_and_week_int):\n", " year_and_week_str = str(year_and_week_int)\n", " year = int(year_and_week_str[:4])\n", " week = int(year_and_week_str[4:])\n", " w = isoweek.Week(year, week)\n", " return pd.Period(w.day(0), 'W')\n", "\n", "data['period'] = [convert_week(yw) for yw in data['week']]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are two more small changes to make.\n", "\n", "First, we define the observation periods as the new index of\n", "our dataset. That turns it into a time series, which will be\n", "convenient later on.\n", "\n", "Second, we sort the points chronologically." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sorted_data = data.set_index('period').sort_index()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We check the consistency of the data. Between the end of a period and\n", "the beginning of the next one, the difference should be zero, or very small.\n", "We tolerate an error of one second.\n", "\n", "This is OK except for one pair of consecutive periods between which\n", "a whole week is missing.\n", "\n", "We recognize the dates: it's the week without observations that we\n", "have deleted earlier!" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "periods = sorted_data.index\n", "for p1, p2 in zip(periods[:-1], periods[1:]):\n", " delta = p2.to_timestamp() - p1.end_time\n", " if delta > pd.Timedelta('1s'):\n", " print(p1, p2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A first look at the data!" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sorted_data['inc'].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A zoom on the last few years shows more clearly that the peaks are situated in winter." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sorted_data['inc'][-200:].plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Study of the annual incidence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the peaks of the epidemic happen in winter, near the transition\n", "between calendar years, we define the reference period for the annual\n", "incidence from August 1st of year $N$ to August 1st of year $N+1$. We\n", "label this period as year $N+1$ because the peak is always located in\n", "year $N+1$. The very low incidence in summer ensures that the arbitrariness\n", "of the choice of reference period has no impact on our conclusions.\n", "\n", "Our task is a bit complicated by the fact that a year does not have an\n", "integer number of weeks. Therefore we modify our reference period a bit:\n", "instead of August 1st, we use the first day of the week containing August 1st.\n", "\n", "A final detail: the dataset starts in October 1984, the first peak is thus\n", "incomplete, We start the analysis with the first full peak." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "first_august_week = [pd.Period(pd.Timestamp(y, 8, 1), 'W')\n", " for y in range(1985,\n", " sorted_data.index[-1].year)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Starting from this list of weeks that contain August 1st, we obtain intervals of approximately one year as the periods between two adjacent weeks in this list. We compute the sums of weekly incidences for all these periods.\n", "\n", "We also check that our periods contain between 51 and 52 weeks, as a safeguard against potential mistakes in our code." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "year = []\n", "yearly_incidence = []\n", "for week1, week2 in zip(first_august_week[:-1],\n", " first_august_week[1:]):\n", " one_year = sorted_data['inc'][week1:week2-1]\n", " assert abs(len(one_year)-52) < 2\n", " yearly_incidence.append(one_year.sum())\n", " year.append(week2.year)\n", "yearly_incidence = pd.Series(data=yearly_incidence, index=year)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here are the annual incidences." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "yearly_incidence.plot(style='*')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A sorted list makes it easier to find the highest values (at the end)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "yearly_incidence.sort_values()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, a histogram clearly shows the few very strong epidemics, which affect about 10% of the French population,\n", "but are rare: there were three of them in the course of 35 years. The typical epidemic affects only half as many people." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "yearly_incidence.hist(xrot=20)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 1 }