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Ambient air pollution is a leading environmental risk factor for premature mortality, and city-level air quality indices (AQI) are widely used to communicate exposure. The Global Air Pollution Dataset records the overall AQI and four pollutant sub-indices (PM2.5, ozone, nitrogen dioxide and carbon monoxide) for 23,463 cities in 175 countries, yet its statistical structure and the validity of analyses built on it are rarely examined together. This review combines a narrative synthesis of the literature with a full statistical re-analysis of the supplied file. We audit data quality and internal consistency, describe distributions, quantify pollutant dominance, correlation and relative importance, measure between-country heterogeneity, and evaluate predictive models under two validation designs. Our synthesis finds that (i) the overall AQI equals the maximum sub-index in 99.4% of records, and the 141 exceptions all occur at extreme PM2.5 levels; (ii) PM2.5 is the highest sub-index in 78.9% of cities and in every city rated Hazardous, and alone explains 96.9% of AQI variance; (iii) country of location explains about half of the variation in log AQI (intraclass correlation 0.54; Kruskal-Wallis ϵ 2 = 0.49), with median AQI ranging from 20 (Bolivia) to 169 (Pakistan); and (iv) when country information is allowed to leak across cross-validation folds, the AUC for predicting unhealthy air from non-PM2.5 pollutants rises from 0.84 to 0.97, an artefact of the validation design. We propose a short reporting checklist and six priority research directions.
Keywords: Air quality index (AQI); PM2.5; ozone; between-country heterogeneity; Kruskal-Wallis test; intraclass correlation; grouped cross-validation; narrative review; Airqualityindex(AQI); between-countryheterogeneity; Kruskal-Wallistest; intra- classcorrelation; groupedcross-validation; and
classcorrelation,groupedcross-validation,narrativereview andwhichpollutantdeterminestheoverallAQI? 1.Introduction RQ3:Howstronglyarethesub-indicesassociated,and 1.1 Motivation what is each pollutant’s relative contribution to the Exposuretoambientairpollution,particularlyfinepar- overallAQI?
ticulatematter(PM2.5),islinkedtocardiovascularand respiratorydiseaseandtoaverylargeglobalburden RQ4: HowmuchofthevariationinAQIliesbetween ofprematuredeath(PopeandDockery,2006;Cohen countries,andwhichcountriesareattheextremes? etal.,2017;Burnettetal.,2018;Landriganetal.,2018). RQ5: Canunhealthyairbepredictedfromtheother Tocommunicateexposuretothepublic,monitoring pollutants,andhowmuchdoesthevalidationdesign agenciesconvertpollutantconcentrationsintounit- matter?
freeindiceswhosecategoriesrangefrom“Good”to “Hazardous” (US EPA, 2018). Because the index is a 2.BackgroundandTheoreticalFoundations transformationofconcentration,anystatisticalanaly- sisofAQIdatamustrespectitsconstruction:theoverall 2.1 TheAirQualityIndexandtheStructureofthe AQIisthemaximumofthepollutantsub-indices,the Dataset scaleiscapped,andvaluesarestronglyclusteredby Thefilehas23,463rows,onepercity,and12columns: geography.
country,city,andforeachoftheoverallAQIandfour TheGlobalAirPollutionDatasetisacompact,city-level pollutants(CO,ozone,NO andPM2.5)anumericin- tablethatiseasytodownloadandanalyse,anditis dexvalueandacategorylabel. Thecategorylabels oftenusedinteaching,dashboardsandintroductory correspondtotheUSEPAscheme(Table2.1;USEPA, machine-learningexamples. Itssimplicityhidessev- 2018). BP=[(I<sub>hi</sub> I<sub>lo</sub>)/ eralstatisticalfeaturesthatinfluenceconclusions:ex- (BP<sub>hi</sub>-BP<sub>lo</sub>)](C-BP< tremeskewness,near-constantsub-indicesfortwoof sub>lo</sub>)-BP<sub>+I<sub>lo</sub>,andthe the four pollutants, a deterministic relationship be- overallAQIisthelargestsub-index.Thefiledoesnot tween the overall AQI and its components, strongly documentitsdatasource,measurementdateoraver- unequalcountrysamplesizes,andclusteringofcities agingperiod,whichlimitsanyclaimaboutthetime withincountriesthatcaninflatetheapparentaccuracy periodortherepresentativenessofthereadings. ofpredictivemodelsifignored.Astatisticalappraisalis Table2.1:AQIcategories(USEPAscheme) thereforeusefulbeforethedataareusedforinference orprediction.
AQIrange Category Healthinterpreta- tion 0-50 Good Airqualityissatis- 1.2 ScopeandContribution factory Thisarticleisanarrativereviewsupportedbyacom- 51-100 Moderate Acceptable;some pletestatisticalre-analysisofthesupplieddataset.Our concern for very sensitivepeople contributionsarefourfold: 101-150 UnhealthyforSen- Sensitive groups A structured description of the dataset, including a sitiveGroups mayexperienceef- quantitativeauditofinternalconsistencybetweenthe fects overallAQI,itssub-indicesanditscategorylabels. 151-200 Unhealthy General popu- lation may be Abatteryofstatisticaltoolssuitedtoheavilyskewed, affected hierarchicaldata(Jarque-Bera,Spearmancorrelation, 201-300 VeryUnhealthy Health alert; ev- Kruskal-Wallis,intraclasscorrelation,Wilsonintervals, eryonemaybeaf- robustregressionandShapley-typerelativeimportance). fected 301-500 Hazardous Emergencycondi- A demonstration, using grouped and random cross- tions validationsidebyside, ofhowignoringthecountry hierarchyinflatespredictiveperformance. 2.2 HealthandPolicyContext A reporting checklist and six priority research direc- Long-termPM2.5exposurehasbeenassociatedwithex- tionsforfutureworkwiththisdataset.
cessmortalityacrossawideconcentrationrange,and globalburdenestimatesattributemillionsofdeaths 1.3 ReviewQuestions ayeartoambientparticulatepollution(Cohenetal., RQ1:Whatisthestructureandinternalconsistencyof 2017; Burnettetal., 2018). Reflectingthisevidence, thedataset?
theWorldHealthOrganization(2021)tighteneditsrec- RQ2: How are the pollutant sub-indices distributed, ommendedguidelinevalues,withthePM2.5guideline nowfarbelowthelevelatwhichtheEPAschemefirst 3.MethodologyoftheReview leavesthe“Good”category. Index-basedcategories 3.1 ReviewDesign arethereforeacoarsecommunicationtoolandnota Thestudyhastwocomponents. Theliteraturecom- substituteforconcentrationdatainexposureanalysis. ponentisaselectivenarrativereviewoffoundational workonairqualityindices,healtheffectsandthestatis- 2.3 Statistical Tools for Skewed and Hierarchical ticalmethodsapplied;itdoesnotclaimtheexhaustive Data searchandscreeningcountsofaformalPRISMAsys- Normalitywasassessedwithskewness,excesskurto- tematicreview. Thequantitativecomponentisafull sisandtheJarque-Beratest(JarqueandBera,1987); re-analysisofthesuppliedfile,inwhicheveryfigure theShapiro-Wilktestisnotsuitableforsamplesabove andtableinSections4and5wascomputeddirectly about5,000.Becausethesub-indicesarehighlyskewed fromthedata.
andcontainmanyties,monotoneassociationswere measured with Spearman’s rank correlation (Spear- man,1904),withapproximate95%confidenceinter- 3.2 DataandPre-processing All23,463recordswereretained. Novalueswereim- vals from Fisher’s z transformation. Agreement be- putedorremoved.427records(1.8%)havenocountry tween category labels was quantified with Cohen’s andonerecordhasnocityname;theformerwereex- kappa(Cohen,1960),interpretedwiththebenchmarks cludedfromcountry-levelanalysesonly.Forcountry ofLandisandKoch(1977).Differencesacrosscountries comparisons,countrieswithatleast30citieswerere- weretestedwiththeKruskal-Wallistest(Kruskaland tained(85countries,21,972cities,93.6%ofthefile), Wallis,1952),withepsilon-squared(ϵ²)asaneffectsize with thresholds of 20 and 50 cities used as sensitiv- (TomczakandTomczak,2014).Theshareofvariation itychecks. Acitywasclassifiedashavingunhealthy lying between countrieswas expressed as the intra- airforsensitivegroupsorworsewhenitsoverallAQI classcorrelation(ICC)fromaone-wayrandom-effects exceeded100(4,244cities,18.1%),followingtheEPA decomposition(ShroutandFleiss,1979;Gelmanand rangesinTable2.1.
Hill,2007),andproportionsofunhealthycitieswere givenwithWilsonscoreintervals(Wilson,1927). 3.3 StatisticalAnalysisPlan 2.4 RegressionandRelativeImportance Theanalysisproceededinsixstages: (i)consistency TherelationbetweentheoverallAQIanditssub-indices auditoftheAQI,itssub-indicesanditslabels;(ii)de- wasexaminedwithordinaryleastsquaresusingheteroscedasticity-scriptivestatisticsanddistributionaltests;(iii)pollu- consistent(HC3)standarderrors(MacKinnonandWhite, tantdominanceandcategoryagreement;(iv)correla- 1985);heteroscedasticitywascheckedwiththeBreusch- tionandregressionwithrelative-importancedecom- Pagantest(BreuschandPagan,1979)andcollinearity position;(v)between-countryheterogeneity(Kruskal- withvarianceinflationfactors.Eachpredictor’sshare Wallis, ICC,chi-squareontheunhealthyshare); and of the explained variance was obtained by the LMG (vi)predictivecomparisonunderrandomandcountry- (Shapley-value)decomposition,whichaveragesapre- groupedvalidation.
dictor’sincrementalR² overallorderingsofthepredic- tors(Lindemanetal.,1980;Grömping,2006). 3.4 ValidationofPredictiveModels Two prediction tasks were defined. In the first, the 2.5 ValidationwithClusteredData PM2.5 sub-index was predicted from the CO, ozone Observationsfromthesamecountryarenotindepen- andNO sub-indicesbylinearregression,ridgeregres- dent.Whenrandomcross-validationplacescitiesfrom sion,k-nearestneighbours(k=15),randomforest(200 onecountryinboththetrainingandthetestfolds,a trees)andgradientboosting,usingten-foldrandom flexiblemodelcanlearncountry-specificsignatures cross-validation(seed42),andR²,RMSEandMAEwere andreportperformancethatwillnotcarryovertonew reported. In the second, unhealthy air (overall AQI countries(Robertsetal.,2017).Groupedcross-validation, above100)waspredictedfromthesamethreenon- whichholdsoutentirecountries, istheappropriate PM2.5sub-indicesbylogisticregression,randomforest check when the goal is generalisation to unseen lo- andgradientboosting,usingten-foldstratifiedrandom cations.Arelatedhazardistargetencodingofahigh- cross-validationandten-foldgroupedcross-validation cardinalityvariablesuchascountry(Micci-Barreca,2001), bycountry(citieswithoutacountryformingtheirown which is legitimate only if it is estimated within the group).PM2.5waswithheldfromthesecondtaskbe- training fold. Model comparisons were tested with causeitalmostcompletelydeterminestheoutcome. thecorrectedresampledt-testofNadeauandBengio Todemonstrateleakage,gradientboostingwasalso (2003).
fittedwithasmoothedcountrytargetencodingesti- matedinsideeachtrainingfold.AnalysesusedPython fallsbelowthelargestsub-index,butin141records withSciPy,statsmodelsandscikit-learn(Seaboldand (0.6%)itexceedsallfour,by56pointsonaverageand Perktold,2010;Pedregosaetal.,2011),andreporting upto166.EverysuchrecordhasaPM2.5sub-indexof followsthespiritoftheTRIPODstatement(Collinset atleast208(median386)and135ofthe141arerated al.,2015).
Hazardous,sothediscrepancyisconfinedtoextreme particulatereadings. Itisconsistentwiththeoverall AQI being computed or capped differently from the 4.StructureandQualityoftheDataset displayedsub-index(theAQIreaches500in103cities 4.1 Variables whilethePM2.5sub-indexreaches500inonly31),but Table4.1:Variablesinthedataset thefiledoesnotallowthistobeverified.Second,148 recordswhoseAQIisexactly100,150or300(52,95and Variable Description Type 1respectively)arelabelledwiththehighercategory, Country Country name Categorical (175 distinct, 427 whereastheEPArangesinTable2.1placetheminthe missing) lowerone. Thisaffectsonly0.6%ofrowsbutwould City Cityname(23,462 Identifier changecountsof“unhealthy”citiesiflabelswereused distinct, 1 miss- insteadofvalues.
ing) AQIValue Overall AQI Integer (maximum of 4.3 DescriptiveStatisticsandDistributionalShape sub-indices) Table4.3:DescriptivestatisticsoftheAQIvalues(n AQICategory EPA category of Ordinal(6) =23,463) theoverallAQI CO/Ozone/NO / Pollutant sub- Integer VariableMean SD MedianQ1- Range Skew Kurt. Skew PM2.5AQIValue indexvalues Q3 of CO/Ozone/NO EPA category of Ordinal log(1+x) Overall72.0 56.1 55 39-79 6-500 3.29 17.6 0.59 / PM2.5 AQI Cate- eachsub-index AQI gory PM2.5 68.5 54.8 54 35-79 0-500 2.82 13.6 0.05 AQI Ozone 35.2 28.1 31 21-40 0-235 3.10 12.1 0.91 4.2 ConsistencyandQualityAudit AQI NO2 3.1 5.3 1 0-4 0-91 3.79 22.4 0.72 Table4.2:Data-qualityandconsistencyaudit AQI CO 1.4 1.8 1 1-1 0-133 23.08 1289.1 0.80 Check Result Shareofrecords AQI Records × 23,463×12 - columns Duplicaterows 0 0.0% TheJarque-Beratestrejectednormalityforeveryvari- Missingcountry 427 1.8% able(allp<0.001),andthedeparturesarelarge:skew- Missingcity 1 0.004% nessrangesfrom2.82(PM2.5)to23.1(CO),andtheCO OverallAQIequals 23,322 99.4% sub-indexhasanexcesskurtosisabove1,000because maximum sub- index 99.99%ofcitiessitinthe“Good”categorywithahand- Overall AQI 141 0.6% fulofoutliersupto133.TheNO andCOsub-indices exceeds all sub- arealmostconstantontheindexscale(median1for indices both;35.1%ofNO valuesarezero).Alog(1+x)trans- OverallAQIbelow 0 0.0% formationbringstheskewnessofPM2.5to0.05andof maximum sub- theoverallAQIto0.59(Figure1),whichsupportsus- index Boundary values 148 0.6% ingthelogscaleforparametricsummariesofAQIand labelledinhigher rank-basedmethodsotherwise.
class (AQI = 100, 150,300) NO2 sub-index 8,242 35.1% equaltozero CO sub-index 3,110 13.3% equaltozero Thefilecontainsnoduplicatesandnomissingvalues inanynumericcolumn.Twointernalinconsistencies deservedocumentation. First,theoverallAQInever Table4.4:Number(%)ofcitiesineachAQIcategory comparedwith48.8%forozone(κ =0.136,slightagree- ment).
Category Overall PM2.5 Ozone NO2 CO AQI Good 9,936 10,208 21,069 23,448 23,460 (42.3%) (43.5%) (89.8%) (99.9%) (100.0%) Moderate 9,231 9,075 1,445 15 2(0.0%) 5.2 CorrelationStructure (39.3%) (38.7%) (6.2%) (0.1%) Table5.2:Spearmanrankcorrelations(95%CI) Unhealthy 1,591 1,624 491 0(0.0%) 1(0.0%) betweenAQIvalues for Sen- (6.8%) (6.9%) (2.1%) sitive Groups Unhealthy2,227 2,129 405 0(0.0%) 0(0.0%) Pair Spearman ρ 95%CI Pearsonr (9.5%) (9.1%) (1.7%) Overall AQI - 0.968 [0.967,0.969] 0.984 Very Un- 287 255 53 0(0.0%) 0(0.0%) PM2.5AQI healthy (1.2%) (1.1%) (0.2%) Overall AQI - 0.246 [0.234,0.258] 0.405 Hazardous191 172 0(0.0%) 0(0.0%) 0(0.0%) OzoneAQI (0.8%) (0.7%) Overall AQI - 0.258 [0.246,0.270] 0.232 NO2 AQI Overall AQI - 0.601 [0.592,0.609] 0.431 Overall, 42.3% of cities are rated Good, 39.3% Mod- COAQI erateand18.1%fallabove100. Thecategorytables PM2.5 AQI - 0.146 [0.134,0.159] 0.340 OzoneAQI showthattheCOandNO sub-indicesessentiallynever PM2.5 AQI - 0.289 [0.277,0.301] 0.260 leavetheGoodcategory(23,460and23,448citiesre- NO2 AQI spectively),whereasPM2.5closelymirrorstheoverall PM2.5 AQI - 0.580 [0.572,0.588] 0.439 AQIandozonecontributesasmallerbutrealtail(2,394 COAQI citiesatModerateorworse).
Ozone AQI - 0.257 [0.269,0.245] 0.182 NO2 AQI Ozone AQI - 0.064 [0.052,0.077] 0.146 5.EmpiricalEvidencefromtheDataset COAQI NO2 AQI-CO 0.502 [0.493,0.512] 0.488 5.1 PollutantDominanceandCategoryAgreement AQI Table5.1:Pollutantwiththehighestsub-index,by overallAQIcategory Overall AQI Cities(n) PM2.5 high- Ozone high- TheoverallAQIisalmostperfectlyrank-correlatedwith category est,n(%) est,n(%) PM2.5( =0.968),moderatelywithCO( =0.60),and ρ ρ Good 9,936 5,898(59.4%) 4,037(40.6%) weaklywithozoneandNO (ρ ≈ 0.25and0.26).TheCO- Moderate 9,231 8,799(95.3%) 432(4.7%) PM2.5(ρ =0.58)andCO-NO (ρ =0.50)associationsare Unhealthy 1,591 1,446(90.9%) 145(9.1%) for Sensitive plausiblegivensharedcombustionsources,whereas Groups ozoneisnegativelycorrelatedwithNO (ρ =0.26),con- Unhealthy 2,227 1,953(87.7%) 274(12.3%) sistent with ozone titration by nitrogen oxides near Very Un- 287 236(82.2%) 51(17.8%) emissionsources.Becausethesampleislarge,allin- healthy tervalsarenarrow,andthedifferencesbetweenSpear- Hazardous 191 191(100.0%) 0(0.0%) Allcities 23,463 18,523 4,939(21.1%) manandPearsoncoefficients(forexampleforCO-AQI, (78.9%) 0.43)reflecttheinfluenceoftiedandextremevalues ratherthansamplingerror.Droppingthe191citieswith AQIof300ormorechangesthePearsoncorrelationof Ties(247citiesinwhichtwoormoresub-indicesshare theAQIwithPM2.5onlyslightly(0.984to0.982)but themaximum)areassignedtoPM2.5first.NO isthe raisesthatwithCOfrom0.43to0.57andwithozone highestsub-indexinonecityandCOinnone. from0.41to0.46,showingthatafewextremecities PM2.5isthehighestsub-indexin78.9%ofcitiesand suppressthelinearassociationofthesecondarypollu- inall191Hazardouscities,anditsdominancegrows tants.
withseverity(from59.4%ofGoodcitiesto87.7%ofUn- healthycities).OzonesetstheoverallAQImainlywhere airqualityisgoodormoderate(40.6%ofGoodcities), wherePM2.5isitselflow.Thecategorylabelsconfirm 5.3 RegressionandRelativeImportance this: PM2.5andoverallcategoriesagreein97.6%of Table5.3:RegressionoftheoverallAQIonthefour cities(Cohen’s κ =0.963,almostperfectagreement), sub-indices(n=23,463)
theNO coefficientisslightlynegative(0.036,p=0.022) andtheCOcoefficientisindistinguishablefromzero (p=0.82).TheLMGdecompositionattributes81.6%of theexplainedvariancetoPM2.5,8.4%toozone,7.6% toCOand2.4%toNO .TheCOsharearisesfromitscor- relationwithPM2.5andnotfromauniqueeffect,since itsregressioncoefficientisnull.PM2.5onitsowngives R² =0.969.Collinearityisnotaproblem(maximumVIF 1.55),buttheBreusch-Pagantestindicatesstronghet- eroscedasticity,whichiswhyrobuststandarderrors wereused.Thismodelshouldbereadasadescription ofhowthemaximum-of-sub-indicesruleappearsina linearfit,andnotasacausalorpredictivemodel,be- causetheoverallAQIisadeterministicfunctionofthe
5.4 Between-CountryHeterogeneity Predictorβ HC3SE 95%CI p Std. β LMG share Table5.4:Kruskal-WallistestofoverallAQIacross ofR² countries PM2.5 0.9801 0.0048 [0.971, <0.001 0.958 81.6% AQI 0.990] Minimum Countries Cities H p ² ϵ Ozone 0.1575 0.0058 [0.146, <0.001 0.079 8.4% citiesper AQI 0.169] country NO2 0.0362 0.0158 [0.067, 0.022 0.003 2.4% 20 107 22,518 11,167 <0.001 0.494 AQI 0.005] 30 85 21,972 10,894 <0.001 0.494 COAQI 0.0171 0.0764 [0.133, 0.823 0.001 7.6% 50 62 21,110 10,342 <0.001 0.488 0.167] Countryisadominantsourceofvariation.Acrossthe Intercept=0.604. R² =0.9746, F=224,721on4and 85countrieswithatleast30cities,theKruskal-Wallis 23,458 df, p < 0.001. Breusch-Pagan LM = 2182, p < testgivesH=10,894(p<0.001)with ϵ² =0.494,and 0.001.MaximumVIF=1.55.
theresultisstabletotheinclusionthreshold(ϵ² be- Thefoursub-indicesexplain97.5%ofthevarianceof tween0.488and0.494;Table5.4).Aone-waydecompo- theoverallAQI.PM2.5hasacoefficientcloseto1(0.980) sitionoflogAQIattributes52.6%ofvariancetocountry andozoneasmallpositivecoefficient(0.158),whereas (45.2%ontherawscale),withanintraclasscorrelation of0.537.TheshareofcitiesexceedingAQI100alsodif- 5.3% above 100, and Germany (1,345 cities) 49 and fersstronglybycountry( 2 =10,273,84df,p<0.001, 0.1%.TheWilsonintervalsforcountrieswithabout30 χ Cramér’sV=0.68),rangingfromzeroin22countriesto to40citiesarewide(forexampleNepal43.7%-75.3%), 97%intheworstcase. Inpracticalterms,knowinga sotheorderingamongcountrieswithsmallsamples city’scountrytellsusaboutasmuchaboutitsAQIas andsimilarmediansisnotreliable.Becausethedata allremaininginformationcombined.
containonerowpercitywithnopopulationweights, countrysummariesdescribethesampledcities,not Table5.5:Tencountrieswiththehighestmedian thepeoplelivinginacountry.
AQI(atleast30cities) Country Cities Median Mean % AQI > 95% Wil- (IQR) 100 sonCI 5.5 PredictiveModellingandtheEffectofValida- Pakistan 307 169(159- 178.8 96.4% [93.7%, tionDesign 184) 98.0%] Table5.7:PredictingthePM2.5sub-indexfromCO, Senegal 33 157(146- 152.4 97.0% [84.7%, 169) 99.5%] ozoneandNO2 (ten-foldrandomcross-validation) India 2488 153 153.0 70.9% [69.1%, (89-172) 72.7%] Model R² (SD) RMSE MAE China 795 137 127.0 65.5% [62.2%, Linearregres- 0.281(0.052) 46.4 28.0 (82-164) 68.8%] sion Nepal 33 120 116.4 60.6% [43.7%, Ridge 0.281(0.052) 46.4 28.0 (68-150) 75.3%] k-NN(k=15) 0.335(0.028) 44.7 26.5 Uzbekistan58 120 119.1 63.8% [50.9%, Random for- 0.371(0.030) 43.4 25.0 (89-146) 74.9%] est Iran 179 105 108.3 51.4% [44.1%, Gradient 0.374(0.030) 43.3 25.0 (74-148) 58.6%] boosting Dominican38 104 108.1 57.9% [42.2%, Republic (80-129) 72.1%] Bangladesh80 100 113.5 48.8% [38.1%, (68-159) 59.5%] SDofPM2.5sub-index=54.8.Aconstantmedianpre- El Sal- 33 98 (75- 97.4 48.5% [32.5%, dictionhasMAE=34.1.
vador 110) 64.8%] Table5.8:DifferenceinfoldR² relativetolinear regression(correctedresampledt-test) Table5.6:TencountrieswiththelowestmedianAQI (atleast30cities) Model Mean R² differ- Correctedp Country Cities Median Mean % AQI > 95% Wil- ence (IQR) 100 sonCI Ridge 0.000 0.710 Bolivia 33 20 (14- 23.8 0.0% [0.0%, k-NN(k=15) 0.053 0.084 29) 10.4%] Randomforest 0.089 0.008 Argentina 68 22 (17- 28.2 1.5% [0.3%, Gradientboosting 0.093 0.004 31) 7.9%] Madagasca6r5 25 (22- 31.0 0.0% [0.0%, 41) 5.6%] Theco-pollutantsexplainonlyamodestpartofthe Tanzania 229 27 (21- 31.6 0.9% [0.2%, PM2.5sub-index(R² =0.28forlinearregressionand 36) 3.1%] Australia 85 27 (23- 33.6 3.5% [1.2%, 0.37forgradientboosting),whichisconsistentwiththe 32) 9.9%] weak-to-moderatecorrelationsinTable5.2.Random Peru 128 32 (25- 36.4 3.1% [1.2%, forestandgradientboostingimprovesignificantlyon 44) 7.8%] thelinearmodel(correctedp=0.008and0.004),while Finland 81 34 (30- 38.4 3.7% [1.3%, 36) 10.3%] ridgeregressionisidenticaltoitandk-NNisnotsignifi- Myanmar 59 34 (26- 40.2 1.7% [0.3%, cantlybetter.EventhebestmodelleavesanRMSEof 51) 9.0%] 43.3indexpoints(MAE25.0,against34.1foraconstant Lithuania 38 35 (34- 38.1 0.0% [0.0%, prediction),soPM2.5cannotbereliablyinferredfrom 40) 9.2%] Portugal 153 35 (29- 34.6 0.0% [0.0%, theotherpollutants. Partofthenonlineargainmay 40) 2.4%] reflectcountry-specificcombinationsofsub-indices, whichtheclassificationexperimentbelowexamines directly.
Amongthelargestsamples,India(2,488cities)hasa medianAQIof153with70.9%ofcitiesabove100,and Table5.9:PredictingAQI>100fromCO,ozoneand China(795cities)amedianof137(65.5%above100). NO underrandomandcountry-grouped TheUnitedStates(2,872cities)hasamedianof55and cross-validation
gression (0.017) (0.051) Random 0.881 0.847 0.503 0.972 forest (0.013) (0.065) Gradient 0.880 0.850 0.493 0.978 boosting (0.014) (0.056) Prevalence of AQI > 100 = 0.181; threshold 0.5. For comparison,theAUCofPM2.5aloneis0.998,CO0.781, ozone0.653andNO 0.600.
Table5.10:Effectofacountrytargetencodingon gradientboosting
CV, country WithoutPM2.5,theotherthreesub-indicesstillsepa- encoding rateunhealthyfromhealthiercitiesreasonablywell Grouped 0.841(0.059) 0.499 0.965 (grouped-CVAUC0.86-0.85),drivenmostlybyCOand CV, country encoding ozone,butsensitivityisonlyabout0.49atthedefault Grouped CV, 0.850(0.056) 0.493 0.978 thresholdbecause82%ofcitiesarehealthy.Thevali- no country dationdesignmatters.Underrandomcross-validation, information randomforestandgradientboostingappearclearly betterthanlogisticregression(AUC0.881and0.880 RQ1Consistency AQI = maximum Table4.2 against0.835).Undercountry-groupedcross-validation sub-index in theadvantagedisappearsandtheorderingreverses 99.4%;141excep- (0.847and0.850against0.855;correctedp=0.71and tions at extreme 0.77). Theflexiblemodelswerethereforeexploiting PM2.5 country-specificpatternsthatareunavailableforanew RQ2 Dominant PM2.5 highest in Table5.1 country.Thetarget-encodingexperimentmakesthis pollutant 78.9%ofcities; κ =0.96 explicit(Table5.10):addingacountryencodingraises RQ3Contribution PM2.5 explains Table5.2,5.3 theAUCto0.968underrandomcross-validationbut 81.6%ofAQIvari- leavesitat0.841, nobetterthanthemodelwithno anceexplained countryinformation, oncewholecountriesareheld RQ4 Heterogene- ICC = 0.54; ² = Table5.4-5.6 ϵ out. Fold-to-foldvariationisalsothreetofourtimes ity 0.49 largerundergroupedcross-validation(SDabout0.05 RQ5Prediction Grouped CV AUC Table5.9,5.10 0.86;nogainover against0.017),reflectingheterogeneitybetweencoun- logisticregression tries.
CountryexplainsabouthalfofthevariationinlogAQI 6.ComparativeAnalysisandDiscussion (ICC0.54),andmedianAQIrangesfrom20to169across 6.1 RQ1:Structureandconsistencyofthedataset countrieswithatleast30cities.Thetenhighest-median Thedatasetiscompleteforallnumericfieldsandhas countriesareconcentratedinSouthandCentralAsia, noduplicates,butitisnotfullyinternallyconsistent. WestAfricaandpartsoftheMiddleEastandCaribbean, TheoverallAQIequalsthemaximumsub-indexin99.4% whereasthelowestareinSouthAmerica,Oceania,North- ofrows,astheEPArulerequires,butexceedsitin141 ernandSouthernEuropeandpartsofAfrica.Thesampled- extreme-PM2.5cities,and148labelsplaceboundary citydesign,smallsamplesformanycountriesandthe valuesinthehighercategory. Countryismissingfor absenceofpopulationweightsmeanthatthesefigures 1.8% of rows. None of these issues is large, but all describemonitoredorreportedcitiesandnotnational shouldbedocumented,andanalysesthatuselabels populations(anecologicalcaveat).
insteadofvalueswillgiveslightlydifferentcounts. 6.5 RQ5:Predictionandtheroleofvalidation 6.2 RQ2:Distributionsandthedominantpollutant Themostimportantmethodologicalfindingofthisre- Allsub-indicesarestronglyright-skewed,andCOand view concerns validation. Random cross-validation NO are nearly constant on the index scale, so they lets cities from the same country appear in training carrylittleinformationabouttheoverallAQI.PM2.5is andtestfolds,andflexiblemodelsandtargetencoding thehighestsub-indexin78.9%ofcitiesandinevery thenexploitcountrysignatures.Whenwholecountries Hazardouscity,whereasozonemattersmainlywhere areheldout,theapparentgainfromnonlinearmod- airisalreadygood. Inanindex-baseddataset,there- elsandfromcountryencodingdisappears(Tables5.9 fore, the overall AQI is in practice a PM2.5 indicator and5.10).Anystudythatreportshighaccuracyonthis withanozonefloor. Userswhoneedinformationon datasetshouldstatewhetheritsvalidationseparates gaseouspollutantsshouldworkwithconcentrations, countries. Thisparallelsthelook-aheadandleakage notwiththisindex.
problemsthathavebeendocumentedinotherfore- castingfields.
6.3 RQ3:Associationandrelativeimportance TheoverallAQIisalmostperfectlyrank-correlatedwith 7.ChallengesandLimitations PM2.5(ρ =0.97),andtheLMGdecompositionattributes 7.1 MethodologicalChallenges 81.6%oftheexplainedvariancetoit.Thesecondary Deterministicoutcome:theoverallAQIisthemaximum pollutantsmatterthroughozonealone;COandNO ofthesub-indices,soregressionofAQIonitscompo- havenouniquecontribution.BecausetheoverallAQI nentsisstructural,notexplanatory.
isadeterministicmaximum,theseresultsdescribethe indexconstructionandshouldnotbetakenasevidence Indexversusconcentration:sub-indicesarenonlinear abouttherelativehealthimportanceofthepollutants. transformationsofconcentration;correlationsandre- gressionsontheindexscalecandifferfromthoseon concentrations.
6.4 RQ4:Between-countryheterogeneity Table6.1:Summaryofevidencebyreviewquestion Extremevalues:afewhundredveryhighobservations influencelinearsummaries(Section5.2);rank-based (iii)statehowboundaryvaluesandmissingcountries andlog-scalemethodswereusedforthisreason. arehandled;(iv)reportsamplesizeswitheverycountry summary;(v)usecountry-groupedvalidationforany Untunedmodels:defaulthyperparameterswereused, predictiveclaim;(vi)compareagainstasimplebaseline somodelcomparisonsrefertodefaultconfigurations. suchaslogisticregression.
7.2 DataChallenges Undocumentedprovenance:thedatasource,measure- 9.Conclusion mentdateandaveragingperiodarenotstatedinthe The Global Air Pollution Dataset is a convenient re- file.
sourcewhosestatisticalstructureiseasytomisread. Singlesnapshot: thereisnotimedimension,sosea- Threeconclusionsarerobust.First,theoverallAQIis sonality,trendsandepisodescannotbestudied. effectivelyaPM2.5indicator:PM2.5isthehighestsub- Unevensampling:countrysamplesizesrangefrom1 indexin78.9%ofcitiesandaccountsfor81.6%ofthe to 2,872 cities (median 28), and city coverage is not explainedvarianceinAQI,whileCOandNO arenearly population-weighted.
constant.Second,geographydominates:countryex- plainsroughlyhalfofthevariationinAQI(ICC0.54), Nocoordinates:theabsenceoflatitudeandlongitude withmedianAQIdifferingabouteight-foldbetween preventsanyanalysisofspatialautocorrelation. thecleanestandmostpollutedcountries.Third,pre- Limitedpollutants: PM10andSO arenotincluded, 2 dictiveperformancereportedonthisdatasetdepends andCOandNO arenearlyconstantontheindexscale. criticallyonthevalidationdesign:modelsthatappear toimproveonlogisticregressionunderrandomcross- 7.3 ReportingChallenges validationdonotdosowhenwholecountriesareheld Accuracyreportedwithoutstatingwhethervalidation out.Futurestudiesshoulddocumentthedatasource, separatescountries.
analyseconcentrationsratherthanindiceswherepos- Useofcategorylabelsinsteadofvalues,withinconsis- sible,reportuncertaintyforcountrysummaries,and tenttreatmentofboundaryvalues.
validatepredictivemodelsacrosscountries. Country-levelrankingspublishedwithoutsamplesizes orconfidenceintervals.