A Comparison of Rule-based Analysis with Regression Methods in Understanding the Risk Factors for Study Withdrawal in a Pediatric Study

1 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 www.na u e.com/scien i ic epo s A Compa ison o Rule-based Analysis wi h Reg ession Me hods in Unde s anding he Risk Fac o s o S udy Wi hd awal in a Pedia ic S udy Mona Haghighi1, Suzanne Benne Johnson2, Xiaoning Qian3, K is ian F. Lynch4, Kend a Vehik4, Shuai Huang5 & The TEDDY S udy G oup† Reg ession models a e ex ensi ely used in many epidemiological s udies o unde s and he linkage be ween speci ic ou comes o in e es and hei isk ac o s. Howe e , eg ession models in gene al examine he a e age e ec s o he isk ac o s and igno e subg oups wi h di e en isk p o iles. As a esul , in e en ions a e o en gea ed owa ds he a e age membe o he popula ion, wi hou conside a ion o he special heal h needs o di e en subg oups wi hin he popula ion. This pape demons a es he alue o using ule-based analysis me hods ha can iden i y subg oups wi h he e ogeneous isk p o iles in a popula ion wi hou imposing assump ions on he subg oups o me hod. The ules de ine he isk pa e n o subse s o indi iduals by no only conside ing he in e ac ions be ween he isk ac o s bu also hei anges. We compa ed he ule-based analysis esul s wi h he esul s om a logis ic eg ession model in The En i onmen al De e minan s o Diabe es in he Young (TEDDY) s udy. Bo h me hods de ec ed a simila sui e o isk ac o s, bu he ule-based analysis was supe io a de ec ing mul iple in e ac ions be ween he isk ac o s ha cha ac e ize he subg oups. A u he in es iga ion o he pa icula cha ac e is ics o each subg oup may de ec he special heal h needs o he subg oup and lead o ailo ed in e en ions. Unde s anding he ac o s associa ed wi h he isk o indi iduals wi hd awing om a s udy is an impo an i s s ep owa ds iden i ying he e en ual heal h needs o di e en indi iduals wi hin a popula ion1. This lays he ounda ion o de elop and deli e app op ia e esou ces o he igh a ge s, called “ ailo ed heal h in e en ions”. E idence sugges s ha indi iduals p e e ailo ed ca e o a s anda dized ca e ha is designa ed o he a e age popula ion2–5. The e o e, heal h p o essionals need o iden i y he subg oups o indi iduals cha ac e ized by di - e en pa e ns o isk ac o s. Howe e , a he han iden i ying subg oups, adi ional in e en ion s udies o en ocus on iden i ica ion o isk ac o s ha a e associa ed wi h he ou come o in e es o he popula ion as a whole1,6,7. One commonly adop ed app oach is o use logis ic eg ession o iden i y ac o s associa ed wi h s udy wi hd awal8–10. Howe e , his app oach only models he a e age e ec s o he isk ac o s. Consequen ly, i is likely ha he in e en ions de eloped om eg ession models will be gea ed owa d he a e age membe o he popula ion, wi h less conside a ion o he special needs o di e en subg oups11. The aim o he p esen s udy is o illus a e he use o he ule-based analysis12–14 as an explo a o y echnique in an epidemiologic con ex . The ule-based analysis12–14 is pa icula ly use ul o iden i ying he subg oups embed- ded in a da ase —whose membe s sha e simila isk pa e ns— ha in luence he ou come o in e es . A ule 1Depa men o Indus ial and Managemen Sys ems Enginee ing, Uni e si y o Sou h Flo ida, Tampa, Flo ida, USA. 2Depa men o Beha io al Sciences and Social Medicine, College o Medicine, Flo ida S a e Uni e si y, Tallahassee, Flo ida, USA. 3Depa men o Elec ical and Compu e Enginee ing, Texas A&M Uni e si y, College S a ion, Texas, USA. 4Heal h In o ma ics Ins i u e, Uni e si y o Sou h Flo ida, Tampa, Flo ida, USA. 5Depa men o Indus ial & Sys ems Enginee ing, Uni e si y o Washing on, Sea le, Washing on, USA. †A comp ehensi e lis o conso ium membe s appea s a he end o he pape . Co espondence and eques s o ma e ials should be add essed o S.H. (email: [email p o ec ed]) ecei ed: 07 Ap il 2016 Accep ed: 11 July 2016 Published: 26 Augus 2016 OPEN www.na u e.com/scien i ic epo s/ 2 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 desc ibes he ange o alues on one o mo e isk ac o s ha a e associa ed wi h ei he an inc ease o dec ease in isk o wi hd awal in a subse o indi iduals. Thus, ules p o ide a na u al seman ics o de ine he isk pa e n o subse s o indi iduals while each ule may indica e a speci ic unme heal h need o wa ning signal o s udy wi hd awal. By iden i ying he unknown ules om obse a ional s udies, a comp ehensi e se o isk-p edic i e ules can be conside ed as a se o senso s, p o iding us pe sonalized isk es ima ion by looking in o he isk pa e ns endo sed by each indi idual. Speci ically, we used a ecen ly de eloped ule-disco e y algo i hm o he ule-based analysis, he RuleFi me hod14, which is one example om a huge a ay o ule-based me hods ha a e p omising o epidemiologic esea ch. The RuleFi me hod has an ad an age o e logis ic eg ession because i elies on a nonpa ame ic model wi h ewe modeling assump ions, andom o es 13, which is capable o iden i ying he isk p edic i e ules. The e is no need o explici ly include co a ia e in e ac ions o ans o ma ions in o he model because o he ecu si e spli ing s uc u e used in gene a ing he andom o es . Also, he ule-based analysis pe mi s an indi idual’s isk o be p edic ed on he basis o only one, o a mos a ew, isk ac o s, whe eas sco es de i ed om eg ession models equi e ha all co a ia es be a ailable. We demons a e he ule-based analysis using da a om a la ge mul ina ional epidemiological na u al his o y s udy o ype 1 diabe es melli us (T1DM), he En i onmen al De e minan s o Diabe es in he Young (TEDDY) s udy15. Speci ically, we use he ule-based analysis o p edic ing s udy wi hd awal du ing he i s yea o he TEDDY s udy, by e ec i ely in eg a ing he psychosocial, demog aphic, and beha io al isk ac o s collec ed a s udy incep ion. We compa e he ule-based analysis wi h a p e ious analysis ha was conduc ed on he same da a10. The p e ious analysis used adi ional logis ic eg ession me hods o iden i y ac o s collec ed a s udy incep ion ha we e s ongly associa ed wi h s udy wi hd awal du ing he i s yea o TEDDY10. Howe e , he way hese ac o s in e ac wi h each o he and he way hese in e ac ions migh de ine subg oups in he s udy popula ion wi h di e en isk le els emain unknown. The e o e, we es ed he hypo hesis ha he ule-based analysis can iden i y he isk-p edic i e ules use ul o s a i ying he s udy popula ion in o di e en subg oups wi h di e en isk le els o s udy wi hd awal in he i s yea o TEDDY. The p e ious analysis10 p o ided us an oppo uni y o c i ically e alua ing he po en ial added alue o a ule-based analysis o e ha p o ided by adi- ional logis ic eg ession me hods. Also, we conside ed how he ule-based me hod could lead o mo e in o med in e en ion s a egies o p io i iza ion o he in e en ion alloca ion o he s udy pa icipan s. By conduc ing his compa ison, we also hoped o iden i y some p ac ical guidelines o when we should use ule-based me hods and when eg essions model would be mo e p e e able, en iching he analy ic oolbox o oday’s epidemiologis s o add ess he eme ging da a challenges. Ma e ials and Me hods The TEDDY s udy. TEDDY is a na u al his o y s udy ha seeks o iden i y he en i onmen al igge s o au oimmuni y and T1DM onse in gene ically a - isk child en iden i ied a h ee cen e s in he Uni ed S a es (Colo ado, Washing on, and Geo gia/Flo ida) and h ee cen e s in Eu ope (Finland, Ge many, and Sweden). In an s om he gene al popula ion wi h no immedia e amily his o y o T1DM, as well as in an s who ha e a i s deg ee ela i e wi h T1DM, a e sc eened o gene ic isk a bi h using human leukocy e an igen geno yping. Pa en s wi h in an s a inc eased gene ic isk o T1DM a e in i ed o pa icipa e in TEDDY. Pa en s a e ully in o med o he child’s inc eased gene ic isk and he p o ocol equi emen s o he TEDDY s udy, including he equi emen ha eligible in an s mus join TEDDY be o e he in an is 4.5 mon hs o age. The TEDDY p o ocol is demanding wi h s udy isi s o blood d aws and o he da a and sample collec ion scheduled e e y h ee mon hs du ing he i s ou yea s o he child’s li e and biannually he ea e . Pa en s a e also asked o keep de ailed eco ds o he child’s die , illnesses, li e s esses and o he en i onmen al exposu es. TEDDY ob ains w i en con- sen om he pa en s sho ly a e child’s bi h o ob aining gene ic and o he samples om he in an and also pa en s. De ailed s udy design and me hods ha e been p e iously published15. The s udy me hods ha e been ca - ied ou in acco dance wi h he app o ed guidelines by local Ins i u ional Re iew o E hics Boa ds and moni o ed by an Ex e nal E alua ion Commi ee o med by he Na ional Ins i u es o Heal h. The expe imen al p o ocols o he s udy we e app o ed by he Na ional Ins i u e o Heal h. S udy sample. This analysis ocused on wo g oups o amilies om he gene al popula ion used in he p e ious logis ic eg ession s udy10: 2,994 amilies who had been ac i e in TEDDY o ≥ 1 yea and 763 amilies who wi hd ew om TEDDY du ing he i s yea . Bo h he p io and cu en analyses we e limi ed o gene al popula ion amilies because s udy wi hd awal among he i s deg ee ela i es popula ion was a e. S udy a iables. S udy a iables we e selec ed om da a collec ed on he sc eening o m a he ime o he child’s bi h and om in e iew and ques ionnai e da a collec ed a he baby’s i s TEDDY isi . These a iables included: demog aphic cha ac e is ics—TEDDY coun y (Finland, Ge many, Sweden, Uni ed S a es); mo he ’s age (in yea s); child’s gende ; ma e nal heal h du ing p egnancy‒ numbe o illnesses, ges a ional diabe es o ype 2 diabe es (yes/no); mo he ’s li es yle beha io s du ing p egnancy—smoked a any ime du ing p egnancy (yes/ no), alcohol consump ion (no alcohol, 1–2 imes pe mon h, ≥ 3 imes pe mon h du ing each imes e ), employ- men s a us (wo ked du ing all 3 imes e s/did no wo k a all o educed wo k hou s); baby’s heal h s a us‒ bi h complica ions (yes/no), heal h p oblems since bi h (yes/no), hospi aliza ions a e bi h (yes/no); numbe o s ess ul li e e en s du ing and a e p egnancy; mo he ’s emo ional s a us including wo y and sadness du ing p egnancy ( a ed on 5 poin scales), anxie y abou he child’s isk o de eloping diabe es measu ed by a six-i em scale adap ed om he S a e componen o he S a e-T ai Anxie y In en o y2–4; he accu acy o he mo he ’s pe - cep ion o he child’s isk o de eloping diabe es (accu a e: indica ing he child’s T1DM isk was highe o much highe han o he child en’s T1DM isk; inaccu a e: indica ing he child’s T1DM isk was he same, somewha www.na u e.com/scien i ic epo s/ 3 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 lowe o much lowe han o he child en’s T1DM isk); and whe he he child’s a he comple ed he ini ial s udy ques ionnai e (yes/no). P e ious logis ic eg ession esul s. Mul iple logis ic eg ession models we e used o iden i y signi ican p edic o s o ea ly wi hd awal om TEDDY. Va iables we e en e ed in blocks in he ollowing o de : demo- g aphic a iables (coun y o esidence, child’s gende , mo he ’s age); p egnancy/bi h a iables (ma e nal diabe- es, illness in mo he o child, bi h complica ions, ma e nal smoking; ma e nal d inking; ma e nal employmen ou side he home, ma e nal wo y o sadness du ing p egnancy, numbe o s ess ul li e e en s occu ing du ing p egnancy o a e he child’s bi h); a he ’s pa icipa ion in TEDDY de ined by a he ’s comple ion o a b ie ques ionnai e; and mo he ’s eac ions o he baby’s inc eased T1DM isk (anxie y and accu acy o mo he ’s pe - cep ion o he child’s T1DM isk). Nine pe cen o he s udy sample (N = 326) had missing da a on one o mo e a iables. As expec ed, hose subjec s who had di icul y in complying wi h all da a collec ion (35%) we e mo e likely o wi hd aw han hose wi h high da a collec ion compliance (19%). While i is unknown wha is he unde - lying mechanism ha could explain his associa ion, we suspec ha his could indica e ha he pe cen age o missing da a is a good indica o ha sugges s a need o TEDDY s udy o be e communica e wi h pa icipan amilies and emo e any possible di icul ies o hem o pa icipa e in he s udy. The analysis was i s comple ed o hose wi h no missing da a and hen e un o he ull sample using mul iple impu a ion me hods o gene a e app op ia e pa ame e es ima es o missing da a using he P oc MI and P oc MIANALYZE p ocedu es a ailable om SAS 9.15. Table1 p o ides he esul s o he inal logis ic eg ession model o he sample o 3,431 TEDDY pa icipan s wi h no missing da a. The model was highly signi ican (Chi-Squa e = 264.87 (12), p < 0001) and accu a ely placed 81.6% o he sample in o hei espec i e g oup (Ac i es e sus Wi hd awals). The da a in Table1 also p o ides he inal logis ic eg ession model o he o al sample, wi h mul iple impu a ion me hods used o eplace missing da a. Because he ea ly wi hd awal a e was highe among pa icipan s wi h missing da a, we added a a iable o he impu ed model, > 1 missing da a poin (yes/no). The p esence o > 1 missing da a poin s p edic ed ea ly d op-ou o e and abo e all o he a iables in he model. The desc ip i e in o ma ion o each o he signi ican p edic o s is p o ided in Table2. S a is ical me hods. Basic idea o he RuleFi me hod. We use RuleFi 14 o disco e he hidden ules ha may be p edic i e o he isk o ea ly wi hd awal in subse s o TEDDY indi iduals. A ule consis s o se e al in e - ac ing isk ac o s and hei anges. We a e in e es ed in he ules by which he subjec s can be s a i ied by dis- inc isk le els. Fo example, a ule consis ing o S a e Anxie y In en o y Sco e > 45 and Dad Pa icipa ion = NO P edic o a iable Sample wi h No Missing Da a (N= 3431) Sample wi h missing da a impu ed (N = 3757) Es ima e SE P- alue OR 95% Con idence In e al βSE P- alue In e cep 1.126 0.424 0.008 0.982 0.400 0.014 Coun y Uni ed S a es e e Finland − 0.420 0.130 0.001 0.657 0.509 0.848 − 0.431 0.123 0.0004 Ge many 0.278 0.222 0.211 1.321 0.854 2.042 0.154 0.218 0.481 Sweden − 0.342 0.110 0.002 0.711 0.572 0.882 − 0.346 0.104 0.002 Child sex emale No e Yes 0.160 0.092 0.081 2.316 1.840 2.915 0.217 0.086 0.012 Ma e nal age (yea s) − 0.058 0.009 < 0.0001 0.944 0.927 0.961 − 0.053 0.009 < 0.0001 Ma e nal Li es yle Beha io s du ing P egnancy Smoked No e e Yes 0.841 0.117 < 0.0001 2.318 1.841 2.918 0.803 0.117 < 0.0001 Alcohol consump ion in las imes e None e 1–2 imes/mon h − 0.343 0.148 0.020 0.709 0.531 0.948 − 0.280 0.140 0.045 > 2 imes/mon h − 0.424 0.319 0.183 0.654 0.350 1.222 − 0.401 0.299 0.180 Wo ked all imes e s No e e Yes − 0.396 0.095 < 0.0001 0.673 0.559 0.811 − 0.364 0.090 < 0.0001 Dad pa icipa ion No e e Yes − 0.569 0.162 0.0005 0.566 0.412 0.778 − 0.608 0.146 < 0.0001 Risk pe cep ion Unde es ima e e e Accu a e − 1.257 0.375 0.0008 0.284 0.137 0.593 − 1.032 0.354 0.004 S a e Anxie y In en o y sco e 0.001 0.006 0.835 1.001 0.989 1.014 0.001 0.006 0.825 S a e Anxie y In en o y sco e x isk pe cep ion 0.023 0.009 0.011 1.023 1.005 1.041 0.018 0.009 0.039 > 1 missing da a poin s 1.321 0.464 0.007 Table 1. P e ious logis ic eg ession esul s o he sample wi h no missing da a and he o al sample wi h missing da a impu ed: Va iables associa ed wi h s udy wi hd awal in he i s yea o TEDDY. (Rep in ed om Johnson, S. B. e al.10 wi h pe mission om John Wiley and Sons Inc). www.na u e.com/scien i ic epo s/ 4 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 would be use ul i he subjec s who can be cha ac e ized by his ule ha e a highe isk o ea ly wi hd awal. RuleFi is a compu a ional algo i hm ha can scale up o high-dimensional applica ions (e.g., wi h a la ge num- be o a iables) o ule disco e y, which is capable o exhaus i ely sea ching o po en ial ules on a la ge num- be o candida e isk ac o s. I has wo phases, he “ ule gene a ion phase” and “ ule p uning phase”. Rule gene a ion. A his s age, andom o es 13 is used o exhaus i ely sea ch o candida e ules o e he po en- ial isk ac o s. Random o es is a high-dimensional ule disco e y app oach ha ex ends adi ional decision ee models12. Speci ically, a andom o es es ima es a numbe o ees, wi h each ee being es ima ed on a ela- i ely homogenous subpopula ion gene a ed by boo s apping he o iginal da ase . Since each ee employs a se o ules o cha ac e ize a subpopula ion, he andom o es is ac ually a comp ehensi e collec ion o ules ha a e able o cha ac e ize he whole da ase . Cha ac e is ic Ac i es (n = 2994) Wi hd awals (n = 763) To al Sample (n = 3757) Coun y N (%) N (%) N Finland 747(84%) 140(16%) 887 Ge many 106(75%) 36(25%) 142 Sweden 1052(82%) 231(18%) 1283 Uni ed S a es 1089(75%) 356(25%) 1445 Child sex N (%) N (%) N Male 1538 (81%) 352 (19%) 1890 Female 1456 (78%) 411 (22%) 1867 Ma e nal age (yea s) M (SD) M (SD) M (SD) 30.8 (5.0) 28.5 (5.7) 30.4(5.2) Ma e nal Li es yle Beha io s Du ing P egnancy Smoking N (%) N (%) N Smoked 296(63%) 171(37%) 467 Did no smoke 2602(84%) 510(16%) 3112 Da a missing 96(54%) 82(46%) 178 Alcohol consump ion a 3 d imes e N (%) N (%) N Alcohol 1-2 imes pe mon h 474(87%) 72(13%) 546 Alcohol ≥ 3 ime pe mon h 105(89%) 13(11%) 118 No alcohol 2359(79%) 609(21%) 2968 Da a missing 56(45%) 69(55%) 125 Employmen s a us N (%) N (%) N Wo ked all 3 imes e s 1418(85%) 251(15%) 1669 Reduced wo k, qui , o did no wo k a all 1426(77%) 417(23%) 1843 Da a missing 150(61%) 95(39%) 245 Dad Pa icipa ion in TEDDY N (%) N (%) N Pa icipa ed 2813(82%) 624(18%) 3437 Did No Pa icipa e 181(57%) 139(43%) 320 Ma e nal Reac ions o Child’s Inc eased TIDM Risk Risk pe cep ion N (%) N (%) N Accu a e 1809(84%) 355(16%) 2164 Unde es ima e 1132(77%) 343(23%) 1475 Da a missing 53(45%) 65(55%) 118 S a e Anxie y In en o y sco e M (SD) M (SD) M (SD) To al Sample 38.7(9.7) 40.8(10.6) 39.1(9.9) Risk Pe cep ion: Accu a e 38.8(10.2) 41.7(10.4) 39.3(9.6) Risk Pe cep ion: Unde es ima e 38.4(10.2) 39.9(10.8) 38.8(10.4) N (%) N (%) N Da a missing 46 (42%) 63 (58%) 109 Missing Da a N (%) N (%) N ≤ 1missing da a poin s 2944 (81%) 695 (19%) 3639 > 1 missing da a poin s 50 (42%) 68 (58%) 118 Table 2. Cha ac e is ics o TEDDY Ac i es and Wi hd awals. (Rep in ed om Johnson, S. B. e al.10 wi h pe mission om John Wiley and Sons Inc). www.na u e.com/scien i ic epo s/ 5 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 Rule p uning. As a heu is ic and exhaus i e sea ch app oach, he andom o es may p oduce a la ge numbe o ules ha can be edundan o i ele an o p edic ing ea ly wi hd awal due o o e i ing. To add ess his, he spa se eg ession model16,17 can be applied o selec a minimum se o isk-p edic i e ules, by using all he po en ial ules as p edic o s and he wi hd awal s a us as he ou come. The spa se eg ession model is a high-dimensional a iable selec ion model ha can be applied on a la ge numbe o a iables, and has been widely used in bioin o ma ics and sys ems biology18,19. In wha ollows, we illus a e he de ails o how he RuleFi me hod uses he h ee models, he decision ee, andom o es , and spa se linea eg ession models, in he ule gene a ion s age and he ule p uning s age: S age 1 o RuleFi - Rule gene a ion. Rule gene a ion is compu a ionally challenging, since he numbe o po en- ial ules g ows exponen ially in ela ionship o he numbe o isk ac o s. Gi en such a la ge numbe o po en ial ules, an in elligen ule gene a o is needed o na ow down he sea ch by e ec i ely de ec ing high-quali y isk-p edic i e ules. Decision ee lea ning me hod p o ides such an in elligen ule gene a o . A decision ee is a echnique o segmen ing he popula ion in o di e en subg oups using a se o ules. Fo example, we use he decision ee model o analyzing he TEDDY da ase o di ide he popula ion in o homogeneous subg oups based on he pe cen age o s udy wi hd awals in each subg oup. The decision ee model is a nonpa ame ic me hod ha au oma ically explo es he gi en isk ac o s and hei in e ac ions o a ee ha has high accu acy in p edic ing s udy wi hd awal. In ou analysis, as shown in Fig.1, h ee subg oups wi h dis inc isk le els a e iden i ied and can be cha ac e ized by ules de ined by ma e nal age, smoking s a us, numbe o missing da a, and a geog aphical indica o o Finland. Fo example, he le mos node cha ac e izes a subg oup o subjec s, in which all o hem ha e Ma e nal age < 27.5 and Finland = NO. The isk o s udy wi hd aw in his subg oup is 0.38. This analysis demons a es ha he decision ee model is a powe ul ool o de ec ing he subg oups ha can be cha ac e ized by ules. No e ha , he cu -o alue o each ac o used in Fig.1 is au oma ically de e mined by he Recu si e Pa i ioning Algo i hm (RPA). One limi a ion o he decision ee is ha only exclusi e ules can be iden i ied. Fo ins ance, he decision ee in Fig.1 implies ha each pa icipan can only be cha ac e ized by one single ule, which doesn’ conside he possibili y ha a pa icipan may ha e mul iple isk pa e ns cha ac e ized by di e en ac o s o di e en in e ac ions be ween ac o s. As a emedy, andom o es 13 is a high-dimensional ule disco e y app oach ha ex ends adi ional decision ee models. I es ima es a numbe o ees: in each i e a ion, we es ima e a decision ee on a boo s apped sample o he aining se , and his p ocess i e a es un il he p e-speci ied numbe o ees is achie ed13. To unde s and he andom o es , i is wo h men ioning ha he essence o his i e a i e p ocedu e is o gene a e a la ge numbe o subs an ially di e en ees, since he mo e simila he ees a e, he less ad an age es ima ing mul iple ees has. In o de o achie e his goal, andomiza ion me hods a e used, which is he eason o he name “ andom o es ”. Speci ically, in es ima ing each ee, he boo s ap echnique is used o gene a - ing a di e en aining sample by andomly eweigh ing he o iginal da ase . Subsequen ly, in he es ima ion o each ee, a subse o isk ac o s is andomly selec ed o es ima ing he ee. The e o e, as each ee is buil o a sub-popula ion using a subse o isk ac o s, he he e ogenei y o he pa icipan s is well add essed in he andom o es model, inc easing he likelihood o de ec ing meaning ul isk-p edic i e ules o di e en subg oups13. As each ee can be decomposed o a numbe o ules, e.g., in Fig.1, we could ex ac a leas i e ules while each ule co esponds o a lea node in he ee, wi h andom o es we could collec many ules. Figu e 1. A decision ee lea ned om he TEDDY da a. www.na u e.com/scien i ic epo s/ 6 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 S age 2 o RuleFi - Rule p uning. Rule p uning is essen ially a p ocedu e o selec ing a subse o ules ou o a pool o q candida e ules, deno ed as R = [R1, R2, … , Rq], which a e p edic i e o he ou pu a iable Y. This p ob- lem is pa icula ly challenging in high-dimensional se ings whe e we ha e a la ge numbe o gene a ed ules and q is la ge. One solu ion o selec he mos c i ical ules is o adop he Leas Absolu e Sh inkage Selec ion Ope a o (LASSO)16, which is a spa se linea eg ession model ha is capable o iden i ying a subse o ele an a iables ou o a huge lis o candida e a iables. Speci ically, he o mula ion o LASSO is βλβ−+. β minY R(1) 2 2 1 He e, he squa e e o e m, β−YR 2 2 is used o measu e he model i . The L1-no m penal y e m ||β||1 (16), de ined as he sum o he absolu e alues o all elemen s in β, is used o measu e he complexi y o he eg ession model. The use -speci ied penal y pa ame e , λ, aims o achie e an op imal balance be ween he model i ness and model complexi y – la ge λ will esul in spa se es ima e o β. I has been shown ha LASSO is consis en on a iable selec ion bo h om heo e ical esea ch16 and empi ical s udies17–20. E icien algo i hms ha e been de eloped o sol e he op imiza ion p oblem, such as he shoo ing algo i hm16, p oximal g adien algo i hms17, e c. Th ough LASSO, we expec ha he ules wi h c i ical isk ac o pa e ns will be iden i ied wi h con olled edundancy. In ou s udy, since he ou pu a iable Y, i.e., he wi hd awal s a us, is a bina y a iable, he spa se logis ic eg ession17 is a be e choice han linea eg ession, which can be eadily implemen ed in he R package o RuleFi 14. In summa y, RuleFi is compu a ionally e icien since e icien algo i hms ha e been de eloped o bo h Random Fo es and spa se linea eg ession models. RuleFi has an au oma ed c oss- alida ion p ocedu e o uning i s pa ame e s, such as he numbe o ees, he size o he ees and he penal y pa ame e λ in LASSO, which can be used o ob ain a se o high-quali y ules. Mo e de ails abou RuleFi can be ound in14. Figu e2 also p o ides a schema ic desc ip ion o he Rule i algo i hm. Resul s Iden i ied isk-p edic i e ules. Table3 p o ides he isk-p edic i e ules iden i ied by he RuleFi algo- i hm o he Ac i e and Wi hd awn amilies used in he p e ious logis ic eg ession analysis10. The isk ac o s iden i ied in he isk-p edic i e ules a e he same as hose iden i ied in he p e ious logis ic eg ession analysis: demog aphic ac o s including ma e nal age and coun y, ma e nal li es yle ac o s du ing p egnancy including as smoking, d inking, and wo king ou side he home, psychosocial ac o s including he mo he ’s pe cep ion o he child’s isk and he anxie y abou he child’s isk, dad pa icipa ion, and he numbe o missing da a poin s. In addi ion, he in e ac ion be ween he s a e anxie y in en o y sco e wi h he isk pe cep ion accu acy ound in he p e ious s udy, which u he alida ed in he ule-based analysis (see Table1 and Table3). Howe e , he ule-based analysis was mo e powe ul a de ec ing he in e ac ions be ween he isk ac o s. In addi ion, he ule- based app oach iden i ied he numbe o nega i e li e e en s as a isk ac o , a a iable ha was no signi ican in he p io logis ic eg ession analysis. And he ule-based app oach ound no signi ican ole o child gende , which had a weak e ec in he p io analysis (see Table3). No e ha he ules shown in Table3 we e iden i ied by LASSO om mo e han 2000 candida e ules gene a ed by andom o es . In es iga ion o he isk le els o endo sing he isk pa e ns. We nex in es iga ed he isk le el o endo sing each o he ules by compu ing he s udy wi hd awal a e o each subg oup ha endo sed a ule. Figu e3 illus a es he wi hd awal a es o each o he eigh iden i ied ules as well as he o e all wi hd awal a e Figu e 2. Flow diag am o he RuleFi algo i hm. www.na u e.com/scien i ic epo s/ 7 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 o he whole s udy popula ion. The numbe o subjec s in each subg oup is also shown in he igu e. I is clea ha endo sing any o he i s ou ules will boos he isk o ea ly wi hd awal d ama ically, while endo sing any o he la e ou ules will help dec ease he isk signi ican ly. App oxima ely 10 pe cen o he s udy popula ion did no all in o any subg oup and hei wi hd awal a es we e ela i ely high. I could be possible ha he e a e o he impo an subg oups ha we e no de ec able wi h he a ailable measu es. I could also be possible ha o his small g oup he RuleFi is no powe ul enough o de ec any signi ican ules, indica ing he need o mo e pow- e ul ule me hods. Mo eo e , i is possible ha because he d opou mechanism could be e y complica ed and in ol es many aspec s such as socioeconomic and psychological ac o s, he exis ence o his subg oup indica es a ce ain le el o unp edic abili y o some cases. In es iga ion o he edundancy o he ules. One impo an echnical issue in he ule-based analysis is he con ol o edundancy o he ules. Two ules a e edundan i a pa icipan endo ses one ule, his pa ic- ipan will endo se he o he ule. Ob iously, i is less desi able o ha e wo ules ha la gely o e lap wi h each o he . We in es iga ed he edundancy o he 8 ules and p esen ed he esul s in Fig.4. Figu e4 can be ead in his way: he pie g aph on ow i (co esponds o ule i) and column j (co esponds o ule j) eco ds he p opo ion o he pa icipan s endo sing ule i who also endo se ule j. I can be seen ha , he o e all edundancy o he ules is sligh , al hough he e a e some co ela ions be ween some ules, such as ule 1 and ule 4, ule 5 and ule 7. The eason o a co ela ion be ween wo ules may be ha bo h ules sha e some common isk ac o s, e.g., bo h ule 1 and ule 4 in ol e ma e nal age < 27.5 in hei de ini ions. Discussion In his a icle, he ule-base analysis14 has been p oposed o en ich he oolbox o epidemiological in e en ion s udies ha ha e been elying on eg ession models. We used da a om he TEDDY s udy and demons a ed ha he ule-based analysis can e ec i ely iden i y isk-p edic i e ules om he psychosocial, demog aphic, and beha io al isk ac o s. The 8 iden i ied ules a e ound p edic i e o ea ly wi hd awal du ing he i s yea o he TEDDY s udy. The 8 ules in ol e di e en se s o isk ac o s, highligh ing he di e en na u e o he wi hd awal Rule 1 ( isk inc easing ule) Rule 2 ( isk inc easing ule) Ma e nal age < 27.5 Finland = NO Smoke du ing p egnancy = YES Accu a e isk pe cep ion = NO S a e anxie y in en o y sco e > 45 Rule 3 ( isk inc easing ule) Rule 4 ( isk inc easing ule) S a e anxie y in en o y sco e > 45 Dad pa icipa ion = NO Ma e nal age < 27.5 Accu a e isk pe cep ion = NO Alcohol consump ion in las imes e < 2 imes pe mon h Rule 5 ( isk dec easing ule) Rule 6 ( isk dec easing ule) Wo ked all imes e s = YES Smoke du ing p egnancy = NO Finland = NO Alcohol consump ion in las imes e > 0 Numbe o nega i e e en s < 2 Rule 7 ( isk dec easing ule) Rule 8 ( isk dec easing ule) Smoke du ing p egnancy = NO S a e anxie y in en o y sco e < 45 Numbe o missing da a poin s < = 1 Ma e nal age > 27.5 Smoke du ing p egnancy = NO Numbe o missing da a poin s < = 1 Table 3. The 8 ules iden i ied by he RuleFi me hod. Figu e 3. P opo ion o ea ly wi hd awal o he eigh ules and he o e all popula ion. www.na u e.com/scien i ic epo s/ 8 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 isk o each o hese subg oups. No e ha hese 8 ules a e no exclusi e, gi ing he lexibili y ha an indi idual can show mul iple isk pa e ns simul aneously. We also compa ed he ule-based analysis wi h he p e ious analysis ha was conduc ed on he same da a10. We ound ha bo h me hods de ec ed almos he same sui e o isk ac o s, p o iding alida ion o ou ule-base analysis. No e ha he p e ious analysis only iden i ied he a e age e ec s o hese isk ac o s ac oss he whole popula ion, wi hou conside ing how hese isk ac o s in e ac wi h each o he in de e mining he isk o ea ly wi hd awal. Al hough i iden i ied he in e ac ion be ween he mo he ’s s a e anxie y in en o y sco e and he isk pe cep ion accu acy, many o he in e ac ions emained unde ec ed. The ule-based analysis was supe io a de ec ing mul iple in e ac ions be ween he isk ac o s, in addi ion o he in e ac ion be ween he mo he ’s s a e anxie y in en o y sco e and he isk pe cep ion accu acy. As each ule cha ac e izes a dis inc isk pa e n ha consis s o di e en isk ac o s, a u he in es iga ion o he pa icula cha ac e is ics o each ule may help iden i y he special heal h needs o he subg oup whose membe s endo se his ule, leading o ailo ed in e en ions. Fo example, as e ealed in ule 3, o mo he s who a e highly anxious abou hei child’s T1D isk wi h a s a e anxie y in en o y sco e > 45, he lack o pa icipa ion o he a he inc eases he isk o s udy wi hd awal. In an e o o ailo an in e en ion o his speci ic subg oup, a s udy nu se migh be assigned o he amily ha ing his isk pa e n o enhance he psychological suppo o he mo he and encou age he pa icipa ion o he a he . On he o he hand, he ules a e also help ul o de elop- ing gene al-pu pose in e en ions. Fo ins ance, as smoking du ing p egnancy was impo an in mul iple ules, in es iga ions may be conduc ed o unde s and why his beha io is ela ed o he isk o s udy wi hd awal. I smoking du ing p egnancy was ound o be an indica o o less heal h-conscious a i udes, a ailo ed in e en ion migh be de eloped o mo he s who smoked du ing p egnancy o inc ease hei heal h consciousness in an e o o educe he isk o s udy wi hd awal. As ailo ed in e en ions a e de eloped and deployed, i is also impo an o e alua e he e icacy o hese in e en ions o he subg oups sepa a ely, in o de o iden i y he bes in e en- ion s a egy o each subg oup. The ule-based analysis also iden i ied he nega i e li e e en s as a isk ac o o he ea ly wi hd awal, which was no de ec ed by he logis ic eg ession model used in he p e ious s udy10. P e ious s udies ha e linked nega- i e li e e en s wi h immune sys em unc ioning21,22 and he onse o T1DM23,24. While he mechanism unde lying he linkage be ween he nega i e li e e en s and s udy wi hd awal emains unknown, i is easonable o expec ha mo he s expe iencing nume ous nega i e li e s esses may no ha e he pe sonal esou ces o emain in he s udy. Ce ainly ailo ing an in e en ion o his subg oup o indi iduals seems wa an ed. The ule-based me hod has a numbe o ad an ages when handling complex da ase s. I can be used wi h a mix o nominal, o dinal, coun o con inuous a iables and i can combine a mix u e o a iables—demog aphic, biological, psychological—wi hou in e p e a ion di icul y. Also, as ules a e scale independen , da a do no need Figu e 4. In es iga ion o he edundancy o he 8 ules. The pie g aph on ow (co esponds o ule) and column (co esponds o ule j) eco ds he p opo ion o he pa icipan s endo sing ule i who also endo se ule. www.na u e.com/scien i ic epo s/ 9 Scien i ic RepoR s | 6:30828 | DOI: 10.1038/s ep30828 o be s anda dized. Finally, he ules will pe mi some indi iduals o be classi ied on he basis o only one, o a mos a ew, isk ac o s, whe eas isk sco es de i ed om eg ession models equi e ha all he isk ac o s a e a ailable. The e a e limi a ions o he ule-based app oach o epidemiologic s udies. Fi s , i is no sui able o s udying he o e all impac o a single independen a iable on he ou come a iable. This is because a single independ- en a iable may play a ole in mul iple ules, which esul s in di icul y o in es iga e i s o e all e ec on he whole popula ion. Also, domain insigh is e y impo an in he iden i ica ion o he ules using RuleFi . Due o he au oma ic na u e o he ule-based app oach, i is emp ing o simply en e all he possible candida e a - iables in o he p og am wi hou jus i ica ion o which independen a iables should be conside ed. I has been ecommended in he li e a u e25 ha he p io knowledge ega ding he ela ionship be ween he independen and dependen a iables should be inco po a ed wi h he ule-based models. One o he easons he ule-based app oach yielded ema kably simila indings o he logis ic eg ession app oach in e ms o iden i ying isk ac o s pe se, is ha conside able hough was pu in o a iable selec ion and measu emen . Rule-based models should no be used o blind explo a ion o la ge da a se s and should bene i om domain expe s’ supe ision. We ag ee ha a gene al guidance o use machine lea ning models o analyzing complex da ase such as TEDDY da a is ha he new ool should be app op ia e o he esea ch ques ion. This is ac ually one main mo i a ion o ou s udy. As wi h mos obse a ional s udies, a signi ican amoun o a ia ion exis s among TEDDY subjec s. Con en ional models such as he logis ic eg ession model canno su icien ly cha ac e ize hese a ia ions, since logis ic eg ession model essen ially aims o cha ac e ize he a e age e ec s o he isk ac o s on a homogeneous popula ion. I is easonable o suspec ha TEDDY popula ion consis s o a mix o he e ogeneous subpopula ions while in e ac ions be ween a iables a e essen ial o de ine and unde s and hese subpopula ions. Thus, he main mo i a ion o his s udy is o demons a e he u ili y o he ule-based app oach o analyzing complex da ase s such as TEDDY da a. Mo eo e , TEDDY da a exhibi s some o he signi ican challenges o con en ional models ha he ule-based me hod can easily handle as we ha e a icula ed abo e. Th ough his s udy, one o ou co-au ho s (who has been a pedia ic psychia is o many yea s and led he p e ious s udy on he same da ase using logis ic eg ession model10) ound ha he ule-based me hod could be a aluable new ool o augmen con en ional hypo hesis-d i en esea ch, pa icula ly when heo y-d i en esea che s ha e limi ed insigh o de ailed knowledge abou he da ase o be analyzed (e.g., his is e y likely as con empo a y epidemiologis s need o analyze da ase s wi h a di e se se o a iables ha include adi ional epi- demiological a iables as well as gene ic a iables (such as SNP a ian s), i us exposu es, omics a iables, e c.). Toge he wi h he ac ha he cu en s udy has demons a ed ha he ule-based app oach could iden i y isk ac o s ha a e consis en wi h he p e ious hypo hesis-d i en esea ch, ou s udy implies ha , o hose complex da ase s, he ule-based me hod could be used o ini ia e he analysis p ocess o iden i y unknown bu in o m- a i e pa e ns om he da ase ha may help heo y-d i en esea che s o gene a e new hypo hesis and be e o mula e hei s udies. To acili a e his ole, we d aw he ollowing p ac ical guidance o how o in eg a e he ule-based analysis me hods in o he exis ing epidemiological oolbox. I he e is a s ong p emise ha mul iple subg oups may exis in he da ase , he ule-based me hod could be a e y use ul app oach. On he o he hand, subg oups may a y om da ase o da ase , and he ules (and he isk ac o s in ol ed in hese subg oups) iden- i ied by he ule-based me hod may a y om da ase o da ase as well. I is impo an o unde s and ha he ule-based me hod is a cus omized me hod ha is ailo ed o analyzing an indi idual da ase , so whe he o no he esul s iden i ied om one da ase could be gene alized o ano he da ase depends on he subg oup s uc u e o he new da ase . While lexibili y o an analy ic me hod usually comes wi h isk o o e i ing, a cus omized me hod also needs cus omized expe ise o solid domain knowledge o he da ase . Finally, ule-based me hods can be conside ed as oppo unis ic me hods ha aim o disco e posi i e pa e ns, bu he esul s iden i ied by ule-based me hods a e no necessa y exclusi e. Fo example, i is possible ha he e a e mo e ules besides he eigh ules iden i ied om TEDDY coho by he RuleFi . In summa y, we belie e ha he ule-based app oach will be use ul in many epidemiologic s udies, pa icu- la ly wi h he e ogeneous popula ions consis ing o subg oups o indi iduals. The dis inc isk ac o s ha de ine each subg oup could also e lec a di e en mechanism o wi hd awing om he s udy, leading o de elopmen o di e en in e en ion s a egies. Besides he u ili y in designing ailo ed in e en ion, i can also help wi h he p io i iza ion o he in e en ion a ge s, e.g., we could choose elimina e a pa icula ly high- isk subg oup a he beginning o a clinical s udy. No e ha he RuleFi algo i hm in oduced he e is one example om a huge a ay o he ule-based me hods ha a e p omising o epidemiologic esea ch in gene al. How o p ope ly adop hem o add essing he inc easing analy ic challenges in epidemiologic s udies will be an impo an u u e esea ch opic. Also, we will in es iga e how o build p edic i e models based on he disco e ed ules, and u he alida e i s p edic i e pe o mance on ano he alida ion da ase ha is being collec ed a TEDDY s udy. Re e ences 1. G eenland, S., Gago-Dominguez, M. & Cas elao, J. E. The alue o isk- ac o (“black-box”) epidemiology. Epidemiology 15, 529–535 (2004). 2. E ans, L. K. Knowing he pa ien : he ou e o indi idualized ca e. J. Ge on ol. Nu s. 22, 15–19; quiz 52 (1996). 3. Radwin, L. & Als e , K. Indi idualized nu sing ca e: an empi ically gene a ed de ini ion. In . Nu s. Re . 49, 54–63 (2002). 4. Ryan, P. & Lau e , D. R. The e icacy o ailo ed in e en ions. Jou nal o Nu sing Schola ship 34, 331–337 (2002). 5. Whi emo e, R. Consequences o No ” Knowing he Pa ien ”. Clinical Nu se Specialis 14, 75–81 (2000). 6. Susse , M. Does isk ac o epidemiology pu epidemiology a isk? Pee ing in o he u u e. J. Epidemiol. Communi y Heal h 52, 608–611 (1998). 7. Sk abanek, P. Risk ac o epidemiology: Science o non-science. Social A ai s Uni , Heal h, Li es yle and En i onmen : Coun e ing he Panic, London: Social A ai s Uni (1991). 8. Seigel, D. G. & G eenhouse, S. W. Mul iple ela i e isk unc ions in case-con ol s udies. Am. J. Epidemiol. 97, 324–331 (1973).