疫学・統計セミナー：疾病の発生の測定

by Shuntaro Sato

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࣬පͷൃੜͷଌఆ $IVOUBSP !4IVOUBSPPP 15 Ӹֶɾ౷ܭηϛφʔ

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16 0WFSWJFX w ࣬පͷൃੜͷଌఆ w ൃੜׂ߹ʢϦεΫʣɾΦοζ w ڝ߹ϦεΫɼ-PTTUPGPMMPXVQ w ൃੜ཰ w ༗ප཰

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Ӹֶʹ͓͚Δଌఆ 17

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࣬පʢ0VUDPNFʣͷൃੜ΍ఔ౓ͷ෼෍ ԿͰԿΛଌఆ͢Δ͔ʁ 18 0VUDPNFNFBTVSFT ࿈ଓई౓ɼॱংई౓ ໊ٛई౓ ׂ߹ɼΦοζɼ཰ ฏۉ஋ɼதԝ஋ .FBTVSFTPGBTTPDJBUJPO Ξ΢τΧϜͱཁҼͱͷؔ࿈Λଌఆ ϦεΫࠩɼϦεΫൺɼΦοζൺɼ཰ൺɼճؼ܎਺

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ई౓ 19 ई౓ʢ4DBMFʣ ྫ ଌఆ 2VBMJUBUJWF PS $BUFHPSJDBM ໊ٛʢOPNJOBMʣ ஋ʢ#JOBSZ %JDIPUPNPVTʣ ࢮ๢ੜଘ ࣬පͷ͋Γͳ͠ ਓछ ࠃ ੑผ ׂ߹ Φοζ ॱংʢPSEJOBMʣ ॏ঱౓ 20- தԝ஋ ׂ߹ 2VBOUJUBUJWF PS $POUJOVPVT ࿈ଓʢ$POUJOVPVTʣ ೥ྸ ਎௕ ମॏ ऩೖ ฏۉ஋ தԝ஋

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ूஂதͷ࣬පൃੜͷଌఆ 20

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ͭͷࢦඪ 21 ࣬පͷൃੜ͸جຊతʹͭͷࢦඪͰଌఆ͢Δ ൃੜׂ߹ʢ*ODJEFODFQSPQPSUJPOʣ ൃੜΦοζʢ*ODJEFODF0EETʣ ൃੜ཰ʢ*ODJEFODFSBUFʣ ༗ප཰ʢ1SFWBMFODFʣ

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ൃੜׂ߹ʢ*ODJEFODFQSPQPSUJPO *1ʣ 22 w ूஂ಺ͷฏۉϦεΫൃੜׂ߹ w ʮϦεΫʯͱ͍͏ݴ༿͸ਓͷਓؒʹରͯ͠࢖͏͜ͱ͕ଟ͍ w ʮൃੜׂ߹ʯ͸ूஂʹରͯ͠࢖͏ "͞Μ #͞Μ $͞Μ %͞Μ ݚڀͰڵຯ͋Δ࣬ප IP = (risk) = ͋ΔҰఆظؒʹ࣬පʹ͔͔ͬͨਓ਺ ͦͷظؒ಺ʹ௥੻ௐࠪ͞Εͨਓ਺ 0 1 2 3 4 5 Year

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ൃੜׂ߹ͷྑ͍఺ɾ஫ҙ఺ 23 w ൃੜׂ߹͸ઐ໳ՈͰͳͯ͘΋ଟ͘ͷਓʹཧղ͠΍͍͢ w Ͳͷ͙Β͍മ࿐΍հೖ͕Ξ΢τΧϜʹӨڹΛ༩͑ͨͷ͔ࣔ͠΍͍͢ w ਓͷूஂʹ͋ΔհೖΛ͓͜ͳͬͨ৔߹ɼ͋ΔΞ΢τΧϜΛ ਓ͔ΒਓʹݮΒ͢͜ͱ͕Ͱ͖Δ ྑ͍఺ w ؍࡯ظؒΛ໌ه͠ͳ͍ͱղऍෆೳ w ্ͷྫͷ৔߹ɼ೥͕؍࡯ظؒͳͷ͔೥͕؍࡯ظؒͳͷ͔Ͱ ղऍ͕ҟͳΔ w ڝ߹ϦεΫɼ-PTTUPGPMMPXVQʢ௥੻ෆೳྫʣʹΑΓաখධՁ ʹͳΔ ஫ҙ఺

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ڝ߹ϦεΫʢ$PNQFUJOHSJTLʣ 24 ڵຯͷ͋ΔΞ΢τΧϜ͕ൃੜ͢ΔલʹɼଞͷΞ΢τΧϜͷൃੜʹΑΓ ݚڀର৅͔Βআ֎͞Εͯ͠·͏͜ͱ "͞Μ #͞Μ $͞Μ ഏ͕Μͷൃੜ ٤Ԏ ഏ͕Μͷൃੜ $2 ࣄނࢮ "͞Μ #͞Μ $͞Μ ഏ͕Μͷൃੜ ΋͔͢͠Δͱ IP = 1 3 IP = 2 3 ڝ߹ϦεΫ աখධՁ w ؍࡯ظ͕ؒ୹ظؒͰ͋Ε͹ɼڝ߹ϦεΫͷӨڹ͸௨ৗখ͍͞ w ڵຯͷ͋ΔΞ΢τΧϜ͕શࢮҼʹΑΔࢮ๢Ͱ͋Ε͹ɼڝ߹ϦεΫ͸ ى͜Βͳ͍

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-PTTUPGPMMPXVQʢ௥੻ෆೳྫʣ 25 Ҿӽ͠΍ಉҙఫճ౳Ͱɼ௥੻͢Δ͜ͱ͕Ͱ͖ͳ͘ͳΔ͜ͱ "͞Μ #͞Μ $͞Μ ഏ͕Μͷൃੜ ٤Ԏ ഏ͕Μͷൃੜ $2 Ҿӽ͠ "͞Μ #͞Μ $͞Μ ഏ͕Μͷൃੜ ΋͔͢͠Δͱ IP = 1 3 IP = 2 3 -PTTUPGPMMPXVQ աখධՁ ؍࡯ظؒதͷ-PTTUPGPMMPXVQ͕ଟ͍ݚڀ͸ղऍ͢Δͷ͕ࠔ೉

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ൃੜΦοζʢ*ODJEFODF0EETʣ 26 ͋ΔҰఆظؒʹ ࣬පʹ͔͔ͬͨਓ਺ ͦͷظؒ಺ʹ ௥੻ௐࠪ͞Εͨਓ਺ ൃੜׂ߹ ൃੜΦοζ ൃੜׂ߹ ൃੜׂ߹ w Φοζ͸ׂ߹ΑΓ௚ײతʹΘ͔ΓͮΒ͍ w ϩδεςΟοΫճؼ෼ੳͰ͸ɼΦοζ͕ܭࢉ͞ΕΔ

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ׂ߹ͱΦοζͱͷؔ܎ 27 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 Proportion Odds 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 Proportion Odds w ׂ߹͕े෼খ͚͞Ε͹ʢҎԼఔ౓ʣɼΦοζ͸ׂ߹ʹۙࣅͰ͖Δ w Φοζׂ߹ͷؔ܎͸ৗʹ੒Γཱͭ w ΦοζͰͷաେධՁʹ஫ҙ

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࣌ؒͷ֓೦Λಋೖ 28 w ͋Δूஂʹ͓͚Δ࣬පͷൃੜΛଌఆ͢ΔͨΊʹ͸ɼ ूஂ಺Ͱͷ࣬පͷൃੜׂ߹Λଌఆ͢Δ͚ͩͰ͸ෆे෼ w ؍࡯ظؒͷ໌ه͕ඞཁ w ڝ߹ϦεΫɼ-PTTUPGPMMPXVQͷଘࡏ ࣌ؒͷ֓೦͕ॏཁ Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern epidemiology (Vol. 3). Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins.ͷFigure 3-1Λࢀߟ 5JNF 5JNF ࢮ๢ ʮࠨͷूஂͷํ͕ࢮ๢཰ʯ͕ߴ͍ͱ͍͏දݱ͸ࣗવ

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ൃੜ཰ʢ*ODJEFODFSBUF *3ʣ 29 "͞Μ #͞Μ $͞Μ %͞Μ &͞Μ '͞Μ IR = ڵຯͷ͋ΔΞ΢τΧϜΛൃੜͨ͠ਓ਺ ௥੻ௐࠪ͞Εͨਓͷ࣌ؒͷ߹ܭ 0 1 2 3 4 5 Year ٤Ԏ ഏ͕Μͷൃੜ $2 ഏ͕Μͷൃੜ ࣄނࢮˠڝ߹ϦεΫ Ҿӽ͠ˠ-PTTUPGPMMPXVQ = 3 3 + 5 + 2 + 4 + 2 + 2 = 3 18 ≃ 0.17 ࣌ؒͷ֓೦ΛऔΓೖΕͨ࣬පͷൃੜͷࢦඪ QFSTPOUJNFʢਓ࣌ؒʣ

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ൃੜ཰ͷղऍ 30 w ൃੜׂ߹ͱҧ͍ɼҎ্΋औΓಘΔ w ୯ҐʹΑΓɼ஋͕มԽ͢Δ 100 cases person − year 10,000 cases person − century 8.33 cases person − month 1.92 cases person − week 0.27 cases person − day × 100 / 12 months / 52 weeks / 365 days ෼฼ʢਓ-࣌ؒʣͷมԽ

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ൃੜ཰ͷྑ͍఺ɾ஫ҙ఺ 31 w ൃੜׂ߹ΑΓɼڝ߹ϦεΫ΍-PTTUPGPMMPXVQͷӨڹΛऑΊΔ͜ ͱ͕Ͱ͖Δ ྑ͍఺ w ൃੜׂ߹ΑΓղऍͮ͠Β͍ w ظؒΛ௨ͯ͠ɼൃੜ཰͕Ұఆͱ͍͏Ծఆ͕͋Δ w ࣌ؒͱͱ΋ʹൃੜ཰͕มԽ͢Δ৔߹͸ɼੜଘ࣌ؒղੳ w ڝ߹ϦεΫͷ໰୊΋ղܾͰ͖ͨΘ͚Ͱ͸ͳ͍ ஫ҙ఺

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ൺɾׂ߹ɾ཰ 32 ൺ 3BUJP ୯७ʹͭͷ਺஋Λׂͬͨ஋ ׂ߹ 1SPQPSUJPO શମʹର͢Δ෦෼Λ શମͰׂͬͨ஋ ཰ 3BUF ෼฼ʹ࣌ؒͷ֓೦ؚ͕·ΕΔ

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༗ප཰ʢ1SFWBMFODFʣ 33 w ͋Δ࣌఺Ͱ࣬පʹ͔͔͍ͬͯΔਓ਺Λ ͦͷ࣌఺ͷશݚڀର৅ऀ਺Ͱׂͬͨ஋ w ཰Ͱͳׂ͘߹ w ্ؾಓײછ͸ɼൃੜ཰͸ߴ͍͕ɼ ͙͢ʹճ෮͢ΔͨΊ୯఺Ͱͷ༗ප཰͸௿͍ͩΖ͏ w ຫੑ࣬ױ͸ɼൃੜ཰͸௿ͯ͘΋ɼ ጶපظ͕ؒ௕͍ͨΊ༗ප཰͸ߴ͍ͩΖ͏ "͞Μ #͞Μ $͞Μ %͞Μ 0 1 2 3 4 5 Year 0/4 =  0 2/4 =  0.5 1/3 =  0.33 1/2 =  0.5

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34 ࠓޙͷྲྀΕ ʢਫʣ Ӹֶͱ͸ʁ ࣬පͷൃੜͷଌఆ ҼՌύΠ ൃੜׂ߹ɼ཰ɼ༗ප཰ ϦεΫൺɼϦεΫࠩɼΦοζൺɼ཰ൺ ʢۚʣ ࣬පͱཁҼͱͷؔ࿈ ϦεΫൺɼϦεΫࠩɼΦοζൺɼ཰ൺ ʢ໦ʣ Ӹֶݚڀͷ෼ྨ ίϗʔτݚڀɼ έʔείϯτϩʔϧݚڀɼ ϥϯμϜԽൺֱࢼݧ 5BSHFUUSJBM ʢۚʣ ਪఆɾݕఆɾਫ਼౓ ਖ਼֬Ͱଥ౰ͳਪఆͱ͸ʁ όΠΞε ৴པ۠ؒɼ1஋ ʢਫʣ ҼՌਪ࿦ɾҼՌϞσϧ ޮՌͱؔ࿈ͷҧ͍ɼ%"(ɼ ަབྷҼࢠͷ੍ޚํ๏ ࠓޙ ҼՌਪ࿦Ͱ༻͍ΒΕΔ౷ܭղੳ ʢ܏޲είΞɼࠩ෼ͷࠩ෼ੳɼෆ࿈ଓճؼσβΠϯͳͲʣ ײ౓෼ੳɼܽଌσʔλͷॲཧ

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4QFDJBM5IBOLT 35 w ຖिҰॹʹؤுͬͯΔ.PEFSO&QJͷօ͞Μʢ5XJUUFSʣ w ࠓճ͸ಛʹ!@WPM@EF@OVJU͞Μɼ!NQI@GPS@EPDUPST͞Μɼࢀ ߟʹͳΓ·ͨ͠ɽʢ5XJUUFSʣ w ͍ͭ΋ॿݴ͍͚ͯͨͩ͠Δ!LPSP͞Μɼ!%S@,*%@͞Μɼ !OVUFQJ͞Μʢ5XJUUFSʣ 5IBOLZPVWFSZNVDI

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5BLF)PNFNFTTBHF 36 w ࣬පͷൃੜͷଌఆ w ൃੜׂ߹ʢϦεΫʣɾΦοζ w ڝ߹ϦεΫɼ-PTTUPGPMMPXVQ w ൃੜ཰ w ༗ප཰ w ׂ߹ʢ1SPQPSUJPOʣͱ཰ʢ3BUFʣ͸ҧ͏

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ࢀߟจݙͱҾ༻จݙ 3PUINBO ,+ (SFFOMBOE 4 -BTI 5- .PEFSOFQJEFNJPMPHZ 7PM 1IJMBEFMQIJB8PMUFST,MVXFS)FBMUI-JQQJODPUU8JMMJBNT8JMLJOT w Ӹֶʹ͍ͭͯ·ͱ·͍ͬͯΔɽҼՌਪ࿦ʹॏ৺Λஔ͘ςΩετɽ೉ղɽ 3PUINBO ,+ ϩεϚϯͷӸֶՊֶతࢥߟ΁ͷ༠ࣰ͍ݪग़൛ࣾ w ΑΓ؆୯ͳ಺༰ +PIO .- "EJDUJPOBSZPGFQJEFNJPMPHZ0YGPSE6OJWFSTJUZ1SFTT w ࣙॻ͔ͩΒͦ͜ɼͱͯ΋ಡΈ΍͍͢ӳޠͰӸֶ༻ޠΛઆ໌͍ͯ͠Δ ୮ޙढ़࿕ দҪໜ೭ ৽൛ҩֶ౷ܭֶϋϯυϒοΫே૔ॻళ ୮ޙढ़࿕ খ੢ఃଇ ҩֶ౷ܭֶͷࣄయே૔ॻళ 37