何が知りたいのか？〜因果推論：効果の定義、 Estimandの前振り〜（医学統計学・疫学セミナー）

by Shuntaro Sato

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Կ͕஌Γ͍͔ͨʁ ҼՌਪ࿦ɿޮՌͷఆٛɺ&TUJNBOEͷલৼΓ ࠤ౻ढ़ଠ࿕ ௕࡚େֶපӃྟচݚڀηϯλʔ TIVOUBSPTBUP!OBHBTBLJVBDKQ

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2 ϩʔυϚοϓ ݚڀͷ෼ྨ w ؔ࿈ͷ୳ࡧ w ҼՌਪ࿦ w ༧ଌ ޮՌ ൓ࣄ࣮ ؔ࿈ ަབྷ ਪఆ͍ͨ͠΋ͷʢ&TUJNBOEʣ ʢपลޮՌʣ ৚݅෇͖ޮՌ ଟมྔղੳ ඪ४Խ ܏޲είΞϚονϯά ٯ֬཰ॏΈ෇͚ "5& "55 ˞ղੳํ๏ͷखॱ͸આ໌͠·ͤΜ

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3 ϩʔυϚοϓ ݚڀͷ෼ྨ w ؔ࿈ͷ୳ࡧ w ҼՌਪ࿦ w ༧ଌ ޮՌ ൓ࣄ࣮ ؔ࿈ ަབྷ ਪఆ͍ͨ͠΋ͷʢ&TUJNBOEʣ ʢपลޮՌʣ ৚݅෇͖ޮՌ ଟมྔղੳ ඪ४Խ ܏޲είΞϚονϯά ٯ֬཰ॏΈ෇͚ "5& "55

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ݚڀͷ෼ྨ 4 %FTDSJQUJPO &YQMPSJOH BTTPDJBUJPOT 1SFEJDUJPO $BVTBMJOGFSFODF %JBHOPTUJD QFSGPSNBODF FWBMVBUJPO ʢهड़ʣ ʢؔ࿈ͷ୳ࡧʣ ʢ༧ଌʣ ʢҼՌਪ࿦ʣ ʢ਍அͷੑೳධՁʣ ม਺͸ͲΜͳ෼෍͔ʁ Ͳͷม਺͕Ξ΢τΧϜʹ ؔ࿈͢Δ͔ʁ Ξ΢τΧϜΛ༧ଌ͢Δ ॲஔ͕Ξ΢τΧϜʹ   Өڹ͢Δ͔ʁ ೚ҙͷධՁํ๏ͷ   ਍அੑೳ͸ʁ w )FSOÂO." )TV+ )FBMZ#"4FDPOE$IBODFUP(FU$BVTBM*OGFSFODF3JHIU"$MBTTJ fi DBUJPOPG%BUB4DJFODF5BTLT$IBODF+BO r w 7JUUJOHIP ff & (MJEEFO%7 4IJCPTLJ4$ .D$VMMPDI$&3FHSFTTJPONFUIPETJOCJPTUBUJTUJDTMJOFBS MPHJTUJD TVSWJWBM BOESFQFBUFENFBTVSFT NPEFMT4QSJOHFS4DJFODF#VTJOFTT.FEJB

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ҼՌਪ࿦ʢ$BVTBMJOGFSFODFʣ 5 " : w ॲஔ"͸ɺΞ΢τΧϜ:ʹӨڹ͢Δ͔ʁ w Ξ΢τΧϜ:ʹର͢Δॲஔ"ͷޮՌ͸ʁ ݪҼ 5SFBUNFOUʢॲஔʣ *OUFSWFOUJPOʢհೖʣ &YQPTVSFʢമ࿐ʣ ݁Ռ 0VUDPNF   ʢΞ΢τΧϜʣ

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ݚڀͷ෼ྨ 6 %FTDSJQUJPO &YQMPSJOH BTTPDJBUJPOT 1SFEJDUJPO $BVTBMJOGFSFODF %JBHOPTUJD QFSGPSNBODF FWBMVBUJPO ʢهड़ʣ ʢؔ࿈ͷ୳ࡧʣ ʢ༧ଌʣ ʢҼՌਪ࿦ʣ ʢ਍அͷੑೳධՁʣ ม਺͸ͲΜͳ෼෍͔ʁ Ͳͷม਺͕Ξ΢τΧϜʹ ؔ࿈͢Δ͔ʁ Ξ΢τΧϜΛ༧ଌ͢Δ ॲஔ͕Ξ΢τΧϜʹ   Өڹ͢Δ͔ʁ ೚ҙͷධՁํ๏ͷ   ਍அੑೳ͸ʁ w )FSOÂO." )TV+ )FBMZ#"4FDPOE$IBODFUP(FU$BVTBM*OGFSFODF3JHIU"$MBTTJ fi DBUJPOPG%BUB4DJFODF5BTLT$IBODF+BO r w 7JUUJOHIP ff & (MJEEFO%7 4IJCPTLJ4$ .D$VMMPDI$&3FHSFTTJPONFUIPETJOCJPTUBUJTUJDTMJOFBS MPHJTUJD TVSWJWBM BOESFQFBUFENFBTVSFT NPEFMT4QSJOHFS4DJFODF#VTJOFTT.FEJB

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7 ଟมྔղੳ΍ ܏޲είΞϚονϯά΍ ٯ֬཰ॏΈ෇͚Ͱ ࠩʢൺʣͱ৴པ۠ؒΛࢉग़͠·ͨ͠ ަབྷΛ੍ޚ͢ΔͨΊʹ

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8 ͜ΕͰ׬ᘳʁ

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9 ҼՌਪ࿦ͯ͠ΔΜ͔ͩΒɺަབྷΛ੍ޚ͢Δͷ͸౰ͨΓલ Ұาઌ΁ʂ

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10 ϩʔυϚοϓ ݚڀͷ෼ྨ w ؔ࿈ͷ୳ࡧ w ҼՌਪ࿦ w ༧ଌ ޮՌ ൓ࣄ࣮ ؔ࿈ ަབྷ ਪఆ͍ͨ͠΋ͷʢ&TUJNBOEʣ ʢपลޮՌʣ ৚݅෇͖ޮՌ ଟมྔղੳ ඪ४Խ ܏޲είΞϚονϯά ٯ֬཰ॏΈ෇͚ "5& "55

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11 ·ͣ͸ޮՌͷఆ͔ٛΒ

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ݸମʹ͓͚ΔޮՌ 12 ࣌ؒ ˆ ˆ ˆ ˆ ࣏ྍ͢Δ   ʢBʣ λΠϜϚγϯ ࣏ྍ͠ͳ͍   ʢBʣ Ya=1 = 36 Ya=0 = 39 Ya=1 − Ya=0 = − 3 ॲஔޮՌʢ5SFBUNFOUF ff FDUʣ ࣄ࣮ ൓ࣄ࣮ જࡏΞ΢τΧϜʢ1PUFOUJBMPVUDPNFʣ ൓ࣄ࣮Ξ΢τΧϜʢ$PVOUFSGBDUVBMPVUDPNFʣ ࣌ؒޙ

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13 ൓ࣄ࣮ͱ͸ɺ   ڵຯͷ͋ΔॲஔҎ֎͸ಉ͡ੈք

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ूஂʹ͓͚ΔޮՌ 14 ࣌ؒ ˆ ฏۉˆ ˆ ฏۉˆ ࣏ྍ͢Δ   ʢBʣ λΠϜϚγϯ ࣏ྍ͠ͳ͍   ʢBʣ E[Ya=1] = 36 E[Ya=0] = 39 E[Ya=1] − E[Ya=0] = − 3 ฏۉॲஔޮՌ   ʢ"WFSBHFUSFBUNFOUF ff FDUʣ ࣄ࣮ ൓ࣄ࣮ ࣌ؒޙ &<>͸ظ଴஋ͷܭࢉ ࿈ଓσʔλͷظ଴஋͸ฏۉ஋ ஋σʔλͷظ଴஋͸ׂ߹

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15 ޮՌͱؔ࿈ͷҧ͍ ݚڀର৅ूஂ ॲஔ͋Γ ॲஔͳ͠ ޮՌʢ& ff FDUʣ ؔ࿈ʢ"TTPDJBUJPOʣ ूஂશମ͕ॲஔ͋Γͷ৔߹ͱ   ॲஔͳ͠ͷ৔߹Λൺֱ ॲஔ͋Γͷूஂͱ   ॲஔͳ͠ͷूஂΛൺֱ )FSOÂO." 3PCJOT+. $BVTBM*OGFSFODF8IBU*G#PDB3BUPO$IBQNBO)BMM$3$'JHVSFΛվม

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16 ؍࡯Ͱ͖Δσʔλͱ؍࡯Ͱ͖ͳ͍σʔλ *% ࣏ྍʢ"ʣ : Ya=1 Ya=0 Y|A = 1 Y|A = 0 ؍࡯Ͱ͖ͳ͍σʔλ ؍࡯Ͱ͖   ͳ͍σʔλ ؍࡯Ͱ͖   ͳ͍σʔλ

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17 ܭࢉͰ͖Δ஋ͱܭࢉͰ͖ͳ͍஋ *% ࣏ྍʢ"ʣ : Ya=1 Ya=0 Y|A = 1 Y|A = 0 E[Ya=1] E[Ya=0] E[Y|A = 1] E[Y|A = 0] ܭࢉͰ͖Δ ܭࢉͰ͖ͳ͍ ܈͝ͱͷฏۉ

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18 ޮՌ͸ܭࢉͰ͖ͳ͍ ఘΊΔͷ͔ʁ

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19 ؔ࿈ΛޮՌʹ͚ۙͮΔ ޮՌʢ& ff FDUʣ ؔ࿈ʢ"TTPDJBUJPOʣ ूஂશମ͕ॲஔ͋Γͷ৔߹ͱ   ॲஔͳ͠ͷ৔߹Λൺֱ ॲஔ͋Γͷूஂͱ   ॲஔͳ͠ͷूஂΛൺֱ ͜ͷσʔλ͸ͳ͍ ͜ͷσʔλ͸͋Δ ؔ࿈ ޮՌ ݚڀσβΠϯ΍౷ܭղੳख๏Λ޻෉ͯ͠ܭࢉ͢Δ

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ޮՌΛܭࢉ͢ΔͨΊͷ৚݅ 20 w $POTJTUFODZ w &YDIBOHFBCJMJUZ w 1PTJUJWJUZ ˞͜͜Ͱͷ$POTJTUFODZ͸౷ܭֶͰͷ$POTJTUFODZʢҰகੑʣͱ͸ҟͳΓ·͢ ˞ͦΕͧΕͷ৚݅ͷৄ͍͠આ໌͸ׂѪ͠·͢ ަབྷΛͳ͘͢͜ͱ͕࠷ॏཁ

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ަབྷʢ$POGPVOEJOHʣ 21 - " : ॲஔ"ͱΞ΢τΧϜ:ͷڞ௨ݪҼʢ$PNNPODBVTFʣʹΑΓੜ͡ΔόΠΞε ަབྷ͋Γ - " : ޻෉͢Δͱަབྷͳ͠ $PNNPO   DBVTF ࢛֯͸   ৚݅෇͚Λද͢ #MPDL #MPDL

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22 ޮՌΛܭࢉ͢ΔͨΊʹ޻෉͢Δखஈ w ϥϯμϜԽൺֱࢼݧ w ࠩ෼ͷࠩ෼ w ճؼෆ࿈ଓσβΠϯ w ࣌ܥྻ෼அσβΠϯ ݚڀσβΠϯ w ʢҰൠతͳʣଟมྔղੳ w ඪ४Խ w ܏޲είΞΛ࢖ͬͨํ๏ w Ϛονϯά w ٯ֬཰ॏΈ෇͚ʢ*18ʣ w ૢ࡞ม਺๏ ౷ܭղੳख๏

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23 ղੳํ๏ʹ༏ྼ͸͋Δʁ ϩδεςΟοΫճؼ෼ੳΈ͍ͨͳ   ଟมྔղੳΑΓɺ   ܏޲είΞ࢖ͬͯٻΊͨޮՌͷํ͕ྑ͍ΜͰ͠ΐʁ w ʢҰൠతͳʣଟมྔղੳ w ඪ४Խ w ܏޲είΞΛ࢖ͬͨํ๏ w Ϛονϯά w ٯ֬཰ॏΈ෇͚ʢ*18ʣ w ૢ࡞ม਺๏

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24 ަབྷΛਖ਼੍͘͠ޚ͢Ε͹   Ͳͷղੳख๏Ͱ΋ޮՌ͸ਪఆͰ͖Δ ޮՌͷ छྨ͕ҧ͏

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25 Կ͕஌Γ͍ͨͷ͔ʁ &TUJNBOE

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26 ϩʔυϚοϓ ݚڀͷ෼ྨ w ؔ࿈ͷ୳ࡧ w ҼՌਪ࿦ w ༧ଌ ޮՌ ൓ࣄ࣮ ؔ࿈ ަབྷ ਪఆ͍ͨ͠΋ͷʢ&TUJNBOEʣ ʢपลޮՌʣ ৚݅෇͖ޮՌ ଟมྔղੳ ඪ४Խ ܏޲είΞϚονϯά ٯ֬཰ॏΈ෇͚ "5& "55