Introduction to gfoRmula / gfoRmula 入門

第110回R勉強会@東京 (TokyoR) 応用セッションでの発表資料です.

Transcript

1. gfoRmula ೖ໳ Kamono Tokyo.R #110 January 20, 2024 1 / 46
2. ࣗݾ঺հ • X (twitter): @Kamono12 • Tokyo.Rʹ͸աڈ਺ճࢀՃ • ͦΖͦΖίϛϡχςΟʹߩݙ͍ͨ͠ • ܦࡁֶܥͷେֶӃੜ • ઐ໳෼໺: ܭྔܦࡁֶ / ҼՌਪ࿦ • ࠓ೔࿩୊ʹ͢Δ g-formula ͸ઐ໳ͱ͸ҟͳΔ • @NoriTokuta ͞ΜΑΓࢿྉఏڙฒͼʹଟ਺ίϝϯτ௖͍ͨ • ͋Γಘ΂͖ޡΓ͸͢΂ͯൃදऀݸਓʹؼଐ 2 / 46
3. 1 Ϟνϕʔγϣϯ: g-formula ͷ໨త͸Կ͔? 2 ཧ࿦(1): g-formula ͷલఏ஌ࣝͱ͸Կ͔? 3 ཧ࿦(2): g-formula ͸ͲΜͳߏ଄͔? 4 ࣮ફ: {gfoRmula} ΛͲ͏࢖͏͔? 3 / 46
4. 1 Ϟνϕʔγϣϯ: g-formula ͷ໨త͸Կ͔? 2 ཧ࿦(1): g-formula ͷલఏ஌ࣝͱ͸Կ͔? 3 ཧ࿦(2): g-formula ͸ͲΜͳߏ଄͔? 4 ࣮ફ: {gfoRmula} ΛͲ͏࢖͏͔? 4 / 46
5. ͦ΋ͦ΋ͷ໰͍ Q. ෳ਺ͷબ୒ࢶͷதͰͲͷબ୒ࢶΛબ΂͹Α͍͔? • ਪન: ϢʔβʔʹޮՌతͳ޿ࠂ / ੡඼ / ΦϑΝʔ͸? • ੓ࡦ: ࣾձްੜΛ޲্ͤ͞ΔΑ͏ͳ੓ࡦ͸? • ҩྍ: ױऀʹޮՌతͳༀ / खज़ / ࣏ྍ๏͸? • ࢀߟ: [1] [2] [3] ⇐ ओʹհೖ͕1࣌఺ͷ৔߹ʹ͍ͭͯߟ͑ΒΕ͖ͯͨ 5 / 46
6. ݱ࣮໰୊ ݱ࣮ʹ͸հೖ͕ෳ਺࣌఺ʹ౉ͬͯߦΘΕΔ৔໘΋ଟ͍ 6 / 46
7. Robins’ g-methods 1 g-computation algorithm formula ʢ ʠg-formulaʡ ʣ 2 IPTW of marginal structural models ʢMSMsʣ 3 g-estimation of structural nested models ʢSNMsʣ 7 / 46
8. ຊൃදͷ໨ඪ 1 հೖ͕ෳ਺࣌఺ͰߦΘΕΔ৔߹ͷҼՌਪ࿦ͷಋೖ 2 g-formula ͷߏ଄ͷ೺Ѳ 3 ύοέʔδ {gfoRmula} ͷར༻ Note • ੩త (static) Ͱܾఆ࿦త (deterministic) ͳ৔߹ʹݶఆ • ڵຯͷର৅Λ௥੻ௐࠪͷ࠷ऴظͷΞ΢τΧϜʹݶఆ • Αͬͯ {gfoRmula} ͷҰ෦ػೳͷΈͷ঺հ 8 / 46
9. 1 Ϟνϕʔγϣϯ: g-formula ͷ໨త͸Կ͔? 2 ཧ࿦(1): g-formula ͷલఏ஌ࣝͱ͸Կ͔? 3 ཧ࿦(2): g-formula ͸ͲΜͳߏ଄͔? 4 ࣮ફ: {gfoRmula} ΛͲ͏࢖͏͔? 9 / 46
10. જࡏΞ΢τΧϜ • A: հೖ (1: treated, 0: untreated) • Y : ؍࡯͞ΕΔΞ΢τΧϜ • Y a: જࡏΞ΢τΧϜ (potential outcome) • Y a=1: հೖΛड͚ͨ৔߹ͷજࡏΞ΢τΧϜ • Y a=0: հೖΛड͚ͳ͔ͬͨ৔߹ͷજࡏΞ΢τΧϜ 10 / 46
11. ݸਓʹର͢ΔҼՌޮՌ • ݸผҼՌޮՌ: Y a=1 − Y a=0 ݸผҼՌޮՌ͸ࣝผͰ͖ͳ͍ (ҼՌਪ࿦ͷࠜຊ໰୊) [4] ⇒ ڵຯͷର৅Λݸਓ͔Βूஂ΁Ҡ͢ 11 / 46
12. ूஂʹର͢ΔҼՌޮՌ • ฏۉҼՌޮՌ: E[Y a=1] − E[Y a=0] • E[Y a=1]: ूஂશһ͕հೖΛड͚Δ৔߹ͷજࡏΞ΢τΧϜͷظ଴஋ • E[Y a=0]: ूஂશһ͕հೖΛड͚ͳ͍৔߹ͷજࡏΞ΢τΧϜͷظ଴஋ 12 / 46
13. ަ׵Մೳੑ (exchangeability) • (Y a=1, Y a=0) ⊥ ⊥ A • E[Y a=1 | A = 1] = E[Y a=1 | A = 0] = E[Y a=1] • E[Y a=0 | A = 1] = E[Y a=0 | A = 0] = E[Y a=0] • ϥϯμϜԽ • ަ׵ՄೳੑΛ୲อ • հೖ܈ͱରর܈Λ୯७ൺֱ͢Δ͜ͱ͕Մೳ 13 / 46
14. ؍࡯ݚڀʹ͓͚Δަ׵Մೳੑ • ؍࡯ݚڀͰ͸հೖ͕ϥϯμϜԽ͞Ε͍ͯͳ͍ • ަ׵Մೳੑ͕୲อ͞Εͳ͍ • ަབྷ (confounding) ͕ൃੜ • E[Y a=1 | A = 1] ̸= E[Y a=1 | A = 0] • ަབྷҼࢠ (confounder) L • ަབྷΛൃੜͤ͞ΔཁҼ • యܕతʹ͸ A ͱ Y ͷڞ௨ݪҼ 14 / 46
15. ؍࡯ݚڀʹ͓͚Δަ׵Մೳੑ • ަབྷҼࢠ L Λௐ੔͢Δ͜ͱͰަ׵Մೳʹ͢Δ • E[Y a=1 | A = 1, L] = E[Y a=1 | A = 0, L] = E[Y a=1 | L] • E[Y a=0 | A = 1, L] = E[Y a=0 | A = 0, L] = E[Y a=0 | L] • ৚݅෇͖ަ׵Մೳੑ: (Y a=1, Y a=0) ⊥ ⊥ A | L • ௐ੔ͷ࢓ํ͸༷ʑ • e.g.) ૚ผԽ / ճؼ / Ϛονϯά / ܏޲είΞΛ༻͍ͨख๏ 15 / 46
16. ฏۉҼՌޮՌͷਪఆʹඞཁͳ৚݅ ࣝผՄೳ৚݅ 1 Ұகੑ (consistency) A = a ⇒ Y a = Y a.s. 2 ৚݅෇͖ަ׵Մೳੑ (conditional exchangeability) Y a ⊥ ⊥ A | L = l ∀a, l 3 ਖ਼஋ੑ (positivity) fL (L = l) ̸= 0 ⇒ fA|L (a | L = l) > 0 a.s. ∀a 16 / 46
17. 1 Ϟνϕʔγϣϯ: g-formula ͷ໨త͸Կ͔? 2 ཧ࿦(1): g-formula ͷલఏ஌ࣝͱ͸Կ͔? 3 ཧ࿦(2): g-formula ͸ͲΜͳߏ଄͔? 4 ࣮ફ: {gfoRmula} ΛͲ͏࢖͏͔? 17 / 46
18. sequential treatments ݱ࣮ʹ͸հೖ͕ෳ਺࣌఺ʹ౉ͬͯߦΘΕΔ৔໘΋ଟ͍ 18 / 46
19. sequential treatments ͷ෼ྨ • ࣌ؒݻఆੑ࣏ྍ(time-fixed treatments) • શͯͷඃݧऀʹର͠, ϕʔεϥΠϯ࣏ྍ͕ͦͷޙશͯͷ࣏ ྍϨϕϧΛܾఆ͢Δ • ϕʔεϥΠϯͰͷΈ࣏ྍ͕ߦΘΕΔ • ϕʔεϥΠϯͰͷ࣏ྍϨϕϧ͕࣌ؒܦաʹΑͬͯෆม • ܾఆ࿦తʹ֤࣌఺ͷ࣏ྍϨϕϧ͕ఆ·Δ • ࣌ؒґଘੑ࣏ྍ (time-varying treatments) • ࣌ؒݻఆతͰͳ͍࣏ྍશͯ • ֤࣌఺Ͱͷ࣏ྍϨϕϧ͕ϕʔεϥΠϯ࣏ྍʹΑܾͬͯఆ͞ Εͳ͍ 19 / 46
20. ௥Ճͷه๏ • At : t ࣌఺ʹ͓͚Δೋ஋࣏ྍ (t = 0, 1, . . . , K) • ¯ At : t ࣌఺·Ͱͷ࣏ྍྺ ( ¯ AK = ¯ A) • Lt : t ࣌఺ʹ͓͚Δڞมྔ (Ұൠʹ͸ϕΫτϧ) • ¯ Lt : t ࣌఺·Ͱͷڞมྔྺ ¯ LK = ¯ L • Y : ࠷ऴ࣌఺ (K) ʹ͓͍ͯ؍ଌ͞ΕΔΞ΢τΧϜ • Y ¯ a: ¯ A = ¯ a Λड͚Δ৔߹ͷજࡏΞ΢τΧϜ 20 / 46
21. ࣏ྍϨδϝϯ (treatment regime) ϕʔεϥΠϯ͔Β K ࣌఺·ͰͷҰ࿈ͷ࣏ྍׂ෇ ¯ A = {a0 , a1 , . . . , aK } • strategy, plan, policy, protocol ͱ΋ݺ͹ΕΔ • e.g.) ࣏ྍ͕2࣌఺ͰߦΘΕΔ৔߹ 1 (a0 , a1 ) = (0, 0): ͱ΋ʹ࣏ྍΛड͚ͳ͍ 2 (a0 , a1 ) = (1, 0): t = 0 Ͱ͸࣏ྍΛड͚, t = 1 Ͱ͸࣏ྍΛड͚ͳ͍ 3 (a0 , a1 ) = (0, 1): t = 0 Ͱ͸࣏ྍΛड͚ͣ, t = 1 Ͱ͸࣏ྍΛड͚Δ 4 (a0 , a1 ) = (1, 1): ͱ΋ʹ࣏ྍΛड͚Δ 21 / 46
22. ੩తϨδϝϯ (static regime) ੩తϨδϝϯ(static regime) • ೚ҙͷ࣌఺ t ʹؔͯ͠, at ͕ڞมྔྺ ¯ lt ʹґଘͤͣ, ࣏ྍྺ ¯ at−1 ʹͷΈʹґଘ • ஋ͷऔΓํ͸ 2K+1 ௨Γଘࡏ • at ͕࣏ྍྺ ¯ at−1 ͷΈͳΒͣڞมྔྺ ¯ lt ʹ΋ґଘ͢Δ ৔߹, ಈతϨδϝϯ (dynamic regime) ͱ͍͏ 22 / 46
23. ࣏ྍϨδϝϯʹର͢ΔજࡏΞ΢τΧϜ • 1࣌఺ͷ࣏ྍͱಉ༷ʹ, ֤Ϩδϝϯ͝ͱʹજࡏΞ΢τ ΧϜ͕ఆٛ͞ΕΔ • ͋ΔҰ࿈ͷ࣏ྍΛड͚ͨ࣌ʹ؍ଌ͞ΕΔͩΖ͏Ξ΢τΧϜ • e.g.) ࣏ྍ͕2࣌఺ͰߦΘΕΔ৔߹ 1 Y a0=0,a1=0: ͱ΋ʹ࣏ྍΛड͚ͳ͍৔߹ͷજࡏΞ΢τΧϜ 2 Y a0=1,a1=0: t = 0 Ͱ͸࣏ྍΛड͚, t = 1 Ͱ͸࣏ྍΛड͚ͳ͍৔߹ͷજࡏΞ΢τΧϜ 3 Y a0=0,a1=1: t = 0 Ͱ͸࣏ྍΛड͚ͣ, t = 1 Ͱ͸࣏ྍΛड͚Δ৔߹ͷજࡏΞ΢τΧϜ 4 Y a0=1,a1=1: ͱ΋ʹ࣏ྍΛड͚Δ৔߹ͷજࡏΞ΢τΧϜ 23 / 46
24. ࣏ྍϨδϝϯʹର͢ΔҼՌޮՌ • ڵຯͷ͋Δ2ͭͷϨδϝϯ ¯ a, ¯ a′(̸= ¯ a) Λબ୒͢Δඞཁ • 1 ࣌఺ͷ࣏ྍͷΑ͏ʹฏۉҼՌޮՌͷఆ͕ٛҰҙʹఆ·Β ͳ͍ • e.g.) ࣏ྍ͕2࣌఺ͰߦΘΕΔ৔߹ {¯ a, ¯ a′} = {"ͣͬͱ࣏ྍΛड͚ͨ", "ͣͬͱ࣏ྍΛड͚ͳ͔ͬͨ"} E[Y a0=1,a1=1] − E[Y a0=0,a1=0] • ೚ҙͷ E[Y ¯ a] ΛਪఆͰ͖Ε͹, ͦͷൺֱʹΑͬͯڵຯ ͷ͋ΔฏۉҼՌޮՌͷ஋ΛܭࢉՄೳ 24 / 46
25. ҼՌਪ࿦ͷલఏ • ަབྷҼࢠ (confounder) L • A ͱ Y ͷڞ௨ݪҼͱͳΔҼࢠ • A ͷ Y ʹର͢ΔҼՌޮՌΛਪఆ͢Δ ৔߹ʹ͸ L Λௐ੔ (৚݅෇͚) ͳ͍ͱ ਪఆ݁ՌʹόΠΞε • தؒҼࢠ (mediator) M • A ͱ Y ͷதؒʹଘࡏ͢ΔҼࢠ • A ͷ Y ʹର͢ΔҼՌޮՌΛਪఆ͢Δ ৔߹ʹ͸ M Λௐ੔ (৚݅෇͚) ͢Δͱ ਪఆ݁ՌʹόΠΞε 25 / 46
26. ࣌ؒґଘੑަབྷ • ࣌ؒґଘੑަབྷҼࢠ(time-dependent confounders)L1 1 A0 ͱ Y ͷதؒҼࢠ A0 → L1 → Y 2 A1 ͱ Y ͷަབྷҼࢠ A1 ← L1 → Y • ඪ४తͳख๏ (ճؼ, ૚ผ, Ϛονϯά) Ͱ͸ରԠෆՄ • No feedback (L1 → A1 ͕ͳ͍) ͱ͍͏ঢ়گͷΈՄೳ 26 / 46
27. Robins’ g-methods 1 g-computation algorithm formula ʢ ʠg-formulaʡ ʣ 2 IPTW of marginal structural models ʢMSMsʣ 3 g-estimation of structural nested models ʢSNMsʣ 27 / 46
28. ฏۉҼՌޮՌͷਪఆʹඞཁͳ৚݅ ࣝผՄೳ৚݅ 1 Ұகੑ(consistency) ¯ A = ¯ a ⇒ Y ¯ a = Y a.s. 2 ஞ࣍৚݅෇͖ަ׵Մೳੑ(sequential conditional exchangeability) Y ¯ a ⊥ ⊥ At | ¯ At−1 = ¯ at−1 , ¯ Lt = ¯ lt ∀¯ a 3 ਖ਼஋ੑ(positivity) f ¯ At−1,¯ Lt (¯ at−1 , ¯ lt ) ̸= 0 ⇒ fAt|¯ at−1,¯ lt (a | ¯ At−1 = ¯ at−1 , ¯ Lt = ¯ lt ) > 0 a.s. ∀at , lt 28 / 46
29. ڞมྔ͕཭ࢄͷ࣌ͷ g-formula E [ Y ¯ a ] = ∑ ¯ l { E [ Y | ¯ AK = ¯ aK , ¯ LK = ¯ lK ] K ∏ t=0 P ( lt | ¯ at−1 , ¯ lt−1 ) } • E [ Y | ¯ AK = ¯ aK , ¯ LK = ¯ lK ] • ڞมྔྺɾ࣏ྍྺͰͷ৚݅෇͖Ξ΢τΧϜͷظ଴஋ • P ( lt | ¯ at−1 , ¯ lt−1 ) • ࣌఺ t − 1 ·Ͱͷڞมྔྺɾ࣏ྍྺͰ৚݅෇͚ͨ, ࣌఺ t Ͱ ͷڞมྔͷ֬཰ؔ਺ 29 / 46
30. nonparametric g-formula • ڞมྔ͕཭ࢄ ⇒ ҎԼͷΑ͏ʹஔ׵ • E [ Y | ¯ AK = ¯ aK , ¯ LK = ¯ lK ] → n−1 ∑ n i=1 ˆ E [ Yi | ¯ AKi , ¯ LKi ] • P ( lt | ¯ at−1 , ¯ lt−1 ) → ˆ P ( lt | ¯ at−1 , ¯ lt−1 ) • ͜ͷํ๏Λ nonparametric g-formula ͱݺͿ • e.g.) Y Ҏ֎ೋ஋ͷ৔߹ͷӈਤ E [ Y a0=0,a1=0 ] = 1 ∑ l=0 {E [ Y | ¯ A = (a0 = 0, a1 = 0) , L1 = l ] Pr [L1 = l | A0 = a0 ]} 30 / 46
31. parametric g-formula E [ Y ¯ a ] = ∫ ¯ l E [ Y | ¯ AK = ¯ aK , ¯ LK = ¯ lK ] K ∏ t=0 P ( lt | ¯ at−1 , ¯ lt−1 ) d¯ l • ڞมྔ͕࿈ଓͰ͋Δ৔߹ • ظ଴஋ / ֬཰෦෼Λ nonparametric ʹࣝผෆՄ • ͦΕͧΕͷ෦෼ʹύϥϝτϦοΫϞσϧΛઃఆ • parametric g-formula: Ϟσϧ͔ΒಘΒΕͨਪఆ஋Λૠೖ • ڞมྔ͕཭ࢄͰ΋ෳ਺ଘࡏ / ࣌఺͕ଟ͍৔߹ • parametric g-formula Λ࠾༻ • ৄࡉ͸ [5] [6] ΍ຊൃද࠷ޙʹ঺հ͢ΔจݙΛࢀর 31 / 46
32. 1 Ϟνϕʔγϣϯ: g-formula ͷ໨త͸Կ͔? 2 ཧ࿦(1): g-formula ͷલఏ஌ࣝͱ͸Կ͔? 3 ཧ࿦(2): g-formula ͸ͲΜͳߏ଄͔? 4 ࣮ફ: {gfoRmula} ΛͲ͏࢖͏͔? 32 / 46
33. gfoRmula ͱ͸ • (ओʹ) parametric g-formula Λܭࢉ͢Δύοέʔδ [7] • ༷ʑͳΞ΢τΧϜ / ঢ়گʹରԠՄೳ • Φϓγϣϯ਺͕ඇৗʹଟ͍ ࠓճ͸... • ੩త (static) Ͱܾఆ࿦త (deterministic) ͳ৔߹ʹݶఆ • ڵຯͷର৅Λ௥੻ௐࠪͷ࠷ऴظͷΞ΢τΧϜʹݶఆ • Ҏ߱, Zt = (At , Lt ) ͱ͢Δ 33 / 46
34. gfoRmula ͷΞϧΰϦζϜ - 1 ΞϧΰϦζϜ: εςοϓ 1 ͢΂ͯͷσʔλΛ࢖ͬͯ࣍Λਪఆ a k(> 0) ࣌఺ͷ j ൪໨ͷڞมྔ Zj,k ͷ৚݅෇͖֬཰ີ౓ f ( Zj,k | Zj−1,k , . . . , Z1,k , ¯ Lk−1 , ¯ Ak−1 ) Λਪఆ b K ࣌఺ͷΞ΢τΧϜͷ৚݅෇͖ظ଴஋ µ(¯ lK , ¯ aK ) = E[Y | ¯ LK = ¯ lK , ¯ AK = ¯ aK ] Λਪఆ εςοϓ 1 ͷίϝϯτ • ਪఆͨ͠৚݅෇͖֬཰ີ౓͸εςοϓ 2.a. Ͱ࢖ΘΕΔ • Zj,k ͕ै͏෼෍΍ཤྺͱͷؔ܎ੑʹ͍ͭͯ͸෼ੳऀ͕ࣄલʹࢦఆ͢Δ • ৚݅෇͖ظ଴஋ͷਪఆͰ͸ઢܗճؼϞσϧ͕ࣗಈͰ༻͍ΒΕ͍ͯΔ 34 / 46
35. gfoRmula ͷΞϧΰϦζϜ - 2 ΞϧΰϦζϜ: εςοϓ 2 s = n ͱͳΔΑ͏ͳ஋ s ≥ 10, 000 Λબ୒͠, k = 0, . . . , K (࣌఺) ͓Αͼ v = 1, . . . , s (ݸਓ) ʹ͍ͭͯ࣍Λ࣮ߦ a k = 0 ࣌఺Ͱ͸, z0,v Λݸਓ v ͷ Z0 = (L0 , A0 ) ʹઃఆ. k > 0 ࣌఺Ͱ͸, j ൪໨ͷڞมྔ zj,k,v Λ৚݅෇͖֬཰ີ౓ f ( Zj,k | Zj−1,k , . . . , Z1,k , ¯ Lk−1 , ¯ Ak−1 ) ͷਪఆ஋͔Β܁Γฦ͠நग़ b Zk,v ϕΫτϧͷ࣏ྍ෦෼Λ a⋆ k,v ͱ͠, Ϣʔβʔࢦఆͷنଇ huser(¯ auser k,v , a⋆ k , ¯ lk,v ) ʹैͬͯ auser k,v Λׂ౰. c εςοϓ 1.b. Ͱͷಛఆʹج͍ͮͯ K ࣌఺ͷ µ(¯ lK , ¯ aK ) Λਪఆ. ͜ͷਪఆ஋Λ ˆ µ(¯ lK,v , ¯ auser K,v ) ͱ͢Δ. 35 / 46
36. gfoRmula ͷΞϧΰϦζϜ - 3 εςοϓ 2 ͷίϝϯτ • s ̸= n ͷ৔߹ɼϦαϯϓϦϯάʹΑͬͯ v = 1, . . . , s ͱͳΔσʔλू߹Λ࡞੒ • ͜͜Ͱ͸ Zj,k = Zj,k,v , ¯ Ak−1 = ¯ auser k−1,v ͱධՁ • Ϣʔβʔࢦఆنଇʹ͍ͭͯ, ྫ͑͹੩తܾఆ࿦తϨδϝϯʮৗʹॲஔͷ஋Λ 1 ʹઃఆʯͱͯ͠ఆٛ͞Ε͍ͯΔͳΒ͹ auser k,v ͸ৗʹ 1 ʹઃఆ͞ΕΔ ΞϧΰϦζϜ: εςοϓ 3 հೖͷฏۉਪఆ஋Λ࣍ͷΑ͏ʹܭࢉ 1 n n ∑ v=1 ˆ µ(¯ lK,v , ¯ auser K,v ) 36 / 46
37. ࣮ફྫ ͜͜Ͱ͸[7]ͷྫʹैͬͯղઆ • n = 2500, t = 0, . . . , 6 • time: ࣌ؒΠϯσοΫε • id num: ݸਓ൪߸ • cov1: ࣌ؒมಈڞมྔ; ೋ஋ • cov2: ࣌ؒมಈڞมྔ; ࿈ଓ • cov3: ϕʔεϥΠϯڞมྔ; ࿈ଓ • treat: ࣏ྍ; ೋ஋ • outcome: Ξ΢τΧϜ; ೋ஋ 37 / 46
38. ίʔυྫ: ೋ஋Ξ΢τΧϜͷ৔߹ -1 1 id <- ’id_num’ 2 time_name <- ’time’ 3 covnames <- c(’cov1’, ’cov2’, ’treat’) 4 covtypes <- c(’binary’, 5 ’zero-inflated␣normal’,’normal’) 6 outcome_name <- ’outcome’ 7 histories <- c(lagged, cumavg) 8 histvars <- list( 9 c(’treat’,’cov1’,’cov2’), c(’cov1’,’cov2’)) ϙΠϯτ • Πϯϓοτͷσʔλ͸ data.table ΦϒδΣΫτͰͳ͚Ε͹ͳΒͳ͍ • ඞཁͳ৘ใ: ݸਓΠϯσοΫε / ࣌ؒ / Ξ΢τΧϜ / ڞมྔ / ॲஔ etc... • covtypes Ͱ͸࣌ؒมԽڞมྔ Zj,k ͕ͲΜͳ෼෍ʹै͏͔Λࢦఆ (cf. εςοϓ 1.a.) • histries Ͱ͸ཤྺΛͲͷΑ͏ʹϞσϦϯά͢Δ͔Λࢦఆ 38 / 46
39. ίʔυྫ: ೋ஋Ξ΢τΧϜͷ৔߹ -2 1 covparams <- list(covmodels = c( 2 cov1 ~ lag1_treat + lag1_cov1 + lag1_cov2 + cov3 + time, 3 cov2 ~ lag1_treat + cov1 + lag1_cov1 + 4 lag1_cov2 + cov3 + time, 5 treat ~ lag1_treat + cumavg_cov1 + 6 cumavg_cov2 + cov3 + time)) 7 8 ymodel <- outcome ~ treat + cov1 + cov2 + 9 lag1_cov1 + lag1_cov2 + cov3 ϙΠϯτ • covparams Ͱ͸ Zj,k ͱཤྺؒͷؔ܎ੑΛࢦఆ (cf. εςοϓ 1.a.) • ϥάͷਂ͞ʹ͍ͭͯ΋ covparams Ͱࢦఆ • ymodel Ͱ͸Ξ΢τΧϜͱཤྺؒͷؔ܎ੑΛࢦఆ (cf. εςοϓ 1.b.) 39 / 46
40. ίʔυྫ: ೋ஋Ξ΢τΧϜͷ৔߹ -3 1 intvars <- list(’treat’, ’treat’) 2 interventions <- list( 3 list(c(static, rep(0, 7))), 4 list(c(threshold, 1, Inf))) 5 int_descript <- c(’Never␣treat’, 6 ’Threshold-lower␣bound␣1’) 7 nsimul <- 10000 8 ncores <- parallel::detectCores() - 1 ϙΠϯτ • intervention ͰϢʔβʔࢦఆͷنଇΛఆٛ (cf. εςοϓ 2.b.) • nsimul Ͱ s = n Λࢦఆ (cf. εςοϓ 2) 40 / 46
41. ίʔυྫ: ೋ஋Ξ΢τΧϜͷ৔߹ -4 1 gform_bin_eof <- gformula_binary_eof( 2 obs_data = binary_eofdata, 3 id = id, time_name = time_name, 4 covnames = covnames, 5 outcome_name = outcome_name, 6 covtypes = covtypes, covparams = covparams, 7 ymodel = ymodel, intvars = intvars, 8 interventions = interventions, 9 int_descript = int_descript, 10 histories = histories, histvars = histvars, 11 basecovs = c("cov3"), seed = 1234, 12 parallel = TRUE, nsamples = 20, 13 nsimul = nsimul, ncores = ncores) 14 gform_bin_eof 15 plot(gform_bin_eof) 41 / 46
42. ίʔυྫ: ೋ஋Ξ΢τΧϜͷ৔߹ -5 k Interv. g-form mean Mean SE Mean lower 95% CI Mean upper 95% CI 6 1 0.09285333 0.009144334 0.08112626 0.1095961 6 2 0.08771817 0.015160129 0.06744307 0.1186075 42 / 46
43. ࣌ؒґଘੑ࣏ྍΛਂ͘஌Δʹ͸ ೔ຊޠͰ͸ [8] [9], ӳޠͰ͸ [10] ͕͓͢͢Ί. ಛʹ11.5અ શମ Part II / III 43 / 46
44. ࣌ؒґଘੑ࣏ྍΛ͞Βʹਂ͘஌Δʹ͸ ڧԽֶशͱͷؔ࿈·Ͱݴٴ[11] 44 / 46
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47. Enjoy!