CAUSAL INFERENCE What If Part III 2020年11⽉7⽇（⼟） Borealis@insearchofsth Chapter 22 Target trial emulation 

III Causal inference from complex longitudinal data Section 22.1 The target trial (revisited) Section 22.2 Causal effects in randomized trials Section 22.3 Causal effects in observational analyses that emulate a target trial Section 22.4 Time zero Section 22.5 A unified analysis for causal inference Chapter Target trial emulation Technical Point 22.1 Technical Point 22.2 Technical Point 22.3 Fine Point 22.1 

III Causal inference from complex longitudinal data Section 22.1 The target trial (revisited) Section 22.2 Causal effects in randomized trials Section 22.3 Causal effects in observational analyses that emulate a target trial Section 22.4 Time zero Section 22.5 A unified analysis for causal inference Chapter Target trial emulation Fine Point 22.1 Technical Point 22.1 Technical Point 22.2 Technical Point 22.3 

p.37 (in Part I), p.277 Observational Data Hypothetical Randomized Trial emulate Target trial “what randomized experiment are you trying to emulate?” Intro to Chapter 22 これ以降、以下の⾊分けをしています n キーワードは⾚字 n Observational Data or Study は⻘字 n Randomized Trial or Experiment は⾚茶⾊ 

Chapter 22 で勉強すること 1. Sustained treatment strategy におけるTarget trialの概念 2. Causal inferenceのフレームワーク (Randomized experiment だろうと Observational study だろうと) 3. Causal effectの分類 (Intention-to-treat effect, Per-protocol effect) p.277 Target trial: A hypothetical randomized experiment to quantify a causal effect (p.37) Causal effect: A contrast between average counterfactual outcomes under different treatment values (p.37) 

22.1 The target trial (revisited) Section 22.1 Section 22.2 Section 22.3 Section 22.4 Section 22.5 

p.277 • Eligible participants: over 18 years old, no AIDS, no previous used of antiretroviral therapy • Randomly assigned to treatment strategy g or gʼ at the start • Start: time of assignment • End: death, loss to follow-up, 60M after baseline 22.1 The target trial (revisited) Randomized trial to estimate the effect of antiretroviral therapy on the 5-year risk of death among HIV-positive individuals Pragmatic Trial Ex n The participants and their treating physicians are aware of the treatment they receive n Nobody receives a placebo (active treatments or no treatment) n Participants are monitored as frequently and intensely as regular patient outside of the study 

p.277 22.1 The target trial (revisited) Pragmatic trial (本書内で定義の記載なし) A study (including randomized clinical trials) whose aim is to determine the effects of an intervention under the usual conditions in which it will be applied. A Dictionary of Epidemiology Six Edition 

22.1 The target trial (revisited) “We resort to observational analyses of existing data because the randomized trial that would answer our causal question— the target trial—is not feasible, ethical, and timely. ” p.277 Target trial Hernán MA, Robins JM. Am J Epidemiol 2016 

p.277 調べたい causal question を特定するためTarget trial のプロトコルを明確にする 22.1 The target trial (revisited) n Eligibility criteria n Start and end of follow-up n Treatment strategies n Outcomes of interest n Causal contrast n Data analysis plan Key Components of Protocol 

p.277 22.1 The target trial (revisited) Target trial Part I and II ：Time-fixed treatment Part III ： Sustained treatment strategy 

22.1 The target trial (revisited) Population Intervention Comparator Outcome p.278 PICO Richardson MA, et al. APC J Club 1995 

22.2 Causal effects in randomized trials Section 22.1 Section 22.2 Section 22.3 Section 22.4 Section 22.5 

22.2 Causal effects in randomized trials p.278‒ Three types of causal effects 1. The effect of assignment to the treatment strategy, regardless of treatment actually received (intention-to-treat effect) 2. The effect of receiving the interventions as specified in the study protocol (per-protocol effect) 3. The effect of receiving interventions other than the ones specified in the study protocol これまでの章で考えてきたこと Causal effect of treatment on an outcome Y measured at the end of follow-up 本章で考えること Causal effect on survival (Technical Point 22.3) 

参 考 （テキストの内容ではありません） <参考> Short Course on Causal Inference, Jun. 3-7, 2019 (Harvard T.H. Chan School of Public Health) Day5の講義資料 Z A Y U Randomization to RTS arm vs non-malaria comparator arm Adherence Malaria status in 12 months of follow-up n アフリカの7カ国で⾏われたマラリアワクチン候補 RTS,S/AS01の第3相試験 n ⽣後6〜12週の児 (N = 6,537) をRTS,S/AS01かnon-malaria comparator vaccineにランダムに割付 n どちらの群もプロトコルに従って3回接種（予定通り接種できなかった児はnonadherentとする） A Phase 3 Trial of RTS,S/A01 Malaria Vaccine in African Infants n 重症マラリアに対する効果： Intention-to-treat population では 26.0% (95% CI, -7.4 to 48.6) Per-protocol populationでは 36.6% (95% CI, 4.6 to 57.7) RTS,S Clinical Trials Partnership, et al. N Engl J Med 2012 (1 minus the risk ratio) 

RTS,S Clinical Trials Partnership, et al. N Engl J Med 2012 の Figure 1.を改変 6537 Infants 4538 Received dose 1 of RTS,S/AS01 ITT population 2179 Received dose 1 of control vaccine ITT population 4235 Received dose 2 4145 Received dose 3 3995 Were included in the per-protocol population 死亡、同意撤回、 転居、追跡不能 2179 Received dose 2 2090 Received dose 3 2008 Were included in the per-protocol population 参 考 （テキストの内容ではありません） 死亡、同意撤回、 転居、追跡不能、 医学的理由による接種 計画からの逸脱 死亡、同意撤回、 転居、追跡不能 死亡、同意撤回、 転居、追跡不能、 医学的理由による接種 計画からの逸脱 

22.2 Causal effects in randomized trials p.278 Ak 1: if the individual receives therapy at time k 0: otherwise Ck 1: if the individual remains uncensored at time k 0: otherwise k 0, 1, 2...K with K =59 (5-year follow-up) Z Assigned to g1 or g0 1: g1 “receive treatment Ak = 1 continuously during the follow-up unless a contraindication or toxicity arises” 0: g0 “receive treatment Ak = 0 continuously during the follow- up” Dk Indicator for death (1: yes, 0: no) by month K = 1, 2….K +1 Key variables 

overbar について p.235 (in Chapter 19) time ０から time k までの治療歴 “We use an overbar to denote treatment history, ...” ̅ "k = "0 , "1 , … ") ̅ " = "0 = 1, "1 = 1, … "59 = 1 = 1, 1, … 1 ̅ " = , 1 ̅ " = 0, 0, … 0 = , 0 or フォローアップ中継続して治療を受けた場合の治療歴 フォローアップ中ずっと治療を受けなかった場合の治療歴 治療歴全体 K を⽰す場合は ̅ "-ではなく以下のように表記 ̅ " 

22.2 Causal effects in randomized trials p.279 Intention-to-treat effect The effect of assignment to the treatment strategy regardless of treatment actually received Pr D $ %&',) * $ &) + = 1 −Pr D $ %&+, ̅ * $ &) + = 1 time k における intention-to-treat effect は the counterfactual risk of death under assignment to strategy g1 (z = 1) vs g0 (z = 0) if nobody had been lost to follow-up through time k () 01 = ) 2) 3つの causal effect 〜その１〜 

22.2 Causal effects in randomized trials p.279 n be assigned to strategy g1 at baseline and remain under study until the end of follow-up n be assigned to strategy g0 at baseline and remain under study until the end of follow-up Intention-to-treat effect 

22.2 Causal effects in randomized trials p.279-280 治療へのassignmentと治療のinitiationが同時に発⽣する場合 Intention-to-treat effect は以下の⼆つの意味を持つ： n The effect of assignment n The effect of initiation Pr D $ % & '(,* + $ '* , = 1 −Pr D $ % & ',, ̅ + $ '* , = 1 Ex ・g1 に割り付けられた全ての⼈が time 0 の時点で治療を受ける （その後、継続治療を受けようとそうでなかろうと） ・g0 に割り付けられた全ての⼈が time 0 の時点で治療を受けない （その後、治療を受けることになろうとも） 

22.2 Causal effects in randomized trials p.280 Intention-to-treat effect is agnostic about any treatment decisions made after baseline, including: n Discontinuation or initiation of the treatments of interest n Use of non-approved concomitant treatments n Any other deviations from protocol ある２つの研究について、 どちらにもバイアスがなく同じプロトコールであったとしても 異なった状況で⾏われれば得られる intention-to-treat effect は違ってくる可能性がある 

22.2 Causal effects in randomized trials p.280 Per-protocol effect The effect of receiving the interventions as specified in the study protocol time k における per-protocol effect effect は… the counterfactual risk of death under full adherence to strategy g1 vs g0 if nobody had been lost to follow-up through time k (4 56 = 8 9) 3つの causal effect 〜その 2〜 The comparison of dynamic strategies rather than static strategies (Fine Point 19.2) Pr D < = > ,8 @ < A8 B = 1 −Pr D < = B , ̅ @ < A8 B = 1 

22.2 Causal effects in randomized trials p.280 n receive treatment strategy g1 continuously between baseline k = 0 and end of follow-up n receive treatment to strategy g0 continuously between baseline k = 0 and end of follow-up Per-protocol effect 

Fine Point 19.2 Per-protocol effects to compare treatment strategies p.239 (in Chapter 19) n Valid estimation of the per-protocol effect generally demands that trail investigators collect post-randomization data on…: ・ adherence to the strategy ・ (time-varying) prognostic factors associated with adherence n Baseline randomization makes us expect baseline exchangeability for the assigned treatment strategy, not sequential exchangeability for the strategy that is actually received. Hernán MA, Robins JM. N Engl J Med 2017 

22.2 Causal effects in randomized trials p.280 Per-protocol effect “In our example above, a couple would have an interest in knowing the effect of the contraception method if all trial participants had used it as indicated in the protocol. This effect, which is referred to as the per-protocol effect, is what would have been observed if all patients had adhered to the trial protocol. ” Hernán MA, Robins JM. N Engl J Med 2017 

22.2 Causal effects in randomized trials p.280 n Contraindication n Toxicity etc. Discontinuation from Study Protocol Discontinuation of the originally assigned treatment or initiation of other treatments cannot possibly be considered a deviation from protocol 

22.2 Causal effects in randomized trials p.281 Intention-to-treat effect でも Per-protocol effect でもない Effect The effect of receiving the interventions other than the ones specified in the study protocol Strategy g0 は g1 よりも劣っているという意⾒が出始めた → 医師のよっては、臨床経過が思わしくない場合に治療を勧めようになった （例えば CD4 cell count がはじめて 200 cells/μL を下回った場合） → 開始時に g0 に割り振られた被験者が実際は modified g’0 に従うようになった “receive treatment Ak = 0 continuously during the follow-up but, after Lk < 200, switch to treatment Ak = 1” 3つの causal effect 〜その 3〜 Ex 

22.2 Causal effects in randomized trials p.281 n receive treatment strategy g1 continuously between baseline k = 0 and end of follow-up n receive treatment strategy g'0 continuously between baseline k = 0 and end of follow-up Per-protocol effects that do not correspond to the original per-protocol effect Per-protocol effects in target trials that can be emulated using the randomized trial data g0 ではない 

22.2 Causal effects in randomized trials p.279-281 █ receive treatment strategy g1 continuously between baseline k = 0 and end of follow-up █ receive treatment strategy g'0 continuously between baseline k = 0 and end of follow-up The effect of receiving the interventions other than the ones specified in the study protocol █ receive treatment strategy g1 continuously between baseline k = 0 and end of follow-up █ receive treatment strategy g0 continuously between baseline k = 0 and end of follow-up Per-protocol effect █ be assigned to strategy g1 at baseline and remain under study until the end of follow-up █ be assigned to strategy g0 at baseline and remain under study until the end of follow-up Intention-to-treat effect 22.2で解説した3つの causal effect 

22.3 Causal effects in observational analyses that emulate a target trial Section 22.1 Section 22.2 Section 22.3 Section 22.4 Section 22.5 

22.3 Causal effects in observational analyses that emulate a target trial p.281 n Randomized trial （←前述） n Observational analyses that emulate a target trial （←これから解説） 以下の2つの Causal effect は同様に定義することができる 

22.2 Causal effects in randomized trials p.278 Ak 1: if the individual receives therapy at time k 0: otherwise Ck 1: if the individual remains uncensored at time k 0: otherwise k 0, 1, 2...K with K =59 (5-year follow-up) Z Assigned to g1 or g0 1: g1 “receive treatment Ak = 1 continuously during the follow-up unless a contraindication or toxicity arises” 0: g0 “receive treatment Ak = 0 continuously during the follow- up” Dk Indicator for death (1: yes, 0: no) by month K = 1, 2….K +1 Key variables (再掲) 

p.281 n initiate treatment A0 = 1 at baseline and remain under study until the end of follow-up n initiate treatment A0 = 0 at baseline and remain under study until the end of follow-up 22.3 Causal effects in observational analyses that emulate a target trial Observational analog of the intention-to-treat effect Pr D $ % & '(,* + $ '* , = 1 −Pr D $ % & ',, ̅ + $ '* , = 1 ... corresponds to the intention-to-treat effect in a target trial in which assignment to and the initiation of the strategies occurs simultaneously Observational analog of the intention-to-treat effect at time k 

22.3 Causal effects in observational analyses that emulate a target trial p.282 n 治療群に割り振られたのに治療を開始しなかった個⼈が含まれる trial の intention-to- treat effectとは少し異なる。 ＜理由（例の場合）＞ Baselineで antiretroviral therapyを開始したか否かで⽐較している Observational analog of the intention-to-treat effect Observational analog of the per-protocol effect n Target trial の per-protocol effect と同様に定義される Randomized trial では以下の2つを区別する必要があるが、Observational study では不要 ・Original per-protocol effect ・Per-protocol effects in alternative target trials ＜理由＞ pre-specified protocol が存在しないため、それぞれの per protocol effect は特定 のtarget trail に⼀致する 

Fine Point 9.4 Effectiveness vs Efficacy p.239 (in Chapter 19) There is a wide spread view that: p.122 (in Chapter 9) To measure... Loosely defined Intention-to-treat effect Effectiveness The effect of treatment that would be observed under realistic conditions Per-protocol effect Efficacy The effect of treatment that would be observed under perfect conditions 

22.3 Causal effects in observational analyses that emulate a target trial p.283 There is a wide spread view that: To measure Loosely defined Intention-to-treat effect Effectiveness The effect of treatment that would be observed under realistic conditions Per-protocol effect Efficacy The effect of treatment that would be observed under perfect conditions しかし effectiveness, efficacy というラベルは sustained strategy においては曖昧である 以下のように主張することが難しいから △ (Realistic condition で) per-protocol effect は efficacy を評価している △ (治療効果が判明した後で)intention-to-treat effect は effectiveness を評価している “especially problematic when interested in sustained treatment strategies” 

22.3 Causal effects in observational analyses that emulate a target trial p.283 Example: Discrepancy between the estimates in observational study and randomized trial ホルモン補充療法が閉経後⼥性の冠動脈疾患のリスクを下げるか？ Hernán MA, Robins JM. Epidemiology 2008 ⽐較対象 冠動脈疾患のリスク(*) Observational study （N = 59,337） F Grodstein. N Engl J Med. 1996 Never users vs Current users (estrogen with progestin, or estrogen alone) Randomized trial （N = 16,608） JE Rossouw. JAMA. 2002 Receive Placebo vs Receive Estrogen with Progestin *ハザード⽐による （ぜひ原著を） “Never users” vs “Current users” の⽐較が Randomized trial でなされることは稀。 ∵ “prevalent users” の背景が時間経過で変化していくのに “prevalent users” vs ”non-users”で⽐較しても介⼊に⼀致しない、selection biasを受けやすい 

ちなみ『疫学⽤語辞典第5版』では EFFECTIVENESS 効果 Archibald L. Cochrane (1909-88) らにより，疫学者間の標準的⽤法とされているのは，特定の介 ⼊，処置，治療法あるいはサービスを⽇常的な状況でフィールドに適⽤した場合に，対象集団に対 して実現しようと意図したことをどの程度実現できるかの指標。ヘルスケア介⼊が現実の⽬標をど の程度実現できるかの指標。EFFICACY有効性や EFFICIENCY効率 とは区別される。 EFFICACY 有効性 特定の介⼊，⼿順，治療法あるいはサービスが理想的な状況でもたらす便益の程度。理想的には， 有効性は RANDOMIZEDCONTROLLEDTRIAL 無作為化⽐較試験の結果に基づいて決定される。 

22.4 Time zero Section 22.1 Section 22.2 Section 22.3 Section 22.4 Section 22.5 

22.4 Time zero p.283 A crucial component of target trial emulation Start of follow-up Baseline Time zero Eligibility criteria need to be met at that point but not later n In randomized experiment: the time when individuals are assigned to a treatment strategy n In observational analysis: the time follow-up would have started in the target trial 

22.4 Time zero p.283 Randomization Not reasonable ・Treatment strategies had yet to be assigned. ・Eligibility criteria had not been defined. Potentially biased -2 years +2 years ・Deaths during the first 2 years of the trial would be excluded from the analysis. ・Short-term effect on mortality would be missed. ・Differential proportion of susceptible individuals (→ selection bias) (Antiretroviral therapy) Ex Time zero 

22.4 Time zero p.283-284 Start of the follow-up in the observational analysis Time the follow-up would have started in the target trial How to emulate the start of follow-up of the target trial is not always obvious Time zero 

22.4 Time zero 1. Eligibility criteria can be met at a single time Immediate initiation of antiretroviral therapy when the CD4 cell count first drops below 500 cells/μL vs Delayed initiation (in HIV-positive individuals) 2. Eligibility criteria can be met at multiple times Initiation vs No initiation of hormone therapy (among postmenopausal women no history of chronic disease and no use of hormone therapy during the previous two year) → At age 51, 52, 53 ...? p.284 How many times the eligibility criteria can be met? Ex Ex 

22.4 Time zero a) The first eligible time b) A randomly chosen eligible time c) Every eligible times ・Fixed schedule for data collection at pre-specified times → emulate a new trial at each pre-specified time every two years, like in many epidemiologic cohorts ・Subject-specific schedule for data collection → emulate a new trial starting at each time unit a day, week or month in electronic medial records p.284 Time zero in settings with multiple eligibility times Ex Ex ・More efficient because of more available data ・Requiring adjustment of the variance of the effect estimate (ex. bootstrapping) 

Fine Point 22.1 Grace periods (1/3) p.285 In the real world, antiretroviral therapy cannot be started exactly on the same day the CD4 cell count is measured. →Investigators need to define a grace period Delayed initiation Immediate initiation of treatment when CD4 cell count first drops below 500 cells/μL vs Redefine … Immediate Initiate therapy within 3 moths after CD4 cell count first drops below 500 cells/μL Immediate Initiate therapy more than 3 moths after CD4 cell count first drops below 500 cells/μL vs Ex 被験者が 2 monthsで死亡してしまったらどちらのarmに割り付けるのか？ Question: Answer 1: その被験者をどちらかのarmにランダムに割り付ける 

Fine Point 22.1 Grace periods (2/3) p.285 Create two exact copies of the individual (clones) l If the individual starts therapy in month 3 l The clone assigned to “start after 3 month” would be censored at that time LE Cain, Hernán MA,et al. Int J Biostat 2010 Ex l If the individual had died in month 2 l The both clones would have died → the death would have been assigned to both arms Ex Double allocation of events To prevent the bias that could arise if events occurring during the grace period were systematically assigned to one of the two arms only Question: 被験者が 2 monthsで死亡してしまったらどちらのarmに割り付けるのか？ Answer 2: 

Fine Point 22.1 Grace periods (3/3) p.285 When using grace periods with cloning and censoring, ... Because each individual is assigned to all strategies at baseline, a contrast based on baseline assignment will compare groups with essentially identical outcomes. Intention-to-treat effect Per-protocol effect cannot be estimated 

22.5 A unified analysis for causal inference Section 22.1 Section 22.2 Section 22.3 Section 22.4 Section 22.5 

22.5 A unified analysis for causal inference p.284‒ Randomized trial を Follow up study without baseline randomization と捉えることができる Randomized experiment (i) No baseline confounding (ii) Known randomization probability (iii) Known assignment to a treatment strategy for each individual at baseline Observational analysis (i) If one measures and appropriately adjusts for a sufficient set of covariates (ii) If the model for treatment assignment is correctly specified (iii) ( Not necessary for estimating the per-protocol effect ) How to emulate randomized experiments Only three things distinguish the data from randomized experiments and observational studies emulate 

22.5 A unified analysis for causal inference p.286 “intention-to-treat analysis” n Lack of adjustment for baseline confounding is justified by randomization n No adjustment for post-randomization confounding is required ∵ There cannot be post-randomization confounding for the effect of baseline assignment “per-protocol analysis” intention-to-treat effect per-protocol effect In a typical intention-to-treat analysis … Validly estimate? In randomized trial 

22.5 A unified analysis for causal inference p.286 “intention-to-treat analysis” n To eliminate selection bias from loss to follow-up, an “intention-to-treat analysis” adjusted for post-randomization (time-varying) prognostic factors is required n When the time-varying prognostic factors are affected by prior treatment, an appropriate adjustment will require the use of g-methods intention-to-treat effect For valid estimation of the intention-to-treat, ... Validly estimate? The probability of dropping out may be influenced by the onset of symptoms ( = a consequence of treatment itself) Ex Post-randomization selection bias ・differential lost to follow-up ・influence from prognostic factors In randomized trial 

22.5 A unified analysis for causal inference p.286-287 “per-protocol analysis” per-protocol effect Validly estimate? (“on treatment analysis”) Only includes individuals who adhered to the instructions specified in the study protocol Problematic for two reasons ■Postrandomization selection bias due to differential loss to follow-up (like “intention-to-treat” analysis) n Partly disregards the randomized groups Naive per-protocol analysis: per-protocol analysis does not even attempt to adjust for confounding In randomized trial 

22.5 A unified analysis for causal inference p.286 “intention-to-treat analysis” Adjustment for baseline and time-varying prognostic factors using g-methods “per-protocol analysis” intention-to-treat effect per-protocol effect To estimate the observational analog of the intention-to-treat effect and the per-protocol effect ... Validly estimate? In Observational Analysis 

22.5 A unified analysis for causal inference p.287 Randomized trial n Adjustment for post-baseline (time-varying) factors: Generally necessary for per-protocol analyses for both randomized trails and observational studies Observational study ・Post-randomization confounding ・Post-randomization selection bias ・Time-varying confounding ・Selection bias Similar 

22.5 A unified analysis for causal inference p.287 Randomized trial “When we cannot conduct the randomized experiment that would answer our causal question, we resort to observational analyses. It is therefore important to use a sound approach to design and analyze observational studies.” Observational study ・expensive ・infeasible ・unethical ・untimely far superior Historically, ... “Making the target trial explicit is one step in that direction.” 

Technical Point 22.1 Controlled direct effects (1/3) p.278 A B Y direct effect (A on Y) 仮に intermediate variable である B が2値(0 or 1)の場合， Bがそれぞれ固定された条件での効果（A on Y）を考察することができる （controlled direct effect） E "#$%,'$% −E "#$),'$% E "#$%,'$) −E "#$),'$) と (treatment) (outcome) 

Technical Point 22.1 Controlled direct effects (2/3) p.278 A B Y direct effect Baseline Randomly assigned to treatment A =1 or A =0 1M Randomly assigned to treatment B =1 or B =0 3M Outcome of interest Y is measured E "#,% = Pr "#,% = 1 Pr " = 1 | + = ,, - = . Counterfactual quantity Observed risk consistently estimated by Ex (treatment) (treatment) (outcome) 

Technical Point 22.1 Controlled direct effects (3/3) p.278 A B Y direct effect (A on Y) (treatment) (outcome) The controlled direct effect can also be validly estimated in observational studies as long as the identifiability conditions of ... ・Consistency ・Positivity ・Exchangeability ... hold for both A and B 

Technical Point 22.2 (1/2) Natural direct effects and Principal stratum direct effects p.279 Natural direct effect Controlled direct effect 以外の direct effect E "#$%, −E "#$(, The average causal effect of A on Y if the value of B had been set to the value that B would taken if A had been set to 0 a=0,a=1で⽰されるconterfactual outcomeを同時に考慮しなくてはないけない “cross-world quality” Randomized experimentではNatural direct effect を同定することはできない Observational data ではNatural direct effect estimate は⽴証されない 

Technical Point 22.2 (2/2) Natural direct effects and Principal stratum direct effects p.279 Controlled direct effect 以外の direct effect Principal stratum direct effect The average causal effect of A on Y in the subset of the population whose value of B would have been equal to b regardless of the value of A ( !"#$ = !"#& = b ) E *"#&,, | !"#$ = !"#& = b − E *"#$,, | !"#$ = !"#& = b E *"#& | !"#$ = !"#& = b − E *"#$ | !"#$ = !"#& = b do not involve joint counterfactuals *",, 

Technical Point 22.3 Survival analysis with time-varying treatments (1/2) p.282 何を⽬的に g-methods を使っているか？ n Chapter 17 (“Causal survival analysis”)では Effect of point interventions on failure time outcomes を推定するため n Chapter 21 (“G-methods for time-varying treatments”)では Effect of sustained treatment strategies on non-failure time outcomes を推定するため n 実際にはしばしば Effect of sustained strategies on failure time outcomes を推定するため Pr D$%& ' ( = 1 under the treatment strategy ' + これを推定するためには g-formula と IP weighting にもとづく、２つのアプローチがある 

Technical Point 22.3 Survival analysis with time-varying treatments (2/2) p.282 数式は転載 n g-formula n IP weighting Pr D$%& ' ( = 1 under the treatment strategy ' + Hernán MA,et al. JASA 2001 Young JG, Hernán MA,et al. Stat Biosci 2011 スライド終わり