causality in biomedicine lecture series lecture 2
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Causality in Biomedicine Lecture Series: Lecture 2 Ava Khamseh (Biomedical AI Lab) IGMM & School of Informatics 30 Oct, 2020 <latexit


  1. Causality in Biomedicine Lecture Series: Lecture 2 Ava Khamseh (Biomedical AI Lab) IGMM & School of Informatics 30 Oct, 2020

  2. <latexit sha1_base64="THysm4IscHt9No/tkD9LNMzeowE=">ACTXicdVFNTxsxEPWmtND0K7THXiyiSpsDkTekTXqohODCESQCSNko8npnEwuvd2vPokQpf7CXSr31X3DhAEILxtQW7UjWXp67814/BzlSlpk7JdXe7Ly9Nnq2vP6i5evXr9prL89slhBAxEpjJzEnELSmoYoEQFJ7kBnkYKjqPT3VI/PgNjZaYPcZ7DKOUTLRMpODpq3IhDBQn6odRI5+PAn7Vyf/YNvwSteEZDukmXCntUmFNCIydTbNFQw9fKEUZy4lcDNit3yZQtzj5uNFmbsW7vE6MOfO73+z0HOh9ZlzEaOKmsJlnW/rjxM4wzUaSgUShu7TBgOY4W3KAUCs7rYWEh5+KUT2DoOYp2NHiPo1z+sExMU0y47b7J79vWPBU2vnaeScKcep/VsryX9pwKT/mghdV4gaFdlBSKYkbLaGksDQhUcwe4MNLtSsWUGy7QfUDdhfDwUvp/cNRpB1vtzkG3ub2zjGONvCcbxCcB6ZFtskf2yYAI8p1ckCty7f3wLr0b7ay1rxlzvyR9VW7wCVIbCm</latexit> <latexit sha1_base64="WBS6W4REKXQyW0MTnj/H3EUrYU=">AB/3icdVDLSgMxFM3UV62vUcGNm2AR2k3J1GrHhVB047KCfUBbSiZN29BMZkwyYm78FfcuFDErb/hzr8x01ZQ0QMXTs65l9x7vJAzpRH6sBILi0vLK8nV1Nr6xuaWvb1TVUEkCa2QgAey7mFORO0opnmtB5Kin2P05o3uIj92i2VigXiWg9D2vJxT7AuI1gbqW3vhZm7sT5zsrAp6A2cvVC2badRDqFC8QRBQ05d1y0akj9GBYSgY6wYaTBHuW2/NzsBiXwqNOFYqYaDQt0aYakZ4XSakaKhpgMcI82DBXYp6o1mu4/gYdG6cBuIE0JDafq94kR9pUa+p7p9LHuq9eLP7lNSLdVsjJsJIU0FmH3UjDnUA4zBgh0lKNB8agolkZldI+lhiok1kKRPC16Xwf1LN5yjXP6qkC6dz+NIgn1wADLAUVQApegDCqAgDF4AE/g2bq3Hq0X63XWmrDmM7vgB6y3TxImlNw=</latexit> Last time: Observational data, what goes wrong? p ( x | t = 1) 6 = p ( x | t = 0) Control treatment Age ✓Z ◆ Z Z � � y 1 ( x ) p ( x | t = 1) dx � y 0 ( x ) p ( x | t = 0) dx 6 = y 1 ( x ) � y 0 ( x ) p ( x ) dx

  3. Simpson’s Paradox • Why concluding causality from purely associational measures, i.e. correlation, can be very wrong (not just neutral): “It would have better not to make any statements!” Causal Inference in Statistics, Pearl (2016)

  4. Simpson’s Paradox • Why concluding causality from purely associational measures, i.e. correlation, can be very wrong (not just neutral): “It would have better not to make any statements!” Causal Inference in Statistics, Pearl (2016)

  5. <latexit sha1_base64="WbTWK3I0Vx5XeT+HXSWxJjiZj3c=">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</latexit> <latexit sha1_base64="fG9hr1wb+mxWBc3sl+X7Dh9wJ0=">ACEHicdZDNSgMxFIUz/tb6V3XpJljEClIytdq6UEQ3LitYFTqlZNKMhmYyQ3JHWsY+ghtfxY0LRdy6dOfbmGoFb0Q+DjnXm7u8WMpDBDy5oyMjo1PTGamstMzs3PzuYXFUxMlmvE6i2Skz31quBSK10GA5Oex5jT0JT/zO4cD/+yKayMidQK9mDdDeqFEIBgFK7Vya3EBdt3r7jr2hMIFsuFaAt6F1Mi8HAf1wrd9T3SyuVJkZByZtgCzvVarViobRFyoRg1qDyqNh1Vq5V68dsSTkCpikxjRcEkMzpRoEk7yf9RLDY8o69I3LCoactNMPw7q41WrtHEQafsU4A/1+0RKQ2N6oW87QwqX5rc3EP/yGgkE1WYqVJwAV+xzUZBIDBEepIPbQnMGsmeBMi3sXzG7pJoysBlmbQhfl+L/4bRUdDeLpeNyfv9gGEcGLaMVEAuqB9dIRqI4YukF36AE9OrfOvfPkPH+2jDmSX0o5yXd/K0mg=</latexit> Potential Outcomes Assumptions (Rubin) • Consistency: The observed outcome is independent of how the treatment is assigned • Unconfoundedness: Treatment assignment is random, given covariants X • Positivity: Every individual has a non-zero chance of receiving the treatment/control p ( t = 1 | x ) ∈ (0 , 1) if P ( x ) > 0 Average treatment effect: X N 0 ] = 1 ⇣ ⌘ E [ y ( i ) − y ( i ) y ( i ) − y ( i ) τ = ˆ E [ τ ( i ) ] = ˆ X 1 1 0 N i =0 T Y

  6. Overview of the course • Estimating causal effects • Randomised trial vs observational data Causal Inference Causal Effect Estimation Casual Discovery Obsv confounders Unobsv confounders Constraint- Score- FCM based based Front- Propensity Regression IV door score Adjustment Modern ML criterion Rubin Rubin, Pearl

  7. Causal inference with observed confounders X T Y

  8. <latexit sha1_base64="9odU2tzoPjKIqzEobcp4SjaO6NY=">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</latexit> <latexit sha1_base64="V+Taq8YIMQSZsckmKN+RsAVF0eI=">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</latexit> <latexit sha1_base64="IrSAICuzpW+6WAEf9p0DoZSw78=">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</latexit> <latexit sha1_base64="lWIDvoFMuna1T+j4f7ZbYD08=">ACXicdVDLSgMxFM3UV62vqks3wSIhTLTltYuhKIblxX6GlLyaS3bWjmQZIRyjBbN/6KGxeKuPUP3Pk3ZtoKnogcDjnXG7ucQLOpDLNDyO1srq2vpHezGxt7+zuZfcP2tIPBYUW9bkvbIdI4MyDlmKgx0IK7DoeNMLxO/cwtCMt9rqlkAfZeMPTZilCgtDbL45rzngCKDyI7t/JI242a+B4FkPInkzIJp1sxKFWtSKxXLJU2KVsWqWtjSVoIcWqIxyL73hj4NXfAU5UTKrmUGqh8RoRjlEGd6oYSA0CkZQ1dTj7g+9H8khifaGWIR7Qz1N4rn6fiIgr5cx1dNIlaiJ/e4n4l9cN1eisHzEvCBV4dLFoFHKsfJzUgodMAFV8pgmhgum/YjohglCly8voEr4uxf+TdrFglQrF63KufrGsI42O0DE6Raqojq6Qg3UQhTdoQf0hJ6Ne+PReDFeF9GUsZw5RD9gvH0CvjmaZA=</latexit> <latexit sha1_base64="WbTWK3I0Vx5XeT+HXSWxJjiZj3c=">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</latexit> <latexit sha1_base64="d6/PjYT/vtO/n2H7zIpejOPMdpM=">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</latexit> <latexit sha1_base64="XcTopXEfSETh7FOlB7N0af2vQ=">ACAnicdVDLSgMxFM3UV62vUVfiJliEuikzbW3trujGZQX7gLYOmTRtQzOZIckIwzC48VfcuFDErV/hzr8x01ZQ0QMXDufcm9x73IBRqSzrw8gsLa+srmXcxubW9s75u5eW/qhwKSFfeaLroskYZSTlqKkW4gCPJcRjru9CL1O7dESOrzaxUFZOChMacjipHSkmMeRDdxgZ4kTtwP+ZCI9J1YJQ5NHDNvFS2rblVrUJN6uVQpa1Kyq3bNhra2UuTBAk3HfO8PfRx6hCvMkJQ92wrUIEZCUcxIkuHkgQIT9GY9DTlyCNyEM9OSOCxVoZw5AtdXMGZ+n0iRp6UkefqTg+pifztpeJfXi9Uo7NBTHkQKsLx/KNRyKDyYZoHFJBsGKRJgLqneFeIEwkqnltMhfF0K/yftUtE+LVpXlXzjfBFHFhyCI1ANqiBrgETdACGNyB/AEno1749F4MV7nrRljMbMPfsB4+wRrRZgc</latexit> Regression Adjustment • X is a sufficient set of confounders if conditioning on X, there would be no confounding bias y ( i ) • For individual (i) there is only one observed outcome: t i • Would like to estimate (infer) counterfactual : h y ( i ) | 1 − t, x ( i ) i y ( i ) 1 − t = ˆ E ˆ • Using a design matrix, fit: Y = � X X + � T T + ✏ Ctrl Drug Young Old y (1)     β t =0 + β x =young     1 0 1 0 y (2) β t =0 + β x =old 1 0 0 1                 T = .. .. X = .. .. = .. ..                 y ( N − 1) β t =1 + β x =young 0 1 1 0         0 1 0 1 y ( N ) β t =1 + β x =old • Assumptions: Overlap and additivity N 0 ] = 1 ⇣ ⌘ E [ y ( i ) − y ( i ) y ( i ) − y ( i ) τ = ˆ E [ τ ( i ) ] = ˆ X 1 1 0 N i =0

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