Causality in Biomedicine Lecture Series: Lecture 2 Ava Khamseh (Biomedical AI Lab) IGMM & School of Informatics 30 Oct, 2020
<latexit sha1_base64="THysm4IscHt9No/tkD9LNMzeowE=">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</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
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)
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)
<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
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
Causal inference with observed confounders X T Y
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