Advanced Statistical Methods for Observational Studies

1 L E C T U R E 0 8 Advanced Statistical Methods for Observational Studiesclass management Today is the last lecture. Presentations tomorrow. Problem Set #2 was posted on Friday. It s due a week from today (Monday, June 12) by 5pm. Get to Professor Baiocchi, MSOB x318 If I m not there then you can slip under the door. ( M A Y B E )real world randomnessBaiocchi, Cheng and Small (2014) Instrumental variable Methods for causal inference OutcomeOutcomeOutcomeOutcomeHHinstrument al variable: excess travel timeHHExcess Travel Timeinstrumental variable: excess travel timeHHExcess Travel Timeinstrumental variable: excess travel timeHHExcess Travel Timeinstrumental variable: excess travel timeHHMcClellan, McNeil & Newhouse; "Does more intensive treatment of acute myocardial infarction reduce mortality?

2 JAMA. 272(11): 859-66, September 1994instrumental variable: excess travel timeN E A R-F A R M A T C H I N Grevised designBaiocchi, Small, Lorchand Rosenbaum (2010) Building a Stronger Instrument in an Observational StudyHHHHHHHHHHHHS orting is potentially biased!HHSorting is potentially biased!HHSorting is potentially biased!Bhattacharya and Vogt (2007) Do Instrumental Variables Belong in Propensity Scores?HHSorting largely due to the randomness!HHSorting largely due to the randomness!HHSorting largely due to the randomness!Baiocchi, Small, Lorchand Rosenbaum (2010) Building a Stronger Instrument in an Observational StudyN E A R-F A R M A T C H I N Ginstrumental variablesBaiocchi, Small, Lorchand Rosenbaum (2010) Building a Stronger Instrument in an Observational Studydesign-based IVs: a quick sketchdesign-based IVs: a quick sketch Use the idea of block design / pair matching to control IVs: a quick sketch Use the idea of block design / pair matching to control observedvariation.

3 Use the idea of instrumental variables/encouragement to control IVs: 1ststep Summarize discrepancies in subjects covariates We used Mahalanobisdistance 1, 2 = ( 1 2) 1( 1 2) design-based IVs: 1ststep =Mahalanobis distance between preemies and = 11 12 21 22 13 1 31 1 design-based IVs: 2ndstep Create a penalty for preemies with similar instrument values ( , calipers)design-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 design-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 design-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 = 11 12 21 22 13 1 31 1 HHSelection is potentially biased!

4 HHSelection largely due to the instrument!design-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 = 11 12 21 22 13 1 31 1 design-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 = 11 12 21 22 13 1 31 1 Diff Covariates + Diff Encouragement = Discrepancy Matrixdesign-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 = 11 12 21 22 13 1 31 1 Diff Covariates + Diff Encouragement = Discrepancy Matrix(near) (far) (barrier to being paired)design-based IVs: 2ndstep = 11 12 21 22 13 1 31 1 = 11 12 21 22 13 1 31 1 + = design-based IVs: 3rdstep Something has got to give:design-based IVs: 3rdstep Something has got to give.

5 As we force separation in the instrument, it will be more difficult to find preemies with similar IVs: 3rdstep Something has got to give: As we force separation in the instrument, it will be more difficult to find preemies with similar covariates. Allow some subjects to be removed from the study design by matching to IVs: 3rdstep Let k=number of sinks. Then augment the matrix like so: = discepancy matrix,after first two steps = matrix,with all entries 0 = matrix,with entries in Travel attending high level weight2, 2, 's - Fee for - - - birth (y/n)

6 's income41, 40, 14, home value97, 95, 48, completed high completed below poverty TypePreemie covariates% of preemies with type of congenital disordersMother covariatesCensus level covariatesHigh NICULow NICUsd in Travel attending high level weight2, 2, TypePreemie covariatesHigh NICULow NICUsd /sd1stQuartile2ndQuartile3rdQuartile4thQ uartilemax( /sd) in Travel Time( )

7 Attending high level weight2, 2, 2, 2, Pairs49, in Travel attending high level weight2, 2, Meansd /sdVariable TypePreemie covariatesEncouraged Meaninferenceinferenceinference Historically: two-stage least squaresinference Historically: two-stage least squares State of the art: residual inclusion modelsinference Historically: two-stage least squares State of the art: residual inclusion models Trusty: permutation-based inferenceinference: two-stage least squares Historically: two-stage least squaresinference: two-stage least squares Historically: two-stage least squares Model two parts of the process:inference: two-stage least squares Historically: two-stage least squares Model two parts of the process:1)Selection into the : two-stage least squares Historically.

8 Two-stage least squares Model two parts of the process:1)Selection into the )The outcome : two-stage least squares Selection into the treatment:inference: two-stage least squares Selection into the treatment: = , inference: two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + + inference: two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + + The outcome model: = , inference: two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + + The outcome model: = , Usually looks like = 0+ 1 1+ 2 2+ + + + inference: two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + The outcome model: = , Usually looks like = 0+ 1 1+ 2 2+ + + + inference: two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + The outcome model: = , Usually looks like = 0+ 1 1+ 2 2+ + + inference.

9 Two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + The outcome model: = , Usually looks like = 0+ 1 1+ 2 2+ + + inference: two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + The outcome model: = , Usually looks like = 0+ 1 1+ 2 2+ + + Generally speaking, 2sls is a predictor substitution : two-stage least squares Selection into the treatment: = , Usually looks like = 0+ 1 1+ 2 2+ + + The outcome model: = , Usually looks like = 0+ 1 1+ 2 2+ + + Generally speaking, 2sls is a predictor substitution which have : two-stage least squares Generally speaking, 2sls is a predictor substitution which have : two-stage least squares Generally speaking, 2sls is a predictor substitution which have problems.

10 Historically, the big problems came up when the outcomes (y) was not : two-stage least squares Generally speaking, 2sls is a predictor substitution which have problems. Historically, the big problems came up when the outcomes (y) was not linear. Take-away: If the outcome is : two-stage least squares Generally speaking, 2sls is a predictor substitution which have problems. Historically, the big problems came up when the outcomes (y) was not linear. Take-away: If the out