#JSM2018 Rod Little up next, talking about multiple Imputation for causal inference 
#JSM2018 Little Statistics is prediction. Multiple Imputation is an all-purpose tool for prediction.
#JSM2018 Little Using Penalized Spline of Propensity Prediction (PSPP). Estimate propensity to respond to Y model, then include propensity as spline in impute for Y with other covariates. Now, extend this to causal inference
#JSM2018 Little Apply to propensity to be assigned to treatment rather than propensity to respond. Easy in one time treatment, but harder in longitudinal causal inference
#JSM2018 Little Longitudinal causal inference can be done when reframing everything as a major missing data problem, with propensities for each treatment and combination of treatments.
#JSM2018 Little Penalized spline does better than augmented weighting approaches. Why? Weighting can be inefficient when propensities are variable.
#JSM2018 Little Causal effects for propensities close to zero and 1 poorly determined. This is exacerbated in longitudinal treatments. Can be combinations of treatments never observed. So, need to modify estimate to subpopulations where true propensities are not close to 0 or 1
#JSM2018 Little argues that propensity models should omit spurious variables. Rubin apparently disagrees.
