Causal inference using regression on the treatment variable

CHAPTER 9 Causal inference using regression on thetreatment Causal inference and predictive comparisonsSo far, we have been interpreting regressionspredictively: given the values of severalinputs, the fitted model allows us to predicty, considering thendata points as asimple random sample from a hypothetical infinite superpopulation or probabilitydistribution. Then we can make comparisons across differentcombinations of valuesfor these chapter and the next considercausal inference , which concerns whatwouldhappento an outcomeyas a result of a hypothesized treatment or a regression framework, the treatment can be written as a variableT:1Ti={1 if unitireceives the treatment 0 if unitireceives the control, or, for a continuous treatment ,Ti= level of the treatment assigned to the usual regression context, predictive inference relates to comparisonsbetweenunits, whereas Causal inference addresses comparisons of different treatments ifapplied to thesameunits.}

Hypothetical example of positive causal effect but zero positive predictive comparison Conversely, it is possible for a truly nonzero treatment effect to not show up in the predictive comparison. Figure 9.2 illustrates. In this scenario, the treatment has a positive effect for all patients, whatever their previous health status, as displayed

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  Comparison, Positive, Of positive

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