Suppose we use the simple linear model to estimate the ITT effect of treatment assignment based on data from a randomized trial. Show that fitting XXXXXXXXXXwould result in a biased estimate of the...

Suppose we use the simple linear model

to estimate the ITT effect of treatment assignment based on data from a randomized trial. Show that fitting (9.21) would result in a biased estimate of the causal effect of treatment. Specifically, show that

where β₁
is the causal effect of treatment received, and
is the expected difference in the proportions of trial participants who receive treatment in the treatment and control groups respectively.