4. Choosing variables for estimating propensity scores is an important consideration when estimating causal effects in non-randomized comparisons. Consider the following statements:

1. Variables hypothesized to be associated with treatment but not with outcome - Should these be included or excluded? Please justify your answer.
2. Variables that predict treatment status perfectly - Should these be included or excluded? Please justify your answer.
3. Theoretically related to treatment and outcome - Should these be included or excluded? Please justify your answer.