Collider bias from conditioning on arrest: the odds ratio among arrestees

Two independent risk factors with prevalences a and e and a background cause of arrest with prevalence pi_bg, combined by an "or" mechanism, are independent in the population (odds ratio one, Research.P2.population_or_one) but have odds ratio exactly pi_bg among arrestees (collider_or_eq_background, collider_or_lt_one): a negative association manufactured by conditioning on being in the record, tending to complete negative dependence as arrests for other reasons become rare (Hernan & Robins, Fine Point 8.2).

Usage

morie_collider_arrest(a, e, pi_bg)

Arguments

a, e: Prevalences of the two risk factors in (0, 1).
pi_bg: Prevalence of the background cause of arrest in [0, 1].

Value

A list with population_or (1), arrestee_or (pi_bg), arrestee_log_or, the four joint cells among arrestees and theorems.

Examples

morie_collider_arrest(a = 0.3, e = 0.2, pi_bg = 0.1)
#> $population_or
#> [1] 1
#> 
#> $arrestee_or
#> [1] 0.1
#> 
#> $arrestee_log_or
#> [1] -2.302585
#> 
#> $cells_among_arrestees
#>      A1E1      A1E0      A0E1      A0E0 
#> 0.1209677 0.4838710 0.2822581 0.1129032 
#> 
#> $theorems
#> [1] "Research.P2.population_or_one"        
#> [2] "Research.P2.collider_or_eq_background"
#> [3] "Research.P2.collider_or_lt_one"       
#>