Frequencies of individuals with 1,024 possible EDS response types in observational studies. We consider 4 binary variables as follows: exposure E, outcome D, confounder C, and selection variable S (see Figure 1). As shown in Tables 1, 2 and 3, we consider 4 response types for E, 16 response types for D, and 16 response types for S. We let EiDjSk denote the EDS response type of [E
T = i, D
T = j, S
T = k], and let P
denote a prevalence of the individuals of EiDjSk response type in the total population. We also let P
and denote probabilities of being exposed and unexposed to C among the individuals of EiDjSk response type, respectively. Further, N denotes the number of total population. Those who are classified into inner dashed rectangles represent individuals selected for analyses (i.e., S = 1) while those who are not classified into the rectangles represent non-selected individuals (i.e., S = 0). See text for details.