Assignment:
A 2-by-2 contingency table is Control on one axis and Experimental on the other. Control and Experimental are further dichotomized as Event and Non-event. The odds ratio (OR), number needed to harm (NNH), and absolute risk increase (ARI) are functions of the cell probabilities of a 2-by-2 contingency table, and conversely, the cell probabilities can be recovered given knowledge of these parameters. Recover the contingency table cell probabilities EE, EN, CE, and CN using OR, NNH, and ARI as knowns and the following definitions as necessary:
Experimental group (E), Control group (C), Events (E), Non-events (N), Total subjects (S), ES = EE + EN, CS = CE + CN, Event rate (ER), EER = EE / ES, CER = CE / CS, ARI = EER − CER, NNH = 1 / (EER − CER), and OR = (EE / EN) / (CE / CN). Also NNH = 1 + [CER x (OR-1)]/(1-CER) x (CER) x (OR-1).
Provide complete and step by step solution for the question and show calculations and use formulas.