Explore BrainMass

# Recovering the Cell Probabilities of a 2-by-2 Contingency Table

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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).

https://brainmass.com/math/basic-algebra/recovering-cell-probabilities-contingency-table-299411

#### Solution Preview

See the attached file.

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). ...

#### Solution Summary

The solution examines recovering the cell probabilities of a 2-by-2 contingency tables.

\$2.19