Statistics - explanations and formulas

2x2 Table

2 x 2 tables are used to examine the relationship between two or more categorical values. In these tables, an exposure variable is usually considered as the risk factor. (https://www.cdc.gov/epiinfo/user-guide/visual-dashboard/analysisgadgets/table.html)

  Disease+ Disease-
Exposure+ A B
Exposure- C D

The 2x2 table allow you to perform mathematical analysis to determine helpful clinical decision making factors including:

Experimental Event Rate EER = a/(a+b)

Control Event Rate CER = c/(c+d)

Absolute Risk Reduction AAR = CER - EER

Relative Risk RR = EER / CER

Relative Risk Reduction  RRR = AAR/CER

Number Needed to Treat NNT = 1/ARR

Example from article: June Choe Y, Yi S, Hwang I, Kim J, Park YJ, Cho E, Jo M, Lee H, Hwa Choi E. Safety and effectiveness of BNT162b2 mRNA Covid-19 vaccine in adolescents. Vaccine. 2022 Jan 31;40(5):691-694. doi: 10.1016/j.vaccine.2021.12.044. Epub 2021 Dec 24. PMID: 35012777; PMCID: PMC8702409.

  COVID-19 No COVID 19 Totals
Received vaccine 15 439064 43079
Did not receive vaccine 3358 959983 963341

Totals

3374 1299047

1302420

EER = 15/438079 = .00003424 = .0034%

CER = 3358/963341 = .003486 = .39%

ARR = CER – EER = .003486 - .00003424 = .00345176 = .345%

RR = EER/CER = .00003424/.003486 = .00982215 = .98%

RRR = ARR/CER = .00385476/ .003486 = 1.1057831 = 110%

NNT = 1/ARR = 1/.00385476 = 259.419523 = 260