Biostatistics: Calculating the Odds Ratio and the Relative Risk Ratio

Biostatistics
Student’s Name:
Institution:
Professor:
Unit Name & Number:
Date of Submission:
Biostatistics
Calculating the Odds Ratio and the Relative Risk Ratio
Odds Ratio
Odds Ratio (OR) is used to measure the association between an exposure and an outcome (Andrade, 2015). In this case, the diagnosis or development of diabetes is highly associated with an individual’s family history, implying a high likelihood of developing diabetes if there is a family history with diabetes.
From the data set, the sample size= 300
The table below is a representation of the distribution of the data in terms of those who have diabetes but whose family has a history of the disease (M), those who do not have diabetes but whose family has a history with the condition (N), those who have diabetes but their family has no history with the disease (O) and those who do not have diabetes and their family has no history with the condition (P).

Diabetes


Yes

No

Family history



Yes

89

23

No

20

168

M=89, N=23, O=20 and P=168
OR= (M/O) / (N/P)
= (89/20) / (23/168)
= 32.50
To determine whether the results are statistically significant at 95% CI, we first calculate the standard error (SE) of the log of OR.
Ln 32.50 = 3.48
SE = square root ((1/89) + (1/23) + (1/20) + (1/168))
=0.33
95% CI is given by effect size ±1.96 * SE
Therefore; 95% CI range is given by exp{ln (32.50) ± 1.96 *0.33}
= exp(3.48- 0.65) to exp(3.48+ 0.65)
= 16.93 to 62.39
The OR value is 32.50, implying that it lies within the 95% CI of 16.93 to 62.39, and thus, the test is statistically significant. Based on Hill’s crit...