Question

A study is conducted on 8,000 individuals free of diabetes and 8,000 individuals with diabetes. The investigators are looking to determine if a newly marketed drug may prevent diabetes. Among patients with diabetes, 1,000 individuals received the new drug. Among patients without diabetes, 2,000 individuals received the drug.

4a. Construct a 2 by 2 table displaying the combination of diabetics/non-diabetics who are exposed/not exposed.

4b. Calculate an odds ratio and provide an interpretation

4c. Calculate the relative risk and provide an interpretation.

4d. If the number of non-diabetic patients was increased to 800,000, would you expect the answers in 2b and 2c to be more or less similar to each other? Explain why.

Answer 1

4a.

	DIABETIC	NON-DIABETIC
Exposed	1000	2000
Not exposed	7000	6000

4b. Odd ratio (OR) is used to measure the relationship between the exposure and its possible outcomes, mainly in case of certain case studies, clinical trial of drugs etc. It is calculated to observe the effect of one situation in the presence or absence of another situation.

It is calculated as follows:

Odds for Diabetic individuals: Exposed/non-exposed = 1000/7000

odds for non-diabetic individuals: Exposed/non-exposed= 2000/6000

so, ODD RATIO is, = odds for diabetic individuals/ odds for non-diabetic individuals

= 1000/7000 2000/6000= 1000 6000 / 7000 2000= 0.42

Interpretation: calculated odd ratio is 0.42. It is less than one. An odd ratio of value less than one predicts the lower odds associated with the experimentation. The odds of drug exposure is more in case of diabetic person than non-diabetic individuals.

4c. Relative Risk (RR) is measured to study the probable success or failure associated with the administration of drug in diseased and non-diseased conditions.

It is measured as follows:

RR= probability of events in diabetic conditions/ probability of events in non diabetic conditions

= 1000/ (1000+7000) 2000/ (2000+6000)= 1000/8000 2000/8000= 1000/2000 = 0.5

Interpretation: the RR of 0.5 indicates that the diabetic group in exposed condition has less risk event than in non exposed condition.

4d. If the no. of non-diabetic patient was increased to 800,000; the OR and RR will be different from each other, but both will be far greater than 1.

OR= 1000 7,98,000 / 7000 2000 = 114.

RR= 1000 8,00,000 / 8000 2000 = 50.

Size of sample has been increased, but the individuals in the experimental situations are similar. Irregular sample size may lead to biasness in the result. It shows relatively much increased odds and relative risks compared to previous sampling. If sample size of one variable is increased, then sample size of other should also be increased for precise and accurate result.