In: Statistics and Probability
In a study of esophageal cancer and chewing tobacco, 1000 subjects with cancer and 1000 healthy controls were enrolled. Each subject was asked about their previous use of chewing tobacco. Three hundred and fifty of the cases and 120 of the controls had experience with chewing tobacco.
What is the population attributable risk percent for this study?
In the above question, risk is defined as the probability of the occurrence of esophagul cancer in the sample of subjects chewing tobacco. Risk is calculated by dividing the number who got cancerduring the defined period by the total population of interest during that period.
Another parameter to understand is the Relative Risk, it is used to determine if the exposure to a specific risk factor(like tobacco) is associated with an increase, decrease, or no change in the esophagul cancer or outcome rate when compared to those without the exposure.
Before we understand PAR, we need to understand Attributional Risk(AR), this risk helps you to determine how much of an outcome may be attributable to a particular risk factor (i.e. an estimate of the excess risk) in a population exposed to that factor(previous exposure to chewing tobacco)
Population attributable Risk - When AR is derived for the entire popopulation, it is called the Population Attributable Risk. This means that, it is often useful to re-define the attributable risk in terms of the whole population, and to determine the proportion of cases in the total population that can be attributed to the risk factor.
Population attributable risk depends on 2 parameters -
1) Excess Risk imposed by the exposure.
2) Proportion of the population that is exposed.
Lets Create the below table for better understanding-
Subjects with Cancer | Healthy Control Group | Total | |
Previous Exposure to Chewing Tobacco | 350(a) | 120(b) | 470(n1) |
No Previous Exposure to Chewing Tobacco | 650(c) | 880(d) | 1530 |
Total | 1000 | 1000 | 2000(N) |
There are 2 ways to calculate PAR -
1) PAR= p0 - p2 , or
2) PAR = (p1 – p2) x n1/N
whre, p0 = the proportion of all subjects with Cancer with the outcome of interest (a + c / a + b + c + d)
p1 = the proportion of subject with cancer with the outcome of interest to the Previous exposure of chewing tobacco(risk factor) (a / a + b)
p2 = the proportion of subject with cancer with the outcome of interest to the NO Previous exposure of chewing tobacco(risk factor) (c / c + d)
N = the total number of Cases (a + b + c + d)
n1= the number of Cases exposed to the risk factor(Chewing Tobacco) (a + b)
Calculations:
1) PAR = p0 - p2
= 1000/2000 – 650/1530
= 0.5 - 0.425 = 0.075 or
2) PAR = (p1 – p2) x n1/N
= [(350/470) - (650/1530)] x (470/2000)
= (0.745 - 0.425)*0.235
= 0.075
This implies that the overall risk of people with esophagul cancer imposed by previously chewing tobacco is 75 per 1000 people.
The Population Attributable Risk Percent (PAR%), which tells us the percent of cases in the total population that can be attributed to chewing tobacco.
PAR% = p0 - p2/p0 x 100
= (0.5 - 0.425) / 0.5 x 100 = 15.03% This means that out of 1000 cancer subjects, including those with previos exposure or NO exposure of Chewing Tobacco, 75 cases or 15.03% can be attributed to chewing Tobacco. The calculation helps estimate the percent of cases in the total population that might be prevented by removing the exposure.