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51: Investigators are interested in the effect of TV watching on obesity rates among young children. They therefore conducted a cohort study in which they enrolled over 1 million children ages 0 - 23 months. At the baseline assessment, they asked parents to report the average number of hours of TV the children watched each day. They then followed up with the children 3 years later to assess their BMI (and to measure the incidence of obesity). Investigators found an incidence rate of obesity of 14 cases per 100 person-years among children who watched 2 hours or more of TV per day and 8 cases per 100 person-years among children who watched less than 2 hours of TV per day. The overall incidence rate of obesity among this population in the U.S. is estimated to be 10 cases per 100 person-years. What is the risk of obesity attributable to watching TV for 2 hours or more per day among young children who watch 2 hours or more of TV per day? A. 2 cases per 100 person-years B. 43% C. 20% D. 6 cases per 100 person-years E. 14%
Answer:
Let the proportion of people who watched TV for 2 hours or more be X. Then the proportion of people who watches less than 2 hours would be (1-x). Therefore from the given number of cases we get:
14*x + 8*(1-x) = 10
14x + 8 - 8x = 10
6x = 2
x = 1/3
Therefore if we stop the population from watching TV greater than 2 hours we would be able to stop extra 6 cases in 1/3 per 100 person-years. because x = 1/3 is the proportion of people watching TV greater than or equal to 2 hours. Therefore we get that:
6*(1/3) = 2 per 100 person-years.
Note: 6 comes from the fact that people watching TV greater than or equal to 2 hours have 6 more cases per 100 person-years than for people watching TV for less than 2 hours.
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