In this paper, the authors reported on the risk of fatal opioid overdose during the first year following non-fatal overdose. In this question, we will look at some of the baseline data. The following questions are loosely based on the data presented in the paper. 1.The data in the table below is loosely based on the data presented in the paper. Using this data, construct two-by-two tables stratified by sex, women versus men (L), describing the relationship between the exposure, Depression (A), and the outcome, Opioid prescription in the prior 180 days (Y). Please include the table margins (row and column totals).
Variable
Total
Number with an opioid
prescription in the past 180 days
Woman, Depression
11,462
8,784
Woman, No Depression
33,267
22,506
Man, Depression
4,858
3,226
Man, No Depression
25,969
14,483
L=1 (women)
A=1 (depression)
A=0(no depression)
Total
Y=1
8784
22506
31290
Y=0
2678
10761
13439
Total
11462
33267
44729
L=0 (men)
A=1 (depression)
A=0(no depression)
Total
Y=1
3226
14483
17709
Y=0
1632
11486
13118
Total
4858
25969
30827
2.Construct the tree corresponding to the data above. Include sample sizes and probabilities at each step.

EPI201: Homework 1
Page 5 of 9
NAME: ____Yiyang Yue________
3.In the entire population: (show your work using appropriate probability notation)a.What was the probability of having an opioid prescription in the past 180 days? b.What was the probability of depression? c.What was the probability of having depression and having an opioid prescription in the past 180 days?
:

EPI201: Homework 1
Page 6 of 9
NAME: ____Yiyang Yue________
4.What was the probability of being a woman (show your work using appropriate probability notation): a.Among those with depression? b.Among those without depression? c.Among those with depression, who had an opioid prescription in the past 180 days?
5.What was the probability of having depression and being a man among those who had an opioid prescription in the past 180 days? (show your work using appropriate probability notation)
6.Quantitatively assess whether having depression and being a woman are marginally independent. Use proper notation and very briefly discuss how your calculations lead to your conclusion. Do not perform a statistical hypothesis test.

EPI201: Homework 1
Page 7 of 9
NAME: ____Yiyang Yue________
Part III