Stat 100 Feb 11 Read Chapter 12, try 1-9

Problem 14 of Chapter 12 Case control study: 239 lung cancer patients and 429 controls 98 of the lung cancer patients had at some time owned a bird 101 of the controls had at some time owned a bird.

Part a Construct a contingency table

Contingency Table Lung cancer ControlsTotal Owned Bird Never Owned Bird Total239429

Contingency Table Lung cancer ControlsTotal Owned Bird Never Owned Bird Total

Risk of Lung Cancer Compute the risk of lung cancer for bird owners and non-owners Risk=percent or proportion falling into the “bad” category For bird owners, 98/199=.492 or 49.2% For non-owners, 141/469=.301, or 30.1%

Comparing Risks Relative Risk Divide risk in one group by risk in other Rel. Risk of lung cancer for bird owners=.492/.301=1.63 Interpretation: For bird-owners, the risk of lung cancer is 1.63 times the risk for non- owners.

Percent Increase in Risk Divide difference in risks by the lower of the two risks. (express as percent) ( )/.301=.191/.301=63% Interpret: Having owned a bird increases the risk of lung cancer by 63%

Thought Question Do you think the risks calculated in this problem correctly describe the risk of lung cancer? Can you think of any other explanation for the results aside from “having owned a bird increases the risk of lung cancer?”

NOTE Because this was a case-control study, cancer patients were purposely “over- sampled” Makes risk of cancer in this sample much higher than normal risk in population

Thought Question Can you think of any other explanation for the results aside from “having owned a bird increases the risk of lung cancer?” Maybe bird owners are more likely to smoke

Odds Comparison of chance something happens to chance it doesn’t Suppose 42 of 92 short kids have been bullied. Odds of being bullied are 42 to 50 Suppose 30 of 111 normal height kids have been bullied Odds of being bullied are 30 to 81

Odds ratio Comparison of odds for two different groups Short kids compared to normal height – Odds of being bullied = (42/50)/(30/81) = 2.27 For short, odds of being bullied are 2.27 times odds for normal height