Consider this logistic regression model that predicts lung cancer from smoking:

Question

Consider this logistic regression model that predicts lung cancer from smoking: where ODDS is the odds of developing lung cancer. The factor SMOKE is in increments of 14 years: 1 = less than 14 years' 2 = 14-28 years' 3 = '28-42 years' 4 = 'more than 42 years' (a) An increase of c = 1/2 units in SMOKE corresponds to 7 extra years of smoking, because 1 unit of SMOKE is 14 years (Look up above at the units of SMOKE.) What is the odds ratio (OR) for c - 1/2? Round to two decimal places. (b) Use your OR from (a) to answer this question: An extra 7 years of smoking (c = 1/2) increases the odds of lung cancer by what percent? Round to the nearest whole number. (c) An Increase of c = 1 unit in SMOKE corresponds to 14 extra years of smoking. What is the odds ratio (OR) for c = 1? Round to two decimal places. (d) An extra 14 years of smoking increases the odds of lung cancer by how many percent? Round to the nearest whole number.

Explanation / Answer

Part-a

As c=1/2 means SMOKE=1, so

Ln(odds)=-1.092+0.752*1=-0.34

So, odds=exp(-0.34)=0.71

Part-b

For this there is unit increase in smoke, so %age=75%

Part-c

Ln(odds)=-1.092+0.752*2=-0.452

So, odds=exp(0.451)=1.51

Part-d

For this there is unit increase in smoke, so %age=75%

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