#Exercise 18:  a second look at logistic regression

 

# In this exercise we will use data from the Western Collaborative Group Study (WCGS), a large epidemiological study designed to study risk factors for coronary heart disease (CHD). More than 3000 men were recruited to the study, and a number of (potential) risk factors were recorded at entry. The men were then followed for about ten years and it was recorded if they developed CHD or not. The WCGS data are used in many of the examples in Section 3.4 and Chapter 6 of the course text book byVittinghoff et al.

 

# You may read the WCGS data into R by the command:

wcgs=read.table("http://www.uio.no/studier/emner/matnat/math/STK4900/data/wcgs.txt",sep="\t", header=T,na.strings=".")

 

# In this exercise we will restrict ourselves to study the effect of smoking and age on the risk for CHD.

 

# Question a)

 

# We first fit a logistic regression model with smoke as covariate:

fit.smoke=glm(chd69~smoke,data=wcgs,family=binomial)

summary(fit.smoke)

 

# Is there a significant effect of smoking on the risk of developing CHD? (Cf. slide 11)

 

# Compute a 95% confidence interval for the regression coefficient for smoking (cf slide 9)

# Also estimate the odds ratio for smoking and determine a 95% confidence interval for the odds ratio (cf slide 9).

 

 

# Question b)

 

# In order to estimate the odds ratio with 95% confidence limits from a fitted logistic model, you may use the function (cf slide 10)

expcoef=function(glmobj)

{

regtab=summary(glmobj)$coef

expcoef=exp(regtab[,1])

lower=expcoef*exp(-1.96*regtab[,2])

upper=expcoef*exp(1.96*regtab[,2])

cbind(expcoef,lower,upper)

}

 

# Use this function to estimate the odds ratio for smoking with 95% confidence limits.

# Check that you get the same results as in question a.

 

 

# Question c)

 

# We then use logistic regression to study the effect of age (at entry to the study) for the risk of developing CHD:

fit.age=glm(chd69~age,data=wcgs,family=binomial)

summary(fit.age)

 

# Use the expcoef-function to estimate the odds ratio for a one-year increase in age with 95% confidence interval.

 

 

# Question d)

 

# When interpreting the effect of age, it may be reasonable to give the odds ratio corresponding to a ten-year increase in age (rather than a one-year increase as we did in question c). The easiest way to achieve this is to fit the logistic model using age/10 as covariate:

fit.age10=glm(chd69~I(age/10),data=wcgs,family=binomial)

summary(fit.age10)

 

# Compare the estimates and standard errors of this model with the one in question c. What do you see?

 

# You may then use the expcoef-function to estimate the odds ratio for a ten-year increase in age with 95% confidence interval. (Why?)