#Exercise 19:  logistic regression with several predictors

 

# 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/v11/wcgs.txt",sep="\t", header=T,na.strings=".")

 

 

 

# Question a)

 

# Our starting point in this exercise is the model for CHD risk using the predictors age (per 10 years), cholesterol (per 50 mg/dL), systolic blood pressure (per 50 mmHg), body mass index (per 10 kg/m²), smoking (yes, no), and behavioral pattern (with the four groups 1=A1, 2=A2, 3=B3, 4=B4).

 

# You may fit this model by the commands on slide 19:

wcgs$behcat=factor(wcgs$behpat)

wcgs.beh=glm(chd69~age_10+chol_50+sbp_50+bmi_10+smoke+behcat, data=wcgs, family=binomial, subset=(chol<600))

summary(wcgs.beh)

 

# Perform the commands and check that you get the results reported on slide 19.

# Comment on the results. In particular discuss the effects of the behavioral patterns

 

 

# Question b)

 

# In question a we consider a model with four behavioral groups. One may wonder if it is sufficient to consider only two behavioral groups (A-behavior and B-behavior). To this end we fit a model with the binary covariate dibpat (which is coded as 0 for B3 and B4, and as 1 for A1 and A2):

wcgs.beh2=glm(chd69~age_10+chol_50+sbp_50+bmi_10+smoke+dibpat, data=wcgs, family=binomial, subset=(chol<600))

 

# To test the null hypothesis that the effects behavioral patterns A1 and A2 are the same and  the effects behavioral patterns B1 and B2 are the same, we compare the (residual) deviances for the model in a and the model considered here:

anova(wcgs.beh2,wcgs.beh, test="Chisq")

 

# Perform the command and explain what the output tells you (cf slide 26). What do you conclude from the test?

 

 

# Question c)

 

# We then fit a model without behavioral pattern and compare the three models in an analysis of deviance table:

wcgs.resc=glm(chd69~age_10+chol_50+bmi_10+sbp_50+smoke, data=wcgs, family=binomial, subset=(chol<600))

anova(wcgs.resc,wcgs.beh2,wcgs.beh, test="Chisq")

 

# Perform the command and explain what you may conclude from the analysis of deviance table?

 

 

# Question d)

 

# Which of the models in question a, b, and c would you prefer?

# Use the expcoef-command from Exercise 18 to obtain the estimated odds ratios with 95% confidence intervals for your preferred model.

# Discuss what these odds ratios tell you about the risk factors for CHD.