Question #3. (30 total points) Consider the following data from a randomized clinical trial to assess
whether an experimental treatment reduces severity of a rash after 2 weeks of treatment (compared to
placebo). Subjects were randomized to either High dose, Low dose, or placebo. The following table
contains data on treatment (High/Low/Placebo), sex (Male/Female), and severity of rash after 2 weeks:
Treatment Sex
Severity of Rash after 2 weeks Total
None Mild Moderate Severe
High Dose Male 8 10 14 18 50
Female 7 15 18 20 60
Low Dose Male 6 8 27 15 56
Female 10 17 11 16 54
Placebo Male 19 15 17 5 56
Female 21 18 10 5 54
a) (6pts) Under minimal assumptions, assess whether there is an association between treatment
and rash severity controlling for sex. Justify your approach and interpret your results.
b) (6pts) Under minimal assumptions, assess whether there is an association between sex and rash
severity controlling for treatment. Justify your approach and interpret your results.
c) (8pts) Specify the mathematical structure for a logistic regression model to describe the
relationship between treatment and severity of rash after 2 weeks (categorized as Moderate or
Severe versus None or Mild), including main effects for treatment and sex as well as their
interaction. Include mathematical definitions of the explanatory variables. Use "placebo" as the
reference group for treatment and "male" as the reference group for sex.
d) (10pts) Fit the model specified in (c) to the data. Conduct a statistical test with a=0.05 to assess
whether the relationship between treatment and severity of rash after 2 weeks is the same for
both males and females.
