Assignment 4

1. You are studying the relationship between having an endocrinologist (yes vs. no), age (old vs. young) and likelihood of getting an a1c test (yes vs. no). An a1c test is a test for diabetes. 7 marks

OR (95%CI)

Age (ref: young) 0.96 0.94,0.98

Endocrinologist (ref: no) 1.65 1.60,1.71

Age X Endocrinologist Int. term 1.07 1.01,1.13

a) How would you evaluate the interaction term? Hint, use the formula for predicted probability.

b) Draw a figure illustrating the interaction.

2. The 2×2 table below shows the proportion of children in each cell who develop ear infections in the first 2 years of life. The exposures of interest are parental smoking and low birth weight.

What should the value of the question mark in the table be if it is assumed that there is homogeneity (no interaction) for the risk difference (either for smoking vs no smoking, or low birth weight vs. no low birth weight?

What should the value of the question mark in the table be if it is assumed that there is homogeneity (no interaction) for the risk ratio? 2 marks

No Parental Smoking Parental smoking

No low birth weight 0.20 0.40

Low birth weight 0.25 ?

3. A large cross-sectional study is conducted to observe the prevalence of cataracts and investigate the history of smoking and excessive exposure to sunlight as possible risk factors 8 marks

Category # with cataracts Total # in group prevalence PD PR

Smoking (-), Sunlight (-) 11 1083 0 (ref) 1 (ref)

Smoking (-), Sunlight (+) 22 544

Smoking (+), Sunlight (-) 26 493

Smoking (+), Sunlight (+) 107 395

a. Calculate the prevalence of cataracts in each of the 4 groups

b. Using the category “ smoking (-) sunlight (-) as the reference group, calculate the prevalence ratios and the prevalence differences for those with sunlight only, those with smoking only and those exposed to both.

Interpret each of the prevalence odds ratios.

c. Calculate the expected joint prevalence ratio (multiplicative model) and the expected joint prevalence difference (additive model).

d. Based on the data provided and assuming no random error, is there multiplicative interaction? Is there additive interaction? If so would you describe it as synergistic or antagonistic interaction?

e. Using an alternative approach (strategy #1 in the lecture), assess the heterogeneity of the smoking prevalence ratio across the two strata of sunlight (+ and -). In other words, is the prevalence ratio for smoking (smoking + vs. smoking -) different between the two sunlight categories.

f. Without doing any calculations, do you think the prevalence ratio for sunlight is modified by smoking? Why or why not?

4. Each question describes a cohort study comparing the risk of disease recurrence using a new therapy (exposed) vs the standard therapy (unexposed). For each question state whether age acts as 1) a confounder (if you do not control for age), 2) an effect modifier, 3) neither or 4) both. Use the risk ratio to determine whether age is an effect modifier (i.e., multiplicative interaction with the risk of recurrence). For simplicity, age is dichotomized into old and young. Assume no random error. 3 marks

a) A randomized trial where the age distribution was balanced with respect to the type of therapy applied. The risk of recurrence was 0.03 for the old on the new therapy, 0.06 for the old on the standard therapy, 0.01 for the young on the new therapy, and 0.01 for the young on the standard therapy.

b) An observational cohort where the age distribution was balanced with respect to the type of therapy applied. The risk of recurrence was 0.03 for the old on the new therapy, 0.06 for the old on the standard therapy, 0.01 for the young on the new therapy, and 0.02 for the young on the standard therapy.

c) An observational cohort where the age distribution was imbalanced with respect to the type of therapy applied. Individuals on the new therapy were predominately old while individuals on the standard therapy were predominately young. The risk of recurrence was 0.03 for the old on the new therapy, 0.06 for the old on the standard therapy, 0.001 for the young on the new therapy, and 0.0008 for the young on the standard therapy.