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Chapter 14 Homework

Hypothesis Testing: Person-Time Data

1. The data relating oral-contraceptive (OC) use and the incidence of breast cancer in the age group 40-44 in the NHS are given in the table below.

Relationship between breast cancer incidence and OC use among 40- to 44-year-old women in the NHS

OC-use group Number of cases Number of person-years Current users 19 4,761

Past users 164 121,091 Never users 113 98,091

(a) Compare the incidence density of breast cancer in current users vs. never users, and report a p-value.

(b) Compare the incidence density of breast cancer in past users vs. never users, and report a p-value.

(c) Estimate the rate ratio comparing current users vs. never users, and provide a 95% confidence interval about this estimate.

(d) Estimate the rate ratio comparing past users vs. never users, and provide a 95% confidence interval.

(e) How much power did the study have detecting an IRR for breast cancer of 1.5, comparing current OC users vs. never OC users among 40- to 44-year-old women if

i. the true incidence rate of breast cancer among never users and the amount of person-time for current and never users are the same in the table above,

ii. the expected number of events for never OC users is the same as the observed number of events in the table above,

iii. the average follow-up time per subject is the same for both current and never OC users?

(f) What is the expected number of events that need to be realized n each group to achieve 80% power to detect an IRR for breast cancer of 1.5 for current OC users vs never OC users under teh same assumptions as in part (e)?

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2. Suppose we wish to study the association between aspirin intake and the incidence of colon cancer. We find that 10% of women take 7 aspirin tablets per week (ASA group), while 50% of women never take aspirin (control group). The ASA group is followed for 50,000 person-years, during which 34 new colon cancers occurred over a 20-year period. The control group is followed for 250,000 person-years, during which 251 new colon cancers developed over a 20-year period.

(a) What are the estimated incidence rates in the ASA and control groups?

(b) Is there a significant difference between these incidence rates? Report a p-value (two-tailed).

(c) What is the estimated rate ratio for colon cancer between the ASA and placebo groups?

(d) Provide a 95% confidence interval for the rate ratio in part (c).

(e) Suppose we look at the subset of women with a family history of colon cancer. Aspirin might be more beneficial in this high-risk subgroup. We have a total of 5000 person-years among ASA women and 2 events. We have a total of 20,000 person-years among control women and 20 events. Is there a significant difference in the incidence rates of colon cancer between these 2 groups? Provide a p-value (two-tailed).

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