1. Suppose that you began a one-year study of tuberculosis (TB) in a subsidized housing community in the Lower East Side of New York City on January 1st, 2010. You enrolled 500 residents in your study and checked on their TB status on a monthly basis. At the start of your study on January 1st, you screened all 500 residents. Upon screening, you found that 20 of the healthy residents were immigrants who were vaccinated for TB and so were not at risk. Another 30 residents already had existing cases of TB on January 1st. On February 1st, 5 residents developed TB. On April 1st, 5 more residents developed TB. On June 1st, 10 healthy residents moved away from New York City were lost to follow-up. On July 1st, 10 of the residents who had existing TB on January 1st died from their disease. The study ended on December 31, 2010. Assume that once a person gets TB, they have it for the duration of the study, and assume that all remaining residents stayed healthy and were not lost to follow-up.

What was the cumulative incidence of TB over the year?

Suppose that you wanted to calculate the incidence rate of TB in the study population. Calculate the amount of person-time that would go in the denominator of this incidence rate. Be sure to show your work.