Question 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.

Is the subsidized housing community in the Lower East Side of New York City a dynamic or fixed population? Briefly explain the rationale for your answer.

What was the prevalence of TB in the screened community on January 1st?

What was the prevalence of TB on June 30th?

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.

QUESTION 2.

An epidemiological investigation was begun on July 1, 2000 among a population of 1,000 individuals. Three individuals were found to have leukemia on July 1st. During the ten-year follow-up period, five new cases of leukemia were diagnosed. Among the eight leukemia cases, four deaths occurred during the ten-year follow-up period. Two additional individuals, neither of whom had leukemia, were lost to follow-up at some point during follow-up. None of the remaining 990 study participants became ill, died, or were lost to follow-up during the follow-up period.

The diagram below indicates the experience of the 10 study participants, using the following symbols:
* :case recognition (diagnosis of leukemia)
*< :onset of leukemia was prior to start of study period
---- :observation period during follow-up
X :status at termination of observation (i.e., alive, dead, lost)

o What was the prevalence of leukemia on January 1, 2005?
o What was the cumulative incidence of leukemia during the 10-year follow-up period?
o What was the incidence rate of leukemia during the 10-year follow-up period?
o What was the case fatality rate during the 10-year follow-up period?

Consider a group of 1,000 newborn infants. 100 infants were born with serious birth defects and 20 of these 100 died during the first year of life. 90 of the 900 remaining infants without any birth defects also died during the first year of life.
o Calculate the prevalence of serious defects in this population at the time of birth.
o Calculate the overall cumulative incidence of mortality in this population.
o Calculate the cumulative incidence difference in mortality between infants born with serious birth defects and without.
o State in words your interpretation of the cumulative incidence difference calculated in part c.