I finished the other problems, but I don't understand how to solve number 21...

Extending the above discussion through some hypothetical data: A group of hardworking young investigators is able to obtain funding for a large study in King George County on Lyme disease. They recruit 5000 adults to their study and decide to follow them for 1 year (when the funding runs out!). In initial blood work they find 85 people who test positive for exposure to the causative bacteria or report a past confirmed positive test. Unfortunately, these people can acquire Lyme disease again but because it will be difficult to know if it is a new infection from blood work the researchers decide they are only interested in first time cases of Lyme disease. Over the next year they test the remaining eligible subjects bimonthly. The study begins in June and the next tests are done August, October, December, February, April, and June (end of year 1). For the purpose of this exercise we can see into the future and below is a summary of their results: Month August October December February April June Year 1 2+'s 1+ 0+ 0+ 1+ O LTEU 15 LTEU S LTEU O LTEU OLTEU JO LTEU LTFU means lost to follow up (therefore they were only followed up to the previous checkup) + is a positive blood test. Once they test positive they are no longer included in the above table. For calculations it is assumed they became positive halfway between the checkups on average. (hint: these footnotes on tables can be very important so read them!!) 15. They want to calculate the incidence rates year 1. Why don't they count the 85 who tested positive at the start? (1 p4) They are trying to test new infections and those 85 tested positive at one point. 16. What was the total person time observed from participants who stayed in the study but never tested positive? (1 RA) 5000-85 (prevalent cases) - [15+5+10] -4= 5000-85 (prevalent cases) - 30 -4 = 4,881 persons remained in the study and never tested positive 4,881 persons x 12 months = 58,572 17. How much at-risk person time can be counted as from the cases? (1pt) 2 persons contributed each 1 month = 2 months 1 person contributed 3 months = 3 months 1 person contributed 11 months = 11 months Total person-months = 16 person-months 18. How much at risk person time did those who dropped out contribute? (1pt) 15 persons contributed each 2 month = 30 months 5 persons contributed each 4 months = 20 months 10 persons contributed each 10 months = 100 months Total person-months = 150 person-months 19. What was the incidence rate for year 1? (1pt) (give rate per 100,000 person years) IN PREP IR = # new cases / total person time at risk - 4 / (58572+16+150) = 4 /58,738 per person-months = (4/58,738 per person-months) x 12 (months/year) x 100,000 = 81.72 per 100,000 person-years 7 20. How would you describe the difference between the rate calculated in this hypothetical study in King George, and those seen in the map? (1 pt.) The calculated rates in this study are higher than those shown on the map. 21. Calculate a cumulative incidence using only the who were followed the entire time and using everyone at risk at the start of the study. How do they compare to the rate with person time (2 pA) IN PREP