A population of 1,000 healthy, at risk people is monitored for one year starting

Question

A population of 1,000 healthy, at risk people is monitored for one year starting on January 1st and the development of cases of chicken pox is noted. No one has chicken pox at the start of the investigation. Twenty people develop chicken pox on June 30th and forty people develop chicken pox on September 30th. Twenty-four people were lost to follow-up on March 31st and twenty-four people were lost to follow-up on November 30th. None of those lost to follow-up had developed chicken pox prior to becoming lost. Assume that you can get chicken pox only once. What is the cumulative incidence of chicken pox in this population during the one-year period from January 1st through December 31st? a. 20/1,000 b. 40/1,000 c. 60/1,000 d. 60/108

I am confused one answer says 40 and other 60. I picked 60

Explanation / Answer

Since the question is asking for the cumulative incidence

On June 30th 20 people developed chicken pox

On 30th September 40 people deveopled chicken pox

So the effective persons for the whole year for observation are

(1000*(31+28+31) + 976*(30+31+20+31+31+30+31+30) + 952*31 )/(365)

( 1000 people remained for the first 3 months after that 976 people (as we lost track for 24 people by 31st march ) remained for next 8 months  (as we lost track for another 24 people by 30th November) and so 952 people were only tracked after that for december

So the effective people under observation becomes (1000*(31+28+31) + 976*(30+31+20+31+31+30+31+30) + 952*31 )/(365) = 953.1397 for the whole year

and out of these 953 people cumulatively 60 people develped the disease

so effectively 60/953 should be the cumulative probability but we don't have any option for the same and the closest pick is 60/1000

Which is correct pick from you!

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!

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