I don't know if there is an equation for this, but I basically pumped out every division across the table to get ~5% on average.
Here they are: 400 / 6,000 = 0.067 250 / 5,600 = 0.045 300 / 5,350 = 0.056 300 / 5,050 = 0.059 250 / 4,800 = 0.052
The average of these %s for all the years = 5.58%. So that's close enough to 5%.
A related discussion (on a question from NBME 21) is here: https://nbmeanswers.com/exam/nbme21/714
The quickest way to do this is to add all the numerator ... = 1500. Then Divide by both year and susceptible population =1500 / (5*6000) = 5%.
incidence = number of new cases/ new cases+ population at risk. new cases= 250. People at risk that year 5050 (including new cases. In one point they were a population at risk) 250/ 5050= 4.9%
Exclude the intake year. Add all the positive results (400+250+300+300+250 = 1500). Divide 1500 by the total number of patients from the start of the incidence period, year 1, so 6000 ---> 1500/6000=0.25, this is the average across all 5 years. For annual, divide 0.25 by the number of years, 5 --> 0.25/5 = 0.05 --> 5%.
That's how I got it.
Incidence is typically calculated as a number diseased per exposed population per unit time, usually year. For each year, divide the people found, by the people exposed. You arrive at figures fr each year being 4%, 5% and 6%, avergae being 5%.
Q: Why not count intake year for which the incidence seems to be 40%?
Ans: So that's the trick of the question. IT seems to imply the intake year also has 4000 new cases, but this isn't incidence, this is prevalence! What happened here was that the population of 10,000 was not being screened for AIDS. Then you started the screening program.
Typically in any screening program, you will establish the baseline prevalence of the disease by testing all of the general population. You find 4000 new cases, but these were just undetected cases. You exclude them from your monitoring. For the next year, you keep a watch on the 6000 left, of which 400 develop AIDS. You calculate incidence for this year as 6.7% and exclude these 400 from the next year and so on.
https://step1.medbullets.com/stats/101011/statistical-hypotheses-and-error
The chart on this site shows alpha/beta/power/True negative(correct). This question asks "likelihood of missing an association" - which basically means what is the false positive rate, which is the definition of alpha/Type I error. Question stem states alpha=0.05, which is 5%.
Beta is Type II error, and would be 10% (false negative). 90% would be Power (1-beta)
I don't know the equation for this, but I did this: The sum of incidence per year/ the sum of number reamainig in population. So... 1,500/28,800 = .05208 or 5.2%
submitted by โyoussefa(162)
So number of cases with positive serology during "intake" represents prevalence and should not be accounted for when calculating population at risk. Population at risk = Total population - prevalence. Doing that, sum up the annual incidences left = 400 + 250 + 250 + 300 + 300 = 1500.
Applying incidence formula = 1500/(10,000-4000) = 0.25 over a total of 5 years.
Annual = 0.25/5 = 0.05%