Question

1.    Suppose that you are funded to engage in a study of chronic obstructive pulmonary disease (COPD) in a fixed population of 2,500 people. The study lasts for three years (January 1, 2012 – December 31, 2014).
At the beginning of the study (January 1, 2012), 15 people are identified as already having COPD. Ten additional people develop COPD during 2012, and five of those people with COPD died (these ten people are at risk for a total of 7.5 person-years during 2012); five additional people developed COPD in 2013, and three of those people with COPD died (these five people are also at risk for a total of 10 person-years); twelve additional people developed COPD in 2014, and one person died with COPD (these twelve people are at risk for a total of 33.5 person-years).

a.    What is the point prevalence rate (per 1,000) of COPD on January 1,
2012?

b.    What is the point prevalence rate (per 1,000) of COPD on January 1,
2013?

c.    What is the period prevalence rate (per 1,000) of COPD during 2013?

d.    What is the incidence rate (per 1,000) of COPD for 2012?

e.    What is the incidence rate (per 1,000) of COPD for 2014?

f.     What is the incidence density (per 1,000 person-years) for COPD for the entire three years?

Answer 1

a. Point prevalence rate(P)=(The number of cases at a given time(C)/ the total population during that time(N))

or P = (C/N)

Number of COPD cases reported as on January 2012 = 15

Total population = 2500

Point prevalence on January 2012 = (15/2500) = 0.006

Point of prevalence per 1000 population = 0.006x 1000 = 6%

b.Point prevalence rate (per 1,000) of COPD on January 1, 2013

No of affected people as on January 1, 2013 = 20

P = (20/2500) x 1000 = 8%

c. Period prevalance(PP) = (C+I)/N

C= No of cases at the begining of a time periods

I= Number of cases developed during that time period

N= Total size of population at that time

Period prevalence rate of COPD per 1000 population during 2013

C = 20, I = 5 and N = 2500

PP = (20+5)/2500 = 0.01

So PP of COPD per 1000 population during 2013 = 10%

d.  Incidence rate (per 1,000) of COPD for 2012

Incidence rate(IR) = I/PT

I = No of new cases in a specified time

PT = Total person time(sum of duration of observation and total peoples not infected during that time)

In 2012 value of I = 10

Duration of observation = 1 year

Non infected cases = 2500 - 25 = 2475

PT = 1 + 2475 = 2476

IR in 2012 = 10/2476= 0.004038

Incidence rate per 1000 population = 0.004 x 1000 = 4.04%

e. Incidence rate (per 1,000) of COPD for 2014

IR= I/PT

I= 12

PT = 1+2488 = 2489

IR = 12/2489 =0.00482

IR per 1000 population = 0.00482 x 1000 = 4.8%

f. Incidence density (per 1,000 person-years) for COPD for the entire three years

Formula for incidence desity(Incidence rate) = I/PT

I= 10+5+12 = 27

Total number of live infected cases during 2012-13 period = 20 (in 2012 excludiing 5 dead cases), 2 in 2013(5new cases-3deaths),11 in 2014(12-1dead case) = 33

Total number of non infected peoples =2500 - 33 = 2467

PT = 3 + 2467 = 2470

IR of 2012-2013 = 27/2470 = 0.0109

IR per 1,000 person for 3 years = 0.0109 x 1000 = 10.93%.