We will use a single worked example to demonstrate how to estimate the different measures of disease frequency.
Worked example
Let us say we have eight pigs being observed over twelve weeks. All pigs are free of disease at the start of the study. The pigs are then checked each week for a disease.
Animal  Week  Time at risk (weeks) 
1  2  3  4 
5  6  7  8 
9  10  11  12 
1           infected  9 
2              12 
3      infected  4 
4              12 
5     withdrawn  3 
6              12 
7              12 
8         infected  7 
Total time at risk:  71 
 Number of new cases
This could be expressed either per week or per month. If we did it per month we would get 0, 2, and 1 for the 3 fourweek periods.
Prevalence
The point prevalence could be calculated for any particular week. For example, on week 8 it is 2/7 = 0.286 (the withdrawn animal is excluded from the calculation). The period prevalence for the last month would be 3/7 = 0.429 (both new and existing cases are included).
Cumulative incidence
This is rather more tricky to calculate because of the animal that was withdrawn. If we use either 7 or 8 as the denominator, we will bias our estimate of the incidence upwards or downwards. In practice the convention is to subtract half the number of withdrawn individuals from the denominator, so the cumulative incidence for the 12week period would be 3/7.5 = 0.4
Incidence rate
Using the exact method, we add up the number of weeks at risk to give a total of 71 pig weeks. The incidence rate is then given by 3/71 which is 0.042 per pig week. Converting the cumulative incidence to the same units we get (1 − 0.6^{1/12}) = 0.042 per pig week.
Using the approximate method, we estimate the average number at risk over the period by adding the number at risk at the start and end of the period and dividing by two. In this case we have 8 present at the start, 4 at the end so the average number present is 6. The approximate incidence rate is then given by 3/(6x12) = 0.042 per pig week.
Note that there are other ways we could have estimated the average number at risk over the period. For example we could have taken the average over weeks 1,4,8 and 12. As it happens in this case we get the same average number alive (24/4 = 6), but estimates may differ. Hence the precise method used should always be specified.
To avoid very low numbers rates are often multiplied by 100 or 1000. So we might express the rate of 0.042 per pig week as 4.2 per 100 pig weeks, or 42 per 1000 pig weeks.

