Quantitative measures of health and disease status
Problem: 1
25 of 400 day-old cross-bred calves were found to have no anal opening [atresia ani]. Estimate and interpret
the prevalence of atresia ani in calves.
𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐞𝐱𝐢𝐬𝐭𝐢𝐧𝐠 𝐜𝐚𝐬𝐞𝐬 𝐚𝐭 𝐚 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐭𝐢𝐦𝐞
Prevalence = 𝐓𝐨𝐭𝐚𝐥 𝐩𝐨𝐩𝐮𝐥𝐚𝐭𝐢𝐨𝐧 𝐚𝐭 𝐫𝐢𝐬𝐤 𝐚𝐭 𝐭𝐡𝐚𝐭 𝐭𝐢𝐦𝐞
Here, Number of cases = 25 and Total population = 400
25
So, Prevalence = 400 = 0.0625 (or, 6.25%)
Interpretation: At the time of examination, 6.25% of the day-old cross-bred calf population was affected by
atresia ani
Problem: 2
Fecal samples of 700 goats and 900 sheep were examined to observe stomach worm eggs. 120 goats and 105
sheep samples were tested positive. Estimate, interpret, and compare the prevalence of hemonchosis in two
species.
120
For Goats, Prevalence = 700 = 0.17 or 17%
105
For sheeps, Prevalence = 900 = 0.116 or, 11.6%
Comparison & Interpretation: The prevalence of hemonchosis is higher in goats (17% or 17 out of 100 is
affected by hemonchosis) compared to sheep (11.6% or approximately 12 out of 100 is affected by
hemonchosis). This suggests that within this study group, goats were more frequently affected by stomach
worms than sheep.
Problem 3: Incidence Risk and
IncidenceRate of SCM
200 dairy cattle under subsistence management and 200 under intensive management were followed for 7
months for subclinical mastitis (SCM). Every months these cattle were testes by CMT for the diagnosis of
subclinical mastitis (SCM). No new cattle entered in the group and none lost to follow-up. 14, 5, 10, 2, and
20 new cases of SCM and 10, 20, 9, 13, and 8 new cases of SCM were developed at the end of 2, 3, 4, 5 and
6 months of follow-up. Calculate and compare the incidence risk and incidence rate in the two systems.
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒐𝒇 𝒏𝒆𝒘 𝒄𝒂𝒔𝒆𝒔 𝒅𝒖𝒓𝒊𝒏𝒈 𝒕𝒉𝒆 𝒔𝒕𝒖𝒅𝒚 𝒑𝒆𝒓𝒊𝒐𝒅
Incidence Risk (Cumulative Incidence) =
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒐𝒇 𝒂𝒏𝒊𝒎𝒂𝒍𝒔 𝒂𝒕 𝒓𝒊𝒔𝒌 𝒂𝒕 𝒕𝒉𝒆 𝒃𝒆𝒈𝒊𝒏𝒏𝒊𝒏𝒈 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒕𝒖𝒅𝒚 𝒑𝒆𝒓𝒊𝒐𝒅
Subsistence Cases: 14 + 5 + 10 + 2 + 20 = 51 cases.
Intensive Cases: 10 + 20 + 9 + 13 + 8 = 60 cases.
So, incidence risk –
51
at Subsistence = 200 = 0.255 or, 25.5%
1
, 60
at Intensive = = 0.30 or, 30%
200
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒐𝒇 𝒏𝒆𝒘 𝒄𝒂𝒔𝒆𝒔
Incidence rate = 𝑻𝒐𝒕𝒂𝒍 𝒂𝒏𝒊𝒎𝒂𝒍−𝒕𝒊𝒎𝒆 𝒂𝒕 𝒓𝒊𝒔𝒌
Subsistence Animal-Months: (14 x 2) + (5 x 3) + (10 x 4) + (2 x 5) + (20 x 6) + (149 x 7) = 1,256 months.
Intensive Animal-Months: (10 x 2) + (20 x 3) + (9 x 4) + (13 x 5) + (8 x 6) + (140 x 7) = 1,209 months
51
so now, Incidence rate for Subsistence Animal = = 0.0406 cases/animal-month
1256
60
Incidence rate for Subsistence Animal = 1209 = 0.0496 cases/ animal-month
Problem 4: Incidence Rate of Clinical Mastitis
Three hundred healthy cows in dirty floor and the same number of cows in clean floor were followed for 36
months to estimate the incidence rate of clinical mastitis. At 13th months of follow-up 10 cows in the dirty
floor and 13 cows in the clean floor were added.
After 20th and 24th months of study period 7 and 8 cows were lost to follow-up in the dirty floor and clean
floor, respectively.
In dirty floor condition, 3, 8, 6 and 2 cows developed clinical mastitis after 9, 12, 20 and 23rd months of
follow-up.
On the other hand, in clean floor condition, 1, 2, 1 and 2 cows developed clinical mastitis after 12, 16, 18
and 21st months of follow-up.
Calculate, compare and interpret incidence rate in two floor conditions.
solve:
Dirty Floor Group
• Initial Cows (300):
o 3 cows (cases) @ 9 months: 3 x 9 = 27
o 8 cows (cases) @ 12 months: 8 x 12 = 96
o 7 cows (lost) @ 20 months: 7 x 20 = 140
o 6 cows (cases) @ 20 months: 6 x 20 = 120
o 2 cows (cases) @ 23 months: 2 x 23 = 46
o Remaining cows (300 - 3 - 8 - 7 - 6 - 2 = 274) @ 36 months: 274 x 36 = 9,864
• Added Cows (10):
• Added at 13 months, followed until 36 months: 10 x (36 - 13) = 230
Total Cow-Months (Dirty): 27 + 96 + 140 + 120 + 46 + 9,864 + 230 = 10,523 cow-months
2
, Clean Floor Group
• Initial Cows (300):
o 1 cow (case) @ 12 months: 1 x 12 = 12
o 2 cows (cases) @ 16 months: 2 x 16 = 32
o 1 cow (case) @ 18 months: 1 x 18 = 18
o 2 cows (cases) @ 21 months: 2 x 21 = 42
o 8 cows (lost) @ 24 months: 8 x 24 = 192
o Remaining cows (300 - 1 - 2 - 1 - 2 - 8 = 286) @ 36 months: 286 x 36 = 10,296
• Added Cows (13):
o Added at 13 months, followed until 36 months: 13 x (36 - 13) = 299
• Total Cow-Months (Clean): 12 + 32 + 18 + 42 + 192 + 10,296 + 299 =10,891cow-months
Now, the incidence rate (IR)-
3+8+6+2 19
IRDirty floor = 10523
= 10523 = 0.0018 cases per cow-month
1+2+1+2 6
IRDirty floor = = 10891 = 0.00055 cases per cow-month
10891
The dirty floor condition resulted in 1.81 new cases of mastitis for every 1,000 months of cow observation,
while the clean floor condition resulted in only 0.55 cases.
Problem 5: mortality risk
Two hundred adult and 200 calves were followed for 12 months to estimate the FMD mortality risk. No cattle
new entered in the group and none lost to follow-up. 1, 2, 1, 1, and 2 adult cattle and 2, 2, 3, 1, and 4 calves
died at the end of 5, 6, 9, 10 and 11 months of follow-up. Calculate and compare the FMD mortality risk in
calves and adult cattle.
Solve:
Mortality Risk (also known as Cumulative Incidence) for both groups. Since the study follows a closed
cohort (no new entries and no losses to follow-up), the risk is simply the proportion of the initial population
that died during the 12-month period.
Calculation for Adult Cattle
• Initial Population (N): 200
• Total Deaths (D): 1 + 2 + 1 + 1 + 2 = 7
3
Problem: 1
25 of 400 day-old cross-bred calves were found to have no anal opening [atresia ani]. Estimate and interpret
the prevalence of atresia ani in calves.
𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐞𝐱𝐢𝐬𝐭𝐢𝐧𝐠 𝐜𝐚𝐬𝐞𝐬 𝐚𝐭 𝐚 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐭𝐢𝐦𝐞
Prevalence = 𝐓𝐨𝐭𝐚𝐥 𝐩𝐨𝐩𝐮𝐥𝐚𝐭𝐢𝐨𝐧 𝐚𝐭 𝐫𝐢𝐬𝐤 𝐚𝐭 𝐭𝐡𝐚𝐭 𝐭𝐢𝐦𝐞
Here, Number of cases = 25 and Total population = 400
25
So, Prevalence = 400 = 0.0625 (or, 6.25%)
Interpretation: At the time of examination, 6.25% of the day-old cross-bred calf population was affected by
atresia ani
Problem: 2
Fecal samples of 700 goats and 900 sheep were examined to observe stomach worm eggs. 120 goats and 105
sheep samples were tested positive. Estimate, interpret, and compare the prevalence of hemonchosis in two
species.
120
For Goats, Prevalence = 700 = 0.17 or 17%
105
For sheeps, Prevalence = 900 = 0.116 or, 11.6%
Comparison & Interpretation: The prevalence of hemonchosis is higher in goats (17% or 17 out of 100 is
affected by hemonchosis) compared to sheep (11.6% or approximately 12 out of 100 is affected by
hemonchosis). This suggests that within this study group, goats were more frequently affected by stomach
worms than sheep.
Problem 3: Incidence Risk and
IncidenceRate of SCM
200 dairy cattle under subsistence management and 200 under intensive management were followed for 7
months for subclinical mastitis (SCM). Every months these cattle were testes by CMT for the diagnosis of
subclinical mastitis (SCM). No new cattle entered in the group and none lost to follow-up. 14, 5, 10, 2, and
20 new cases of SCM and 10, 20, 9, 13, and 8 new cases of SCM were developed at the end of 2, 3, 4, 5 and
6 months of follow-up. Calculate and compare the incidence risk and incidence rate in the two systems.
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒐𝒇 𝒏𝒆𝒘 𝒄𝒂𝒔𝒆𝒔 𝒅𝒖𝒓𝒊𝒏𝒈 𝒕𝒉𝒆 𝒔𝒕𝒖𝒅𝒚 𝒑𝒆𝒓𝒊𝒐𝒅
Incidence Risk (Cumulative Incidence) =
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒐𝒇 𝒂𝒏𝒊𝒎𝒂𝒍𝒔 𝒂𝒕 𝒓𝒊𝒔𝒌 𝒂𝒕 𝒕𝒉𝒆 𝒃𝒆𝒈𝒊𝒏𝒏𝒊𝒏𝒈 𝒐𝒇 𝒕𝒉𝒆 𝒔𝒕𝒖𝒅𝒚 𝒑𝒆𝒓𝒊𝒐𝒅
Subsistence Cases: 14 + 5 + 10 + 2 + 20 = 51 cases.
Intensive Cases: 10 + 20 + 9 + 13 + 8 = 60 cases.
So, incidence risk –
51
at Subsistence = 200 = 0.255 or, 25.5%
1
, 60
at Intensive = = 0.30 or, 30%
200
𝑻𝒐𝒕𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒐𝒇 𝒏𝒆𝒘 𝒄𝒂𝒔𝒆𝒔
Incidence rate = 𝑻𝒐𝒕𝒂𝒍 𝒂𝒏𝒊𝒎𝒂𝒍−𝒕𝒊𝒎𝒆 𝒂𝒕 𝒓𝒊𝒔𝒌
Subsistence Animal-Months: (14 x 2) + (5 x 3) + (10 x 4) + (2 x 5) + (20 x 6) + (149 x 7) = 1,256 months.
Intensive Animal-Months: (10 x 2) + (20 x 3) + (9 x 4) + (13 x 5) + (8 x 6) + (140 x 7) = 1,209 months
51
so now, Incidence rate for Subsistence Animal = = 0.0406 cases/animal-month
1256
60
Incidence rate for Subsistence Animal = 1209 = 0.0496 cases/ animal-month
Problem 4: Incidence Rate of Clinical Mastitis
Three hundred healthy cows in dirty floor and the same number of cows in clean floor were followed for 36
months to estimate the incidence rate of clinical mastitis. At 13th months of follow-up 10 cows in the dirty
floor and 13 cows in the clean floor were added.
After 20th and 24th months of study period 7 and 8 cows were lost to follow-up in the dirty floor and clean
floor, respectively.
In dirty floor condition, 3, 8, 6 and 2 cows developed clinical mastitis after 9, 12, 20 and 23rd months of
follow-up.
On the other hand, in clean floor condition, 1, 2, 1 and 2 cows developed clinical mastitis after 12, 16, 18
and 21st months of follow-up.
Calculate, compare and interpret incidence rate in two floor conditions.
solve:
Dirty Floor Group
• Initial Cows (300):
o 3 cows (cases) @ 9 months: 3 x 9 = 27
o 8 cows (cases) @ 12 months: 8 x 12 = 96
o 7 cows (lost) @ 20 months: 7 x 20 = 140
o 6 cows (cases) @ 20 months: 6 x 20 = 120
o 2 cows (cases) @ 23 months: 2 x 23 = 46
o Remaining cows (300 - 3 - 8 - 7 - 6 - 2 = 274) @ 36 months: 274 x 36 = 9,864
• Added Cows (10):
• Added at 13 months, followed until 36 months: 10 x (36 - 13) = 230
Total Cow-Months (Dirty): 27 + 96 + 140 + 120 + 46 + 9,864 + 230 = 10,523 cow-months
2
, Clean Floor Group
• Initial Cows (300):
o 1 cow (case) @ 12 months: 1 x 12 = 12
o 2 cows (cases) @ 16 months: 2 x 16 = 32
o 1 cow (case) @ 18 months: 1 x 18 = 18
o 2 cows (cases) @ 21 months: 2 x 21 = 42
o 8 cows (lost) @ 24 months: 8 x 24 = 192
o Remaining cows (300 - 1 - 2 - 1 - 2 - 8 = 286) @ 36 months: 286 x 36 = 10,296
• Added Cows (13):
o Added at 13 months, followed until 36 months: 13 x (36 - 13) = 299
• Total Cow-Months (Clean): 12 + 32 + 18 + 42 + 192 + 10,296 + 299 =10,891cow-months
Now, the incidence rate (IR)-
3+8+6+2 19
IRDirty floor = 10523
= 10523 = 0.0018 cases per cow-month
1+2+1+2 6
IRDirty floor = = 10891 = 0.00055 cases per cow-month
10891
The dirty floor condition resulted in 1.81 new cases of mastitis for every 1,000 months of cow observation,
while the clean floor condition resulted in only 0.55 cases.
Problem 5: mortality risk
Two hundred adult and 200 calves were followed for 12 months to estimate the FMD mortality risk. No cattle
new entered in the group and none lost to follow-up. 1, 2, 1, 1, and 2 adult cattle and 2, 2, 3, 1, and 4 calves
died at the end of 5, 6, 9, 10 and 11 months of follow-up. Calculate and compare the FMD mortality risk in
calves and adult cattle.
Solve:
Mortality Risk (also known as Cumulative Incidence) for both groups. Since the study follows a closed
cohort (no new entries and no losses to follow-up), the risk is simply the proportion of the initial population
that died during the 12-month period.
Calculation for Adult Cattle
• Initial Population (N): 200
• Total Deaths (D): 1 + 2 + 1 + 1 + 2 = 7
3
