Exercise 2: Mastitis
Two new products are being marketed by competing animal health companies. Both products are a combination product of a rapid diagnostic test and dry cow therapy to use in dairy cows at drying off.
Product A consists of a rapid test which uses mammary associated amyloid A to detect mastitis. The cut off has been assigned at 100 µg/ml and at this cut off the label claims to have 100% sensitivity and 90% specificity. The product also contains dry cow tubes which are used to treat any quarters with mastitis. The product also contains a sterile teat sealant which is used on healthy quarters. The label claims it is a superior product as it always finds mastitis cows.
Product B is very similar. But in this case the cut-off point is 400 µg/ml of mammary associated amyloid A. The sensitivity is 95% and specificity 97%. Here the label claims that this is the best test as it makes the fewest misdiagnoses.
Both product A and B cost 5 Euros per quarter to test the cow and then treat the quarter with either antibiotic dry cow tube or teat sealant.
You are in farm animal practice and you have a major dairy client with a 1000 cow dairy herd. He is thinking about switching from routine dry cow therapy of all cows to selective dry cow therapy. Presently he uses an antibiotic product which costs 5 Euros to treat each quarter. If he switches, he can avoid using antibiotic treatment in many of his cows and obtain a premium by selling the milk from these cows as organic milk.
Which product would you recommend? Assume that approximately 30% of quarters have mastitis at drying off (to make it easier, assume if a cow is positive it is only positive in one quarter). Of these cows, approximately one quarter will suffer acute mastitis the following lactation if not treated during the dry period. This will result in a loss of 25% productivity in these cows in that lactation. The others that are not treated will have subclinical mastitis resulting in a loss of 10% production. Healthy cows will not suffer any loss. The average (healthy!) dairy cow produces 25,000 lbs of milk in a lactation which is sold at 36 cents a lb. Any milk from a cow that has not been treated with antibiotics can command a premium of 40 cents a lb.
Calculator:
Test your knowledge|
300
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950
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970
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1000
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With Test A: 285 and with Test B: 300
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With Test A: 15 and with Test B: 0
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With Test A: 30 and with Test B: 9
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With Test A: 300 and with Test B: 285
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With Test A: 0 and with Test B: 15
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With Test A: 15 and with Test B: 0
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With Test A: 30 and with Test B: 9
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With Test A: 300 and with Test B: 285
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Misallocation costs of a false negative = 30,000 for test A and 9,000 Euros for test B
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Misallocation costs of a false negative = 8,564.30 for test A and 14,523.10 Euros for test B
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Misallocation costs of a false negative = 0 for test A and 18,562.50 Euros for test B
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Misallocation costs of a false negative = 0 for test A and 16,430.20 Euros for test B
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Test A: 0 cows and Test B: 15 cows
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Test A: 15 cows and Test B: 0 cows
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Test A: 70 cows and Test B: 21 cows
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Test A: 21 cows and Test B: 70 cows
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Misallocation costs of a false positive= 30,000 Euros for test A and 0 Euros for test B
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Misallocation costs of a false positive= 0 Euros for test A and 18,562.50 Euros for test B
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Misallocation costs of a false positive= 70,000 Euros for test A and 21,000 Euros for test B
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Misallocation costs of a false positive= 2,870.20 Euros for test A and 12,000 Euros for test B
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Product A
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Product B
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