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1996 Dairy Report - Iowa State University Adjusting for Preferential Treatment in Genetic Evaluation M. T. Kuhn, graduate student in animal breeding, number of lactations for which she has received PT. When and A. E. Freeman, Distinguished PT is on second and later lactations only (i.e., no PT in first lactation), bias in the cow's PTA is 6% of the PT effect if Professor of Agriculture she has 2 records and 9% of the PT effect if she has 3 records. When PT is practiced in all lactations, including DSL-84 first, biases are 9, 13, and 15 percent of the PT effect when the cow has 1, 2, and 3 records, respectively. Summary and Implications When a cow's dam also receives PT, biases in her PTA Preferential treatment (PT) is treating one cow better are 15, 18, and 20% of the PT effect when she has 1, 2, or 3 than herdmates. It can substantially bias both male and records, respectively. When a cow is flushed and PT is female Predicted Transmitting Abilities (PTAs) for milk applied to both the flush dam and each of the flush yield. Research into methods for reducing this potential bias daughters, bias in PTA depends on the number of flush is in progress but it appears that something called power daughters; biases are as large as 39% of the PT effect for the transformations may be an effective way to remove the bias flush dam and 23% of the PT effect for the daughters when in PTAs caused by PT. there are 20 flush daughters. Sire PTAs can also be biased by PT of their daughters, Introduction the level of bias depending on total number of daughters, PT can be described as any management practice that the proportion of daughters receiving PT, and on how increases production and is applied to one or maybe several daughters are spread across herds. Bias becomes smaller as cows but is not applied to the herdmates. Some of these more PT daughters are placed in a single herd; bias practices might be separate housing (e.g., boxstall), better or increases as total number of daughters increases and as the more feed, greater number of days open, or longer milking proportion of daughters receiving PT increases. When a bull intervals on test day for the cow receiving PT. Use of has each daughter in a separate herd, biases range from 10 bovine somatotropin, on only the preferentially treated cow, (number of daughters = 20, 25% with PT) to 77 (number of has now become another possible tool for PT. It is not daughters = 100, 100% with PT) percent of the PT effect. known how much these practices can inflate a cow's record When PT daughters are all placed in a single herd, biases but certainly 2,000 to 5,000 lb. would not be unreasonable range from 8 to 18% of the PT effect. to expect. So the potential for bias in both cow and sire PTAs is Though some PT may be just good management (e.g., large. For example, if a cow has 3 records, each with a PT cows are sometimes fed according to their level of effect of 3,000 lbs, then the bias in her PTA would be .15 x production), popular opinion is that some cows are 3,000 = 450 lbs. If a sire has, say, 50 daughters, each intentionally treated better than herdmates with the intent to daughter in a different herd, and only 25% with PT, then the make the cow look better than she really is. The motivation bias in his PTA would be .17 x 3,000 = 510 lbs. - assuming may be to make her more appealing to AI organizations for an average PT effect of 3,000 lbs. If 50% of his daughters contract matings or to other producers for sale as breeding receive PT then the bias in his PTA would be .34 x 3,000 = stock. Also, daughters of a particular young sire may be 1,020 lbs. These are very large yet very obtainable biases. preferentially treated in an attempt to inflate his proof. Furthermore, with the advent of BST, PT will occur, PT would not be a serious problem if it did not affect unintentionally, much more frequently than in the past. This (bias) PTAs. However, research has shown that PT can is not to credit or discredit the use of BST, but it is a simple increase PTAs by a considerable amount. The amount that fact that if it is not used uniformly in a herd, it will bias an individual's PTA is increased by PT is called bias. The PTAs. The goal of the research discussed here was to find a size of the bias always depends on how much PT was given. way to remove or at least largely reduce these biases. In For example, bias is larger when a cow's record is increased, particular, the effectiveness of power transformations in say, by 3,000 lbs., than when it is increased by only 2,000 reducing bias caused by PT will be described. lbs. So to discuss the size of biases that PT can cause, it is easier to express the biases as a percentage of the PT effect. Materials and Methods So, for example, a bias of 10% means that if the PT effect is The first question is: what are power transformations? 1,000 lbs., then the bias in PTA is .10 x 1,000 = 100 lbs.; if One possible power transformation is the square root bias is 10% and the PT effect (the amount that PT increases transformation. The square root of a number is another the record) is 2,000 lbs., then bias is .10 x 2,000 = 200 lbs. number which, when multiplied by itself gives the original When an individual cow receives PT, the amount of number back. For example, the square root of 4 is 2 because bias depends on the total number of records she has and the 2 x 2 = 4; the square root of 25 is 5 because 5 x 5 = 25; and the square root of 100 is 10 because 10 x 10 = 100. Now 2) PTAs based on the records with PT but without the suppose I replace a set of numbers with their square roots. transformation; and, For example, suppose I have the numbers 4, 25, 64, and 3) PTAs based on transformed records with PT. 100; then I would replace them with the numbers 2, 5, 8, and 10 which are their square roots. Notice that the bigger Bias without the transformation would be the difference the number, the more it is reduced when we take its square between the PTAs in the first and second sets of PTAs; call root. For example 4 is reduced by 2 (if we replace it with its this "Bias1." square root) but 25 is reduced by 20 and 100 is reduced by 90. Bias after the transformation would be the difference How might this help in correcting for PT? Suppose two between the PTAs in the first and third sets of PTAs; call cows would each make a 22,500 record if there was no PT. this "Bias2." But suppose the second cow receives PT which increases her record to 25,600 so the difference between cow 2's and If all this information was available, then to see if a cow 1's records with no PT is zero but with PT the transformation was effective in reducing bias, all you would difference between their records is 3,100. Now suppose I have to do is see if Bias2 was smaller than Bias1. To see replace both their records with the square roots of their which power gave the smallest bias just calculate the third records. Cow 1's new record would be 150 (the square root set of PTAs for each power and see which gives the smallest of 22,500) and cow 2's new record will be 160. Now the bias. difference between their "new" records is only 10. So the The problem is that this cannot be done with actual actual difference between cow 1's record and cow 2's record cows or records. You cannot get a cow to produce the exact is supposed to be zero (without PT) and by replacing their same amount of milk so you cannot get the PT records you records with the square root of their records, we have made need. It would be impossible to completely control all that difference much closer to zero than it was. So if PTAs factors affecting the records of different cows. are calculated using the "transformed" (square root, for One way the approach described could be used is if example) records, then there is the possibility that bias in records were simulated on a computer. These would not be PTAs will be smaller because the square root has reduced records on real cows, but they would be realistic records. A the effect of the PT. computer can be programmed so as to create a set of records Another way to say "take the square root of a record" which, for all intents and purposes, are the same as a set of (or any number for that matter) is to say "take the record to records from real cows, the only difference being that there the power of .5." Say the record is 19,600 and we want its is complete control over the records. Then it is no problem square root; the square root of 19,600 can also be written as to have a cow with two records: the first record without PT .5 (19,600) . The .5, in this context, is called a "power" and and the second record the exact same as the first except the procedure of taking a record to some power is called a including a PT effect. So this was the approach used to power transformation. As mentioned before, when the determine if power transformations could be effective in power is .5, the power transformation is the same as taking reducing bias in PTAs caused by PT. the square root of the record, but the power can be anything - it doesn't have to be .5. For example, records could be Results and Discussion taken to the power of .1, .3, .7 or anything else. The general Biases were expressed in what are called standard effect of taking a record to some power will be the same (as deviation units. This makes it difficult to interpret the actual long as you use powers less than 1 and greater than 0) as for values of the biases but it makes it easy to compare biases the .5 (square root) transformation; it will decrease the size when different powers are used to transform the data. of the PT effect but the amount of decrease will depend on Only two scenarios for PT have been studied so far; the the power. case where only the cow herself has a single record and it Once again, then, the goal of this research was to has PT and the case where the cow and her dam both determine the effectiveness of these so-called power received PT. transformations in reducing bias in PTAs caused by PT. For the case when only the cow herself received PT, Four different powers were tried: .1, .3, .5, and .7. bias was .083 standard deviation units when there was no The question is, how can it be determined if these transformation compared to biases of .086, .082, and .078 power transformations will reduce bias in PTAs and if so, when the data were transformed using powers of .7, .5, and which is the best power to use? Ideally, you would have two .3, respectively. However, when a power of .1 was used, sets of records on a set of cows: 1) records without PT and bias was zero. Bias was also zero, using the .1 power 2) the exact same records but with some of the cows transformation, when both the cow and her dam received receiving PT. You could then calculate three sets of PTAs: PT. Thus; a power transformation using, a power of .1, 1) PTAs based on the records without PT; these would be looks like a promising way to remove bias in PTAs caused the correct PTAs; by PT. However, some further research still needs to be done. We need to see if the power transformations will also remove bias in sire PTAs when their daughters receive PT. Also, the PTAs come out on a different scale when they are computed from transformed records so an effective way to rescale the PTAs is also needed. Finally, we need to make sure that the transformations do not obscure differences among cows. This has been briefly investigated and so far it appears that the best cows in the population can still be identified when PTAs are computed from transformed records.