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cow transformation

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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
(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

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