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1 EFFECT OF AGE, STAGE OF LACTATON, MLK YELD AND HEALTH EVENTS ON LENGTH OF PRODUCTVE LFE N SWEDSH DARY CATTLE ASSESSED BY SURVVAL ANALYSS. P.A. Oltenacu l, J. Carvalhera, U. Emanuelson 2 and V. Ducrocq 3. Dept. Anmal Scence, Cornell Unversty, thaca, NY , USA 2Swedsh Assocaton for Lvestock Breedng and Producton, Esklstuna, Sweden 3Staton de G6n_tque Quanttatve et Applqu6e, NRA, Jouy-en-Josas, France Forty Nnth Annual Natonal Breeders' Roundtable. May 4-5, 2000, St. Lous, MO. 60

2 EFFECT OF AGE, STAGE OF LACTATON, MLK YELD AND HEALTH 1 EVENTS ON LENGTH OF PRODUCTVE LFE N SWEDSH DARY CATTLE ASSESSED BY SURVVAL ANALYSS. P.A. Oltenacu ], J. Carvalhera ], U. Emanuelson 2 and V. Ducrocq 3. ]Dept. Anmal Scence, Cornell Unversty, thaca, NY , USA 2Swedsh Assocaton for Lvestock Breedng and Producton, Esklstuna, Sweden 3Staton de G6n6tque Quanttatve et Applqu6e, NRA, Jouy-en-Josas, France NRODUCTON Longevty and survval analyss. Cullng of dary cows can be voluntary -- a healthy cow s no longer consdered as economcally compettve relatve to her possble 1 replacement -- or nvoluntary -- a cow, whatever her actual or potental producton, s no longer able to be mlked n a proftable way because ofnfertlty, lameness, mastts or other dseases --. Length of productve lfe (LPL) defned as the number of days between frst calvng and cullng (or death) s a contnuous measure of"longevty" and reflects how quckly cullng occurs. As a consequence, LPL s hghly related to the darymen's proft: n a gven herd, n f the average LPL s hgh, less replacement hefers need to be rased and replacement costs are decreased. Furthermore, f one can correct actual LPL records for dfferences n due to voluntary cullng, e.g., related to low mlk producton, better LPLs mean more "robust" anmals, less lkely to be nvoluntary culled. Consequently, LPL s a trat that m has receved an ncreasng attenton n the anmal breedng feld (for revews see Dekkers and Jarath 1994; Strandberg and S61kner 1997) and mproved LPL s regarded as a major management goal. To acheve ths, a better understandng of the factors nfluencng LPL s essental, But the analyss of survval data, such as LPL, usng standard methods based on lnear models s often mpossble due to the presence of censorng. Censorng s the exstence of partal records: some anmals are stll alve at the end of the study perod and only a n lower bound of ther true LPL s known. To edt those records or to consder them as exact ones results n severely based analyses. There are ways to avod censored records; n

3 e.g., usng bnary response varables (presence or absence of anmals at a gven age) or replacng censored records by projected ones. These approaches are lkely to be neffcent as substantal amount of nformaton s lost when contnuous LPL records are transformed nto a 0-1 trat and the nformaton avalable to project censored records s often scarce and loosely related to actual LPL. However, statstcal methods to evaluate LPL are avalable,.e. falure tme analyss, that do account for censorng wthout any loss of nformaton (Smth 1983, Smth and Quaas 1984, Ducrocq et al, 1988). These methods were used by Ducrocq (1994) and by Beaudeau et. al, (1985) to nvestgate the effect of health and other factors on LPL n dary cattle. They are based on the concept of hazard rate _.(t), whch s defned as the that probablty an anmal fals (.e., s culled, n our case) at tme t, gven t was alve just before t. n the presence ofcovarates, a frequently used model s the proportonal hazards model, where _.(t) s descrbed as the product of a baselne hazard functon _(t), representng the overall ageng process, and a postve functon of the explanatory varables supposed to nfluence cullng rate. n such a model, the relatve probablty of beng culled of tow ndvduals s assumed to be constant over tme (.e., ther hazards are proportonal). An extremely powerful extenson of ths model s the ncluson of tmedependent covarates, where the proportonalty assumpton has to hold only for restrcted tme ntervals. Typcal tme-dependent covarates n a dary context are herd-year-season combnatons, lactaton number, and health or reproductve status. mplementaton of these survval analyss technques may be found n most large statstcal software packages (e.g., SAS, BMDP)but these programs do not handle anmal-breedng data well. They are usually very restrcted n the number of levels of effects allowed and often do not even allow for "class" effects. ncluson of random effects s seldom possble and use of tme-dependent varables s cumbersome. n addton, they are computatonally general. not very effcent, probably because they are too A Fortran package, named "the Survval Kt", was wrtten by Ducrocq and Solkner (1994, 1998) to provde anmal scentsts wth a user-frendly software specally

4 adapted to ther needs, n partcular for the analyss of very large data sets. The program has three parts: FRONT END program recodes the data for use n the two other programs. For each anmal, a record ncludes the actual LPL (or dates for the "orgn" and "end" ponts), a censorng code and the ntal values for each covarate. There s no lmtaton n the number of covarates and these can be contnuous or dscrete. f tme-dependent covarates are used, the record must also nclude tmes of change (as dates or number of days snce the orgn pont) of covarates and the correspondng new values. Changes of covarates nfluencng whole sets of anmals (e.g., on a gven date, for herd-year-season effects) need not be ncluded n each ndvdual record. COX program fts a Cox model,.e., a proportonal hazard model where the baselne hazard functon _(t) s completely arbtrary. Some effects can be declared as random, followng a normal, multvarate normal (wth a relatonshp matrx) or a loggamma dstrbuton. The program computes estmates of each fxed and random effect and, upon request, performs lkelhood rato tests (testng the sgnfcance of all or some effects), provdes asymptotc standard errors of the estmates, or computes the expected survvor curves of any real or reference anmal. WEBULL program fts a Webull model,.e., a proportonal hazard model where the baselne hazard functon _(t) follows a Webull hazard dstrbuton. The Webull model s a very flexble generalzaton of the exponental regresson model and s less computatonally demandng than the Cox model. t ncludes all the features of the COX program as well as the possble estmaton of the varance components of the random effects. MATERALS AND METHODS The Data. The data came from a random sample comprsng 20% of all herds, wth more than 15 cows, n the offcal Swedsh mlk-, A- and dsease-recordng schemes. Complete lfetme nformaton on pedgree, calvng, mlk producton, dseases, A, and

5 date of ext was avalable on all cows calvng n these herds between Jan. 1 and Dec Edtng process: - Only records from the Swedsh Red and Whte (SRB) and the Swedsh Fresan (SLB) breed were kept Only one calvng per cow was kept (823 cows calved twce n 1991) Records for whch tme of dsorder occurrence was > then days between calvng and cullng or censorng were deleted Cows wth calvng number equal to 0 or > 11 were deleted. The two breeds were analyzed separately. The fnal data sets ncluded records from 35,407 SRB cows n 1,647 herds and 27,598 SLB cows n 1,509 herds. The data also had nformaton on 1,904 SRB bulls and 1,514 SLB bulls for whch breedng values for adjusted LPL were estmated n the survval analyss. The data dd not nclude new cows calvng n subsequent years, and for ths reason, the analyss was restrcted to the events recorded only durng the lactaton ntated n To nclude n the analyss cows calvng at the end of 1991, 12/31/92 was used as end of study censorng date. n ths paper only the analyss of SRB breed s presented. The descrptve statstcs for SRB breed are: - Numberofrecords: 35,407 - Number and proporton of rght censored records: 22,252 (62.846%) Mnmum censorng tme: 367 days Maxmum censorng tme: 731 days Average censorng tme: days Mnmum falure tme: 1 day Maxmum falure tme: 722 days Average falure tme: days The objectves of ths study were to estmate the effect of several dseases on length of productve lfe (LPL) of Swedsh dary cows by survval analyss and to estmate the genetc varance and Hertablty for LPL adjusted for the effect of mlk

6 producton and health status. LPL s defned as the number of days between date of frst calvng and date at cullng or death. The Model. A Webull regresson model was used to estmate the effect of consdered dsorders on LPL takng nto account that the data was rght censored at December 31, The model was as follows: ;_(t; x(t), z(t))=;qa(;_t) 'lexp{x(t)'b where: + z(t)'u} _,(t; x(t), z(t)) s the hazard functon of an ndvdual dependng on tme t, _,p(_,t) - s the Webull baselne hazard functon, b s the parameter vector of fxed effects, x(t) s the vector of fxed covarates, u s the parameter vector of random effects, and.. z(t) s the vector of the random covarates. The fxed effects n the model were party (1,2,3,4, >4), stage of lactaton (0-30d, 31-60d, d, d and >270d), mlk yeld, rsk factor dseases (by tme of occurrence) and the nteractons between stage of lactaton and dseases, where stage of lactaton, dseases and ther nteracton were treated as tme-dependent. Mlk yeld was the average of fat-corrected mlk recorded at second and thrd test months after calvng, shown to be closely related to 305-d lactaton yeld (Danell, 1982). Rsk factor dseases consdered were veternary treated cases of dystoca (DY), retaned placenta (RP), mlk fever (MF), metrts (ME), ketoss (KE), mastts (MA), locomotor dsorders (LD) and cystc ovares (CY). Four seasons of calvng were consdered: Jan-Mar, Apr-Jun, Jul-Sept and Oct- Dec). Random effects were herd-season (assumed to follow a log-gamma dstrbuton and algebracally ntegrated out from the jont posteror densty) and sre, where the

7 addtve genetc relatonshp matrx for all bulls based on ther sre and maternal grand sre relatonshps was ncorporated. The sre's breedng values for adjusted LPL were obtaned as a by-product at convergence. A descrpton of all factors ncluded n the model and the number of levels for each factor s n Table 1and 2. Table 1. Descrpton of the random effects and party, stage of lactaton and mlk yeld fxed effects ncluded n the model. Effect Levels Comments Man Effects: Herd Season (hs) 5565 Assumed random followng a Sre(s) 1904 Assumed Log-_amma random dstrbuton followng a normal dstrbuton Party Stage of lactaton* 5 1 through - DM _<30 4 and d > < DM <60d 3-60 < DM < 150d 4-150< DM_<270d 5 - DM > 270 d Mlkyed 3 l-mlk 16kg 2-16<mlk 3 - > 25 kg25kg *Tme dependent covarates.

8 Table 2. Descrpton of the dsease man effects ncluded nthe model. Effect Levels Comments 1 l Man effects: Mastts* Healthy cows (Only 1 case occurrng n): n - DM < 30 d 2-30 < DM <60 d 3-60 < DM < 150 d < DM <270 d 5 - DM > 270 d (> wth frst occurrng n): 6 - DM < 30 d ll <DM <60d 8-60 < DM < 150 d 1 U <DM <270d 10 - DM > 270 d dystoca* Healthy cows (frst case occurrng n): 1 - DM _<30 d Cystc Ovares* Healthy cows (frst case occurrng n): 1 - DlM < 30 d n 2-30<DM< 60d 3-60<DM< 150d <DM< 270d 5- DM > 270d l.locomotor dsorders* 6 0- Healthy cows (frst case occurrng n): 1 - DM < 30 d 2-30 < DM <60d 3-60 < DM < 150d < DM <270 d 5 - DM > 270 d U Ketoss* 4 0- Healthy cows (frst case occurrng n): -DM _<30d 2-30 < DM <60d 3-60 < DM < 150d *Tme dependent covarates. Metrts* 6 0- Healthy cows (frst case occurrng n): n. DM < 30 d 2-30 < DM <60 d < DM < 150d < DM <270 d 5- DM > 270d Mlk Fever* 2 0- Healthy cows (frst case occurrng n): - DM < 30 d Retaned Placenta* 2 0- Healthy cows (frst case occurrng n): 1 - DM < 30 d

9 1 Lkelhood Rato Tests. Table 3 shows the results of the lkelhood rato tests when the covarates were added sequentally to the model. As stated above, hs were assumed to random, followng a Log-gamma dstrbuton and were. algebracally ntegrated out from the jont posteror densty. to absorbng Thsthe technque group of decreases equatonsthe correspondng number of parameters to the hs effect. to estmate and s equvalent All tests for the effects ncluded n the model were sgnfcant for KE, RP*ST and ME*ST nteractons. (P < 0.05), except Table 3. Testng for sgnfcance of the effects n SRB breed (Lkelhood rato tests). Effects nclude n the model" lkelhood 2*Alog b- df(f) c Sgnf- canoe d PA PA+ST PA+ST+M PA+ST+M+MA PA+ST+M+MA+DY PA+ST+M+MA+DY+CY+FE PA+ST+M+MA+DY+CY+FE+KE '5 PA+ST+M+MA+DY+CY+FE+KE+ME+MF PA+ST+M+MA+DY+CY+FE+KE+ME+M F+RP PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS+DYS PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS+DYS RPS +RPS+MES PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS+DYS PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS+DYS RPS+MES+KES PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS+DYS RPS+MES+KES+CYS PA+ST+M+MA+DY+CY+FE+KE+ME+M F+RP+MAS+DYS RPS+MES+KES+CYS+FES PA+ST+M+MA+DY+CY+FE+KE+ME+MF+RP+MAS+DYS RPS+MES+KES+CYS+FES+MFS 'PA FE = = Locomotor Party, ST = dsorders, Stage of lactaton, KE = Ketoss, M = Mlk, ME = MA Metrts, = Mastts, MF = DY Mlk= Fever, dystoca, RP CY = Retaned = Cystc Placenta, Ovares, MAS = MA by ST, DYS = DY by ST. RPS = RP by ST, MES = ME by ST, KES = KE by ST, CYS = CY by ST, FES = FEby ST, MFS = MF by ST. bchange when the last effect s ncluded n the model. CTest statstc follows a ch-squared dstrbuton wth f df. d(p > test statstc)

10 RESULTS AND DSCUSON Clncal mastts was the most frequent of the dseases consdered n ths study. The ncdence of the 8 health dsorders n SRB breed s shown n Table 4. Table 4. The lactatonal ncdence of 8 health dsorders (SRB breed). Dsorder ncdence Mastts Number 4730 Percentage 13.4 D),stoca Retaned Placenta Metrts Ketoss Cystc Ovares Locomotor Dsorders Mlk Fever The effects of party, stage of lactaton and mlk yeld on LPL are shown n Table 5. Rsk of cullng ncreased wth party and stage of lactaton and decreased wth mlk yeld. Table 5. The effect of party, stage of lactaton and mlk yeld on rsk of cullng n SRB breed. Effect Party: Cullng Rsk Rato Party Party Party Party Party > Stage of lactaton 0 < DM < 30d < DM_< 60d < DM < 150d n 150 < DM_< 270d DM > 270d Mlk Yeld 0 < mlk < 16 k_ < mlk < 25 kg Mlk > 25 kg breference s a healthy cow n Party 1 (hefer), n late lactaton (DM > 270d) and a hgh producer (Mlk 3). n

11 one Mastts s of the economcally most mportant dsease n dary on cattle. ts effects LPL, expressed as rsk rato, as decrease of LPL for frst quartle and as fracton of cows stll alve at 365 days are shown n Table 6. Cows wth only one epsode of clncal mastts lactaton durng were at hgher rsk ofbeng culled. Hgher rsk of cullng was assocated wth mastts occurrence n the frst two stages of lactaton. Cows wth two or more clncal mastts epsodes were also at hgher rsk, but the rsk of cullng was smlar, ndependent of the stage of lactaton when frst epsode occurred. Table 6. The effect of mastts on LPL n SRB breed.. Effect Rsk Decrease n frst Fracton stll Rato quartle LPL (d) a alve at 365d b Mastts: One case occurrng n: DM < 30d 2.5* < DM < 60d 2.8* < DM < 150d 2.1" DM 150 < > DM 270d_<270d 1.5' 1.4* > 1 case wth frst case n: DM < 30d 1.6' < DM < 60d 1.8' < DM _<150d 1.6' 36 0_ < DM < 270d DM > 270d *P < areference s an alve (censored) healthy cow n Party 1 (hefer) and n hgh producng _Rroup(Mlk 3). eference s a healthy cow n Party 1 (hefer), n late lactaton (DM > 270d) and a hgh producer (Mlk 3).

12 The effects of veternary asssted dystoca, cystc ovares, locomotor dsorders, ketoss, == metrts and mlk fever on LPL are shown n Table 7. All dseases were sgnfcant rsk m factors for cullng. Table 7. The effect of dystoca, cystc ovares, locomotor dsorders, ketoss, metrts and retaned placenta on LPL n SRB breed. Effect Rsk Decrease n frst Fracton stll Rato quartle LPL (d) a alve at 365 d b Dystoca: DM _<30d 1.6" Cystc Ovares: DM < 30d < DM < 60d 0.8* < DM _<150d t 150 < DM _<270d 1.8* DM > 270d Locomotor DM < Dsorders: 30d 1.7' < DM < 60d 1.5" < DM < 150d 2.5* < DM < 270d 1.6' DM > 270d 1.5" Ketoss: l DM < 30d 1.3" < DM < 60d t 60 < DM < 150d Metrts: DM < 30d H 30 < DM < 60d < DM < 150d l 150 < DM < 270d Mlk Fever: DM < 30d 1.4" Retaned Placenta: DM < 30d 1.3" *P <0.10. areference s an alve (censored) healthy cow n Party 1 (hefer) and n hgh producng _roup Reference (Mlks3). a healthy cow n Party 1 (hefer), n late lactaton (DM > 270d) and a hgh producer (Mlk 3).

13 SUMARY The effect of party (1,2,3,4, >4), stage of lactaton (0-30d, 31-60d, d, d and >270d), mlk yeld (FCM averaged for 2ndand 3rdtest month after calvng) and occurrence of dseases, all fxed effects, on length of productve lfe (LPL) was evaluated. Stage' of lactaton and dseases and ther nteracton were treated as tmedependent. Herd-seasons and sres were also ncluded n the model and treated as random effects. Dseases consdered were veternary treated cases of dystoca, retaned placenta, metrts, ketoss, mlk fever, cystc ovares, locomotor dsorders and clncal mastffs. Data conssted of 35,407 Swedsh Red and Whte (SRB) cows n 1,647 herds and 27,598 B Swedsh Fresan (SLB) cows n 1,509 herds. A Webull regresson model was used to explan the effect of the dseases on LPL measured by the number of days from calvng to cullng. All dseases had a sgnfcant and smlar effect on LPL for the two breeds. Mastffs had the largest on LPL effect followed by locomotor dsorders, dystoca and retaned placenta. For SRB cows cullng rsk ratos for clncal mastts occurrng n stage 1 to 5 of lactaton were 2.5 a, 2.7 a, 2.1a, 1t 5 _ and and for locomotor dsorders were 1.8a, 1.6a, 2.7 a, 1.6a and 1.6a, respectvely (ap<0.10). Tme of cullng was nfluenced by how each dsease mpacted the performance of a cow. Hghest probablty for cullng was mmedately after occurrence for dseases affectng cows' mlk producton (mastts, locomotor dsease, mlk fever and ketoss) and delayed for dseases affectng cows' reproductve performance (cystc ovares and metrts). REFERENCES Ducrocq, V. and S61kner, J. (1994). "The Survval Kt", a Fortran package for the Congress on analyss of survval data. Proc. 5 th World Genetcs Appled to Lvestock Producton 22: Danell, B. (1982). Acta Agrc. Scand. 32: Ducrocq, V., R.L. Quaas, E.J. Pollak, G. Casella (1988). Length of productve lfe of " dary cows. 1- Justfcaton of a Webull model; 2- Varance component estmaton and sre evaluaton. J. Dary Sc., 71, and V. 1 Statstcal of Ducrocq, (994). analyss length of productve lfe for dary cows of the Normande breed. J. Dary Sc., 77, Beaudeau, F., V. Ducrocq, C. Fourchon, H. Seegers (1995). Effect of dsease on length of productve,lfe of French Holsten dary cows assessed by survval analyss. J. Dary Sc., 78, Dekkers, JC.M. and Jarath, L.K. (1994). Proc. 5thWorld Congress on Genetcs Appled to Lvestock Producton 17: Ducrocq, V. and S61kner J. (1998). Proc. 6th World Congress on Genetcs Appled to Lvestock Producton. ll ]1 Smth, S.P. (1983). Ph.D. Thess, Comell Unversty. Smth, S.P. and Quaas, R.L. (1984). J. Dary Sc. 67: Strandberg. E. and S61kner, J. (1996). NTERBULL Bulletn 12:

14 Audence Questons and Answers for Dr. Oltenacu Queston: Jm Arthur. Can ths model be used to predct age of death for ndvdual anmals survvng to the end of the test? Answer: Yes. Queston: Davd Pollock. How good was the accuracy of classfcaton of dsease and other reasons for cullng? Answer: Qute Good. n Sweden only veternarans can dspense treatment and drugs, consequently each and every ncdent was documented. Queston: Melvn Kuhn. Have BV estmates from survval models been compared to other crtera for rankng sres; e.g. BLUP, or mean of sre's progeny for survval? Answer: Yes, survval method s preferred because t ncludes varous dsease covarates not ncluded n BLUP.

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