J. Anim Sci. 2007. 85:512-517. doi:10.2527/jas.2006-435
© 2007 American Society of Animal Science
Survival analysis from birth to slaughter of Ripollesa lambs under semi-intensive management1
J. Casellas2,
G. Caja,
X. Such and
J. Piedrafita
Grup de Recerca en Remugants, Departament de Ciéncia Animal i dels Aliments, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
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Abstract
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The survivability from birth to slaughter of 1,487 Ripollesa lambs with a preslaughter overall mortality of 9.6% was studied under the proportional hazards framework, assuming a Weibull distribution for the baseline hazards function. A sire frailty model was fitted, with the common environment received by the lamb as an additional random source of variation. Common environment was considered time-dependent and was characterized by the dam and the contemporary lamb group during the preweaning and fattening periods, respectively. Only 3 fixed effects were statistically significant: the linear and quadratic effects of birth weight (P < 0.001), the relative position of the delivery within the lambing season (P < 0.001), and the presence of stillbirths or mummified fetuses within the litter (P < 0.05). Birth type and parity of the ewe were significant only when birth weight was removed from the model (P < 0.001 and P < 0.05, respectively). Nevertheless, the model including birth weight became preferable according to the Akaike’s information criterion. Survivability dramatically decreased with extreme birth weights, although it reached a survival probability greater than 93.5% within the 3.3 to 5.4 kg range, indicating an optimum birth weight range of Ripollesa lambs for survival purposes. The hazard ratio (HR) increased for births occurring within the last third of the lambing period (HR = 1.70; P < 0.05), as well as for primiparous ewes that lambed in December and January (HR = 5.36; P < 0.001). Survival probability decreased for lambs born from litters with 1 or more stillbirths or mummified fetuses (HR = 1.61; P < 0.05). The variance component estimated for sire variance (0.07) was clearly lower than that of the common environment (1.87), with a heritability estimate of 0.027.
Key Words: lamb survival • proportional hazard • Ripollesa breed • survival analysis
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INTRODUCTION
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Lamb mortality rate averages 9 to 20% in most sheep-producing countries (Gama et al., 1991b
; Binns et al., 2002), representing an important economic loss for farmers. In recent decades, many attempts have been made to identify the key factors involved in neonatal vulnerability, but the results are heterogeneous and are highly influenced by breed and production system (Gama et al., 1991a; Mukasa-Mugerwa et al., 2000; Binns et al., 2002). Lamb survivability has not been studied in native sheep breeds in Mediterranean production systems. The Ripollesa breed is an example of a southern European breed with a semiintensive management and moderate BW at slaughter (20 to 25 kg).
Lamb mortality can be analyzed as a binary trait (Fogarty, 1995), but it suffers from a severe information loss because it ignores the continuity of the mortality process and the precise time of death (Allison, 1997). This simplification implies that dead animals 1 d or 3 mo after birth are treated alike and contribute the same amount of information. Thus, survival analysis techniques (Cox, 1972), recently adapted for animal breeding purposes (Ducrocq et al., 1988) and implemented in available software packages such as the Survival Kit (Ducrocq and Sölkner, 1998), have become a preferred procedure, given that they account for the continuity of mortality and also allow inclusion of censored records from animals with an unknown death age. Although logistic regression provides comparable results regarding fixed effects, survival analysis is preferable for genetic studies of mortality, providing a better estimation of genetic variance components (Southey et al., 2001).
This paper analyzed the genetic and environmental factors that influence Ripollesa lamb survival under semiintensive management throughout the suckling and fattening period, within the framework of the proportional hazard models.
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MATERIALS AND METHODS
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Animals
Animal Care and Use Committee approval was not obtained for this study because the data were obtained from an existing database; the analyzed records were registered in the experimental farm of the Universitat Autònoma of Barcelona (Barcelona, Spain), between the years 1988 and 2002.
The Ripollesa breed is a meat-purpose, Catalonian (Spain), indigenous ovine breed. Animals come from the entrefino Spanish trunk and have dark marks on the head and legs and white wool with closed fleece (wool fiber diameter 23 to 26 µm; Sánchez Belda and Sánchez Trujillano, 1986). This flock lambed once yearly, using natural mating and concentrating births during September to November, with the exception of replacement ewe lambs that lambed in December to January since 1995. Note that all lambings in December to January were from primiparous ewes.
Lambs were generally weaned at approximately 15 kg of BW and at 30 to 45 d of age, and were fed commercial concentrate and barley straw ad libitum. Slaughter was done when lambs reached a BW of 20 to 25 kg (90 to 120 d). For each lamb, date of birth, birth type, and birth weight were recorded as well as date of death or slaughter, for uncensored and censored records, respectively. A total of 1,487 lambs born alive were available for analysis, 143 of which died before slaughter (9.6%), after rejecting individuals with unknown sire (515 lambs), stillbirths (87 lambs; 5.5%), and mummified fetuses (15 lambs; 0.9%). Lambs in the final data set were obtained from 22 Ripollesa rams and 316 Ripollesa ewes.
Statistical Analysis
Under the proportional hazards model, the hazard function h(t; xi) is the instantaneous death rate at time t of a particular animal i characterized by a set of explanatory variables xi, and can be written as the baseline hazard function h0(t) multiplied by the exponential effect (ß) of xi variables (Ducrocq et al., 2000):
The inclusion of random effects modify the previous equation by adding a vector of random effects (u) and its associated incidence vector zi (Ducrocq and Casella, 1996; Ducrocq et al., 2000):
When the additive genetic relationships between animals are considered, frailty models provide estimates of the additive genetic variance, an essential previous step to estimate survival heritability. These frailty models have been extensively described by Ducrocq and Casella (1996).
The baseline hazard function h0(t) can be estimated unparametrically (Cox, 1972) or assuming a parametric form, usually the Weibull distribution, with parameters 
and 
(h0(t) = (t)–1; Ducrocq et al., 1988). Unfortunately, the Cox model is not appropriate when several deaths occur at the same age (Cox, 1972), as happens during the early neonatal period (Southey et al., 2001). On the other hand, the Weibull model is remarkably robust for grouped deaths (Ducrocq, 1999), although the Weibull assumption for baseline has to be tested accurately. Thus, if the baseline follows a Weibull distribution, the plot of log[–log(SKM)] against log(t) should give a straight line (Ducrocq et al., 2000), where SKM represents the survival function estimated by the Kaplan-Meier method (Kaplan and Meier, 1958). To determine an adequate temporal scale, the Weibull assumption was tested for daily and weekly survival data. Model fitting was assessed with the Casellas et al. (2006) parametric bootstrap.
Selection of Fixed Effects
The fixed effects initially considered were 1) linear and quadratic effect of birth weight, 2) parity of the ewe including 6 categories (first parity, second, third, fourth or fifth, sixth or seventh, and eighth and following parities), 3) birth type including single, twin, and triplet births, 4) sex of lamb (male or female), 5) presence of mummies or stillbirths in the litter, and 6) relative position of the delivery within the birth distribution during the lambing season with 4 levels (within the first, second, and last third of parturitions, and an extra category for replacement ewes that delivered in December to January). A sequential likelihood ratio test (Ducrocq and Sölkner, 1998) allowed us to determine which effects reached statistical significance. Comparisons between fixed effect models were carried out through the Akaike’s information criterion (AIC; Akaike, 1973). The most adequate model was the one that minimized:
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with p being the total number of parameters estimated, including and .
Estimation of Random Sources of Variation
The previously selected fixed model was extended to a mixed model including 2 random effects, the common environment received by the lamb and the genetic sire effect. The common environment was treated as a time-dependent variable characterized by the ewe during the preweaning period and the contemporary group throughout the fattening period. It can be viewed as the permanent environment provided by the ewe before weaning, indistinguishable for successive litters, and the year effect during the fattening period. In this sense, contemporary grouping captures year-to-year variation, whereas within-year variation is accounted for by the baseline hazard function. The common environment and the sire genetic effects were assumed to be log-gamma(
,) distributed and multivariate normal distributed, MVN(0, A
), respectively, where represents the variance of the common environment (
), and was the genetic variance between sires. Variance components of both random sources of variation were estimated using the Bayesian approach described by Ducrocq and Casella (1996). Heritability on the binary scale was determined with the Tarrés et al. (2005) formula. All analyses were carried out using the Survival Kit package (Ducrocq and Sölkner, 1998).
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RESULTS
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The probability of survival of 1,487 live-born Ripollesa lambs was studied, showing a preslaughter overall mortality of 9.6%. Seventy-three deaths occurred during the first week of life (50.1%), 44 of them during the first 3 d, and 20 lambs died during the second week of life (14.0%). This distribution of deaths confirms an important grouping during the early postnatal period, incompatible with Cox survival analysis. In order to determine the adequate temporal scale of survival data for a Weibull survival analysis, the Weibull hypothesis for baseline (h0) was tested for the age at failure (death or censoring) measured with days and weeks. The graphical test applied showed that baseline for daily data failed to follow a Weibull distribution, whereas the weekly temporal scale showed a straight line when we plotted the ln(–ln(SKM)) vs. ln(t) (Figure 1). Those results were confirmed through a parametric bootstrap (Casellas et al., 2006). Model fitting of daily data showed significant biases (P < 0.05), whereas model fitting of weekly data did not provid significant misadjusts (P > 0.1). As a consequence, the analyses were carried out assuming a weekly data grouping and Weibull distribution for h0.
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Figure 1. Graphical test for the Weibull assumption of the baseline hazards function for the whole population (daily and weekly data).
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Only 3 fixed effects were significant for lamb survival: linear and quadratic effect of birth weight (both with P < 0.001), relative position of the delivery within the birth distribution (P < 0.001), and presence of mummified fetuses or stillbirths in the litter (P < 0.05). The remaining fixed effects did not reach statistical significance, except when birth weight was not considered. When we excluded the birth weight effect, birth type was clearly significant (P < 0.001), showing an increased hazard ratio (HR) for twin (HR = 1.98; P < 0.001) and triplet births (HR = 2.36; P < 0.05), and the parity of the ewe also reached statistical significance (P < 0.05), with an increased mortality for lambs coming from primiparous ewes (HR = 1.71; P < 0.05) or eighth and posterior parities (HR = 1.85; P < 0.05). Nevertheless, inclusion of birth weight provided us a most adequate model (AIC = 1,534.9) compared with the alternative model excluding it (AIC = 1,580.1).
Regression coefficients for linear and quadratic effects of birth weight were –2.78 (P < 0.001) and 0.32 (P < 0.001), respectively. It implied that survival probability was maximum for a birth weight of 4.34 kg, and omitting the influence of the remaining fixed effects, the reduction of survivability was not more than 2% between 3.3 and 5.4 kg of birth weight (Figure 2). The relative position of the delivery within the birth distribution did not show significant differences between the first 2 lambing periods, whereas the lambs born during the last of the lambing period suffered an increased HR (HR = 1.70; P < 0.05). Primiparous parities occurring during winter reached the worst survival probability with a hazard ratio of 5.36 (P < 0.001). The presence of stillbirths or mummified fetuses within litter reduced the survivability of the remaining siblings (HR = 1.61, P < 0.05; Table 1).
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Figure 2. Distribution of birth weight in Ripollesa lambs (left y-axis) and evolution of survival probability related to lamb birth weight (right y-axis). The influence of the remaining significant effects was not considered.
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Table 1. Number of lambs (No.), number of deaths (deaths), and hazard ratios for significant categorical fixed effects
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Variance parameters for the common environment and the genetic sire effects are shown in Table 2. Both variance parameters showed a skewed posterior density, with slightly different mode and mean. Binary heritability of lamb survival to slaughter was 0.027.
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DISCUSSION
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Almost 10% of lambs born alive died during the suckling or fattening periods, and half of these losses corresponded to the first week of life. This initial concentration of deaths has also been reported by several authors, with similar (Mukasa-Mugerwa et al., 2000) or greater death percentages (Southey et al., 2001, 2003). It implies substantial economic losses (Amer et al., 1999) given the high mortality of initially viable individuals.
Birth weight influenced lamb survivability (P < 0.001), showing that the smallest and biggest lambs suffered from a reduced survival probability. In this sense, birth weight has been historically considered a major risk factor for lamb mortality (Gama et al., 1991a; Mukasa-Mugerwa et al., 2000) with linear (Huffman et al., 1985; Mukasa-Mugerwa et al., 2000) or quadratic effects on lamb survival (Gama et al., 1991a; Christley et al., 2003). Small lambs need to spend more energy for the maintenance of body temperature, given that they have a greater surface to body mass ratio, which involves greater heat losses. However, light birth weights have been related to reduced fetal lipid reserves, attenuated lamb vitality, and to dams with an impaired colostrum and milk production. All of these are factors that increase susceptibility to hypothermia and starvation (Mellor and Murray, 1985a,b). Moreover, when colostrum intake decreases, the passive immunity acquired is also reduced and the risk of infectious diseases become greater (Christley et al., 2003). An early colostrum ingestion plays an important role in the process of ewe-lamb recognition (García Gonzalez and Goddard, 1998), which conditions the future access of the lamb to food resources. Moreover, lambs with low birth weight may have a reduced capacity to access colostrums, and they probably suffered a disadvantage when competing for resources with bigger siblings in multiple deliveries (Gama et al., 1991a). On the opposite extreme, the increased mortality for heavier lambs has been related to the risk of dystocia during delivery with associated hypoxia (Gamma et al., 1991a), which reduces the vitality of lambs. However, survivability varied minimally within an important interval of intermediate birth weights (Figure 2
). Assuming that the remaining sources of variation had a null effect, lambs weighing between 3.3 and 5.4 kg at birth showed a survival probability greater than 93.5%, with a maximum value for 4.3 kg (95.6%), which probably describes an optimum birth weight interval of the Ripollesa breed. Similar optimum birth weight values for survival purposes have been described in Finnsheep (Gama et al., 1991a), despite the greater litter size of this breed. Heavier lambs for maximum value of survival probability were observed for Suffolk, Rambouillet, and Dorset lambs, although the shape of the survival curves was more pronounced (Gama et al., 1991a). Unfortunately, almost 50% of Ripollesa lambs were born with light birth weight, below the optimum range of 3.3 to 5.4 kg, and were at an increased risk of death (Figure 2). These facts suggested 2 possible ways to reduce lamb mortality, both closely related with birth weight. A medium-long term genetic improvement of birth weight seems possible because heritability for lamb birth weight reaches moderate values. Also, adoption of adequate feeding strategies during pregnancy could increase the average birth weight, as well as colostrum production of the ewe (Kleemann et al., 1990; Nowak, 1996). However, the effect of a greater birth weight on lambing ease, dystocia frequency, and mortality at birth should be analyzed accurately.
Inclusion of birth weight meant effects of birth type and parity of the ewe were removed from the definitive model. Both of these effects have been related previously to lamb survival (Gama et al., 1991a; Christley et al., 2003), sometimes without considering birth weight within the model (Southey et al., 2001, 2003), and their influence over birth weight has also been reported (Cloete et al., 2002). Our results showed that the effect of birth type or parity of the ewe may be accounted for by birth weight, obtaining a preferable survival model. In addition, the reduced survivability of lambs of primiparous ewes was explained in part by the relative position of the parturition within the birth distribution. Nevertheless, when we excluded birth weight from the model, death risk increased with the number of lambs born per litter, and also for lambs of primiparous ewes. Similar results were reported by Gama et al. (1991a) and Southey et al. (2001, 2003).
The effect of the relative position of birth within the lambing period on lamb survival has not been reported. Recent research has shown that lambs born later in the lambing season could be smaller than lambs born earlier, although results were not conclusive (Christley et al., 2003). The authors hypothesized that this reduction in birth weight might be related to ewe health, considering that ewes in poor health may have had a prolonged gestation or conceived later in the breeding season (Christley et al., 2003). On the contrary, we observed significant changes in lamb survival throughout the lambing season (Table 1), whereas average birth weight for the first (3.4 ± 0.04 kg), second (3.4 ± 0.03 kg), last third (3.4 ± 0.04 kg), and replacement ewes delivered in December-January (3.5 ± 0.14 kg) did not change. The hazard ratio increased significantly for deliveries that occurred during the last third of the birth distribution (Table 1), possibly due to ewe health, just as Christley et al. (2003) indicated for birth weight, and possibly due to the build-up of infectious agents in the environment (Christley et al., 2003). On the other hand, lambs born in winter, from primiparous ewes, suffered greater mortality probably caused by several factors, including failure to establish a sufficient bond between the ewe and her lamb, is most frequent in primiparous dams (Nowak, 1996), milk production of primiparous ewes is lower (Cardellino and Benson, 2002), and environmental conditions of winter are harmful for the thermal balance of newborn lambs.
When 1 or more littermates were born dead or mummified, the remaining siblings suffered 1.61 times more risk of death (P < 0.05) than those litters with all individuals born alive. Other estimates of this effect on lamb survival do not exist, although the negative effect caused by the presence of mummies or stillbirths has been described in swine (Casellas et al., 2004). Multiple factors can cause fetal death during gestation and the subsequent birth of mummified lambs, although infectious agents play a central role (Kirkbride, 1993). On the other hand, the presence of stillbirths is closely related to delivery, hypoxemia during birth being the major cause of those deaths (Norton et al., 1998). On the whole, stillbirths and mummies show the presence of deleterious factors influencing sibling survival, probably due to injuries that killed a fetus during gestation or delivery, which may also damage the remaining littermates, and harmful changes in the uterine environment caused by the presence of mummified fetuses, which could have repercussions on the viability of lambs born alive.
The mode of sire variance was 0.07, similar to that reported by Shoutey et al. (2001, 2003) and clearly lower than the common environment variance estimate (1.87), with a heritability of 0.027. The direct genetic improvement for Ripollesa lamb survival seems difficult, although future studies might clarify this hypothesis. Recent research applying animal logistic models with maternal effects has indicated heritabilities for lamb survival lower than 0.1, generally ranging between 0 and 0.05, with maternal heritabilities being slightly greater, oscillating between 0.08 and 0.17 (Southey et al., 2003). Indirect selection for lamb survival may be carried out through a more highly heritable trait closely correlated with survivability, as reported Gama et al. (1991b). The indirect genetic improvement through birth weight has been proposed in swine (Knol et al., 2002) and also may be useful in ovine populations. Other traits have been suggested such as biochemical markers, resistance to cold, maternal, and neonatal behavior, maternal pelvic size and milk production (Gama et al., 1991b), although only selection for maternal ability has been used effectively to improve lamb survival (Haughey, 1983).
Survival analysis can be a powerful tool to investigate and assess the survival from birth to slaughter in Ripollesa lambs. To improve lamb survival, 2 types of actions could be undertaken. On the environmental side, special attention must be paid to lambs born with birth weight lower than 3.3 kg or heavier than 5.4 kg, lambs of primiparous ewes or delayed parturitions within the lambing season, and lambs from deliveries with 1 or more stillbirths of mummified fetuses. On the genetic side, the heritability found for lamb survival in our data set was very low, and it suggested that the direct genetic improvement for Ripollesa lamb survival was difficult.
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Footnotes
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1 Research supported by a contract with the Departament d’Agricultura, Ramaderia i Pesca de la Generalitat de Catalunya (Spain) and a Universitat Autònoma de Barcelona (Bellaterra, Spain) fellowship granted to J. Casellas. The authors appreciate the assistance of R. Costa and the crew of the S1GCE (Servei de Granges i Camps Experimentals de la UAB, Bellaterra, Spain) for feeding and taking care of the animals. The English revision of N. Aldam is also acknowledged. 
2 Corresponding author: joaquim.casellas{at}uab.es
Received for publication July 5, 2006.
Accepted for publication September 6, 2006.
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Abstract
INTRODUCTION
) and common environment (
)