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Analysis of censored survival data in Japanese quail divergently selected for growth and their control
Analysis of Censored Survival Data in Japanese Quail Divergently Selected for Growth and Their Control1 S. E. Aggrey2 and H. L. Marks Poultry Genetics and Biotechnology Laboratory, Department of Poultry Science, The University of Georgia, Athens, Georgia 30602-2772 compared to the divergently selected lines (57 vs. 22%). Any factor that influences growth after hatching may likely have a direct impact on mortality. Lack of accessibility to water, feed, warmth, and potential negative social interaction are factors that could affect mortality immediately after hatch. The posthatch BW at time of mortality used as a risk factor indicated that the divergently selected lines have about the same risk and are less sensitive to reduced BW compared to the control population. Through survival analysis, the present study has demonstrated that factors causing reduction in posthatch BW are likely risk factors for mortality in growing birds.
(Key words: survival analysis, quail, mortality, Cox regression model, hazard ratio) 2002 Poultry Science 81:1618–1620
INTRODUCTION Stayability is the survival rate in animals, and in commercial operations profitability is increased if all individuals in the flock survive to marketing age. Therefore, factors that cause survival rates to decrease would inherently affect profitability. Survival analysis is often used to analyze data for which the outcome of interest is time until some event occurs (Famula, 1981; Ducrocq, 1997). This event can be the response to a treatment, development of a disease, or, more traditionally, death. Data collected from animal studies are often censored because the study may end before the event is observed or because an animal is eliminated from the study for reasons other than the defined event. Observations made on such individuals should be right censored. A right censored or incomplete observation occurs when an individual did not reach the event of interest during the study period (Lee, 1992). Use of linear or logistic regression, and analysis of variance methods in the analysis of event time data (Allore et al., 2001) are not appropriate because of bias from censoring.
2002 Poultry Science Association, Inc. Received for publication March 19, 2002. Accepted for publication June 6, 2002. 1 Supported by State and Hatch funds allocated to the Georgia Agricultural Experimental Stations of the University of Georgia. 2 To whom correspondence should be addressed: saggrey@ arches.uga.edu.
Survival analysis permits the use of complete information on uncensored and censored data and accounts for the heavily skewed distribution of stayability data. Among the frequently used survival models is a proportional hazard model, which is also known as a Cox regression (Cox, 1972). The Cox model is a semi-parametric procedure that does not require the choice of a particular probability distribution to represent survival times. This model also makes it relatively easy to incorporate time-dependent covariates, that is, covariates that may change in value over the course of the observation period. Survival analysis techniques are able to evaluate not only occurrence of a disease problem but also the relative timing of events and can assess the relative importance of risk factors toward the events. Yet within the poultry industry there is no known study using this type of analysis to evaluate productivity, occurrence of diseases, or to assess mortality. Genetic selection has played a vital role in the improvement of production efficiency in poultry (Havenstein et al., 1994). However, selection for growth rate has resulted in deterioration in livability, skeletal problems, and cardiovascular and immunological deficiencies (McKay et al., 2000). Assessing the relative importance of risk factors associated with the negative impact of selection for increased production would be important in prioritiz-
1618
Abbreviation Key: HR = hazard ratio.
Downloaded from http://ps.oxfordjournals.org/ by guest on April 9, 2015
ABSTRACT The aim of the current study was to characterize and quantify risk factors involved in juvenile mortality in divergently selected and control lines of Japanese quail. Survival analysis and Cox proportional hazards regression were used to describe mortality in the three experimental lines with hatch weight and posthatch BW evaluated as risk factors. Survival function distribution indicated that the proportional mortality was highest in the line selected for high 4-wk BW compared to the low and control lines. In all the experimental lines mortality declined when posthatch BW increased; however, the magnitude of reduction was highest in the control line
1619
SURVIVAL ANALYSIS IN POULTRY TABLE 1. The number of censored and uncensored records in three experimental Japanese quail lines
1
time of death for birds that died before 56 d of age. Mortality in the present study was defined as the time from hatch to the date the bird died. A record was considered to be complete (uncensored) if the quail died for any reason before 56 d of age. Censored records, therefore, represented quail that were still alive on Day 56 when quail reached mature BW.
Line Mortality record
Low
Control
High
Censored Uncensored Total
201 35 236
187 25 212
167 47 214
1 Censored = quail alive at Day 56; Uncensored = quail died before Day 56.
Statistical Analysis
ing ameliorating strategies. The objective of the current study was to conduct survival analysis, using Cox’s (1972) proportional hazard regression model, to evaluate risk factors with occurrence of mortality in divergently selected lines and controls of Japanese quail.
MATERIALS AND METHODS
hi(t) = λ(t;zi) = λ0(t)exp(zi) where λ0(t) is a baseline hazard function that is arbitrary and unspecified, except that it cannot be negative, and zi is the vector of covariate for individual i and β the vector of unknown regression parameters associated with the covariates. Hatch weight and BW at death were used as covariates in the model. Baseline hazard function can be regarded as the hazard function for an individual whose covariates all have values of zero. The Cox’s proportionalhazard model also provides the hazard ratio (HR). The HR is eβ. For quantitative covariates (e.g., hatch weight and BW at death) subtracting 1.0 from HR and multiplying by 100 gives the estimated percentage change in the hazard for each unit increase in the covariate. SAS PROC PHREG (SAS Institute, 1996) was used to determine the baseline hazard function and to model the effects of hatch weight and BW at death as risk factors. Two chi-squared statistics (likelihood ratio and Wald test) were used to test for the significance of the overall model and for the risk factors (i.e., hatch weight and BW at death on time of death).
FIGURE 1. Survival curves in three experimental Japanese quail lines. Control = unselected; Low = selected for low 4-wk BW; High = selected for high 4-wk BW. The function was Sˆ(t) =
d
j Π 1 − nj
j:tj≤t such that each time tj, there are nj individuals who are at risk of mortality, and dj is the number of birds that died at time tj.
RESULTS AND DISCUSSION The number of censored and uncensored birds for each line used in the analysis is shown in Table 1. Figure 1 shows the estimated baseline survivor function (λ0(t)) for all birds in the analysis. Baseline survivor function is a
TABLE 2. Cox proportional-hazard regression1 of mortality in Japanese quail Risk factor
df
Parameter estimate
Standard error
χ2
Pr > χ2
Hazard ratio2
Hatch weight BW at death
1 1
0.12064 −0.29186
0.15499 0.05409
0.6059 29.1149
0.4363 0.0001
1.128 0.747
Likelihood ratio of regression model: (χ2df=2 = 609.54; P ≤ 0.0001); Wald: (χ2df=2 = 29.52; P ≤ 0.0001). Hazard ratio (HR): [(HR-1) × 100] = change in risk for each unit increase in risk factor.
1 2
Downloaded from http://ps.oxfordjournals.org/ by guest on April 9, 2015
Mortality data were collected from 30 generations of Japanese quail lines divergently selected for 4-wk BW (Darden and Marks, 1988) and their controls. The lines hereafter are referred to as high, low, and control. Quail chicks were hatched, wing-banded, and placed in quail battery brooders. All quail had access ad libitum to a diet containing 28% CP and 2,947 kcal ME diet and to water. Hatch weights were collected on all birds, as well as BW at the
Survival analysis was performed by using the KaplanMeier survival curves and examining risk factors in a multivariate Cox proportional hazard model (Cox, 1972). The survival function S(t) describes in this case the probability that a line survived death for longer than a specified time t (Kleinbaum, 1996). The Cox proportional hazard model (Cox, 1972) was used to analyze time until death. A hazard function describes a continuous probability distribution that quantifies the instantaneous risk of an event occurring at time t. The hazard function, hi(t), for an observation, or mortality time, is
1620
AGGREY AND MARKS TABLE 3. Stratified Cox proportional-hazard regression of mortality in three experimental Japanese quail lines1 Risk factor Hatch weight BW at death Hatch weight BW at death Hatch weight BW at death
df
Parameter estimate
SE
χ2
Pr > χ2
Hazard ratio2
Control (LR3:χ2df=2 = 158.11; P ≤0.0001; Wald:χ2df=2 = 7.30; P ≤0.0259) 1 1.18976 0.60366 3.8845 0.0487 1 −0.84794 0.32074 6.9890 0.0082 Low (LR3:χ2df=2 = 244.35; P ≤ 0.0001; Wald:χ2df=2 = 24.22; P ≤ 0.0008) 1 0.23493 0.22065 1.1336 0.2870 1 −0.25003 0.06725 13.8047 0.0002 High (LR3:χ2df=2 = 214.61; P ≤ 0.0001; Wald:χ2df=2 = 10.76; P ≤ 0.0046) 1 −0.16528 0.27320 0.3360 0.5452 1 −0.25732 0.08656 8.8377 0.0030
3.286 0.428 1.265 0.779 0.848 0.773
Control = unselected; Low = selected for low 4-wk BW; High = selected for high 4-wk BW. Hazard ratio (HR): (HR-1) × 100 = Change in risk for each unit increase in risk factor. 3 LR = Likelihood ratio of regression model. 1 2
The use of survival analysis has provided a mechanism to account for mortality and for some risk factors that affect mortality. Through survival analysis, the current study has demonstrated that factors causing reduction in posthatch BW are risk factors for mortality in growing birds.
ACKNOWLEDGMENTS The authors thank Cheryl Pearson Gresham, Department of Poultry Science, University of Georgia, Athens, GA, for her technical assistance and collection of data.
REFERENCES Allore, H. G ., L. D. Warnick, J. Hertl, and Y. T. Grhn. 2001. Censoring in survival analysis: A simulation study of the effect of milk yield on conception. Prev. Vet. Med. 49:223–234. Ankra-Badu, G. A., H. L. Marks, and S. E. Aggrey. 2002. Effect of long-term selection on growth characteristics in Japanese quail. Southern Poult. Sci. Abstr. 117. Cox, D. R. 1972. Regression models and life tables. J. R. Stat. Soc. B34:187–220. Darden J. R., and H. L. Marks. 1988. Divergent selection for growth in Japanese quail under split and complete nutritional environments. 1. Genetic and correlated responses to selection. Poult. Sci. 67:519–529. Ducrocq, V. 1997. Survival analysis, a statistical tool for longevity data. Page 29 in Proc. 48th Annu. Meeting Eur. Assoc. Anim. Prod., Vienna, Austria. Famula, T. 1981. Exponential stayability model with censoring and covariates. J. Dairy Sci. 64:538–545. Havenstein, G. B., P. R. Ferket, S. E. Scheideler, and B. T. Larsen. 1994. Growth, livability, and feed conversion of 1957 vs 1991 broiler when fed ‘typical’ 1957 and 1991 broiler diets. Poult. Sci. 73:1785–1794. Kleinbaum, D. G. 1996. Kaplan-Meier survival curves and the log-rank test. Pages 45–82 in Survival Analysis—A Self Learning Text. Springer, New York. Lee, E. T. 1992. Introduction-censored observation. Pages 1–7 in Statistical Methods for Survival Data Analysis, Probability and Mathematical Statistics. Wiley, New York. McKay, J. C., N. F. Barton, A. N. M. Koerhuis, and J. McAdam. 2000. Broiler production around the world. Proc XXI World’s Poult. Congr., Montreal, Canada. SAS Institute. 1996. SAS User’s Guide. Version 6.12. SAS Institute Inc., Cary, NC.
Downloaded from http://ps.oxfordjournals.org/ by guest on April 9, 2015
fraction of birds that will still be alive t days after hatch if mortality was not influenced by hatch weight and posthatch BW. Survival function distribution indicated that the proportional mortality was highest in the high line compared to the low and control lines. The low line was similar to the control line. As pointed out by Ankra-Badu et al. (2002), the growth function of the low line was similar to that of the control line. Thus, the direction of selection for growth may have different impact on growth trajectory and mortality. When the data were pooled across the divergently selected lines and the control lines, as shown in Table 2, BW at hatch did not significantly influence mortality. However, posthatch BW affected mortality significantly in all three lines. In all the experimental lines mortality declined when posthatch BW increased (Table 3); however, the magnitude of reduction was highest in the control line when compared to the divergently selected lines (57 vs. 22%). Factors that influence growth after hatching may likely have a direct impact on mortality. Lack of accessibility to water and feed, warmth, and potential negative social interaction are factors that could affect mortality immediately after hatch. The posthatch BW at time of mortality, used as a risk factor, indicated that the divergently selected lines have about the same risk and were less sensitive to reduced BW, compared to the control population. Hatch weight, on the other hand, was a risk factor only in the control population, in which mortality would increase when hatch weight increased. In the control population, chicks with high hatch weight carry the highest risk of mortality when they suffer from reduced posthatch growth due to known or unknown causes. The effect of hatch weight as a risk factor was not significant in the selected lines. Growth analysis from the same experimental lines demonstrated that the deviation from the control line was not the same in the high and low lines (Ankra-Badu et al., 2002). Ankra-Badu et al. (2002) observed that the line selected for high 4-wk BW has diverged more from the control line than the line selected for low 4-wk BW. This finding may explain the similarities between the low line and the control for hatch weight as a risk factor for mortality.
(Key words: survival analysis, quail, mortality, Cox regression model, hazard ratio) 2002 Poultry Science 81:1618–1620
INTRODUCTION Stayability is the survival rate in animals, and in commercial operations profitability is increased if all individuals in the flock survive to marketing age. Therefore, factors that cause survival rates to decrease would inherently affect profitability. Survival analysis is often used to analyze data for which the outcome of interest is time until some event occurs (Famula, 1981; Ducrocq, 1997). This event can be the response to a treatment, development of a disease, or, more traditionally, death. Data collected from animal studies are often censored because the study may end before the event is observed or because an animal is eliminated from the study for reasons other than the defined event. Observations made on such individuals should be right censored. A right censored or incomplete observation occurs when an individual did not reach the event of interest during the study period (Lee, 1992). Use of linear or logistic regression, and analysis of variance methods in the analysis of event time data (Allore et al., 2001) are not appropriate because of bias from censoring.
2002 Poultry Science Association, Inc. Received for publication March 19, 2002. Accepted for publication June 6, 2002. 1 Supported by State and Hatch funds allocated to the Georgia Agricultural Experimental Stations of the University of Georgia. 2 To whom correspondence should be addressed: saggrey@ arches.uga.edu.
Survival analysis permits the use of complete information on uncensored and censored data and accounts for the heavily skewed distribution of stayability data. Among the frequently used survival models is a proportional hazard model, which is also known as a Cox regression (Cox, 1972). The Cox model is a semi-parametric procedure that does not require the choice of a particular probability distribution to represent survival times. This model also makes it relatively easy to incorporate time-dependent covariates, that is, covariates that may change in value over the course of the observation period. Survival analysis techniques are able to evaluate not only occurrence of a disease problem but also the relative timing of events and can assess the relative importance of risk factors toward the events. Yet within the poultry industry there is no known study using this type of analysis to evaluate productivity, occurrence of diseases, or to assess mortality. Genetic selection has played a vital role in the improvement of production efficiency in poultry (Havenstein et al., 1994). However, selection for growth rate has resulted in deterioration in livability, skeletal problems, and cardiovascular and immunological deficiencies (McKay et al., 2000). Assessing the relative importance of risk factors associated with the negative impact of selection for increased production would be important in prioritiz-
1618
Abbreviation Key: HR = hazard ratio.
Downloaded from http://ps.oxfordjournals.org/ by guest on April 9, 2015
ABSTRACT The aim of the current study was to characterize and quantify risk factors involved in juvenile mortality in divergently selected and control lines of Japanese quail. Survival analysis and Cox proportional hazards regression were used to describe mortality in the three experimental lines with hatch weight and posthatch BW evaluated as risk factors. Survival function distribution indicated that the proportional mortality was highest in the line selected for high 4-wk BW compared to the low and control lines. In all the experimental lines mortality declined when posthatch BW increased; however, the magnitude of reduction was highest in the control line
1619
SURVIVAL ANALYSIS IN POULTRY TABLE 1. The number of censored and uncensored records in three experimental Japanese quail lines
1
time of death for birds that died before 56 d of age. Mortality in the present study was defined as the time from hatch to the date the bird died. A record was considered to be complete (uncensored) if the quail died for any reason before 56 d of age. Censored records, therefore, represented quail that were still alive on Day 56 when quail reached mature BW.
Line Mortality record
Low
Control
High
Censored Uncensored Total
201 35 236
187 25 212
167 47 214
1 Censored = quail alive at Day 56; Uncensored = quail died before Day 56.
Statistical Analysis
ing ameliorating strategies. The objective of the current study was to conduct survival analysis, using Cox’s (1972) proportional hazard regression model, to evaluate risk factors with occurrence of mortality in divergently selected lines and controls of Japanese quail.
MATERIALS AND METHODS
hi(t) = λ(t;zi) = λ0(t)exp(zi) where λ0(t) is a baseline hazard function that is arbitrary and unspecified, except that it cannot be negative, and zi is the vector of covariate for individual i and β the vector of unknown regression parameters associated with the covariates. Hatch weight and BW at death were used as covariates in the model. Baseline hazard function can be regarded as the hazard function for an individual whose covariates all have values of zero. The Cox’s proportionalhazard model also provides the hazard ratio (HR). The HR is eβ. For quantitative covariates (e.g., hatch weight and BW at death) subtracting 1.0 from HR and multiplying by 100 gives the estimated percentage change in the hazard for each unit increase in the covariate. SAS PROC PHREG (SAS Institute, 1996) was used to determine the baseline hazard function and to model the effects of hatch weight and BW at death as risk factors. Two chi-squared statistics (likelihood ratio and Wald test) were used to test for the significance of the overall model and for the risk factors (i.e., hatch weight and BW at death on time of death).
FIGURE 1. Survival curves in three experimental Japanese quail lines. Control = unselected; Low = selected for low 4-wk BW; High = selected for high 4-wk BW. The function was Sˆ(t) =
d
j Π 1 − nj
j:tj≤t such that each time tj, there are nj individuals who are at risk of mortality, and dj is the number of birds that died at time tj.
RESULTS AND DISCUSSION The number of censored and uncensored birds for each line used in the analysis is shown in Table 1. Figure 1 shows the estimated baseline survivor function (λ0(t)) for all birds in the analysis. Baseline survivor function is a
TABLE 2. Cox proportional-hazard regression1 of mortality in Japanese quail Risk factor
df
Parameter estimate
Standard error
χ2
Pr > χ2
Hazard ratio2
Hatch weight BW at death
1 1
0.12064 −0.29186
0.15499 0.05409
0.6059 29.1149
0.4363 0.0001
1.128 0.747
Likelihood ratio of regression model: (χ2df=2 = 609.54; P ≤ 0.0001); Wald: (χ2df=2 = 29.52; P ≤ 0.0001). Hazard ratio (HR): [(HR-1) × 100] = change in risk for each unit increase in risk factor.
1 2
Downloaded from http://ps.oxfordjournals.org/ by guest on April 9, 2015
Mortality data were collected from 30 generations of Japanese quail lines divergently selected for 4-wk BW (Darden and Marks, 1988) and their controls. The lines hereafter are referred to as high, low, and control. Quail chicks were hatched, wing-banded, and placed in quail battery brooders. All quail had access ad libitum to a diet containing 28% CP and 2,947 kcal ME diet and to water. Hatch weights were collected on all birds, as well as BW at the
Survival analysis was performed by using the KaplanMeier survival curves and examining risk factors in a multivariate Cox proportional hazard model (Cox, 1972). The survival function S(t) describes in this case the probability that a line survived death for longer than a specified time t (Kleinbaum, 1996). The Cox proportional hazard model (Cox, 1972) was used to analyze time until death. A hazard function describes a continuous probability distribution that quantifies the instantaneous risk of an event occurring at time t. The hazard function, hi(t), for an observation, or mortality time, is
1620
AGGREY AND MARKS TABLE 3. Stratified Cox proportional-hazard regression of mortality in three experimental Japanese quail lines1 Risk factor Hatch weight BW at death Hatch weight BW at death Hatch weight BW at death
df
Parameter estimate
SE
χ2
Pr > χ2
Hazard ratio2
Control (LR3:χ2df=2 = 158.11; P ≤0.0001; Wald:χ2df=2 = 7.30; P ≤0.0259) 1 1.18976 0.60366 3.8845 0.0487 1 −0.84794 0.32074 6.9890 0.0082 Low (LR3:χ2df=2 = 244.35; P ≤ 0.0001; Wald:χ2df=2 = 24.22; P ≤ 0.0008) 1 0.23493 0.22065 1.1336 0.2870 1 −0.25003 0.06725 13.8047 0.0002 High (LR3:χ2df=2 = 214.61; P ≤ 0.0001; Wald:χ2df=2 = 10.76; P ≤ 0.0046) 1 −0.16528 0.27320 0.3360 0.5452 1 −0.25732 0.08656 8.8377 0.0030
3.286 0.428 1.265 0.779 0.848 0.773
Control = unselected; Low = selected for low 4-wk BW; High = selected for high 4-wk BW. Hazard ratio (HR): (HR-1) × 100 = Change in risk for each unit increase in risk factor. 3 LR = Likelihood ratio of regression model. 1 2
The use of survival analysis has provided a mechanism to account for mortality and for some risk factors that affect mortality. Through survival analysis, the current study has demonstrated that factors causing reduction in posthatch BW are risk factors for mortality in growing birds.
ACKNOWLEDGMENTS The authors thank Cheryl Pearson Gresham, Department of Poultry Science, University of Georgia, Athens, GA, for her technical assistance and collection of data.
REFERENCES Allore, H. G ., L. D. Warnick, J. Hertl, and Y. T. Grhn. 2001. Censoring in survival analysis: A simulation study of the effect of milk yield on conception. Prev. Vet. Med. 49:223–234. Ankra-Badu, G. A., H. L. Marks, and S. E. Aggrey. 2002. Effect of long-term selection on growth characteristics in Japanese quail. Southern Poult. Sci. Abstr. 117. Cox, D. R. 1972. Regression models and life tables. J. R. Stat. Soc. B34:187–220. Darden J. R., and H. L. Marks. 1988. Divergent selection for growth in Japanese quail under split and complete nutritional environments. 1. Genetic and correlated responses to selection. Poult. Sci. 67:519–529. Ducrocq, V. 1997. Survival analysis, a statistical tool for longevity data. Page 29 in Proc. 48th Annu. Meeting Eur. Assoc. Anim. Prod., Vienna, Austria. Famula, T. 1981. Exponential stayability model with censoring and covariates. J. Dairy Sci. 64:538–545. Havenstein, G. B., P. R. Ferket, S. E. Scheideler, and B. T. Larsen. 1994. Growth, livability, and feed conversion of 1957 vs 1991 broiler when fed ‘typical’ 1957 and 1991 broiler diets. Poult. Sci. 73:1785–1794. Kleinbaum, D. G. 1996. Kaplan-Meier survival curves and the log-rank test. Pages 45–82 in Survival Analysis—A Self Learning Text. Springer, New York. Lee, E. T. 1992. Introduction-censored observation. Pages 1–7 in Statistical Methods for Survival Data Analysis, Probability and Mathematical Statistics. Wiley, New York. McKay, J. C., N. F. Barton, A. N. M. Koerhuis, and J. McAdam. 2000. Broiler production around the world. Proc XXI World’s Poult. Congr., Montreal, Canada. SAS Institute. 1996. SAS User’s Guide. Version 6.12. SAS Institute Inc., Cary, NC.
Downloaded from http://ps.oxfordjournals.org/ by guest on April 9, 2015
fraction of birds that will still be alive t days after hatch if mortality was not influenced by hatch weight and posthatch BW. Survival function distribution indicated that the proportional mortality was highest in the high line compared to the low and control lines. The low line was similar to the control line. As pointed out by Ankra-Badu et al. (2002), the growth function of the low line was similar to that of the control line. Thus, the direction of selection for growth may have different impact on growth trajectory and mortality. When the data were pooled across the divergently selected lines and the control lines, as shown in Table 2, BW at hatch did not significantly influence mortality. However, posthatch BW affected mortality significantly in all three lines. In all the experimental lines mortality declined when posthatch BW increased (Table 3); however, the magnitude of reduction was highest in the control line when compared to the divergently selected lines (57 vs. 22%). Factors that influence growth after hatching may likely have a direct impact on mortality. Lack of accessibility to water and feed, warmth, and potential negative social interaction are factors that could affect mortality immediately after hatch. The posthatch BW at time of mortality, used as a risk factor, indicated that the divergently selected lines have about the same risk and were less sensitive to reduced BW, compared to the control population. Hatch weight, on the other hand, was a risk factor only in the control population, in which mortality would increase when hatch weight increased. In the control population, chicks with high hatch weight carry the highest risk of mortality when they suffer from reduced posthatch growth due to known or unknown causes. The effect of hatch weight as a risk factor was not significant in the selected lines. Growth analysis from the same experimental lines demonstrated that the deviation from the control line was not the same in the high and low lines (Ankra-Badu et al., 2002). Ankra-Badu et al. (2002) observed that the line selected for high 4-wk BW has diverged more from the control line than the line selected for low 4-wk BW. This finding may explain the similarities between the low line and the control for hatch weight as a risk factor for mortality.