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Maximising the cost-efficiency of assay procedures
Meat Science 35 (1993) 299-304
Maximising the Cost-efficiency of Assay Procedures P. N. Jones CSIRO Institute of Plant Production and Processing, Biometrics Unit, Cunningham Laboratory, St Lucia, Queensland 4067, Australia
& F. D. Shaw CSIRO Division of Food Processing, Meat Research Laboratory, PO Box 12, Cannon Hill, Queensland 4170, Australia (Received 27 July 1992; revised version 30 September 1992; accepted 4 October 1992)
ABSTRACT
Cortisol concentrations were measured in cattle plasma and pig muscle juice samples obtained from groups of animals slaughtered at different abattoirs. Statistically significant (P < 0.001) differences were obtained for between-abattoir comparisons for both the cattle and pig samples. Cortisol concentrations were determined using a radio-immunoassay kit. In accordance with the instructions, assays were performed in duplicate. An analysis of variance indicated that the use of a single determination on more samples, instead of duplicate determinations of fewer samples, would have led to an important increase in accuracy for detecting differences between means. It would have been more cost-efficient to collect additional samples and perform one assay only on each sample.
INTRODUCTION T h e m o n e y available for research is n o w p r e d o m i n a n t l y d i s t r i b u t e d o n the basis o f f u n d i n g for specific projects. R e s e a r c h e r s w h o s u b m i t 299 Meat Science 0309-1740/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain
300
P. N. Jones, F. D. Shaw
proposals that are likely to achieve maximum results for minimum cost increase their chances of receiving research funds. Thus there is a need for cost-efficiency in research. Traditionally, most assays on biological samples have been performed in duplicate, or even triplicate, but there seems to have been little consideration as to whether the extra cost involved in doing more than one assay is justified, or whether for the same expenditure more information could be obtained from a single assay of more samples. Statisticians frequently advise on the numbers of replicates per treatment to ensure a minimal-cost experiment (Dransfield & MacFie, 1980; Berndtson, 1991) but there is comparatively little published work on the most effective number of replicates per assay procedure. Physical limitations on the number of determinations that can be performed at a single time can put undue emphasis on certain levels of replication that may in the end be unwarranted. In this paper we consider these aspects in regard to measurement of a stress-related variable involved in studies of cattle and pigs. It is generally accepted that cortisol is an indicator of stress in animals and measurements of plasma cortisol are frequently used to evaluate the stress status of individual animals or groups of animals. Pearson et al. (1977) collected post-slaughter blood samples from lambs slaughtered at either a large commercial abattoir or a small research abattoir. Animals slaughtered at the small abattoir had lower levels of cortisol than those slaughtered at the commercial abattoir. This was believed to reflect the reduced levels of handling, lower killing rate, absence of dogs and the quieter environment of the small abattoir. Thus, measurement of cortisol levels in groups of animals may provide an indication of the stress status of the animals. Measurements of plasma cortisol concentrations have recently been used to assist in the evaluation of pre-slaughter and slaughter treatments of cattle (Dunn, 1990; Cockram & Corley, 1991; Ewbank et al., 1992). A statistically significant (P < 0.05) difference was found when the mean plasma cortisol concentrations of two groups of cattle, representative of those slaughtered at two different abattoirs, were compared (Tume & Shaw, 1992). The mean value for one group (+ SE) was 41-0 + 3.7 nmol/litre while for the other it was 123-2 + 5-3 nmol/litre. Similarly, a statistically significant difference was found when the mean plasma cortisol concentrations of two groups of pigs, representative of those slaughtered at two different abattoirs, were compared (Shaw & Tume, 1990). The mean value (+ SE) for one group was 150 + 21 nmol/litre while for the other it was 343 + 30 nmol/litre, It is believed that, with both species, the differences reflect different levels of stress associated with transport, holding and slaughter. As stress has economic conse-
Maximising the cost-efficiency of assay procedures
301
quences (meat quality defects of dark cutting beef; pale, soft, exudative (PSE) pork and dark, firm, dry (DFD) pork), as well as welfare connotations, it was felt that investigations into the causes of between-abattoir differences in stress status of animals would be a fruitful area for research. There are many factors associated with variation in cortisol levels between animals. These include diurnal variation and, with pigs, the incidence of 'high responding' and 'low responding' animals (Hennessy et aL, 1986). It was thus considered that large numbers of samples would be required for these investigations. Laboratory determinations of cortisol concentration involve radio-immunoassay (RIA) kits and these specify that assays should be performed in duplicate. However, it is generally intended that these kits allow for the measurement of cortisol levels in individuals, rather than in groups of individuals. It was conjectured that if a mean value for a group of individuals was required it may not be cost-effective to perform assays in duplicate. To investigate this and to assist in the financial planning of future research it was decided to statistically assess the need for duplicate assays. This paper presents the results of our investigation into the necessity for duplicate assays for plasma and muscle juice cortisol and provides information on how to determine whether duplicate (or triplicate) assays are costeffective.
MATERIALS AND METHODS The data used for analysis were obtained from continuing experiments in which cortisol assays, in duplicate, were being conducted as part of investigations into the relationship between stress and meat quality. In these experiments cortisol was being measured in plasma samples of cattle and in centrifugally expressed muscle juice samples (Bouton et al., 1972) of pigs. To obtain the cattle plasma samples, blood samples were collected at the time of exsanguination. At each of four different abattoirs 30 blood samples (minimum) were collected, but, for the purposes of the statistical analysis, only 24 samples, randomly selected from the group, were used, The plasma was assayed for cortisol, in duplicate, as described below. To obtain the muscle juice samples, longissimus dorsi muscles were removed, the day following slaughter, from 24 pig carcasses at each of four different abattoirs. Weighed muscle samples of 3-4 g were centrifuged at 100 000 g for 1 h in stainless steel tubes (Bouton et al., 1972). The centrifugally expressed muscle juice was assayed for cortisol,
302
,P. N. Jones, F. D. Shaw
TABLE 1
(a) Mean Cattle Plasma Cortisol Concentrations (nmol/litre) Abattoir
Mean
SE
1 2 3 4
121.1 60.3 146.0 40.3
9.5 5.3 9.0 5.6
(b) Mean Pig Muscle Juice Cortisol Concentrations (nmol/litre) Abattoir
1 2 3 4
Mean
SE
31.8 48.0 48.7 62.3
2.5 4.9 2.9 5.1
in duplicate, using a radio-immunoassay method (Incstar Corp., Stillwater, MN). A single run of the RIA method included standards, quality control samples and 40 test samples. Thus three separate runs were needed to assay all the test samples. A curve-fitting program (Immunofit, Beckman, Fullerton, CA) was used to convert gamma counter readings (counts per minute) to cortisol concentrations using a four-parameter logistic equation. Analysis of variance was used to compare abattoir means and estimate components of variance
RESULTS A N D DISCUSSION The mean concentrations of cortisol in plasma of cattle and muscle juice of pigs for the different abattoirs are given in Table 1, along with their corresponding standard errors. Analyses of variance were performed on the cortisol measurements and the results are given in Table 2. The F ratios of 42.8 and 9-4 (3,92 df) for comparing abattoir means were highly significant (P < 0.001), and from the means in Table 1 the orderings of abattoirs 2,4 < 1 < 3 (for cattle) and 1 < 2,3 < 4 (for pigs) were significant. In Table 2 the mean squares (MS) for the sources of variation associated with abattoirs, animals and determinations are presented. From these mean squares, the corresponding components of variance (denoted by o~, o~b and ~ respectively) were estimated. This was done by equating the expected mean squares to the observed mean squares and
Maximising the cost-efficiency of assay procedures
303
TABLE 2
Analysis of Variance of Cortisol Concentrations
Source of variation
df
Cattle MS
Pig MS
Expected MS
Abattoirs Animals Determinations
3 92 96
118 951-7 2 779.8 68-3
7 497.3 796.9 12.9
~ + 2~ + 48~ ~ + 2~
solving for ~ , ~ and ~ . The corresponding estimates of these components of variance are given in Table 3. From the estimates of o'2 and ~ a measure of correlation between duplicate determinations, R l (Snedecor & Cochran, 1976), is calculated using
0-2 RI
0"2 + 0-c2
For both cattle plasma and pig muscle juice the R I values are extremely high (0.968 and 0.952 respectively). As a further use of the components of variance, the variance of the mean cortisol level from a single abattoir can be calculated as follows: n
rn
where ~ and ~ are obtained from Table 3, n is the number of animals sampled and r is the number of determinations performed for each animal. This formula can be used to evaluate the efficiency of various sampling strategies for a representative abattoir. For instance, if two determinations of muscle juice cortisol are performed on each of 24 animals (n = 24, r = 2), as was done in the experiment reported here, the standard error of a mean cortisol level is estimated to be 4.07. However, the standard error of a mean obtained from one determination on each of 48 animals (n -- 48, r = 1) is estimated to be 2.90. This second strategy gives TABLE 3 Estimates of Variance Components of Cortisol Concentration
Source of variation
Component
Cattle
Pig
Abattoirs Animals Determinations
~ ~ ~
2 420.3 1 355.7 68- 3
139.6 392.0 12.9
304
P. N. Jones, F. D. Shaw
a noticeable reduction in the standard error for the mean cortisol level, and hence an important increase in accuracy for detecting differences between means. The total costs involved in performing one assay on a sample from each of two replicate animals are almost identical to those involved in performing two replicate assays on a sample from a single animal. Therefore, for the same cost almost twice as many samples can be assayed by single assay as can be assayed in duplicate, thus giving considerably more information on between-abattoir differences. It should be emphasised, however, that where one is interested in the results of an individual animal, rather than in the mean of a group of animals, duplicate assays may be desirable.
ACKNOWLEDGEMENTS This work was supported by the Meat Research Corporation and the Pig Research and Development Corporation.
REFERENCES Berndtson, W. E. (1991). J. Anim. Sci., 69, 67. Bouton, P. E., Harris, P. V. & Shorthouse, W. R. (1972). J. Food Sci., 37, 351 Cockram, M. S. & Corley, K. T. T. (1991). Brit. Vet. J., 147, 444. Dransfield, E. & MacFie, H. J. (1980). J. Sci. FoodAgric., 31, 62. Dunn, C. S. (1990). Vet. Rec., 126, 522. Ewbank, R., Parker, M. J. & Mason, C. W. (1992). Anim. Welfare, 1, 55. Hennessy, D. P., Conn, R. J. & Wan, S. S. (1986). Res. Vet. Sci., 41, 361. Pearson, A. J., Kilgour, R~, deLangen, H. & Payne, E. (1977). Proc. N. Z. Soc. Anita. Prod., 37, 243, Shaw, F. D. & Tume, R. K. (1990). In Proc. llth Congr. Inter. Pig Vet. Soc., Lausanne, p. 427. Snedecor, C. W. & Cochran, W. G. (1976). Statistical Methods, 6th edn. Iowa State University Press, Ames, IA, p. 294. Tume, R. K. & Shaw, F. D. (1992). Meat Sci., 31,211.
Maximising the Cost-efficiency of Assay Procedures P. N. Jones CSIRO Institute of Plant Production and Processing, Biometrics Unit, Cunningham Laboratory, St Lucia, Queensland 4067, Australia
& F. D. Shaw CSIRO Division of Food Processing, Meat Research Laboratory, PO Box 12, Cannon Hill, Queensland 4170, Australia (Received 27 July 1992; revised version 30 September 1992; accepted 4 October 1992)
ABSTRACT
Cortisol concentrations were measured in cattle plasma and pig muscle juice samples obtained from groups of animals slaughtered at different abattoirs. Statistically significant (P < 0.001) differences were obtained for between-abattoir comparisons for both the cattle and pig samples. Cortisol concentrations were determined using a radio-immunoassay kit. In accordance with the instructions, assays were performed in duplicate. An analysis of variance indicated that the use of a single determination on more samples, instead of duplicate determinations of fewer samples, would have led to an important increase in accuracy for detecting differences between means. It would have been more cost-efficient to collect additional samples and perform one assay only on each sample.
INTRODUCTION T h e m o n e y available for research is n o w p r e d o m i n a n t l y d i s t r i b u t e d o n the basis o f f u n d i n g for specific projects. R e s e a r c h e r s w h o s u b m i t 299 Meat Science 0309-1740/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain
300
P. N. Jones, F. D. Shaw
proposals that are likely to achieve maximum results for minimum cost increase their chances of receiving research funds. Thus there is a need for cost-efficiency in research. Traditionally, most assays on biological samples have been performed in duplicate, or even triplicate, but there seems to have been little consideration as to whether the extra cost involved in doing more than one assay is justified, or whether for the same expenditure more information could be obtained from a single assay of more samples. Statisticians frequently advise on the numbers of replicates per treatment to ensure a minimal-cost experiment (Dransfield & MacFie, 1980; Berndtson, 1991) but there is comparatively little published work on the most effective number of replicates per assay procedure. Physical limitations on the number of determinations that can be performed at a single time can put undue emphasis on certain levels of replication that may in the end be unwarranted. In this paper we consider these aspects in regard to measurement of a stress-related variable involved in studies of cattle and pigs. It is generally accepted that cortisol is an indicator of stress in animals and measurements of plasma cortisol are frequently used to evaluate the stress status of individual animals or groups of animals. Pearson et al. (1977) collected post-slaughter blood samples from lambs slaughtered at either a large commercial abattoir or a small research abattoir. Animals slaughtered at the small abattoir had lower levels of cortisol than those slaughtered at the commercial abattoir. This was believed to reflect the reduced levels of handling, lower killing rate, absence of dogs and the quieter environment of the small abattoir. Thus, measurement of cortisol levels in groups of animals may provide an indication of the stress status of the animals. Measurements of plasma cortisol concentrations have recently been used to assist in the evaluation of pre-slaughter and slaughter treatments of cattle (Dunn, 1990; Cockram & Corley, 1991; Ewbank et al., 1992). A statistically significant (P < 0.05) difference was found when the mean plasma cortisol concentrations of two groups of cattle, representative of those slaughtered at two different abattoirs, were compared (Tume & Shaw, 1992). The mean value for one group (+ SE) was 41-0 + 3.7 nmol/litre while for the other it was 123-2 + 5-3 nmol/litre. Similarly, a statistically significant difference was found when the mean plasma cortisol concentrations of two groups of pigs, representative of those slaughtered at two different abattoirs, were compared (Shaw & Tume, 1990). The mean value (+ SE) for one group was 150 + 21 nmol/litre while for the other it was 343 + 30 nmol/litre, It is believed that, with both species, the differences reflect different levels of stress associated with transport, holding and slaughter. As stress has economic conse-
Maximising the cost-efficiency of assay procedures
301
quences (meat quality defects of dark cutting beef; pale, soft, exudative (PSE) pork and dark, firm, dry (DFD) pork), as well as welfare connotations, it was felt that investigations into the causes of between-abattoir differences in stress status of animals would be a fruitful area for research. There are many factors associated with variation in cortisol levels between animals. These include diurnal variation and, with pigs, the incidence of 'high responding' and 'low responding' animals (Hennessy et aL, 1986). It was thus considered that large numbers of samples would be required for these investigations. Laboratory determinations of cortisol concentration involve radio-immunoassay (RIA) kits and these specify that assays should be performed in duplicate. However, it is generally intended that these kits allow for the measurement of cortisol levels in individuals, rather than in groups of individuals. It was conjectured that if a mean value for a group of individuals was required it may not be cost-effective to perform assays in duplicate. To investigate this and to assist in the financial planning of future research it was decided to statistically assess the need for duplicate assays. This paper presents the results of our investigation into the necessity for duplicate assays for plasma and muscle juice cortisol and provides information on how to determine whether duplicate (or triplicate) assays are costeffective.
MATERIALS AND METHODS The data used for analysis were obtained from continuing experiments in which cortisol assays, in duplicate, were being conducted as part of investigations into the relationship between stress and meat quality. In these experiments cortisol was being measured in plasma samples of cattle and in centrifugally expressed muscle juice samples (Bouton et al., 1972) of pigs. To obtain the cattle plasma samples, blood samples were collected at the time of exsanguination. At each of four different abattoirs 30 blood samples (minimum) were collected, but, for the purposes of the statistical analysis, only 24 samples, randomly selected from the group, were used, The plasma was assayed for cortisol, in duplicate, as described below. To obtain the muscle juice samples, longissimus dorsi muscles were removed, the day following slaughter, from 24 pig carcasses at each of four different abattoirs. Weighed muscle samples of 3-4 g were centrifuged at 100 000 g for 1 h in stainless steel tubes (Bouton et al., 1972). The centrifugally expressed muscle juice was assayed for cortisol,
302
,P. N. Jones, F. D. Shaw
TABLE 1
(a) Mean Cattle Plasma Cortisol Concentrations (nmol/litre) Abattoir
Mean
SE
1 2 3 4
121.1 60.3 146.0 40.3
9.5 5.3 9.0 5.6
(b) Mean Pig Muscle Juice Cortisol Concentrations (nmol/litre) Abattoir
1 2 3 4
Mean
SE
31.8 48.0 48.7 62.3
2.5 4.9 2.9 5.1
in duplicate, using a radio-immunoassay method (Incstar Corp., Stillwater, MN). A single run of the RIA method included standards, quality control samples and 40 test samples. Thus three separate runs were needed to assay all the test samples. A curve-fitting program (Immunofit, Beckman, Fullerton, CA) was used to convert gamma counter readings (counts per minute) to cortisol concentrations using a four-parameter logistic equation. Analysis of variance was used to compare abattoir means and estimate components of variance
RESULTS A N D DISCUSSION The mean concentrations of cortisol in plasma of cattle and muscle juice of pigs for the different abattoirs are given in Table 1, along with their corresponding standard errors. Analyses of variance were performed on the cortisol measurements and the results are given in Table 2. The F ratios of 42.8 and 9-4 (3,92 df) for comparing abattoir means were highly significant (P < 0.001), and from the means in Table 1 the orderings of abattoirs 2,4 < 1 < 3 (for cattle) and 1 < 2,3 < 4 (for pigs) were significant. In Table 2 the mean squares (MS) for the sources of variation associated with abattoirs, animals and determinations are presented. From these mean squares, the corresponding components of variance (denoted by o~, o~b and ~ respectively) were estimated. This was done by equating the expected mean squares to the observed mean squares and
Maximising the cost-efficiency of assay procedures
303
TABLE 2
Analysis of Variance of Cortisol Concentrations
Source of variation
df
Cattle MS
Pig MS
Expected MS
Abattoirs Animals Determinations
3 92 96
118 951-7 2 779.8 68-3
7 497.3 796.9 12.9
~ + 2~ + 48~ ~ + 2~
solving for ~ , ~ and ~ . The corresponding estimates of these components of variance are given in Table 3. From the estimates of o'2 and ~ a measure of correlation between duplicate determinations, R l (Snedecor & Cochran, 1976), is calculated using
0-2 RI
0"2 + 0-c2
For both cattle plasma and pig muscle juice the R I values are extremely high (0.968 and 0.952 respectively). As a further use of the components of variance, the variance of the mean cortisol level from a single abattoir can be calculated as follows: n
rn
where ~ and ~ are obtained from Table 3, n is the number of animals sampled and r is the number of determinations performed for each animal. This formula can be used to evaluate the efficiency of various sampling strategies for a representative abattoir. For instance, if two determinations of muscle juice cortisol are performed on each of 24 animals (n = 24, r = 2), as was done in the experiment reported here, the standard error of a mean cortisol level is estimated to be 4.07. However, the standard error of a mean obtained from one determination on each of 48 animals (n -- 48, r = 1) is estimated to be 2.90. This second strategy gives TABLE 3 Estimates of Variance Components of Cortisol Concentration
Source of variation
Component
Cattle
Pig
Abattoirs Animals Determinations
~ ~ ~
2 420.3 1 355.7 68- 3
139.6 392.0 12.9
304
P. N. Jones, F. D. Shaw
a noticeable reduction in the standard error for the mean cortisol level, and hence an important increase in accuracy for detecting differences between means. The total costs involved in performing one assay on a sample from each of two replicate animals are almost identical to those involved in performing two replicate assays on a sample from a single animal. Therefore, for the same cost almost twice as many samples can be assayed by single assay as can be assayed in duplicate, thus giving considerably more information on between-abattoir differences. It should be emphasised, however, that where one is interested in the results of an individual animal, rather than in the mean of a group of animals, duplicate assays may be desirable.
ACKNOWLEDGEMENTS This work was supported by the Meat Research Corporation and the Pig Research and Development Corporation.
REFERENCES Berndtson, W. E. (1991). J. Anim. Sci., 69, 67. Bouton, P. E., Harris, P. V. & Shorthouse, W. R. (1972). J. Food Sci., 37, 351 Cockram, M. S. & Corley, K. T. T. (1991). Brit. Vet. J., 147, 444. Dransfield, E. & MacFie, H. J. (1980). J. Sci. FoodAgric., 31, 62. Dunn, C. S. (1990). Vet. Rec., 126, 522. Ewbank, R., Parker, M. J. & Mason, C. W. (1992). Anim. Welfare, 1, 55. Hennessy, D. P., Conn, R. J. & Wan, S. S. (1986). Res. Vet. Sci., 41, 361. Pearson, A. J., Kilgour, R~, deLangen, H. & Payne, E. (1977). Proc. N. Z. Soc. Anita. Prod., 37, 243, Shaw, F. D. & Tume, R. K. (1990). In Proc. llth Congr. Inter. Pig Vet. Soc., Lausanne, p. 427. Snedecor, C. W. & Cochran, W. G. (1976). Statistical Methods, 6th edn. Iowa State University Press, Ames, IA, p. 294. Tume, R. K. & Shaw, F. D. (1992). Meat Sci., 31,211.