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RESEARCH ARTICLE (Open Access)

Meta-analysis of the published effects of HGP use on beef palatability in steers as measured by objective and sensory testing

Ray Watson
+ Author Affiliations
- Author Affiliations

Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic. 3010, Australia. Email: rayw@ms.unimelb.edu.au

Australian Journal of Experimental Agriculture 48(11) 1425-1433 https://doi.org/10.1071/EA07174
Submitted: 12 June 2007  Accepted: 20 June 2008   Published: 16 October 2008

Abstract

Evidence is presented that suggests strongly that hormone growth promotant (HGP) implantation has a negative effect on beef palatability. This is based on a meta-analysis of results reported in refereed papers that have appeared in the meat-science literature. To be included in this analysis, a paper must have reported results for control samples (no HGP) and treatment samples (HGP) for either objective testing (Warner-Bratzler shear-force) or consumer preference (tenderness score). The paper must also have reported estimates and standard errors. Further, we consider only the case of steers, and the M. longissimus dorsi (striploin). While most of these studies yielded non-significant differences, most gave an estimate indicating that the HGP treatment had a negative effect on beef palatability. When these results are combined using a meta-analysis, they provide significant evidence that the use of HGP implants negatively influences palatability.

Additional keywords: beef palatability, meta-analysis, tenderness score, Warner-Bratzler shear-force.


Acknowledgements

The author is grateful to two anonymous referees for their thorough reviews and helpful criticisms.


References


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Appendix: Meta-analysis

Consider a collection of k studies, each of which measures the effect of a particular intervention. It can be assumed that from each of these studies a point estimate of the effect of intervention and a standard error of that estimate are available. This Appendix considers two standard methods by which these studies may be combined in order to obtain an estimate and confidence interval for the overall effect of the intervention of interest.

For each of the k studies let EA07174_E1c.gif (i = 1,2,…,k) denote the estimated effect of intervention and θi the true effect of intervention. A general model is then specified by

EA1

and the ei are assumed to be independent. The estimated effect size EA07174_E1c.gif can be any measure of effect provided the assumption of normality is (at least approximately) appropriate.

In practice the σi2 are unknown and so estimated variances are used. It is widely assumed, however, that the individual studies provide reasonable estimates of the σi2. This assumption is almost universally made when the studies are analysed individually and should be the case provided the studies are at least moderate in size. In order to emphasize that the within study variances are estimated, the notation EA07174_E1d.gif is used, where EA07174_E1k.gif is the standard error of EA07174_E1c.gif. The general model is therefore rewritten as

EA2

For the meta-analyses considered here, the parameter of interest is the overall effect of intervention, denoted μ. In the remainder of this Appendix outlines both the fixed and random effects models and describes how each relates μ to the θi. In both cases the estimates EA07174_E1c.gif are point estimates of μ. Mention is also made of a test of homogeneity, widely used to select either the fixed or random effects model.

The fixed effects approach

The fixed effects model for meta-analysis assumes that the k studies are homogeneous—each having the same true effect of intervention. Therefore θi = μ for all i = 1,2,…,k, giving the model

EA3

This model only allows for within-study variation.

The overall effect μ is commonly estimated using a weighted average. Ignoring the sampling error in the EA07174_E1d.gif, it is optimal to use weights proportional to EA07174_E1d.gif giving

EA4

The notation EA07174_E1e.gif is used to indicate that the weights use estimates EA07174_E1d.gif, although the variation associated with these estimates is ignored in practice. Under the assumptions of independence and normality,

EA5

and an approximate 95% confidence interval for μ is given by

EA6

The random effects method and testing for homogeneity

Under the random effects model a distribution is assumed for the θi giving the two-stage model

EA7

and where the ei and εi are assumed to be independent. In this model, the true effect for study i is centred around the overall effect μ, allowing the individual studies to vary in both estimated and true effect. The between-study variance parameter, τ2, is a measure of the heterogeneity between studies and clearly this model permits both within and between-study variation.

This model can be written

EA8

giving

EA9

under the assumptions of normality and independence. The variance of EA07174_E1c.gif includes both within and between-study variance components. The fixed effects model is a special case of the random effects model with τ2 = 0. Selection of either the fixed effects or random effects models can therefore be carried out by testing the hypothesis τ2 = 0 against a one-sided alternative. If τ2 = 0 the studies are considered to be homogeneous. If the σi2 are known, a test of the homogeneity between studies can be carried out using a statistic defined by Cochran (1937):

EA10

which has a χ2k−1 distribution under the hypothesis τ2 = 0. In practice however the σi2 are not known and the statistic

EA11

is used. If τ2 = 0 then EA07174_E1f.gif approximately, and the hypothesis of homogeneity is rejected if EA07174_E1g.gif.

This test is frequently used to determine whether the fixed or random effects model should be adopted (for example Touloumi et al. 1997; Danesh et al. 1998). It has been suggested, however, that the power of this test can be low (Thompson and Pocock 1991; Hardy and Thompson 1998).

In order to estimate μ under the random effects model an estimate of τ2, the between-study variance parameter, is required.

Under the random effects model it is assumed that EA07174_E1h.gif. As for the fixed effects method a weighted average is generally used to estimate μ where the weights are derived from the variances of the EA07174_E1c.gif, i = 1,2,…,k. Therefore

EA12

where

EA13

Here the sampling error in the EA07174_E1d.gif is ignored and it is assumed that τ2 is known. Under these assumptions

EA14

In practice however, τ2 must be estimated. The most widely-used estimate of τ2 is one proposed by DerSimonian and Laird (1986):

EA15

where EA07174_E1i.gif denotes the observed value of the homogeneity statistic and

EA16

This estimate is obtained by equating the expected value of EA07174_E1i.gif with the observed value, and truncating to ensure that EA07174_E1j.gif.

The estimate of τ2 is then directly incorporated into the random effects weights, giving

EA17

This yields

EA18

Confidence intervals for μ are calculated under the assumption of normality; thus a 95% confidence interval for μ is given by

EA19

In cases where EA07174_E1a.gif the random effects method estimate and interval for μ are the same as those for the fixed effects method.