The feed conversion ratio (FCR) is, in addition to the cost of the feed, the most influential variable in the cost structure of poultry production^{1,2} and consequently, drives the economic efficiency of poultry operations. As a result, the FCR represents an important response variable in nutrition experiments, irrespective of whether or not they are complex, as metabolism studies^{3,4}, or as simple as the experiments that are usually conducted to evaluate nutritional and feeding interventions. Standard nutritional experiments are frequently used to examine changes in nutrient requirements^{5}, use of supra-nutritional nutrient levels to modulate physiological responses, the inclusion of feed additives to optimize performance and the application of feeding strategies in broilers or layer hens^{6}.

The trend to produce antibiotic-free broilers is pressing the allied industry to develop technologies that help to overcome the multimodal action mechanisms of antimicrobial growth promoters^{7}. An important area of research is related to the use of plant-derived products (phytogenics) to exert positive effects. Indeed, oregano (Origanum vulgare) represents a widely studied plant-derivative, as its essential oil and its main secondary metabolites (carvacrol and thymol)8 have shown several biologically important activities, including antimicrobial^{9,10}, antioxidant^{11,12}, endogenous enzyme activity promoting^{13,14} and prebiotic^{15} properties, as well as its ability to promote intestinal mucosa structure and health^{16} and prevent coccidia^{17,18}. However, the overall effect of oregano essential oil on broiler performance could be challengedependent^{19} and may vary if the chemical composition is inconstant^{20}.

In this regard, it becomes a complex task to perform an experiment to test these technologies, while also satisfying statistical power and meeting growing conditions similar to the industry, where natural pathogenic challenges limit the expression of the genetic potential^{21}. The main reason for this is that the larger the experimental unit, the lower the statistical power, as less experimental units will be available^{22}. In contrast, statistical power can be increased if more replications are made available using smaller floor pens or cages; however, the growing conditions would become less similar to the commercial ones, which would lower the challenging conditions.

One of the main limiting aspects faced by the industry and researchers is to design experiments that are sensitive enough to detect numerically small effects^{3,4}, such as those expected in FCR when phytogenic feed additives are tested. Usually, most of these can be economically justified with an improvement in FCR lower than 1.5%; however, the design of experiments offering such statistical sensitivity is not only a complex task^{23} but is also rare. As a result, detecting these small effects becomes extremely unlikely if the study is performed under commercial conditions to test a particular technology in a real usage scenario.

In this context, meta-analysis of independent studies has been proposed as a strategy to increase statistical power^{24,25}. Consequently, this is expected to support decision-making processes based on commercial-scale experiments where statistical sensitivity is insufficient, or when the expected effect is relatively low but still economically relevant. Therefore, the objective of this case study was to determine the overall effect of a phytogenic feed additive on the performance variables of broilers. In addition, we sought to compare these results with those from independent experiments included in the analysis.

The response variables were final body weight (BW, g bird^{−1}), feed intake (FI, g bird^{−1}), FCR (g g^{−1}) mortality (%) and European Production Efficiency Factor (EPEF) following the calculation reported by Marcu et al.^{27}

In broiler houses, the BW was obtained by weighing 10 sub-samples of 50 birds, each one in different locations within the house and the FI was calculated assuming that all of the feed provided was eaten. In the floor pens and cages, the BW was obtained by weighing all the birds and the FI was calculated as the actual net amount of feed eaten.

The additive linear model for the analysis of each independent experiment was Y_{ij} = μ + Ti + ε_{ij}, where Y_{ij} is the observed value in the i-th treatment (i: 1,...t) and j-th replication (j: 1,...r); μ is the effect of the general mean; T_{i} is the effect of the i-th treatment; ε_{ij} is the effect of the experimental error in the i-th treatment and j-th replication; t is the number of treatments; r is the number of replications in the i-th treatment; being that ε_{ij}~ N(µ,σ^{2}) and independently, where N denotes the normal distribution among replications and σ^{2} is the variance among the experimental error of the different EU.

In contrast, the additive linear model for the analysis of variance of the whole data was Y_{ijk} = μ + Ti + β_{j} + ε_{ijk}, where Y_{ijk} is the observed value in the i-th treatment (i: 1,...t), j-th block (j: 1,...p) and k-th replication (k: 1,...r); μ is the effect of the general mean; Ti is the effect of the i-th treatment; β_{j} is the effect of the j-th block; ε_{ijk} is the effect of the experimental error in the i-th treatment, j-th block and k-th replication; t is the number of treatments; p is the number of blocks; r is the number of replications in the i-th treatment; being that εijk~N(μ,σ^{2}) and independently, where N denotes the normal distribution among replications and σ^{2} is the variance among the experimental error of the different EU.

The heterogeneity was determined considering the following linear additive model: y_{i} = µ+u_{i} +e_{i}, where y_{i} is the observed effect size in the i-th experiment (i: 1,...k) (and also, y_{i} = θi +e_{i}, where θi is the unknown true effect in the i-th experiment; e_{i} is the intra-experimental sampling error in the i-th experiment); u_{i} is the inter-experimental deviation regarding the overall effect size in the i-th experiment; e_{i} is the intra-experimental sampling error in the i-th study; k is the number of experiments; N denotes the normal distribution of the random inter-experimental deviation (u) and the intraexperimental sampling error (e); being that u_{i}~N(0,τ^{2}) y e_{i}~N(0,ν_{i}) and both independently, where τ2 indicates the heterogeneity (variability among the true effects in the different experiments) and ν_{i} is the approximately known sampling variance of the estimated effect size in the i-th experiment.

To adjust the model, a weighted least square method was applied, implying that the adjusted model provides an estimate of ¯θ_{w} = Σw_{i}θ_{i} /Σw_{i,} where is the true weighted average effect size; w_{i} is the weighing factor considered, θ_{i} is the true effect size in the i-th experiment; that is, is the weighted average of the true effects (θ_{i}) in the set of k studies, with weights equal to the inverse of the corresponding variances (w_{i} = 1/ν_{i}).

In addition, the goodness of fit of model residues were evaluated with the Shapiro-Wilk test (normal if p>0.05). In cases where the residues were non-normally distributed, the data were analyzed again to determine the probability associated to the global effect size but this time, with applying a permutation test with 10,000 iterations.

Finally, the presence of bias within the data of each response variable was evaluated through the Egger regression test to determine the asymmetry of the distribution of the data, based on both the effect sizes and the precision of each experiment. Trim and Fill analysis was then performed to estimate the effect size values that would compensate distribution imbalances, if they existed, and if so, their magnitude and influence on the overall effect size were determined. As a result, each variable eventually had two sets of effect sizes: dO, being the set of effect sizes calculated from the experiments and dA, being the set of effect sizes that also included the values estimated through the Trim and Fill analysis. Thereafter, the bias was considered relevant if the Egger test was significant (p≤0.05) and if the CI_{95%} of the overall effect sizes, calculated with both the adjusted data (dA) and with the original data (dO), were not overlapped.

This study investigated the effect of a phytogenic feed additive on the performance of broilers. We sought to explore three different approaches to analyze the data from nine

Fig. 1: Forest plot of the effects of a phytogenic feed additive on the body weight of 42-day-old broilers (nine experiments)

Fig. 2: Forest plot of the effects of a phytogenic feed additive on the feed intake of 42-day-old broilers (nine experiments)

Fig. 3: Forest plot of the effects of a phytogenic feed additive on the mortality of 42-day-old broilers (nine experiments)

experiments to increase the likelihood of finding statistically significant effects, if they existed. The aim of this study was to determine a suitable method to improve decision-making processes related to nutrition and feeding strategies in the poultry industry.

The results showed that neither analyzing the data from the different experiments independently under completely randomised designs, nor combining all the data under a block design, led to statistically significant effects in any of the tested variables. The lack of sensitivity to detect differences as big as +5.28, -4.50 and +6.65% in BW, FCR and EPEF, respectively, was influenced by the low number of replications used in the experiments^{21}. However, this is the usual scenario faced by the industry when evaluating nutrition or feeding

Fig. 4: Forest plot of the effects of a phytogenic feed additive on the European production efficiency factor of 42-day-old broilers (nine experiments)

Fig. 5: Forest plot of the effects of a phytogenic feed additive on the feed conversion ratio of 42-day-old broilers (nine experiments)

strategies under actual commercial-scale conditions^{40}. Under such situations, there are three main consequences: (1) Companies take positive decisions but without the desired confidence and, consequently, become short-lived, (2) decision-making processes become complex and longer; or (3) no decision is taken, status quo is maintained and the opportunity to improve results may be lost. In addition, it has been reported that when it is more difficult for a person to make decisions based on rigorous reasoning, it ultimately leads to a more intuitive and heuristic thinking process due to decision fatigue; consequently, less judicious decisions are taken^{41}.

Although none of the independent experiments showed significant effects on the studied variables (p>0.05), this should not be interpreted as that the evaluated product does not produce an effect on these response variables. Instead, this may be explained by the fact that in hypothesis testing, the null hypothesis (that both means are equal) can only be rejected and not proved^{42,43}. In this regard, under the Neyman-Pearson dichotomous approach, a p-value greater than the pre-established α level of significance in a hypothesis test of the difference of two means determines that the null hypothesis must be exhaustively accepted as true. However, the Fischer approach considers the p-value as a continuous measure of the strength of evidence^{44} and states that the absence of a significant effect could only indicate that, if such an effect exists, it is not sufficiently large to be detected by an experiment of the size used^{45}.

Although the meta-analyses did not detect effects on BW, FI, mortality, or EPEF, we demonstrated an improvement in FCR that was due to the feed additive tested, in that the supplemented birds converted feed to body weight more efficiently (35 g less feed per kg body weight obtained). No significant heterogeneity was detected among experiments (p>0.87), indicating that the effect of the feed additive on the FCR was not inconsistent across the nine experiments. In addition, the CI of the effect size in FCR (0.0006 to 0.0686 less FCR points) indicates that, regardless of the accuracy of the estimation of the effect, the real effect of the phytogenic on feed efficiency is positive^{43}.

The effect of the tested phytogenic feed additive found in FCR agrees with previous reports about the effect of oregano essential oil on the FCR of broilers^{17,46-49}. This finding is consistent with the antimicrobial^{9,10}, antioxidant^{11-13}, endogenous enzyme activity promoting^{10,14}, prebiotic^{15}, anticoccidial^{18} and gut mucosa promoting effects^{16} of oregano essential oil that have been previously shown. Besides, previous studies have reported positive effects of oregano essential oil on intestinal mucosa structure, nutrient absorption capacity, bone mineralization and overall performance^{50}. It has been reported that the effect of oregano essential oil on broiler performance could be challenge-dependent^{19}; however, in the current study, the experiments were conducted under commercial conditions, unavoidably implying certain intestinal challenges, since reused litter material was used in all experiments^{51-53}.

In the present study, when combining the data from all the experiments under a completely randomized block design, the statistical power for FCR increased and, therefore, the p-value (p = 0.085) was lower in comparison to that observed in individual experiments (p-values: 0.151-0.867). However, the p-value was not only not considered significant but also was 85% higher than that obtained for the overall effect on FCR through meta-analysis (p = 0.046).

Thus, in the present analysis, we demonstrate how meta-analyses of the results obtained in different experiments favour the probability of detecting an effect, when it exists, that may not be evident in independent experiments. In this regard, although the meta-analyses carried out using random effects models do not guarantee that the inclusion of additional studies increases the statistical power of the analysis, in general, it does increase the statistical power in comparison to the independent studies^{24,25}. This is particularly useful when the critical response variable in an experiment is FCR, as usually a small percentage effect, even less than 2%^{54}, is sufficient for the poultry producer to justify making a favourable decision regarding the nutritional benefit of the feeding strategy tested. In addition, significant effect sizes obtained by meta-analysis also allows the nutritionist to make a cost-sensitivity analysis^{55,56}. Previous meta-analyses have detected small percentage effects on FCR in broilers^{54}, layer hens^{57} and pigs^{58}; however, to the best of our knowledge, a meta-analysis approach has not yet been reported for analysing commercial size trials with a low number of replications to help improve statistical sensitivity.

Experiment standardization is a common strategy to increase the sensitivity of the test; however, this also reduces the reproducibility of the results^{59}. In this regard, meta-analysis of commercial-scale experiments not only allows the sensitivity of the analysis to be increased^{24} but also preserves the reproducibility of the results, as they are performed in conditions less homogeneous than those of a highly controlled research facility. Therefore, the higher the systematic variation, the greater the reproducibility of the experiment^{59}. Finally, in poultry nutrition research, statistical sensitivity and growing conditions similar to the industry are commonly opposite objectives, as the more sensitive a design is, the more replications it takes and the smaller they become^{21}; however, a meta-analysis can go some way to help solve this dichotomy.

In the present study, we tested a phytogenic feed additive, based on oregano essential oil, providing no less than 45 g carvacrol per kg of product and fed at an inclusion rate of 0.05%, continuously from 1-42 day. Based on the observed results, it can be concluded that the tested product improved the FCR of broilers under commercial-scale conditions, in that it increased the efficiency of converting feed into BW (35 g less feed per 1 kg of BW obtained). In addition, the analysis of the nine conducted experiments using a meta-analysis approach improved the statistical power to a greater magnitude than that observed by applying a block design. Moreover, the meta-analysis was sensitive enough to detect a statistical significance that, otherwise, would have remained undetected.

This study demonstrated that meta-analysis is a useful technique to improve statistical power and to help find statistically significant differences, if they exist, when testing nutritional interventions under commercial conditions. We postulate that the use of meta-analysis in the poultry industry would help industry nutritionists and researchers to establish a more efficient but still simple, system to evaluate nutrition interventions, including feed additives and consequently, provide a means to facilitate and objectivize decision-making processes.

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