ANALYSIS OF REPEATED MEASURES DATA

Data with repeated measures occur frequently in agricultural research. This paper is a brief overview of statistical methods for repeated measures data. Statistical analysis of repeated measures data requires special attention due to the correlation structure, which may render standard analysis of variance techniques invalid. For balanced data, multivariate analysis of variance methods can be employed and adjustments can be applied to univariate methods, as means of accounting for the correlation structure. But these analysis of variance methods do not apply readily with unbalanced data, and they overlook the regression on time. Regression curves for treatment groups can be obtained by fitting a curve to each experimental unit; and then averaging the coefficients over the units. Treatment groups can be compared by applying univariate and multivariate methods to the group means of the coefficients. This approach does not require knowledge of the correlation structure of the repeated measures, and an approximate version of it can be applied with unbalanced data

ANALYSIS OF UNBALANCED MIXED MODEL DATA: Traditional ANOVA Versus Contemporary Methods

Analysis of unbalanced data and analysis of mixed model data are important topics of statistical discussion. Analysis of unbalanced data with fixed effects gives rise to the different types of sums of squares in analysis of variance. Mixed model riata raises issues of determining appropriate error terms for test statistics and standard errors Clf estimates. The situation is even more difficult when the two topics occur together, resulting in unbalanced mixed model data. These problems have plagued users ofPROC GLM in the SAS System. Now, with PROC MIXED available, some of the problems are resolved while others remain. This paper gives an overview of two areas of difficulty in analysis of variance using PROC GLM, and describes which problems carry over to PROC MIXED, and which are essentially solved with PROC MIXED

IMPACT OF VARIANCE COMPONENT ESTIMATES ON FIXED EFFECT INFERENCE IN UNBALANCED LINEAR MIXED MODELS

Inference on fixed effects in mixed models depends on standard errors or test statistics which in turn depend on estimates of variance and covariance components. For unbalanced mixed models, even relatively simple models such as two-way cross-classification models with interaction where one factor is fixed and the other is random, dilemmas arise that have received inadequate attention to date. For example, if one uses SAS PROC MIXED, one can estimate variance components using expected means squares from Type I, II, or III sums of squares, or one can use likelihood-based algorithms such as the default restricted maximum likelihood. If there is a negative variance component estimate, one can set the estimate to zero and proceed with fixed effects inference, or one can allow the variance estimate to remain negative. These decisions affect inference on fixed effects in ways that are not generally well-understood. The purposes of this presentation are to 1) clarify what the main issues are and 2) present some guidelines data analysts can use

PLANNING A SAFETY STUDY OF AN AGRICULTURAL PRODUCT: EFFECTS OF LAND APPLICATION OF PHOSPHOGYPSUM ON RADON FLUX

Traditional agricultural research has been concerned largely with demonstrating that new products or new practices increase yield from plants or animals; i.e. that a change has occurred. Concepts of experimental design have been effectively employed in production-agriculture research planning to control extraneous variation and thereby reduce experimental error. Good data analysis practices have been employed to control type 1 error rate and to correctly compute errors of estimation. In recent years, increased emphasis has been placed on food safety and environmental impact of agricultural products. Studies of these issues are concerned with measuring small effects with required precision or establishing upper bounds on the effects. Statistical emphasis is on limiting the margin of error and the type 2 error rates. This paper discusses these concepts in the context of an environmental study of effect of phosphogypsum (PG) on radon flux. An experiment in progress revealed essentially no statistically significant effect of the phosphogypsum. Two statistical questions were then raised: 1) How large of an effect would have been detected in the study? and 2) How should a future study be conducted that would produce measurements of the effect with specified precision? A retrospective power analysis was performed to estimate the minimum detectable effect (MDE) in the existing study in response to question 1. In response to question 2, a new study was designed with required numbers of plots and measurements to meet precision and power objectives, using variance component estimates from existing data

ESTIMATION OF AND ADJUSTMENT FOR RESIDUAL EFFECTS IN DAIRY FEEDING EXPERIMENTS UTILIZING CHANGEOVER DESIGNS

A procedure is presented which demonstrates estimation of and adjustment for residual effects in changeover designs. The method utilizes all data collected in an experiment by including treatments imposed on animals prior to initiation of data collection. Estimation is achieved via general linear models. An example is given of a nutrition experiment conducted with dairy cattle. Such analyses should increase efficacy of changeover designs and reduce concern by researchers about biased estimates of direct effects which could result from residual effects. Methods from popular computer programs for estimating direct effect treatment means are compared. Practical problems encountered in computing standard errors of mean estimates in mixed linear models

Different resource allocation strategies result from selection for litter size at weaning in rabbit does

This study examined the effect of long-term selection of a maternal rabbit line, solely for a reproductive criterion, on the ability of female rabbits to deal with constrained environmental conditions. Female rabbits from generations 16 and 36 (n = 72 and 79, respectively) of a line founded and selected to increase litter size at weaning were compared simultaneously. Female rabbits were subjected to normal (NC), nutritional (NF) or heat (HC) challenging conditions from 1st to 3rd parturition. Animals in NC and NF were housed at normal room temperatures (18°C to 25°C) and respectively fed with control (11.6 MJ digestible energy (DE)/kg dry matter (DM), 126 g digestible protein (DP)/kg DM, and 168 g of ADF/kg DM) or low-energy fibrous diets (9.1 MJ DE/kg DM, 104 g DP/kg DM and 266 g ADF/kg DM), whereas those housed in HC were subjected to high room temperatures (25°C to 35°C) and the control diet. The litter size was lower for female rabbits housed in both NF and HC environments, but the extent and timing where this reduction took place differed between generations. In challenging conditions (NF and HC), the average reduction in the reproductive performance of female rabbits from generation 16, compared with NC, was &#8722;2.26 (P<0.05) and &#8722;0.51 kits born alive at 2nd and 3rd parturition, respectively. However, under these challenging conditions, the reproductive performance of female rabbits from generation 36 was less affected at 2nd parturition (&#8722;1.25 kits born alive), but showed a greater reduction at the 3rd parturition (&#8722;3.53 kits born alive; P<0.05) compared with NC. The results also showed differences between generations in digestible energy intake, milk yield and accretion, and use of body reserves throughout lactation in NC, HC and NF, which together indicate that there were different resource allocation strategies in the animals from the different generations. Selection to increase litter size at weaning led to increased reproductive robustness at the onset of an environmental constraint, but failure to sustain the reproductive liability when the challenge was maintained in the long term. This response could be directly related to the shortterm environmental fluctuations (less severe) that frequently occur in the environment where this line has been selected.The authors thank Professor Enrique Blas Ferrer for his valuable comments on the initial version of this document, Juan Carlos Moreno for his help in conducting the trial at the experimental farm, and the Ministry of Economy and Competitiveness (Project: AGL2011-30170-C02-01) for economic support.Savietto, D.; Cervera Fras, MC.; Ródenas Martínez, L.; Martínez Paredes, EM.; Baselga Izquierdo, M.; García Diego, FJ.; Larsen, T.... (2014). Different resource allocation strategies result from selection for litter size at weaning in rabbit does. Animal. 8(4):618-628. https://doi.org/10.1017/S1751731113002437S61862884García-Diego, F.-J., Pascual, J. J., & Marco, F. (2011). Technical Note: Design of a large variable temperature chamber for heat stress studies in rabbits. World Rabbit Science, 19(4). doi:10.4995/wrs.2011.938Ragab, M., & Baselga, M. (2011). A comparison of reproductive traits of four maternal lines of rabbits selected for litter size at weaning and founded on different criteria. Livestock Science, 136(2-3), 201-206. doi:10.1016/j.livsci.2010.09.009Friggens, N. C. (2003). Body lipid reserves and the reproductive cycle: towards a better understanding. Livestock Production Science, 83(2-3), 219-236. doi:10.1016/s0301-6226(03)00111-8Littell, R. C., Henry, P. R., & Ammerman, C. B. (1998). Statistical analysis of repeated measures data using SAS procedures. Journal of Animal Science, 76(4), 1216. doi:10.2527/1998.7641216xEstany, J., Baselga, M., Blasco, A., & Camacho, J. (1989). Mixed model methodology for the estimation of genetic response to selection in litter size of rabbits. Livestock Production Science, 21(1), 67-75. doi:10.1016/0301-6226(89)90021-3Fernández-Carmona, J., Alqedra, I., Cervera, C., Moya, J., & Pascual, J. J. (2003). Effect of lucerne-based diets on performance of reproductive rabbit does at two temperatures. Animal Science, 76(2), 283-295. doi:10.1017/s1357729800053534Fernández-Carmona, J., Cervera, C., Sabater, C., & Blas, E. (1995). Effect of diet composition on the production of rabbit breeding does housed in a traditional building and at 30°C. Animal Feed Science and Technology, 52(3-4), 289-297. doi:10.1016/0377-8401(94)00715-lHarano, Y., Ohtsuki, M., Ida, M., Kojima, H., Harada, M., Okanishi, T., … Shigeta, Y. (1985). Direct automated assay method for serum or urine levels of ketone bodies. Clinica Chimica Acta, 151(2), 177-183. doi:10.1016/0009-8981(85)90321-3Dauncey, M. J. (1990). Thyroid hormones and thermogenesis. Proceedings of the Nutrition Society, 49(2), 203-215. doi:10.1079/pns19900024Savietto, D., Blas, E., Cervera, C., Baselga, M., Friggens, N. C., Larsen, T., & Pascual, J. J. (2012). Digestive efficiency in rabbit does according to environment and genetic type. World Rabbit Science, 20(3). doi:10.4995/wrs.2012.1152Falconer, D. S. (1990). Selection in different environments: effects on environmental sensitivity (reaction norm) and on mean performance. Genetical Research, 56(1), 57-70. doi:10.1017/s0016672300028883Vicente, J., & García-Ximénez, F. (1993). Effects of strain and embryo transfer model (embryos from one versus two donor does/recipient) on results of cryopreservation in rabbit. Reproduction Nutrition Development, 33(1), 5-13. doi:10.1051/rnd:19930101Quiniou, N., Renaudeau, D., Dubois, S., & Noblet, J. (2000). Influence of high ambient temperatures on food intake and feeding behaviour of multiparous lactating sows. Animal Science, 70(3), 471-479. doi:10.1017/s1357729800051821Theilgaard, P., Sánchez, J. P., Pascual, J. J., Friggens, N. C., & Baselga, M. (2006). Effect of body fatness and selection for prolificacy on survival of rabbit does assessed using a cryopreserved control population. Livestock Science, 103(1-2), 65-73. doi:10.1016/j.livsci.2006.01.007Brecchia, G., Bonanno, A., Galeati, G., Federici, C., Maranesi, M., Gobbetti, A., … Boiti, C. (2006). Hormonal and metabolic adaptation to fasting: Effects on the hypothalamic–pituitary–ovarian axis and reproductive performance of rabbit does. Domestic Animal Endocrinology, 31(2), 105-122. doi:10.1016/j.domaniend.2005.09.006Piles, M., Garreau, H., Rafel, O., Larzul, C., Ramon, J., & Ducrocq, V. (2006). Survival analysis in two lines of rabbits selected for reproductive traits1. Journal of Animal Science, 84(7), 1658-1665. doi:10.2527/jas.2005-678Sanchez, J. P., Baselga, M., & Ducrocq, V. (2006). Genetic and environmental correlations between longevity and litter size in rabbits. Journal of Animal Breeding and Genetics, 123(3), 180-185. doi:10.1111/j.1439-0388.2006.00590.xQuevedo, F., Cervera, C., Blas, E., Baselga, M., & Pascual, J. J. (2006). 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Analysing trajectories of a longitudinal exposure: A causal perspective on common methods in lifecourse research

Longitudinal data is commonly analysed to inform prevention policies for diseases that may develop throughout life. Commonly methods interpret the longitudinal data as a series of discrete measurements or as continuous patterns. Some of the latter methods condition on the outcome, aiming to capture ‘average’ patterns within outcome groups, while others capture individual-level pattern features before relating these to the outcome. Conditioning on the outcome may prevent meaningful interpretation. Repeated measurements of a longitudinal exposure (weight) and later outcome (glycated haemoglobin levels) were simulated to match three scenarios: one with no causal relationship between growth rate and glycated haemoglobin; two with a positive causal effect of growth rate on glycated haemoglobin. Two methods that condition on the outcome and one that did not were applied to the data in 1000 simulations. The interpretation of the two-step method matched the simulation in all causal scenarios, but that of the methods conditioning on the outcome did not. Methods that condition on the outcome do not accurately represent a causal relationship between a longitudinal pattern and outcome. Researchers considering longitudinal data should carefully determine if they wish to analyse longitudinal data as a series of discrete time points or by extracting pattern features