scholarly journals Variance modelling of longitudinal height data from a Pinus radiata progeny test

2000 ◽  
Vol 30 (4) ◽  
pp. 645-654 ◽  
Author(s):  
Luis A Apiolaza ◽  
Arthur R Gilmour ◽  
Dorian J Garrick
Keyword(s):  
Repeated Measures ◽  
Model Fitting ◽  
Covariance Structure ◽  
Progeny Test ◽  
Genetic Covariance ◽  
Alternative Structures ◽  
Natural Logarithm ◽  
Unequally Spaced ◽  
Residual Matrix ◽  
Autoregressive Correlation

Variance components were estimated using alternative structures for the additive genetic covariance matrix (G0), for height (m) of trees measured at 10 unequally spaced ages in an open-pollinated progeny test. These structures reflected unstructured, autoregressive, banded correlation and random regressions models. The residual matrix (R0) was unstructured, and the block and plot strata matrices were autoregressive. The best model for G0 considering the likelihood value and number of parameters was the autoregressive correlation form with age-specific variances and time on a natural logarithm basis. The genetic correlation between successive measures ranged from 0.93 at age 1 to 0.99 at age 14 years. Heritability increased with age from 0.09 (age 1) to 0.24 (age 7) and then declined to 0.13 at age 15. Heritabilities from the unstructured model were similar, while heritabilities assuming banded correlations were lower after age 7. The covariance structure implicit in the random regressions model was considered unsatisfactory. Using structures in G0 facilitated model fitting and convergence of the likelihood maximisation algorithm. Fitting a structured matrix that reflects the relationships present in repeated measures may overcome problems of nonpositive definiteness of unstructured matrices from longitudinal data, especially when genetic variation is small.

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

scholarly journals Evaluation of a novel threonine source for nursery pig diets

2020 ◽  
Vol 4 (4) ◽  
Author(s):  
Dalton Humphrey ◽  
Spenser Becker ◽  
Jason Lee ◽  
Keith Haydon ◽  
Laura Greiner
Keyword(s):  
Repeated Measures ◽  
Fixed Effects ◽  
Average Daily Gain ◽  
Covariance Structure ◽  
Treatment Phase ◽  
Positive Control ◽  
Negative Control ◽  
Feed Ratio ◽  
Experimental Unit ◽  
Nursery Pigs

Abstract Four hundred and eighty (PIC 337 X 1050, PIC Genus, Hendersonville, TN) pigs were used to evaluate a novel threonine source (ThrPro, CJ America Bio, Fort Dodge, IA) for nursery pigs from approximately 7 to 20 kg body weight (BW). After weaning, pigs were sorted by sex and fed a common diet for 1 wk. Upon completion of the first week, pigs were sorted into randomized complete blocks, equalized by weight, within 16 replications. Pigs were allocated to one of three dietary treatments: positive control (POS)—standard ileal digestible threonine-to-lysine ratio (SID; Thr:Lys) 0.60, negative control (NEG)—SID Thr:Lys ≤0.46, and alternative Thr source (TEST)—SID Thr:Lys 0.60. The alternative Thr source included fermentative biomass and was assumed to contain 75% Thr and a digestibility coefficient of 100% based on the manufacturer’s specifications. All other nutrients met or exceeded the NRC recommendations. Growth and intake data were analyzed as repeated measures with a compound symmetry covariance structure using the MIXED procedure in SAS 9.4 (SAS Institute Inc., Cary, NC) with pen as the experimental unit. Treatment, phase, the interaction between treatment and phase, and block were included as fixed effects in the model. Differences in total removals were tested using Fisher’s Exact Test of PROC FREQ. Results were considered significant at P ≤ 0.05 and considered a trend at P > 0.05 and P ≤ 0.10. During the first 14 d, pigs fed TEST had decreased gain-to-feed ratio (G:F; 0.77 vs. 0.80, P = 0.022) compared to POS and increased G:F (0.77 vs. 0.73, P < 0.001) compared to NEG. Over days 14–28, pigs fed TEST had similar G:F (0.71 vs. 0.70, P = 0.112) compared to POS and increased G:F (0.71 vs. 0.63, P < 0.001) compared to NEG. Overall (days 0–28), pigs fed TEST had similar average daily gain (ADG; 0.47 vs. 0.47 kg/d, P = 0.982) and G:F (0.76 vs. 0.74, P = 0.395) compared to POS and increased ADG (0.47 vs. 0.43 kg/d, P < 0.001) and G:F (0.76 vs. 0.67, P < 0.001) compared to NEG. The average daily feed intake was not significantly different across treatments for the entirety of the study. In conclusion, the replacement of crystalline L-Thr with a novel Thr source resulted in similar growth performance in nursery pigs from approximately 7 to 20 kg.

Testing of multivariate repeated measures data with block exchangeable covariance structure

Test ◽  
2017 ◽  
Vol 27 (2) ◽  
pp. 360-378 ◽  
Author(s):  
Ivan Žežula ◽  
Daniel Klein ◽  
Anuradha Roy
Keyword(s):  
Repeated Measures ◽  
Covariance Structure ◽  
Repeated Measures Data

scholarly journals Effects of Low-Stress Weaning on Calf Growth Performance and Carcass Characteristics

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
E. Gubbels ◽  
R. R. Salverson ◽  
K. M. Cammack ◽  
J. K. Grubbs ◽  
K. R. Underwood ◽  
...  
Keyword(s):  
Growth Performance ◽  
Repeated Measures ◽  
Covariance Structure ◽  
Carcass Characteristics ◽  
Marbling Score ◽  
Time Period ◽  
Body Weights ◽  
Haptoglobin Concentration ◽  
Wire Fence ◽  
Α Level

ObjectivesThe objective of this study was to compare the influence of two low stress weaning methods with conventional weaning on post-weaning performance and carcass characteristics of beef steers.Materials and MethodsAngus × Simmental crossbred steer calves (n = 90) from a single source were stratified by body weight and dam age into three groups; one treatment was randomly assigned to each group: ABRUPT (calves isolated from dams on the day of weaning), FENCE (calves separated from dams via a barbed wire fence for 7 d prior to completely weaning), and NOSE (nose-flap inserted and calves remained with dams for 7 d prior to completely weaning). At d +7 post-weaning calves were transported to a commercial feedlot where they received standard step-up and finishing rations typical for a Northern Plains feedlot. To understand the influence of each weaning method on haptoglobin (an acute-phase protein), blood samples were collected via coccygeal venipuncture at d –7 (PreTreat), 0 (Weaning), and +7 (PostWean) from a subsample of calves (n = 10 per treatment) and analyzed using a bovine haptoglobin ELISA kit. Body weights (BW) were recorded on study d –34 (PreWean), –7 (PreTreat), 0 (Weaning), 7 (PostWean), 32 (Receiving), 175 (Ultrasound), and 253 (Final) and average daily gains (ADG) were calculated between each time period. On d 175 post-weaning BW were recorded, and ultrasound fat thickness and intramuscular fat were determined and utilized to project marketing dates. Carcass measurements were recorded at the time of harvest and included hot carcass weight, 12th rib backfat, ribeye area, USDA Yield Grade and Quality Grade, and marbling score. Haptoglobin, BW, and ADG data were analyzed as repeated measures using the ante-dependence covariance structure in the MIXED procedure of SAS (SAS Inst. Inc., Cary, NC) for effects of weaning treatment, day, and their interaction; birth weight was included as a covariate for ADG and BW. Carcass traits were analyzed for the effect of weaning treatment using the MIXED procedure. Separation of least-squares means was performed using LSD with a Tukey’s adjustment and assuming an α level of 0.05.ResultsWeaning method interacted (P < 0.0001) with time period for ADG and BW. Calf BW increased in all treatments until the PostWean period, wherein BW decreased (P < 0.0001) in ABRUPT and NOSE and was maintained (P > 0.05) in FENCE. From the Receiving to Final time periods BW increased similarly (P > 0.05) for all treatments. Calf ADG was greater (P < 0.01) in calves in the NOSE treatment at Weaning than ABRUPT or FENCE. In the PostWean period, the FENCE calves had ADG that was not different (P > 0.05) than zero but was greater (P < 0.0001) than the negative ADG of ABRUPT and NOSE calves. During the Receiving period ADG was greater (P < 0.05) for ABRUPT compared to NOSE and FENCE. Time influenced (P < 0.001) haptoglobin concentration. No difference in haptoglobin was observed between the PreTreat and Weaning or PostWean periods; however, haptoglobin concentration was greater (P < 0.001) at PostWean compared to Weaning. Weaning method did not influence (P > 0.05) carcass measurements.ConclusionCollectively these data suggest low stress weaning methods do not significantly improve post-weaning growth performance or carcass merit compared to calves weaned using conventional methods.

scholarly journals Evaluation of the pharmacokinetics and efficacy of transdermal flunixin for pain mitigation following castration in goats

2020 ◽  
Vol 4 (4) ◽  
Author(s):  
Meggan T Graves ◽  
Liesel Schneider ◽  
Sherry Cox ◽  
Marc Caldwell ◽  
Peter Krawczel ◽  
...  
Keyword(s):  
Repeated Measures ◽  
Treatment Time ◽  
Small Ruminants ◽  
Covariance Structure ◽  
Mean Body Temperature ◽  
Physiological Indicators ◽  
Flunixin Meglumine ◽  
Mixed Analysis ◽  
Management Procedures ◽  
Pain Mitigation

Abstract The mitigation of pain associated with common management procedures is a rising concern among veterinarians, producers and consumers. Nonsteroidal anti-inflammatory drugs are vital compounds for this purpose due to their cost, convenience, and efficacy. A transdermal formulation of flunixin meglumine (FM) was approved for the treatment of pain in cattle; however, the efficacy has yet to be determined for small ruminants. The current study had two aims: 1) to determine the pharmacokinetics of transdermal flunixin meglumine (TD FM) in bucklings and 2) to evaluate pain mitigation by TD FM following castration. To evaluate pharmacokinetics, 12 male goats (mean age = 6 mo) received 2.2 mg/kg of FM IV (n = 6) or 3.3 mg/kg TD FM (n = 6). Plasma FM concentrations were measured. The mean Cmax, Tmax, and harmonic mean half-life for TD FM were 1.09 ± 0.65 μg/mL, 5.50 ± 2.95 h, and 7.16 ± 2.06 h, respectively. To evaluate the efficacy of pain mitigation, 18 goats were randomly assigned to three treatment groups: 1) TD FM and castration (FM CAST) (n = 6); 2) transdermal placebo and castration (PL CAST) (n = 6); and 3) TD FM and sham castration (SHAM) (n = 6). Plasma samples were collected at 0, 12, 24, 36, 48, 72, and 96 h to assess cortisol and prostaglandin E2 (PGE2). Daily dry matter intake (DMI) was recorded and body weight was measured at the beginning and end of the study. Thermography (IRT) images of the scrotum, as well as heart rate (HR), respiratory rate (RR), and rectal temperature, were taken twice daily. Separate mixed analysis of variance models were used to test the effects of treatment, time, and their interaction on mean body temperature, IRT, HR, and RR. Autoregressive covariance structure was utilized to account for repeated measures and individual goat DMI prior to the study was added as a covariate. There were no differences in vital parameters, IRT measurements, cortisol, or PGE2 in animals receiving either TD FM or placebo following castration (P &gt; 0.05). DMI had a treatment by hour interaction and was significantly higher in FM CAST and SHAM groups than the PL CAST group (P = 0.04). Goats in the SHAM group gained weight throughout the study, whereas goats in all other groups lost weight (P = 0.02). Results indicate that TD FM may mitigate pain as demonstrated by increased DMI; however, a single dose may not be sufficient to reduce physiological indicators of pain associated with castration in goats.

Modelling multiple outcomes in repeated measures studies: Comparing aesthetic eyelid surgery techniques

2020 ◽  
pp. 1471082X2094331
Author(s):  
Wagner H. Bonat ◽  
Ricardo R. Petterle ◽  
Priscilla Balbinot ◽  
Alexandre Mansur ◽  
Ruth Graf
Keyword(s):  
Longitudinal Data ◽  
Repeated Measures ◽  
Hypothesis Test ◽  
Covariance Structure ◽  
Likelihood Estimation ◽  
Horizontal Line ◽  
Multiple Outcomes ◽  
Forehead Lift ◽  
Eyelid Surgery ◽  
Lateral Canthus

We propose a multivariate regression model to deal with multiple outcomes along with repeated measures in the context of longitudinal data analysis. Our model allows for flexible and interpretable modelling of the covariance structure within outcomes by using a linear combination of known matrices, while the generalized Kronecker product is employed to take into account the correlation between outcomes. We present maximum likelihood estimation along with extensions of the classical multivariate analysis of variance and multiple comparison hypothesis tests to deal with multivariate longitudinal data. The model and the associated multivariate hypothesis test are motivated by a prospective study conducted to compare three aesthetic eyelid surgery techniques, namely blepharoplasty, endoscopic forehead lift and endoscopic forehead lift associated with blepharoplasty. The effect of the techniques was assessed using measurements of a horizontal line through pupil centre and then three vertical lines, which go in direction to lateral canthus, middle pupil and medial canthus to the top of the brow. In this study, 30 female patients were randomly divided into three groups. Preoperative measurements were compared with postoperative measurements taken 30 days, 90 days and 10 years after the surgery. The presented multivariate model provided a better fit than its univariate counterpart. The results showed that the three surgery techniques tend to increase all considered outcomes in a long-term perspective, that is, from preoperative to 10 years postoperative evaluations. The only exception was for the outcome lateral eyebrow, for which the blepharoplasty had no significant effect.

scholarly journals Growth Trajectories in Genetic Subtypes of Prader–Willi Syndrome

Genes ◽  
2020 ◽  
Vol 11 (7) ◽  
pp. 736
Author(s):  
Daisy A. Shepherd ◽  
Niels Vos ◽  
Susan M. Reid ◽  
David E. Godler ◽  
Angela Guzys ◽  
...  
Keyword(s):  
Mixed Models ◽  
Repeated Measures ◽  
Molecular Subtypes ◽  
Growth Trajectories ◽  
Prader Willi Syndrome ◽  
Growth Data ◽  
Expression Of Genes ◽  
Subject Specific ◽  
Data Points ◽  
Autoregressive Correlation

Prader–Willi syndrome (PWS) is a rare disorder caused by the loss of expression of genes on the paternal copy of chromosome 15q11-13. The main molecular subtypes of PWS are the deletion of 15q11-13 and non-deletion, and differences in neurobehavioral phenotype are recognized between the subtypes. This study aimed to investigate growth trajectories in PWS and associations between PWS subtype (deletion vs. non-deletion) and height, weight and body mass index (BMI). Growth data were available for 125 individuals with PWS (63 males, 62 females), of which 72 (57.6%) had the deletion subtype. There was a median of 28 observations per individual (range 2–85), producing 3565 data points distributed from birth to 18 years of age. Linear mixed models with cubic splines, subject-specific random effects and an autoregressive correlation structure were used to model the longitudinal growth data whilst accounting for the nature of repeated measures. Height was similar for males in both PWS subtypes, with non-deletion females being shorter than deletion females for older ages. Weight and BMI were estimated to be higher in the deletion subtype compared to the non-deletion subtype, with the size of difference increasing with advancing age for weight. These results suggest that individuals with deletion PWS are more prone to obesity.

The use of MIXED models in the analysis of animal experiments with repeated measures data

2004 ◽  
Vol 84 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Z. Wang and L. A. Goonewardene
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Repeated Measures ◽  
Mixed Model ◽  
Covariance Structure ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
General Linear ◽  
Repeated Measures Data ◽  
Split Plot

The analysis of data containing repeated observations measured on animals (experimental unit) allocated to different treatments over time is a common design in animal science. Conventionally, repeated measures data were either analyzed as a univariate (split-plot in time) or a multivariate ANOVA (analysis of contrasts), both being handled by the General Linear Model procedure of SAS. In recent times, the mixed model has become more appealing for analyzing repeated data. The objective of this paper is to provide a background understanding of mixed model methodology in a repeated measures analysis and to use balanced steer data from a growth study to illustrate the use of PROC MIXED in the SAS system using five covariance structures. The split-plot in time approach assumes a constant variance and equal correlations (covariance) between repeated measures or compound symmetry, regardless of their proximity in time, and often these assumptions are not true. Recognizing this limitation, the analysis of contrasts was proposed. If there are missing measurements, or some of the data are measured at different times, such data were excluded resulting in inadequate data for a meaningful analysis. The mixed model uses the generalized least squares method, which is generally better than the ordinary least squares used by GLM, if the appropriate covariance structure is adopted. The presence of unequally spaced and/or missing data does not pose a problem for the mixed model. In the example analyzed, the first order ante dependence [ANTE(1)] covariance model had the lowest value for the Akaike and Schwarz’s Bayesian information criteria fit statistics and is therefore the model that provided the best fit to our data. Hence, F values, least square estimates and standard errors based on the ANTE (1) were considered the most appropriate from among the five models demonstrated. It is recommended that the mixed model be used for the analysis of repeated measures designs in animal studies. Key words: Repeated measures, General Linear Model, Mixed Model, split-plot, covariance structure

scholarly journals A comparison of empirical BLUP with different considerations of residual error variance for genotype evaluation of multi-location trials

2019 ◽  
Vol 17 (1) ◽  
pp. e0701
Author(s):  
Renhe Zhang ◽  
Xiyuan Hu
Keyword(s):  
Mixed Model ◽  
Type I Error ◽  
Block Design ◽  
Model Fitting ◽  
Covariance Structure ◽  
Error Variance ◽  
Error Rates ◽  
Residual Error ◽  
Type I ◽  
The North

AbstractThe empirical best linear unbiased prediction (eBLUP) is usually based on the assumption that the residual error variance (REV) is homogenous. This may be unrealistic, and therefore limits the accuracy of genotype evaluations for multi-location trials, where the REV often varies across locations. The objective of this contribution was to investigate the direct implications of the eBLUP with different considerations about REV based on the mixed model for evaluation of genotype simple effects (i.e. genotype effects at individual locations). A series of 14 multi-location trials from a rape-breeding program in the north of China were simultaneously analyzed from 2012 to 2014 using a randomized complete block design at each location. The results showed that the model with heterogeneous REV was more appropriate than the one with homogeneous REV in all of the trials according to model fitting statistics. Whether the REV differences across locations were accounted for in the analysis procedure influenced the variance estimate of related random effects and testing of the variance of genotype-location (G-L) interactions. Ignoring REV differences by use of the eBLUP could result not only in an inflation or deflation of statistical Type I error rates for pair-wise testing but also in an inaccurate ranking of genotype simple effects for these trials. Therefore, it is suggested that in application of the eBLUP for evaluation of genotype simple effects in multi-location trials, the heterogeneity of REV should be accounted for based on mixed model approaches with appropriate variance-covariance structure.

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