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

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.

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Analyzing Repeated Measurements while Accounting for Derivative Tracking, Varying Within-subject Variance, and Autocorrelation: The Xtmixediou Command

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x1701700303 ◽

2017 ◽

Vol 17 (3) ◽

pp. 573-599

Author(s):

Rachael A. Hughes ◽

Michael G. Kenward ◽

Jonathan A. C. Sterne ◽

Kate Tilling

Keyword(s):

Optimization Algorithm ◽

Repeated Measures ◽

Covariance Structure ◽

Likelihood Estimation ◽

Mixed Effects ◽

Repeated Measurements ◽

Mixed Effects Model ◽

Linear Mixed Effects Model ◽

Linear Mixed Effects ◽

Restricted Maximum Likelihood Estimation

Linear mixed-effects models are commonly used to model trajectories of repeated measures of biomarkers of disease. Taylor, Cumberland, and Sy (1994, Journal of the American Statistical Association 89: 727–736) proposed a linear mixed-effects model with an added integrated Ornstein–Uhlenbeck (IOU) process (linear mixed-effects IOU model). This allows for autocorrelation, changing within-subject variance, and the incorporation of derivative tracking (that is, how much a subject tends to maintain the same trajectory for extended periods of time). They argued that the covariance structure induced by the stochastic process in this model was interpretable and more biologically plausible than the standard linear mixed-effects model. However, their model is rarely used, partly because of the lack of available software. In this article, we present the new command xtmixediou, which fits the linear mixed-effects IOU model and its special case, the linear mixed-effects Brownian motion model. The model is fit to balanced and unbalanced data using restricted maximum-likelihood estimation, where the optimization algorithm is the Newton–Raphson, Fisher scoring, or average information algorithm, or any combination of these. To aid convergence, xtmixediou allows the user to change the method for deriving the starting values for optimization, the optimization algorithm, and the parameterization of the IOU process. We also provide a predict command to generate predictions under the model. We illustrate xtmixediou and predict with a simulated example of repeated biomarker measurements from HIV-positive patients.

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Consequences of Misspecifying the Error Covariance Structure in Linear Mixed Models for Longitudinal Data

Methodology ◽

10.1027/1614-2241.4.1.10 ◽

2008 ◽

Vol 4 (1) ◽

pp. 10-21 ◽

Cited By ~ 16

Author(s):

Guillermo Vallejo ◽

Manuel Ato ◽

Tamara Valdés

Keyword(s):

Longitudinal Data ◽

Repeated Measures ◽

Fixed Effects ◽

Error Control ◽

Mixed Model ◽

Linear Mixed Model ◽

Covariance Structure ◽

Correct Selection ◽

Type I ◽

Negative Consequences

Abstract. Repeated measures and longitudinal data are frequently analyzed using a linear mixed model. According to this approach, rather than presuming a certain type of covariance structure analysts choose the model that best describes their data prior to carrying out inferences of interest. Because it is not possible to know the underlying covariance structure in advance, researchers often use fit criteria to select from possible covariance structures. SAS Institute's (2004) Proc Mixed program, allows users to model the correct covariance structure by comparing Akaike's Information Criterion (AIC), Hurvich and Tsai's Criterion (AICC), Schwarz's Bayesian Criterion (BIC), Bozdogan's Criterion (CAIC), and Hannan and Quinn's Criterion (HQIC). Monte Carlo methods are used to examine performance of these criteria. The program also investigated the effects of misspecification on properties of the inferences. The results of the simulation show that neither criterion always lead to correct selection of model and that misspecification has negative consequences on estimates of standard errors of linear combinations and tests. When data were generated from symmetric distributions, the best AIC model generally provided robust Type I error control for tests of fixed effects. However, when data were generated from distributions with moderate or severe skewness, neither criterion provided valid tests.

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Maximum Likelihood Estimation for Incomplete Repeated-Measures Experiments under an ARMA Covariance Structure

Biometrics ◽

10.2307/2532046 ◽

1989 ◽

Vol 45 (1) ◽

pp. 207 ◽

Cited By ~ 19

Author(s):

James Rochon ◽

Ronald W. Helms

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Repeated Measures ◽

Covariance Structure ◽

Likelihood Estimation

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

Methodology ◽

10.1027/1614-2241/a000124 ◽

2017 ◽

Vol 13 (1) ◽

pp. 9-22 ◽

Cited By ~ 1

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.

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Evaluation of a novel threonine source for nursery pig diets

Translational Animal Science ◽

10.1093/tas/txaa182 ◽

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.

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Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Psychometrika ◽

10.1007/bf02294626 ◽

1989 ◽

Vol 54 (3) ◽

pp. 409-425 ◽

Cited By ~ 56

Author(s):

Gerhard Arminger ◽

Ronald J. Schoenberg

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Covariance Structure ◽

Likelihood Estimation ◽

Pseudo Maximum Likelihood Estimation ◽

Pseudo Maximum Likelihood ◽

Covariance Structure Models

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Testing of multivariate repeated measures data with block exchangeable covariance structure

Test ◽

10.1007/s11749-017-0549-z ◽

2017 ◽

Vol 27 (2) ◽

pp. 360-378 ◽

Cited By ~ 3

Author(s):

Ivan Žežula ◽

Daniel Klein ◽

Anuradha Roy

Keyword(s):

Repeated Measures ◽

Covariance Structure ◽

Repeated Measures Data

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Classification Based on Multivariate Repeated Measures with Time Effect on Mean Vector and an AR (1) Correlation Structure on the Repeated Measures

Calcutta Statistical Association Bulletin ◽

10.1177/0008068320050105 ◽

2005 ◽

Vol 57 (1-2) ◽

pp. 49-66 ◽

Cited By ~ 1

Author(s):

Anuradba Roy ◽

Ravindra Khattree

Keyword(s):

Maximum Likelihood ◽

Repeated Measures ◽

Likelihood Estimation ◽

Covariance Matrices ◽

Time Effect ◽

Population Parameters ◽

Time Effects ◽

Mean Vectors ◽

Mean Vector ◽

Over Time

In repeated measures studies how observations change over time is often of prime interest. Modelling this time effect in the context of discrimination, is the objective of this article. We study the problem of classification with multiple q-variate observations with time effect on each individual. The covariance matrices as well as mean vectors are mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population parameters are provided.

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

Meat and Muscle Biology ◽

10.22175/mmb.10713 ◽

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.

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