Ramon C. Littell

Modelling covariance structure in the analysis of repeated measures data.

The term ‘repeated measures’ refers to data with multiple observations on the same sampling unit. In most cases, the multiple observations are taken over time, but they could be over space. It is usually plausible to assume that observations on the same unit are correlated. Hence, statistical analysis of repeated measures data must address the issue of covariation between measures on the same unit. Until recently, analysis techniques available in computer software only offered the user limited and inadequate choices. One choice was to ignore covariance structure and make invalid assumptions. Another was to avoid the covariance structure issue by analysing transformed data or making adjustments to otherwise inadequate analyses. Ignoring covariance structure may result in erroneous inference, and avoiding it may result in inefficient inference. Recently available mixed model methodology permits the covariance structure to be incorporated into the statistical model. The MIXED procedure of the SAS® System provides a rich selection of covariance structures through the RANDOM and REPEATED statements. Modelling the covariance structure is a major hurdle in the use of PROC MIXED. However, once the covariance structure is modelled, inference about fixed effects proceeds essentially as when using PROC GLM. An example from the pharmaceutical industry is used to illustrate how to choose a covariance structure. The example also illustrates the effects of choice of covariance structure on tests and estimates of fixed effects. In many situations, estimates of linear combinations are invariant with respect to covariance structure, yet standard errors of the estimates may still depend on the covariance structure. Copyright

Asymptotic Optimality of Fisher's Method of Combining Independent Tests

Abstract Four methods of combining independent tests of hypothesis are compared via exact Bahadur relative efficiency. The methods considered are Fishers method, the mean of the normal transforms of the significance levels, the maximum significance level, and the minimum significance level. None of these is uniformly more powerful than the others, but, according to Bahadur efficiency, Fishers method is the most efficient of the four. In some cases, Fishers method is most efficient of all tests based on the data, but this is not generally true.

ANALYSIS OF REPEATED MEASURES DATA

1 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.

Projected multivariate linear models for directional data

Abstract We introduce the spherically projected multivariate linear model for directional data. This model treats directional observations as projections onto the unit sphere of unobserved responses from a multivariate linear model. Focusing on the important case of circular data, we show that maximum likelihood estimates for the model are readily computed using iterative methods, in sharp contrast with competing approaches. Examples are given to demonstrate the resulting methodology in realistic applications.

Analysis of unbalanced mixed model data: A case study comparison of ANOVA versus REML/GLS

Major transition has occurred in recent years in statistical methods for analysis of linear mixed model data from analysis of variance (ANOVA) to likelihood-based methods. Prior to the early 1990s, most applications used some version of analysis of variance because computer software was either not available or not easy to use for likelihood-based methods. ANOVA is based on ordinary least squares computations, with adoptions for mixed models. Computer programs for such methodology were plagued with technical problems of estimability, weighting, and handling missing data. Likelihood-based methods mainly use a combination of residual maximum likelihood (REML) estimation of covariance parameters and generalized least squares (GLS) estimation of mean parameters. Software for REML/GLS methods became readily available early in the 1990s, but the methodology still is not universally embraced. Although many of the computational inadequacies have been overcome, conceptual problems remain. Also, technical problems with REML/GLS have emerged, such as the need for adjustments for effects due to estimating covariance parameters. This article attempts to identify the major problems with ANOVA, describe the problems which remain with REML/GLS, and discuss new problems with REML/GLS.

A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories

The logistic or S-shaped curve of growth is one of the few universal laws in biology. It is certain that there exist specific genes affecting growth curves, but, due to a lack of statistical models, it is unclear how these genes cause phenotypic differentiation in growth and developmental trajectories. In this paper we present a statistical model for detecting major genes responsible for growth trajectories. This model is incorporated with pervasive logistic growth curves under the maximum likelihood framework and, thus, is expected to improve over previous models in both parameter estimation and inference. The power of this model is demonstrated by an example using forest tree data, in which evidence of major genes affecting stem growth processes is successfully detected. The implications for this model and its extensions are discussed.

Comparing nutrient intake from food to the estimated average requirements shows middle- to upper-income pregnant women lack iron and possibly magnesium

OBJECTIVE To determine whether nutrient intake from food alone was adequate across trimesters for middle- to upper-income pregnant women when compared with estimated average requirements (EAR), and to determine whether food intake exceeded the tolerable upper intake level (UL) for any nutrient. DESIGN Observational study in which pregnant women completed 3-day diet records each month during their pregnancy. Records were analyzed for nutrient content, and usual intake distributions were determined. SUBJECTS/SETTING Subjects were low-risk women in their first trimester of pregnancy (living in middle- to upper-income households). Ninety-four women were recruited, and sixty-three participated. STATISTICAL ANALYSIS PERFORMED Nutrient intake data were adjusted to achieve normality by using a power transformation. A mixed model method was used to assess trends in intake over time, and to estimate mean intake and within-subjects and between-subjects variance. The usual intake distribution for each nutrient was determined and compared with the EAR and UL. RESULTS The probabilities of usual nutrient intake from food being less than the EAR were highest for iron (.91), magnesium (.53), zinc (.31), vitamin B6 (.21), selenium (.20), and vitamin C (.12). Women were not at risk of exceeding the UL from food intake for any nutrient studied. APPLICATIONS/CONCLUSIONS Study participants did not consume adequate amounts of iron from food to meet the needs of pregnancy, and therefore iron supplementation is warranted in this population. Intake of magnesium was suboptimal using the EAR as a cut-point for adequacy.

Goodness-of-fit tests for the two parameter Weibull distribution

The Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling statistics are considered for testing the goodness of fit of the two-parameter Weibull distribution. The statistics for testing the goodness of fit of a completely specified distribution are modified by replacing the Weibull parameters by their maximum likelihood estimates. Also considered are two tests due to Mann, Scheuer, and Fertig (1973), and to Smith and Bain (1976). Tables of critical values are presented for the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling statistics. The results of a power study are presented comparing all five tests.

Improved Enzyme-Linked Immunosorbent Assay To Reveal Mycoplasma agassizii Exposure: a Valuable Tool in the Management of Environmentally Sensitive Tortoise Populations

ABSTRACT The precarious status of desert (Gopherus agassizii) and gopher (Gopherus polyphemus) tortoises has resulted in research and conservation efforts that include health assessments as a substantial component of management decision-making. Therefore, it is critical that available diagnostic tests for diseases impacting these species undergo rigorous standardization and validation. Since 1992, analysis of exposure of tortoises to Mycoplasma agassizii, an etiological agent of upper respiratory tract disease, has relied on the detection of specific M. agassizii antibody by enzyme-linked immunosorbent assay (ELISA). We report here substantive refinements in the diagnostic assay and discuss the implications of its use in wildlife conservation and management. The ELISA has been refined to include more stringent quality control measures and has been converted to a clinically more meaningful titer reporting system, consistent with other diagnostic serologic tests. The ELISA results for 5,954 desert and gopher tortoises were plotted, and a subset of these serum samples (n = 90) was used to determine end-point titers, to establish an optimum serum dilution for analyzing samples, and to construct a standard curve. The relationship between titer and A405 was validated using 77 serum samples from known positive (n = 48) and negative (n = 29) control tortoises from prior transmission studies. The Youden index, J, and the optimal cut point, c, were estimated using ELISA results from the 77 control sera. Based on this evaluation, the refinement has substantially improved the performance of the assay (sensitivity of 0.98, specificity of 0.99, and J of 0.98), thus providing a clinically more reliable diagnostic test for this important infection of tortoises.

Effect of calcium-energy supplements on calving-related disorders, fertility and milk yield during the transition period in cows fed anionic diets

The objective of this study was to determine the effect of a calcium-energy supplement at calving on the incidence of calving-related disorders (CRD), fertility, BCS and milk yield in cows fed anionic diets and to establish any associations among outcome variables. In Florida, from October to December 1997, 479 cows were assigned to three groups and treated at calving as follows: Group 1: 160 nontreated cows; Group 2: 158 cows, treated orally with 60g Ca as CaCl2; Group 3: 161 cows, treated orally with 110g Ca as calcium propionate (510g) plus propylene glycol (400g). No treatment effect was detected for any of the outcome variables. An association was found between dystocia and age and retained fetal membranes (RFM). Age and RFM were associated with metritis. RFM and displacement of the abomasum were associated with ketosis. Ketosis and age were related to displacement of the abomasum. Parity, BCS, ovarian cysts, RFM and metritis were associated with fertility.