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PubMed1999

Generalised linear mixed models analysis of risk factors for contamination of Danish broiler flocks with Salmonella typhimurium.

We present a retrospective observational study of risk factors associated with the occurrence of Salmonella typhimurium (ST) in Danish broiler flocks. The study is based on recordings from 1994 in the ante-mortem database maintained by the Danish Poultry Council. The epidemiological units are the broiler flocks (about 4000 flocks) which are clustered within producers. Broiler flocks with ST-infected parent stocks show increased risk of salmonella infection, and also the hatchery affects the salmonella status significantly. Among the rearing factors, only the use of medicine as well as the time of rearing, and the sampling method are significant. Epidemiological control would seem most efficient on starting at the top levels of the production hierarchy from which a major part of the ST contamination is derived. A secondary purpose of the study is to evaluate different statistical approaches and software for the analysis of a moderately-sized data set of veterinary origin. We compare the results from five analyses of the generalised linear mixed model (GLMM) type. The first observation is that the results agree reasonably well and lead to similar conclusions. A closer look reveals certain patterns of bias and estimation accuracy that correspond well with theoretical findings and practical experience reported in the statistical literature.

Animal Husbandry↗
PubMed1996

Least squares Lehmann-Scheffé estimation of variances and covariances with mixed linear models.

Variances of quadratic estimators of (co)variances are functions of the numeric values of the (co)variance parameters being estimated. This situation makes estimation of (co)variances problematical. Uniformly best quadratic, unbiased estimators exist for balanced designs but not for unbalanced designs. This article tackles the problem by providing explicit quadratic estimators of (co)variances that are uniformly best in the sense that they are uniformly minimum variance, unbiased to the maximum extent possible over the entire range of possible parameter values of the (co)variances being estimated. This was accomplished by determining the restrictions on the elements of the matrix of the quadratic-form matrix necessary to satisfy the Lehmann-Scheffé criterion for uniformly minimum variance, unbiased estimation and then solving the resulting linear equations via the principle of least squares. The context is any mixed linear model, and the approach does not require that there be equal numbers of observations in the case of multivariate data. A detailed development of the method is given. That the procedure is completely general is discussed. A modification that forces unbiasedness is presented. An example with a three-variance-component model is provided and results discussed. A miscellaneous section discusses, among other topics, how this method can be used to compare other (co)variance component estimation procedures. The final section illustrates how the method handles multivariate situations (i.e., models with both variances and covariances) by detailing the expressions involved with the bivariate model.

Analysis of Variance↗
PubMed2004

A new approach to the solution of the linear mixing model for a single isotope: application to the case of an opportunistic predator.

Mixing models are used to determine diets where the number of prey items are greater than one, however, the limitation of the linear mixing method is the lack of a unique solution when the number of potential sources is greater than the number (n) of isotopic signatures +1. Using the IsoSource program all possible combinations of each source contribution (0-100%) in preselected small increments can be examined and a range of values produced for each sample analysed. We propose the use of a Moore Penrose (M-P) pseudoinverse, which involves the inverse of a 2x2 matrix. This is easily generalized to the case of a single isotope with (p) prey sources and produces a specific solution. The Antarctic leopard seal (Hydrurga leptonyx) was used as a model species to test this method. This seal is an opportunistic predator, which preys on a wide range of species including seals, penguins, fish and krill. The M-P method was used to determine the contribution to diet from each of the four prey types based on blood and fur samples collected over three consecutive austral summers. The advantage of the M-P method was the production of a vector of fractions f for each predator isotopic value, allowing us to identify the relative variation in dietary proportions. Comparison of the calculated fractions from this method with 'means' from IsoSource allowed confidence in the new approach for the case of a single isotope, N.

Animals↗
PubMed2001

Local influence to detect influential data structures for generalized linear mixed models.

This article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects. For these models, it is shown that the subject-oriented influence measure is a special case of the proposed observation-oriented influence measure. A two-step diagnostic procedure is proposed. The first step is to search for influential subjects. A search for influential observations is proposed as the second step. An illustration of a two-treatment, multiple-period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects.

Aspartame↗
PubMed2001

A comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials.

Response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters, within which data are usually positively correlated. Therefore, estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial. Data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures: for continuous outcomes, restricted maximum likelihood (REML) and estimating equations (EE); for binary outcomes, restricted pseudo-likelihood (REPL) and estimating equations (EE). We evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components. REML seems the better choice for estimating terms related to correlation for models with normal outcomes, especially in group randomized trial situations. Results for REML and EE are mixed when outcomes are continuous and non-normal. With binary outcomes neither REPL nor EE provides satisfactory estimation or inference in longitudinal study situations, while REPL is preferable for group randomized trials.

Cluster Analysis↗
PubMed2006

Robust estimation in mixed linear models with non-monotone missingness.

We introduce a model to account for abrupt changes among repeated measures with non-monotone missingness. Development of likelihood inferences for such models is hard because it involves intractable integration to obtain the marginal likelihood. We use hierarchical likelihood to overcome such difficulty. Abrupt changes among repeated measures can be well described by introducing random effects in the dispersion. A simulation study shows that the resulting estimator is efficient, robust against misspecification of fatness of tails. For illustration we use a schizophrenic behaviour data presented by Rubin and Wu.

Computer Simulation↗
PubMed2003

Use of a generalized linear mixed model to reduce excessive heterogeneity in petroleum spray oil bioassay data.

High heterogeneity (variance) is a consistent and significant problem in petroleum spray oil derived bioassay data. It can mask small statistical differences sought by researchers in relative toxicity or potency analysis. To compensate for excessive heterogeneity, researchers often use very large sample sizes to improve statistical accuracy. We present a statistical method of modeling heterogeneity extending the conventional probit model by adding random effects to it. We illustrate this by reanalyzing 26 of our own published experiments. Twelve of these had excessive heterogeneity that was significantly reduced in ten cases by including random replicate effects with or without random slopes. Five were further improved by allowing a nonlinear (spline) response. The result was tighter confidence intervals for the estimates of lethal dose.

Animals↗
PubMed2002

Discovering subpopulation structure with latent class mixed models.

The linear mixed model is a well-known method for incorporating heterogeneity (for example, subject-to-subject variation) into a statistical analysis for continuous responses. However heterogeneity cannot always be fully captured by the usual assumptions of normally distributed random effects. Latent class mixed models offer a way of incorporating additional heterogeneity which can be used to uncover distinct subpopulations, to incorporate correlated non-normally distributed outcomes and to classify individuals. The methodology is motivated with examples in health care studies and a detailed illustration is drawn from the Nutritional Prevention of Cancer trials. Latent class models are used with longitudinal data on prostate specific antigen (PSA) as well as incidence of prostate cancer. The models are extended to accommodate prostate cancer as a survival endpoint; this is compared to treating it as a binary endpoint. Four subpopulations are identified which differ both with regard to their PSA trajectories and their incidence rates of prostate cancer.

Adolescent↗
PubMed2007

A boosting approach to flexible semiparametric mixed models.

In linear mixed models the influence of covariates is restricted to a strictly parametric form. With the rise of semi- and non-parametric regression also the mixed model has been expanded to allow for additive predictors. The common approach uses the representation of additive models as mixed models. An alternative approach that is proposed in the present paper is likelihood based boosting. Boosting originates in the machine learning community where it has been proposed as a technique to improve classification procedures by combining estimates with reweighted observations. Likelihood based boosting is a general method which may be seen as an extension of L2 boost. In additive mixed models the advantage of boosting techniques in the form of componentwise boosting is that it is suitable for high dimensional settings where many explanatory variables are present. It allows to fit additive models for many covariates with implicit selection of relevant variables and automatic selection of smoothing parameters. Moreover, boosting techniques may be used to incorporate the subject-specific variation of smooth influence functions by specifying 'random slopes' on smooth effects. This results in flexible semiparametric mixed models which are appropriate in cases where a simple random intercept is unable to capture the variation of effects across subjects.

Cohort Studies↗
PubMed2005

Concordance correlation coefficient applied to discrete data.

In any field in which decisions are subject to measurements, interchangeability between the methods used to obtain these measurements is essential. To consider methods as interchangeable, a certain degree of agreement is needed between the measurements they provide. The concordance correlation coefficient is an index that assesses the strength of agreement and it has been widely applied in situations in which measurements are made on a continuous scale. Recently the concordance correlation coefficient has been defined as a specific intraclass correlation coefficient estimated by the variance components of a Normal-Normal mixed linear model. Although this coefficient was defined for the continuous scale case, it may also be used with a discrete scale. In this case the data are often transformed and normalized, and the concordance correlation is applied. This study discusses the expression of the concordance correlation coefficient for discrete Poisson data by means of the Poisson-Normal generalized linear mixed model. The behaviour of the concordance correlation coefficient estimate is assessed by means of a simulation study, in which the estimates were compared using four models: three Normal-Normal mixed models with raw data, log-transformed data and square-root transformed data, and the Poisson-Normal generalized linear mixed model. An example is provided in which two different methods are used to measure CD34+ cells.

Biomedical Research↗
PubMed2002

Strip-plot designs, mixed models, and comparisons between linear and non-linear models for microtitre plate bioassays.

By paying careful attention to the experimental units and, randomizing where it is reasonable, we are able to devise designs for cell culture bioassay which are statistically legitimate and practical in the laboratory. These designs, strip-plot layouts, can accommodate linear or non-linear models, fixed or mixed models, and can provide good protection from location effects. Non-linear mixed models using these designs can be extended to address serial dilution error. A statistically based approach which includes randomization and proper design is a powerful tool for identifying subtle effects of factors within and outside bioassays; this attention to statistical detail is a necessary first step towards continuous improvement of biological assays.

Biological Assay↗
PubMed2007

An autoregressive linear mixed effects model for the analysis of longitudinal data which show profiles approaching asymptotes.

In longitudinal data, a continuous response sometimes shows a profile approaching an asymptote. For such data, we propose a new class of models, autoregressive linear mixed effects models in which the current response is regressed on the previous response, fixed effects, and random effects. Asymptotes can shift depending on treatment groups, individuals, and so on, and can be modelled by fixed and random effects. We also propose error structures that are useful in practice. The estimation methods of linear mixed effects models can be used as long as there is no intermittent missing.

Azathioprine↗
PubMed1996

Comparing non-hierarchical models: application to non-linear mixed effects modeling.

There is no method available to compare the fit of two non-hierarchical non-linear mixed effects models, although the common practice is to select the model with the lower objective function. Bootstrapping the log-likelihood differences (LLDs) of non-hierarchical models and constructing a bootstrap confidence interval on the LLDs is proposed for comparing the goodness-of-fit of such models. This is illustrated with different parameterizations of clearance models for an anti-infective agent in a longitudinal pharmacokinetic study which are compared. Additive and exponential models of creatinine clearance as a predictor of clearance are used as examples.

Adult↗
PubMed2002

Identification of significant host factors for HIV dynamics modelled by non-linear mixed-effects models.

Non-linear mixed-effects models are powerful tools for modelling HIV viral dynamics. In AIDS clinical trials, the viral load measurements for each subject are often sparse. In such cases, linearization procedures are usually used for inferences. Under such linearization procedures, however, standard covariate selection methods based on the approximate likelihood, such as the likelihood ratio test, may not be reliable. In order to identify significant host factors for HIV dynamics, in this paper we consider two alternative approaches for covariate selection: one is based on individual non-linear least square estimates and the other is based on individual empirical Bayes estimates. Our simulation study shows that, if the within-individual data are sparse and the between-individual variation is large, the two alternative covariate selection methods are more reliable than the likelihood ratio test, and the more powerful method based on individual empirical Bayes estimates is especially preferable. We also consider the missing data in covariates. The commonly used missing data methods may lead to misleading results. We recommend a multiple imputation method to handle missing covariates. A real data set from an AIDS clinical trial is analysed based on various covariate selection methods and missing data methods.

Acquired Immunodeficiency Syndrome↗
PubMed2005

Covariate detection in population pharmacokinetics using partially linear mixed effects models.

PURPOSE: To introduce partially linear mixed effects models (PLMEMs), to illustrate their use, and to compare the power and Type I error rate in detecting a covariate effect with nonlinear mixed effects modeling using NONMEM. METHODS: Sparse concentration-time data from males and females (1:1) were simulated under a 1-compartment oral model where clearance was sex-dependent. All possible combinations of number of subjects (50, 75, 100, 150, 250), samples per subject (2, 4, 6), and clearance multipliers (1 to 1.25) were generated. Data were analyzed with and without sex as a covariate using PLMEM (maximum likelihood estimation) and NONMEM (first-order conditional estimation). Four covariate screening methods were examined: NONMEM using the likelihood ratio test (LRT), PLMEM using the LRT, PLMEM using Wald's test, and analysis of variance (ANOVA) of the empirical Bayes estimates (EBEs) for CL treating sex as a categorical variable. The percent of simulations rejecting the null hypothesis of no covariate effect at the 0.05 level was determined. 300 simulations were done to calculate power curves and 1000 simulations were done (with no covariate effect) to calculate Type I error rate. Actual implementation of PLMEMs is illustrated using previously published teicoplanin data. RESULTS: Type I error rates were similar between PLMEM and NONMEM using the LRT, but were inflated (as high as 36%) based on PLMEM using Wald's test. Type I error rate tended to increase as the number of observations per subject increased for the LRT methods. Power curves were similar between the PLMEM and NONMEM LRT methods and were slightly more than the power curve using ANOVA on the EBEs of CL. 80% power was achieved with 4 samples per subject and 50 subjects total when the effect size was approximately 1.07, 1.07, 1.08, and 1.05 for LRT using PLMEMs, LRT using NONMEM, ANOVA on the EBEs, and Wald's test using PLMEMs, respectively. CONCLUSIONS: PLMEM and NONMEM covariate screening using the LRT had similar Type I error rates and power under the data generating model. PLMEMs offers a viable alternative to NONMEM-based covariate screening.

Computer Simulation↗
PubMed2004

A sample size computation method for non-linear mixed effects models with applications to pharmacokinetics models.

We propose a simple method to compute sample size for an arbitrary test hypothesis in population pharmacokinetics (PK) studies analysed with non-linear mixed effects models. Sample size procedures exist for linear mixed effects model, and have been recently extended by Rochon using the generalized estimating equation of Liang and Zeger. Thus, full model based inference in sample size computation has been possible. The method we propose extends the approach using a first-order linearization of the non-linear mixed effects model and use of the Wald chi(2) test statistic. The proposed method is general. It allows an arbitrary non-linear model as well as arbitrary distribution of random effects characterizing both inter- and intra-individual variability of the mixed effects model. To illustrate possible uses of the method we present tables of minimum sample sizes, in particular, with an illustration of the effect of sampling design on sample size. We demonstrate how (D-)optimal or frequent sampling requires fewer subjects in comparison to a sparse sampling design. We also present results from Monte Carlo simulations showing that the computed sample size can produce the desired power. The proposed method greatly reduces computing times compared with simulation-based methods of estimating sample sizes for population PK studies.

Black People↗