EM-REML estimation of covariance parameters in Gaussian mixed models for longitudinal data analysis

This paper presents procedures for implementing the EM algorithm to compute REML estimates of variance covariance components in Gaussian mixed models for longitudinal data analysis. The class of models considered includes random coefficient factors, stationary time processes and measurement errors. The EM algorithm allows separation of the computations pertaining to parameters involved in the random coefficient factors from those pertaining to the time processes and errors. The procedures are illustrated with Pothoff and Roy''s data example on growth measurements taken on 11 girls and 16 boys at four ages. Several variants and extensions are discussed.     

Stability results for delayed-recruitment models in population dynamics

This paper relates the stability properties of a class of delay-difference equations to those of an associated scalar difference equation. Simple but powerful conditions for testing global stability are presented which are independent of the length of the time delay involved. For models which do not have globally stable equilibria, estimates of stability regions are obtained. Some well known baleen whale models are used to illustrate the results.     

Detection and modelling of time-dependent QTL in animal populations

A longitudinal approach is proposed to map QTL affecting function-valued traits and to estimate their effect over time. The method is based on fitting mixed random regression models. The QTL allelic effects are modelled with random coefficient parametric curves and using a gametic relationship matrix. A simulation study was conducted in order to assess the ability of the approach to fit different patterns of QTL over time. It was found that this longitudinal approach was able to adequately fit the simulated variance functions and considerably improved the power of detection of time-varying QTL effects compared to the traditional univariate model. This was confirmed by an analysis of protein yield data in dairy cattle, where the model was able to detect QTL with high effect either at the beginning or the end of the lactation, that were not detected with a simple 305 day model.     

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach

Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well-known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.     

Enhanced process understanding and multivariate prediction of the relationship between cell culture process and monoclonal antibody quality

This work investigates the insights and understanding which can be deduced from predictive process models for the product quality of a monoclonal antibody based on designed high‐throughput cell culture experiments performed at milliliter (ambr‐15^®) scale. The investigated process conditions include various media supplements as well as pH and temperature shifts applied during the process. First, principal component analysis (PCA) is used to show the strong correlation characteristics among the product quality attributes including aggregates, fragments, charge variants, and glycans. Then, partial least square regression (PLS1 and PLS2) is applied to predict the product quality variables based on process information (one by one or simultaneously). The comparison of those two modeling techniques shows that a single (PLS2) model is capable of revealing the interrelationship of the process characteristics to the large set product quality variables. In order to show the dynamic evolution of the process predictability separate models are defined at different time points showing that several product quality attributes are mainly driven by the media composition and, hence, can be decently predicted from early on in the process, while others are strongly affected by process parameter changes during the process. Finally, by coupling the PLS2 models with a genetic algorithm first the model performance can be further improved and, most importantly, the interpretation of the large‐dimensioned process–product‐interrelationship can be significantly simplified. The generally applicable toolset presented in this case study provides a solid basis for decision making and process optimization throughout process development. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1368–1380, 2017