Incorporating measurement error in the estimation of autoregressive models for longitudinal data

A mixed hidden Markov model for multivariate monotone disease processes in the presence of measurement errors

Motivated by a longitudinal oral health study, the Signal-Tandmobiel® study, an inhomogeneous mixed hidden Markov model with continuous state-space is proposed to explain the caries disease process in children between 6 and 12 years of age. The binary caries experience outcomes are subject to misclassification. We modelled this misclassification process via a longitudinal latent continuous response subject to a measurement error process and showing a monotone behaviour. The baseline distributions of the unobservable continuous processes are defined as a function of the covariates through the specification of conditional distributions making use of the Markov property. In addition, random effects are considered to model the relationships among the multivariate responses. Our approach is in contrast with a previous approach working on the binary outcome scale. This method requires conditional independence of the possibly corrupted binary outcomes on the true binary outcomes. We assumed conditional independence on the latent scale, which is a weaker assumption than conditional independence on the binary scale. The aim of this article is therefore to show the properties of a model for a progressive longitudinal response with misclassification on the manifest scale but modelled on the latent scale. The model parameters are estimated in a Bayesian way using an efficient Markov chain Monte Carlo method. The model performance is shown through a simulation-based example, and the analysis of the motivating dataset is presented.

Meta-analysis and meta-regression of transcriptomic responses to water stress in Arabidopsis

The large amounts of transcriptome data available for Arabidopsis thaliana make a compelling case for the need to generalize results across studies and extract the most robust and meaningful information possible from them. The results of various studies seeking to identify water stress-responsive genes only partially overlap. The aim of this work was to combine transcriptomic studies in a systematic way that identifies commonalities in response, taking into account variation among studies due to batch effects as well as sampling variation, while also identifying the effect of study-specific variables, such as the method of applying water stress, and the part of the plant the mRNA was extracted from. We used meta-analysis, the quantitative synthesis of independent research results, to summarize expression responses to water stress across studies, and meta-regression to model the contribution of covariates that may affect gene expression. We found that some genes with small but consistent differential responses become evident only when results are synthesized across experiments, and are missed in individual studies. We also identified genes with expression responses that are attributable to use of different plant parts and alternative methods for inducing water stress. Our results indicate that meta-analysis and meta-regression provide a powerful approach for identifying a robust gene set that is less sensitive to idiosyncratic results and for quantifying study characteristics that result in contrasting gene expression responses across studies. Combining meta-analysis with individual analyses may contribute to a richer understanding of the biology of water stress responses, and may prove valuable in other gene expression studies.

On reverse engineering of gene interaction networks using time course data with repeated measurements

MOTIVATION

Gene expression measurements are the most common data source for reverse engineering gene interaction networks. When dealing with destructive sampling in time course experiments, it is common to average any available measurements for each time point and to treat this as the actual time series data for fitting the network, neglecting the variability contained in the repeated measurements. Proceeding in such a way can affect the retrieved network topology.

RESULTS

We propose a fully Bayesian method for reverse engineering a gene interaction network, based on time course data with repeated measurements. The observations are treated as surrogate measurements of the underlying gene expression. As these measurements often contain outliers, we use a non-Gaussian specification for dealing with measurement error. The network interactions are assumed linear and an autoregressive model is specified, augmented with indicator variables that allow inference on the topology of the network. We analyse two in silico and one in vivo experiments, the latter dealing with the circadian clock in Arabidopsis thaliana. A systematic attenuation of the estimated regulation strengths and a concomitant overestimation of their precision is demonstrated when measurement error is disregarded. Thus, a clear improvement in the inferred topology for the synthetic datasets is demonstrated when this is included. Also, the influence of outliers in the retrieved network is demonstrated when using the in vivo data.

AVAILABILITY

Matlab code and data used in the article are available from http://go.warwick.ac.uk/majuarez/home/materials.

Estimation in semiparametric transition measurement error models for longitudinal data

We consider semiparametric transition measurement error models for longitudinal data, where one of the covariates is measured with error in transition models, and no distributional assumption is made for the underlying unobserved covariate. An estimating equation approach based on the pseudo conditional score method is proposed. We show the resulting estimators of the regression coefficients are consistent and asymptotically normal. We also discuss the issue of efficiency loss. Simulation studies are conducted to examine the finite-sample performance of our estimators. The longitudinal AIDS Costs and Services Utilization Survey data are analyzed for illustration.

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.

Bias correction of two-state latent Markov process parameter estimates under misclassification

A discretely observed two-state process may misclassify the state of an unobservable continuous-time, two-state Markov process. We examine the behaviour of maximum likelihood transition probability estimates as functions of known misclassification probabilities. Since maximum likelihood estimators are not available in closed form, we provide two alternatives for bias-adjusted estimation. In the case of large samples, the asymptotic bias is quantified and estimators are constructed iteratively using transition counts and specified misclassification probabilities. For finite samples, we provide an approximation based on partial derivatives. Estimators that are bias-adjusted to a first approximation are easily constructed and may serve well when misclassification probabilities are known to be small. Simulation studies reveal the effect of misclassification on estimation. Repeated diagnostic testing data illustrate the approaches.