Methods for analysis of unbalanced,longitudinal, growth data

We describe an approach to analysis of growth that does not depend on assumptions about the underlying functional growth pattern and that allows for multiple observations arising from individual-specific, irregularly spaced data. We produce estimated growth curves for predefined subject groups by using LOWESS, a nonparametric smoothing algorithm. We describe how statistical significance of curve features may be evaluated by using the “jackknife,” a sample re-use method; this technique can be used to assess differences between subject groups. We then obtain residuals at each data point by reference to the estimated curve. Consistency of residuals is evaluated as a characteristic of individual subjects, and in the presence of individual consistency, relative size-for-age is then scored by the average residual for each individual. This allows study of relationships between relative size and other individual characteristics such as birth order, dominance rank, or age of maturation. Finally, we indicate flexibility of these methods and alternatives, propose uses related to other questions about growth, and suggest potential applications to variables other than body size. Appendices demonstrate application of the LOWESS and jackknife algorithms to the problem of testing sex differences in growth. © 1992 Wiley-Liss, Inc.     

Efficient approximations for learning phylogenetic HMM models from data

MOTIVATION: We consider models useful for learning an evolutionary or phylogenetic tree from data consisting of DNA sequences corresponding to the leaves of the tree. In particular, we consider a general probabilistic model described in Siepel and Haussler that we call the phylogenetic-HMM model which generalizes the classical probabilistic models of Neyman and Felsenstein. Unfortunately, computing the likelihood of phylogenetic-HMM models is intractable. We consider several approximations for computing the likelihood of such models including an approximation introduced in Siepel and Haussler, loopy belief propagation and several variational methods. RESULTS: We demonstrate that, unlike the other approximations, variational methods are accurate and are guaranteed to lower bound the likelihood. In addition, we identify a particular variational approximation to be best-one in which the posterior distribution is variationally approximated using the classic Neyman-Felsenstein model. The application of our best approximation to data from the cystic fibrosis transmembrane conductance regulator gene region across nine eutherian mammals reveals a CpG effect.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates

Stochastic compartmental models of the SEIR type are often used to make inferences on epidemic processes from partially observed data in which only removal times are available. For many epidemics, the assumption of constant removal rates is not plausible. We develop methods for models in which these rates are a time-dependent step function. A reversible jump MCMC algorithm is described that permits Bayesian inferences to be made on model parameters, particularly those associated with the step function. The method is applied to two datasets on outbreaks of smallpox and a respiratory disease. The analyses highlight the importance of allowing for time dependence by contrasting the predictive distributions for the removal times and comparing them with the observed data.      

Semiparametric models and inference for biomedical time series with extra-variation

Biomedical trials often give rise to data having the form of time series of a common process on separate individuals. One model which has been proposed to explain variations in such series across individuals is a random effects model based on sample periodograms. The use of spectral coefficients enables models for individual series to be constructed on the basis of standard asymptotic theory, whilst variations between individuals are handled by permitting a random effect perturbation of model coefficients. This paper extends such methodology in two ways: first, by enabling a nonparametric specification of underlying spectral behaviour; second, by addressing some of the tricky computational issues which are encountered when working with this class of random effect models. This leads to a model in which a population spectrum is specified nonparametrically through a dynamic system, and the processes measured on individuals within the population are assumed to have a spectrum which has a random effect perturbation from the population norm. Simulation studies show that standard MCMC algorithms give effective inferences for this model, and applications to biomedical data suggest that the model itself is capable of revealing scientifically important structure in temporal characteristics both within and between individual processes.     

Bayesian multimodel inference for geostatistical regression models

The problem of simultaneous covariate selection and parameter inference for spatial regression models is considered. Previous research has shown that failure to take spatial correlation into account can influence the outcome of standard model selection methods. A Markov chain Monte Carlo (MCMC) method is investigated for the calculation of parameter estimates and posterior model probabilities for spatial regression models. The method can accommodate normal and non-normal response data and a large number of covariates. Thus the method is very flexible and can be used to fit spatial linear models, spatial linear mixed models, and spatial generalized linear mixed models (GLMMs). The Bayesian MCMC method also allows a priori unequal weighting of covariates, which is not possible with many model selection methods such as Akaike's information criterion (AIC). The proposed method is demonstrated on two data sets. The first is the whiptail lizard data set which has been previously analyzed by other researchers investigating model selection methods. Our results confirmed the previous analysis suggesting that sandy soil and ant abundance were strongly associated with lizard abundance. The second data set concerned pollution tolerant fish abundance in relation to several environmental factors. Results indicate that abundance is positively related to Strahler stream order and a habitat quality index. Abundance is negatively related to percent watershed disturbance.     

Nonparametric quantile inference with competing risks data

A conceptually simple quantile inference procedure is proposedfor cause-specific failure probabilities with competing risksdata. The quantiles are defined using the cumulative incidencefunction, which is intuitively meaningful in the competing–risksset–up. We establish the uniform consistency and weakconvergence of a nonparametric estimator of this quantile function.These results form the theoretical basis for extensions of standardone–sample and two–sample quantile inference forindependently censored data. This includes the constructionof confidence intervals and bands for the quantile function,and two–sample tests. Simulation studies and a real dataexample illustrate the practical utility of the methodology.     

Joint inference for nonlinear mixed-effects models and time to event at the presence of missing data

In many longitudinal studies, the individual characteristics associated with the repeated measures may be possible covariates of the time to an event of interest, and thus, it is desirable to model the time-to-event process and the longitudinal process jointly. Statistical analyses may be further complicated in such studies with missing data such as informative dropouts. This article considers a nonlinear mixed-effects model for the longitudinal process and the Cox proportional hazards model for the time-to-event process. We provide a method for simultaneous likelihood inference on the 2 models and allow for nonignorable data missing. The approach is illustrated with a recent AIDS study by jointly modeling HIV viral dynamics and time to viral rebound.     

Pairwise curve synchronization for functional data

Data collected by scientists are increasingly in the form oftrajectories or curves. Often these can be viewed as realizationsof a composite process driven by both amplitude and time variation.We consider the situation in which functional variation is dominatedby time variation, and develop a curve-synchronization methodthat uses every trajectory in the sample as a reference to obtainpairwise warping functions in the first step. These initialpairwise warping functions are then used to create improvedestimators of the underlying individual warping functions inthe second step. A truncated averaging process is used to obtainrobust estimation of individual warping functions. The methodcompares well with other available time-synchronization approachesand is illustrated with Berkeley growth data and gene expressiondata for multiple sclerosis.     

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. A simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rock lobsters to assess the possible seasonal effect on growth.