An order estimation based approach to identify response genes for microarray time course data.

Gene expression profiles from microarray time course experiments provide a unique opportunity to examine genome-wide signal processing and gene responses. A fundamental issue in microarray experiments is that the treatment condition can only be controlled at the cell level rather than at the gene level. The treatment condition does not affect all genes equally. Some genes depend on other genes to detect external changes. The dependency between genes is not fully deterministic and may vary with treatment condition. Thus the expression of each gene is potentially affected by two confounding effects: the treatment effect and the gene context effect arising from the regulatory interactions among genes. This gene context effect is hard to isolate. Neither can it be simply ignored. Instead, this gene context information which may be different under different treatment conditions is of primary biological interest. We introduce an approach which deals with the confounding effects and takes into account the uncontrollable gene context effect. Our method is based on the estimation of the number of hidden states, which, in our development, corresponds to the order of a hidden Markov model (HMM). For each gene, its observed expression is modeled by a gamma distribution determined by the corresponding hidden state at each time point. Those genes showing evidence for more than one hidden state can be categorized as the signalling genes, or in a wider sense, as the response genes which are coordinated by a cell system in reaction to a specific external condition. These response genes can be used in the comparison of different treatment conditions, to investigate the gene context effect under different treatments. Microarray time course data are also analyzed to demonstrate our method.

A competing risks model for correlated data based on the subdistribution hazard.

Family-based follow-up study designs are important in epidemiology as they enable investigations of disease aggregation within families. Such studies are subject to methodological complications since data may include multiple endpoints as well as intra-family correlation. The methods herein are developed for the analysis of age of onset with multiple disease types for family-based follow-up studies. The proposed model expresses the marginalized frailty model in terms of the subdistribution hazards (SDH). As with Pipper and Martinussen's (Scand J Stat 30:509-521, 2003) model, the proposed multivariate SDH model yields marginal interpretations of the regression coefficients while allowing the correlation structure to be specified by a frailty term. Further, the proposed model allows for a direct investigation of the covariate effects on the cumulative incidence function since the SDH is modeled rather than the cause specific hazard. A simulation study suggests that the proposed model generally offers improved performance in terms of bias and efficiency when a sufficient number of events is observed. The proposed model also offers type I error rates close to nominal. The method is applied to a family-based study of breast cancer when death in absence of breast cancer is considered a competing risk.

A pseudo-EM algorithm for clustering incomplete longitudinal data.

A method for clustering incomplete longitudinal data, and gene expression time course data in particular, is presented. Specifically, an existing method that utilizes mixtures of multivariate Gaussian distributions with modified Cholesky-decomposed covariance structure is extended to accommodate incomplete data. Parameter estimation is carried out in a fashion that is similar to an expectation-maximization algorithm. We focus on the particular application of clustering incomplete gene expression time course data. In this application, our approach gives good clustering performance when compared to the results when there is no missing data. Possible extensions of this work are also suggested.

Review and implementation of cure models based on first hitting times for Wiener processes.

The development of models and methods for cure rate estimation has recently burgeoned into an important subfield of survival analysis. Much of the literature focuses on the standard mixture model. Recently, process-based models have been suggested. We focus on several models based on first passage times for Wiener processes. Whitmore and others have studied these models in a variety of contexts. Lee and Whitmore (Stat Sci 21(4):501-513, 2006) give a comprehensive review of a variety of first hitting time models and briefly discuss their potential as cure rate models. In this paper, we study the Wiener process with negative drift as a possible cure rate model but the resulting defective inverse Gaussian model is found to provide a poor fit in some cases. Several possible modifications are then suggested, which improve the defective inverse Gaussian. These modifications include: the inverse Gaussian cure rate mixture model; a mixture of two inverse Gaussian models; incorporation of heterogeneity in the drift parameter; and the addition of a second absorbing barrier to the Wiener process, representing an immunity threshold. This class of process-based models is a useful alternative to the standard model and provides an improved fit compared to the standard model when applied to many of the datasets that we have studied. Implementation of this class of models is facilitated using expectation-maximization (EM) algorithms and variants thereof, including the gradient EM algorithm. Parameter estimates for each of these EM algorithms are given and the proposed models are applied to both real and simulated data, where they perform well.