The gamma-frailty Poisson model for the nonparametric estimation of panel count data

In this article, we study nonparametric estimation of the mean function of a counting process with panel observations. We introduce the gamma frailty variable to account for the intracorrelation between the panel counts of the counting process and construct a maximum pseudo-likelihood estimate with the frailty variable. Three simulated examples are given to show that this estimation procedure, while preserving the robustness and simplicity of the computation, improves the efficiency of the nonparametric maximum pseudo-likelihood estimate studied in Wellner and Zhang (2000, Annals of Statistics 28, 779-814). A real example from a bladder tumor study is used to illustrate the method.     

Bayesian nonparametric inference for panel count data with an informative observation process

In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is proposed to jointly model the observation process and the recurrent event process. Bayesian nonparametric inference is proposed for simultaneously estimating regression parameters, bivariate frailty effects, and baseline intensity functions. Inference is done through Markov chain Monte Carlo, with fully developed computational techniques. Predictive inference is also discussed under the Bayesian setting. The proposed method is shown to be efficient via simulation studies. A clinical trial dataset on skin cancer patients is analyzed to illustrate the proposed approach.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.     

Joint analysis of longitudinal data with informative right censoring

Longitudinal data arise when subjects are followed over a period of time. A commonly encountered complication in the analysis of such data is the variable length of follow-up due to right censorship. This can be further exacerbated by the possible dependency between the censoring time and the longitudinal measurements. This article proposes a combination of a semiparametric transformation model for the censoring time and a linear mixed effects model for the longitudinal measurements. The dependency is handled via latent variables which are naturally incorporated. We show that the likelihood function has an explicit form and develops a two-stage estimation procedure to avoid direct maximization over a high-dimensional parameter space. The resulting estimators are shown to be consistent and asymptotically normal, with a closed form for the variance-covariance matrix that can be used to obtain a plug-in estimator. Finite sample performance of the proposed approach is assessed through extensive simulations. The method is applied to renal disease data.     

On the Bayesian analysis of ring-recovery data

Vounatsou and Smith (1995, Biometrics 51, 687-708) describe the modern Bayesian analysis of ring-recovery data. Here we discuss and extend their work. We draw different conclusions from two major data analyses. We emphasize the extreme sensitivity of certain parameter estimates to the choice of prior distribution and conclude that naive use of Bayesian methods in this area can be misleading. Additionally, we explain the discrepancy between the Bayesian and classical analyses when the likelihood surface has a flat ridge. In this case, when there is no unique maximum likelihood estimate, the Bayesian estimators are remarkably precise.     

Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture

This paper presents a new method to analyze clonal data on oligodendrocyte development in cell culture. The process of oligodendrocyte generation from precursor cells is modelled as a multi-type Bellman-Harris branching process as suggested in an earlier paper [K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Proschel, M. Noble, An alternative stochastic model of generation of oligodendrocytes in cell culture, J. Math. Biol. 43 (2001) 22]. This model has been extended to allow for death of oligodendrocytes as well as a dissimilar distribution of the first mitotic cycle duration as compared to the subsequent cycles of precursor cells, which lengths are assumed to be independent and identically distributed random variables. Since the time-span of oligodendrocytes is not directly observable in clonal data, plausible parametric assumptions are invoked to make estimation problems tractable. In particular, the time to cell death follows a two-parameter gamma distribution, while the lapse of time between the event of cell death and the event of cell disintegration is assumed to be exponentially distributed. A simulated pseudo maximum likelihood method for estimation of model parameters has been developed using simulation-based approximations of the expected numbers and variance-covariance matrices for different types of cells. Finite sample properties of the estimation procedure are studied by computer simulations. The proposed method is illustrated with an analysis of the clonal development of O-2A progenitor cells isolated from the rat optic nerve and the corpus callosum.     

Comparing the performances of Diggle's tests of spatial randomness for small samples with and without edge-effect correction: application to ecological data

Diggle's tests of spatial randomness based on empirical distributions of interpoint distances can be performed with and without edge-effect correction. We present here numerical results illustrating that tests without the edge-effect correction proposed by Diggle (1979, Biometrics 35, 87-101) have a higher power for small sample sizes than those with correction. Ignoring the correction enables detection of departure from spatial randomness with smaller samples (down to 10 points vs. 30 points for the tests with correction). These results are confirmed by an example with ecological data consisting of maps of two species of trees in a West African savanna. Tree numbers per species per map were often less than 20. For one of the species, for which maps strongly suggest an aggregated pattern, tests without edge-effect correction enabled rejection of the null hypothesis on three plots out of five vs. on only one for the tests with correction.     

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).