Regret‐Regression for Optimal Dynamic Treatment Regimes

Summary We consider optimal dynamic treatment regime determination in practice. Model building, checking, and comparison have had little or no attention so far in this literature. Motivated by an application on optimal dosage of anticoagulants, we propose a modeling and estimation strategy that incorporates the regret functions of Murphy (2003, Journal of the Royal Statistical Society, Series B 65, 331–366) into a regression model for observed responses. Estimation is quick and diagnostics are available, meaning a variety of candidate models can be compared. The method is illustrated using simulation and the anticoagulation application.     

Risk‐Group‐Specific Dose Finding Based on an Average Toxicity Score

Summary We propose a Bayesian dose‐finding design that accounts for two important factors, the severity of toxicity and heterogeneity in patients' susceptibility to toxicity. We consider toxicity outcomes with various levels of severity and define appropriate scores for these severity levels. We then use a multinomial‐likelihood function and a Dirichlet prior to model the probabilities of these toxicity scores at each dose, and characterize the overall toxicity using an average toxicity score (ATS) parameter. To address the issue of heterogeneity in patients' susceptibility to toxicity, we categorize patients into different risk groups based on their susceptibility. A Bayesian isotonic transformation is applied to induce an order‐restricted posterior inference on the ATS. We demonstrate the performance of the proposed dose‐finding design using simulations based on a clinical trial in multiple myeloma.     

COLONY: a program for parentage and sibship inference from multilocus genotype data

Pedigrees, depicting genealogical relationships between individuals, are important in several research areas. Molecular markers allow inference of pedigrees in wild species where relationship information is impossible to collect by observation. Marker data are analysed statistically using methods based on Mendelian inheritance rules. There are numerous computer programs available to conduct pedigree analysis, but most software is inflexible, both in terms of assumptions and data requirements. Most methods only accommodate monogamous diploid species using codominant markers without genotyping error. In addition, most commonly used methods use pairwise comparisons rather than a full-pedigree likelihood approach, which considers the likelihood of the entire pedigree structure and allows the simultaneous inference of parentage and sibship. Here, we describe colony, a computer program implementing full-pedigree likelihood methods to simultaneously infer sibship and parentage among individuals using multilocus genotype data. colony can be used for both diploid and haplodiploid species; it can use dominant and codominant markers, and can accommodate, and estimate, genotyping error at each locus. In addition, colony can carry out these inferences for both monoecious and dioecious species. The program is available as a Microsoft Windows version, which includes a graphical user interface, and a Macintosh version, which uses an R-based interface.     

Random Partition Models and Exchangeability for Bayesian Identification of Population Structure

We introduce a Bayesian theoretical formulation of the statistical learning problem concerning the genetic structure of populations. The two key concepts in our derivation are exchangeability in its various forms and random allocation models. Implications of our results to empirical investigation of the population structure are discussed.     

Amplified fragment length polymorphisms and sequence data in the phylogenetic analysis of polyploids: multiple origins of Veronica cymbalaria (Plantaginaceae)

The origin of polyploid Veronica cymbalaria (Plantaginaceae) was investigated using DNA sequence data and amplified fragment length polymorphism (AFLP) fingerprints to reveal the parentage of this taxon. The use of AFLP fingerprints in phylogenetic analysis is problematic and various methods have therefore been compared. DNA sequence data (for the internal transcribed spacer (ITS) region and the plastid trnL-F region (trnL intron, 3'exon, and trnL-F spacer)) and polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) analysis of the ITS region suggested a reliable hypothesis for the evolution of the V. cymbalaria complex. This hypothesis allowed evaluation of the effect of different distance measures (Jaccard and Nei-Li) in phenetic, character-state weighted parsimony, and Bayesian analyses of AFLP markers. The study establishes that tetraploid V. cymbalaria originated at least twice in the eastern Mediterranean, with one parent differing in the two separate origins. Hexaploid V. cymbalaria originated even more often. The results illustrate that even subtle differences in the analyses of AFLP markers can lead to drastically different conclusions. The study reveals multiple origins of a Mediterranean polyploid species. Furthermore, it demonstrates that the analysis of a complex marker system such as AFLP fingerprints using only one type of analysis can easily be misleading.     

A Markov chain Monte Carlo strategy for sampling from the joint posterior distribution of pedigrees and population parameters under a Fisher-Wright model with partial selfing

A simple population genetic model is presented for a hermaphrodite annual species, allowing both selfing and outcrossing. Those male gametes (pollen) responsible for outcrossing are assumed to disperse much further than seeds. Under this model, the pedigree of a sample from a single locality is loop-free. A novel Markov chain Monte Carlo strategy is presented for sampling from the joint posterior distribution of the pedigree of such a sample and the parameters of the population genetic model (including the selfing rate) given the genotypes of the sampled individuals at unlinked marker loci. The computational costs of this Markov chain Monte Carlo strategy scale well with the number of individuals in the sample, and the number of marker loci, but increase exponentially with the age (time since colonisation from the source population) of the local population. Consequently, this strategy is particularly suited to situations where the sample has been collected from a population which is the result of a recent colonisation process.     

Application of the secondary structure model of rRNA for phylogeny: D2-D3 expansion segments of the LSU gene of plant-parasitic nematodes from the family Hoplolaimidae Filipjev, 1934

Knowledge of rRNA structure is increasingly important to assist phylogenetic analysis through reconstructing optimal alignment, utilizing molecule features as an additional source of data and refining appropriate models of evolution of the molecule. We describe a procedure of optimization for alignment and a new coding method for nucleotide sequence data using secondary structure models of the D2 and D3 expansion fragments of the LSU-rRNA gene reconstructed for fifteen nematode species of the agriculturally important and diverse family Hoplolaimidae, order Tylenchida. Using secondary structure information we converted the original sequence data into twenty-eight symbol codes and submitted the transformed data to maximum parsimony analysis. We also applied the original sequence data set for Bayesian inference. This used the doublet model with sixteen states of nucleotide doublets for the stem region and the standard model of DNA substitution with four nucleotide states for loops and bulges. By this approach, we demonstrate that using structural information for phylogenetic analyses led to trees with lower resolved relationships between clades and likely eliminated some artefactual support for misinterpreted relationships, such as paraphyly of Helicotylenchus or Rotylenchus. This study as well as future phylogenetic analyses is herein supported by the development of an on-line database, NEMrRNA, for rRNA molecules in a structural format for nematodes. We also have developed a new computer program, RNAstat, for calculation of nucleotide statistics designed and proposed for phylogenetic studies.     

Performance of a new invariants method on homogeneous and nonhomogeneous quartet trees

An attempt to use phylogenetic invariants for tree reconstruction was made at the end of the 80s and the beginning of the 90s by several researchers (the initial idea due to Lake [1987] and Cavender and Felsenstein [1987]). However, the efficiency of methods based on invariants is still in doubt (Huelsenbeck 1995; Jin and Nei 1990). Probably because these methods only used few generators of the set of phylogenetic invariants. The method studied in this paper was first introduced in Casanellas et al. (2005) and it is the first method based on invariants that uses the "whole" set of generators for DNA data. The simulation studies performed in this paper prove that it is a very competitive and highly efficient phylogenetic reconstruction method, especially for nonhomogeneous models on phylogenetic trees.     

Bayesian modeling of dynamic motion integration

The quality of the representation of an object's motion is limited by the noise in the sensory input as well as by an intrinsic ambiguity due to the spatial limitation of the visual motion analyzers (aperture problem). Perceptual and oculomotor data demonstrate that motion processing of extended objects is initially dominated by the local 1D motion cues, related to the object's edges and orthogonal to them, whereas 2D information, related to terminators (or edge-endings), takes progressively over and leads to the final correct representation of global motion. A Bayesian framework accounting for the sensory noise and general expectancies for object velocities has proven successful in explaining several experimental findings concerning early motion processing [Weiss, Y., Adelson, E., 1998. Slow and smooth: a Bayesian theory for the combination of local motion signals in human vision. MIT Technical report, A.I. Memo 1624]. In particular, these models provide a qualitative account for the initial bias induced by the 1D motion cue. However, a complete functional model, encompassing the dynamical evolution of object motion perception, including the integration of different motion cues, is still lacking. Here we outline several experimental observations concerning human smooth pursuit of moving objects and more particularly the time course of its initiation phase, which reflects the ongoing motion integration process. In addition, we propose a recursive extension of the Bayesian model, motivated and constrained by our oculomotor data, to describe the dynamical integration of 1D and 2D motion information. We compare the model predictions for object motion tracking with human oculomotor recordings.