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Background: Adaptive designs offer added flexibility in the execution of clinical trials, including the possibilities of allocating more patients to the treatments that turned out more successful, and early stopping due to either declared success or futility. Commonly applied adaptive designs, such as group sequential methods, are based on the frequentist paradigm and on ideas from statistical significance testing. Interim checks during the trial will have the effect of inflating the Type 1 error rate, or, if this rate is controlled and kept fixed, lowering the power., Results: The purpose of the paper is to demonstrate the usefulness of the Bayesian approach in the design and in the actual running of randomized clinical trials during phase II and III. This approach is based on comparing the performance of the different treatment arms in terms of the respective joint posterior probabilities evaluated sequentially from the accruing outcome data, and then taking a control action if such posterior probabilities fall below a pre-specified critical threshold value. Two types of actions are considered: treatment allocation, putting on hold at least temporarily further accrual of patients to a treatment arm, and treatment selection, removing an arm from the trial permanently. The main development in the paper is in terms of binary outcomes, but extensions for handling time-to-event data, including data from vaccine trials, are also discussed. The performance of the proposed methodology is tested in extensive simulation experiments, with numerical results and graphical illustrations documented in a Supplement to the main text. As a companion to this paper, an implementation of the methods is provided in the form of a freely available R package 'barts'., Conclusion: The proposed methods for trial design provide an attractive alternative to their frequentist counterparts., (© 2022. The Author(s).)

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and unique information, but at the cost of requiring a more complex statistical analysis. In this work we derive the distributions of eigenvalues and eigenvectors in the special but important case of m×m symmetric random matrices, D , observed with isotropic matrix-variate Gaussian noise. The properties of these distributions depend strongly on the symmetries of the mean tensor/matrix, D̄ . When D̄ has repeated eigenvalues, the eigenvalues of D are not asymptotically Gaussian, and repulsion is observed between the eigenvalues corresponding to the same D̄ eigenspaces. We apply these results to diffusion tensor imaging (DTI), with m = 3, addressing an important problem of detecting the symmetries of the diffusion tensor, and seeking an experimental design that could potentially yield an isotropic Gaussian distribution. In the 3-dimensional case, when the mean tensor is spherically symmetric and the noise is Gaussian and isotropic, the asymptotic distribution of the first three eigenvalue central moment statistics is simple and can be used to test for isotropy. In order to apply such tests, we use quadrature rules of order t ≥ 4 with constant weights on the unit sphere to design a DTI-experiment with the property that isotropy of the underlying true tensor implies isotropy of the Fisher information. We also explain the potential implications of the methods using simulated DTI data with a Rician noise model.

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation., (Copyright © 2015 Elsevier B.V. All rights reserved.)

This paper was inspired by the studies of Niels Keiding and co-authors on estimating the waiting time-to-pregnancy (TTP) distribution, and in particular on using the current duration design in that context. In this design, a cross-sectional sample of women is collected from those who are currently attempting to become pregnant, and then by recording from each the time she has been attempting. Our aim here is to study the identifiability and the estimation of the waiting time distribution on the basis of current duration data. The main difficulty in this stems from the fact that very short waiting times are only rarely selected into the sample of current durations, and this renders their estimation unstable. We introduce here a Bayesian method for this estimation problem, prove its asymptotic consistency, and compare the method to some variants of the non-parametric maximum likelihood estimators, which have been used previously in this context. The properties of the Bayesian estimation method are studied also empirically, using both simulated data and TTP data on current durations collected by Slama et al. (Hum Reprod 27(5):1489-1498, 2012).

We assume that allele frequency data have been extracted from several large DNA pools, each containing genetic material of up to hundreds of sampled individuals. Our goal is to estimate the haplotype frequencies among the sampled individuals by combining the pooled allele frequency data with prior knowledge about the set of possible haplotypes. Such prior information can be obtained, for example, from a database such as HapMap. We present a Bayesian haplotyping method for pooled DNA based on a continuous approximation of the multinomial distribution. The proposed method is applicable when the sizes of the DNA pools and/or the number of considered loci exceed the limits of several earlier methods. In the example analyses, the proposed model clearly outperforms a deterministic greedy algorithm on real data from the HapMap database. With a small number of loci, the performance of the proposed method is similar to that of an EM-algorithm, which uses a multinormal approximation for the pooled allele frequencies, but which does not utilize prior information about the haplotypes. The method has been implemented using Matlab and the code is available upon request from the authors.

We assume that quantitative measurements on a considered trait and unphased genotype data at certain marker loci are available on a sample of individuals from a background population. Our goal is to map quantitative trait loci by using a Bayesian model that performs, and makes use of, probabilistic reconstructions of the recent unobserved genealogical history (a pedigree and a gene flow at the marker loci) of the sampled individuals. This work extends variance component-based linkage analysis to settings where the unobserved pedigrees are considered as latent variables. In addition to the measured trait values and unphased genotype data at the marker loci, the method requires as an input estimates of the population allele frequencies and of a marker map, as well as some parameters related to the population size and the mating behavior. Given such data, the posterior distribution of the trait parameters (the number, the locations, and the relative variance contributions of the trait loci) is studied by using the reversible-jump Markov chain Monte Carlo methodology. We also introduce two shortcuts related to the trait parameters that allow us to do analytic integration, instead of stochastic sampling, in some parts of the algorithm. The method is tested on two simulated data sets. Comparisons with traditional variance component linkage analysis and association analysis demonstrate the benefits of our approach in a gene mapping context.

Recent studies show that the PHASE algorithm is a state-of-the-art method for population-based haplotyping from individually genotyped data. We present a modified version of PHASE for estimating population haplotype frequencies from pooled DNA data. The algorithm is compared with (i) a maximum likelihood estimation under the multinomial model and (ii) a deterministic greedy algorithm, on both simulated and real data sets (HapMap data). Our results suggest that the PHASE algorithm is a method of choice also on pooled DNA data. The main reason for improvement over the other approaches is assumed to be the same as with individually genotyped data: the biologically motivated model of PHASE takes into account correlated genealogical histories of the haplotypes by modelling mutations and recombinations. The important questions of efficiency of DNA pooling as well as influence of the pool size on the accuracy of the estimates are also considered. Our results are in line with the earlier findings in that the pool size should be relatively small, only 2-5 individuals in our examples, in order to provide reliable estimates of population haplotype frequencies.

Twin studies have been used to understand the sources of genetic and environmental variation in body height, body weight and other common human quantitative traits. However, it is rather unclear whether these two sources of variation could be really separated in practice. Here, we consider a special study design where phenotype data from married couples and their siblings have been collected. The marital status gives information about the shared environment, while siblings give information about both genetic and environmental variation. To dissect sources of variation and to allow some deviations and pedigree errors in the data, we model such data using a robust polygenic model with finite genome length assumption. As a summary, we provide the estimates for age-dependent proportions of total variation which are due to polygenic and environmental effects. Here, these estimates are provided for body height, weight, systolic blood pressure and total serum cholesterol measured from subjects of the Indian Migration Study.

An issue often encountered in statistical genetics is whether, or to what extent, it is possible to estimate the degree to which individuals sampled from a background population are related to each other, on the basis of the available genotype data and some information on the demography of the population. In this article, we consider this question using explicit modelling of the pedigrees and gene flows at unlinked marker loci, but then restricting ourselves to a relatively recent history of the population, that is, considering the genealogy at most some tens of generations backwards in time. As a computational tool we use a Markov chain Monte Carlo numerical integration on the state space of genealogies of the sampled individuals. As illustrations of the method, we consider the question of relatedness at the level of genes/genomes (IBD estimation), using both simulated and real data.

Background: Answers to several fundamental questions in statistical genetics would ideally require knowledge of the ancestral pedigree and of the gene flow therein. A few examples of such questions are haplotype estimation, relatedness and relationship estimation, gene mapping by combining pedigree and linkage disequilibrium information, and estimation of population structure., Results: We present a probabilistic method for genealogy reconstruction. Starting with a group of genotyped individuals from some population isolate, we explore the state space of their possible ancestral histories under our Bayesian model by using Markov chain Monte Carlo (MCMC) sampling techniques. The main contribution of our work is the development of sampling algorithms in the resulting vast state space with highly dependent variables. The main drawback is the computational complexity that limits the time horizon within which explicit reconstructions can be carried out in practice., Conclusion: The estimates for IBD (identity-by-descent) and haplotype distributions are tested in several settings using simulated data. The results appear to be promising for a further development of the method.

A heuristic algorithm for finding gene transmission patterns on large and complex pedigrees with partially observed genotype data is proposed. The method can be used to generate an initial point for a Markov chain Monte Carlo simulation or to check that the given pedigree and the genotype data are consistent. In small pedigrees, the algorithm is exact by exhaustively enumerating all possibilities, but, in large pedigrees, with a considerable amount of unknown data, only a subset of promising configurations can actually be checked. For that purpose, the configurations are ordered by combining the approximative conditional probability distribution of the unknown genotypes with the information on the relationships between individuals. We also introduce a way to divide the task into subparts, which has been shown to be useful in large pedigrees. The algorithm has been implemented in a program called APE (Allelic Path Explorer) and tested in three different settings with good results.

A new statistical approach for construction of the genetic linkage map and estimation of the parental linkage phase based on allele frequency data from pooled gametic (sperm or egg) samples is introduced. This method can be applied for estimation of recombination fractions (over distances <1 cM) and ordering of large numbers (even hundreds) of closely linked markers. This method should be extremely useful in species with a long generation interval and a large genome size such as in dairy cattle or in forest trees; the conifer species have haploid tissues available in megagametophytes. According to Mendelian expectation, two parental alleles should occur in gametes in 1:1 proportions, if segregation distortion does not occur. However, due to mere sampling variation, the observed proportions may deviate from their expected value in practice. These deviations and their dependence along the chromosome can provide information on the parental linkage phase and on the genetic linkage map. Usefulness of the method is illustrated with simulations. The role of segregation distortion as a source of these deviations is also discussed. The software implementing this method is freely available for research purposes from the authors.

If the population is large and the sampling mechanism is random, the coalescent is commonly used to model the haplotypes in the sample. Ordered genotypes can then be formed by random matching of the derived haplotypes. However, this approach is not realistic when (1) there is departure from random mating (e.g., dominant individuals in breeding populations or monogamy in humans), or (2) the population is small and/or the individuals in the sample are ascertained by applying some particular non-random sampling scheme, as is usually the case when considering the statistical modeling and analysis of pedigree data. For such situations, we present here a data generation method where an ancestral graph with non-overlapping generations is first generated backwards in time, using ideas from coalescent theory. Alleles are randomly assigned to the founders, and subsequently the gene flow over the entire genome is simulated forwards in time by dropping alleles down the graph according to recombination model without interference. The parameters controlling the mating behavior of generated individuals in the graph (degree of monogamy) can be tuned in order to match a particular demographic situation, without restriction to simple random mating. The performance of the approach is illustrated with a simulation example. The software (written in C-language) is freely available for research purposes at http://www.rni.helsinki.fi/~dag/.

In this paper, a class of tests is developed for comparing the cause-specific hazard rates of m competing risks simultaneously in K (> or = 2) groups. The data available for a unit are the failure time of the unit along with the identifier of the risk claiming the failure. In practice, the failure time data are generally right censored. The tests are based on the difference between the weighted averages of the cause-specific hazard rates corresponding to each risk. No assumption regarding the dependence of the competing risks is made. It is shown that the proposed test statistic has asymptotically chi-squared distribution. The proposed test is shown to be optimal for a specific type of local alternatives. The choice of weight function is also discussed. A simulation study is carried out using multivariate Gumbel distribution to compare the optimal weight function with a proposed weight function which is to be used in practice. Also, the proposed test is applied to real data on the termination of an intrauterine device.

It is common in the analysis of aggregate data in epidemiology that the variances of the aggregate observations are available. The analysis of such data leads to a measurement error situation, where the known variances of the measurement errors vary between the observations. Assuming multivariate normal distribution for the 'true' observations and normal distributions for the measurement errors, we derive a simple EM algorithm for obtaining maximum likelihood estimates of the parameters of the multivariate normal distributions. The results also facilitate the estimation of regression parameters between the variables as well as the 'true' values of the observations. The approach is applied to re-estimate recent results of the WHO MONICA Project on cardiovascular disease and its risk factors, where the original estimation of the regression coefficients did not adjust for the regression attenuation caused by the measurement errors., (Copyright 2002 John Wiley & Sons, Ltd.)