Inferences from DNA data: population histories, evolutionary processes and forensic match probabilities

Summary. We develop a flexible class of Metropolis–Hastings algorithms for drawing inferences about population histories and mutation rates from deoxyribonucleic acid (DNA) sequence data. Match probabilities for use in forensic identification are also obtained, which is particularly useful for mitochondrial DNA profiles. Our data augmentation approach, in which the ancestral DNA data are inferred at each node of the genealogical tree, simplifies likelihood calculations and permits a wide class of mutation models to be employed, so that many different types of DNA sequence data can be analysed within our framework. Moreover, simpler likelihood calculations imply greater freedom for generating tree proposals, so that algorithms with good mixing properties can be implemented. We incorporate the effects of demography by means of simple mechanisms for changes in population size and structure, and we estimate the corresponding demographic parameters, but we do not here allow for the effects of either recombination or selection. We illustrate our methods by application to four human DNA data sets, consisting of DNA sequences, short tandem repeat loci, single-nucleotide polymorphism sites and insertion sites. Two of the data sets are drawn from the male-specific Y-chromosome, one from maternally inherited mitochondrial DNA and one from the β -globin locus on chromosome 11.     

A BRANCHING PROCESS MODEL FOR FLOW CYTOMETRY AND BUDDING INDEX MEASUREMENTS IN CELL SYNCHRONY EXPERIMENTS

We present a flexible branching process model for cell population dynamics in synchrony/time-series experiments used to study important cellular processes. Its formulation is constructive, based on an accounting of the unique cohorts in the population as they arise and evolve over time, allowing it to be written in closed form. The model can attribute effects to subsets of the population, providing flexibility not available using the models historically applied to these populations. It provides a tool for in silico synchronization of the population and can be used to deconvolve population-level experimental measurements, such as temporal expression profiles. It also allows for the direct comparison of assay measurements made from multiple experiments. The model can be fit either to budding index or DNA content measurements, or both, and is easily adaptable to new forms of data. The ability to use DNA content data makes the model applicable to almost any organism. We describe the model and illustrate its utility and flexibility in a study of cell cycle progression in the yeast Saccharomyces cerevisiae.     

Interpreting forensic DNA mixtures: allowing for uncertainty in population substructure and dependence

We consider the assessment of deoxyribonucleic acid (DNA) profiles from biological samples containing a mixture of DNA from more than one person. The problem has been investigated in the context of likelihood ratios by Weir and co-workers under the assumption of independent alleles in DNA profiles. However, uncertainty about independence may arise from various factors such as population substructure and relatedness. This issue has received considerable attention in recent years. Ignoring this uncertainty may seriously overstate the strength of the evidence and therefore disadvantage innocent suspects. Taking this uncertainty into account, we develop a general formula for calculating the match probabilities of DNA profiles. Thus, we extend the result derived by Weir and co-workers to the dependence situation, which is often more to the benefit of the defendant in comparison with the simple product rule result based on an independence assumption. The effect of dependence of alleles on likelihood ratio estimates can be seen in the analysis of two real data sets.     

Bayesian Analysis of DNA Profiling Data in Forensic Identification Applications

The utilization of DNA evidence in cases of forensic identification has become widespread over the last few years. The strength of this evidence against an individual standing trial is typically presented in court in the form of a likelihood ratio (LR) or its reciprocal (the profile match probability). The value of this LR will vary according to the nature of the genetic relationship between the accused and other possible perpetrators of the crime in the population. This paper develops ideas and methods for analysing data and evaluating LRs when the evidence is based on short tandem repeat profiles, with special emphasis placed on a Bayesian approach. These are then applied in the context of a particular quadruplex profiling system used for routine case-work by the UK Forensic Science Service.     

Maximum-likelihood estimation for the removal method

We prove that the profile log-likelihood function for the removal method of estimating population size is unimodal. The result is obtained by a variation-diminishing property of the Laplace transform. An implication of this result is that the likelihood-ratio confidence region for the population size is always an interval. Necessary and sufficient conditions for the existence of a finite maximum-likelihood estimator are presented. We also present evidence that the likelihood-ratio confidence interval for the population size has acceptable small-sample coverage properties.     

Grey seals red in tooth and claw: how Darwin helps model their population

Grey seals in Britain are a conservation success, brought back from the brink of extinction by protection in the early 20th century. The public love them. Fishermen hate them. The resurgence of the "grey guzzlers" threatens their livelihood, they say. Len Thomas shows how Charles Darwin's ideas are used to determine seal numbers and population dynamics. Surprisingly, Darwin's theories have also influenced the statistical tools that are used.     

Estimating the population median by nomination sampling

In nomination sampling, the largest values from several independent random samples (nominees) are rank ordered, and an estimate of the population median is formed by interpolating between 2 of these order statistics. The resulting estimate compares favorably to the sample median of a simple random sample from the same population. When historical data sets retain only extreme values, nomination sampling may offer the only practical way to estimate the population median. The approach may also be useful when potential survey respondents will only participate if they can actively influence the selection of cases for analysis.     

Practical performance of local likelihood for circular density estimation

ABSTRACT

Local likelihood has been mainly developed from an asymptotic point of view, with little attention to finite sample size issues. The present paper provides simulation evidence of how likelihood density estimation practically performs from two points of view. First, we explore the impact of the normalization step of the final estimate, second we show the effectiveness of higher order fits in identifying modes present in the population when small sample sizes are available. We refer to circular data, nevertheless it is easily seen that our findings straightforwardly extend to the Euclidean setting, where they appear to be somehow new.     

Assessing the Quality of Household Panel Data: The Case of the Panel Study of Income Dynamics

Evidence from a number of methodological studies are used to assess the overall quality of data from the Panel Study of Income Dynamics (PSID). Despite substantial cumulative non-response over the nearly two decades spanned by the study, the sample is found to maintain its representation of the nonimmigrant population of the United States. The most important reasons for this result are that the study's following rules insure that the sample replaces itself in the same manner as the population (through the formation of new families by the offspring of old) and that nonresponse is largely unsystematic. Nonresponse also appears to be largely random with respect to parameters in a number of behavioral models. The accuracy of measures is assessed by comparing survey measures with national aggregates and with highly accurate individual validating data. PSID reports of transfer income appear to compare more favorably with program aggregates than do reports from other large-scale surveys such as the Current Population Survey. Finally, although PSID survey measures generally are unbiased when compared to validating data, they contain amounts of measurement-error variance that range from trivially small to very large.     

Statistical methodology for assessing homology of intronic regions of genes

We consider the problem of statistically evaluating the similarity of DNA intronic regions of genes. Present algorithms are based on matching a sequence of interest with known DNA sequences in a gene bank and are designed primarily to assess homology among exonic regions of genes. Most research focuses on exonic regions because they have a clear biological significance, coding for proteins, and therefore tend to be more conserved in evolution than intronic regions. To investigate whether the intronic features of genes whose expression is highly sensitive to environmental perturbations differ from genes that have a more constant expression, a collection of oncogenes, tumor suppressor genes, and nonregulatory genes involved in energy metabolism are compared. An analysis of the features of these genes' intronic regions result in clustering by regulatory group. In addition, Billingsley's test for Markov structure (1961) suggests that 67% of the intronic regions in this collection of genes show evidence of nonrandom structure, indicating the possibility of a biological function for these regions. The result of Billingsley's test for homology is used as input to a clustering algorithm. The biological significance of this methodology lies in the identification of groups based on the intronic regions from genes of unknown function. With the advent of rapid sequencing techniques, there is a great need for statistical techniques to help identify the purpose of poorly understood portions of genes. These methods can be utilized to assess the functional group to which such a gene might possibly belong.     

On the determination of sizes of markets

The number of specialized dealers is of interest to market research institutes. They need those market sizes to project sample results to the whole population of shops. A basis to get to know the size of such a population is given by address registers. These registers contain also dead addresses and they are incorrect as they do not contain all addresses of existing shops. We present an approach to deal with these two kinds of errors and derive an estimator with negligible bias.     

Bayesian inference and data cloning in the calibration of population projection matrices

Discrete time models are used in Ecology for describing the dynamics of an age-structured population. They can be introduced from a deterministic or from a stochastic viewpoint. We analyze a stochastic model for the case in which the dynamics of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters which are estimated by using a Bayesian approach and also data cloning, which is a simulation-based method especially useful with complex hierarchical models.

Both methodologies are applied to real data from the population of Steller sea lions located in the Alaska coast since 1978–2004. The estimates obtained from these methods show a good behavior when they are compared to the nonmissing actual values.     

A Discrete-Time Multilevel Mixture Model for Event History Data with Long-Term Survivors,with an Application to an Analysis of Contraceptive Sterilization in Bangladesh

Event history models typically assume that the entire population is at risk of experiencing the event of interest throughout the observation period. However, there will often be individuals, referred to as long-term survivors, who may be considered a priori to have a zero hazard throughout the study period. In this paper, a discrete-time mixture model is proposed in which the probability of long-term survivorship and the timing of event occurrence are modelled jointly. Another feature of event history data that often needs to be considered is that they may come from a population with a hierarchical structure. For example, individuals may be nested within geographical regions and individuals in the same region may have similar risks of experiencing the event of interest due to unobserved regional characteristics. Thus, the discrete-time mixture model is extended to allow for clustering in the likelihood and timing of an event within regions. The model is further extended to allow for unobserved individual heterogeneity in the hazard of event occurrence. The proposed model is applied in an analysis of contraceptive sterilization in Bangladesh. The results show that a woman's religion and education level affect her probability of choosing sterilization, but not when she gets sterilized. There is also evidence of community-level variation in sterilization timing, but not in the probability of sterilization.     

Simultaneous upper confidence bounds for distances from the best two-parameter exponentlal distribution

Consider k independent exponential distributions possibly with different location parameters and a common scale parameter. If the best population is defined to be the one having the largest mean or equivalently having the largest location parameter, we then derive a set of simultaneous upper confidence bounds for all distances of the means from the largest one. These bounds not only can serve as confidence intervals for all distances from the largest parameter but they also can be used to identify the best population. Relationships to ranking and selection procedures are pointed out. Cases in which scale parameters are known or unknown and samples are complete or type II censored are considered. Tables to implement this procedure are given.     

Parameterized multistate population dynamics and projections

"This article reports progress on the development of a population projection process that emphasizes model selection over demographic accounting. Transparent multiregional/multistate population projections that rely on parameterized model schedules are illustrated [using data primarily from a number of developed countries, particularly Sweden], together with simple techniques that extrapolate the recent trends exhibited by the parameters of such schedules." The author notes that "the parameterized schedules condense the amount of demographic information, expressing it in a language and variables that are more readily understood by the users of the projections. In addition, they permit a concise specification of the expected temporal patterns of variation among these variables, and they allow a disaggregated focus on demographic change that otherwise would not be feasible."     

A Unified Approach of Meta-Analysis: Application to an Antecedent Biomarker Study in Alzheimer's Disease

This article provides a unified methodology of meta-analysis that synthesizes medical evidence by using both available individual patient data (IPD) and published summary statistics within the framework of likelihood principle. Most up-to-date scientific evidence on medicine is crucial information not only to consumers but also to decision makers, and can only be obtained when existing evidence from the literature and the most recent individual patient data are optimally synthesized. We propose a general linear mixed effects model to conduct meta-analyses when individual patient data are only available for some of the studies and summary statistics have to be used for the rest of the studies. Our approach includes both the traditional meta-analyses in which only summary statistics are available for all studies and the other extreme case in which individual patient data are available for all studies as special examples. We implement the proposed model with statistical procedures from standard computing packages. We provide measures of heterogeneity based on the proposed model. Finally, we demonstrate the proposed methodology through a real life example studying the cerebrospinal fluid biomarkers to identify individuals with high risk of developing Alzheimer's disease when they are still cognitively normal.     

A class of maximum-entropy multivariate distributions

This paper characterizes a class of multivariate distributions that includes the multinormal and is contained in the exponential family. The wide range of possible applications of these distributions is suggested by some of hte characteristics germane to them: First, they maximize Shannon's entropy among all distributions that have finite moments of given orders. As such, they constitute a class of distributions that includes the multinormal and some likely alternatives. Second, they can exhibit several modes, and, further-more, they do so with a relatively small number of parameters (compared to mixtures of multinormals). Third, they are the stationary distributions of certain diffusion processes. Fourth, they approximate, near the multinormal, the multivariate Pearson family. And fifth, the maximum likelihood estimators of their population moments are the sample moments. Two possible methods of estimating the distributions are studied in this paper: maximum likelihood estimation, and a fast procedure that can be used to find consistent estimators of the parameters via sample moments. A FORTTAN subroutine that implements the latter method is also provided.     

Evidence From Marginally Significant t Statistics

ABSTRACT

This article examines the evidence contained in t statistics that are marginally significant in 5% tests. The bases for evaluating evidence are likelihood ratios and integrated likelihood ratios, computed under a variety of assumptions regarding the alternative hypotheses in null hypothesis significance tests. Likelihood ratios and integrated likelihood ratios provide a useful measure of the evidence in favor of competing hypotheses because they can be interpreted as representing the ratio of the probabilities that each hypothesis assigns to observed data. When they are either very large or very small, they suggest that one hypothesis is much better than the other in predicting observed data. If they are close to 1.0, then both hypotheses provide approximately equally valid explanations for observed data. I find that p-values that are close to 0.05 (i.e., that are “marginally significant”) correspond to integrated likelihood ratios that are bounded by approximately 7 in two-sided tests, and by approximately 4 in one-sided tests.

The modest magnitude of integrated likelihood ratios corresponding to p-values close to 0.05 clearly suggests that higher standards of evidence are needed to support claims of novel discoveries and new effects.     

Simultaneous confidence intervals for one-way layout based on generalized pivotal quantities

In this paper, we consider simultaneous confidence intervals for all-pairwise comparisons of treatment means in a one-way layout under heteroscedasticity. Two kinds of simultaneous intervals are provided based on the fiducial generalized pivotal quantities of the interest parameters. We prove that they both have asymptotically correct coverage. Simulation results and an example are also reported. It is concluded from calculational evidence that the second kind of simultaneous confidence intervals, which we provide, performs better than existing methods.     

Weighing the Evidence for Hypotheses with Small Samples of Right-censored Exponential Data

The p-value evidence for an alternative to a null hypothesis regarding the mean lifetime can be unreliable if based on asymptotic approximations when there is only a small sample of right-censored exponential data. However, a guarded weight of evidence for the alternative can always be obtained without approximation, no matter how small the sample, and has some other advantages over p-values. Weights of evidence are defined as estimators of 0 when the null hypothesis is true and 1 when the alternative is true, and they are judged on the basis of the ensuing risks, where risk is mean squared error of estimation. The evidence is guarded in that a preassigned bound is placed on the risk under the hypothesis. Practical suggestions are given for choosing the bound and for interpreting the magnitude of the weight of evidence. Acceptability profiles are obtained by inversion of a family of guarded weights of evidence for two-sided alternatives to point hypotheses, just as confidence intervals are obtained from tests; these profiles are arguably more informative than confidence intervals, and are easily determined for any level and any sample size, however small. They can help understand the effects of different amounts of censoring. They are found for several small size data sets, including a sample of size 12 for post-operative cancer patients. Both singly Type I and Type II censored examples are included. An examination of the risk functions of these guarded weights of evidence suggests that if the censoring time is of the same magnitude as the mean lifetime, or larger, then the risks in using a guarded weight of evidence based on a likelihood ratio are not much larger than they would be if the parameter were known.