Estimating relatedness between individuals in general populations with a focus on their use in conservation programs

Relatedness estimators are widely used in genetic studies, but effects of population structure on performance of estimators, criteria to evaluate estimators, and benefits of using such estimators in conservation programs have to date received little attention. In this article we present new estimators, based on the relationship between coancestry and molecular similarity between individuals, and compare them with existing estimators using Monte Carlo simulation of populations, either panmictic or structured. Estimators were evaluated using statistical criteria and a diversity criterion that minimized relatedness. Results show that ranking of estimators depends on the population structure. An existing estimator based on two-gene and four-gene coefficients of identity performs best in panmictic populations, whereas a new estimator based on coancestry performs best in structured populations. The number of marker alleles and loci did not affect ranking of estimators. Statistical criteria were insufficient to evaluate estimators for their use in conservation programs. The regression coefficient of pedigree relatedness on estimated relatedness (beta2) was substantially lower than unity for all estimators, causing overestimation of the diversity conserved. A simple correction to achieve beta2 = 1 improves both existing and new estimators. Using relatedness estimates with correction considerably increased diversity in structured populations, but did not do so or even decreased diversity in panmictic populations.     

A Generalized Class of Synthetic Estimators with Application to Crop Acreage Estimation for Small Domains

This paper defines and discusses a generalized class of synthetic estimators for small domains, using auxiliary information, under simple random sampling and stratified random sampling schemes. The generalized class of synthetic estimators, among others, includes the simple, ratio and product synthetic estimators. The proposed class of synthetic estimators gives consistent estimators if the synthetic assumption holds. Further, it demonstrates the use of the generalized synthetic and ratio synthetic estimators for estimating crop acreage for small domains and also compare their relative performance with direct estimators, empirically, through a simulation study.     

Estimation of a common effect parameter from sparse follow-up data

Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.     

The Utilization of Kurtosis in the Estimation of the Parameters of the One‐Way Random Effects Model

This paper deals with the problem of estimating the components of the variance of one‐way random effects model under non‐normality situation using a prior knowledge of coefficient of kurtosis. We have suggested two classes of estimators and for the within and between variances respectively. Optimum estimators in the classes of and are identified with their mean squared errors formulae and compared with that of usual ANOVA unbiased and Shoukri , Tracy and Mian 's (1990) estimators. It is found that the proposed estimators are more efficient than the ANOVA unbiased estimators and Shoukri , Tracy and Mian (1990) estimators.     

Nonparametric estimation for the three-stage irreversible illness-death model

In this paper, we present new nonparametric estimators of the stage-occupation probabilities in the three-stage irreversible illness-death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage-dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study.     

Estimating the Tumour Onset Distribution Using Kernel Estimators

Kernel estimators are used to obtain new estimators for the tumour onset distribution and its density. Asymptotical properties of the estimators are studied and confidence tests are constructed.     

Improved variance estimators for one- and two-parameter models of nucleotide substitution

The current variance estimators for Jukes and Cantor's one-parameter model and Kimura's two-parameter model tend to underestimate the true variances when the true proportion of differences between the two sequences under study is not small. In this paper, we developed improved variance estimators, using a higher-order Taylor expansion and empirical methods. The new estimators outperform the conventional estimators and provide accurate estimates of the true variances.     

Limits to the estimation of species richness: The use of relative abundance distributions

The present study demonstrates the possibility of estimating species numbers of animal or plant communities from samples using relative abundance distributions. We use log‐abundance–species‐rank order plots and derive two new estimators that are based on log‐series and lognormal distributions. At small to moderate sample sizes these estimators appear to be more precise than previous parametric and nonparametric estimators. We test our estimators using samples from 171 published medium‐sized to large animal and plant communities taken from the literature. By this we show that our new estimators define also limits of precision.     

Estimation of a Concordance Probability for Doubly Censored Time-to-Event Data

Evaluating the relationship between a response variable and explanatory variables is important to establish better statistical models. Concordance probability is one measure of this relationship and is often used in biomedical research. Concordance probability can be seen as an extension of the area under the receiver operating characteristic curve. In this study, we propose estimators of concordance probability for time-to-event data subject to double censoring. A doubly censored time-to-event response is observed when either left or right censoring may occur. In the presence of double censoring, existing estimators of concordance probability lack desirable properties such as consistency and asymptotic normality. The proposed estimators consist of estimators of the left-censoring and the right-censoring distributions as a weight for each pair of cases, and reduce to the existing estimators in special cases. We show the statistical properties of the proposed estimators and evaluate their performance via numerical experiments.     

Efficient Utilization of Auxiliary Information at Estimation Stage

Modified ratio or product estimators are suggested by making use of a very simple linear transformation on the auxiliary variable, which allows for a wider applicability of the modified estimators than that of customary ratio and product estimators.     

Optimal estimator for the survival distribution and related quantities for treatment policies in two-stage randomization designs in clinical trials

Two-stage designs, where patients are initially randomized to an induction therapy and then depending upon their response and consent, are randomized to a maintenance therapy, are common in cancer and other clinical trials. The goal is to compare different combinations of primary and maintenance therapies to find the combination that is most beneficial. In practice, the analysis is usually conducted in two separate stages which does not directly address the major objective of finding the best combination. Recently Lunceford, Davidian, and Tsiatis (2002, Biometrics58, 48-57) introduced ad hoc estimators for the survival distribution and mean restricted survival time under different treatment policies. These estimators are consistent but not efficient, and do not include information from auxiliary covariates. In this article we derive estimators that are easy to compute and are more efficient than previous estimators. We also show how to improve efficiency further by taking into account additional information from auxiliary variables. Large sample properties of these estimators are derived and comparisons with other estimators are made using simulation. We apply our estimators to a leukemia clinical trial data set that motivated this study.     

Discrete-time nonlinear observer-based estimators for the on-line estimation of the kinetic rates in bioreactors

Simple discrete-time estimators which allow the on-line estimation of the kinetic rates from the measurements of components' concentrations inside a bioreactor are proposed. In fact, the proposed estimators are obtained by a direct forward Euler discretization of continuous-time estimators. The design of the estimators in the continuous as well as in the discrete-time does not require or assume any model for the kinetic rates. One of the main characteristics of these estimators lies in the easiness of their calibration. We here emphasize on the performances of the discrete version of these estimators, whose stability and convergence are proved under the same conditions as in the continuous case with an additional mild assumption on the sampling time. Simulation and real-life experiments results corresponding to the discrete estimation are given. The accuracy of the obtained estimates as well as the easiness of the estimators' implementation do constitute reliable and powerful arguments for their use, in particular in adaptive control schemes.     

Nonlinear mixed effects models for repeated measures data

We propose a general, nonlinear mixed effects model for repeated measures data and define estimators for its parameters. The proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood (or restricted maximum likelihood) estimators for linear mixed effects models. We implement Newton-Raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models. Two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed.     

Inferring admixture proportions from molecular data

We derive here two new estimators of admixture proportions based on a coalescent approach that explicitly takes into account molecular information as well as gene frequencies. These estimators can be applied to any type of molecular data (such as DNA sequences, restriction fragment length polymorphisms [RFLPs], or microsatellite data) for which the extent of molecular diversity is related to coalescent times. Monte Carlo simulation studies are used to analyze the behavior of our estimators. We show that one of them (mY) appears suitable for estimating admixture from molecular data because of its absence of bias and relatively low variance. We then compare it to two conventional estimators that are based on gene frequencies. mY proves to be less biased than conventional estimators over a wide range of situations and especially for microsatellite data. However, its variance is larger than that of conventional estimators when parental populations are not very differentiated. The variance of mY becomes smaller than that of conventional estimators only if parental populations have been kept separated for about N generations and if the mutation rate is high. Simulations also show that several loci should always be studied to achieve a drastic reduction of variance and that, for microsatellite data, the mean square error of mY rapidly becomes smaller than that of conventional estimators if enough loci are surveyed. We apply our new estimator to the case of admixed wolflike Canid populations tested for microsatellite data.      

Estimating selective advantage of two alleles in discrete time

A class of estimators for the selective advantage, s, in a Wright-Fisher model with two alleles, variable population size, and genic selection is derived via martingale theory. Explicit expressions are given for these estimators which only involve simple computation. The optimal estimate among this class of estimators is obtained. Asymptotic results are readily established by an application of a martingale central limit theorem. The performance of this optimal estimator is compared to known estimators by means of a simulation study.     

An Estimate of the Variance of Estimators for Lead Time and Screening Benefit Time in Randomized Cancer Screening Trials

Variance estimators are derived for estimators of the average lead time and average benefit time due to screening in a randomized screening trial via influence functions. The influence functions demonstrate that these estimators are asymptotically equivalent to the mean difference, between the study and control case groups, in the appropriate survival times. For estimating benefit time, the survival time is measured since start of study; for estimating lead time, the survival time is measured since time of diagnosis. Asymptotic variances of these estimators can be calculated in a straightforward manner from the influence functions, and these variances can be estimated from actual trial data. The performance of the variance estimators is assessed via a simulated screening trial. The situation involving censored data is also discussed.     

2SUR回归模型系数估计的优良性比较

对于2SUR回归模型的参数估计问题,给出了一些一般均方误差矩阵比较结果,据此提出了一类线性估计和一类基于离差阵广义非限定估计的非线性两步估计,并获得了该两步估计类的一些有限样本性质。     

Homogeneity/Heterogeneity Hypotheses for Standardized Mortality Ratios Based on Minimum Power‐divergence Estimators

This paper analyzes the power divergence estimators when homogeneity/heterogeneity hypotheses among standardized mortality ratios (SMRs) are taken into account. A Monte Carlo study shows that when the standard mortality rate is not external, that is it is estimated from the sample data, these estimators have a good performance even for small sample sets and in particular the minimum chi‐square estimators have a better behavior compared to the classical maximum likelihood estimators. In order to make decisions under homogeneity/heterogeneity hypotheses of SMRs we propose some test‐statistics which consider the minimum power divergence estimators. Through a numerical example focused on SMRs of melanoma mortality ratios in different regions of the US, a homogeneity/heterogeneity study is illustrated.     

Estimating the richness of species with variable mobility

The vast majority of species are animals that, unlike most plants and fungi, are variably and often highly mobile. While species' mobility affects species' probabilities of being sampled, effects of movement on the estimation of species richness have yet to be systematically investigated. Information-rich abundance-based estimators may be able to address variably mobile species but the accuracy of these estimators has also yet to be investigated. Here, we address both issues by variably sampling simulated landscapes with up to 250 species and evaluating the performance of ten non-parametric estimators and one species accumulation curve. Our results show that some abundance-based estimators are as accurate as better known and tested incidence-based estimators. Increased movement heterogeneity between the species reduced estimator performance by reducing the sample coverage, which systematically determined which estimator was most accurate. Based on these findings, we present the first decision framework for choosing the most accurate of many available abundance-based species-richness estimators. These decisions, based on data coverage, can significantly improve investigators' ability to estimate faunal species richness.     

Detecting Trait-Dependent Diversification Under Diversification Slowdowns

Testing whether a certain biological trait significantly affects clade diversification is central to macroevolutionary research. To this end, many scientists use constant-rate estimators (CR estimators) of diversification. However, it has never been examined whether these estimators report meaningful relationships between traits and diversification even when the diversification itself decelerates over time. In this study, I simulate trait-driven diversification concurrently with diversification slowdowns. Then, I test whether CR estimators manage to uncover the simulated relationships. Results suggest that CR estimators are robust against violation of rate constancy and successfully detect trait-dependent diversification in spite of diversification declines. Interestingly, correct results were recovered whether clade age correlated with clade diversity or not. Further comparison of CR estimators with QuaSSE suggested that QuaSSE performs better under constant diversification, but tends to report spuriously significant outcomes when diversification decelerates (=elevated Type I error). Given that diversification slowdowns have been recently reported for a wide range of taxa, these findings may be of particular relevance for future diversification studies.