Accuracy of the endpoint assay for virus titration

The statistics of estimators used with the endpoint assay for virus titration were investigated. For a standard assay with 10 wells/dilution, the graphical estimator traditionally used was found to produce estimates with significant positive bias and a relatively low accuracy. Furthermore, the graphical estimator was found to be inconsistent. A superior estimator based on the maximum likelihood principle was developed. The results are discussed in relation to the choice between the endpoint titration assay and the plaque assay, and an alternative two-stage assay is presented.     

A comparison of non-iterative and iterative estimators of heterogeneity variance for the standardized mortality ratio

This paper continues work presented in B?hning et al. (2002b, Annals of the Institute of Statistical Mathematics 54, 827-839, henceforth BMSRB) where a class of non-iterative estimators of the variance of the heterogeneity distribution for the standardized mortality ratio was discussed. Here, these estimators are further investigated by means of a simulation study. In addition, iterative estimators including the Clayton-Kaldor procedure as well as the pseudo-maximum-likelihood (PML) approach are added in the comparison. Among all candidates, the PML estimator often has the smallest mean square error, followed by the non-iterative estimator where the weights are proportional to the external expected counts. This confirms the theoretical result in BMSRB in which an asymptotic efficiency could be proved for this estimator (in the class of non-iterative estimators considered). Surprisingly, the Clayton-Kaldor iterative estimator (often recommended and used by practitioners) performed poorly with respect to the MSE. Given the widespread use of these estimators in disease mapping, medical surveillance, meta-analysis and other areas of public health, the results of this study might be of considerable interest.     

Estimation of a common odds ratio in case-control studies of familial aggregation

A new estimator of a common odds ratio is proposed for case-control studies of familial aggregation. The proposed estimator is a modification to the usual Mantel-Haenszel estimator that relies on an empirical adjustment for the within-family clustering which is typical of such designs. A simulation study shows that the estimator tends to have smaller mean squared error than the unmodified Mantel-Haenszel estimator under conditions likely to arise in practice. The construction of confidence intervals is also discussed.     

二次等距抽样

本文提出了一种二次等距抽样方法,并提出了总体平均值的一个估计量：拼配部分的比型估计与轮换部分的样本均值的加权平均。当样本量较大时,求出了估计量的方差及最优轮换比．并对特殊情形进行了讨论和数值比较．     

Analysis of Covariance in Split Block Design

In this paper the analysis of covariance in the split block design with many concomitant variables is presented. The problems concerning the estimation of parametric functions and testing hypotheses are discussed. In the presentation of the model three kinds of regression coefficients for individual sources of variation are taken into consideration. It is shown that for every estimable function of fixed effects, the best linear unbiased estimator under the assumed model is the same as the best linear unbiased estimator under the model with covariance matrix equal to identity matrix multiplied by a positive constant. A variance of this estimator can be calculated by the method presented here. Test functions for standard hypotheses concerning fixed effects are obtained.     

Estimating the Mahalanobis distance from mixed continuous and discrete data

We present a method for estimating the Mahalanobis distance between two multivariate normal populations when a subset of the measurements is observed as ordered categorical responses. Asymptotic properties of the proposed estimator are developed. Two examples are discussed.     

Logistic regression in capture-recapture models

The effect of population heterogeneity in capture-recapture, or dual registration, models is discussed. An estimator of the unknown population size based on a logistic regression model is introduced. The model allows different capture probabilities across individuals and across capture times. The probabilities are estimated from the observed data using conditional maximum likelihood. The resulting population estimator is shown to be consistent and asymptotically normal. A variance estimator under population heterogeneity is derived. The finite-sample properties of the estimators are studied via simulation. An application to Finnish occupational disease registration data is presented.     

On the Estimation of the Mean with Random Number Of Observations. (Comments on a Paper by M. Singh and V. K. Gupta)

In this paper we study the problem of estimating the mean when the number of observations taken on each unit is a random variable. The estimator proposed by M. Singh and V. K. Gupta (1980) is discussed and modified. It is argued, however, that the arithmetic mean is a more appropriate choice of estimator.     

A Monte Carlo evaluation of five interval estimators for the relative risk in sparse data

The relative risk (RR) is one of the most frequently used indices to measure the strength of association between a disease and a risk factor in etiological studies or the efficacy of an experimental treatment in clinical trials. In this paper, we concentrate attention on interval estimation of RR for sparse data, in which we have only a few patients per stratum, but a moderate or large number of strata. We consider five asymptotic interval estimators for RR, including a weighted least-squares (WLS) interval estimator with an ad hoc adjustment procedure for sparse data, an interval estimator proposed elsewhere for rare events, an interval estimator based on the Mantel-Haenszel (MH) estimator with a logarithmic transformation, an interval estimator calculated from a quadratic equation, and an interval estimator derived from the ratio estimator with a logarithmic transformation. On the basis of Monte Carlo simulations, we evaluate and compare the performance of these five interval estimators in a variety of situations. We note that, except for the cases in which the underlying common RR across strata is around 1, using the WLS interval estimator with the adjustment procedure for sparse data can be misleading. We note further that using the interval estimator suggested elsewhere for rare events tends to be conservative and hence leads to loss of efficiency. We find that the other three interval estimators can consistently perform well even when the mean number of patients for a given treatment is approximately 3 patients per stratum and the number of strata is as small as 20. Finally, we use a mortality data set comparing two chemotherapy treatments in patients with multiple myeloma to illustrate the use of the estimators discussed in this paper.     

Estimating the number of species in a stochastic abundance model

Consider a stochastic abundance model in which the species arrive in the sample according to independent Poisson processes, where the abundance parameters of the processes follow a gamma distribution. We propose a new estimator of the number of species for this model. The estimator takes the form of the number of duplicated species (i.e., species represented by two or more individuals) divided by an estimated duplication fraction. The duplication fraction is estimated from all frequencies including singleton information. The new estimator is closely related to the sample coverage estimator presented by Chao and Lee (1992, Journal of the American Statistical Association 87, 210-217). We illustrate the procedure using the Malayan butterfly data discussed by Fisher, Corbet, and Williams (1943, Journal of Animal Ecology 12, 42-58) and a 1989 Christmas Bird Count dataset collected in Florida, U.S.A. Simulation studies show that this estimator compares well with maximum likelihood estimators (i.e., empirical Bayes estimators from the Bayesian viewpoint) for which an iterative numerical procedure is needed and may be infeasible.     

Uniformly minimum variance unbiased estimation of gene diversity

Gene diversity is an important measure of genetic variability in inbred populations. The survival of species in changing environments depends on, among other factors, the genetic variability of the population. In this communication, I have derived the uniformly minimum variance unbiased estimator of gene diversity. The proposed estimator of gene diversity does not assume that the inbreeding coefficient is known. I have also provided the approximate variance of this estimator according to Fisher's method. In addition, I have developed a numerical resampling-based method for obtaining variances and confidence intervals based on the maximum likelihood estimator and the uniformly minimum variance unbiased estimator. Efficiency in estimation of the gene diversity based on these two estimators is discussed. In accordance with the simulation results, I found that the uniformly minimum variance estimator developed in this report is more accurate for estimation of gene diversity than the maximum likelihood estimator.     

Nonparametric estimation of the causal effect of a stochastic threshold-based intervention

Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. In view of this goal, we consider a covariate-adjusted threshold-based interventional estimand, which happens to equal the binary treatment–specific mean estimand from the causal inference literature obtained by dichotomizing the continuous biomarker or treatment as above or below a threshold. The unadjusted version of this estimand was considered in Donovan et al.. Expanding upon Stitelman et al., we show that this estimand, under conditions, identifies the expected outcome of a stochastic intervention that sets the treatment dose of all participants above the threshold. We propose a novel nonparametric efficient estimator for the covariate-adjusted threshold-response function for the case of informative outcome missingness, which utilizes machine learning and targeted minimum-loss estimation (TMLE). We prove the estimator is efficient and characterize its asymptotic distribution and robustness properties. Construction of simultaneous 95% confidence bands for the threshold-specific estimand across a set of thresholds is discussed. In the Supporting Information, we discuss how to adjust our estimator when the biomarker is missing at random, as occurs in clinical trials with biased sampling designs, using inverse probability weighting. Efficiency and bias reduction of the proposed estimator are assessed in simulations. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.     

The tuning of a model-based estimator for the specific growth rate of Candida utilis

Control of microbial conversion processes is frequently inhibited by the infeasibility of measuring important process variables. In order to circumvent this lack of measurements, an accurate or valuable and conveniently measurable on-line hardware measurement can be combined with the balance equations describing the process to obtain estimates of less easily measurable variables. In this article the on-line estimation of the specific growth rate of Candida utilis is evaluated. The observer-based estimator requires a hardware measurement of the biomass during fermentations in conjuction with a model of the process; therefore the Biomass Monitor, giving an on-line measurement of viable biomass, is used in the bioreactor experiments described. The optimal tuning of the estimation for the experimental conditions is described and several alternative adaptations of the design of the estimator are presented. The influence of implemented time intervals for discretization of the estimator on the reliability of the estimated growth rate values is discussed. Additionally, the necessary choice of an initial value of the estimated specific growth rate has proven to be of great importance in practice.     

Can minimum convex polygon home ranges be used to draw biologically meaningful conclusions?

Many conclusions about mammalian ranging behaviour have been drawn based on minimum convex polygon (MCP) estimates of home range size, although several studies have revealed its unpredictable nature compared to that of the kernel density estimator. We investigated to what extent the choice of home range estimator affected the biological interpretation in comparative studies. We found no discrepancy when the question asked covered a wide range of taxa, as real and very large differences in range size were likely to have masked smaller differences due to the choice of home range estimator. However, when the question asked concerned within-species characteristics, the choice of home range estimator explained as much of the variation in range size as did the ecological variable in question. The implications for macro-ecological and intraspecific studies are discussed.     

Asymptotically efficient two-step estimators of the hazards ratio for follow-up studies and survival data

Asymptotically efficient estimators of a common hazard rate ratio (for follow-up studies) and the proportional hazards ratio (for survival studies) are obtained by a single iteration of the "Mantel-Haenszel" estimator appropriate for each setting. Estimators of their variance are also developed. The two-step estimator for survival data and its variance estimator are shown by simulation to be minimally biased and the estimator is shown to be efficient relative to the Cox partial likelihood estimator in small samples.     

A Note on Balanced Sampling and Robust Genetic Predictors

The concept of balanced sampling is applied to prediction in finite samples using model based inference procedures. Necessary and sufficient conditions are derived for a general linear model with arbitrary covariance structure to yield the expansion estimator as the best linear unbiased predictor for the mean. The analysis is extended to produce a robust estimator for the mean squared error under balanced sampling and the results are discussed in the context of statistical genetics where appropriate sampling produces simple efficient and robust genetic predictors free from unnecessary genetic assumptions.     

On the use of concordant pairs in matched case-control studies

A new estimator of the common odds ratio in one-to-one matched case-control studies is proposed. The connection between this estimator and the James-Stein estimating procedure is highlighted through the argument of estimating functions. Comparisons are made between this estimator, the conditional maximum likelihood estimator, and the estimator ignoring the matching in terms of finite sample bias, mean squared error, coverage probability, and length of confidence interval. In many situations, the new estimator is found to be more efficient than the conditional maximum likelihood estimator without being as biased as the estimator that ignores matching. The extension to multiple risk factors is also outlined.     

A critical look at some widely used estimators in mark-resighting experiments

1. For many species and circumstances, mark-resighting procedures constitute valid alternatives to capture-recapture methods. Indeed, resightings are generally cheaper to acquire than physically recapturing and rehandling the animals, especially when radiotelemetry or other tracking devices are available. 2. In order to estimate population abundance, the joint hypergeometric maximum likelihood estimator, the Minta-Mangel estimator and the Bowden estimator are implemented in noremark, software which has become very popular with biologists in the past decade. 3. In this paper, the basic assumptions regarding these widely applied procedures are delineated and discussed. A simulation study is performed in order to investigate the robustness of the estimators under failure of the assumptions. 4. Theoretical considerations and simulation results motivate the use of the Bowden estimator which, when marks are distributed quite evenly among groups, constitutes the sole reliable method, offering computational simplicity and robustness. On the other hand, if the marks are distributed unevenly, no mark-resighting procedure seems reliable. An application to a case study is considered.     

一维响应变量时最高无毒副作用剂量水平的识别

在毒性试验中,将暴露在某一剂量水平下的处理组与接受相当于零剂量处理的对照组相比,随着药物剂量的增加,感兴趣的变量通常会呈现一种递增的趋势。考虑不会导致风险显著增加的最高剂量,本文使用AIC(Akaike information criterion)方法得到该剂量水平的强相合估计,并且通过两组数据及模拟的结果来说明AIC方法的优良性.     

利用多重抽样估计稀有物种的种类数

利用矩估计和二个稳健估计方法（jackknife估计,bootstrap估计）来处理野外生态学工作者的调查数据,在假定已经发现一些稀有物种的情形下,通过统计推断得到那些未被发现的物种的种类数。利用本文所提出的方法调查水稻水稻田的昆虫群落和林地的在面植被群落的稀有种是十分有效的。