Symmetric Intervals and Confidence Intervals

We show that the symmetric “confidence intervals” of WESTLAKE (1972, 1976), widely used and referred to in bioequivalence studies, are not confidence intervals in any accepted sense. Nevertheless, meaningful symmetric intervals can be constructed in the context of Bayesian or fiducial inference.     

自花授粉作物杂交育种组合潜势的预测和比较

在黄花烟草Nicotiana russica中,开花期这一性状用V_5作亲本可能产生较大变异,无论是选择早开花的还是选择迟开花的,都有较大机会得到理想目标株系;对于株高这一性状,含有V(?)的组合可望有较大机会产生高于标准品种的株系。通过组合间育种潜势的比较,能了解各亲本中基因分布的基本情况,进而进行客观评价并对杂交组合做出取舍。试验证明,用一个组合的早期世代的参数m和D来预测高世代或纯系的育种潜势是可行的。     

A method to construct confidence interval for expected response to multi-trait selection

Summary Confidence intervals are constructed for the expected responses to three types of multi-trait selection. The influence of numbers of replicates and genotypes used in a progeny test experiment on the precision of response of multi-trait selection is discussed based on the structure of the established intervals. Special attention is paid to the characteristics of the intervals constructed for the conventional least square selection indices.     

Approximate Confidence Interval on Ratio of Two Variances in a Two-way Crossed Model

The model considered is a two-factor cross-classification variance components model with one observation per cell. Let the two factors be A and B, the problem is to obtain an approximate confidence interval for the ratio of variance component A over variance component B. In this paper, a method of solving this problem is established and simulations are performed to check the method.     

A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y = α + βx + ? (model I) of linear regression we dealt with in KUHNERT and HORN (1980) the determination of a confidence interval for that x₀ where the expectation Ey reaches a given value y₀. Here we start with realizations of random variables y (i = 1,…, m) being independent of x which are given in addition to the realizations of-y. Now y₀ denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ciEy and x₀ the x-value where the expectation Ey reaches that value y₀. For this x₀ we give a confidence interval. Applications stem from dose response assays.     

An interval estimation of expected response to selection

Summary A method is presented here for obtaining an interval estimate of expected response to selection based on results of a progeny test experiment. The structure of the constructed confidence limits is then examined for the influence of the numbers of lines and replicates on the precision of predicting the expected response to selection.     

Normative cervical spine kinematics of a circumduction task

Neck pain is a prevalent condition and clinical examination techniques are limited and unable to assess out-of-plane motion. Recent works investigating cervical kinematics during neck circumduction (NC), a dynamic 3D task, has shown the ability to discern those with and without neck pain. The purposes of this study were to establish 1) confidence and prediction intervals of head-to-torso kinematics during NC in a healthy cohort, 2) a baseline summative metric to quantify the duration and magnitude of deviations outside the prediction interval, and 3) the reliability of NC. Thirty-nine participants (25.6 ± 6.3 years, 19F/20M) without neck pain completed left and right NC. A two-way smoothing spline analysis of variance was utilized to determine the mean-fitted values and 90% confidence and prediction intervals for NC. A standardized effect size was calculated and aggregated across all axes (Delta RMSD aggregate), as a summative metric of motion quality. Confidence and prediction intervals were comparable for left and right NC and demonstrated excellent reliability. The average sum of the Delta RMSD aggregate was 2.76 ± 0.55 for left NC and 2.74 ± 0.63 for right NC. The results of this study demonstrate the feasibility of utilizing normative intervals of a NC task to assess head-to-torso kinematics.     

Comparing biomarker measurements to a normal range: when to use standard error of the mean (SEM) or standard deviation (SD) confidence intervals tests

This commentary is the second of a series outlining one specific concept in interpreting biomarkers data. In the first, an observational method was presented for assessing the distribution of measurements before making parametric calculations. Here, the discussion revolves around the next step, the choice of using standard error of the mean or the calculated standard deviation to compare or predict measurement results     

The empirical coverage of confidence intervals: Point estimates and confidence intervals for confidence levels

Many confidence intervals calculated in practice are potentially not exact, either because the requirements for the interval estimator to be exact are known to be violated, or because the (exact) distribution of the data is unknown. If a confidence interval is approximate, the crucial question is how well its true coverage probability approximates its intended coverage probability. In this paper we propose to use the bootstrap to calculate an empirical estimate for the (true) coverage probability of a confidence interval. In the first instance, the empirical coverage can be used to assess whether a given type of confidence interval is adequate for the data at hand. More generally, when planning the statistical analysis of future trials based on existing data pools, the empirical coverage can be used to study the coverage properties of confidence intervals as a function of type of data, sample size, and analysis scale, and thus inform the statistical analysis plan for the future trial. In this sense, the paper proposes an alternative to the problematic pretest of the data for normality, followed by selection of the analysis method based on the results of the pretest. We apply the methodology to a data pool of bioequivalence studies, and in the selection of covariance patterns for repeated measures data.     

Estimation of the incubation period of influenza A (H1N1-2009) among imported cases: addressing censoring using outbreak data at the origin of importation

Empirical estimates of the incubation period of influenza A (H1N1-2009) have been limited. We estimated the incubation period among confirmed imported cases who traveled to Japan from Hawaii during the early phase of the 2009 pandemic (n=72). We addressed censoring and employed an infection-age structured argument to explicitly model the daily frequency of illness onset after departure. We assumed uniform and exponential distributions for the frequency of exposure in Hawaii, and the hazard rate of infection for the latter assumption was retrieved, in Hawaii, from local outbreak data. The maximum likelihood estimates of the median incubation period range from 1.43 to 1.64 days according to different modeling assumptions, consistent with a published estimate based on a New York school outbreak. The likelihood values of the different modeling assumptions do not differ greatly from each other, although models with the exponential assumption yield slightly shorter incubation periods than those with the uniform exposure assumption. Differences between our proposed approach and a published method for doubly interval-censored analysis highlight the importance of accounting for the dependence of the frequency of exposure on the survival function of incubating individuals among imported cases. A truncation of the density function of the incubation period due to an absence of illness onset during the exposure period also needs to be considered. When the data generating process is similar to that among imported cases, and when the incubation period is close to or shorter than the length of exposure, accounting for these aspects is critical for long exposure times.     

重复力估计值的概率分布及其假设检验和区间估计

本文用概率论的方法导出了重复力估计值的概率分布密度函数,并对重复力的假设检验和区间估计也进行了讨论。     

Unbiased Confidence Intervals for the Odds Ratio of Two Independent Binomial Samples with Application to Case–Control Data

The problem of confidence interval construction for the odds ratio of two independent binomial samples is considered. Two methods of eliminating the nuisance parameter from the exact likelihood, conditioning and maximization, are described. A conditionally exact tail method exists by putting together upper and lower bounds. A shorter interval can be obtained by simultaneous consideration of both tails. We present here new methods that extend the tail and simultaneous approaches to the maximized likelihood. The methods are unbiased and applicable to case-control data, for which the odds ratio is important. The confidence interval procedures are compared unconditionally for small sample sizes in terms of their expected length and coverage probability. A Bayesian confidence interval method and a large-sample chi2 procedure are included in the comparisons.     

Generalized inferences on the overall treatment effect in meta-analysis with normally distributed outcomes

This paper focuses on inferences about the overall treatment effect in meta-analysis with normally distributed responses based on the concepts of generalized inference. A refined generalized pivotal quantity based on t distribution is presented and simulation study shows that it can provide confidence intervals with satisfactory coverage probabilities and perform hypothesis testing with satisfactory type-I error control at very small sample sizes.