Inference Procedures for Assessing Interobserver Agreement among Multiple Raters

We propose a new procedure for constructing inferences about a measure of interobserver agreement in studies involving a binary outcome and multiple raters. The proposed procedure, based on a chi-square goodness-of-fit test as applied to the correlated binomial model (Bahadur, 1961, in Studies in Item Analysis and Prediction, 158-176), is an extension of the goodness-of-fit procedure developed by Donner and Eliasziw (1992, Statistics in Medicine 11, 1511-1519) for the case of two raters. The new procedure is shown to provide confidence-interval coverage levels that are close to nominal over a wide range of parameter combinations. The procedure also provides a sample-size formula that may be used to determine the required number of subjects and raters for such studies.     

Confidence Interval of a Proportion with Over‐dispersion

A new approach that extends the classical Clopper‐Pearson procedure is proposed for the estimation of the (1–α)% confidence interval of a proportion with over‐dispersion. Over‐dispersion occurs when a proportion of interest shows more variation (variance inflation) than predicted by the binomial distribution. There are two steps in the approach. The first step consists of the estimation of the variance inflation factor. In the second step, an extended Clopper‐Pearson procedure is applied to calculate the confidence interval after the effective sample size is obtained by adjusting with the estimated variance inflation factor. The performance of the extended Clopper‐Pearson procedure is evaluated via a Monte Carlo study under the setup motivated from head lice studies. It is demonstrated that the 95% confidence intervals constructed from the new approach generally have the closest coverage rate to target (95%) when compared with those constructed from competing procedures.     

A new method for choosing sample size for confidence interval-based inferences

Scientists often need to test hypotheses and construct corresponding confidence intervals. In designing a study to test a particular null hypothesis, traditional methods lead to a sample size large enough to provide sufficient statistical power. In contrast, traditional methods based on constructing a confidence interval lead to a sample size likely to control the width of the interval. With either approach, a sample size so large as to waste resources or introduce ethical concerns is undesirable. This work was motivated by the concern that existing sample size methods often make it difficult for scientists to achieve their actual goals. We focus on situations which involve a fixed, unknown scalar parameter representing the true state of nature. The width of the confidence interval is defined as the difference between the (random) upper and lower bounds. An event width is said to occur if the observed confidence interval width is less than a fixed constant chosen a priori. An event validity is said to occur if the parameter of interest is contained between the observed upper and lower confidence interval bounds. An event rejection is said to occur if the confidence interval excludes the null value of the parameter. In our opinion, scientists often implicitly seek to have all three occur: width, validity, and rejection. New results illustrate that neglecting rejection or width (and less so validity) often provides a sample size with a low probability of the simultaneous occurrence of all three events. We recommend considering all three events simultaneously when choosing a criterion for determining a sample size. We provide new theoretical results for any scalar (mean) parameter in a general linear model with Gaussian errors and fixed predictors. Convenient computational forms are included, as well as numerical examples to illustrate our methods.     

Estimating the Population Mean Using Extreme Ranked Set Sampling

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean. ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.     

Estimation of heritability from varietal trials data

We present the estimation of heritabilities of an observed trait in situations where evaluation of several pure breeding lines is performed in a trial at a single location and in trials from several locations. For the single location situation, we evaluate exact confidence intervals, the probability of invalid estimates, and the percentage points of the distribution of heritability. Simulations were performed to numerically verify the results. Additionally, approximations to the bias and standard error of the estimate were obtained and are presented along with their simulated values and coefficients of skewness and kurtosis. For trials in several locations, explicit expressions for exact values of confidence limits are not available. Further, one would require knowledge of one more parameter, represented by the ratio of genotype x environment (G x E) interaction variance to error variance, in addition to the number of genotypes, replication and true heritability value. Approximations were made for bias and the standard error of estimates of heritability. The evaluation of the distribution of heritability and its moments was recognized as a problem of the linear function of an independent chi-square. The methods have been illustrated by data from experiments on grain and straw yield of 64 barley genotypes evaluated at three locations.     

Interval Estimation of Simple Difference in Dichotomous Data with Repeated Measurements

When comparing two treatments, we often use the simple difference between the probabilities of response to measure the efficacy of one treatment over the other. When the measurement of outcome is unreliable or the cost of obtaining additional subjects is high relative to that of additional measurements from the obtained subjects, we may often consider taking more than one measurement per subject to increase the precision of an interval estimator. This paper focuses discussion on interval estimation of simple difference when we take repeated measurements per subject. This paper develops four asymptotic interval estimators of simple difference for any finite number of measurements per subject. This paper further applies Monte Carlo simulation to evaluate the finite‐sample performance of these estimators in a variety of situations. Finally, this paper includes a discussion on sample size determination on the basis of both the average length and the probability of controlling the length of the resulting interval estimate proposed elsewhere.     

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.     

A simulation study on the accuracy of position and effect estimates of linked QTL and their asymptotic standard deviations using multiple interval mapping in an F2 scheme

Approaches like multiple interval mapping using a multiple-QTL model for simultaneously mapping QTL can aid the identification of multiple QTL, improve the precision of estimating QTL positions and effects, and are able to identify patterns and individual elements of QTL epistasis. Because of the statistical problems in analytically deriving the standard errors and the distributional form of the estimates and because the use of resampling techniques is not feasible for several linked QTL, there is the need to perform large-scale simulation studies in order to evaluate the accuracy of multiple interval mapping for linked QTL and to assess confidence intervals based on the standard statistical theory. From our simulation study it can be concluded that in comparison with a monogenetic background a reliable and accurate estimation of QTL positions and QTL effects of multiple QTL in a linkage group requires much more information from the data. The reduction of the marker interval size from 10 cM to 5 cM led to a higher power in QTL detection and to a remarkable improvement of the QTL position as well as the QTL effect estimates. This is different from the findings for (single) interval mapping. The empirical standard deviations of the genetic effect estimates were generally large and they were the largest for the epistatic effects. These of the dominance effects were larger than those of the additive effects. The asymptotic standard deviation of the position estimates was not a good criterion for the accuracy of the position estimates and confidence intervals based on the standard statistical theory had a clearly smaller empirical coverage probability as compared to the nominal probability. Furthermore the asymptotic standard deviation of the additive, dominance and epistatic effects did not reflect the empirical standard deviations of the estimates very well, when the relative QTL variance was smaller/equal to 0.5. The implications of the above findings are discussed.