scholarly journals Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

2016 ◽  
Vol 27 (5) ◽  
pp. 1559-1574 ◽  
Author(s):  
Andrew Carkeet ◽  
Yee Teng Goh
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Interval Methods ◽  
Tolerance Interval ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Approximate Methods ◽  
Exact Confidence Intervals ◽  
Tolerance Factors

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes <40 (1999 approximation) and <76 (1986 approximation). For inner confidence limits the approximations are poorer, being permissive for sample sizes of <490 (1986 approximation) and all practical sample sizes (1999 approximation). Exact confidence intervals for 95% limits of agreements, based on two-sided tolerance factors, can be calculated easily based on tables and should be used in preference to the approximate methods, especially for small sample sizes.

Bootstrap confidence limits for groundfish trawl survey estimates of mean abundance

1997 ◽  
Vol 54 (3) ◽  
pp. 616-630 ◽  
Author(s):  
S J Smith
Keyword(s):  
Confidence Intervals ◽  
Probability Model ◽  
Small Sample ◽  
Trawl Survey ◽  
Confidence Limits ◽  
Complex Sampling ◽  
Survey Estimates ◽  
Small Sample Sizes ◽  
Complex Sampling Designs ◽  
Trawl Surveys

Trawl surveys using stratified random designs are widely used on the east coast of North America to monitor groundfish populations. Statistical quantities estimated from these surveys are derived via a randomization basis and do not require that a probability model be postulated for the data. However, the large sample properties of these estimates may not be appropriate for the small sample sizes and skewed data characteristic of bottom trawl surveys. In this paper, three bootstrap resampling strategies that incorporate complex sampling designs are used to explore the properties of estimates for small sample situations. A new form for the bias-corrected and accelerated confidence intervals is introduced for stratified random surveys. Simulation results indicate that the bias-corrected and accelerated confidence limits may overcorrect for the trawl survey data and that percentile limits were closer to the expected values. Nonparametric density estimates were used to investigate the effects of unusually large catches of fish on the bootstrap estimates and confidence intervals. Bootstrap variance estimates decreased as increasingly smoother distributions were assumed for the observations in the stratum with the large catch. Lower confidence limits generally increased with increasing smoothness but the upper bound depended upon assumptions about the shape of the distribution.

Likelihood-based confidence intervals of relative fitness for a common experimental design

2005 ◽  
Vol 62 (3) ◽  
pp. 693-699 ◽  
Author(s):  
Steven T Kalinowski ◽  
Mark L Taper
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Confidence Intervals ◽  
Maximum Likelihood Estimates ◽  
Relative Fitness ◽  
Literature Analysis ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Statistical Inferences ◽  
Different Types

Statistical inferences concerning the relative fitness of different types of individuals in a population have not been well developed. We present a method for calculating confidence intervals for maximum likelihood estimates of relative fitness obtained from an experimental design that is common in the fisheries literature. Analysis and simulation show that these confidence limits are reliable. We also show that the bias of the estimates is low for realistic sample sizes.

A new procedure to construct confidence intervals for genotypic variance and expected response to selection

Genome ◽  
1989 ◽  
Vol 32 (2) ◽  
pp. 307-308 ◽  
Author(s):  
G. C. C. Tai
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Progeny Test ◽  
Variance Ratio ◽  
Confidence Limits ◽  
Response To Selection ◽  
Genotypic Variance ◽  
Exact Confidence Intervals

This paper describes a procedure to construct confidence intervals for genotypic variance and expected response to selection estimated from progeny test experiments. It involves the introduction of parameters into the confidence limits of existing exact confidence intervals for variance and variance ratio. The parameters in the limits of the derived intervals are estimated by comparing the limits of different potential intervals covering the same parameter, i.e., genotypic variance or expected response to selection. This leads to the construction of a confidence interval for the concerned parameter.Key words: confidence intervals, genotypic variance, expected response to selection.

A novel confidence interval for a single proportion in the presence of clustered binary outcome data

2019 ◽  
Vol 29 (1) ◽  
pp. 111-121
Author(s):  
Meghan I Short ◽  
Howard J Cabral ◽  
Janice M Weinberg ◽  
Michael P LaValley ◽  
Joseph M Massaro
Keyword(s):  
Confidence Interval ◽  
Clustered Data ◽  
Epidemiological Studies ◽  
Outcome Data ◽  
Small Sample ◽  
Interval Methods ◽  
Sample Sizes ◽  
Wide Range ◽  
Small Sample Sizes ◽  
Over Dispersion

Estimating the precision of a single proportion via a 100(1−α)% confidence interval in the presence of clustered data is an important statistical problem. It is necessary to account for possible over-dispersion, for instance, in animal-based teratology studies with within-litter correlation, epidemiological studies that involve clustered sampling, and clinical trial designs with multiple measurements per subject. Several asymptotic confidence interval methods have been developed, which have been found to have inadequate coverage of the true proportion for small-to-moderate sample sizes. In addition, many of the best-performing of these intervals have not been directly compared with regard to the operational characteristics of coverage probability and empirical length. This study uses Monte Carlo simulations to calculate coverage probabilities and empirical lengths of five existing confidence intervals for clustered data across various true correlations, true probabilities of interest, and sample sizes. In addition, we introduce a new score-based confidence interval method, which we find to have better coverage than existing intervals for small sample sizes under a wide range of scenarios.

scholarly journals The construction of confidence intervals for frequency analysis using resampling techniques: a supplementary note

2004 ◽  
Vol 8 (6) ◽  
pp. 1174-1178 ◽  
Author(s):  
H. F. P. van den Boogaard ◽  
M. J. Hall
Keyword(s):  
Weibull Distribution ◽  
Confidence Intervals ◽  
Frequency Analysis ◽  
Likelihood Method ◽  
Bootstrap Resampling ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Recent Contribution ◽  
Percentile Method ◽  
Coverage Rates

Abstract. In a recent contribution, Hall et al. (2004) examined the use of the Bootstrap resampling technique as a means of constructing confidence limits for the quantiles of the (two-parameter) Gumbel and the (three-parameter) Weibull distributions. Particular emphasis was placed on the behaviour of sample sizes of the order of 30, which are typical of those encountered in hydrological frequency analysis. The resampled confidence limits obtained for the Gumbel distribution were found to be comparable with those based upon a well-known theoretical approximation. However, those for samples of size 30 from the Weibull distribution were shown to be more problematical, with the results dependent upon the skewnesses of the resampled distributional parameters. For a further and more quantitative assessment of the suitability of Bootstrap resampling for constructing confidence intervals, so-called coverage rates were evaluated for the Weibull distribution in a supplementary study. The results show a satisfactory performance when using the percentile method but do not really mitigate the conclusion of the original study that resampled confidence limits should be employed with caution when sample sizes are of the order of 30. Keywords: Bootstrap, Jack-knife, frequency analysis, maximum likelihood method, maximum product of spacings method, confidence intervals, coverage rates

A Monte Carlo Study of Confidence Interval Methods for Generalizability Coefficient

2021 ◽  
pp. 001316442110338
Author(s):  
Zhehan Jiang ◽  
Mark Raymond ◽  
Christine DiStefano ◽  
Dexin Shi ◽  
Ren Liu ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Generalizability Theory ◽  
Monte Carlo Study ◽  
Small Sample ◽  
Interval Methods ◽  
Point Estimate ◽  
Linear Mixed Effect Model ◽  
Mixed Effect ◽  
Measurement Design

Computing confidence intervals around generalizability coefficients has long been a challenging task in generalizability theory. This is a serious practical problem because generalizability coefficients are often computed from designs where some facets have small sample sizes, and researchers have little guide regarding the trustworthiness of the coefficients. As generalizability theory can be framed to a linear mixed-effect model (LMM), bootstrap and simulation techniques from LMM paradigm can be used to construct the confidence intervals. The purpose of this research is to examine four different LMM-based methods for computing the confidence intervals that have been proposed and to determine their accuracy under six simulated conditions based on the type of test scores (normal, dichotomous, and polytomous data) and data measurement design ( p× i× r and p× [ i:r]). A bootstrap technique called “parametric methods with spherical random effects” consistently produced more accurate confidence intervals than the three other LMM-based methods. Furthermore, the selected technique was compared with model-based approach to investigate the performance at the levels of variance components via the second simulation study, where the numbers of examines, raters, and items were varied. We conclude with the recommendation generalizability coefficients, the confidence interval should accompany the point estimate.

Exact one-sided confidence limits for Cohen’s kappa as a measurement of agreement

2014 ◽  
Vol 26 (2) ◽  
pp. 615-632 ◽  
Author(s):  
Guogen Shan ◽  
Weizhen Wang
Keyword(s):  
Confidence Intervals ◽  
Coverage Probability ◽  
Interval Estimation ◽  
Confidence Limits ◽  
Cohen’S Kappa ◽  
Nominal Level ◽  
Statistical Inferences ◽  
Cohen's Kappa ◽  
Exact Confidence Intervals ◽  
Level 1

Cohen’s kappa coefficient, κ, is a statistical measure of inter-rater agreement or inter-annotator agreement for qualitative items. In this paper, we focus on interval estimation of κ in the case of two raters and binary items. So far, only asymptotic and bootstrap intervals are available for κ due to its complexity. However, there is no guarantee that such intervals will capture κ with the desired nominal level 1– α. In other words, the statistical inferences based on these intervals are not reliable. We apply the Buehler method to obtain exact confidence intervals based on four widely used asymptotic intervals, three Wald-type confidence intervals and one interval constructed from a profile variance. These exact intervals are compared with regard to coverage probability and length for small to medium sample sizes. The exact intervals based on the Garner interval and the Lee and Tu interval are generally recommended for use in practice due to good performance in both coverage probability and length.

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