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Statistics in Medicine Jun 2019Regression to the mean (RTM) occurs when subjects having relatively high or low measurements are remeasured and found closer to the population mean. This phenomenon can...
Regression to the mean (RTM) occurs when subjects having relatively high or low measurements are remeasured and found closer to the population mean. This phenomenon can potentially lead to an inaccurate conclusion in a pre-post study design. Expressions are available for quantifying RTM when the distribution of pre and post observations are bivariate normal and bivariate Poisson. However, situations exist where the response variables are the number of successes in a fixed number of trials and follow the bivariate binomial distribution. In this article, expressions for quantifying RTM effects are derived when the underlying distribution is the bivariate binomial. Unlike the normal and Poisson distributions, the correlation between pre and post observations can be either negative or positive under the bivariate binomial distribution and the severity of RTM is greater in the former case. The percentage relative difference is used to highlight the differences in quantifying RTM under the bivariate binomial distribution and normal and Poisson approximations to the bivariate binomial distribution. Expressions for estimating RTM using the method of maximum likelihood along with its asymptotic distribution are derived. A simulation study is conducted to empirically assess the statistical properties of the RTM estimator and its asymptotic distribution. Data examples using the number of obese individuals and the number of nonconforming cardboard cans are discussed.
Topics: Adolescent; Age Factors; Binomial Distribution; Child; Child, Preschool; Computer Simulation; Efficiency, Organizational; Equipment Design; Female; Humans; Iowa; Male; Models, Statistical; Obesity; Poisson Distribution; Probability; Research Design; Risk
PubMed: 30743311
DOI: 10.1002/sim.8115 -
The Journal of the Acoustical Society... Sep 2022Speech-recognition tests are a routine component of the clinical hearing evaluation. The most common type of test uses recorded monosyllabic words presented in quiet....
Speech-recognition tests are a routine component of the clinical hearing evaluation. The most common type of test uses recorded monosyllabic words presented in quiet. The interpretation of test scores relies on an understanding of the variance of repeated tests. Confidence intervals are useful for determining if two scores are significantly different or if the difference is due to the variability of test scores. Because the response to each test item is binary, either correct or incorrect, the binomial distribution has been used to estimate confidence intervals. This method requires that test scores be independent. If the scores are not independent, the binomial distribution will not accurately estimate the variance of repeated scores. A previously published dataset with repeated scores from normal-hearing and hearing-impaired listeners was used to derive confidence intervals from actual test scores in contrast to the predicted confidence intervals in earlier reports. This analysis indicates that confidence intervals predicted by the binomial distribution substantially overestimate the variance of repeated scores resulting in erroneously broad confidence intervals. High correlations were found for repeated scores, indicating that scores are not independent. The interdependence of repeated scores invalidates confidence intervals predicted by the binomial distribution. Confidence intervals and confidence levels for repeated measures were determined empirically from measured test scores to assist in interpreting differences between repeat scores.
Topics: Binomial Distribution; Confidence Intervals; Hearing Loss, Sensorineural; Humans; Speech; Speech Discrimination Tests; Speech Perception; Speech Reception Threshold Test
PubMed: 36182306
DOI: 10.1121/10.0013826 -
Nature Jun 1960
Topics: Binomial Distribution; Genetics; Humans
PubMed: 13819389
DOI: 10.1038/1861074a0 -
Journal of Biopharmaceutical Statistics 2013People exposed to certain diseases are required to be treated with a safe and effective dose level of a drug. In epidemiological studies to find out an effective dose...
People exposed to certain diseases are required to be treated with a safe and effective dose level of a drug. In epidemiological studies to find out an effective dose level, different dose levels are applied to the exposed and a certain number of cures is observed. Negative binomial distribution is considered to fit overdispersed Poisson count data. This study investigates the time effect on the response at different time points as well as at different dose levels. The point estimation and confidence bands for ED(100p)(t) and LT(100p)(d) are formulated in closed form for the proposed dose-time-response model with the negative binomial distribution. Numerical illustrations are carried out in order to check the performance level of the proposed model.
Topics: Animals; Binomial Distribution; Biological Assay; Coleoptera; Data Interpretation, Statistical; Dose-Response Relationship, Drug; Drug Dosage Calculations; Female; Humans; Insecticides; Least-Squares Analysis; Male; Models, Statistical; Pyrethrins; Research Design; Time Factors
PubMed: 24138430
DOI: 10.1080/10543406.2013.834916 -
PloS One 2020Sequence count data are commonly modelled using the negative binomial (NB) distribution. Several empirical studies, however, have demonstrated that methods based on the...
Sequence count data are commonly modelled using the negative binomial (NB) distribution. Several empirical studies, however, have demonstrated that methods based on the NB-assumption do not always succeed in controlling the false discovery rate (FDR) at its nominal level. In this paper, we propose a dedicated statistical goodness of fit test for the NB distribution in regression models and demonstrate that the NB-assumption is violated in many publicly available RNA-Seq and 16S rRNA microbiome datasets. The zero-inflated NB distribution was not found to give a substantially better fit. We also show that the NB-based tests perform worse on the features for which the NB-assumption was violated than on the features for which no significant deviation was detected. This gives an explanation for the poor behaviour of NB-based tests in many published evaluation studies. We conclude that nonparametric tests should be preferred over parametric methods.
Topics: Binomial Distribution; Microbiota; Poisson Distribution; RNA, Ribosomal, 16S; RNA-Seq; Regression Analysis
PubMed: 32352970
DOI: 10.1371/journal.pone.0224909 -
Statistics in Medicine Aug 2019We propose two measures of performance for a confidence interval for a binomial proportion p: the root mean squared error and the mean absolute deviation. We also devise...
We propose two measures of performance for a confidence interval for a binomial proportion p: the root mean squared error and the mean absolute deviation. We also devise a confidence interval for p based on the actual coverage function that combines several existing approximate confidence intervals. This "Ensemble" confidence interval has improved statistical properties over the constituent confidence intervals. Software in an R package, which can be used in devising and assessing these confidence intervals, is available on CRAN.
Topics: Algorithms; Binomial Distribution; Biostatistics; Computational Biology; Computer Simulation; Confidence Intervals; Humans; Models, Statistical; Monte Carlo Method; Software; Statistics, Nonparametric
PubMed: 31099897
DOI: 10.1002/sim.8189 -
IEEE Journal of Biomedical and Health... Jul 2021Clinical visual field testing is performed with commercial perimetric devices and employs psychophysical techniques to obtain thresholds of the differential light...
Clinical visual field testing is performed with commercial perimetric devices and employs psychophysical techniques to obtain thresholds of the differential light sensitivity (DLS) at multiple retinal locations. Current thresholding algorithms are relatively inefficient and tough to get satisfied test accuracy, stability concurrently. Thus, we propose a novel Bayesian perimetric threshold method called the Trail-Traced Threshold Test (T4), which can better address the dependence of the initial threshold estimation and achieve significant improvement in the test accuracy and variability while also decreasing the number of presentations compared with Zippy Estimation by Sequential Testing (ZEST) and FT. This study compares T4 with ZEST and FT regarding presentation number, mean absolute difference (MAD between the real Visual field result and the simulate result), and measurement variability. T4 uses the complete response sequence with the spatially weighted neighbor responses to achieve better accuracy and precision than ZEST, FT, SWeLZ, and with significantly fewer stimulus presentations. T4 is also more robust to inaccurate initial threshold estimation than other methods, which is an advantage in subjective methods, such as in clinical perimetry. This method also has the potential for using in other psychophysical tests.
Topics: Algorithms; Bayes Theorem; Binomial Distribution; Computer Simulation; Glaucoma; Humans; Reproducibility of Results; Sensory Thresholds; Visual Field Tests
PubMed: 33544681
DOI: 10.1109/JBHI.2021.3057437 -
Nutrition (Burbank, Los Angeles County,... Sep 1997
Topics: Binomial Distribution; Humans; Models, Statistical; Nutrition Disorders; Poisson Distribution; Probability; United States
PubMed: 9290106
DOI: 10.1016/s0899-9007(97)00248-7 -
Journal of Theoretical Biology Aug 1993Calculations are presented demonstrating a class of hypothetical channel interactions which cannot be recognized by means of the commonly used binomial test. On the...
Calculations are presented demonstrating a class of hypothetical channel interactions which cannot be recognized by means of the commonly used binomial test. On the contrary, ion channels which interact in such a way will be identified with the help of the binomial test as independent. Thus, the binomial test cannot be used to prove the absence of interactions. Furthermore, in cases in which existing interactions are recognized by the binomial test, estimation of the strength of the interactions may be inaccurate.
Topics: Animals; Binomial Distribution; Ion Channels; Kinetics; Models, Biological
PubMed: 7504148
DOI: 10.1006/jtbi.1993.1133 -
Annals of Work Exposures and Health Mar 2017The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of...
The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions.
Topics: Asbestos, Serpentine; Binomial Distribution; Confidence Intervals; Humans; Limit of Detection
PubMed: 28395351
DOI: 10.1093/annweh/wxw020