Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification

Boese, Doyle; Young, Dean M.; Stamey, James D.

doi:10.1016/j.csda.2005.08.007

Cited by 41 publications

(47 citation statements)

References 17 publications

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“…The recommended interval seems to have a good frequentist property in that it has the coverage probability close to the nominal level. Under the same model, Lee and Byun (2008) gave a Bayesian confidence interval which slightly outperforms the confidence interval recommended by Boese et al (2006).…”

Section: Introductionmentioning

confidence: 96%

“…Note that W EM is actually Wald confidence interval constructed by the maximum likelihood estimate and estimate of its asymptotic variance. It was demonstrated in many sampling designs that the performance of Wald confidence interval is poor; see for example, Agresti and Coull (1998), Agresti and Caffo (2000), Brownet al (2001), Boese et al (2006), and Lee (2010). The small value of coverage probability with the wide expected width suggests that the location of interval would not be proper.…”

Section: Comparison Of Confidence Intervalsmentioning

confidence: 99%

“…However, their claim is not suitable for this case. In view of Boese et al (2006), the preferred information seems to be the expected information for the interval estimation of a proportion. See also Lee (2010).…”

Section: Comparison Of Confidence Intervalsmentioning

confidence: 99%

“…There are numerous examples using the advantages of the double sampling scheme; see Geng and Asano (1989), York et al(1995), Moors et al(2000), Barnett et al (2001), Raats and Moor (2003) and Boese et al (2006). For instance, York et al (1995) illustrated the advantage of the double sampling scheme in estimating the proportion of infants born with Down's syndrome nationwide.…”

Section: Introductionmentioning

confidence: 99%

“…They put the corresponding error rate equal to zero a priori, and gave one-sided confidence intervals for the population proportion. Boese et al (2006) gave five likelihood-based confidence intervals in the false-positive misclassification model. Among them, they recommended the interval based on the Rao score function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

Lee¹

2010

Communications for Statistical Applications and Methods

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Lee (2010) developed a confidence interval for the difference of binomial proportions in two doubly sampled data subject to false-positive errors. The confidence interval seems to be adequate for a general double sampling model subject to false-positive misclassification. However, in many applications, the false-positive error rates could be the same. On this note, the construction of asymptotic confidence interval is considered when the false-positive error rates are common. The coverage behaviors of nine likelihood based confidence intervals are examined. It is shown that the confidence interval based Rao score with the expected information has good performance in terms of coverage probability and expected width.

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Section: Introductionmentioning

confidence: 96%

Section: Comparison Of Confidence Intervalsmentioning

confidence: 99%

Section: Comparison Of Confidence Intervalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

Lee¹

2010

Communications for Statistical Applications and Methods

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Bayesian inference for unidirectional misclassification of a binary response trait

Xia

Gustafson

2017

Statistics in Medicine

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When assessing association between a binary trait and some covariates, the binary response may be subject to unidirectional misclassification. Unidirectional misclassification can occur when revealing a particular level of the trait is associated with a type of cost, such as a social desirability or financial cost. The feasibility of addressing misclassification is commonly obscured by model identification issues. The current paper attempts to study the efficacy of inference when the binary response variable is subject to unidirectional misclassification. From a theoretical perspective, we demonstrate that the key model parameters possess identifiability, except for the case with a single binary covariate. From a practical standpoint, the logistic model with quantitative covariates can be weakly identified, in the sense that the Fisher information matrix may be near singular. This can make learning some parameters difficult under certain parameter settings, even with quite large samples. In other cases, the stronger identification enables the model to provide more effective adjustment for unidirectional misclassification. An extension to the Poisson approximation of the binomial model reveals the identifiability of the Poisson and zero-inflated Poisson models. For fully identified models, the proposed method adjusts for misclassification based on learning from data. For binary models where there is difficulty in identification, the method is useful for sensitivity analyses on the potential impact from unidirectional misclassification.

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Exact interval estimation for three parameters subject to false positive misclassification

Lu,

Wang,

Xie

2024

Stat

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SummaryBinary data subject to one type of misclassification exist in various fields. It is collected in a double‐sampling scheme that includes a gold standard test and a fallible test. The main parameter of interest for this type of data is the positive probability of the gold standard test. Existing intervals are unreliable because the given nominal level is not achieved. In this paper, we construct an exact interval by inverting the E+M score tests and improve it by the general ‐function method. We find that the total length of the improved interval is shorter than the exact intervals that are also the improved intervals when we apply the ‐function to several existing approximate intervals, including the score and Bayesian intervals. Therefore, it is recommended for practice. We are also interested in two other parameters: —the difference between the two positive rates for the fallible and gold standard tests—and —the false positive rate for the fallible test. To the best of our knowledge, the research on these two parameters is limited. For , we find that any interval for can be converted to an interval for . So, the interval converted from the aforementioned recommended interval for is recommended for inferring . For , the improved interval by the ‐function method over the E+M score interval is derived. We use an example to illustrate how the intervals are computed and provide a real data analysis.

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Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification

Cited by 41 publications

References 17 publications

Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

Bayesian inference for unidirectional misclassification of a binary response trait

Exact interval estimation for three parameters subject to false positive misclassification

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