Confidence Interval Estimation for Sensitivity to the Early Diseased Stage Based on Empirical Likelihood

Dong, Tuochuan; Tian, Lili

doi:10.1080/10543406.2014.971173

Cited by 7 publications

(22 citation statements)

References 35 publications

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“…th percentile of bootstrap resample estimates. Dong and Tian 22 proposed another nonparametric approach that utilizes bootstrap variance estimation to the EL approach, where the EL ratio test statistic approximately follows scaled chi-square distribution. Dong and Tian 22 established the following result…”

Section: Existing Approachesmentioning

confidence: 99%

“…Then, the

100 ((), 1 - α) %

ELB confidence interval can be constructed as follows

I ((), α) goodbreak= ({}, P_{2} ((),, P_{1}, P_{3}) : r_{P_{1}, P_{2}, P_{3}}^{*} l ((), P_{2}) \leq χ_{1}^{2} ((), α)),

where

χ_{1}^{2} ((), α)

is the upper α–quantile of

χ_{1}^{2}

distribution and an estimate of scale constant is,

r_{P_{1}, P_{2}, P_{3}}^{*} = {\overset{truê}{P}}_{2} ((), 1 - {\overset{truê}{P}}_{2}) / ((), n_{2} {\overset{truê}{σ}}_{{\overset{P}{true}}_{2}}^{2}) .

22 For the ELB method,

{\overset{truê}{σ}}_{{\overset{P}{true}}_{2}}^{2}

is estimated from

b = 500

bootstrap resamples.…”

Section: Sensitivity To the Early Disease Stagementioning

confidence: 99%

“…Dong and Tian 22 proposed another nonparametric approach that utilizes bootstrap variance estimation to the EL approach, where the EL ratio test statistic approximately follows scaled chi‐square distribution. Dong and Tian 22 established the following result

r_{P_{1}, P_{2}, P_{3}} l ((), P_{2}) \to χ_{1}^{2},

where

l ((), P_{2}) = - 2 \log r ((), P_{2}),

r ((), P_{2})

is the EL ratio and

r_{P_{1}, P_{2}, P_{3}} goodbreak= \frac{σ_{{\overset{truê}{U}}_{i}}^{2}}{n_{2} σ_{{\overset{P}{true}}_{2}}^{2}} .

…”

Section: Sensitivity To the Early Disease Stagementioning

confidence: 99%

“…Zhou and Qin 18 and Qin et al 19 incorporated empirical likelihood (EL) and bootstrap procedures to improve the accuracy of the confidence interval estimation for the sensitivity, whereas Tian 20 proposed interval estimation for the sensitivity for a combination of markers at fixed level of specificity. Dong et al, 21 Dong and Tian 22 proposed different parametric and nonparametric approaches along with an EL approach to the estimation and the construction of confidence intervals for the sensitivity to the early disease stage at the given specificity level. More nonparametric developments like jackknife EL confidence interval in the related area such as ROC curve, AUC, ordinal dominance curve, VUS and Youden index are observed 23,24,25,26,27,28 …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Empirical likelihood confidence interval for sensitivity to the early disease stage

Rahman

Zhao

2021

Pharmaceutical Statistics

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Disease status can naturally be classified into three or more ordinal stages rather than just being binary stages. Many works have been done for the estimation and inference procedure regarding three ordinal disease stages, which are non‐disease, early disease, and full disease stages. The early disease stage can be very important for therapeutic intervention and prevention potentiality. As a diagnostic measure, sensitivity to the early disease stage is often used. In this article, we propose confidence intervals for the sensitivity to early disease stage based on given target specificity for non‐disease stage and target sensitivity to full disease stage using both empirical likelihood (EL) and adjusted EL procedures. We compare the performance of the proposed EL confidence intervals with other procedures in our simulation study. The proposed procedures are further applied to Alzheimer's Disease Neuroimaging Initiative data set.

show abstract

Section: Existing Approachesmentioning

confidence: 99%

“…Then, the

100 ((), 1 - α) %

ELB confidence interval can be constructed as follows

I ((), α) goodbreak= ({}, P_{2} ((),, P_{1}, P_{3}) : r_{P_{1}, P_{2}, P_{3}}^{*} l ((), P_{2}) \leq χ_{1}^{2} ((), α)),

where

χ_{1}^{2} ((), α)

is the upper α–quantile of

χ_{1}^{2}

distribution and an estimate of scale constant is,

r_{P_{1}, P_{2}, P_{3}}^{*} = {\overset{truê}{P}}_{2} ((), 1 - {\overset{truê}{P}}_{2}) / ((), n_{2} {\overset{truê}{σ}}_{{\overset{P}{true}}_{2}}^{2}) .

22 For the ELB method,

{\overset{truê}{σ}}_{{\overset{P}{true}}_{2}}^{2}

is estimated from

b = 500

bootstrap resamples.…”

Section: Sensitivity To the Early Disease Stagementioning

confidence: 99%

r_{P_{1}, P_{2}, P_{3}} l ((), P_{2}) \to χ_{1}^{2},

where

l ((), P_{2}) = - 2 \log r ((), P_{2}),

r ((), P_{2})

is the EL ratio and

r_{P_{1}, P_{2}, P_{3}} goodbreak= \frac{σ_{{\overset{truê}{U}}_{i}}^{2}}{n_{2} σ_{{\overset{P}{true}}_{2}}^{2}} .

…”

Section: Sensitivity To the Early Disease Stagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Empirical likelihood confidence interval for sensitivity to the early disease stage

Rahman

Zhao

2021

Pharmaceutical Statistics

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show abstract

“…It is available in the “Test Data/Data for Challenges” section of the LONI website (ADNI database). Here we only consider non-missing records based on three commonly used biomarkers 28–30 : ratio of levels of total protein Tau and protein Aβ42 (TAU/ABETA), fluorodeoxyglucose (FDG), and Alzheimer’s Disease Assessment Scale 11 (ADAS11). The dataset we used consists of 170 AD patients and 152 control subjects (CN).…”

Section: A Real Example In the Detection Of Alzheimer’s Diseasementioning

confidence: 99%

Bayesian and influence function-based empirical likelihoods for inference of sensitivity in diagnostic tests

Hai

Min

Qin

et al. 2020

Stat Methods Med Res

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In medical diagnostic studies, a diagnostic test can be evaluated based on its sensitivity under a desired specificity. Existing methods for inference on sensitivity include normal approximation-based approaches and empirical likelihood (EL)-based approaches. These methods generally have poor performance when the specificity is high, and some require choosing smoothing parameters. We propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to overcome such problems. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. The proposed methods are shown to perform better in terms of both coverage probability and interval length. A real data set from Alzheimer’s Disease Neuroimaging Initiative (ANDI) is analyzed.

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Bayesian and influence function‐based empirical likelihoods for inference of sensitivity to the early diseased stage in diagnostic tests

et al. 2023

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In practice, a disease process might involve three ordinal diagnostic stages: the normal healthy stage, the early stage of the disease, and the stage of full development of the disease. Early detection is critical for some diseases since it often means an optimal time window for therapeutic treatments of the diseases. In this study, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to construct confidence/credible intervals for the sensitivity of a test to patients in the early diseased stage given a specificity and a sensitivity of the test to patients in the fully diseased stage. Numerical studies are performed to compare the finite sample performances of the proposed approaches with existing methods. The proposed methods are shown to outperform existing methods in terms of coverage probability. A real dataset from the Alzheimer's Disease Neuroimaging Initiative (ANDI) is used to illustrate the proposed methods.

show abstract

Confidence Interval Estimation for Sensitivity to the Early Diseased Stage Based on Empirical Likelihood

Cited by 7 publications

References 35 publications

Empirical likelihood confidence interval for sensitivity to the early disease stage

Empirical likelihood confidence interval for sensitivity to the early disease stage

Bayesian and influence function-based empirical likelihoods for inference of sensitivity in diagnostic tests

Bayesian and influence function‐based empirical likelihoods for inference of sensitivity to the early diseased stage in diagnostic tests

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