Joint Regression Analysis for Discrete Longitudinal Data

Madsen, Lisa; Yan, Fang

doi:10.1111/j.1541-0420.2010.01494.x

Cited by 37 publications

(55 citation statements)

References 5 publications

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“…One such family is the Gaussian family , which has been widely used in applications because of its convenient marginal and conditional properties. Adopting the Gaussian copula probit model for Y i 1 L ∼Bernoulli ( π 1 L ), Y i 1 R ∼Bernoulli ( π 1 R ), Y i 2 L ∼Bernoulli ( π 2 L ), and Y i 2 R ∼Bernoulli ( π 2 R ), the resulting joint model

P_{ℓ_{1} r_{1} ℓ_{2} r_{2}} = P (Y_{i 1 L} = ℓ_{1}, Y_{i 1 R} = r_{1}, Y_{i 2 L} = ℓ_{2}, Y_{i 2 R} = r_{2})

is given by

P_{ℓ_{1} r_{1} ℓ_{2} r_{2}} = {falsefalse}_{\sum}^{j_{1} = 0} {falsefalse}_{\sum}^{j_{2} = 0} {falsefalse}_{\sum}^{j_{3} = 0} {falsefalse}_{\sum}^{j_{4} = 0} {(- 1)}^{4 + {falsefalse}_{\sum}^{h = 1} j_{h}} {normal Φ}_{boldD} ((), \begin{matrix} array \\ array {normalΦ}^{- 1} (u_{i 1 L j_{1}}), {normalΦ}^{- 1} (u_{i 1 R j_{2}}), \\ array {normalΦ}^{- 1} (u_{i 2 L j_{3}}), {normalΦ}^{- 1} ( \end{matrix})

…”

Section: Case Of Non‐exchageability Of Organsmentioning

confidence: 99%

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Binocular sensitivity and specificity of screening tests in cross‐sectional diagnostic studies of paired organs

Perera

Ren

Punzalan

et al. 2017

Statistics in Medicine

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We introduce new binocular accuracy measures as alternatives to conventional marginal measures that can be used to evaluate screening tests in diagnostic studies involving paired organs (e.g. eyes and ears). Specifically, we consider screening studies based on a cross-sectional design, where both diagnosis and disease status are determined after study enrolment or sampling, yielding paired binocular binary data described via two models, namely, the extended common correlation model and the Gaussian copula probit model. The first relies on the assumption of exchangeability of fellow organs, while the second is more flexible. Binocular versions of sensitivity and specificity are defined, respectively, as the probability of at least one correct positive diagnosis in patients with one or both organs truly diseased and the probability of two correct negative diagnoses for patients with both organs truly un-diseased. Comparisons between the conventional marginal and binocular sensitivities and specificities are illustrated for both models using data from a diabetic retinopathy study. We show that our methodology provides a viable alternative to conventional ways of assessing diagnostic accuracy of screening tests for paired organs. The binocular versions of sensitivity and specificity reflect the way screening tests are conducted in practice, and they overcome the shortcomings of conventional measures. Copyright © 2017 John Wiley & Sons, Ltd.

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P_{ℓ_{1} r_{1} ℓ_{2} r_{2}} = P (Y_{i 1 L} = ℓ_{1}, Y_{i 1 R} = r_{1}, Y_{i 2 L} = ℓ_{2}, Y_{i 2 R} = r_{2})

is given by

P_{ℓ_{1} r_{1} ℓ_{2} r_{2}} = {falsefalse}_{\sum}^{j_{1} = 0} {falsefalse}_{\sum}^{j_{2} = 0} {falsefalse}_{\sum}^{j_{3} = 0} {falsefalse}_{\sum}^{j_{4} = 0} {(- 1)}^{4 + {falsefalse}_{\sum}^{h = 1} j_{h}} {normal Φ}_{boldD} ((), \begin{matrix} array \\ array {normalΦ}^{- 1} (u_{i 1 L j_{1}}), {normalΦ}^{- 1} (u_{i 1 R j_{2}}), \\ array {normalΦ}^{- 1} (u_{i 2 L j_{3}}), {normalΦ}^{- 1} ( \end{matrix})

…”

Section: Case Of Non‐exchageability Of Organsmentioning

confidence: 99%

“…One such family is the Gaussian family [17], which has been widely used in applications because of its convenient marginal and conditional properties. Adopting the Gaussian copula probit model [18,19]…”

Section: Case Of Non-exchageability Of Organsmentioning

confidence: 99%

Binocular sensitivity and specificity of screening tests in cross‐sectional diagnostic studies of paired organs

Perera

Ren

Punzalan

et al. 2017

Statistics in Medicine

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show abstract

“…Though copulas have been extensively explored for modeling dependency for continuous data, the applications for discrete data are just emerging. Some of the recent studies in this area include Prieger (2002), Smith (2003), Cameron et al (2004), Purcaru and Denuit (2005) and Karlis (2008, 2010), Madsen (2009) and Madsen and Fang (2010).…”

Section: Specification Of the Copula Modelmentioning

confidence: 99%

A copula approach to test asymmetric information with applications to predictive modeling

Shi¹,

Valdez²

2011

Insurance: Mathematics and Economics

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“…Some recent work includes Smith (), Zimmer and Trivedi () and Lo and Wilke () in economics, Song et al . (), Chen () and Madsen and Fang () in statistics, and Frees and Valdez (), Shi () and Shi et al . () in insurance.…”

Section: Methodsmentioning

confidence: 98%

Private Information in Healthcare Utilization: Specification of a Copula-Based Hurdle Model

Shi

Zhang

2014

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary We study whether individuals' private information on health risk affects their medical care utilization. The presence of such information asymmetry is critical to the optimal payment design in healthcare systems. To do so, we examine the relationship between self‐perceived health status and healthcare expenditures. Because of simultaneity, we employ a copula regression to model jointly the mixed outcomes, with the association parameter capturing the residual dependence conditional on covariates. The semicontinuous nature of healthcare expenditures leads to a two‐part interpretation of private health information: the hurdle component assesses its effect on the likelihood of using medical care services, and the conditional component quantifies its effect on the expenditures given consumption of care. The methodology proposed is applied to a survey data set of a sample of the US civilian non‐institutionalized population to test and quantify the effects of private health information. We find evidence of adverse selection in the utilization of various types of medical care services.

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Joint Regression Analysis for Discrete Longitudinal Data

Cited by 37 publications

References 5 publications

Binocular sensitivity and specificity of screening tests in cross‐sectional diagnostic studies of paired organs

Binocular sensitivity and specificity of screening tests in cross‐sectional diagnostic studies of paired organs

A copula approach to test asymmetric information with applications to predictive modeling

Private Information in Healthcare Utilization: Specification of a Copula-Based Hurdle Model

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