Bayesian inference for disease prevalence using negative binomial group testing

Pritchard, Nicholas A.; Tebbs, Joshua M.

doi:10.1002/bimj.201000148

Cited by 15 publications

(17 citation statements)

References 22 publications

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“…Uncertainty about the period prevalence of schizophrenia was estimated with an informative independent beta prior distribution constructed by directly matching the sensitivity from each scenario to the mean of the beta distribution (Joseph, Gyorkos, & Coupal, 1995 ). When there is a priori knowledge that the prevalence, θ, is small, the class of Beta(1,α) prior distributions is considered more appropriate (Pritchard & Tebbs, 2011 ). Period prevalence rates of 0.20%, 0.17%, and 0.15% were examined in this study, exploring the sensitivity of the model to prior beliefs.…”

Section: Methodsmentioning

confidence: 99%

A Bayesian Approach to Modeling Risk of Hospital Admissions Associated With Schizophrenia Accounting for Underdiagnosis of the Disorder in Administrative Records

Stock¹,

Stamey²,

Zeber³

et al. 2018

Computational Psychiatry

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Schizophrenia is a debilitating serious mental illness characterized by a complex array of symptoms with varying severity and duration. Patients may seek treatment only intermittently, contributing to challenges diagnosing the disorder. A misdiagnosis may potentially bias and reduce study validity. Thus we developed a statistical model to assess the risk of 1-year hospitalization for patients diagnosed with schizophrenia, accounting for when schizophrenia is underreported in administrative databases. A retrospective study design identified patients seeking care during 2010 within an integrated health care system from the Health Maintenance Organization Research Network located in the southwestern United States. Bayesian analysis addressed the problem of underdiagnosed schizophrenia with a statistical measurement error model assuming varying rates of underreporting. Results were then compared to classical multivariable logistic regression. Assuming no underreporting, there was an 87% greater relative odds of hospitalization associated with schizophrenia, OR = 1.87, CI [1.08, 3.23]. Effect sizes and interval estimates representing the association between hospitalization and schizophrenia were reduced with the Bayesian approach accounting for underdiagnosis, suggesting that less severe patients may be underrepresented in studies of schizophrenia. The analytical approach has useful applications in other contexts where the identification of patients with a given condition may be underreported in administrative records.

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Section: Methodsmentioning

confidence: 99%

A Bayesian Approach to Modeling Risk of Hospital Admissions Associated With Schizophrenia Accounting for Underdiagnosis of the Disorder in Administrative Records

Stock¹,

Stamey²,

Zeber³

et al. 2018

Computational Psychiatry

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“…If the testing continues until the r th positive pool is found, where r >1, this implies that we will observe data as Y 1 , Y 2 , Y 3 ,…, Y r . Therefore, the total number of pools tested to find r positive pools is equal to (Pritchard and Tebbs, 2010, 2011). We shall denote the size of the pools collected by k , we assume equal pool size, the prevalence of infection is denoted by p , the number of pools tested to find one positive pool is Y i = y i , and the number of times this experiment is carried out is denoted by r .…”

Section: Methodsmentioning

confidence: 99%

Sample size for detecting transgenic plants using inverse binomial group testing with dilution effect

Montesinos‐López

Crossa

et al. 2013

Seed Sci. Res.

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In this study we developed a sample size procedure for estimating the proportion of genetically modified plants (adventitious presence of unwanted transgenic plants, AP) under inverse negative binomial group testing sampling, which guarantees that exactly r positive pools will be present in the sample. To achieve this aim, pools are drawn one by one until the sample contains r positive pools. The use of group testing produces significant savings because groups that contain several units (plants) are analysed without having to inspect individual plants. However, when using group testing we need to consider an appropriate pool size (k) because if the k individuals that form a pool are mixed and homogenized, the AP will be diluted. This effect increases with the size of the pool; it may also decrease the AP concentration in the pool below the laboratory test detection limit (d), thereby increasing the number of false negatives. The method proposed in this study determines the required sample size considering the dilution effect and guarantees narrow confidence intervals. In addition, we derived the maximum likelihood estimator of p and an exact confidence interval (CI) under negative binomial pool testing considering the detection limit of the laboratory test, d, and the concentration of AP per unit (c). Simulated data were created and tables presented showing different potential scenarios that a researcher may encounter. We also provide an R program that can be used to create other scenarios.

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“…Most applications for detecting and estimating a proportion are developed using binomial sampling; however, Pritchard and Tebbs [9] have suggested that inverse (negative) binomial pooled sampling may be preferred when prevalence p is known to be small, when sampling and testing occur sequentially, or when positive pool results require immediate analysis—for example, in the case of many rare diseases. Unlike binomial sampling, in this model the number of positive pools to be observed is fixed a priori , and testing is complete when the rth positive pool is reached [10] .…”

Section: Introductionmentioning

confidence: 99%

“…Recently Pritchard and Tebbs [9] used maximum likelihood as a basis for developing three point and interval estimators for p under inverse pooled sampling; they compared its performance with Katholi's [14] proposed point and interval estimators. Pritchard and Tebbs [10] extended their work to Bayesian point and interval estimation of the prevalence under negative binomial group testing. They used different distributions to incorporate prior knowledge of disease incidence and different loss functions, and derived closed-form expressions for posterior distributions and point and credible interval estimators [10] .…”

Section: Introductionmentioning

confidence: 99%

“…Pritchard and Tebbs [10] extended their work to Bayesian point and interval estimation of the prevalence under negative binomial group testing. They used different distributions to incorporate prior knowledge of disease incidence and different loss functions, and derived closed-form expressions for posterior distributions and point and credible interval estimators [10] . However, until now sample size procedures under inverse (negative) binomial sampling for group testing have not been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Sample Size under Inverse Negative Binomial Group Testing for Accuracy in Parameter Estimation

Montesinos‐López

Crossa

et al. 2012

PLoS ONE

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BackgroundThe group testing method has been proposed for the detection and estimation of genetically modified plants (adventitious presence of unwanted transgenic plants, AP). For binary response variables (presence or absence), group testing is efficient when the prevalence is low, so that estimation, detection, and sample size methods have been developed under the binomial model. However, when the event is rare (low prevalence <0.1), and testing occurs sequentially, inverse (negative) binomial pooled sampling may be preferred.Methodology/Principal FindingsThis research proposes three sample size procedures (two computational and one analytic) for estimating prevalence using group testing under inverse (negative) binomial sampling. These methods provide the required number of positive pools (), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model and inverse (negative) binomial sampling. We give real and simulated examples to show how to apply these methods and the proposed sample-size formula. The Monte Carlo method was used to study the coverage and level of assurance achieved by the proposed sample sizes. An R program to create other scenarios is given in Appendix S2.ConclusionsThe three methods ensure precision in the estimated proportion of AP because they guarantee that the width (W) of the confidence interval (CI) will be equal to, or narrower than, the desired width (), with a probability of . With the Monte Carlo study we found that the computational Wald procedure (method 2) produces the more precise sample size (with coverage and assurance levels very close to nominal values) and that the samples size based on the Clopper-Pearson CI (method 1) is conservative (overestimates the sample size); the analytic Wald sample size method we developed (method 3) sometimes underestimated the optimum number of pools.

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Bayesian inference for disease prevalence using negative binomial group testing

Cited by 15 publications

References 22 publications

A Bayesian Approach to Modeling Risk of Hospital Admissions Associated With Schizophrenia Accounting for Underdiagnosis of the Disorder in Administrative Records

A Bayesian Approach to Modeling Risk of Hospital Admissions Associated With Schizophrenia Accounting for Underdiagnosis of the Disorder in Administrative Records

Sample size for detecting transgenic plants using inverse binomial group testing with dilution effect

Sample Size under Inverse Negative Binomial Group Testing for Accuracy in Parameter Estimation

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