Estimating the False Negative Fraction for a Multiple Screening Test for Bowel Cancer When Negatives Are Not Verified

Lloyd, Chris J.; Frommer, D.

doi:10.1111/j.1467-842x.2004.00351.x

Cited by 10 publications

(14 citation statements)

References 19 publications

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“…For instance, if tests are independent then π.x|k,P/ is binomial. If the sequence of K test results is a Markov process then π.x|k,P/ is the Markov-binomial distribution; see Lloyd and Frommer (2004).…”

Section: Problem Formulation and Notationmentioning

confidence: 99%

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Regression-Based Estimation of the False Negative Fraction When Multiple Negatives are Unverified

Lloyd¹,

Frommer

2004

Journal of the Royal Statistical Society Series C: Applied Statistics

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The paper describes a method of estimating the false negative fraction of a multiple-screening test when individuals who test negatively on all "K" tests do not have their true disease status verified. The method proposed makes no explicit assumptions about the underlying heterogeneity of the population or about serial correlation of test results within an individual. Rather, it is based on estimating false negative fractions conditionally on observed diagnostic histories and extrapolating the observed patterns in these empirical frequencies by using logistic regression. The method is illustrated on, and motivated by, data on a multiple-screening test for bowel cancer. Copyright 2004 Royal Statistical Society.

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Section: Problem Formulation and Notationmentioning

confidence: 99%

“…It is quite difficult to devise a distribution π.x|k, p/ which violates these conditions. For instance, the beta binomial distribution satisfies them, as does the distribution of X k supposing that the binary sequence is a Markov process; see Lloyd and Frommer (2004).…”

Section: A1 Remarks On Assumptionsmentioning

confidence: 99%

Regression-Based Estimation of the False Negative Fraction When Multiple Negatives are Unverified

Lloyd¹,

Frommer

2004

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…This might be indicative of a problem such as cancer but also something else such as polyps or nothing at all. Lloyd and Frommer (2008, 2004a, 2004b) present results of a screening study for bowel cancer in Sydney (Australia). From 1984 onwards about 50000 subjects were screened for bowel cancer using the FOBT.…”

Section: Screening For Bowel Cancermentioning

confidence: 99%

“…For more details see Lovison (1998). The ratio regression approach for the multiplicative-binomial yields (23) log r x = log…”

Section: Applicationsmentioning

confidence: 99%

Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences

Böhning¹

2016

Statist. Sci.

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Abstract. We consider count data modeling, in particular, the zerotruncated case as it arises naturally in capture-recapture modeling as the marginal distribution of the count of identifications of the members of a target population. Whereas in wildlife ecology these distributions are often of a well-defined type, this is less the case for social and medical science applications since study types are often entirely observational. Hence, in these applications, violations of the assumptions underlying closed capture-recapture are more likely to occur than in carefully designed capture-recapture experiments. In consequence, the marginal count distribution might be rather complex. The purpose of this note is to sketch some of the major ideas in the recent developments in ratio plotting and ratio regression designed to explore the pattern of the distribution underlying the capture process. Ratio plotting and ratio regression are based upon considering the ratios of neighboring probabilities which can be estimated by ratios of observed frequencies. Frequently, these ratios show patterns which can be easily modeled by a regression model. The fitted regression model is then used to predict the frequency of hidden zero counts. Particular attention is given to regression models corresponding to the negative-binomial, multiplicative binomial and the Conway-Maxwell-Poisson distribution.

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“…Over several years, from 1984 onwards, about 50,000 subjects were screened for bowel cancer at St Vincent's Hospital in Sydney (Australia), see Lloyd and Frommer (, , ). The screening procedure was based on a sequence of binary diagnostic tests, self‐administered on

T = 6

successive days.…”

Section: Examplesmentioning

confidence: 99%

A Flexible Ratio Regression Approach for Zero-Truncated Capture–Recapture Counts

et al. 2016

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Summary. Capture-recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the truncated count distribution to estimate the number of unobserved units. We consider ratios of neighboring count probabilities, estimated by ratios of observed frequencies, regardless of whether we have a zero-truncated or an untruncated distribution. Rocchetti et al. (2011) have shown that, for densities in the Katz family, these ratios can be modeled by a regression approach, and Rocchetti et al. (2014) have specialized the approach to the beta-binomial distribution. Once the regression model has been estimated, the unobserved frequency of zero counts can be simply derived. The guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution. However, a full analysis of the connection between the regression model and the associated count distribution has been missing. In this manuscript, we fill the gap and show that the regression model approach leads, under general conditions, to a valid count distribution; we also consider a wider class of regression models, based on fractional polynomials. The proposed approach is illustrated by analyzing various empirical applications, and by means of a simulation study.

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Estimating the False Negative Fraction for a Multiple Screening Test for Bowel Cancer When Negatives Are Not Verified

Cited by 10 publications

References 19 publications

Regression-Based Estimation of the False Negative Fraction When Multiple Negatives are Unverified

Regression-Based Estimation of the False Negative Fraction When Multiple Negatives are Unverified

Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences

A Flexible Ratio Regression Approach for Zero-Truncated Capture–Recapture Counts

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