On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables

Gustafson, Paul

doi:10.1214/088342305000000098

Cited by 165 publications

(204 citation statements)

References 27 publications

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“…This suggests that with the current priors some parameters of model 4 are not identifiable or only weakly identifiable with these data. In a Bayesian context, defining additional informative priors may help overcome this problem (31)(32)(33). We therefore adopted a Bayesian Lasso approach (34) to estimate the 10 additional covariate associations in model 4 (Table 3).…”

Section: Bayesian Estimationmentioning

confidence: 99%

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Schumacher¹,

Smeden²,

Dendukuri³

et al. 2016

American Journal of Epidemiology

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Evaluation of tests for the diagnosis of childhood pulmonary tuberculosis (CPTB) is complicated by the absence of an accurate reference test. We present a Bayesian latent class analysis in which we evaluated the accuracy of 5 diagnostic tests for CPTB. We used data from a study of 749 hospitalized South African children suspected to have CPTB from 2009 to 2014. The following tests were used: mycobacterial culture, smear microscopy, Xpert MTB/RIF (Cepheid Inc.), tuberculin skin test (TST), and chest radiography. We estimated the prevalence of CPTB to be 27% (95% credible interval (CrI): 21, 35). The sensitivities of culture, Xpert, and smear microscopy were estimated to be 60% (95% CrI: 46, 76), 49% (95% CrI: 38, 62), and 22% (95% CrI: 16, 30), respectively; specificities of these tests were estimated in accordance with prior information and were close to 100%. Chest radiography was estimated to have a sensitivity of 64% (95% CrI: 55, 73) and a specificity of 78% (95% CrI: 73, 83). Sensitivity of the TST was estimated to be 75% (95% CrI: 61, 84), and it decreased substantially among children who were malnourished and infected with human immunodeficiency virus (56%). The specificity of the TST was 69% (95% CrI: 63%, 76%). Furthermore, it was estimated that 46% (95% CrI: 42, 49) of CPTB-negative cases and 93% (95% CrI: 82; 98) of CPTB-positive cases received antituberculosis treatment, which indicates substantial overtreatment and limited undertreatment. childhood pulmonary tuberculosis; diagnosis; latent class analysis; overtreatment; sensitivity; specificity Abbreviations: CPTB, childhood pulmonary tuberculosis; CrI, credible interval; HIV, human immunodeficiency virus; PTB, pulmonary tuberculosis; TST, tuberculin skin test.Tuberculosis in children is an important global health problem. There are an estimated 0.5 to 1 million new cases each year (1, 2), with childhood pulmonary tuberculosis (CPTB) being the most common form. One of the major challenges in diagnosing CPTB is the lack of sensitive diagnostic tests (3-6). In clinical practice, the diagnosis of CPTB therefore relies on a combination of imperfect tests, which gives rise to unknown degrees of under-or overtreatment (7,8).In recent years, new tests for CPTB have been developed, and their accuracy has been evaluated using mycobacterial culture as a reference standard (4, 9). Although culture is currently considered the best available reference standard, its sensitivity for detecting CPTB is acknowledged to be imperfect (3,4,10). The culture reference standard thus inevitably leads to true CPTB case patients being misclassified as being negative for CPTB. If these misclassifications by the reference standard are ignored, then the assessment of the test accuracy can be biased (11)(12)(13)(14).To address the problem of the lack of an accurate reference standard, multivariable diagnostic algorithms for CPTB have been proposed to combine information from multiple imperfect diagnostic tests (including tests for tuberculosis infection and clinical data) in a sy...

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Section: Bayesian Estimationmentioning

confidence: 99%

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Schumacher¹,

Smeden²,

Dendukuri³

et al. 2016

American Journal of Epidemiology

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“…It is increasingly realized that data collected from observational studies cannot give unbiased estimates of epidemiological quantities of interest (e.g. [17,20]), and that standard confidence intervals often underestimate the true uncertainty associated with estimates as they ignore bias. Therefore it has often been suggested that realistic models of epidemiologic data should take into account of uncertainty of bias by using models that integrate data with subjective "expert" knowledge [17,20,25].…”

Section: Discussionmentioning

confidence: 99%

“…[17,20]), and that standard confidence intervals often underestimate the true uncertainty associated with estimates as they ignore bias. Therefore it has often been suggested that realistic models of epidemiologic data should take into account of uncertainty of bias by using models that integrate data with subjective "expert" knowledge [17,20,25]. Some have proposed that we seek out feasible region of inference given subjectively specified constraints for the unidentifiable parameters [31].…”

Section: Discussionmentioning

confidence: 99%

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Robust Bayesian Sensitivity Analysis for Case–Control Studies with Uncertain Exposure Misclassification Probabilities

Mak

Best

Rushton

2015

The International Journal of Biostatistics

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Exposure misclassification in case-control studies leads to bias in odds ratio estimates. There has been considerable interest recently to account for misclassification in estimation so as to adjust for bias as well as more accurately quantify uncertainty. These methods require users to elicit suitable values or prior distributions for the misclassification probabilities. In the event where exposure misclassification is highly uncertain, these methods are of limited use, because the resulting posterior uncertainty intervals tend to be too wide to be informative. Posterior inference also becomes very dependent on the subjectively elicited prior distribution. In this paper, we propose an alternative "robust Bayesian" approach, where instead of eliciting prior distributions for the misclassification probabilities, a feasible region is given. The extrema of posterior inference within the region are sought using an inequality constrained optimization algorithm. This method enables sensitivity analyses to be conducted in a useful way as we do not need to restrict all of our unknown parameters to fixed values, but can instead consider ranges of values at a time.

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“…As the causal parameter of interest, b 1 , lies in φ I , the same must be true for this parameter in the 'full' model [10]. The 'full' and correlated errors models should therefore both yield the correct mean value for b 1 in large samples.…”

Section: The Relationship Between the Full Model And The Correlated Ementioning

confidence: 98%

On the choice of parameterisation and priors for the Bayesian analyses of Mendelian randomisation studies

Jones

Thompson

Didelez

et al. 2012

Statistics in Medicine

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Mendelian randomisation is a form of instrumental variable analysis that estimates the causal effect of an intermediate phenotype or exposure on an outcome or disease in the presence of unobserved confounding, using a genetic variant as the instrument. A Bayesian approach allows current knowledge to be incorporated into the analysis in the form of informative prior distributions, and the unobserved confounder can be modelled explicitly. We consider Bayesian methods for Mendelian randomisation in the case where all relationships are linear, and there are no interactions.A 'full' model in which the unobserved confounder is included explicitly is not completely identifiable, although the causal parameter can be estimated. We compare inferences from this general but nonidentified model with a reduced parameter model that is identifiable. We show that, theoretically, additional information about the causal parameter can be obtained by using the non-identifiable full model, rather than the identifiable reduced model, but that this is advantageous only when realistically informative priors are used and when the instrument is weak or the sample size is small. Furthermore, we consider the impact of using 'vague' versus 'informative' priors.

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On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables

Cited by 165 publications

References 27 publications

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Diagnostic Test Accuracy in Childhood Pulmonary Tuberculosis: A Bayesian Latent Class Analysis

Robust Bayesian Sensitivity Analysis for Case–Control Studies with Uncertain Exposure Misclassification Probabilities

On the choice of parameterisation and priors for the Bayesian analyses of Mendelian randomisation studies

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