In this article we consider unidirectional covariate misclassification, meaning that the direction of classification error is known. We investigate the identifiability of Bayesian regression models when a binary covariate is subject to unidirectional misclassification. In the Bayesian framework we consider whether knowledge of the direction of error suffices, so that adjustment for misclassification can be undertaken without any source of information on the magnitude of error. Although measurement error models are generally non‐identified without such information, for the case of unidirectional misclassification, we do obtain model identifiability when the response variable is non‐binary. For the binary response model that is non‐identified we examine the extent of partial identification. The limiting posterior distributions of the parameters are obtained for this partially identified model, for two different prior distributions. We perform computational studies that illustrate statistical learning, for the three cases where the model is easily identified, weakly identified, and partially identified. A case study is performed using real data. The Canadian Journal of Statistics 44: 198–218; 2016 © 2016 Statistical Society of Canada

In insurance underwriting, misrepresentation represents the type of insurance fraud when an applicant purposely makes a false statement on a risk factor that may lower his or her cost of insurance. Under the insurance ratemaking context, we propose to use the expectation-maximization (EM) algorithm to perform maximum likelihood estimation of the regression effects and the prevalence of misrepresentation for the misrepresentation model proposed by Xia and Gustafson [(2016) The Canadian Journal of Statistics, 44, 198–218]. For applying the EM algorithm, the unobserved status of misrepresentation is treated as a latent variable in the complete-data likelihood function. We derive the iterative formulas for the EM algorithm and obtain the analytical form of the Fisher information matrix for frequentist inference on the parameters of interest for lognormal losses. We implement the algorithm and demonstrate that valid inference can be obtained on the risk effect despite the unobserved status of misrepresentation. Applying the proposed algorithm, we perform a loss severity analysis with the Medical Expenditure Panel Survey data. The analysis reveals not only the potential impact misrepresentation may have on the risk effect but also statistical evidence on the presence of misrepresentation in the self-reported insurance status.

Venue sampling is a common sampling method for populations of men who have sex with men (MSM); however, men who visit venues frequently are more likely to be recruited. While statistical adjustment methods are recommended, these have received scant attention in the literature. We developed a novel approach to adjust for frequency of venue attendance (FVA) and assess the impact of associated bias in the ManCount Study, a venue-based survey of MSM conducted in Vancouver, British Columbia, Canada, in 2008-2009 to measure the prevalence of human immunodeficiency virus and other infections and associated behaviors. Sampling weights were determined from an abbreviated list of questions on venue attendance and were used to adjust estimates of prevalence for health and behavioral indicators using a Bayesian, model-based approach. We found little effect of FVA adjustment on biological or sexual behavior indicators (primary outcomes); however, adjustment for FVA did result in differences in the prevalence of demographic indicators, testing behaviors, and a small number of additional variables. While these findings are reassuring and lend credence to unadjusted prevalence estimates from this venue-based survey, adjustment for FVA did shed important insights on MSM subpopulations that were not well represented in the sample.

Universal screening for Lynch syndrome has been advocated for colorectal carcinoma but its utility in small bowel adenocarcinoma has not been reported. We analyzed a consecutive series of 71 small bowel adenocarcinomas identified over an 8-year period for DNA mismatch repair (MMR) protein expression to (1) compare the clinicopathologic features of small bowel adenocarcinoma stratified into MMR-deficient (MMRD) and MMR-proficient (MMRP) groups and (2) examine the patterns of MMR protein expression in small bowel adenocarcinoma compared with colorectal carcinoma. Six of 71 (8.5%) small bowel adenocarcinomas and 149 of 1291 (11.5%) colorectal carcinomas demonstrated MMRD. The 6 MMRD small bowel adenocarcinomas had the following expression pattern: 3 with concurrent loss of MSH2 and MSH6, 1 with isolated loss of MSH6, and 2 with concurrent loss of MLH1 and PMS2 in patients with a family history suggestive of genetic cancer susceptibility. Histopathology suggestive of MMR protein deficiency as proposed by the revised Bethesda guidelines was commonly seen in both MMRP (63%) and MMRD (67%) small bowel adenocarcinomas (P>0.05). MMRD small bowel adenocarcinoma more frequently demonstrated abnormalities of MSH2 and/or MSH6 (4/6, 67%) compared with MMRD colorectal carcinoma (23/149, 15%) (P=0.01). None of the MMRD small bowel adenocarcinomas harbored the BRAF V600E mutation, whereas 60% of MMRD colorectal carcinomas were positive for BRAF V600E with concurrent loss of MLH1 and PMS2 expression. Small bowel adenocarcinoma more frequently harbored Lynch syndrome-associated MMRD compared with colorectal carcinoma, providing support for screening of small bowel adenocarcinoma to identify patients at risk for Lynch syndrome. In contrast to colorectal carcinoma, sporadic MLH1 deficiency is not seen in small bowel adenocarcinoma. Clinicopathologic and histologic features do not distinguish between MMRP and MMRD small bowel adenocarcinoma indicating that universal screening in small bowel adenocarcinoma is necessary to detect patients at risk for Lynch syndrome.

This article considers misclassification of categorical covariates in the context of regression analysis; if unaccounted for, such errors usually result in mis-estimation of model parameters. With the presence of additional covariates, we exploit the fact that explicitly modelling non-differential misclassification with respect to the response leads to a mixture regression representation. Under the framework of mixture of experts, we enable the reclassification probabilities to vary with other covariates, a situation commonly caused by misclassification that is differential on certain covariates and/or by dependence between the misclassified and additional covariates. Using Bayesian inference, the mixture approach combines learning from data with external information on the magnitude of errors when it is available. In addition to proving the theoretical identifiability of the mixture of experts approach, we study the amount of efficiency loss resulting from covariate misclassification and the usefulness of external information in mitigating such loss. The method is applied to adjust for misclassification on self-reported cocaine use in the Longitudinal Studies of HIV-Associated Lung Infections and Complications.

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When estimating the prevalence of a binary trait in a population, the presence of a hidden sub-population that cannot be sampled will lead to nonidentifiability and potentially biased estimation. We propose a Bayesian model of trait prevalence for a weighted sample from the non-hidden portion of the population, by modeling the relationship between prevalence and sampling probability. We studied the behavior of the posterior distribution on population prevalence, with the large-sample limits of posterior distributions obtained in simple analytical forms that give intuitively expected properties. We performed MCMC simulations on finite samples to evaluate the effectiveness of statistical learning. We applied the model and the results to two illustrative datasets arising from weighted sampling. Our work confirms that sensible results can be obtained using Bayesian analysis, despite the nonidentifiability in this situation.

When assessing association between a binary trait and some covariates, the binary response may be subject to unidirectional misclassification. Unidirectional misclassification can occur when revealing a particular level of the trait is associated with a type of cost, such as a social desirability or financial cost. The feasibility of addressing misclassification is commonly obscured by model identification issues. The current paper attempts to study the efficacy of inference when the binary response variable is subject to unidirectional misclassification. From a theoretical perspective, we demonstrate that the key model parameters possess identifiability, except for the case with a single binary covariate. From a practical standpoint, the logistic model with quantitative covariates can be weakly identified, in the sense that the Fisher information matrix may be near singular. This can make learning some parameters difficult under certain parameter settings, even with quite large samples. In other cases, the stronger identification enables the model to provide more effective adjustment for unidirectional misclassification. An extension to the Poisson approximation of the binomial model reveals the identifiability of the Poisson and zero-inflated Poisson models. For fully identified models, the proposed method adjusts for misclassification based on learning from data. For binary models where there is difficulty in identification, the method is useful for sensitivity analyses on the potential impact from unidirectional misclassification.