Curious phenomena in Bayesian adjustment for exposure misclassification

Many epidemiologic investigations involve some discussion of exposure misclassification, but rarely is there an attempt to adjust for misclassification formally in the statistical analysis. Rather, investigators tend to rely on intuition to comment qualitatively on how misclassification might impact their findings. We point out several ways in which intuition might fail, in the context of unmatched case-control analysis with non-differential exposure misclassification. Particularly, we focus on how intuition can conflict with the results of a Bayesian analysis that accounts for the various uncertainties at hand. First, the Bayesian adjustment for misclassification can weaken the evidence about the direction of an exposure-disease association. Second, admitting uncertainty about the misclassification parameters can lead to narrower interval estimates concerning the association. We focus on the simple setting of unmatched case-control analysis with binary exposure and without adjustment for confounders, though much of our discussion should be relevant more generally.     

Bayesian analysis of a matched case–control study with expert prior information on both the misclassification of exposure and the exposure–disease association

We propose a Bayesian adjustment for the misclassification of a binary exposure variable in a matched case–control study. The method admits a priori knowledge about both the misclassification parameters and the exposure–disease association. The standard Dirichlet prior distribution for a multinomial model is extended to allow separation of prior assertions about the exposure–disease association from assertions about other parameters. The method is applied to a study of occupational risk factors for new‐onset adult asthma. Copyright © 2009 John Wiley & Sons, Ltd.     

Using full‐cohort data in nested case–control and case–cohort studies by multiple imputation

In many large prospective cohorts, expensive exposure measurements cannot be obtained for all individuals. Exposure–disease association studies are therefore often based on nested case–control or case–cohort studies in which complete information is obtained only for sampled individuals. However, in the full cohort, there may be a large amount of information on cheaply available covariates and possibly a surrogate of the main exposure(s), which typically goes unused. We view the nested case–control or case–cohort study plus the remainder of the cohort as a full‐cohort study with missing data. Hence, we propose using multiple imputation (MI) to utilise information in the full cohort when data from the sub‐studies are analysed. We use the fully observed data to fit the imputation models. We consider using approximate imputation models and also using rejection sampling to draw imputed values from the true distribution of the missing values given the observed data. Simulation studies show that using MI to utilise full‐cohort information in the analysis of nested case–control and case–cohort studies can result in important gains in efficiency, particularly when a surrogate of the main exposure is available in the full cohort. In simulations, this method outperforms counter‐matching in nested case–control studies and a weighted analysis for case–cohort studies, both of which use some full‐cohort information. Approximate imputation models perform well except when there are interactions or non‐linear terms in the outcome model, where imputation using rejection sampling works well. Copyright © 2013 John Wiley & Sons, Ltd.     

Bayesian inference for the stereotype regression model: Application to a case–control study of prostate cancer

The stereotype regression model for categorical outcomes, proposed by Anderson (J. Roy. Statist. Soc. B. 1984; 46 :1–30) is nested between the baseline‐category logits and adjacent category logits model with proportional odds structure. The stereotype model is more parsimonious than the ordinary baseline‐category (or multinomial logistic) model due to a product representation of the log‐odds‐ratios in terms of a common parameter corresponding to each predictor and category‐specific scores. The model could be used for both ordered and unordered outcomes. For ordered outcomes, the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable, but are inherently multi‐dimensional in nature. As pointed out by Greenland (Statist. Med. 1994; 13 :1665–1677), an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome‐stratified sampling as in case–control studies. In addition, for matched case–control studies, the stereotype model is amenable to classical conditional likelihood principle, whereas there is no reduction due to sufficiency under the proportional odds model. In spite of these attractive features, the model has been applied less, as there are issues with maximum likelihood estimation and likelihood‐based testing approaches due to non‐linearity and lack of identifiability of the parameters. We present comprehensive Bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach. We illustrate our methodology by analyzing data from The Flint Men's Health Study, a case–control study of prostate cancer in African‐American men aged 40–79 years. We use clinical staging of prostate cancer in terms of Tumors, Nodes and Metastasis as the categorical response of interest. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian analysis of pair‐matched case‐control studies subject to outcome misclassification

We examine the impact of nondifferential outcome misclassification on odds ratios estimated from pair‐matched case‐control studies and propose a Bayesian model to adjust these estimates for misclassification bias. The model relies on access to a validation subgroup with confirmed outcome status for all case‐control pairs as well as prior knowledge about the positive and negative predictive value of the classification mechanism. We illustrate the model's performance on simulated data and apply it to a database study examining the presence of ten morbidities in the prodromal phase of multiple sclerosis.     

Calibration and seasonal adjustment for matched case–control studies of vitamin D and cancer

Vitamin D measurements are influenced by seasonal variation and specific assay used. Motivated by multicenter studies of associations of vitamin D with cancer, we formulated an analytic framework for matched case–control data that accounts for seasonal variation and calibrates to a reference assay. Calibration data were obtained from controls sampled within decile strata of the uncalibrated vitamin D values. Seasonal sine–cosine series were fit to control data. Practical findings included the following: (1) failure to adjust for season and calibrate increased variance, bias, and mean square error and (2) analysis of continuous vitamin D requires a variance adjustment for variation in the calibration estimate. An advantage of the continuous linear risk model is that results are independent of the reference date for seasonal adjustment. (3) For categorical risk models, procedures based on categorizing the seasonally adjusted and calibrated vitamin D have near nominal operating characteristics; estimates of log odds ratios are not robust to choice of seasonal reference date, however. Thus, public health recommendations based on categories of vitamin D should also define the time of year to which they refer. This work supports the use of simple methods for calibration and seasonal adjustment and is informing analytic approaches for the multicenter Vitamin D Pooling Project for Breast and Colorectal Cancer. Published 2016. This article has been contributed to by US Government employees and their work is in the public domain in the USA.     

A concordance index for matched case–control studies with applications in cancer risk

In unmatched case–control studies, the area under the receiver operating characteristic (ROC) curve (AUC) may be used to measure how well a variable discriminates between cases and controls. The AUC is sometimes used in matched case–control studies by ignoring matching, but it lacks interpretation because it is not based on an estimate of the ROC for the population of interest. We introduce an alternative measure of discrimination that is the concordance of risk factors conditional on the matching factors. Parametric and non‐parametric estimators are given for different matching scenarios, and applied to real data from breast and lung cancer case–control studies. Diagnostic plots to verify the constancy of discrimination over matching factors are demonstrated. The proposed simple measure is easy to use, interpret, more efficient than unmatched AUC statistics and may be applied to compare the conditional discrimination performance of risk factors. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessing risk prediction models in case–control studies using semiparametric and nonparametric methods

The predictiveness curve is a graphical tool that characterizes the population distribution of Risk(Y)=P(D=1|Y), where D denotes a binary outcome such as occurrence of an event within a specified time period and Y denotes predictors. A wider distribution of Risk(Y) indicates better performance of a risk model in the sense that making treatment recommendations is easier for more subjects. Decisions are more straightforward when a subject's risk is deemed to be high or low. Methods have been developed to estimate predictiveness curves from cohort studies. However, early phase studies to evaluate novel risk prediction markers typically employ case–control designs. Here, we present semiparametric and nonparametric methods for evaluating a continuous risk prediction marker that accommodates case–control data. Small sample properties are investigated through simulation studies. The semiparametric methods are substantially more efficient than their nonparametric counterparts under a correctly specified model. We generalize them to settings where multiple prediction markers are involved. Applications to prostate cancer risk prediction markers illustrate methods for comparing the risk prediction capacities of markers and for evaluating the increment in performance gained by adding a marker to a baseline risk model. We propose a modified Hosmer–Lemeshow test for case–control study data to assess calibration of the risk model that is a natural complement to this graphical tool. Copyright © 2010 John Wiley & Sons, Ltd.     

A Bayesian approach to strengthen inference for case‐control studies with multiple error‐prone exposure assessments

In case‐control studies, exposure assessments are almost always error‐prone. In the absence of a gold standard, two or more assessment approaches are often used to classify people with respect to exposure. Each imperfect assessment tool may lead to misclassification of exposure assignment; the exposure misclassification may be differential with respect to case status or not; and, the errors in exposure classification under the different approaches may be independent (conditional upon the true exposure status) or not. Although methods have been proposed to study diagnostic accuracy in the absence of a gold standard, these methods are infrequently used in case‐control studies to correct exposure misclassification that is simultaneously differential and dependent. In this paper, we proposed a Bayesian method to estimate the measurement‐error corrected exposure‐disease association, accounting for both differential and dependent misclassification. The performance of the proposed method is investigated using simulations, which show that the proposed approach works well, as well as an application to a case‐control study assessing the association between asbestos exposure and mesothelioma. Copyright © 2013 John Wiley & Sons, Ltd.     

A polytomous conditional likelihood approach for combining matched and unmatched case–control studies

In genetic association studies it is becoming increasingly imperative to have large sample sizes to identify and replicate genetic effects. To achieve these sample sizes, many research initiatives are encouraging the collaboration and combination of several existing matched and unmatched case–control studies. Thus, it is becoming more common to compare multiple sets of controls with the same case group or multiple case groups to validate or confirm a positive or negative finding. Usually, a naive approach of fitting separate models for each case–control comparison is used to make inference about disease–exposure association. But, this approach does not make use of all the observed data and hence could lead to inconsistent results. The problem is compounded when a common case group is used in each case–control comparison. An alternative to fitting separate models is to use a polytomous logistic model but, this model does not combine matched and unmatched case–control data. Thus, we propose a polytomous logistic regression approach based on a latent group indicator and a conditional likelihood to do a combined analysis of matched and unmatched case–control data. We use simulation studies to evaluate the performance of the proposed method and a case–control study of multiple myeloma and Inter‐Leukin‐6 as an example. Our results indicate that the proposed method leads to a more efficient homogeneity test and a pooled estimate with smaller standard error. Copyright © 2010 John Wiley & Sons, Ltd.     

Using family members to augment genetic case–control studies of a life‐threatening disease

Survival bias is difficult to detect and adjust for in case–control genetic association studies but can invalidate findings when only surviving cases are studied and survival is associated with the genetic variants under study. Here, we propose a design where one genotypes genetically informative family members (such as offspring, parents, and spouses) of deceased cases and incorporates that surrogate genetic information into a retrospective maximum likelihood analysis. We show that inclusion of genotype data from first‐degree relatives permits unbiased estimation of genotype association parameters. We derive closed‐form maximum likelihood estimates for association parameters under the widely used log‐additive and dominant association models. Our proposed design not only permits a valid analysis but also enhances statistical power by augmenting the sample with indirectly studied individuals. Gene variants associated with poor prognosis can also be identified under this design. We provide simulation results to assess performance of the methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Adjusting for differential misclassification in matched case-control studies utilizing health administrative data

In epidemiological studies of secondary data sources, lack of accurate disease classifications often requires investigators to rely on diagnostic codes generated by physicians or hospital systems to identify case and control groups, resulting in a less-than-perfect assessment of the disease under investigation. Moreover, because of differences in coding practices by physicians, it is hard to determine the factors that affect the chance of an incorrectly assigned disease status. What results is a dilemma where assumptions of non-differential misclassification are questionable but, at the same time, necessary to proceed with statistical analyses. This paper develops an approach to adjust exposure-disease association estimates for disease misclassification, without the need of simplifying non-differentiality assumptions, or prior information about a complicated classification mechanism. We propose to leverage rich temporal information on disease-specific healthcare utilization to estimate each participant's probability of being a true case and to use these estimates as weights in a Bayesian analysis of matched case-control data. The approach is applied to data from a recent observational study into the early symptoms of multiple sclerosis (MS), where MS cases were identified from Canadian health administrative databases and matched to population controls that are assumed to be correctly classified. A comparison of our results with those from non-differentially adjusted analyses reveals conflicting inferences and highlights that ill-suited assumptions of non-differential misclassification can exacerbate biases in association estimates.     

Sample size/power calculation for stratified case–cohort design

The case–cohort (CC) study design usually has been used for risk factor assessment in epidemiologic studies or disease prevention trials for rare diseases. The sample size/power calculation for a stratified CC (SCC) design has not been addressed before. This article derives such result based on a stratified test statistic. Simulation studies show that the proposed test for the SCC design utilizing small sub‐cohort sampling fractions is valid and efficient for situations where the disease rate is low. Furthermore, optimization of sampling in the SCC design is discussed and compared with proportional and balanced sampling techniques. An epidemiological study is provided to illustrate the sample size calculation under the SCC design. Copyright © 2014 John Wiley & Sons, Ltd.     

Bayesian adjustment for the misclassification in both dependent and independent variables with application to a breast cancer study

In this paper, we propose a Bayesian method to address misclassification errors in both independent and dependent variables. Our work is motivated by a study of women who have experienced new breast cancers on two separate occasions. We call both cancers primary, because the second is usually not considered as the result of a metastasis spreading from the first. Hormone receptors (HRs) are important in breast cancer biology, and it is well recognized that the measurement of HR status is subject to errors. This discordance in HR status for two primary breast cancers is of concern and might be an important reason for treatment failure. To sort out the information on true concordance rate from the observed concordance rate, we consider a logistic regression model for the association between the HR status of the two cancers and introduce the misclassification parameters (i.e., sensitivity and specificity) accounting for the misclassification in HR status. The prior distribution for sensitivity and specificity is based on how HR status is actually assessed in laboratory procedures. To account for the nonlinear effect of one error‐free covariate, we introduce the B‐spline terms in the logistic regression model. Our findings indicate that the true concordance rate of HR status between two primary cancers is greater than the observed value. Copyright © 2016 John Wiley & Sons, Ltd.     

An easy‐to‐implement approach for analyzing case–control and case‐only studies assuming gene–environment independence and Hardy–Weinberg equilibrium

The case–control study is a simple and an useful method to characterize the effect of a gene, the effect of an exposure, as well as the interaction between the two. The control‐free case‐only study is yet an even simpler design, if interest is centered on gene–environment interaction only. It requires the sometimes plausible assumption that the gene under study is independent of exposures among the non‐diseased in the study populations. The Hardy–Weinberg equilibrium is also sometimes reasonable to assume. This paper presents an easy‐to‐implement approach for analyzing case–control and case‐only studies under the above dual assumptions. The proposed approach, the ‘conditional logistic regression with counterfactuals’, offers the flexibility for complex modeling yet remains well within the reach to the practicing epidemiologists. When the dual assumptions are met, the conditional logistic regression with counterfactuals is unbiased and has the correct type I error rates. It also results in smaller variances and achieves higher powers as compared with using the conventional analysis (unconditional logistic regression). Copyright © 2010 John Wiley & Sons, Ltd.