Analysis of multivariate categorical data with misclassification errors by triple sampling schemes

Previous work has been carried out on the use of double-sampling schemes for inference from categorical data subject to misclassification. The double-sampling schemes utilize a sample of n units classified by both a fallible and true device and another sample of n₂ units classified only by a fallible device. In actual applications, one often hasavailable a third sample of n₁ units, which is classified only by the true device. In this article we develop techniques of fitting log-linear models under various misclassification structures for a general triple-sampling scheme. The estimation is by maximum likelihood and the fitted models are hierarchical. The methodology is illustrated by applying it to data in traffic safety research from a study on the effectiveness of belts in reducing injuries.     

The estimation of gross flows in the presence of measurement error using auxiliary variables

Classification error can lead to substantial biases in the estimation of gross flows from longitudinal data. We propose a method to adjust flow estimates for bias, based on fitting separate multinomial logistic models to the classification error probabilities and the true state transition probabilities using values of auxiliary variables. Our approach has the advantages that it does not require external information on misclassification rates, it permits the identification of factors that are related to misclassification and true transitions and it does not assume independence between classification errors at successive points in time. Constraining the prediction of the stocks to agree with the observed stocks protects against model misspecification. We apply the approach to data on women from the Panel Study of Income Dynamics with three categories of labour force status. The model fitted is shown to have interpretable coefficient estimates and to provide a good fit. Simulation results indicate good performance of the model in predicting the true flows and robustness against departures from the model postulated.     

Maximum-likelihood and closed-form estimators of epidemiologic measures under misclassification

There is a large literature on estimation under misclassification. The present paper reviews epidemiologic inference under misclassification in the multiway contingency-table setting, and addresses a few controversial issues. In the 1990s, claims of inefficiency of early closed-form estimators of odds ratios under misclassification arose from misapplication of the estimators to studies with internal validation. In reality, these estimators are maximum likelihood (ML) and hence efficient under the external-validation assumptions used for their derivation. For the internal-validation case, a new closed-form estimator is derived that incorporates the nondifferentiality constraint into the predictive-value (“direct” or “inverse-matrix”) estimator. Results are presented in a general framework that applies to misclassification in models for multiway tables, and that allows the target parameter to be any measure of association or effect.     

Can efficiency be gained by correcting for misclassification?

This paper considers 2×2 tables arising from case–control studies in which the binary exposure may be misclassified. We found circumstances under which the inverse matrix method provides a more efficient odds ratio estimator than the naive estimator. We provide some intuition for the findings, and also provide a formula for obtaining the minimum size of a validation study such that the variance of the odds ratio estimator from the inverse matrix method is smaller than that of the naive estimator, thereby ensuring an advantage for the misclassification corrected result. As a corollary of this result, we show that correcting for misclassification does not necessarily lead to a widening of the confidence intervals, but, rather, in addition to producing a consistent estimate, can also produce one that is more efficient.     

A comparative study of the K-means algorithm and the normal mixture model for clustering: Bivariate homoscedastic case

The K-means algorithm and the normal mixture model method are two common clustering methods. The K-means algorithm is a popular heuristic approach which gives reasonable clustering results if the component clusters are ball-shaped. Currently, there are no analytical results for this algorithm if the component distributions deviate from the ball-shape. This paper analytically studies how the K-means algorithm changes its classification rule as the normal component distributions become more elongated under the homoscedastic assumption and compares this rule with that of the Bayes rule from the mixture model method. We show that the classification rules of both methods are linear, but the slopes of the two classification lines change in the opposite direction as the component distributions become more elongated. The classification performance of the K-means algorithm is then compared to that of the mixture model method via simulation. The comparison, which is limited to two clusters, shows that the K-means algorithm provides poor classification performances consistently as the component distributions become more elongated while the mixture model method can potentially, but not necessarily, take advantage of this change and provide a much better classification performance.     

Comparisons of decision tree methods using water data

This article demonstrates the application of classification trees (decision trees), logistic regression (LR), and linear discriminant function (LDR) to classify data of water quality (i.e., whether the water is fit for drinking on not fit for drinking). The data on water quality were obtained from Pakistan Council of Research in Water Resources (PCRWR) for two cities of Pakistan—one representing industrial environment (Sialkot) and the other one representing non-industrial environment (Narowal). To classify data on water quality, three statistical tools were employed—the Decision Tree methodology using Gini Index, LR, and LDA—using R software library. The results obtained by the said three techniques were compared using misclassification rates (a model with minimum value of misclassification rate is better). It was witnessed that LR performed well than the other two techniques while the Decision trees and LDA performed equally well. But for illustration purposes decision trees technique is comparatively easy to draw and interpret.     

Variance-penalized response-adaptive randomization with mismeasurement

We consider response-adaptive design of clinical trials under a variance-penalized criterion in the presence of mismeasurement. An explicit expression for the variance-penalized criterion with misclassified dichotomous responses is derived for response-adaptive designs and some properties are discussed. A new target proportion of treatment allocation is proposed under the criterion and related simulation results are presented.     

A New Estimator for a Population Proportion Using Group Testing

The maximum likelihood estimator is widely used in estimating the population proportion using group testing. However, it is positive biased and some alternatives have been raised in literatures. In this study, we propose a new estimator by weighted combination of order statistics. Two rules are supplied to determine the unknown weight. Using the rule of minimizing the absolute bias, our estimator is almost unbiased in most cases shown by simulations. Using the rule of minimizing the mean square error, a simple estimator with weight 1 is recommended for its good performance.     

Divergence-based confidence intervals in false-positive misclassification model

In this article, we introduce minimum divergence estimators of parameters of a binary response model when data are subject to false-positive misclassification and obtained using a double-sampling plan. Under this set up, the problem of goodness-of-fit is considered and divergence-based confidence intervals (CIs) for a population proportion parameter are derived. A simulation experiment is carried out to compare the coverage probabilities of the new CIs. An application to real data is also given.