Test procedures for disease prevalence with partially validated data

Multiple test procedures of disease prevalence based on stratified partially validated series in the presence of a gold standard

This paper discusses the problem of disease prevalence in clinical studies, focusing on multiple comparisons based on stratified partially validated series in the presence of a gold standard. Five test statistics, including two Wald-type test statistics, the inverse hyperbolic tangent transformation test statistic, likelihood ratio test statistic, and score test statistic, are proposed to conduct multiple comparisons. To control the overall type I error rate, several adjustment procedures are developed, namely the Bonferroni, Single-step adjusted MaxT, Single-step adjusted MinP, Holm's Step-down, and Hochberg's step-up procedures, based on these test statistics. The performance of the proposed methods is evaluated through simulation studies in terms of the empirical type I error rate and empirical power. Simulation results show that the Single-step adjusted MaxT procedure and Single-step adjusted MinP procedure generally outperform the other three procedures, and these two test procedures based on all test statistics have satisfactory performance. Notably, the Single-step adjusted MinP procedure tends to exhibit higher empirical power than the Single-step adjusted MaxT procedure. Furthermore, the Step-down and Step-up procedures show greater power compared to the Bonferroni method. The study also observes that as the validated ratio increases, the empirical type I errors of all test procedures approach the nominal level while maintaining higher power. Two real examples are presented to illustrate the proposed methods.

Confidence interval construction for proportion difference from partially validated series with two fallible classifiers

This article investigates the confidence interval (CI) construction of proportion difference for two independent partially validated series under the double-sampling scheme in which both classifiers are fallible. Several CIs based on the variance estimates recovery method of combining confidence limits from asymptotic, bootstrap, and Bayesian methods for two independent binomial proportions are developed under two models. Simulation results show that all CIs except for the bootstrap percentile-t CI and Bayesian credible interval with uniform prior under the independence model and all CIs under the dependence model generally perform well and are recommended. Two examples are used to illustrate the methodologies.

Homogeneity testing for binomial proportions under stratified double-sampling scheme with two fallible classifiers

This article investigates the homogeneity testing problem of binomial proportions for stratified partially validated data obtained by double-sampling method with two fallible classifiers. Several test procedures, including the weighted-least-squares test with/without log-transformation, logit-transformation and double log-transformation, and likelihood ratio test and score test, are developed to test the homogeneity under two models, distinguished by conditional independence assumption of two classifiers. Simulation results show that score test performs better than other tests in the sense that the empirical size is generally controlled around the nominal level, and hence be recommended to practical applications. Other tests also perform well when both binomial proportions and sample sizes are not small. Approximate sample sizes based on score test, likelihood ratio test and the weighted-least-squares test with double log-transformation are generally accurate in terms of the empirical power and type I error rate with the estimated sample sizes, and hence be recommended. An example from the malaria study is illustrated by the proposed methodologies.

Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example.

Interval estimation for a proportion using a double-sampling scheme with two fallible classifiers

Double-sampling schemes using one classifier assessing the whole sample and another classifier assessing a subset of the sample have been introduced for reducing classification errors when an infallible or gold standard classifier is unavailable or impractical. Inference procedures have previously been proposed for situations where an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Here, we consider the case where both classifiers are fallible, proposing and evaluating several confidence interval procedures for a proportion under two models, distinguished by the assumption regarding ascertainment of two classifiers. Simulation results suggest that the modified Wald-based confidence interval, Score-based confidence interval, two Bayesian credible intervals, and the percentile Bootstrap confidence interval performed reasonably well even for small binomial proportions and small validated sample under the model with the conditional independent assumption, and the confidence interval derived from the Wald test with nuisance parameters appropriately evaluated, likelihood ratio-based confidence interval, Score-based confidence interval, and the percentile Bootstrap confidence interval performed satisfactory in terms of coverage under the model without the conditional independent assumption. Moreover, confidence intervals based on log- and logit-transformations also performed well when the binomial proportion and the ratio of the validated sample are not very small under two models. Two examples were used to illustrate the procedures.

Confidence intervals for proportion difference from two independent partially validated series

Partially validated series are common when a gold-standard test is too expensive to be applied to all subjects, and hence a fallible device is used accordingly to measure the presence of a characteristic of interest. In this article, confidence interval construction for proportion difference between two independent partially validated series is studied. Ten confidence intervals based on the method of variance estimates recovery (MOVER) are proposed, with each using the confidence limits for the two independent binomial proportions obtained by the asymptotic, Logit-transformation, Agresti–Coull and Bayesian methods. The performances of the proposed confidence intervals and three likelihood-based intervals available in the literature are compared with respect to the empirical coverage probability, confidence width and ratio of mesial non-coverage to non-coverage probability. Our empirical results show that (1) all confidence intervals exhibit good performance in large samples; (2) confidence intervals based on MOVER combining the confidence limits for binomial proportions based on Wilson, Agresti–Coull, Logit-transformation, Bayesian (with three priors) methods perform satisfactorily from small to large samples, and hence can be recommended for practical applications. Two real data sets are analysed to illustrate the proposed methods.

Estimation of diagnostic test accuracy without full verification: a review of latent class methods

The performance of a diagnostic test is best evaluated against a reference test that is without error. For many diseases, this is not possible, and an imperfect reference test must be used. However, diagnostic accuracy estimates may be biased if inaccurately verified status is used as the truth. Statistical models have been developed to handle this situation by treating disease as a latent variable. In this paper, we conduct a systematized review of statistical methods using latent class models for estimating test accuracy and disease prevalence in the absence of complete verification.

Sample size determination for disease prevalence studies with partially validated data

Summary

Disease prevalence is an important topic in medical research, and its study is based on data that are obtained by classifying subjects according to whether a disease has been contracted. Classification can be conducted with high-cost gold standard tests or low-cost screening tests, but the latter are subject to the misclassification of subjects. As a compromise between the two, many research studies use partially validated datasets in which all data points are classified by fallible tests, and some of the data points are validated in the sense that they are also classified by the completely accurate gold-standard test. In this article, we investigate the determination of sample sizes for disease prevalence studies with partially validated data. We use two approaches. The first is to find sample sizes that can achieve a pre-specified power of a statistical test at a chosen significance level, and the second is to find sample sizes that can control the width of a confidence interval with a pre-specified confidence level. Empirical studies have been conducted to demonstrate the performance of various testing procedures with the proposed sample sizes. The applicability of the proposed methods are illustrated by a real-data example.