Shi-Fang Qiu

Testing the equality of proportions for correlated otolaryngologic data

In otolaryngologic (or ophthalmologic) studies, each subject usually contributes information for each of two ears (or eyes), and the values from the two ears (or eyes) are generally highly correlated. Statistical procedures that fail to take into account the correlation between responses from two ears could lead to incorrect results. On the other hand, asymptotic procedures that overlook small sample designs, sparse data structures, or the discrete nature of data could yield unacceptably high type I error rates even when the intraclass correlation is taken into consideration. In this article, we investigate eight procedures for testing the equality of proportions in such correlated data. These test procedures will be implemented via the asymptotic and approximate unconditional methods. Our empirical results show that tests based on the approximate unconditional method usually produce empirical type I error rates closer to the pre-chosen nominal level than their asymptotic tests. Amongst these, the approximate unconditional score test performs satisfactorily in general situations and is hence recommended. A data set from an otolaryngologic study is used to illustrate our proposed methods.

Asymptotic confidence interval construction for proportion difference in medical studies with bilateral data

Bilateral dichotomous data are very common in modern medical comparative studies (e.g. comparison of two treatments in ophthalmologic, orthopaedic and otolaryngologic studies) in which information involving paired organs (e.g. eyes, ears and hips) is available from each subject. In this article, we study various confidence interval estimators for proportion difference based on Wald-type statistics, Fieller theorem, likelihood ratio statistic, score statistics and bootstrap resampling method under the dependence or/and independence models for bilateral binary data. Performance is evaluated with respect to the coverage probability and expected width via simulation studies. Our empirical results show that (1) ignoring the dependence feature of bilateral data could lead to severely incorrect coverage probabilities; and (2) Wald-type, score-type and bootstrap confidence intervals based on the dependence model perform satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the pre-specified nominal confidence level and are hence recommended. A real data from an otolaryngologic study is used to illustrate the proposed methods.

Test procedures for disease prevalence with partially validated data.

Investigating the prevalence of a disease is an important topic in medical studies. Such investigations are usually based on the classification results of a group of subjects according to whether they have the disease. To classify subjects, screening tests that are inexpensive and nonintrusive to the test subjects are frequently used to produce results in a timely manner. However, such screening tests may suffer from high levels of misclassification. Although it is often possible to design a gold-standard test or device that is not subject to misclassification, such devices are usually costly and time-consuming, and in some cases intrusive to the test subjects. As a compromise between these two approaches, it is possible to use data that are obtained by the method of double-sampling. In this article, we derive and investigate four test statistics for testing a hypothesis on disease prevalence with double-sampling data. The test statistics are implemented through both the asymptotic method suitable for large samples and approximate unconditional method suitable for small samples. Our simulation results show that the approximate unconditional method usually produces a more satisfactory empirical type I error rate and power than its asymptotic counterpart, especially for small to moderate sample sizes. The results also suggest that the score test and the Wald test based on an estimate of variance with parameters estimated under the null hypothesis outperform the others. An real example is used to illustrate the proposed methods.

Confidence interval construction for disease prevalence based on partial validation series

It is desirable to estimate disease prevalence based on data collected by a gold standard test, but such a test is often limited due to cost and ethical considerations. Data with partial validation series thus become an alternative. The construction of confidence intervals for disease prevalence with such data is considered. A total of 12 methods, which are based on two Wald-type test statistics, score test statistic, and likelihood ratio test statistic, are developed. Both asymptotic and approximate unconditional confidence intervals are constructed. Two methods are employed to construct the unconditional confidence intervals: one involves inverting two one-sided tests and the other involves inverting one two-sided test. Moreover, the bootstrapping method is used. Two real data sets are used to illustrate the proposed methods. Empirical results suggest that the 12 methods largely produce satisfactory results, and the confidence intervals derived from the score test statistic and the Wald test statistic with nuisance parameters appropriately evaluated generally outperform the others in terms of coverage. If the interval location or the non-coverage at the two ends of the interval is also of concern, then the aforementioned interval based on the Wald test becomes the best choice.

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.

Sample Size for Testing Difference Between Two Proportions for the Bilateral-Sample Design

In this article, we consider approximate sample size formulas for testing difference between two proportions for bilateral studies with binary outcomes. Sample size formulas are derived to achieve a prespecified power of a statistical test at a prechosen significance level. Four statistical tests are considered. Simulation studies are conducted to investigate the accuracy of various formulas. In general, the sample size formula for Rosners statistic based on the dependence assumption is highly recommended in the sense that its actual power is satisfactorily close to the desired power level. An example from an otolaryngological study is used to demonstrate the proposed methodologies.

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.

Confidence interval construction for the Youden index based on partially validated series

Confidence interval construction for the Youden index of a diagnostic test based on partially validated series with dichotomous response is considered in this article. Using the Wald and Agresti-Coull, the Wilson score, logit-transformation and the method of variance estimates recovery, eight methods for constructing confidence intervals for a single Youden index and nine methods for the difference between two independent Youden indices are developed. Comparisons among the various methods with respect to their empirical coverage probabilities and confidence interval widths are conducted through simulation studies over a variety of parameter settings. Based on the simulation results, recommendations for practical use under different conditions are provided. A real aplastic anemia data set is used to illustrate the proposed methods.

Simultaneous Confidence Intervals of Risk Differences in Stratified Paired Designs

In stratified matched-pair studies, risk difference between two proportions is one of the most frequently used indices in comparing efficiency between two treatments or diagnostic tests. This article presents five simultaneous confidence intervals and two bootstrap simultaneous confidence intervals for risk differences in stratified matched-pair designs. The proposed confidence intervals are evaluated with respect to their coverage probabilities, expected widths, and ratios of the mesial noncoverage to noncoverage probability. Empirical results show that (1) hybrid simultaneous confidence intervals outperform nonhybrid simultaneous confidence intervals; (2) hybrid simultaneous confidence intervals based on median estimator outperform those based on maximum likelihood estimator; and (3) hybrid simultaneous confidence intervals incorporated with Wilson score and Agresti coull intervals and the bootstrap t-percentile simultaneous interval based on median unbiased estimators behave satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the prespecified nominal confidence level, and their ratios of the mesial noncoverage to noncoverage probabilities lie in [0.4,0.6] and are hence recommended. Real examples from clinical studies are used to illustrate the proposed methodologies.