Sample size calculation for comparing two screening tests when the gold standard is missing at random.

Sample size formulas have been proposed for comparing two sensitivities (specificities) in the presence of verification bias under a paired design. However, the existing sample size formulas involve lengthy calculations of derivatives and are too complicated to implement. In this paper, we propose alternative sample size formulas for each of three existing tests, two Wald tests and one weighted McNemar's test. The proposed sample size formulas are more intuitive and simpler to implement than their existing counterparts. Furthermore, by comparing the sample sizes calculated based on the three tests, we can show that the three tests have similar sample sizes even though the weighted McNemar's test only use the data from discordant pairs whereas the two Wald tests also use the additional data from accordant pairs.

Simple methods for comparing two predictive values with incomplete data.

Statistical methods have been well developed for comparing the predictive values of two binary diagnostic tests under a paired design. However, existing methods do not make allowance for incomplete data. Although maximum likelihood based method can be used to deal with incomplete data, it requires iterative algorithm for implementation. A simple and easily implemented statistical method is therefore needed. Simple methods exist for comparing two sensitivities or specificities with incomplete data but such simple methods are not available for comparing two predictive values with incomplete data. In this paper, we propose two simple methods for comparing two predictive values with incomplete data. The test statistics derived by these two methods are simple to compute, only involving some minor modification of the existing weighted generalized score statistics with complete data. Simulation results demonstrate that the proposed methods are more efficient than the ad-hoc method that only uses the subjects wit complete data. As an illustration, the proposed methods are applied to an observational study comparing two non-invasive methods in detecting endometriosis.

Optimal two-phase sampling for comparing correlated areas under the ROC curves of two screening tests in the presence of verification bias.

The accuracy of a screening test is often measured by the area under the receiver characteristic (ROC) curve (AUC) of a screening test. Two-phase designs have been widely used in diagnostic studies for estimating one single AUC and comparing two AUCs where the screening test results are measured for a large sample (Phase one sample) while the disease status is only verified for a subset of Phase one sample (Phase two sample) by a gold standard. In this paper, we consider the optimal two-phase sampling design for comparing the performance of two ordinal screening tests in classifying disease status. Specifically, we derive an analytical variance formula for the AUC difference estimator and use it to find the optimal sampling probabilities that minimize the variance formula for the AUC difference estimator. According to the proposed optimal two-phase design, the strata with the levels of two tests far apart from each other should be over-sampled while the strata with the levels of two tests close to each other should be under-sampled. Simulation results indicate that two-phase sampling under optimal allocation (OA) achieves a substantial amount of variance reduction, compared with two-phase sampling under proportional allocation (PA). Furthermore, in comparison with a one-phase random sampling, two-phase sampling under OA or PA has a clear advantage in reducing the variance of AUC difference estimator when the variances of the two screening test results in the disease population differ greatly from their counterparts in non-disease population.

Joint comparison of the predictive values of multiple binary diagnostic tests: an extension of McNemar's test.

Positive and negative predictive values are important measures of the clinical accuracy of a diagnostic test. Various test statistics have been proposed to compare positive predictive values or negative predictive values of two binary diagnostic tests separately. However, such separate comparisons do not present a complete picture of the relative accuracy of the two diagnostic tests. In this paper, we propose an extension of McNemar's test for the joint comparison of predictive values of multiple diagnostic tests. The proposed extended McNemar's test is intuitive and simple to compute, only involving cell counts of discordant pairs from multiple 2×2 tables. Furthermore, we also propose a re-formulation of an existing Wald test statistic so that it can be implemented more easily than its original form. Simulations demonstrate that the proposed extended McNemar's test statistic preserves type one error much better than the existing Wald test statistic. Thus, we believe that the proposed extended McNemar's test statistic is the preferred statistic to simultaneously compare the predictive values of multiple binary diagnostic tests.

Weighted generalized score test for comparing predictive values in the presence of verification bias.

Positive and negative predictive values of a diagnostic test are two important measures of test accuracy, which are more relevant in clinical settings than sensitivity and specificity. Statistical methods have been well-developed to compare the predictive values of two binary diagnostic tests when test results and disease status fully observed for all study patients. In practice, however, it is common that only a subset of study patients have the disease status verified due to ethical or cost considerations. Methods applied directly to the verified subjects may lead to biased results. A bias-corrected method has been developed to compare two predictive values in the presence of verification bias. However, the complexity of the existing method and the computational difficulty in implementing it has restricted its use. A simple and easily implemented statistical method is therefore needed. In this paper, we propose a weighted generalized score (WGS) test statistic for comparing two predictive values in the presence of verification bias. The proposed WGS test statistic is intuitive and simple to compute, only involving some minor modification of the WGS test statistic when disease status is verified for each study patient. Simulations demonstrate that the proposed WGS test statistic preserves type I error much better than the existing Wald statistic. The method is illustrated with data from a study of methods for the diagnosis of coronary artery disease.

Weighted McNemar's test for the comparison of two screening tests in the presence of verification bias.

Statistical methods have been well-developed for comparing two binary screening tests in the presence of verification bias. However, the complexity of existing methods and the computational difficulty in implementing them have restricted their use. A simple and easily implemented statistical method is therefore needed. In this paper, we propose a weighted McNemar's test statistic for comparing two sensitivities(specificities). The proposed test statistics are intuitive and simple to compute, only involving some minor modification of a McNemar's test statistic using the estimated verification probabilities for discordant pairs. Simulations demonstrate that the proposed weighted McNemar's test statistics preserve type I error as well as or better than the existing statistics. Furthermore, unlike the existing methods, the proposed weighted McNemar's test statistics can still be applied even when none of the accordant pairs are verified.

Nonparametric inference of the area under ROC curve under two-phase cluster sampling.

Nonparametric inference of the area under ROC curve (AUC) has been well developed either in the presence of verification bias or clustering. However, current nonparametric methods are not able to handle cases where both verification bias and clustering are present. Such a case arises when a two-phase study design is applied to a cohort of subjects (verification bias) where each subject might have multiple test results (clustering). In such cases, the inference of AUC must account for both verification bias and intra-cluster correlation. In the present paper, we propose an IPW AUC estimator that corrects for verification bias and derive a variance formula to account for intra-cluster correlations between disease status and test results. Results of a simulation study indicate that the method that assumes independence underestimates the true variance of the IPW AUC estimator in the presence of intra-cluster correlations. The proposed method, on the other hand, provides a consistent variance estimate for the IPW AUC estimator by appropriately accounting for correlations between true disease statuses and between test results.

Assess predictive values of a binary diagnostic test under a nested case-control design.

Predictive values of a binary diagnostic test are often evaluated under a random sample design. When the disease is rare, however, such a design might not be as efficient as a nested case-control design where the cases are oversampled from a large existing cohort. Under a nested case-control design, direct proportion estimators of predictive values are biased because cases are oversampled. Consistent estimates of predictive values can be easily obtained by inverse probability weighting (IPW) method. The only difficulty with these IPW estimators has been the absence of expressions for their variances. To fill this gap, in the current paper, we obtain the asymptotic variance formulas for the IPW estimators of predictive values. Unlike their counterparts from weighted logistic regression, our variance formulas take into account the variance of the estimated weights in the IPW estimators of predictive values. We further use the proposed variance formulas to examine the gain in efficiency under a nested case-control design compared with a simple random sampling design. Our results clearly show that when the disease is rare, a nested case-control design can achieve a substantial amount of variance reduction by oversampling cases, compared with a random sample design. Finally, we compare via simulation the accuracy of the proposed variance formulas with the existing methods and illustrate the proposed method by a real data example evaluating the accuracy of D-dimer test.

Optimal two-phase sampling for estimating the area under the receiver operating characteristic curve.

Statistical methods are well developed for estimating the area under the receiver operating characteristic curve (AUC) based on a random sample where the gold standard is available for every subject in the sample, or a two-phase sample where the gold standard is ascertained only at the second phase for a subset of subjects sampled using fixed sampling probabilities. However, the methods based on a two-phase sample do not attempt to optimize the sampling probabilities to minimize the variance of AUC estimator. In this paper, we consider the optimal two-phase sampling design for evaluating the performance of an ordinal test in classifying disease status. We derived the analytic variance formula for the AUC estimator and used it to obtain the optimal sampling probabilities. The efficiency of the two-phase sampling under the optimal sampling probabilities (OA) is evaluated by a simulation study, which indicates that two-phase sampling under OA achieves a substantial amount of variance reduction with an over-sample of subjects with low and high ordinal levels, compared with two-phase sampling under proportional allocation (PA). Furthermore, in comparison with an one-phase random sampling, two-phase sampling under OA or PA have a clear advantage in reducing the variance of AUC estimator when the variance of diagnostic test results in the disease population is small relative to its counterpart in nondisease population. Finally, we applied the optimal two-phase sampling design to a real-world example to evaluate the performance of a questionnaire score in screening for childhood asthma.

Simple confidence interval and region formulas for comparing diagnostic likelihood ratios under a paired design.

A population-based paired design is often used for comparing the diagnostic likelihood ratios of two binary diagnostic tests. However, a case-control paired design, which involves the application of both diagnostic tests to two independent samples, is a good alternative study design especially when the disease is rare. Existing methods for comparing two diagnostic likelihood ratios have been mainly focused on the population-based paired design with little attention paid to the case-control paired design. In this paper, we derive a confidence interval formula for the relative diagnostic likelihood ratio (the ratio of two diagnostic likelihood ratios), which can be used for the comparison of two positive or negative diagnostic likelihood ratios separately. We also derive a confidence region formula for the two relative positive and negative diagnostic likelihood ratios, which allows simultaneous comparison of two positive and negative diagnostic likelihood ratios. The proposed confidence interval and region formulas are simple to compute and can be used for both population-based paired design and case-control paired designs. Simulation studies are used to assess the finite sample performance of the confidence interval and region formulas. The proposed methods are applied to a real data set on coronary artery disease and two diagnostic tests.

True verification probabilities should not be used in estimating the area under receiver operating characteristic curve.

In medical research, a two-phase study is often used for the estimation of the area under the receiver operating characteristic curve (AUC) of a diagnostic test. However, such a design introduces verification bias. One of the methods to correct verification bias is inverse probability weighting (IPW). Since the probability a subject is selected into phase 2 of the study for disease verification is known, both true and estimated verification probabilities can be used to form an IPW estimator for AUC. In this article, we derive explicit variance formula for both IPW AUC estimators and show that the IPW AUC estimator using the true values of verification probabilities even when they are known are less efficient than its counterpart using the estimated values. Our simulation results show that the efficiency loss can be substantial especially when the variance of test result in disease population is small relative to its counterpart in nondiseased population.

Power calculation of adjusted McNemar's test based on clustered data of varying cluster size.

McNemars test is often used to compare two proportions estimated from paired observations. When the observations are sampled in clusters, adjustment is needed to ensure that the size of McNemars test does not exceed the nominal level. Eliasziw and Donner (1991) developed an adjustment to McNemars test that involves first estimating the correlation between discordant pairs within a cluster, then using the estimate of the correlation to adjust the usual McNemar's test statistic. Gönen (2004) derived two approximations for calculating the power and sample size for the adjusted McNemar's test. He reported that the accuracy of the two approximations is compromised for large value of intracluster correlation and small value of proportion of discordant pairs; the error of the approximation can be higher than 10 per cent. In this paper, we extend his power formula, developed under fixed cluster size assumption, to accommodate the case where the cluster sizes are not constant. We show via simulations that the theoretical powers calculated from our proposed power formula are close to their empirical counterparts under a variety of settings. More significantly, in the case of fixed cluster size, our reduced power formula provides a more accurate power approximation than Gönen's power formula regardless of the values of intracluster correlation and the proportion of discordant pairs.

Heat stress risk profiles for three non-woven coveralls.

The ACGIH® Threshold Limit Value® (TLV®) is used to limit heat stress exposures so that most workers can maintain thermal equilibrium. That is, the TLV was set to an upper limit of Sustainable exposures for most people. This article addresses the ability of the TLV to differentiate between Sustainable and Unsustainable heat exposures for four clothing ensembles over a range of environmental factors and metabolic rates (M). The four clothing ensembles (woven clothing, and particle barrier, water barrier and vapor barrier coveralls) represented a wide range of evaporative resistances. Two progressive heat stress studies provided data on 480 trials with 1440 pairs of Sustainable and Unsustainable exposures for the clothing over three levels of relative humidity (rh) (20, 50 and 70%), three levels of metabolic rate (115, 180, and 254 Wm-2) using 29 participants. The exposure metric was the difference between the observed wet bulb globe temperature (WBGT) and the TLV. Risk was characterized by odds ratios (ORs), Receiver Operating Characteristic (ROC) curves, and dose-response curves for the four ensembles. Conditional logistic regression models provided information on ORs. Logistic regressions were used to determine ROC curves with area under the curve (AUC), model the dose-response curve, and estimate offsets from woven clothing. The ORs were about 2.5 per 1°C-WBGT for woven clothing, particle barrier, and water barrier and for vapor barrier at 50% rh. When using the published Clothing Adjustment Values (CAVs, also known as Clothing Adjustment Factors, CAFs) or the offsets that included different values for vapor barrier based on rh, the AUC for all clothing was 0.86. When the fixed CAVs of the TLV were used, the AUC was 0.81. In conclusion, (1) ORs and the shapes of the dose-response curves for the nonwoven coveralls were similar to woven clothing, and (2) CAVs provided a robust way to account for the risk of nonwoven clothing. The robust nature of CAV extended to the exclusion of different adjustments for vapor barrier by rh.

Exertional heat illness and acute injury related to ambient wet bulb globe temperature.

BACKGROUND: The Deepwater Horizon disaster cleanup effort provided an opportunity to examine the effects of ambient thermal conditions on exertional heat illness (EHI) and acute injury (AI). METHODS: The outcomes were daily person-based frequencies of EHI and AI. Exposures were maximum estimated WBGT (WBGTmax) and severity. Previous day's cumulative effect was assessed by introducing previous day's WBGTmax into the model. RESULTS: EHI and AI were higher in workers exposed above a WBGTmax of 20°C (RR 1.40 and RR 1.06/°C, respectively). Exposures above 28°C-WBGTmax on the day of the EHI and/or the day before were associated with higher risk of EHI due to an interaction between previous day's environmental conditions and the current day (RRs from 1.0-10.4). CONCLUSIONS: The risk for EHI and AI were higher with increasing WBGTmax. There was evidence of a cumulative effect from the prior day's WBGTmax for EHI. Am. J. Ind. Med. 59:1169-1176, 2016. © 2016 Wiley Periodicals, Inc.

Incidence rates of dementia, Alzheimer disease, and vascular dementia in the Japanese American population in Seattle, WA: the Kame Project.

There are few studies on the incidence of dementia in representative minority populations in the United States; however, no population-based study has been conducted on Japanese American women. We identified 3045 individuals aged 65+ with at least 1 parent of Japanese descent living in King County, WA in the period 1992 to 1994, of whom 1836 were dementia-free and were examined every 2 years (1994 to 2001) to identify incident cases of all dementias, Alzheimer disease (AD), vascular dementia (VaD), and other dementias. Cox regression was used to examine associations with age, sex, years of education, and apolipoprotein (APOE)-ε4. Among 173 incident cases of dementia, the overall rate was 14.4/1000/y, with rates being slightly higher among women (15.9/1000) than men (12.5/1000). Rates roughly doubled every 5 years for dementia and AD; the age trend for VaD and other dementias was less consistent. Sex was not significantly related to incidence of dementia or its subtypes in adjusted models. There was a trend for an inverse association with increasing years of education. APOE-ε4 was a strong risk factor for all dementias [hazard ratio (HR)=2.89; 95% confidence interval (CI), 1.88-4.46], AD (HR=3.27; 95% CI, 2.03-5.28), and VaD (HR=3.33; 95% CI, 1.34-8.27). This study is the first to report population-based incidence rates for both Japanese American men and women.

Risk factors for incident condyloma in a multinational cohort of men: the HIM study.

Identifying factors associated with condyloma are necessary for prevention efforts. Risk factors for incident condyloma were examined in a cohort of 2487 men from the United States, Brazil, and Mexico and were followed up every 6 months (median, 17.9 months). Factors strongly associated with condyloma were incident infection with human papillomavirus (HPV) types 6 and 11 (hazard ratio [HR], 12.42 [95% confidence interval {CI}, 3.78-40.77]), age (HR, 0.43 [95% CI, .26-.77]; 45-70 vs 18-30 years), high lifetime number of female partners (HR, 5.69 [95% CI, 1.80-17.97]; ≥21 vs 0 partners), and number of male partners (HR, 4.53 [95% CI, 1.68-12.20]; ≥3 vs 0 partners). The results suggest that HPV types 6 and 11 and recent sexual behavior are strongly associated with incident condyloma.

Incidence and human papillomavirus (HPV) type distribution of genital warts in a multinational cohort of men: the HPV in men study.

BACKGROUND: Data on the natural history of human papillomavirus (HPV)-related genital warts (GWs) in men are sparse. We described the distribution of HPV types in incident GWs and estimated GW incidence and time from type-specific incident HPV infections to GW detection in a multinational cohort of men aged 18-70 years. METHODS: Participants included 2487 men examined for GWs and tested for HPV every 6 months and followed up for a median of 17.9 months. Samples were taken from 112 men with incident GWs to test for HPV DNA by polymerase chain reaction. RESULTS: Incidence of GWs was 2.35 cases per 1000 person-years, with highest incidence among men aged 18-30 years (3.43 cases per 1000 person-years). HPV 6 (43.8%), HPV 11 (10.7%), and HPV 16 (9.8%) were the genotypes most commonly detected in GWs. The 24-month cumulative incidence of GWs among men with incident HPV 6/11 infections was 14.6% (95% confidence interval [CI], 7.5%-21.1%). Median time to GW detection was 17.1 months (95% CI, 12.4-19.3 months), with shortest time to detection among men with incident infections with HPV 6/11 only (6.2 months; 95% CI, 5.6-24.2 months). CONCLUSIONS: HPV 6/11 plays an important role in GW development, with the highest incidence and shortest time to detection among men with incident HPV 6/11 infection.

Pre-MCI and MCI: neuropsychological, clinical, and imaging features and progression rates.

OBJECTIVE: To compare clinical, imaging, and neuropsychological characteristics and longitudinal course of subjects with pre-mild cognitive impairment (pre-MCI), who exhibit features of MCI on clinical examination but lack impairment on neuropsychological examination, to subjects with no cognitive impairment (NCI), nonamnestic MCI (naMCI), amnestic MCI (aMCI), and mild dementia. METHODS: For 369 subjects, clinical dementia rating sum of boxes (CDR-SB), ApoE genotyping, cardiovascular risk factors, parkinsonism (UPDRS) scores, structural brain MRIs, and neuropsychological testing were obtained at baseline, whereas 275 of these subjects received an annual follow-up for 2-3 years. RESULTS: At baseline, pre-MCI subjects showed impairment on tests of executive function and language, higher apathy scores, and lower left hippocampal volumes (HPCV) in comparison to NCI subjects. Pre-MCI subjects showed less impairment on at least one memory measure, CDR-SB and UPDRS scores, in comparison to naMCI, aMCI and mild dementia subjects. Follow-up over 2-3 years showed 28.6% of pre-MCI subjects, but less than 5% of NCI subjects progressed to MCI or dementia. Progression rates to dementia were equivalent between naMCI (22.2%) and aMCI (34.5%) groups, but greater than for the pre-MCI group (2.4%). Progression to dementia was best predicted by the CDR-SB, a list learning and executive function test. CONCLUSION: This study demonstrates that clinically defined pre-MCI has cognitive, functional, motor, behavioral and imaging features that are intermediate between NCI and MCI states at baseline. Pre-MCI subjects showed accelerated rates of progression to MCI as compared to NCI subjects, but slower rates of progression to dementia than MCI subjects.

Optimal weight in estimating and comparing areas under the receiver operating characteristic curve using longitudinal data.

In the setting of longitudinal study, subjects are followed for the occurrence of some dichotomous outcome. In many of these studies, some markers are also obtained repeatedly during the study period. Emir et al. introduced a non-parametric approach to the estimation of the area under the ROC curve of a repeated marker. Their non-parametric estimate involves assigning a weight to each subject. There are two weighting schemes suggested in their paper: one for the case when within-patient correlation is low, and the other for the case when within-subject correlation is high. However, it is not clear how to assign weights to marker measurements when within-patient correlation is modest. In this paper, we consider the optimal weights that minimize the variance of the estimate of the area under the ROC curve (AUC) of a repeated marker, as well as the optimal weights that minimize the variance of the AUC difference between two repeated markers. Our results in this paper show that the optimal weights depend not only on the within-patient control--case correlation in the longitudinal data, but also on the proportion of subjects that become cases. More importantly, we show that the loss of efficiency by using the two weighting schemes suggested by Emir et al. instead of our optimal weights can be severe when there is a large within-subject control--case correlation and the proportion of subjects that become cases is small, which is often the case in longitudinal study settings.

Volumetric and visual rating of magnetic resonance imaging scans in the diagnosis of amnestic mild cognitive impairment and Alzheimer's disease.

BACKGROUND: In the diagnosis of Alzheimer's disease (AD), structural magnetic resonance imaging (MRI) scans have been used primarily to exclude non-Alzheimer's causes of dementia. However, the pattern and the extent of medial temporal atrophy on structural MRI scans, which correlate strongly with the pathological severity of AD, can be used to support the diagnosis of a degenerative dementia, especially AD, even in its early predementia stage. METHODS: Elderly subjects (n = 224) were diagnosed with either no cognitive impairment (NCI), amnestic mild cognitive impairment (aMCI), or AD. Hippocampal and hemispheric gray matter volumes were measured on structural MRI scans, and a new visual rating system was used to score the severity of medial temporal atrophy (VRS-MTA) of the hippocampus (HPC), entorhinal cortex, and perirhinal cortex on a coronal image intersecting the mammillary bodies. RESULTS: Although both VRS-MTA scores and HPC volumes distinguished between subjects with NCI, aMCI, and AD, subjects with aMCI and NCI could be better distinguished using right VRS-MTA scores, in comparison with right HPC volumes. VRS-MTA scores were more highly correlated with episodic memory and Clinical Dementia Rating scores. A combination of left sided VRS-MTA scores and left sided hippocampal volume was the most predictive measure of diagnostic classification. CONCLUSION: VRS-MTA is a clinically convenient method or distinguishing aMCI or AD from NCI. As compared with volumetric measures, it provides better discriminatory power and correlates more strongly with memory and functional scores.