Cost-effectiveness analysis under multiple effectiveness outcomes: A probabilistic approach

Probability based criteria are proposed for the assessment of cost-effectiveness of a new treatment compared to a standard treatment when there are multiple effectiveness measures. Depending on the preferences of a policy maker, there are several options to define such criteria. Two such metrics are investigated in detail. One metric is defined as the conditional probability that a new treatment is more effective with respect to the multiple effectiveness measures for patients having lower costs under the new treatment. A second metric is defined as the conditional probability that a new treatment is less costly for patients having greater health benefits under the new treatment. The metrics offer considerable flexibility to a policy maker as thresholds for cost and effectiveness can be incorporated into the metrics. Parametric confidence limits are developed using a percentile bootstrap approach assuming multivariate normality for the joint distribution of the log(cost) and effectiveness measures. A non-parametric estimation procedure is also developed using the theory of U-statistics. Numerical results indicate that the proposed confidence limits accurately maintain coverage probabilities. The methodologies are illustrated using a study on the treatment of type two diabetes. Code implementing the proposed methods are provided in the supporting information.

Double reduction estimation and equilibrium tests in natural autopolyploid populations

Many bioinformatics pipelines include tests for equilibrium. Tests for diploids are well studied and widely available, but extending these approaches to autopolyploids is hampered by the presence of double reduction, the comigration of sister chromatid segments into the same gamete during meiosis. Though a hindrance for equilibrium tests, double reduction rates are quantities of interest in their own right, as they provide insights about the meiotic behavior of autopolyploid organisms. Here, we develop procedures to (i) test for equilibrium while accounting for double reduction, and (ii) estimate the double reduction rate given equilibrium. To do so, we take two approaches: a likelihood approach, and a novel U-statistic minimization approach that we show generalizes the classical equilibrium χ2 test in diploids. For small sample sizes and uncertain genotypes, we further develop a bootstrap procedure based on our U-statistic to test for equilibrium. We validate our methods on both simulated and real data.

Specification testing for ordinary differential equation models with fixed design and applications to COVID-19 epidemic models

Checking the models about the ongoing Coronavirus Disease 2019 (COVID-19) pandemic is an important issue. Some famous ordinary differential equation (ODE) models, such as the SIR and SEIR models have been used to describe and predict the epidemic trend. Still, in many cases, only part of the equations can be observed. A test is suggested to check possibly partially observed ODE models with a fixed design sampling scheme. The asymptotic properties of the test under the null, global and local alternative hypotheses are presented. Two new propositions about U-statistics with varying kernels based on independent but non-identical data are derived as essential tools. Some simulation studies are conducted to examine the performances of the test. Based on the available public data, it is found that the SEIR model, for modeling the data of COVID-19 infective cases in certain periods in Japan and Algeria, respectively, maybe not be appropriate by applying the proposed test.

Testing generalized linear models with high-dimensional nuisance parameter

Generalized linear models often have a high-dimensional nuisance parameters, as seen in applications such as testing gene-environment interactions or gene-gene interactions. In these scenarios, it is essential to test the significance of a high-dimensional sub-vector of the model's coefficients. Although some existing methods can tackle this problem, they often rely on the bootstrap to approximate the asymptotic distribution of the test statistic, and thus are computationally expensive. Here, we propose a computationally efficient test with a closed-form limiting distribution, which allows the parameter being tested to be either sparse or dense. We show that under certain regularity conditions, the type I error of the proposed method is asymptotically correct, and we establish its power under high-dimensional alternatives. Extensive simulations demonstrate the good performance of the proposed test and its robustness when certain sparsity assumptions are violated. We also apply the proposed method to Chinese famine sample data in order to show its performance when testing the significance of gene-environment interactions.

Goodness of fit test for uniform distribution with censored observation

We develop new goodness of fit test for uniform distribution based on a conditional moment characterization. We study the asymptotic properties of the proposed test statistic. We also present a goodness of fit test for uniform distribution to incorporate the right censored observations and studied its properties. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed tests. We illustrate the test procedures using real data sets.

On recurrent-event win ratio

The win ratio approach proposed by Pocock et al. (2012) has become a popular tool for analyzing composite endpoints of death and non-fatal events like hospitalization. Its standard version, however, draws on the non-fatal event only through the first occurrence. For statistical efficiency and clinical interpretability, we construct and compare different win ratio variants that make fuller use of recurrent events. We pay special attention to a variant called last-event-assisted win ratio, which compares two patients on the cumulative frequency of the non-fatal event, with ties broken by the time of its latest episode. It is shown that last-event-assisted win ratio uses more data than the standard win ratio does but reduces to the latter when the non-fatal event occurs at most once. We further prove that last-event-assisted win ratio rejects the null hypothesis with large probability if the treatment stochastically delays all events. Simulations under realistic settings show that the last-event-assisted win ratio test consistently enjoys higher power than the standard win ratio and other competitors. Analysis of a real cardiovascular trial provides further evidence for the practical advantages of the last-event-assisted win ratio. Finally, we discuss future work to develop meaningful effect size estimands based on the extended rules of comparison. The R-code for the proposed methods is included in the package WR openly available on the Comprehensive R Archive Network.

A unified Bayesian framework for exact inference of area under the receiver operating characteristic curve

The area under the receiver operating characteristic curve is a widely used measure for evaluating the performance of a diagnostic test. Common approaches for inference on area under the receiver operating characteristic curve are usually based upon approximation. For example, the normal approximation based inference tends to suffer from the problem of low accuracy for small sample size. Frequentist empirical likelihood based approaches for area under the receiver operating characteristic curve estimation may perform better, but are usually conducted through approximation in order to reduce the computational burden, thus the inference is not exact. By contrast, we proposed an exact inferential procedure by adapting the empirical likelihood into a Bayesian framework and draw inference from the posterior samples of the area under the receiver operating characteristic curve obtained via a Gibbs sampler. The full conditional distributions within the Gibbs sampler only involve empirical likelihoods with linear constraints, which greatly simplify the computation. To further enhance the applicability and flexibility of the Bayesian empirical likelihood, we extend our method to the estimation of partial area under the receiver operating characteristic curve, comparison of multiple tests, and the doubly robust estimation of area under the receiver operating characteristic curve in the presence of missing test results. Simulation studies confirm the desirable performance of the proposed methods, and a real application is presented to illustrate its usefulness.

ASYMPTOTICALLY INDEPENDENT U-STATISTICS IN HIGH-DIMENSIONAL TESTING

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the ℓ p -norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed. Moreover, they are also asymptotically independent with the maximum-type test statistic, whose limiting distribution is an extreme value distribution. Based on the asymptotic independence property, we propose an adaptive testing procedure which combines p-values computed from the U-statistics of different orders. We further establish power analysis results and show that the proposed adaptive procedure maintains high power against various alternatives.

Extending the Mann-Whitney-Wilcoxon rank sum test to survey data for comparing mean ranks

Statistical methods for analysis of survey data have been developed to facilitate research. More recently, Lumley and Scott (2013) developed an approach to extend the Mann-Whitney-Wilcoxon (MWW) rank sum test to survey data. Their approach focuses on the null of equal distribution. In many studies, the MWW test is called for when two-sample t-tests (with or without equal variance assumed) fail to provide meaningful results, as they are highly sensitive to outliers. In such situations, the null of equal distribution is too restrictive, as interest lies in comparing centers of groups. In this article, we develop an approach to extend the MWW test to survey data to test the null of equal mean rank. Although not as popular as the mean and median, the mean rank is also a meaningful measure of the center of a distribution and is the same as the median for a symmetric distribution. We illustrate the proposed approach and show major differences with Lumley and Scott's alternative using both real and simulated data.

Event-specific win ratios and testing with terminal and non-terminal events

BACKGROUND/AIMS

In clinical trials, the primary outcome is often a composite endpoint defined as time to the first occurrence of either death or certain non-fatal events. Thus, a portion of available data would be omitted. In the win ratio approach, priorities are given to the clinically more important events, and more data are used. However, its power may be low if the treatment effect is predominantly on the non-terminal event.

METHODS

We propose event-specific win ratios obtained separately on the terminal and non-terminal events. They can then be used to form global tests such as a linear combination test, the maximum test, or a χ2 test.

RESULTS

In simulations, these tests often improve the power of the original win ratio test. Furthermore, when the terminal and non-terminal events experience differential treatment effects, the new tests are often more powerful than the log-rank test for the composite outcome. Whether the treatment effect is primarily on the terminal events or not, the new tests based on the event-specific win ratios can be useful when different types of events are present. The new tests can reject the null hypothesis of no difference in the event distributions in the two treatment arms with the terminal event showing detrimental effect and the non-terminal event showing beneficial effect. The maximum test and the χ2 test do not have test-estimation coherency, but the maximum test has the coherency that the global null is rejected if and only if the null for one of the event types is rejected. When applied to data from the trial Aldosterone Antagonist Therapy for Adults With Heart Failure and Preserved Systolic Function (TOPCAT), the new tests all reject the null hypothesis of no treatment effect while both the log-rank test used in TOPCAT and the original win ratio approach show non-significant p-values.

CONCLUSION

Whether the treatment effect is primarily on the terminal events or the non-terminal events, the maximum test based on the event-specific win ratios can be a useful alternative for testing treatment effect in clinical trials with time-to-event outcomes when different types of events are present.

Tests for regression coefficients in high dimensional partially linear models

We propose a U-statistics test for regression coefficients in high dimensional partially linear models. In addition, the proposed method is extended to test part of the coefficients. Asymptotic distributions of the test statistics are established. Simulation studies demonstrate satisfactory finite-sample performance.

Two-sample test for correlated data under outcome-dependent sampling with an application to self-reported weight loss data

Standard methods for two-sample tests such as the t-test and Wilcoxon rank sum test may lead to incorrect type I errors when applied to longitudinal or clustered data. Recent alternatives of two-sample tests for clustered data often require certain assumptions on the correlation structure and/or noninformative cluster size. In this paper, based on a novel pseudolikelihood for correlated data, we propose a score test without knowledge of the correlation structure or assuming data missingness at random. The proposed score test can capture differences in the mean and variance between two groups simultaneously. We use projection theory to derive the limiting distribution of the test statistic, in which the covariance matrix can be empirically estimated. We conduct simulation studies to evaluate the proposed test and compare it with existing methods. To illustrate the usefulness proposed test, we use it to compare self-reported weight loss data in a friends' referral group, with the data from the Internet self-joining group.

Prioritized concordance index for hierarchical survival outcomes

We propose an extension of Harrell's concordance (C) index to evaluate the prognostic utility of biomarkers for diseases with multiple measurable outcomes that can be prioritized. Our prioritized concordance index measures the probability that, given a random subject pair, the subject with the worst disease status as of a time τ has the higher predicted risk. Our prioritized concordance index uses the same approach as the win ratio, by basing generalized pairwise comparisons on the most severe or clinically important comparable outcome. We use an inverse probability weighting technique to correct for study-specific censoring. Asymptotic properties are derived using U-statistic properties. We apply the prioritized concordance index to two types of disease processes with a rare primary outcome and a more common secondary outcome. Our simulation studies show that when a predictor is predictive of both outcomes, the new concordance index can gain efficiency and power in identifying true prognostic variables compared to using the primary outcome alone. Using the prioritized concordance index, we examine whether novel clinical measures can be useful in predicting risk of type II diabetes in patients with impaired glucose resistance whose disease status can also regress to normal glucose resistance. We also examine the discrimination ability of four published risk models among ever smokers at risk of lung cancer incidence and subsequent death.

A multi-locus predictiveness curve and its summary assessment for genetic risk prediction

Genetic association studies using high-throughput genotyping and sequencing technologies have identified a large number of genetic variants associated with complex human diseases. These findings have provided an unprecedented opportunity to identify individuals in the population at high risk for disease who carry causal genetic mutations and hold great promise for early intervention and individualized medicine. While interest is high in building risk prediction models based on recent genetic findings, it is crucial to have appropriate statistical measurements to assess the performance of a genetic risk prediction model. Predictiveness curves were recently proposed as a graphic tool for evaluating a risk prediction model on the basis of a single continuous biomarker. The curve evaluates a risk prediction model for classification performance as well as its usefulness when applied to a population. In this article, we extend the predictiveness curve to measure the collective contribution of multiple genetic variants. We further propose a nonparametric, U-statistics-based measurement, referred to as the U-Index, to quantify the performance of a multi-locus predictiveness curve. In particular, a global U-Index and a partial U-Index can be used in the general population and a subpopulation of particular clinical interest, respectively. Through simulation studies, we demonstrate that the proposed U-Index has advantages over several existing summary statistics under various disease models. We also show that the partial U-Index can have its own uniqueness when rare variants have a substantial contribution to disease risk. Finally, we use the proposed predictiveness curve and its corresponding U-Index to evaluate the performance of a genetic risk prediction model for nicotine dependence.

All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously

Variable importance (VI) tools describe how much covariates contribute to a prediction model's accuracy. However, important variables for one well-performing model (for example, a linear model f (x) = x ^T β with a fixed coefficient vector β) may be unimportant for another model. In this paper, we propose model class reliance (MCR) as the range of VI values across all well-performing model in a prespecified class. Thus, MCR gives a more comprehensive description of importance by accounting for the fact that many prediction models, possibly of different parametric forms, may fit the data well. In the process of deriving MCR, we show several informative results for permutation-based VI estimates, based on the VI measures used in Random Forests. Specifically, we derive connections between permutation importance estimates for a single prediction model, U-statistics, conditional variable importance, conditional causal effects, and linear model coefficients. We then give probabilistic bounds for MCR, using a novel, generalizable technique. We apply MCR to a public data set of Broward County criminal records to study the reliance of recidivism prediction models on sex and race. In this application, MCR can be used to help inform VI for unknown, proprietary models.

Reexamining Dis/Similarity-Based Tests for Rare-Variant Association with Case-Control Samples

A properly designed distance-based measure can capture informative genetic differences among individuals with different phenotypes and can be used to detect variants responsible for the phenotypes. To detect associated variants, various tests have been designed to contrast genetic dissimilarity or similarity scores of certain subject groups in different ways, among which the most widely used strategy is to quantify the difference between the within-group genetic dissimilarity/similarity (i.e., case-case and control-control similarities) and the between-group dissimilarity/similarity (i.e., case-control similarities). While it has been noted that for common variants, the within-group and the between-group measures should all be included; in this work, we show that for rare variants, comparison based on the two within-group measures can more effectively quantify the genetic difference between cases and controls. The between-group measure tends to overlap with one of the two within-group measures for rare variants, although such overlap is not present for common variants. Consequently, a dissimilarity or similarity test that includes the between-group information tends to attenuate the association signals and leads to power loss. Based on these findings, we propose a dissimilarity test that compares the degree of SNP dissimilarity within cases to that within controls to better characterize the difference between two disease phenotypes. We provide the statistical properties, asymptotic distribution, and computation details for a small sample size of the proposed test. We use simulated and real sequence data to assess the performance of the proposed test, comparing it with other rare-variant methods including those similarity-based tests that use both within-group and between-group information. As similarity-based approaches serve as one of the dominating approaches in rare-variant analysis, our results provide some insight for the effective detection of rare variants.

Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics

The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd.

A U-statistics based approach to sample size planning of two-arm trials with discrete outcome criterion aiming to establish either superiority or noninferiority

In current practice, the most frequently applied approach to the handling of ties in the Mann-Whitney-Wilcoxon (MWW) test is based on the conditional distribution of the sum of mid-ranks, given the observed pattern of ties. Starting from this conditional version of the testing procedure, a sample size formula was derived and investigated by Zhao et al. (Stat Med 2008). In contrast, the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two U-statistics estimators involved in the Mann-Whitney form of the test statistic. The accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the MWW test for superiority with arbitrarily tied data is comparatively evaluated by means of simulation. The key qualitative conclusions to be drawn from these numerical comparisons are as follows: With the sample sizes calculated by means of the respective formula, both versions of the test maintain the level and the prespecified power with about the same degree of accuracy. Despite the equivalence in terms of accuracy, the sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test. Perhaps, a still more important advantage of the nonconditional approach based on U-statistics is that it can be also adopted for noninferiority trials. Copyright © 2016 John Wiley & Sons, Ltd.

Conditional independence test by generalized Kendall's tau with generalized odds ratio

Determining conditional dependence is a challenging but important task in both model building and in applications such as genetic association studies and graphical models. Research on this topic has focused on kernel-based methods or has used categorical conditioning variables because of the challenge of the curse of dimensionality. To overcome this challenge, we propose a class of tests for conditional independence without any restriction on the distribution of the conditioning variables. The proposed test statistic can be treated as a generalized weighted Kendall's tau, in which the generalized odds ratio is utilized as a weight function to account for the distance between different values of the conditioning variables. The test procedure has desirable asymptotic properties and is easy to implement. We evaluate the finite sample performance of the proposed test through simulation studies and illustrate it using two real data examples.

Pearson's chi-square test and rank correlation inferences for clustered data

Pearson's chi-square test has been widely used in testing for association between two categorical responses. Spearman rank correlation and Kendall's tau are often used for measuring and testing association between two continuous or ordered categorical responses. However, the established statistical properties of these tests are only valid when each pair of responses are independent, where each sampling unit has only one pair of responses. When each sampling unit consists of a cluster of paired responses, the assumption of independent pairs is violated. In this article, we apply the within-cluster resampling technique to U-statistics to form new tests and rank-based correlation estimators for possibly tied clustered data. We develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations. The proposed methods are applied to a data set collected from a PET/CT imaging study for illustration.

Probabilistic measures of cost-effectiveness

Several probability-based measures are introduced in order to assess the cost-effectiveness of a treatment. The basic measure consists of the probability that one treatment is less costly and more effective compared with another. Several variants of this measure are suggested as flexible options for cost-effectiveness analysis. The proposed measures are invariant under monotone transformations of the cost and effectiveness measures. Interval estimation of the proposed measures are investigated under a parametric model, assuming bivariate normality, and also non-parametrically. The delta method and a generalized pivotal quantity approach are both investigated under the bivariate normal model. A non-parametric U-statistics-based approach is also investigated for computing confidence intervals. Numerical results show that under bivariate normality, the solution based on generalized pivotal quantities exhibits accurate performance in terms of maintaining the coverage probability of the confidence interval. The non-parametric U-statistics-based solution is accurate for sample sizes that are at least moderately large. The results are illustrated using data from a clinical trial for prostate cancer therapy. Copyright © 2016 John Wiley & Sons, Ltd.

Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.

A Three-Way Interaction among Maternal and Fetal Variants Contributing to Congenital Heart Defects

Congenital heart defects (CHDs) develop through a complex interplay between genetic variants, epigenetic modifications, and maternal environmental exposures. Genetic studies of CHDs have commonly tested single genetic variants for association with CHDs. Less attention has been given to complex gene-by-gene and gene-by-environment interactions. In this study, we applied a recently developed likelihood-ratio Mann-Whitney (LRMW) method to detect joint actions among maternal variants, fetal variants, and maternal environmental exposures, allowing for high-order statistical interactions. All subjects are participants from the National Birth Defect Prevention Study, including 623 mother-offspring pairs with CHD-affected pregnancies and 875 mother-offspring pairs with unaffected pregnancies. Each individual has 872 single nucleotide polymorphisms encoding for critical enzymes in the homocysteine, folate, and trans-sulfuration pathways. By using the LRMW method, three variants (fetal rs625879, maternal rs2169650, and maternal rs8177441) were identified with a joint association to CHD risk (nominal P-value = 1.13e-07). These three variants are located within genes BHMT2, GSTP1, and GPX3, respectively. Further examination indicated that maternal SNP rs2169650 may interact with both fetal SNP rs625879 and maternal SNP rs8177441. Our findings suggest that the risk of CHD may be influenced by both the intragenerational interaction within the maternal genome and the intergenerational interaction between maternal and fetal genomes.

Power calculation for comparing diagnostic accuracies in a multi-reader, multi-test design

Receiver operating characteristic (ROC) analysis is widely used to evaluate the performance of diagnostic tests with continuous or ordinal responses. A popular study design for assessing the accuracy of diagnostic tests involves multiple readers interpreting multiple diagnostic test results, called the multi-reader, multi-test design. Although several different approaches to analyzing data from this design exist, few methods have discussed the sample size and power issues. In this article, we develop a power formula to compare the correlated areas under the ROC curves (AUC) in a multi-reader, multi-test design. We present a nonparametric approach to estimate and compare the correlated AUCs by extending DeLong et al.'s (1988, Biometrics 44, 837-845) approach. A power formula is derived based on the asymptotic distribution of the nonparametric AUCs. Simulation studies are conducted to demonstrate the performance of the proposed power formula and an example is provided to illustrate the proposed procedure.

Test Statistics and Confidence Intervals to Establish Noninferiority between Treatments with Ordinal Categorical Data

The problem for establishing noninferiority is discussed between a new treatment and a standard (control) treatment with ordinal categorical data. A measure of treatment effect is used and a method of specifying noninferiority margin for the measure is provided. Two Z-type test statistics are proposed where the estimation of variance is constructed under the shifted null hypothesis using U-statistics. Furthermore, the confidence interval and the sample size formula are given based on the proposed test statistics. The proposed procedure is applied to a dataset from a clinical trial. A simulation study is conducted to compare the performance of the proposed test statistics with that of the existing ones, and the results show that the proposed test statistics are better in terms of the deviation from nominal level and the power.

A short note on jackknifing the concordance correlation coefficient

Lin's concordance correlation coefficient (CCC) is a very popular scaled index of agreement used in applied statistics. To obtain a confidence interval (CI) for the estimate of CCC, jackknifing was proposed and shown to perform well in simulation as well as in applications. However, a theoretical proof of the validity of the jackknife CI for the CCC has not been presented yet. In this note, we establish a sufficient condition for using the jackknife method to construct the CI for the CCC.

Semiparametric analysis of linear transformation models with covariate measurement errors

We take a semiparametric approach in fitting a linear transformation model to a right censored data when predictive variables are subject to measurement errors. We construct consistent estimating equations when repeated measurements of a surrogate of the unobserved true predictor are available. The proposed approach applies under minimal assumptions on the distributions of the true covariate or the measurement errors. We derive the asymptotic properties of the estimator and illustrate the characteristics of the estimator in finite sample performance via simulation studies. We apply the method to analyze an AIDS clinical trial data set that motivated the work.

On Inference for Kendall's τ within a Longitudinal Data Setting

Kendall's τ is a non-parametric measure of correlation based on ranks and is used in a wide range of research disciplines. Although methods are available for making inference about Kendall's τ, none has been extended to modeling multiple Kendall's τs arising in longitudinal data analysis. Compounding this problem is the pervasive issue of missing data in such study designs. In this paper, we develop a novel approach to provide inference about Kendall's τ within a longitudinal study setting under both complete and missing data. The proposed approach is illustrated with simulated data and applied to an HIV prevention study.