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Functional markers and their quantitative features (eg, maximum value, time to maximum, area under the curve [AUC], etc) are increasingly being used in clinical studies to diagnose diseases. It is thus of interest to assess the diagnostic utility of functional markers by assessing alignment between their quantitative features and an ordinal gold standard test that reflects the severity of disease. The concept of broad sense agreement (BSA) has recently been introduced for studying the relationship between continuous and ordinal measurements, and provides a promising tool to address such a question. Our strategy is to adopt a general class of summary functionals (SFs), each of which flexibly captures a different quantitative feature of a functional marker, and study its alignment according to an ordinal outcome via BSA. We further illustrate the proposed framework using three special classes of SFs (AUC-type, magnitude-specific, and time-specific) that are widely used in clinical settings. The proposed BSA estimator is proven to be consistent and asymptotically normal given a consistent estimator for the SF. We further provide an inferential framework for comparing a pair of candidate SFs in terms of their importance on the ordinal outcome. Our simulation results demonstrate satisfactory finite-sample performance of the proposed framework. We demonstrate the application of our methods using a renal study.

Summary Assessing agreement is often of interest in biomedical and clinical research when measurements are obtained on the same subjects by different raters or methods. Most classical agreement methods have been focused on global summary statistics, which cannot be used to describe various local agreement patterns. The objective of this work is to study the local agreement pattern between two continuous measurements subject to censoring. In this article, we propose a new agreement measure based on bivariate hazard functions to characterize the local agreement pattern between two correlated survival outcomes. The proposed measure naturally accommodates censored observations, fully captures the dependence structure between bivariate survival times and provides detailed information on how the strength of agreement evolves over time. We develop a nonparametric estimation method for the proposed local agreement pattern measure and study theoretical properties including strong consistency and asymptotical normality. We then evaluate the performance of the estimator through simulation studies and illustrate the method using a prostate cancer data example.

In many biomedical studies that involve correlated data, an outcome is often repeatedly measured for each individual subject along with the number of these measurements, which is also treated as an observed outcome. This type of data has been referred as multivariate random length data by Barnhart and Sampson (1995). A common approach to handling such type of data is to jointly model the multiple measurements and the random length. In previous literature, a key assumption is the multivariate normality for the multiple measurements. Motivated by a reproductive study, we propose a new copula-based joint model which relaxes the normality assumption. Specifically, we adopt the Clayton-Oakes model for multiple measurements with flexible marginal distributions specified as semi-parametric transformation models. The random length is modeled via a generalized linear model. We develop an approximate EM algorithm to derive parameter estimators and standard errors of the estimators are obtained through bootstrapping procedures and the finite-sample performance of the proposed method is investigated using simulation studies. We apply our method to the Mount Sinai Study of Women Office Workers (MSSWOW), where women were prospectively followed for 1 year for studying fertility.

In many observational longitudinal studies, the outcome of interest presents a skewed distribution, is subject to censoring due to detection limit or other reasons, and is observed at irregular times that may follow a outcome-dependent pattern. In this work, we consider quantile regression modeling of such longitudinal data, because quantile regression is generally robust in handling skewed and censored outcomes and is flexible to accommodate dynamic covariate-outcome relationships. Specifically, we study a longitudinal quantile regression model that specifies covariate effects on the marginal quantiles of the longitudinal outcome. Such a model is easy to interpret and can accommodate dynamic outcome profile changes over time. We propose estimation and inference procedures that can appropriately account for censoring and irregular outcome-dependent follow-up. Our proposals can be readily implemented based on existing software for quantile regression. We establish the asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulations suggest good finite-sample performance of the new method. We also present an analysis of data from a long-term study of a population exposed to polybrominated biphenyls (PBB), which uncovers an inhomogeneous PBB elimination pattern that would not be detected by traditional longitudinal data analysis.

Epidemiological studies involving biomarkers are often hindered by prohibitively expensive laboratory tests. Strategically pooling specimens prior to performing these lab assays has been shown to effectively reduce cost with minimal information loss in a logistic regression setting. When the goal is to perform regression with a continuous biomarker as the outcome, regression analysis of pooled specimens may not be straightforward, particularly if the outcome is right-skewed. In such cases, we demonstrate that a slight modification of a standard multiple linear regression model for poolwise data can provide valid and precise coefficient estimates when pools are formed by combining biospecimens from subjects with identical covariate values. When these x-homogeneous pools cannot be formed, we propose a Monte Carlo expectation maximization (MCEM) algorithm to compute maximum likelihood estimates (MLEs). Simulation studies demonstrate that these analytical methods provide essentially unbiased estimates of coefficient parameters as well as their standard errors when appropriate assumptions are met. Furthermore, we show how one can utilize the fully observed covariate data to inform the pooling strategy, yielding a high level of statistical efficiency at a fraction of the total lab cost.

The need to assess agreement arises in many scenarios in biomedical sciences when measurements were taken by different methods on the same subjects. When the endpoints are survival outcomes, the study of agreement becomes more challenging given the special characteristics of time-to-event data. In this article, we propose a new framework for assessing agreement based on survival processes that can be viewed as a natural representation of time-to-event outcomes. Our new agreement measure is formulated as the chance-corrected concordance between survival processes. It provides a new perspective for studying the relationship between correlated survival outcomes and offers an appealing interpretation as the agreement between survival times on the absolute distance scale. We provide a multivariate extension of the proposed agreement measure for multiple methods. Furthermore, the new framework enables a natural extension to evaluate time-dependent agreement structure. We develop nonparametric estimation of the proposed new agreement measures. Our estimators are shown to be strongly consistent and asymptotically normal. We evaluate the performance of the proposed estimators through simulation studies and then illustrate the methods using a prostate cancer data example.

Assessing agreement is often of interest in biomedical and clinical research when measurements are obtained on the same subjects by different raters or methods. Most classical agreement methods have been focused on global summary statistics, which cannot be used to describe various local agreement patterns. The objective of this work is to study the local agreement pattern between two continuous measurements subject to censoring. In this article, we propose a new agreement measure based on bivariate hazard functions to characterize the local agreement pattern between two correlated survival outcomes. The proposed measure naturally accommodates censored observations, fully captures the dependence structure between bivariate survival times and provides detailed information on how the strength of agreement evolves over time. We develop a nonparametric estimation method for the proposed local agreement pattern measure and study theoretical properties including strong consistency and asymptotical normality. We then evaluate the performance of the estimator through simulation studies and illustrate the method using a prostate cancer data example.

In many biomedical studies that involve correlated data, an outcome is often repeatedly measured for each individual subject along with the number of these measurements, which is also treated as an observed outcome. This type of data has been referred as multivariate random length data by Barnhart and Sampson (1995). A common approach to handling such type of data is to jointly model the multiple measurements and the random length. In previous literature, a key assumption is the multivariate normality for the multiple measurements. Motivated by a reproductive study, we propose a new copula-based joint model which relaxes the normality assumption. Specifically, we adopt the Clayton-Oakes model for multiple measurements with flexible marginal distributions specified as semi-parametric transformation models. The random length is modeled via a generalized linear model. We develop an approximate EM algorithm to derive parameter estimators and standard errors of the estimators are obtained through bootstrapping procedures and the finite-sample performance of the proposed method is investigated using simulation studies. We apply our method to the Mount Sinai Study of Women Office Workers (MSSWOW), where women were prospectively followed for one year for studying fertility.

The need to assess agreement arises in many scenarios in biomedical sciences when measurements were taken by different methods on the same subjects. When the endpoints are survival outcomes, the study of agreement becomes more challenging given the special characteristics of time-to-event data. In this article, we propose a new framework for assessing agreement based on survival processes that can be viewed as a natural representation of time-to-event outcomes. Our new agreement measure is formulated as the chance-corrected concordance between survival processes. It provides a new perspective for studying the relationship between correlated survival outcomes and offers an appealing interpretation as the agreement between survival times on the absolute distance scale. We provide a multivariate extension of the proposed agreement measure for multiple methods. Furthermore, the new framework enables a natural extension to evaluate time-dependent agreement structure. We develop nonparametric estimation of the proposed new agreement measures. Our estimators are shown to be strongly consistent and asymptotically normal. We evaluate the performance of the proposed estimators through simulation studies and then illustrate the methods using a prostate cancer data example.

Assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects. We present a modified weighted kappa coefficient to measure agreement between bivariate discrete survival times. The proposed kappa coefficient accommodates censoring by redistributing the mass of censored observations within the grid where the unobserved events may potentially happen. A generalized modified weighted kappa is proposed for multivariate discrete survival times. We estimate the modified kappa coefficients nonparametrically through a multivariate survival function estimator. The asymptotic properties of the kappa estimators are established and the performance of the estimators are examined through simulation studies of bivariate and trivariate survival times. We illustrate the application of the modified kappa coefficient in the presence of censored observations with data from a prostate cancer study.

Assessing agreement is often of interest in clinical studies to evaluate the similarity of measurements produced by different raters or methods on the same subjects. Lin's (1989, Biometrics 45, 255-268) concordance correlation coefficient (CCC) has become a popular measure of agreement for correlated continuous outcomes. However, commonly used estimation methods for the CCC do not accommodate censored observations and are, therefore, not applicable for survival outcomes. In this article, we estimate the CCC nonparametrically through the bivariate survival function. The proposed estimator of the CCC is proven to be strongly consistent and asymptotically normal, with a consistent bootstrap variance estimator. Furthermore, we propose a time-dependent agreement coefficient as an extension of Lin's (1989) CCC for measuring the agreement between survival times among subjects who survive beyond a specified time point. A nonparametric estimator is developed for the time-dependent agreement coefficient as well. It has the same asymptotic properties as the estimator of the CCC. Simulation studies are conducted to evaluate the performance of the proposed estimators. A real data example from a prostate cancer study is used to illustrate the method.

Summary. We present a method for computing sample size for cluster-randomized studies involving a large number of clusters with relatively small numbers of observations within each cluster. For multivariate survival data, only the marginal bivariate distribution is assumed to be known. The validity of this assumption is also discussed.

Bayesian methods are commonly used in some analyses of human genetic data, such as segregation and linkage analyses, but they are not typically used for analyses of human twin data. In this paper we develop a scheme for a Bayesian analysis of human twin data. We develop prior elicitation schemes to incorporate historical information. We consider three prior schemes: fully informative, semi-informative and noninformative. We use Markov chain Monte Carlo sampling algorithms to facilitate Bayesian computation and provide detailed implementation schemes. We also develop model diagnostics for assessing the goodness of fit of twin models. Using a simulation study, we show that if the purpose of the study is to estimate the intraclass correlations or heritability in twin studies, then the semi-informative prior is as informative as the fully informative prior. Finally, a real data example is used to illustrate the proposed methodologies.

Estimation of interrater agreement for ordered categorical data is examined when the same sample is being assessed by various raters with different methods. We investigate the use of a latent model proposed by Qu, Piedmonte, and Medendorp (1995, Biomerics 51, 268-275) to estimate the correlation between raters for each method, and test for their equality. For each of the assessment methods, these correlations can be interpreted as the variance components of random effects representing subject and rater. This method is applied to an HIV study, in which the amount of ectopy on a woman's cervix is measured by both direct visual assessment and a computer planimetry method.