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Correlation coefficient estimates are often attenuated for truncated samples in the sense that the estimates are biased towards zero. Motivated by real data collected in South Sudan, we consider correlation coefficient estimation with singly truncated bivariate data. By considering a linear regression model in which a truncated variable is used as an explanatory variable, a consistent estimator for the regression slope can be obtained from the ordinary least squares method. A consistent estimator of the correlation coefficient is then obtained by multiplying the regression slope estimator by the variance ratio of the two variables. Results from two limited simulation studies confirm the validity and robustness of the proposed method. The proposed method is applied to the South Sudanese children's anthropometric and nutritional data collected by World Vision. Copyright © 2017 John Wiley & Sons, Ltd.

In many biomedical experiments one may often encounter bivariate data which are component-wise ordinal. The data set of the ophthalmologic experiment of the Wisconsin Epidemiologic Study of Diabetic Retinopathy (WESDR) is an example of such data. Several authors considered the analysis of such data from different viewpoints. The present work reviews the existing literature based on the WESDR data and on the basis of some latent variables provide the technique for analysing such data more easily in a Bayesian framework. Computation supports the methodology to a great extent. A comparison between our approach and the likelihood based approach considered by Kim has also been made.

Bivariate survival data arise, for example, in twin studies and studies of both eyes or ears of the same individual. Often it is of interest to regress the survival times on a set of predictors. In this paper we extend Wei and Tanner's multiple imputation approach for linear regression with univariate censored data to bivariate censored data. We formulate a class of censored bivariate linear regression methods by iterating between the following two steps: 1, the data is augmented by imputing survival times for censored observations; 2, a linear model is fit to the imputed complete data. We consider three different methods to implement these two steps. In particular, the marginal (independence) approach ignores the possible correlation between two survival times when estimating the regression coefficient. To improve the efficiency, we propose two methods that account for the correlation between the survival times. First, we improve the efficiency by using generalized least squares regression in step 2. Second, instead of generating data from an estimate of the marginal distribution we generate data from a bivariate log-spline density estimate in step 1. Through simulation studies we find that the performance of the two methods that take the dependence into account is close and that they are both more efficient than the marginal approach. The methods are applied to a data set from an otitis media clinical trial. Copyright © 1999 John Wiley & Sons, Ltd.

Non-parametric tests of independence, as well as accompanying measures of association, are essential tools for the analysis of bivariate data. Such tests and measures have been developed for uncensored and right censored failure time data, but have not been developed for interval censored failure time data. Bivariate interval censored data arise in AIDS studies in which screening tests for early signs of viral and bacterial infection are done at clinic visits. Because of missed clinic visits, the actual times of first positive screening tests are interval censored. To handle such data, we propose an extension of Kendall's coefficient of concordance. We apply it to data from an AIDS study that recorded times of shedding of cytomegalovirus (CMV) and times of colonization of mycobacterium avium complex (MAC). We examine the performance of our proposed measure through a simulation study.

We derive a non-parametric maximum likelihood estimator for bivariate interval censored data using standard techniques for constrained convex optimization. Our approach extends those taken for univariate interval censored data. We illustrate the estimator with bivariate data from an AIDS study.

Bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate probability model or by exploiting certain odds ratio-based association models. However, the joint bivariate probability model yields marginal probabilities, which are complicated functions of marginal and association parameters for both variables, and the odds ratio-based association model treats the odds ratios involved in the joint probabilities as 'working' parameters, which are consequently estimated through certain arbitrary 'working' regression models. Also, this later odds ratio-based model does not provide any easy interpretations of the correlations between two categorical variables. On the basis of pre-specified marginal probabilities, in this paper, we develop a bivariate normal type linear conditional multinomial probability model to understand the correlations between two categorical variables. The parameters involved in the model are consistently estimated using the optimal likelihood and generalized quasi-likelihood approaches. The proposed model and the inferences are illustrated through an intensive simulation study as well as an analysis of the well-known Wisconsin Diabetic Retinopathy status data.

Bimodal distributions of counts with one mode at zero are often seen in medical research. In a health survey parents were asked the number of days their children missed their activities (Y(1)) and the number of days their children spent in bed (Y(2)) due to illness in the past four weeks. Both variables exhibited zero inflation. We consider a bivariate Poisson-Poisson regression model, in which the two variables are regarded as indicators of an unobserved health status variable. Based on this, we further develop a bivariate Poisson-Poisson model that constrains Y(1)>or=Y(2). It is often claimed that there is a critical window of growth and nutrition in foetal life and infancy during which subsequent health status is affected. It is not clear whether the claim is true and whether childhood growth matters more. We analyse the bivariate data in relation to weight-for-age in infancy and weight gain from infancy to age 7 years. The findings do not support the existence of a critical window in infancy. There is some indication that childhood weight gain might affect health status.

Kappa statistics are often used for measuring agreement or association. The original measure suggested by Cohen for use with nominal data has since been generalized in a number of ways, including the incorporation of weights, adaptation for use with more than one rater and the application to bivariate data. Each modification requires a new approximation to the standard error and these have usually been derived by the delta method. This paper illustrates the use of estimating equations for kappa which offer a unified approach to many previously considered situations and which is also applicable to more complex designs.

This paper proposes a latent variable regression model for bivariate ordered categorical data and develops the necessary numerical procedure for parameter estimation. The proposed model is an extension of the standard bivariate probit model for dichotomous data to ordered categorical data with more than two categories for each margin. In addition, the proposed model allows for different covariates for the margins, which is characteristic of data from typical ophthalmological studies. It utilizes the stochastic ordering implicit in the data and the correlation coefficient of the bivariate normal distribution in expressing intra-subject dependency. Illustration of the proposed model uses data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy for identifying risk factors for diabetic retinopathy among younger-onset diabetics. The proposed regression model also applies to other clinical or epidemiological studies that involve paired organs.

Medical studies often involve comparing the toxicity and efficacy of drugs. Separately evaluating toxicity and efficacy, the usual practice, does not correspond to how doctors manage patients and does not use the information provided in their bivariate relationship. This paper presents methods for analysing the bivariate data. One method is based on assessing the benefit for patient values to lie in different regions of the toxicity–efficacy plane. A second method includes patient thresholds for tolerating drugs. We propose dividing the toxicity–efficacy plane into regions where patients are likely to tolerate the drug. Several statistics are defined on these regions for measuring the toxic–therapeutic relationship, and the bootstrap is proposed for estimating their variances. We illustrate with treatment information available on rheumatoid arthritis patients.

We use a penalized likelihood approach to obtain a smooth estimate of a bivariate distribution from grouped data where each observation consists of a region in a plane. The purpose of the analysis is to estimate the incubation period distribution of AIDS from the Multicenter AIDS Cohort Study, a prevalent cohort of homosexual men. In this article we illustrate the usefulness of the penalized likelihood approach. We also discuss the use of a cross-validation and a Bayesian scheme to choose the smoothing parameters and bootstrap samples to assess uncertainty.