Multivariate Censored Data Research Articles

An information ratio-based goodness-of-fit test for copula models on censored data.

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right-censored data. No formal goodness-of-fit (GOF) test exists for interval-censored or recurrent events data. We develop a general GOF test for copula-based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D-vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type-I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of modelfitness.

Bayesian Local Influence of Generalized Failure Time Models with Latent Variables and Multivariate Censored Data

We develop a Bayesian local influence procedure for generalized failure time models with latent variables and multivariate censored data. We propose to use the penalized splines (P-splines) approach to formulate the unknown functions of the proposed models. We assess the effects of minor perturbations to individual observations, the prior distributions of parameters, and the sampling distribution on statistical inference through various perturbation schemes. The first-order local influence measure is used to quantify the degree of minor perturbations to different aspects of a statistical model with the use of Bayes factor as an objective function. Simulation studies show that the empirical performance of the Bayesian local influence procedure is satisfactory. An application to a study of renal disease for type 2 diabetes patients is presented.

Bayesian semiparametric failure time models for multivariate censored data with latent variables.

In this paper, we propose a semiparametric failure time model to analyze multivariate censored data with latent variables. The proposed model generalizes the conventional accelerated failure time model to accommodate latent risk factors that could be measured by multiple observed variables through a factor analysis and to incorporate additive nonparametric functions of observed and latent risk factors to examine their functional effects on multivariate failure times of interest. A Bayesian approach, along with Bayesian P-splines and Markov chain Monte Carlo techniques, is developed to estimate the unknown parameters and functions. The empirical performance of the proposed methodology is evaluated by a simulation study. An application to a study on the risk factors of two diabetes complications is presented.

Bayesian analysis of transformation latent variable models with multivariate censored data

Transformation latent variable models are proposed in this study to analyze multivariate censored data. The proposed models generalize conventional linear transformation models to semiparametric transformation models that accommodate latent variables. The characteristics of the latent variables were assessed based on several correlated observed indicators through measurement equations. A Bayesian approach was developed with Bayesian P-splines technique and the Markov chain Monte Carlo algorithm to estimate the unknown parameters and transformation functions. Simulation shows that the performance of the proposed methodology is satisfactory. The proposed method was applied to analyze a cardiovascular disease data set.

Simple Non-Parametric Estimators for Unemployment Duration Analysis

Summary We consider an extension of conventional univariate Kaplan–Meier-type estimators for the hazard rate and the survivor function to multivariate censored data with a censored random regressor. It is an Akritas-type estimator which adapts the non-parametric conditional hazard rate estimator of Beran to more typical data situations in applied analysis. We show with simulations that the estimator has nice finite sample properties and our implementation appears to be fast. As an application we estimate non-parametric conditional quantile functions with German administrative unemployment duration data.

Application of a Simple Nonparametric Conditional Quantile Function Estimator in Unemployment Duration Analysis

We consider an extension of conventional univariate Kaplan-Meier type estimators for the hazard rate and the survivor function to multivariate censored data with a censored random regressor. It is an Akritas (1994) type estimator which adapts the nonparametric conditional hazard rate estimator of Beran (1981) to more typical data situations in applied analysis. We show with simulations that the estimator has nice finite sample properties and our implementation appears to be fast. As an application we estimate nonparametric conditional quantile functions with German administrative unemployment duration data.

Non-parametric tests for the two-group comparison with multivariate censored data

We developped a multivariate version of weighted logrank tests to compare two multivariate time-to-event distributions; our method is based on the marginal approach, and uses martingale properties. Our results can be extended to the study of several risk factors in a multivariate proportional hazard model. To cite this article: C. Pinçon, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Exploratory Tobit Factor Analysis for Multivariate Censored Data

We propose Multivariate Tobit models with a factor structure on the covariance matrix. Such models are particularly useful in the exploratory analysis of multivariate censored data and the identification of latent variables from behavioral data. The factor structure provides a parsimonious representation of the censored data and reduces the dimensionality of the integration required in evaluating the likelihood. In addition, the factor model parameters lend themselves to substantive interpretation and graphical display. The models are estimated with simulated maximum likelihood. Applications to the prescription of pharmaceutical products and the analysis of multi-category buying behavior are provided.

Model testing for multivariate censored data

In the fields like Astronomy and Ecology, the need for proper statistical analysis of data that are censored is being increasingly recognized. Such data occur when, due to noise or other factors, instruments fail to detect low luminosities of celestial objects, or low concentrations of certain pollutants. For multivariate censored data sets there are very few distribution free methods available and researchers in the various fields often impose an assumption on the joint distribution, such as multivariate normality, and carry out parametric inferences. Under censoring, however, such parametric inferences are asymptotically wrong if the imposed assumption is incorrect. In this paper we propose a class of goodness-of-fit procedures for testing assumptions about the multivariate distribution under random censoring. The test procedures generalize Pearson's goodness-of-fit test in the sense that they are based on the concept of observed-minus-expected frequencies. The theory of the test statistic, however, differs from that for the classical Pearson test due to the accommodation of censored data.

On an analog of empirical distribution for multivariate censored data

A model of a “censored” experiment is formally defined. A functional is proposed which can be considered as an analog of the empirical distribution. Some properties of this functional are investigated.

Natural History of Indeterminate Pigmented Choroidal Tumors

The purpose of this study is to delineate the natural history of indeterminate pigmented choroidal lesions and identify parameters from the initial visit that correlate with lesion enlargement. The authors retrospectively reviewed the records of all patients with indeterminate pigmented choroidal lesions seen in consultation at the Ocular Oncology Unit at the University of California, San Francisco, after 1975. Clinical examination, fundus photography, fluorescein angiography, and ultrasound data were examined. Investigators masked to outcome coded sequential parameters of each of these modalities. Data were analyzed using both univariate and multivariate censored data techniques. Of 293 lesions, 98 grew. The 5-year actuarial rate of growth was 36%. Greater tumor thickness, presence of symptoms, orange pigment, internal quiet zone on B-scan, and hot spots on fluorescein angiography all were significant predictors of tumor enlargement (relative risk of detectable tumor growth, > 1.8). Risk scores were calculated, and subsets with higher probability of future growth were identified. In five of the patients with growing lesions, metastatic disease developed after a median posttreatment follow-up period of 51 months. Most small indeterminate pigmented lesions can be followed safely by serial observation and ancillary testing. The authors identified models based on data from the initial visit that can be used as an adjunct to planning tumor management.

The two-sample problem with multivariate censored data: a new rank test family

A new rank test family is proposed to test the equality of two multivariate failure times distributions with censored observations. The tests are very simple: they are based on a transformation of the multivariate rank vectors to a univariate rank score and the resulting statistics belong to the familiar class of the weighted logrank test statistics. The new procedure is also applicable to multivariate observations in general, such as repeated measures, some of which may be missing. To investigate the performance of the proposed tests, a simulation study was conducted with bivariate exponential models for various censoring rates. The size and power of these tests against Lehmann alternatives were compared to the size and power of two other tests (Wei and Lachin, 1984 and Wei and Knuiman, 1987). In all simulations the new procedures provide a relatively good power and an accurate control over the size of the test. A real example from the National Cooperative Gallstone Study is given