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Censoring due to a limit of detection or limit of quantification happens quite often in many medical studies. Conventional approaches to deal with censoring when analyzing these data include, for example, the substitution method and the complete case (CC) analysis. More recently, maximum likelihood estimation (MLE) has been increasingly used. While the CC analysis and the substitution method usually lead to biased estimates, the MLE approach appears to perform well in many situations. This article proposes an MLE approach to estimate the association between two measurements in the presence of censoring in one or both quantities. The central idea is to use a copula function to join the marginal distributions of the two measurements. In various simulation studies, we show that our approach outperforms existing conventional methods (CC and substitution analyses). In addition, rank-based measures of global association such as Kendall's tau or Spearman's rho can be studied, hence, attention is not only confined to Pearson's product-moment correlation coefficient capturing solely linear association. We have shown in our simulations that our approach is robust to misspecification of the copula function or marginal distributions given a small association. Furthermore, we propose a straightforward MLE method to fit a (multiple) linear regression model in the presence of censoring in a covariate or both the covariate and the response. Given the marginal distribution of the censored covariate, our method outperforms conventional approaches. We also compare and discuss the performance of our method with multiple imputation and missing indicator model approaches. [ABSTRACT FROM AUTHOR]

The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data. [ABSTRACT FROM AUTHOR]