A Fast EM Algorithm for Fitting Joint Models of a Binary Response and Multiple Longitudinal Covariates Subject to Detection Limits

Mediation analysis in a case-control study when the mediator is a censored variable

Mediation analysis is an approach for assessing the direct and indirect effects of an initial variable on an outcome through a mediator. In practice, mediation models can involve a censored mediator (eg, a woman's age at menopause). The current research for mediation analysis with a censored mediator focuses on scenarios where outcomes are continuous. However, the outcomes can be binary (eg, type 2 diabetes). Another challenge when analyzing such a mediation model is to use data from a case-control study, which results in biased estimations for the initial variable-mediator association if a standard approach is directly applied. In this study, we propose an approach (denoted as MAC-CC) to analyze the mediation model with a censored mediator given data from a case-control study, based on the semiparametric accelerated failure time model along with a pseudo-likelihood function. We adapted the measures for assessing the indirect and direct effects using counterfactual definitions. We conducted simulation studies to investigate the performance of MAC-CC and compared it to those of the naïve approach and the complete-case approach. MAC-CC accurately estimates the coefficients of different paths, the indirect effects, and the proportions of the total effects mediated. We applied the proposed and existing approaches to the mediation study of genetic variants, a woman's age at menopause, and type 2 diabetes based on a case-control study of type 2 diabetes. Our results indicate that there is no mediating effect from the age at menopause on the association between the genetic variants and type 2 diabetes.

Joint analysis of left-censored longitudinal biomarker and binary outcome via latent class modeling

Joint latent class modeling is an appealing approach for evaluating the association between a longitudinal biomarker and clinical outcome when the study population is heterogeneous. The link between the biomarker trajectory and the risk of event is reflected by the latent classes, which accommodate the underlying population heterogeneity. The estimation of joint latent class models may be complicated by the censored data in the biomarker measurements due to detection limits. We propose a modified likelihood function under the parametric assumption of biomarker distribution and develop a Monte Carlo expectation-maximization algorithm for joint analysis of a biomarker and a binary outcome. We conduct simulation studies to demonstrate the satisfactory performance of our Monte Carlo expectation-maximization algorithm and the superiority of our method to the naive imputation method for handling censored biomarker data. In addition, we apply our method to the Genetic and Inflammatory Markers of Sepsis study to investigate the role of inflammatory biomarker profile in predicting 90-day mortality for patients hospitalized with community-acquired pneumonia.

Estimation of indirect effect when the mediator is a censored variable

A mediation model explores the direct and indirect effects of an initial variable ( X) on an outcome variable ( Y) by including a mediator ( M). In many realistic scenarios, investigators observe censored data instead of the complete data. Current research in mediation analysis for censored data focuses mainly on censored outcomes, but not censored mediators. In this study, we proposed a strategy based on the accelerated failure time model and a multiple imputation approach. We adapted a measure of the indirect effect for the mediation model with a censored mediator, which can assess the indirect effect at both the group and individual levels. Based on simulation, we established the bias in the estimations of different paths (i.e. the effects of X on M [ a], of M on Y [ b] and of X on Y given mediator M [ c']) and indirect effects when analyzing the data using the existing approaches, including a naïve approach implemented in software such as Mplus, complete-case analysis, and the Tobit mediation model. We conducted simulation studies to investigate the performance of the proposed strategy compared to that of the existing approaches. The proposed strategy accurately estimates the coefficients of different paths, indirect effects and percentages of the total effects mediated. We applied these mediation approaches to the study of SNPs, age at menopause and fasting glucose levels. Our results indicate that there is no indirect effect of association between SNPs and fasting glucose level that is mediated through the age at menopause.