Joint modeling approaches for censored predictors due to detection limits with applications to metabolites data.

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, exact measures cannot be obtained, and thus are left censored. The problem becomes more challenging when the censored data come from heterogeneous populations consisting of exposed and non-exposed subjects. If the censored data come from non-exposed subjects, their measures are always zero and hence censored, forming a latent class governed by a distinct censoring mechanism compared with the exposed subjects. The exposed group's censored measurements are always greater than zero, but less than the detection limit. It is very often that the exposed and non-exposed subjects may have different disease traits or different relationships with outcomes of interest, so we need to disentangle the two different populations for valid inference. In this article, we aim to fill the methodological gaps in the literature by developing a novel joint modeling approach to not only address the censoring issue in predictors, but also untangle different relationships of exposed and non-exposed subjects with the outcome. Simulation studies are performed to assess the numerical performance of our proposed approach when the sample size is small to moderate. The joint modeling approach is also applied to examine associations between plasma metabolites and blood pressure in Bogalusa Heart Study, and identify new metabolites that are highly associated with blood pressure.

On modelling relative risks for longitudinal binomial responses: implications from two dueling paradigms.

Although logistic regression is the most popular for modelling regression relationships with binary responses, many find relative risk (RR), or risk ratio, easier to interpret and prefer to use this measure of risk in regression analysis. Indeed, since Zou published his modified Poisson regression approach for modelling RR for cross-sectional data, his paper has been cited over 7 000 times, demonstrating the popularity of this alternative measure of risk in regression analysis involving binary responses. As longitudinal studies have become increasingly popular in clinical trials and observational studies, it is imperative to extend Zou's approach for longitudinal data. The two most popular approaches for longitudinal data analysis are the generalised linear mixed-effects model (GLMM) and generalised estimating equations (GEE). However, the parametric GLMM cannot be used for the extension within the current context, because Zou's approach treats the binary response as a Poisson variable, which is at odds with the Bernoulli distribution for the binary response. On the other hand, as it imposes no mathematical model on data distributions, the semiparametric GEE is coherent with Zou's modified Poisson regression. In this paper, we develop a GEE-based longitudinal model for binary responses to provide inference about RR.