A Note on Comparing Exposure Data to a Regulatory Limit in the Presence of Unexposed and a Limit of Detection

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.

A new statistical test for latent class in censored data due to detection limit

Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.

Comparison of models for analyzing two-group, cross-sectional data with a Gaussian outcome subject to a detection limit

A potential difficulty in the analysis of biomarker data occurs when data are subject to a detection limit. This detection limit is often defined as the point at which the true values cannot be measured reliably. Multiple, regression-type models designed to analyze such data exist. Studies have compared the bias among such models, but few have compared their statistical power. This simulation study provides a comparison of approaches for analyzing two-group, cross-sectional data with a Gaussian-distributed outcome by exploring statistical power and effect size confidence interval coverage of four models able to be implemented in standard software. We found using a Tobit model fit by maximum likelihood provides the best power and coverage. An example using human immunodeficiency virus type 1 ribonucleic acid data is used to illustrate the inferential differences in these models.

The effect of HAART on HIV RNA trajectory among treatment-naïve men and women: a segmental Bernoulli/lognormal random effects model with left censoring

BACKGROUND

Highly active antiretroviral therapy (HAART) rapidly suppresses human immunodeficiency virus (HIV) viral replication and reduces circulating viral load, but the long-term effects of HAART on viral load remain unclear.

METHODS

We evaluated HIV viral load trajectories over 8 years following HAART initiation in the Multicenter AIDS Cohort Study and the Women's Interagency HIV Study. The study included 157 HIV-infected men and 199 HIV-infected women who were antiretroviral naive and contributed 1311 and 1837 semiannual person-visits post-HAART, respectively. To account for within-subject correlation and the high proportion of left-censored viral loads, we used a segmental Bernoulli/lognormal random effects model.

RESULTS

Approximately 3 months (0.30 years for men and 0.22 years for women) after HAART initiation, HIV viral loads were optimally suppressed (ie, with very low HIV RNA) for 44% (95% confidence interval = 39%-49%) of men and 43% (38%-47%) of women, whereas the other 56% of men and 57% of women had on average 2.1 (1.5-2.6) and 3.0 (2.7-3.2) log10 copies/mL, respectively.

CONCLUSION

After 8 years on HAART, 75% of men and 80% of women had optimal suppression, whereas the rest of the men and women had suboptimal suppression with a median HIV RNA of 3.1 and 3.7 log10 copies/mL, respectively.