Properly assessing the effects of environmental chemical exposures on disease risk remains a challenging problem in environmental epidemiology. Various analytic approaches have been proposed, but there are few papers that have compared the performance of different statistical methods on a single dataset. In this paper, we compare different regression-based approaches for estimating interactions between chemical mixture components using data from a case–control study on non-Hodgkin’s lymphoma. An analytic challenge is the high percentage of exposures that are below the limit of detection (LOD). Using imputation for LOD, we compare different Bayesian shrinkage prior approaches including an approach that incorporates the hierarchical principle where interactions are only included when main effects exist. Further, we develop an approach where main and interactive effects are represented by a series of distinct latent functions. We also fit the Bayesian kernel machine regression to these data. All of these approaches show little evidence of an interaction among the chemical mixtures when measurements below the LOD were imputed. The imputation approach makes very strong assumptions about the relationship between exposure and disease risk for measurements below the LOD. As an alternative, we show the results of an analysis where we model the exposure relationship with two parameters per mixture component; one characterizing the effect of being below the LOD and the other being a linear effect above the LOD. In this later analysis, we identify numerous strong interactions that were not identified in the analyses with imputation. This case study demonstrated the importance of developing new approaches for mixtures when the proportions of exposure measurements below the LOD are high.

Two-part mixed effects models are often used for analyzing longitudinal data with many zeros. Typically, these models are formulated with binary and continuous components separately with random effects that are correlated between the two components. Researchers have developed maximum-likelihood and Bayesian approaches for fitting these models that often require using particular software packages or very specialized software. We propose an imputation approach that will allow practitioners to separately use standard linear and generalized linear mixed models to estimate the fixed effects for two-part mixed effects models with complex random effects structures. An approximation to the conditional distribution of positive measurements given an individual’s pattern of non-zero measurements is proposed that can be easily estimated and then imputed from. We show that for a wide range of parameter values, the imputation approach results in nearly unbiased estimation and can be implemented with standard software. We illustrate the proposed imputation approach for the analysis of longitudinal clinical trial data with many zeros.

Analyzing health effects associated with exposure to environmental chemical mixtures is a challenging problem in epidemiology, toxicology, and exposure science. In particular, when there are a large number of chemicals under consideration it is difficult to estimate the interactive effects without incorporating reasonable prior information. Based on substantive considerations, researchers believe that true interactions between chemicals need to incorporate their corresponding main effects. In this paper, we use this prior knowledge through a shrinkage prior that a priori assumes an interaction term can only occur when the corresponding main effects exist. Our initial development is for logistic regression with linear chemical effects. We extend this formulation to include non-linear exposure effects and to account for exposure subject to detection limit. We develop an MCMC algorithm using a shrinkage prior that shrinks the interaction terms closer to zero as the main effects get closer to zero. We examine the performance of our methodology through simulation studies and illustrate an analysis of chemical interactions in a case-control study in cancer.

Background: Despite the therapeutic advances made in castration-sensitive prostate cancer, progression to castration-resistant disease is inevitable. Lutetium-177 vipivotide tetraxetan (¹⁷⁷Lu-PSMA-617) is a novel radioligand approved for use in metastatic castration-resistant prostate cancer (mCRPC). With promising efficacy, it is not without numerous potential side effects, namely cytopenias, which are often a reason for early discontinuation of ¹⁷⁷Lu-PSMA-617. We sought to describe the incidence of cytopenias associated with permanent discontinuation of ¹⁷⁷Lu-PSMA-617 at our institution. Methods: We conducted a retrospective review of patients who received ¹⁷⁷Lu-PSMA-617at the University of Virginia Comprehensive Cancer Center from 2018 to 2025. From this we assessed for the incidence of toxicities resulting in permanent discontinuation of ¹⁷⁷Lu-PSMA-617, which we refer to as dose-limiting toxicities. Descriptive statistics were used to summarize characteristics of the study population. Median overall survival from time of initiation of ¹⁷⁷Lu-PSMA-617 was estimated using a Kaplan–Meier curve. Results: Of the patients who received ¹⁷⁷Lu-PSMA-617 (n = 64), grade 3 or greater anemia occurred in 36% (n = 23), thrombocytopenia in 3% (n = 2), leukopenia in 3% (n = 2), neutropenia in 0% (n = 0), and lymphopenia in 33% (n = 21). In our cohort, 10.9% (n = 7) developed toxicities necessitating permanent discontinuation. Of these, 9.3% (n = 6) were attributable to cytopenias. Those cytopenias consisted of anemias in 100% (n = 6) of cases, leukopenia in 83% (n = 5), thrombocytopenia in 67% (n = 4), lymphopenia in 100% (n = 6), and neutropenia in 33% (n = 2). Aside from cytopenias, the remaining 1.6% (n = 1) of dose-limiting toxicities were attributable to renal injury. In the VISION trial, the ¹⁷⁷Lu-PSMA-617 treatment arm reported dose-limiting toxicities necessitating permanent discontinuation in 11.9% of participants, but did not report if these were attributable to cytopenia or other toxicities. Notably, 2 patients developed grade 5 pancytopenia and 1 patient developed grade 5 bone marrow failure in the VISION ¹⁷⁷Lu-PSMA-617 treatment arm. Compared to the VISION ¹⁷⁷Lu-PSMA-617 treatment arm, our cohort differed in the distribution of organ metastases, younger median age of patients, and a higher portion of those with ECOG 2 functional status. From the time of ¹⁷⁷Lu-PSMA-617 initiation, median overall survival was estimated to be 18.5 months, compared to 15.3 months in the VISION ¹⁷⁷Lu-PSMA-617 treatment arm. Conclusions: In our real-world analysis, 85% of dose-limiting toxicities necessitating ¹⁷⁷Lu-PSMA-617 discontinuation were attributed to cytopenias. Though a direct comparison cannot be made with the VISION ¹⁷⁷Lu-PSMA-617 treatment arm in terms of dose-limiting toxicity attributable specifically to cytopenias, they reported total dose-limiting toxicity to a similar degree, and cytopenias were the most common causes of grade 3 or greater toxicities. Therefore, it is important to recognize the ubiquity of these adverse events as well as the role that they play in therapy-limiting toxicity.