Exploratory subgroup identification in the heterogeneous Cox model: A relatively simple procedure

For survival analysis applications we propose a novel procedure for identifying subgroups with large treatment effects, with focus on subgroups where treatment is potentially detrimental. The approach, termed forest search, is relatively simple and flexible. All-possible subgroups are screened and selected based on hazard ratio thresholds indicative of harm with assessment according to the standard Cox model. By reversing the role of treatment one can seek to identify substantial benefit. We apply a splitting consistency criteria to identify a subgroup considered "maximally consistent with harm." The type-1 error and power for subgroup identification can be quickly approximated by numerical integration. To aid inference we describe a bootstrap bias-corrected Cox model estimator with variance estimated by a Jacknife approximation. We provide a detailed evaluation of operating characteristics in simulations and compare to virtual twins and generalized random forests where we find the proposal to have favorable performance. In particular, in our simulation setting, we find the proposed approach favorably controls the type-1 error for falsely identifying heterogeneity with higher power and classification accuracy for substantial heterogeneous effects. Two real data applications are provided for publicly available datasets from a clinical trial in oncology, and HIV.

Estimating individualized treatment rules by optimizing the adjusted probability of a longer survival

Individualized treatment rules inform tailored treatment decisions based on the patient's information, where the goal is to optimize clinical benefit for the population. When the clinical outcome of interest is survival time, most of current approaches typically aim to maximize the expected time of survival. We propose a new criterion for constructing Individualized treatment rules that optimize the clinical benefit with survival outcomes, termed as the adjusted probability of a longer survival. This objective captures the likelihood of living longer with being on treatment, compared to the alternative, which provides an alternative and often straightforward interpretation to communicate with clinicians and patients. We view it as an alternative to the survival analysis standard of the hazard ratio and the increasingly used restricted mean survival time. We develop a new method to construct the optimal Individualized treatment rule by maximizing a nonparametric estimator of the adjusted probability of a longer survival for a decision rule. Simulation studies demonstrate the reliability of the proposed method across a range of different scenarios. We further perform data analysis using data collected from a randomized Phase III clinical trial (SWOG S0819).

Tail Risk Dynamics under Price-Limited Constraint: A Censored Autoregressive Conditional Fréchet Model

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management.

A matching-based machine learning approach to estimating optimal dynamic treatment regimes with time-to-event outcomes

Observational data (e.g. electronic health records) has become increasingly important in evidence-based research on dynamic treatment regimes, which tailor treatments over time to patients based on their characteristics and evolving clinical history. It is of great interest for clinicians and statisticians to identify an optimal dynamic treatment regime that can produce the best expected clinical outcome for each individual and thus maximize the treatment benefit over the population. Observational data impose various challenges for using statistical tools to estimate optimal dynamic treatment regimes. Notably, the task becomes more sophisticated when the clinical outcome of primary interest is time-to-event. Here, we propose a matching-based machine learning method to identify the optimal dynamic treatment regime with time-to-event outcomes subject to right-censoring using electronic health record data. In contrast to the established inverse probability weighting-based dynamic treatment regime methods, our proposed approach provides better protection against model misspecification and extreme weights in the context of treatment sequences, effectively addressing a prevalent challenge in the longitudinal analysis of electronic health record data. In simulations, the proposed method demonstrates robust performance across a range of scenarios. In addition, we illustrate the method with an application to estimate optimal dynamic treatment regimes for patients with advanced non-small cell lung cancer using a real-world, nationwide electronic health record database from Flatiron Health.

Mixtures of t $$ t $$ factor analysers with censored responses and external covariates: An application to educational data from Peru

Analysing data from educational tests allows governments to make decisions for improving the quality of life of individuals in a society. One of the key responsibilities of statisticians is to develop models that provide decision-makers with pertinent information about the latent process that educational tests seek to represent. Mixtures oft $$ t $$ factor analysers (MtFA) have emerged as a powerful device for model-based clustering and classification of high-dimensional data containing one or several groups of observations with fatter tails or anomalous outliers. This paper considers an extension of MtFA for robust clustering of censored data, referred to as the MtFAC model, by incorporating external covariates. The enhanced flexibility of including covariates in MtFAC enables cluster-specific multivariate regression analysis of dependent variables with censored responses arising from upper and/or lower detection limits of experimental equipment. An alternating expectation conditional maximization (AECM) algorithm is developed for maximum likelihood estimation of the proposed model. Two simulation experiments are conducted to examine the effectiveness of the techniques presented. Furthermore, the proposed methodology is applied to Peruvian data from the 2007 Early Grade Reading Assessment, and the results obtained from the analysis provide new insights regarding the reading skills of Peruvian students.

Nonparametric analysis of delayed treatment effects using single-crossing constraints

Clinical trials involving novel immuno-oncology therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and, in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and, moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. Our estimates of these measures may be used together with efficacy measures from a primary analysis to provide further insight into differences in survival across treatment arms. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination therapy trial.

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.

Ball divergence for the equality test of crossing survival curves

It is a very common problem to test survival equality using the right-censored time-to-event data in clinical research. Although the log-rank test is popularly used in various studies, it may become insensitive when the proportional hazards assumption is violated. As follows, there have a variety of statistical methods being proposed to identify the discrepancy between crossing survival curves or hazard functions. The omnibus tests against general alternatives are usually preferred due to their wide applicability to complicated scenarios in real applications. In this paper, we propose two novel statistics to estimate the ball divergence using the right-censored survival data, and then implement them in the equality test on survival time in two independent groups. The simulation analysis demonstrates their efficiency in identifying the survival discrepancy. Compared to the existing methods, our proposed methods present higher power in situations with complex distributions, especially when there is a scale shift between groups. Real examples illustrate its advantage in practical applications.

Clustering minimal inhibitory concentration data through Bayesian mixture models: An application to detect Mycobacterium tuberculosis resistance mutations

Antimicrobial resistance is becoming a major threat to public health throughout the world. Researchers are attempting to contrast it by developing both new antibiotics and patient-specific treatments. In the second case, whole-genome sequencing has had a huge impact in two ways: first, it is becoming cheaper and faster to perform whole-genome sequencing, and this makes it competitive with respect to standard phenotypic tests; second, it is possible to statistically associate the phenotypic patterns of resistance to specific mutations in the genome. Therefore, it is now possible to develop catalogues of genomic variants associated with resistance to specific antibiotics, in order to improve prediction of resistance and suggest treatments. It is essential to have robust methods for identifying mutations associated to resistance and continuously updating the available catalogues. This work proposes a general method to study minimal inhibitory concentration distributions and to identify clusters of strains showing different levels of resistance to antimicrobials. Once the clusters are identified and strains allocated to each of them, it is possible to perform regression method to identify with high statistical power the mutations associated with resistance. The method is applied to a new 96-well microtiter plate used for testing Mycobacterium tuberculosis.

Implementing competing risks in discrete event simulation: the event-specific probabilities and distributions approach

Background: Although several strategies for modelling competing events in discrete event simulation (DES) exist, a methodological gap for the event-specific probabilities and distributions (ESPD) approach when dealing with censored data remains. This study defines and illustrates the ESPD strategy for censored data. Methods: The ESPD approach assumes that events are generated through a two-step process. First, the type of event is selected according to some (unknown) mixture proportions. Next, the times of occurrence of the events are sampled from a corresponding survival distribution. Both of these steps can be modelled based on covariates. Performance was evaluated through a simulation study, considering sample size and levels of censoring. Additionally, an oncology-related case study was conducted to assess the ability to produce realistic results, and to demonstrate its implementation using both frequentist and Bayesian frameworks in R. Results: The simulation study showed good performance of the ESPD approach, with accuracy decreasing as sample sizes decreased and censoring levels increased. The average relative absolute error of the event probability (95%-confidence interval) ranged from 0.04 (0.00; 0.10) to 0.23 (0.01; 0.66) for 60% censoring and sample size 50, showing that increased censoring and decreased sample size resulted in lower accuracy. The approach yielded realistic results in the case study. Discussion: The ESPD approach can be used to model competing events in DES based on censored data. Further research is warranted to compare the approach to other modelling approaches for DES, and to evaluate its usefulness in estimating cumulative event incidences in a broader context.

Systematic Handling of Environmental Fate Data for Model Development-Illustrated for the Case of Biodegradation Half-Life Data

The assessment of environmental hazard indicators such as persistence, mobility, toxicity, or bioaccumulation of chemicals often results in highly variable experimental outcomes. Persistence is particularly affected due to a multitude of influencing environmental factors, with biodegradation experiments resulting in half-lives spanning several orders of magnitude. Also, half-lives may lie beyond the limits of reliable half-life quantification, and the number of available data points per substance may vary considerably, requiring a statistically robust approach for the characterization of data. Here, we apply Bayesian inference to address these challenges and characterize the distributions of reported soil half-lives. Our model estimates the mean, standard deviation, and corresponding uncertainties from a set of reported half-lives experimentally obtained for a single substance. We apply our inference model to 893 pesticides and pesticide transformation products with experimental soil half-lives of varying data quantity and quality, and we infer the half-life distribution for each compound. By estimating average half-lives, their experimental variability, and the uncertainty of the estimations, we provide a reliable data source for building predictive models, which are urgently needed by regulatory authorities to manage existing chemicals and by industry to design benign, nonpersistent chemicals. Our approach can be readily adapted for other environmental hazard indicators.

A New Truncated Lindley-Generated Family of Distributions: Properties, Regression Analysis, and Applications

We present the truncated Lindley-G (TLG) model, a novel class of probability distributions with an additional shape parameter, by composing a unit distribution called the truncated Lindley distribution with a parent distribution function G(x). The proposed model's characteristics including critical points, moments, generating function, quantile function, mean deviations, and entropy are discussed. Also, we introduce a regression model based on the truncated Lindley-Weibull distribution considering two systematic components. The model parameters are estimated using the maximum likelihood method. In order to investigate the behavior of the estimators, some simulations are run for various parameter settings, censoring percentages, and sample sizes. Four real datasets are used to demonstrate the new model's potential.

Dynamics of glucose concentration during the initiation of ketogenic diet treatment in children with refractory epilepsy: Results of continuous glucose monitoring

OBJECTIVE

The ketogenic diet (KD) is a diet low in carbohydrates and rich in fats which has long been used to treat refractory epilepsy. The metabolic changes related to the KD may increase the risk of hypoglycemia, especially during the first days. The study focused on the impact of KD initiation on glycemia in non-diabetic patients with refractory epilepsy.

METHODS

The subjects were 10 pediatric patients (6 boys, mean age 6.1 ± 2.4 years), treated for intractable epilepsy. Blinded continuous glucose monitoring system (CGM) Dexcom G4 was used. Patients started on their regular diet in the first 36 hours of monitoring, followed by an increase in lipids intake and a gradual reduction of carbohydrates (relations 1:1; 2:1; 3:1; 3.5:1). We analyzed changes in glycemia during fat: nonfat ratio changes using a generalized linear model.

RESULTS

The mean monitored time per person was 6 days, 10 hours and 44 minutes. The mean ± SD glycemia for the regular diet was 4.84 ± 0.20 mmol/L, for the carbohydrates/fat ratio of 1:1 it was 4.03 ± 0.16, for the ratio of 2:1 it was 3.57 ± 0.10, for the ratio 3:1 it was 3.39 ± 0.13 and for the final ratio of 3.5:1 it was 2.79 ± 0.06 mmol/L (P < 0.001). The portions of time spent in glycemia ≤3.5 mmol/L (≤2.5 mmol/L respectively) were: on the normal diet 0.88% (0.31%) of the monitored period, during 1:1 KD ratio 1.92% (0.95%), during 2:1 ratio 3.18% (1.02%), and during 3:1 and 3.5:1 ratios 13.64% (2.36%) of the monitored time (P < 0.05).

SIGNIFICANCE

Continuous glucose monitoring system shows the dynamic of glucose concentration in ketogenic diet treatment initiation. It may be a useful tool to control the effects of this diet on glucose metabolism, especially in hypoglycemia detection.

Generalized fiducial inference for the restricted mean survival time

The standard modeling approach for time-to-event outcomes subject to censoring is based on the hazard function, with hazard ratios capturing the effect of exposures on the risk of outcome. The restricted mean survival time, defined as the expected time to event up to a pre-specified time horizon, provides an alternative useful summary of time-to-event outcomes. Restricted mean survival time can be estimated nonparametrically and can be used to compare groups or interventions when the proportional hazards (PHs) assumption does not hold. Moreover, even when the proportional hazards assumption holds, the restricted mean survival time, an additive measure of risk, provides additional information to the hazard ratio, which is a measure of relative risk that can be difficult to interpret in absence of an estimate of the reference risk. Herein, a generalized fiducial approach is proposed for restricted mean survival time, and its asymptotic properties are investigated. Numerical simulations show the proposed approach provides one- and two-sided confidence intervals with coverage probabilities close to nominal values and controls the type-I error for two-group comparisons even for small sample sizes with a low number of events. Data from a type 1 diabetes study is used for illustration.

Stochastic Expectation Maximization Algorithm for Linear Mixed-Effects Model with Interactions in the Presence of Incomplete Data

The purpose of this paper is to propose a new algorithm based on stochastic expectation maximization (SEM) to deal with the problem of unobserved values when multiple interactions in a linear mixed-effects model (LMEM) are present. We test the effectiveness of the proposed algorithm with the stochastic approximation expectation maximization (SAEM) and Monte Carlo Markov chain (MCMC) algorithms. This comparison is implemented to highlight the importance of including the maximum effects that can affect the model. The applications are made on both simulated psychological and real data. The findings demonstrate that our proposed SEM algorithm is highly preferable to the other competitor algorithms.

Generalized mean residual life models for survival data with missing censoring indicators

The mean residual life (MRL) function is an important and attractive alternative to the hazard function for characterizing the distribution of a time-to-event variable. In this article, we study the modeling and inference of a family of generalized MRL models for right-censored survival data with censoring indicators missing at random. To estimate the model parameters, augmented inverse probability weighted estimating equation approaches are developed, in which the non-missingness probability and the conditional probability of an uncensored observation are estimated by parametric methods or nonparametric kernel smoothing techniques. Asymptotic properties of the proposed estimators are established and finite sample performance is evaluated by extensive simulation studies. An application to brain cancer data is presented to illustrate the proposed methods.

Regularized Buckley-James method for right-censored outcomes with block-missing multimodal covariates

High-dimensional data with censored outcomes of interest are prevalent in medical research. To analyze such data, the regularized Buckley-James estimator has been successfully applied to build accurate predictive models and conduct variable selection. In this paper, we consider the problem of parameter estimation and variable selection for the semiparametric accelerated failure time model for high-dimensional block-missing multimodal neuroimaging data with censored outcomes. We propose a penalized Buckley-James method that can simultaneously handle block-wise missing covariates and censored outcomes. This method can also perform variable selection. The proposed method is evaluated by simulations and applied to a multimodal neuroimaging dataset and obtains meaningful results.

Bayesian sparse modeling to identify high-risk subgroups in meta-analysis of safety data

Meta-analysis allows researchers to combine evidence from multiple studies, making it a powerful tool for synthesizing information on the safety profiles of new medical interventions. There is a critical need to identify subgroups at high risk of experiencing treatment-related toxicities. However, this remains quite challenging from a statistical perspective as there are a variety of clinical risk factors that may be relevant for different types of adverse events, and adverse events of interest may be rare or incompletely reported. We frame this challenge as a variable selection problem and propose a Bayesian hierarchical model which incorporates a horseshoe prior on the interaction terms to identify high-risk groups. Our proposed model is motivated by a meta-analysis of adverse events in cancer immunotherapy, and our results uncover key factors driving the risk of specific types of treatment-related adverse events.

Net-benefit regression with censored cost-effectiveness data from randomized or observational studies

Cost-effectiveness analysis is an essential part of the evaluation of new medical interventions. While in many studies both costs and effectiveness (eg, survival time) are censored, standard survival analysis techniques are often invalid due to the induced dependent censoring problem. We propose methods for censored cost-effectiveness data using the net-benefit regression framework, which allow covariate-adjustment and subgroup identification when comparing two intervention groups. The methods provide a straightforward way to construct cost-effectiveness acceptability curves with censored data. We also propose a more efficient doubly robust estimator of average causal incremental net benefit, which increases the likelihood that the results will represent a valid inference in observational studies. Lastly, we conduct extensive numerical studies to examine the finite-sample performance of the proposed methods, and illustrate the proposed methods with a real data example using both survival time and quality-adjusted survival time as the measures of effectiveness.

Doubly robust estimation of optimal dynamic treatment regimes with multicategory treatments and survival outcomes

Patients with chronic diseases, such as cancer or epilepsy, are often followed through multiple stages of clinical interventions. Dynamic treatment regimes (DTRs) are sequences of decision rules that assign treatments at each stage based on measured covariates for each patient. A DTR is said to be optimal if the expectation of the desirable clinical benefit reaches a maximum when applied to a population. When there are three or more options for treatments at each decision point and the clinical outcome of interest is a time-to-event variable, estimating an optimal DTR can be complicated. We propose a doubly robust method to estimate optimal DTRs with multicategory treatments and survival outcomes. A novel blip function is defined to measure the difference in expected outcomes among treatments, and a doubly robust weighted least squares algorithm is designed for parameter estimation. Simulations using various weight functions and scenarios support the advantages of the proposed method in estimating optimal DTRs over existing approaches. We further illustrate the practical value of our method by applying it to data from the Standard and New Antiepileptic Drugs study. In this analysis, the proposed method supports the use of the new drug lamotrigine over the standard option carbamazepine. When the actual treatments match the estimated optimal treatments, survival outcomes tend to be better. The newly developed method provides a practical approach for clinicians that is not limited to cases of binary treatment options.

The Effect of Health on the Elderly's Labor Supply in Rural China: Simultaneous Equation Models With Binary, Ordered, and Censored Variables

In this study, we examined the effect of health on the elderly's labor supply in rural China based on the data of the Chinese Health and Nutrition Survey (CHNS) from 1997 to 2006. We used simultaneous equations to address the endogeneity problem of health and estimate the models with censored data of labor supply by the full information maximum likelihood estimation. We found that the failing health does not significantly decrease the elderly's labor supply in rural areas when using both the subjective (self-reported health status) and objective (hypertension diagnosed or not) health indicators. Our finding indicates the phenomenon of "ceaseless toil" for the elderly in rural China, i.e., the elderly almost work their whole life even if they are not physically capable. The results remain robust when using a two-stage limited information maximum likelihood estimation.

Extending multivariate Student's- t $$ t $$ semiparametric mixed models for longitudinal data with censored responses and heavy tails

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's t $$ t $$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Exposure Assessment Techniques Applied to the Highly Censored Deepwater Horizon Gulf Oil Spill Personal Measurements

The GuLF Long-term Follow-up Study (GuLF STUDY) is investigating potential adverse health effects of workers involved in the Deepwater Horizon (DWH) oil spill response and cleanup (OSRC). Over 93% of the 160 000 personal air measurements taken on OSRC workers were below the limit of detection (LOD), as reported by the analytic labs. At this high level of censoring, our ability to develop exposure estimates was limited. The primary objective here was to reduce the number of measurements below the labs' reported LODs to reflect the analytic methods' true LODs, thereby facilitating the use of a relatively unbiased and precise Bayesian method to develop exposure estimates for study exposure groups (EGs). The estimates informed a job-exposure matrix to characterize exposure of study participants. A second objective was to develop descriptive statistics for relevant EGs that did not meet the Bayesian criteria of sample size ≥5 and censoring ≤80% to achieve the aforementioned level of bias and precision. One of the analytic labs recalculated the measurements using the analytic method's LOD; the second lab provided raw analytical data, allowing us to recalculate the data values that fell between the originally reported LOD and the analytical method's LOD. We developed rules for developing Bayesian estimates for EGs with >80% censoring. The remaining EGs were 100% censored. An order-based statistical method (OBSM) was developed to estimate exposures that considered the number of measurements, geometric standard deviation, and average LOD of the censored samples for N ≥ 20. For N < 20, substitution of ½ of the LOD was assigned. Recalculation of the measurements lowered overall censoring from 93.2 to 60.5% and of the THC measurements, from 83.1 to 11.2%. A total of 71% of the EGs met the ≤15% relative bias and <65% imprecision goal. Another 15% had censoring >80% but enough non-censored measurements to apply Bayesian methods. We used the OBSM for 3% of the estimates and the simple substitution method for 11%. The methods presented here substantially reduced the degree of censoring in the dataset and increased the number of EGs meeting our Bayesian method's desired performance goal. The OBSM allowed for a systematic and consistent approach impacting only the lowest of the exposure estimates. This approach should be considered when dealing with highly censored datasets.

Estimates of Occupational Inhalation Exposures to Six Oil-Related Compounds on the Four Rig Vessels Responding to the Deepwater Horizon Oil Spill

BACKGROUND

The 2010 Deepwater Horizon (DWH) oil spill involved thousands of workers and volunteers to mitigate the oil release and clean-up after the spill. Health concerns for these participants led to the initiation of a prospective epidemiological study (GuLF STUDY) to investigate potential adverse health outcomes associated with the oil spill response and clean-up (OSRC). Characterizing the chemical exposures of the OSRC workers was an essential component of the study. Workers on the four oil rig vessels mitigating the spill and located within a 1852 m (1 nautical mile) radius of the damaged wellhead [the Discoverer Enterprise (Enterprise), the Development Driller II (DDII), the Development Driller III (DDIII), and the HelixQ4000] had some of the greatest potential for chemical exposures.

OBJECTIVES

The aim of this paper is to characterize potential personal chemical exposures via the inhalation route for workers on those four rig vessels. Specifically, we presented our methodology and descriptive statistics of exposure estimates for total hydrocarbons (THCs), benzene, toluene, ethylbenzene, xylene, and n-hexane (BTEX-H) for various job groups to develop exposure groups for the GuLF STUDY cohort.

METHODS

Using descriptive information associated with the measurements taken on various jobs on these rig vessels and with job titles from study participant responses to the study questionnaire, job groups [unique job/rig/time period (TP) combinations] were developed to describe groups of workers with the same or closely related job titles. A total of 500 job groups were considered for estimation using the available 8139 personal measurements. We used a univariate Bayesian model to analyze the THC measurements and a bivariate Bayesian regression framework to jointly model the measurements of THC and each of the BTEX-H chemicals separately, both models taking into account the many measurements that were below the analytic limit of detection.

RESULTS

Highest THC exposures occurred in TP1a and TP1b, which was before the well was mechanically capped. The posterior medians of the arithmetic mean (AM) ranged from 0.11 ppm ('Inside/Other', TP1b, DDII; and 'Driller', TP3, DDII) to 14.67 ppm ('Methanol Operations', TP1b, Enterprise). There were statistical differences between the THC AMs by broad job groups, rigs, and time periods. The AMs for BTEX-H were generally about two to three orders of magnitude lower than the THC AMs, with benzene and ethylbenzene measurements being highly censored.

CONCLUSIONS

Our results add new insights to the limited literature on exposures associated with oil spill responses and support the current epidemiologic investigation of potential adverse health effects of the oil spill.

Quantifying the feasibility of shortening clinical trial duration using surrogate markers

The potential benefit of using a surrogate marker in place of a long-term primary outcome is very attractive in terms of the impact on study length and cost. Many available methods for quantifying the effectiveness of a surrogate endpoint either rely on strict parametric modeling assumptions or require that the primary outcome and surrogate marker are fully observed that is, not subject to censoring. Moreover, available methods for quantifying surrogacy typically provide a proportion of treatment effect explained (PTE) measure and do not directly address the important questions of whether and how the trial can be ended earlier using the surrogate marker. In this article, we specifically address these important questions by proposing a PTE measure to quantify the feasibility of ending trials early based on endpoint information collected at an earlier landmark point t 0 in a time-to-event outcome setting. We provide a framework for deriving an optimally predicted outcome for individual patients at t 0 based on a combination of surrogate marker and event time information in the presence of censoring. We propose a non-parametric estimator for the PTE measure and derive the asymptotic properties of our estimators. Finite sample performance of our estimators are illustrated via extensive simulation studies and a real data application examining the potential of hemoglobin A1c and fasting plasma glucose to predict treatment effects on long term diabetes risk based on the Diabetes Prevention Program study.