Semiparametric methods for incomplete longitudinal count data with an application to health and retirement study.

In this paper, we propose and explore a novel semiparametric approach to analyzing longitudinal count data. We address the issue of missingness in longitudinal data and propose a weighted generalized estimations equations approach to fitting marginal mean response models for count responses with dropouts. Also, we investigate a spline regression approach to approximating the curvilinear relationship between the mean response and covariates. The asymptotic properties of the proposed estimators are studied in some detail. The empirical properties of the estimators are investigated using Monte Carlo simulations. An application is also provided using actual survey data obtained from the Health and Retirement Study (HRS).

Joint modeling of longitudinal continuous, longitudinal ordinal, and time-to-event outcomes.

In this paper, we propose an innovative method for jointly analyzing survival data and longitudinally measured continuous and ordinal data. We use a random effects accelerated failure time model for survival outcomes, a linear mixed model for continuous longitudinal outcomes and a proportional odds mixed model for ordinal longitudinal outcomes, where these outcome processes are linked through a set of association parameters. A primary objective of this study is to examine the effects of association parameters on the estimators of joint models. The model parameters are estimated by the method of maximum likelihood. The finite-sample properties of the estimators are studied using Monte Carlo simulations. The empirical study suggests that the degree of association among the outcome processes influences the bias, efficiency, and coverage probability of the estimators. Our proposed joint model estimators are approximately unbiased and produce smaller mean squared errors as compared to the estimators obtained from separate models. This work is motivated by a large multicenter study, referred to as the Genetic and Inflammatory Markers of Sepsis (GenIMS) study. We apply our proposed method to the GenIMS data analysis.

Joint modeling of longitudinal and survival data with a covariate subject to a limit of detection.

We develop and study an innovative method for jointly modeling longitudinal response and time-to-event data with a covariate subject to a limit of detection. The joint model assumes a latent process based on random effects to describe the association between longitudinal and time-to-event data. We study the role of the association parameter on the regression parameters estimators. We model the longitudinal and survival outcomes using linear mixed-effects and Weibull frailty models, respectively. Because of the limit of detection, missing covariate (explanatory variable, x) values may lead to the non-ignorable missing, resulting in biased parameter estimates with poor coverage probabilities of the confidence interval. We define and estimate the probability of missing due to the limit of detection. Then we develop a novel joint density and hence the likelihood function that incorporates the effect of left-censored covariate. Monte Carlo simulations show that the estimators of the proposed method are approximately unbiased and provide expected coverage probabilities for both longitudinal and survival submodels parameters. We also present an application of the proposed method using a large clinical dataset of pneumonia patients obtained from the Genetic and Inflammatory Markers of Sepsis study.

Robust estimation in accelerated failure time models.

The accelerated failure time model is widely used for analyzing censored survival times often observed in clinical studies. It is well-known that the ordinary maximum likelihood estimators of the parameters in the accelerated failure time model are generally sensitive to potential outliers or small deviations from the underlying distributional assumptions. In this paper, we propose and explore a robust method for fitting the accelerated failure time model to survival data by bounding the influence of outliers in both the outcome variable and associated covariates. We also develop a sandwich-type variance-covariance function for approximating the variances of the proposed robust estimators. The finite-sample properties of the estimators are investigated based on empirical results from an extensive simulation study. An application is provided using actual data from a clinical study of primary breast cancer patients.

Estimation in generalized linear models under censored covariates with an application to MIREC data.

In many biological experiments, certain values of a biomarker are often nondetectable due to low concentrations of an analyte or the limitations of a chemical analysis device, resulting in left-censored values. There is an increasing demand for the analysis of data subject to detection limits in clinical and environmental studies. In this paper, we develop a novel statistical method for the maximum likelihood estimation in generalized linear models with covariates subject to detection limits. Simulations are carried out to study the relative performance of the proposed estimators, as compared to other existing estimators. The proposed method is also applied to a real dataset from the Maternal-Infant Research on Environmental Chemicals cohort study, where we investigate how different chemical mixtures affect the health outcomes of infants and pregnant women.

Identification of chemical mixtures to which Canadian pregnant women are exposed: The MIREC Study.

Depending on the chemical and the outcome, prenatal exposures to environmental chemicals can lead to adverse effects on the pregnancy and child development, especially if exposure occurs during early gestation. Instead of focusing on prenatal exposure to individual chemicals, more studies have taken into account that humans are exposed to multiple environmental chemicals on a daily basis. The objectives of this analysis were to identify the pattern of chemical mixtures to which women are exposed and to characterize women with elevated exposures to various mixtures. Statistical techniques were applied to 28 chemicals measured simultaneously in the first trimester and socio-demographic factors of 1744 participants from the Maternal-Infant Research on Environment Chemicals (MIREC) Study. Cluster analysis was implemented to categorize participants based on their socio-demographic characteristics, while principal component analysis (PCA) was used to extract the chemicals with similar patterns and to reduce the dimension of the dataset. Next, hypothesis testing determined if the mean converted concentrations of chemical substances differed significantly among women with different socio-demographic backgrounds as well as among clusters. Cluster analysis identified six main socio-demographic clusters. Eleven components, which explained approximately 70% of the variance in the data, were retained in the PCA. Persistent organic pollutants (PCB118, PCB138, PCB153, PCB180, OXYCHLOR and TRANSNONA) and phthalates (MEOHP, MEHHP and MEHP) dominated the first and second components, respectively, and the first two components explained 25.8% of the source variation. Prenatal exposure to persistent organic pollutants (first component) were positively associated with women who have lower education or higher income, were born in Canada, have BMI ≥25, or were expecting their first child in our study population. MEOHP, MEHHP and MEHP, dominating the second component, were detected in at least 98% of 1744 participants in our cohort study; however, no particular group of pregnant women was identified to be highly exposed to phthalates. While widely recognized as important to studying potential health effects, identifying the mixture of chemicals to which various segments of the population are exposed has been problematic. We present an approach using factor analysis through principal component method and cluster analysis as an attempt to determine the pregnancy exposome. Future studies should focus on how to include these matrices in examining the health effects of prenatal exposure to chemical mixtures in pregnant women and their children.

Robust inference for mixed censored and binary response models with missing covariates.

In biomedical and epidemiological studies, often outcomes obtained are of mixed discrete and continuous in nature. Furthermore, due to some technical inconvenience or else, continuous responses are censored and also a few covariates cease to be observed completely. In this paper, we develop a model to tackle these complex situations. Our methodology is developed in a more general framework and provides a full-scale robust analysis of such complex models. The proposed robust maximum likelihood estimators of the model parameters are resistant to potential outliers in the data. We discuss the asymptotic properties of the robust estimators. To avoid computational difficulties involving irreducibly high-dimensional integrals, we propose a Monte Carlo method based on the Metropolis algorithm for approximating the robust maximum likelihood estimators. We study the empirical properties of these estimators in simulations. We also illustrate the proposed robust method using clustered data on blood sugar content from a clinical trial of individuals who were investigated for diabetes.

NY-ESO-1-specific TCR-engineered T cells mediate sustained antigen-specific antitumor effects in myeloma.

Despite recent therapeutic advances, multiple myeloma (MM) remains largely incurable. Here we report results of a phase I/II trial to evaluate the safety and activity of autologous T cells engineered to express an affinity-enhanced T cell receptor (TCR) recognizing a naturally processed peptide shared by the cancer-testis antigens NY-ESO-1 and LAGE-1. Twenty patients with antigen-positive MM received an average 2.4 × 10(9) engineered T cells 2 d after autologous stem cell transplant. Infusions were well tolerated without clinically apparent cytokine-release syndrome, despite high IL-6 levels. Engineered T cells expanded, persisted, trafficked to marrow and exhibited a cytotoxic phenotype. Persistence of engineered T cells in blood was inversely associated with NY-ESO-1 levels in the marrow. Disease progression was associated with loss of T cell persistence or antigen escape, in accordance with the expected mechanism of action of the transferred T cells. Encouraging clinical responses were observed in 16 of 20 patients (80%) with advanced disease, with a median progression-free survival of 19.1 months. NY-ESO-1-LAGE-1 TCR-engineered T cells were safe, trafficked to marrow and showed extended persistence that correlated with clinical activity against antigen-positive myeloma.

Frailty models for pneumonia to death with a left-censored covariate.

Frailty models are multiplicative hazard models for studying association between survival time and important clinical covariates. When some values of a clinical covariate are unobserved but known to be below a threshold called the limit of detection (LOD), naive approaches ignoring this problem, such as replacing the undetected value by the LOD or half of the LOD, often produce biased parameter estimate with larger mean squared error of the estimate. To address the LOD problem in a frailty model, we propose a flexible smooth nonparametric density estimator along with Simpson's numerical integration technique. This is an extension of an existing method in the likelihood framework for the estimation and inference of the model parameters. The proposed new method shows the estimators are asymptotically unbiased and gives smaller mean squared error of the estimates. Compared with the existing method, the proposed new method does not require distributional assumptions for the underlying covariates. Simulation studies were conducted to evaluate the performance of the new method in realistic scenarios. We illustrate the use of the proposed method with a data set from Genetic and Inflammatory Markers of Sepsis study in which interlekuin-10 was subject to LOD.

Inference for longitudinal data with nonignorable nonmonotone missing responses.

For the analysis of longitudinal data with nonignorable and nonmonotone missing responses, a full likelihood method often requires intensive computation, especially when there are many follow-up times. The authors propose and explore a Monte Carlo method, based on importance sampling, for approximating the maximum likelihood estimators. The finite-sample properties of the proposed estimators are studied using simulations. An application of the proposed method is also provided using longitudinal data on peptide intensities obtained from a proteomics experiment of trauma patients.

A Parametric Survival Model When a Covariate is Subject to Left-Censoring.

PROBLEM STATEMENT: Modeling survival data with a set of covariates usually assumes that the values of the covariates are fully observed. However, in a variety of applications, some values of a covariate may be left-censored due to inadequate instrument sensitivity to quantify the biospecimen. When data are left-censored, the true values are missing but are known to be smaller than the detection limit. The most commonly used ad-hoc method to deal with nondetect values is to substitute the nondetect values by the detection limit. Such ad-hoc analysis of survival data with an explanatory variable subject to left-censoring may provide biased and inefficient estimators of hazard ratios and survivor functions. METHOD: We consider a parametric proportional hazards model to analyze time-to-event data. We propose a likelihood method for the estimation and inference of model parameters. In this likelihood approach, instead of replacing the nondetect values by the detection limit, we adopt a numerical integration technique to evaluate the observed data likelihood in the presence of a left-censored covariate. Monte Carlo simulations were used to demonstrate various properties of the proposed regression estimators including the consistency and efficiency. RESULTS: The simulation study shows that the proposed likelihood approach provides approximately unbiased estimators of the model parameters. The proposed method also provides estimators that are more efficient than those obtained under the ad-hoc method. Also, unlike the ad-hoc estimators, the coverage probabilities of the proposed estimators are at their nominal level. Analysis of a large cohort study, genetic and inflammatory marker of sepsis study, shows discernibly different results based on the proposed method. CONCLUSION: Naive use of detection limit in a parametric survival model may provide biased and inefficient estimators of hazard ratios and survivor functions. The proposed likelihood approach provides approximately unbiased and efficient estimators of hazard ratios and survivor functions.

A bivariate pseudolikelihood for incomplete longitudinal binary data with nonignorable nonmonotone missingness.

For analyzing longitudinal binary data with nonignorable and nonmonotone missing responses, a full likelihood method is complicated algebraically, and often requires intensive computation, especially when there are many follow-up times. As an alternative, a pseudolikelihood approach has been proposed in the literature under minimal parametric assumptions. This formulation only requires specification of the marginal distributions of the responses and missing data mechanism, and uses an independence working assumption. However, this estimator can be inefficient for estimating both time-varying and time-stationary effects under moderate to strong within-subject associations among repeated responses. In this article, we propose an alternative estimator, based on a bivariate pseudolikelihood, and demonstrate in simulations that the proposed method can be much more efficient than the previous pseudolikelihood obtained under the assumption of independence. We illustrate the method using longitudinal data on CD4 counts from two clinical trials of HIV-infected patients.

Multivariate logistic regression with incomplete covariate and auxiliary information.

In this article, we propose and explore a multivariate logistic regression model for analyzing multiple binary outcomes with incomplete covariate data where auxiliary information is available. The auxiliary data are extraneous to the regression model of interest but predictive of the covariate with missing data. describe how the auxiliary information can be incorporated into a regression model for a single binary outcome with missing covariates, and hence the efficiency of the regression estimators can be improved. We consider extending the method of Horton and Laird (2001) to the case of a multivariate logistic regression model for multiple correlated outcomes, and with missing covariates and completely observed auxiliary information. We demonstrate that in the case of moderate to strong associations among the multiple outcomes, one can achieve considerable gains in efficiency from estimators in a multivariate model as compared to the marginal estimators of the same parameters.