The one-sample problem from eradication studies of chronic viral infections

In studies of chronic viral infections, the objective is to estimate probabilities of developing viral eradication and resistance. Complications arise as the laboratory methods used to assess eradication status result in unusual types of censored observations. This paper proposes nonparametric methods for the one-sample analysis of viral eradication/resistance data. We show that the unconstrained nonparametric maximum likelihood estimator of the subdistributions of eradication and resistance are obtainable in closed form. In small samples, these estimators may be inadmissible; thus, we also present an algorithm for obtaining the constrained MLEs based on an isotonic regression of the unconstrained MLEs. Estimators of several functionals of the eradication and resistance subdistributions are also developed and discussed. The methods are illustrated with results from recent hepatitis C clinical trials.     

Analysis of a partially observed binary covariate process and a censored failure time in the presence of truncation and competing risks

We develop methods for assessing the association between a binary time-dependent covariate process and a failure time endpoint when the former is observed only at a single time point and the latter is right censored, and when the observations are subject to truncation and competing causes of failure. Using a proportional hazards model for the effect of the covariate process on the failure time of interest, we develop an approach utilizing EM algorithm and profile likelihood for estimating the relative risk parameter and cause-specific hazards for failure. The methods are extended to account for other covariates that can influence the time-dependent covariate process and cause-specific risks of failure. We illustrate the methods with data from a recent study on the association between loss of hepatitis B e antigen and the development of hepatocellular carcinoma in a population of chronic carriers of hepatitis B.     

Cox regression model with randomly censored covariates

This paper deals with a Cox proportional hazards regression model, where some covariates of interest are randomly right‐censored. While methods for censored outcomes have become ubiquitous in the literature, methods for censored covariates have thus far received little attention and, for the most part, dealt with the issue of limit‐of‐detection. For randomly censored covariates, an often‐used method is the inefficient complete‐case analysis (CCA) which consists in deleting censored observations in the data analysis. When censoring is not completely independent, the CCA leads to biased and spurious results. Methods for missing covariate data, including type I and type II covariate censoring as well as limit‐of‐detection do not readily apply due to the fundamentally different nature of randomly censored covariates. We develop a novel method for censored covariates using a conditional mean imputation based on either Kaplan–Meier estimates or a Cox proportional hazards model to estimate the effects of these covariates on a time‐to‐event outcome. We evaluate the performance of the proposed method through simulation studies and show that it provides good bias reduction and statistical efficiency. Finally, we illustrate the method using data from the Framingham Heart Study to assess the relationship between offspring and parental age of onset of cardiovascular events.     

Functional additive models for optimizing individualized treatment rules

A novel functional additive model is proposed, which is uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional and/or scalar pretreatment covariates. The primary motivation for this approach is to optimize individualized treatment rules based on data from a randomized clinical trial. We generalize functional additive regression models by incorporating treatment-specific components into additive effect components. A structural constraint is imposed on the treatment-specific components in order to provide a class of additive models with main effects and interaction effects that are orthogonal to each other. If primary interest is in the interaction between treatment and the covariates, as is generally the case when optimizing individualized treatment rules, we can thereby circumvent the need to estimate the main effects of the covariates, obviating the need to specify their form and thus avoiding the issue of model misspecification. The methods are illustrated with data from a depression clinical trial with electroencephalogram functional data as patients' pretreatment covariates.     

Missing covariates in longitudinal data with informative dropouts: bias analysis and inference

We consider estimation in generalized linear mixed models (GLMM) for longitudinal data with informative dropouts. At the time a unit drops out, time-varying covariates are often unobserved in addition to the missing outcome. However, existing informative dropout models typically require covariates to be completely observed. This assumption is not realistic in the presence of time-varying covariates. In this article, we first study the asymptotic bias that would result from applying existing methods, where missing time-varying covariates are handled using naive approaches, which include: (1) using only baseline values; (2) carrying forward the last observation; and (3) assuming the missing data are ignorable. Our asymptotic bias analysis shows that these naive approaches yield inconsistent estimators of model parameters. We next propose a selection/transition model that allows covariates to be missing in addition to the outcome variable at the time of dropout. The EM algorithm is used for inference in the proposed model. Data from a longitudinal study of human immunodeficiency virus (HIV)-infected women are used to illustrate the methodology.     

An extension of the Cormack-Jolly-Seber model for continuous covariates with application to Microtus pennsylvanicus

Recent developments in the Cormack-Jolly-Seber (CJS) model for analyzing capture-recapture data have focused on allowing the capture and survival rates to vary between individuals. Several methods have been developed in which capture and survival are functions of auxiliary variables that may be discrete, constant over time, or apply to the population as a whole, but the problem has not been solved for continuous covariates that vary with both time and individual. This article proposes a new method to handle such covariates by modeling changes over time via a diffusion process and using logistic functions to link the variable to the CJS capture and survival rates. Bayesian methods are used to estimate the model parameters. The method is applied to study the effect of body mass on the survival of the North American meadow vole, Microtus pennsylvanicus.     

A flexible approach to measurement error correction in case-control studies

SUMMARY: We investigate the use of prospective likelihood methods to analyze retrospective case-control data where some of the covariates are measured with error. We show that prospective methods can be applied and the case-control sampling scheme can be ignored if one adequately models the distribution of the error-prone covariates in the case-control sampling scheme. Indeed, subject to this, the prospective likelihood methods result in consistent estimates and information standard errors are asymptotically correct. However, the distribution of such covariates is not the same in the population and under case-control sampling, dictating the need to model the distribution flexibly. In this article, we illustrate the general principle by modeling the distribution of the continuous error-prone covariates using the skewnormal distribution. The performance of the method is evaluated through simulation studies, which show satisfactory results in terms of bias and coverage. Finally, the method is applied to the analysis of two data sets which refer, respectively, to a cholesterol study and a study on breast cancer.     

An estimator for the proportional hazards model with multiple longitudinal covariates measured with error

In many longitudinal studies, it is of interest to characterize the relationship between a time-to-event (e.g. survival) and several time-dependent and time-independent covariates. Time-dependent covariates are generally observed intermittently and with error. For a single time-dependent covariate, a popular approach is to assume a joint longitudinal data-survival model, where the time-dependent covariate follows a linear mixed effects model and the hazard of failure depends on random effects and time-independent covariates via a proportional hazards relationship. Regression calibration and likelihood or Bayesian methods have been advocated for implementation; however, generalization to more than one time-dependent covariate may become prohibitive. For a single time-dependent covariate, Tsiatis and Davidian (2001) have proposed an approach that is easily implemented and does not require an assumption on the distribution of the random effects. This technique may be generalized to multiple, possibly correlated, time-dependent covariates, as we demonstrate. We illustrate the approach via simulation and by application to data from an HIV clinical trial.     

Helicobacter spp. Other Than Helicobacter pylori

Non- H. pylori Helicobacter species (NHPHS) are associated with several important human and animal diseases. In the past year research into this group of bacteria has continued to gain attention, and novel species have been described in new niches owing to improvements in detection methods. Polymerase chain reaction and/or sequencing remain the gold standard for the detection of this genus. New insights into the pathogenesis of the NHPHS in hepatobiliary, gastric, and intestinal diseases were gained. In particular, data revealed interaction between hepatic steatosis and infectious hepatitis in the development of hepatocellular carcinoma. Evidence of an association between hepatitis C virus and Helicobacter spp. in hepatocarcinoma development was also provided; and male sex hormone signaling appeared to influence infectious hepatitis induced by Helicobacter hepaticus . More findings support an association between Helicobacter heilmannii and gastric adenocarcinoma; and in mice, mucins MUC4 and MUC5 but not MUC1 influence the colonization and pathogenesis of Helicobacter felis . Data indicated that the roles of the adaptive immune system in H. hepaticus -induced intestinal tumorigenesis are different in the small and large intestines, and environmental factors, such as bile acids may modulate H. hepaticus carcinogenic potential. New reports in the prevention and eradication of NHPHS showed a protective response against Helicobacter suis induced by vaccine administration, and a successful cross-foster rederivation method successfully eradicated Helicobacter spp. from contaminated mice litters. Overall, the studies provided insights into the pathophysiology of Helicobacter species other than Helicobacter pylori.     

Bayesian semiparametric zero-inflated Poisson model for longitudinal count data

This paper presents new methods, using a Bayesian approach, for analyzing longitudinal count data with excess zeros and nonlinear effects of continuously valued covariates. In longitudinal count data there are many problems that can make the use of a zero-inflated Poisson (ZIP) model ineffective. These problems are unobserved heterogeneity and nonlinear effects of continuously valued covariates. Our proposed semiparametric model can simultaneously handle these problems in a unified framework. The framework accounts for heterogeneity by incorporating random effects and has two components. The parametric component of the model which deals with the linear effects of time invariant covariates and the non-parametric component which gives an arbitrary smooth function to model the effect of time or time-varying covariates on the logarithm of mean count. The proposed methods are illustrated by analyzing longitudinal count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly.     

An open spatial capture–recapture model for estimating density,movement, and population dynamics from line‐transect surveys

The purpose of many wildlife population studies is to estimate density, movement, or demographic parameters. Linking these parameters to covariates, such as habitat features, provides additional ecological insight and can be used to make predictions for management purposes. Line‐transect surveys, combined with distance sampling methods, are often used to estimate density at discrete points in time, whereas capture–recapture methods are used to estimate movement and other demographic parameters. Recently, open population spatial capture–recapture models have been developed, which simultaneously estimate density and demographic parameters, but have been made available only for data collected from a fixed array of detectors and have not incorporated the effects of habitat covariates. We developed a spatial capture–recapture model that can be applied to line‐transect survey data by modeling detection probability in a manner analogous to distance sampling. We extend this model to a) estimate demographic parameters using an open population framework and b) model variation in density and space use as a function of habitat covariates. The model is illustrated using simulated data and aerial line‐transect survey data for North Atlantic right whales in the southeastern United States, which also demonstrates the ability to integrate data from multiple survey platforms and accommodate differences between strata or demographic groups. When individuals detected from line‐transect surveys can be uniquely identified, our model can be used to simultaneously make inference on factors that influence spatial and temporal variation in density, movement, and population dynamics.     

Attenuation caused by infrequently updated covariates in survival analysis

This paper deals with hazard regression models for survival data with time-dependent covariates consisting of updated quantitative measurements. The main emphasis is on the Cox proportional hazards model but also additive hazard models are discussed. Attenuation of regression coefficients caused by infrequent updating of covariates is evaluated using simulated data mimicking our main example, the CSL1 liver cirrhosis trial. We conclude that the degree of attenuation depends on the type of stochastic process describing the time-dependent covariate and that attenuation may be substantial for an Ornstein-Uhlenbeck process. Also trends in the covariate combined with non-synchronous updating may cause attenuation. Simple methods to adjust for infrequent updating of covariates are proposed and compared to existing techniques using both simulations and the CSL1 data. The comparison shows that while existing, more complicated methods may work well with frequent updating of covariates the simpler techniques may have advantages in larger data sets with infrequent updatings.     

Robust covariate-adjusted log-rank statistics and corresponding sample size formula for recurrent events data

Summary .   Recurrent events data are frequently encountered in clinical trials. This article develops robust covariate-adjusted log-rank statistics applied to recurrent events data with arbitrary numbers of events under independent censoring and the corresponding sample size formula. The proposed log-rank tests are robust with respect to different data-generating processes and are adjusted for predictive covariates. It reduces to the Kong and Slud (1997, Biometrika 84, 847–862) setting in the case of a single event. The sample size formula is derived based on the asymptotic normality of the covariate-adjusted log-rank statistics under certain local alternatives and a working model for baseline covariates in the recurrent event data context. When the effect size is small and the baseline covariates do not contain significant information about event times, it reduces to the same form as that of Schoenfeld (1983, Biometrics 39, 499–503) for cases of a single event or independent event times within a subject. We carry out simulations to study the control of type I error and the comparison of powers between several methods in finite samples. The proposed sample size formula is illustrated using data from an rhDNase study.     

Smooth individual level covariates adjustment in disease mapping

Spatial models for disease mapping should ideally account for covariates measured both at individual and area levels. The newly available “indiCAR” model fits the popular conditional autoregresssive (CAR) model by accommodating both individual and group level covariates while adjusting for spatial correlation in the disease rates. This algorithm has been shown to be effective but assumes log‐linear associations between individual level covariates and outcome. In many studies, the relationship between individual level covariates and the outcome may be non‐log‐linear, and methods to track such nonlinearity between individual level covariate and outcome in spatial regression modeling are not well developed. In this paper, we propose a new algorithm, smooth‐indiCAR, to fit an extension to the popular conditional autoregresssive model that can accommodate both linear and nonlinear individual level covariate effects while adjusting for group level covariates and spatial correlation in the disease rates. In this formulation, the effect of a continuous individual level covariate is accommodated via penalized splines. We describe a two‐step estimation procedure to obtain reliable estimates of individual and group level covariate effects where both individual and group level covariate effects are estimated separately. This distributed computing framework enhances its application in the Big Data domain with a large number of individual/group level covariates. We evaluate the performance of smooth‐indiCAR through simulation. Our results indicate that the smooth‐indiCAR method provides reliable estimates of all regression and random effect parameters. We illustrate our proposed methodology with an analysis of data on neutropenia admissions in New South Wales (NSW), Australia.     

Effects of residual smoothing on the posterior of the fixed effects in disease-mapping models

Disease-mapping models for areal data often have fixed effects to measure the effect of spatially varying covariates and random effects with a conditionally autoregressive (CAR) prior to account for spatial clustering. In such spatial regressions, the objective may be to estimate the fixed effects while accounting for the spatial correlation. But adding the CAR random effects can cause large changes in the posterior mean and variance of fixed effects compared to the nonspatial regression model. This article explores the impact of adding spatial random effects on fixed effect estimates and posterior variance. Diagnostics are proposed to measure posterior variance inflation from collinearity between the fixed effect covariates and the CAR random effects and to measure each region's influence on the change in the fixed effect's estimates by adding the CAR random effects. A new model that alleviates the collinearity between the fixed effect covariates and the CAR random effects is developed and extensions of these methods to point-referenced data models are discussed.     

Generalized additive models with interval-censored data and time-varying covariates: application to human immunodeficiency virus infection in hemophiliacs

We describe a method for extending smooth nonparametric modeling methods to time-to-event data where the event may be known only to lie within a window of time. Maximum penalized likelihood is used to fit a discrete proportional hazards model that also models the baseline hazard, and left-truncation and time-varying covariates are accommodated. The implementation follows generalized additive modeling conventions, allowing both parametric and smooth terms and specifying the amount of smoothness in terms of the effective degrees of freedom. We illustrate the method on a well-known interval-censored data set on time of human immunodeficiency virus infection in a multicenter study of hemophiliacs. The ability to examine time-varying covariates, not available with previous methods, allows detection and modeling of nonproportional hazards and use of a time-varying covariate that fits the data better and is more plausible than a fixed alternative.     

Fitting the log-F accelerated failure time model with incomplete covariate data

Data obtained from studies in the health sciences often have incompletely observed covariates as well as censored outcomes. In this paper, we present methods for fitting the log-F accelerated failure time model with incomplete continuous and/or categorical time-independent covariates using the Gibbs sampler. A general location model that allows different covariance structures across cells is specified for the covariates, and ignorable missingness of the covariates is assumed. Techniques that accommodate standard assumptions of ignorable censoring as well as certain types of nonignorable censoring are developed. We compare our approach to traditional complete-case analysis in an application to data obtained from a study of melanoma. The comparison indicates that substantial gains in efficiency are possible with our approach.     

Improving estimation efficiency for regression with MNAR covariates

For regression with covariates missing not at random where the missingness depends on the missing covariate values, complete-case (CC) analysis leads to consistent estimation when the missingness is independent of the response given all covariates, but it may not have the desired level of efficiency. We propose a general empirical likelihood framework to improve estimation efficiency over the CC analysis. We expand on methods in Bartlett et al. (2014, Biostatistics 15 , 719–730) and Xie and Zhang (2017, Int J Biostat 13 , 1–20) that improve efficiency by modeling the missingness probability conditional on the response and fully observed covariates by allowing the possibility of modeling other data distribution-related quantities. We also give guidelines on what quantities to model and demonstrate that our proposal has the potential to yield smaller biases than existing methods when the missingness probability model is incorrect. Simulation studies are presented, as well as an application to data collected from the US National Health and Nutrition Examination Survey.     

Factors influencing soay sheep survival: a Bayesian analysis

This article presents a Bayesian analysis of mark-recapture-recovery data on Soay sheep. A reversible jump Markov chain Monte Carlo technique is used to determine age classes of common survival, and to model the survival probabilities in those classes using logistic regression. This involves environmental and individual covariates, as well as random effects. Auxiliary variables are used to impute missing covariates measured on individual sheep. The Bayesian approach suggests different models from those previously obtained using classical statistical methods. Following model averaging, features that were not previously detected, and which are of ecological importance, are identified.     

Assessing Population Level Genetic Instability via Moving Average

Tumoral tissues tend to generally exhibit aberrations in DNA copy number that are associated with the development and progression of cancer. Genotyping methods such as array-based comparative genomic hybridization (aCGH) provide means to identify copy number variation across the entire genome. To address some of the shortfalls of existing methods of DNA copy number data analysis, including strong model assumptions, lack of accounting for sampling variability of estimators, and the assumption that clones are independent, we propose a simple graphical approach to assess population-level genetic alterations over the entire genome based on moving average. Furthermore, existing methods primarily focus on segmentation and do not examine the association of covariates with genetic instability. In our methods, covariates are incorporated through a possibly mis-specified working model and sampling variabilities of estimators are approximated using a resampling method that is based on perturbing observed processes. Our proposal, which is applicable to partial, entire or multiple chromosomes, is illustrated through application to aCGH studies of two brain tumor types, meningioma and glioma.