Marginal regression approach for additive hazards models with clustered current status data

Current status data arise naturally from tumorigenicity experiments, epidemiology studies, biomedicine, econometrics and demographic and sociology studies. Moreover, clustered current status data may occur with animals from the same litter in tumorigenicity experiments or with subjects from the same family in epidemiology studies. Because the only information extracted from current status data is whether the survival times are before or after the monitoring or censoring times, the nonparametric maximum likelihood estimator of survival function converges at a rate of n ^1∕3 to a complicated limiting distribution. Hence, semiparametric regression models such as the additive hazards model have been extended for independent current status data to derive the test statistics, whose distributions converge at a rate of n ^1∕2 , for testing the regression parameters. However, a straightforward application of these statistical methods to clustered current status data is not appropriate because intracluster correlation needs to be taken into account. Therefore, this paper proposes two estimating functions for estimating the parameters in the additive hazards model for clustered current status data. The comparative results from simulation studies are presented, and the application of the proposed estimating functions to one real data set is illustrated. Copyright © 2013 John Wiley & Sons, Ltd.     

Structure detection of semiparametric structural equation models with Bayesian adaptive group lasso

Structural equation models (SEMs) are widely recognized as the most important statistical tool for assessing the interrelationships among latent variables. This study develops a Bayesian adaptive group least absolute shrinkage and selection operator procedure to perform simultaneous model selection and estimation for semiparametric SEMs, wherein the structural equation is formulated using the additive nonparametric functions of observed and latent variables. We propose the use of basis expansions to approximate the unknown functions. By introducing adaptive penalties to the groups of basis expansions, the nonlinear, linear, or non‐existent effects of observed and latent variables in the structural equation can be automatically detected. A simulation study demonstrates that the proposed method performs satisfactorily. This paper presents an application of revealing the observed and latent risk factors of diabetic kidney disease. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical analysis of current status data with informative observation times

Current status data arise when each study subject is observed only once and the survival time of interest is known only to be either less or greater than the observation time. Such data often occur in, for example, cross-sectional studies, demographical investigations and tumorigenicity experiments and several semi-parametric and non-parametric methods for their analysis have been proposed. However, most of these methods deal only with the situation where observation time is independent of the underlying survival time completely or given covariates. This paper discusses regression analysis of current status data when the observation time may be related to the underlying survival time and inference procedures are presented for estimation of regression parameters under the additive hazards regression model. The procedures can be easily implemented and are applied to two motivating examples.     

Multikernel linear mixed model with adaptive lasso for complex phenotype prediction

Linear mixed models (LMMs) and their extensions have been widely used for high-dimensional genomic data analyses. While LMMs hold great promise for risk prediction research, the high dimensionality of the data and different effect sizes of genomic regions bring great analytical and computational challenges. In this work, we present a multikernel linear mixed model with adaptive lasso (KLMM-AL) to predict phenotypes using high-dimensional genomic data. We develop two algorithms for estimating parameters from our model and also establish the asymptotic properties of LMM with adaptive lasso when only one dependent observation is available. The proposed KLMM-AL can account for heterogeneous effect sizes from different genomic regions, capture both additive and nonadditive genetic effects, and adaptively and efficiently select predictive genomic regions and their corresponding effects. Through simulation studies, we demonstrate that KLMM-AL outperforms most of existing methods. Moreover, KLMM-AL achieves high sensitivity and specificity of selecting predictive genomic regions. KLMM-AL is further illustrated by an application to the sequencing dataset obtained from the Alzheimer's disease neuroimaging initiative.     

A test for comparing current status survival data with crossing hazard functions and its application to immunogenicity of biotherapeutics

Several tests have been recently implemented in the nonparametric comparison of current status survival data. However, they are not suited for the situation of crossing hazards. In this setting, we propose a new test specifically designed for crossing hazards alternatives. The proposed test is compared to classical implemented tests through simulations mimicking crossing hazards situations with various schemes of censoring. The results show that the proposed test has a correct type I error and generally outperforms the existing methods. The application of the proposed test on a real dataset on immunogenicity of interferon‐β among multiple sclerosis patients highlights the interest of the proposed test.     

A frequentist design for basket trials using adaptive lasso

A basket trial aims to expedite the drug development process by evaluating a new therapy in multiple populations within the same clinical trial. Each population, referred to as a “basket”, can be defined by disease type, biomarkers, or other patient characteristics. The objective of a basket trial is to identify the subset of baskets for which the new therapy shows promise. The conventional approach would be to analyze each of the baskets independently. Alternatively, several Bayesian dynamic borrowing methods have been proposed that share data across baskets when responses appear similar. These methods can achieve higher power than independent testing in exchange for a risk of some inflation in the type 1 error rate. In this paper we propose a frequentist approach to dynamic borrowing for basket trials using adaptive lasso. Through simulation studies we demonstrate adaptive lasso can achieve similar power and type 1 error to the existing Bayesian methods. The proposed approach has the benefit of being easier to implement and faster than existing methods. In addition, the adaptive lasso approach is very flexible: it can be extended to basket trials with any number of treatment arms and any type of endpoint.     

Checking hazard regression models using pseudo-observations

Graphical methods for model diagnostics are an essential part of the model fitting procedure. However, in survival analysis, the plotting is always hampered by the presence of censoring. Although model specific solutions do exist and are commonly used, we present a more general approach that covers all the models using the same framework. The pseudo-observations enable us to calculate residuals for each individual at each time point regardless of censoring and provide methods for simultaneously checking all the assumptions of both the Cox and the additive model. We introduce methods for single as well as multiple covariate cases and complement them with corresponding goodness-of-fit tests. The methods are illustrated on simulated as well as real data examples.     

Analysis of a nonsusceptible fraction with current status data

In studies involving subclinical events, times of events are often subject to interval censoring since their occurrence is only detected at inspection times. When individuals are event-free at an initial time and a single follow-up inspection is made, current status data are obtained. In many settings, however, the population comprised a susceptible and a nonsusceptible subpopulation, where only susceptible individuals will go on to experience the event. Then interest often lies primarily in identifying prognostic variables for susceptibility, and secondarily in the event time distribution among the susceptible individuals. We give a simple mixture model that facilitates estimation of the proportion of susceptible individuals, covariate effects on the odds of susceptibility, and the event time distribution under a current status observation scheme. Asymptotic relative efficiency of maximum likelihood estimators is considered based on the Fisher information for a variety of settings. EM algorithms are proposed for parametric, weakly parametric, and nonparametric estimation of the event time distribution. The methods are applied to motivating studies examining an immunological response to low molecular weight heparin in patients undergoing orthopedic surgery.     

Sampling‐based estimation for massive survival data with additive hazards model

For massive survival data, we propose a subsampling algorithm to efficiently approximate the estimates of regression parameters in the additive hazards model. We establish consistency and asymptotic normality of the subsample‐based estimator given the full data. The optimal subsampling probabilities are obtained via minimizing asymptotic variance of the resulting estimator. The subsample‐based procedure can largely reduce the computational cost compared with the full data method. In numerical simulations, our method has low bias and satisfactory coverage probabilities. We provide an illustrative example on the survival analysis of patients with lymphoma cancer from the Surveillance, Epidemiology, and End Results Program.     

Regression analysis of multivariate current status data with dependent censoring: application to ankylosing spondylitis data

Multivariate current‐status failure time data consist of several possibly related event times of interest, in which the status of each event is determined at a single examination time. If the examination time is intrinsically related to the event times, the examination is referred to as dependent censoring and needs to be taken into account. Such data often occur in clinical studies and animal carcinogenicity experiments. To accommodate for possible dependent censoring, this paper proposes a joint frailty model for event times and dependent censoring time. We develop a likelihood approach using Gaussian quadrature techniques for obtaining maximum likelihood estimates. We conduct extensive simulation studies for investigating finite‐sample properties of the proposed method. We illustrate the proposed method with an analysis of patients with ankylosing spondylitis, where the examination time may be dependent on the event times of interest. Copyright © 2013 John Wiley & Sons, Ltd.     

Smooth estimation of survival functions and hazard ratios from interval-censored data using Bayesian penalized B-splines

We discuss the use of Bayesian P-spline and of the composite link model to estimate survival functions and hazard ratios from interval-censored data. If one further assumes proportionality of the hazards, the proposed strategy provides a smoothed estimate of the baseline hazard along with estimates of global covariate effects. The frequentist properties of our Bayesian estimators are assessed by an extensive simulation study. We further illustrate the methodology by two examples showing that the proportionality of the hazards might also be found inappropriate from interval-censored data.     

Practicable confidence intervals for current status data

Although confidence intervals (CIs) for binary isotonic regression and current status survival data have been well studied theoretically, their practical application has been limited, in part because of poor performance in small samples and in part because of computational difficulties. Ghosh, Banerjee, and Biswas (2008, Biometrics 64 , 1009‐1017) described three approaches to constructing CIs: (i) the Wald‐based method; (ii) the subsampling‐based method; and (iii) the likelihood‐ratio test (LRT)‐based method. In simulation studies, they found that the subsampling‐based method and LRT‐based method tend to have better coverage probabilities than a simple Wald‐based method that may perform poorly in realistic sample sizes. However, software implementing these approaches is currently unavailable. In this article, we show that by using transformations, simple Wald‐based CIs can be improved with small and moderate sample sizes to have competitive performance with LRT‐based method. Our simulations further show that a simple nonparametric bootstrap gives approximately correct CIs for the data generating mechanisms that we consider. We provide an R package that can be used to compute the Wald‐type and the bootstrap CIs and demonstrate its practical utility with two real data analyses. Copyright © 2012 John Wiley & Sons, Ltd.     

Bayesian methods of analysis for cluster randomized trials with count outcome data

Bayesian approaches to inference in cluster randomized trials have been investigated for normally distributed and binary outcome measures. However, relatively little attention has been paid to outcome measures which are counts of events. We discuss an extension of previously published Bayesian hierarchical models to count data, which usually can be assumed to be distributed according to a Poisson distribution. We develop two models, one based on the traditional rate ratio, and one based on the rate difference which may often be more intuitively interpreted for clinical trials, and is needed for economic evaluation of interventions. We examine the relationship between the intracluster correlation coefficient (ICC) and the between‐cluster variance for each of these two models. In practice, this allows one to use the previously published evidence on ICCs to derive an informative prior distribution which can then be used to increase the precision of the posterior distribution of the ICC. We demonstrate our models using a previously published trial assessing the effectiveness of an educational intervention and a prior distribution previously derived. We assess the robustness of the posterior distribution for effectiveness to departures from a normal distribution of the random effects. Copyright © 2009 John Wiley & Sons, Ltd.     

Hierarchical Bayesian spatiotemporal analysis of revascularization odds using smoothing splines

Hierarchical Bayesian models are proposed for over-dispersed longitudinal spatially correlated binomial data. This class of models accounts for correlation among regions by using random effects and allows a flexible modelling of spatiotemporal odds by using smoothing splines. The aim is (i) to develop models which will identify temporal trends of odds and produce smoothed maps including regional effects, (ii) to specify Markov chain Monte Carlo (MCMC) inference for fitting such models, (iii) to study the sensitivity of such Bayesian binomial spline spatiotemporal analyses to prior assumptions, and (iv) to compare mechanisms for assessing goodness of fit. An analysis of regional variation for revascularization odds of patients hospitalized for acute coronary syndrome in Quebec motivates and illustrates the methods developed.     

Modelling,Bayesian inference,and model assessment for nosocomial pathogens using whole-genome-sequence data

Whole-genome sequencing of pathogens in outbreaks of infectious disease provides the potential to reconstruct transmission pathways and enhance the information contained in conventional epidemiological data. In recent years, there have been numerous new methods and models developed to exploit such high-resolution genetic data. However, corresponding methods for model assessment have been largely overlooked. In this article, we develop both new modelling methods and new model assessment methods, specifically by building on the work of Worby et al. Although the methods are generic in nature, we focus specifically on nosocomial pathogens and analyze a dataset collected during an outbreak of MRSA in a hospital setting.     

Bayesian adaptive group lasso with semiparametric hidden Markov models

This paper presents a Bayesian adaptive group least absolute shrinkage and selection operator method to conduct simultaneous model selection and estimation under semiparametric hidden Markov models. We specify the conditional regression model and the transition probability model in the hidden Markov model into additive nonparametric functions of covariates. A basis expansion is adopted to approximate the nonparametric functions. We introduce multivariate conditional Laplace priors to impose adaptive penalties on regression coefficients and different groups of basis expansions under the Bayesian framework. An efficient Markov chain Monte Carlo algorithm is then proposed to identify the nonexistent, constant, linear, and nonlinear forms of covariate effects in both conditional and transition models. The empirical performance of the proposed methodology is evaluated via simulation studies. We apply the proposed model to analyze a real data set that was collected from the Alzheimer's Disease Neuroimaging Initiative study. The analysis identifies important risk factors on cognitive decline and the transition from cognitive normal to Alzheimer's disease.     

Penalized estimation for proportional hazards models with current status data

We provide a simple and practical, yet flexible, penalized estimation method for a Cox proportional hazards model with current status data. We approximate the baseline cumulative hazard function by monotone B‐splines and use a hybrid approach based on the Fisher‐scoring algorithm and the isotonic regression to compute the penalized estimates. We show that the penalized estimator of the nonparametric component achieves the optimal rate of convergence under some smooth conditions and that the estimators of the regression parameters are asymptotically normal and efficient. Moreover, a simple variance estimation method is considered for inference on the regression parameters. We perform 2 extensive Monte Carlo studies to evaluate the finite‐sample performance of the penalized approach and compare it with the 3 competing R packages: C1.coxph, intcox, and ICsurv. A goodness‐of‐fit test and model diagnostics are also discussed. The methodology is illustrated with 2 real applications.     

ComPAS: A Bayesian drug combination platform trial design with adaptive shrinkage

Combining different treatment regimens provides an effective approach to induce a synergistic treatment effect and overcome resistance to monotherapy. The challenge is that, given the large number of existing monotherapies, the number of possible combinations is huge and new potentially more efficacious compounds may become available any time during drug development. To address this challenge, we propose a flexible Bayesian drug combination platform design with adaptive shrinkage (ComPAS), which allows for dropping futile combinations, graduating effective combinations, and adding new combinations during the course of the trial. A new adaptive shrinkage method is developed to adaptively borrow information across combinations and efficiently identify the efficacious combinations based on Bayesian model selection and hierarchical models. Simulation studies show that ComPAS identifies the effective combinations with higher probability than some existing designs. ComPAS provides an efficient and flexible platform to accelerate drug development in a seamless and timely fashion.     

贝叶斯累加回归树模型在高血压药物个性化疗效评价中的应用

目的  以高血压合并糖尿病人群为例,应用贝叶斯累加回归树(Bayesian additive regression tree, BART)模型评价卡托普利及其联合尼群地平用药对血压控制的个性化疗效,并识别高收益患者亚组特征。 方法  纳入2011年1月至2015年7月山东省胶南市“全人群高血压、糖尿病综合防治项目”中的高血压合并糖尿病患者,按不同用药方式分为三组,采用倾向性得分随机化匹配形成可比样本后,建立BART模型探索用药的个性化疗效。 结果  在单用卡托普利与不用药、联合用药与不用药,联合用药与单用卡托普利三组对比中,三组模型曲线下面积(area under curre, AUC)及其95% CI分别为0.710(0.686~0.734)、0.796(0.754~0.838)、0.768(0.725~0.812)。对于大多数患者,联合用药效果优于单用卡托普利和不用药,其中,相比不用药者,SBP较低且有良好运动习惯是单用卡托普利和联合用药疗效更佳者的共同特征。 结论  构建的BART模型用于预测高血压合并糖尿病患者的高血压药物个性化疗效效果良好,并且能够用于总结高收益亚组特征,为精准医疗在高血压治疗中的实践提供依据。     

Two-part hidden Markov models for semicontinuous longitudinal data with nonignorable missing covariates

This study develops a two-part hidden Markov model (HMM) for analyzing semicontinuous longitudinal data in the presence of missing covariates. The proposed model manages a semicontinuous variable by splitting it into two random variables: a binary indicator for determining the occurrence of excess zeros at all occasions and a continuous random variable for examining its actual level. For the continuous longitudinal response, an HMM is proposed to describe the relationship between the observation and unobservable finite-state transition processes. The HMM consists of two major components. The first component is a transition model for investigating how potential covariates influence the probabilities of transitioning from one hidden state to another. The second component is a conditional regression model for examining the state-specific effects of covariates on the response. A shared random effect is introduced to each part of the model to accommodate possible unobservable heterogeneity among observation processes and the nonignorability of missing covariates. A Bayesian adaptive least absolute shrinkage and selection operator (lasso) procedure is developed to conduct simultaneous variable selection and estimation. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative dataset. New insights into the pathology of Alzheimer's disease and its potential risk factors are obtained.