Penalized estimation of semiparametric transformation models with interval-censored data and application to Alzheimer's disease

A new and unified method for regression analysis of interval-censored failure time data under semiparametric transformation models with missing covariates

This paper discusses regression analysis of interval-censored failure time data arising from semiparametric transformation models in the presence of missing covariates. Although some methods have been developed for the problem, they either apply only to limited situations or may have some computational issues. Corresponding to these, we propose a new and unified two-step inference procedure that can be easily implemented using the existing or standard software. The proposed method makes use of a set of working models to extract partial information from incomplete observations and yields a consistent estimator of regression parameters assuming missing at random. An extensive simulation study is conducted and indicates that it performs well in practical situations. Finally, we apply the proposed approach to an Alzheimer's Disease study that motivated this study.

Martingale-residual-based greedy model averaging for high-dimensional current status data

Current status data are a type of failure time data that arise when the failure time of study subject cannot be determined precisely but is known only to occur before or after a random monitoring time. Variable selection methods for the failure time data have been discussed extensively in the literature. However, the statistical inference of the model selected based on the variable selection method ignores the uncertainty caused by model selection. To enhance the prediction accuracy for risk quantities such as survival probability, we propose two optimal model averaging methods under semiparametric additive hazards models. Specifically, based on martingale residuals processes, a delete-one cross-validation (CV) process is defined, and two new CV functional criteria are derived for choosing model weights. Furthermore, we present a greedy algorithm for the implementation of the techniques, and the asymptotic optimality of the proposed model averaging approaches is established, along with the convergence of the greedy averaging algorithms. A series of simulation experiments demonstrate the effectiveness and superiority of the proposed methods. Finally, a real-data example is provided as an illustration.

Group variable selection for the Cox model with interval-censored failure time data

Group variable selection is often required in many areas, and for this many methods have been developed under various situations. Unlike the individual variable selection, the group variable selection can select the variables in groups, and it is more efficient to identify both important and unimportant variables or factors by taking into account the existing group structure. In this paper, we consider the situation where one only observes interval-censored failure time data arising from the Cox model, for which there does not seem to exist an established method. More specifically, a penalized sieve maximum likelihood variable selection and estimation procedure is proposed and the oracle property of the proposed method is established. Also, an extensive simulation study is performed and suggests that the proposed approach works well in practical situations. An application of the method to a set of real data is provided.

Variable selection for mixed panel count data under the proportional mean model

Mixed panel count data have attracted increasing attention in medical research based on event history studies. When such data arise, one either observes the number of event occurrences or only knows whether the event has happened or not over an observation period. In this article, we discuss variable selection in event history studies given such complex data, for which there does not seem to exist an established procedure. For the problem, we propose a penalized likelihood variable selection procedure and for the implementation, an expectation-maximization algorithm is developed with the use of the coordinate descent algorithm in the M-step. Furthermore, the oracle property of the proposed method is established, and a simulation study is performed and indicates that the proposed method works well in practical scenarios. Finally, the method is applied to identify the risk factors associated with medical non-adherence arising from the Sequenced Treatment Alternatives to Relieve Depression Study.

Model detection for semiparametric accelerated failure additive model with right-censored data

Censored data frequently appeared in applications across a variety of different areas like epidemiology or medical research. Traditionally statistical inference on this data mechanism was based on some pre-assigned models that will suffer from the risk of model-misspecification. This article proposes a two-folded shrinkage procedure for simultaneous structure identification and variable selection of the semiparametric accelerated failure additive model with right-censored data, in which the nonparametric functions are addressed by spline approximation. Under some regularity conditions, the consistency of model structure identification is theoretically established in the sense that the proposed method can automatically separate the linear and zero components from the nonlinear ones with probability approaching to one. Detailed issues in computation and turning parameter selection are also discussed. Finally, we illustrate the proposed method by some simulation studies and two real data applications to the primary biliary cirrhosis data and skin cutaneous melanoma data.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

Regularization approaches in clinical biostatistics: A review of methods and their applications

A range of regularization approaches have been proposed in the data sciences to overcome overfitting, to exploit sparsity or to improve prediction. Using a broad definition of regularization, namely controlling model complexity by adding information in order to solve ill-posed problems or to prevent overfitting, we review a range of approaches within this framework including penalization, early stopping, ensembling and model averaging. Aspects of their practical implementation are discussed including available R-packages and examples are provided. To assess the extent to which these approaches are used in medicine, we conducted a review of three general medical journals. It revealed that regularization approaches are rarely applied in practical clinical applications, with the exception of random effects models. Hence, we suggest a more frequent use of regularization approaches in medical research. In situations where also other approaches work well, the only downside of the regularization approaches is increased complexity in the conduct of the analyses which can pose challenges in terms of computational resources and expertise on the side of the data analyst. In our view, both can and should be overcome by investments in appropriate computing facilities and educational resources.

Variable selection for nonparametric additive Cox model with interval-censored data

The standard Cox model is perhaps the most commonly used model for regression analysis of failure time data but it has some limitations such as the assumption on linear covariate effects. To relax this, the nonparametric additive Cox model, which allows for nonlinear covariate effects, is often employed, and this paper will discuss variable selection and structure estimation for this general model. For the problem, we propose a penalized sieve maximum likelihood approach with the use of Bernstein polynomials approximation and group penalization. To implement the proposed method, an efficient group coordinate descent algorithm is developed and can be easily carried out for both low- and high-dimensional scenarios. Furthermore, a simulation study is performed to assess the performance of the presented approach and suggests that it works well in practice. The proposed method is applied to an Alzheimer's disease study for identifying important and relevant genetic factors.

The sparse estimation of the semiparametric linear transformation model with dependent current status data

In this paper, we study the sparse estimation under the semiparametric linear transformation models for the current status data, also called type I interval-censored data. For the problem, the failure time of interest may be dependent on the censoring time and the association parameter between them is left unspecified. To address this, we employ the copula model to describe the dependence between them and a two-stage estimation procedure to estimate both the association parameter and the regression parameter. In addition, we propose a penalized maximum likelihood estimation procedure based on the broken adaptive ridge regression, and Bernstein polynomials are used to approximate the nonparametric functions involved. The oracle property of the proposed method is established and the numerical studies suggest that the method works well for practical situations. Finally, the method is applied to an Alzheimer's disease study that motivated this investigation.

Simultaneous variable selection in regression analysis of multivariate interval-censored data

Multivariate interval-censored data arise when each subject under study can potentially experience multiple events and the onset time of each event is not observed exactly but is known to lie in a certain time interval formed by adjacent examination times with changed statuses of the event. This type of incomplete and complex data structure poses a substantial challenge in practical data analysis. In addition, many potential risk factors exist in numerous studies. Thus, conducting variable selection for event-specific covariates simultaneously becomes useful in identifying important variables and assessing their effects on the events of interest. In this paper, we develop a variable selection technique for multivariate interval-censored data under a general class of semiparametric transformation frailty models. The minimum information criterion (MIC) method is embedded in the optimization step of the proposed expectation-maximization (EM) algorithm to obtain the parameter estimator. The proposed EM algorithm greatly reduces the computational burden in maximizing the observed likelihood function, and the MIC naturally avoids selecting the optimal tuning parameter as needed in many other popular penalties, making the proposed algorithm promising and reliable. The proposed method is evaluated through extensive simulation studies and illustrated by an analysis of patient data from the Aerobics Center Longitudinal Study.

A new approach to estimation of the proportional hazards model based on interval-censored data with missing covariates

This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.

Variable selection for bivariate interval-censored failure time data under linear transformation models

Variable selection is needed and performed in almost every field and a large literature on it has been established, especially under the context of linear models or for complete data. Many authors have also investigated the variable selection problem for incomplete data such as right-censored failure time data. In this paper, we discuss variable selection when one faces bivariate interval-censored failure time data arising from a linear transformation model, for which it does not seem to exist an established procedure. For the problem, a penalized maximum likelihood approach is proposed and in particular, a novel Poisson-based EM algorithm is developed for the implementation. The oracle property of the proposed method is established, and the numerical studies suggest that the method works well for practical situations.

Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease

Studies of Alzheimer's disease (AD) often collect multiple longitudinal clinical outcomes, which are correlated and predictive of AD progression. It is of great scientific interest to investigate the association between the outcomes and time to AD onset. We model the multiple longitudinal outcomes as multivariate sparse functional data and propose a functional joint model linking multivariate functional data to event time data. In particular, we propose a multivariate functional mixed model to identify the shared progression pattern and outcome-specific progression patterns of the outcomes, which enables more interpretable modeling of associations between outcomes and AD onset. The proposed method is applied to the Alzheimer's Disease Neuroimaging Initiative study (ADNI) and the functional joint model sheds new light on inference of five longitudinal outcomes and their associations with AD onset. Simulation studies also confirm the validity of the proposed model. Data used in preparation of this article were obtained from the ADNI database.

Variable Selection for Generalized Linear Models with Interval-Censored Failure Time Data

Variable selection is often needed in many fields and has been discussed by many authors in various situations. This is especially the case under linear models and when one observes complete data. Among others, one common situation where variable selection is required is to identify important risk factors from a large number of covariates. In this paper, we consider the problem when one observes interval-censored failure time data arising from generalized linear models, for which there does not seem to exist an established method. To address this, we propose a penalized least squares method with the use of an unbiased transformation and the oracle property of the method is established along with the asymptotic normality of the resulting estimators of regression parameters. Simulation studies were conducted and demonstrated that the proposed method performed well for practical situations. In addition, the method was applied to a motivating example about children’s mortality data of Nigeria.