Deep partially linear cox model for current status data.

Deep learning has continuously attained huge success in diverse fields, while its application to survival data analysis remains limited and deserves further exploration. For the analysis of current status data, a deep partially linear Cox model is proposed to circumvent the curse of dimensionality. Modeling flexibility is attained by using deep neural networks (DNNs) to accommodate nonlinear covariate effects and monotone splines to approximate the baseline cumulative hazard function. We establish the convergence rate of the proposed maximum likelihood estimators. Moreover, we derive that the finite-dimensional estimator for treatment covariate effects is $\sqrt{n}$-consistent, asymptotically normal, and attains semiparametric efficiency. Finally, we demonstrate the performance of our procedures through extensive simulation studies and application to real-world data on news popularity.

Conditional modeling of panel count data with partly interval-censored failure event.

In longitudinal follow-up studies, panel count data arise from discrete observations on recurrent events. We investigate a more general situation where a partly interval-censored failure event is informative to recurrent events. The existing methods for the informative failure event are based on the latent variable model, which provides indirect interpretation for the effect of failure event. To solve this problem, we propose a failure-time-dependent proportional mean model with panel count data through an unspecified link function. For estimation of model parameters, we consider a conditional expectation of least squares function to overcome the challenges from partly interval-censoring, and develop a two-stage estimation procedure by treating the distribution function of the failure time as a functional nuisance parameter and using the B-spline functions to approximate unknown baseline mean and link functions. Furthermore, we derive the overall convergence rate of the proposed estimators and establish the asymptotic normality of finite-dimensional estimator and functionals of infinite-dimensional estimator. The proposed estimation procedure is evaluated by extensive simulation studies, in which the finite-sample performances coincide with the theoretical results. We further illustrate our method with a longitudinal healthy longevity study and draw some insightful conclusions.

Semiparametric estimation and testing for panel count data with informative interval-censored failure event.

Panel count data and interval-censored data are two types of incomplete data that often occur in event history studies. Almost all existing statistical methods are developed for their separate analysis. In this paper, we investigate a more general situation where a recurrent event process and an interval-censored failure event occur together. To intuitively and clearly explain the relationship between the recurrent current process and failure event, we propose a failure time-dependent mean model through a completely unspecified link function. To overcome the challenges arising from the blending of nonparametric components and parametric regression coefficients, we develop a two-stage conditional expected likelihood-based estimation procedure. We establish the consistency, the convergence rate and the asymptotic normality of the proposed two-stage estimator. Furthermore, we construct a class of two-sample tests for comparison of mean functions from different groups. The proposed methods are evaluated by extensive simulation studies and are illustrated with the skin cancer data that motivated this study.

Subgroup analysis in the heterogeneous Cox model.

In the analysis of censored survival data, to avoid a biased inference of treatment effects on the hazard function of the survival time, it is important to consider the treatment heterogeneity. Without requiring any prior knowledge about the subgroup structure, we propose a data driven subgroup analysis procedure for the heterogeneous Cox model by constructing a pairwise fusion penalized partial likelihood-based objective function. The proposed method can determine the number of subgroups, identify the group structure, and estimate the treatment effect simultaneously and automatically. A majorized alternating direction method of multipliers algorithm is then developed to deal with the numerically challenging high-dimensional problems. We also establish the oracle properties and the model selection consistency for the proposed penalized estimator. Our proposed method is evaluated by simulation studies and further illustrated by the analysis of the breast cancer data.

Semiparametric efficient estimation for additive hazards regression with case II interval-censored survival data.

Interval-censored data often arise naturally in medical, biological, and demographical studies. As a matter of routine, the Cox proportional hazards regression is employed to fit such censored data. The related work in the framework of additive hazards regression, which is always considered as a promising alternative, remains to be investigated. We propose a sieve maximum likelihood method for estimating regression parameters in the additive hazards regression with case II interval-censored data, which consists of right-, left- and interval-censored observations. We establish the consistency and the asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The finite-sample performance of the proposed method is assessed via comprehensive simulation studies, which is further illustrated by a real clinical example for patients with hemophilia.

Robust estimation for panel count data with informative observation times and censoring times.

We consider the semiparametric regression of panel count data occurring in longitudinal follow-up studies that concern occurrence rate of certain recurrent events. The analysis of panel count data involves two processes, i.e, a recurrent event process of interest and an observation process controlling observation times. However, the model assumptions of existing methods, such as independent censoring time and Poisson assumption, are restrictive and questionable. In this paper, we propose new joint models for panel count data by considering both informative observation times and censoring times. The asymptotic normality of the proposed estimators are established. Numerical results from simulation studies and a real data example show the advantage of the proposed method.

Bayesian variable selection and estimation in semiparametric joint models of multivariate longitudinal and survival data.

This paper presents a novel semiparametric joint model for multivariate longitudinal and survival data (SJMLS) by relaxing the normality assumption of the longitudinal outcomes, leaving the baseline hazard functions unspecified and allowing the history of the longitudinal response having an effect on the risk of dropout. Using Bayesian penalized splines to approximate the unspecified baseline hazard function and combining the Gibbs sampler and the Metropolis-Hastings algorithm, we propose a Bayesian Lasso (BLasso) method to simultaneously estimate unknown parameters and select important covariates in SJMLS. Simulation studies are conducted to investigate the finite sample performance of the proposed techniques. An example from the International Breast Cancer Study Group (IBCSG) is used to illustrate the proposed methodologies.

Semiparametric partially linear varying coefficient models with panel count data.

This paper studies semiparametric regression analysis of panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. To explore the nonlinear interactions between covariates, we propose a class of partially linear models with possibly varying coefficients for the mean function of the counting processes with panel count data. The functional coefficients are estimated by B-spline function approximations. The estimation procedures are based on maximum pseudo-likelihood and likelihood approaches and they are easy to implement. The asymptotic properties of the resulting estimators are established, and their finite-sample performance is assessed by Monte Carlo simulation studies. We also demonstrate the value of the proposed method by the analysis of a cancer data set, where the new modeling approach provides more comprehensive information than the usual proportional mean model.

Sieve estimation of Cox models with latent structures.

This article considers sieve estimation in the Cox model with an unknown regression structure based on right-censored data. We propose a semiparametric pursuit method to simultaneously identify and estimate linear and nonparametric covariate effects based on B-spline expansions through a penalized group selection method with concave penalties. We show that the estimators of the linear effects and the nonparametric component are consistent. Furthermore, we establish the asymptotic normality of the estimator of the linear effects. To compute the proposed estimators, we develop a modified blockwise majorization descent algorithm that is efficient and easy to implement. Simulation studies demonstrate that the proposed method performs well in finite sample situations. We also use the primary biliary cirrhosis data to illustrate its application.

Monotone spline-based least squares estimation for panel count data with informative observation times.

This article discusses the statistical analysis of panel count data when the underlying recurrent event process and observation process may be correlated. For the recurrent event process, we propose a new class of semiparametric mean models that allows for the interaction between the observation history and covariates. For inference on the model parameters, a monotone spline-based least squares estimation approach is developed, and the resulting estimators are consistent and asymptotically normal. In particular, our new approach does not rely on the model specification of the observation process. The proposed inference procedure performs well through simulation studies, and it is illustrated by the analysis of bladder tumor data.

Sieve estimation in semiparametric modeling of longitudinal data with informative observation times.

Analyzing irregularly spaced longitudinal data often involves modeling possibly correlated response and observation processes. In this article, we propose a new class of semiparametric mean models that allows for the interaction between the observation history and covariates, leaving patterns of the observation process to be arbitrary. For inference on the regression parameters and the baseline mean function, a spline-based least squares estimation approach is proposed. The consistency, rate of convergence, and asymptotic normality of the proposed estimators are established. Our new approach is different from the usual approaches relying on the model specification of the observation scheme, and it can be easily used for predicting the longitudinal response. Simulation studies demonstrate that the proposed inference procedure performs well and is more robust. The analyses of bladder tumor data and medical cost data are presented to illustrate the proposed method.

A new class of generalized log rank tests for interval-censored failure time data.

This paper discusses nonparametric comparison of survival functions when one observes only interval-censored failure time data (Peto and Peto, 1972; Sun, 2006; Zhao et al., 2008). For the problem, a few procedures have been proposed in the literature. However, most of the existing test procedures determine the test results or p-values based on ad hoc methods or the permutation approach. Furthermore for the test procedures whose asymptotic distributions have been derived, the results are only for the null hypothesis. In other words, no nonparametric test procedure exists that has a known asymptotic distribution under the alternative hypothesis and thus can be employed to carry out the power and test size calculation. In this paper, a new class of generalized log-rank tests is proposed and their asymptotic distributions are derived under both null and alternative hypotheses. A simulation study is conducted to assess their performance for finite sample situations and an illustrative example is provided.

Analysis of multivariate recurrent event data with time-dependent covariates and informative censoring.

Multivariate recurrent event data are usually encountered in many clinical and longitudinal studies in which each study subject may experience multiple recurrent events. For the analysis of such data, most existing approaches have been proposed under the assumption that the censoring times are noninformative, which may not be true especially when the observation of recurrent events is terminated by a failure event. In this article, we consider regression analysis of multivariate recurrent event data with both time-dependent and time-independent covariates where the censoring times and the recurrent event process are allowed to be correlated via a frailty. The proposed joint model is flexible where both the distributions of censoring and frailty variables are left unspecified. We propose a pairwise pseudolikelihood approach and an estimating equation-based approach for estimating coefficients of time-dependent and time-independent covariates, respectively. The large sample properties of the proposed estimates are established, while the finite-sample properties are demonstrated by simulation studies. The proposed methods are applied to the analysis of a set of bivariate recurrent event data from a study of platelet transfusion reactions.

Replication of genetic variation in the MYO9B gene in Crohn's disease.

Various genes that may influence the intestinal barrier have been identified, including MAGI2, PARD3, and MYO9B. These genes are associated with inflammatory bowel disease (IBD) in several European studies. A total of 2,049 individuals (656 Crohn's disease [CD], 544 ulcerative colitis [UC], and 849 controls) were genotyped and association studies were performed for 1 single nucleotide polymorphism (SNP) in MAGI2, 1 SNP in PARD3, and 6 SNPs in MYO9B. We reported an association between 3 SNPs in MYO9B and ileal involvement with rs1457092 as the most significant SNP (p = 0.0073, odds ratio [OR] 0.69 [95% confidence interval (95% CI) 0.52-0.90]). The nonsynonymous SNP rs1545620 exhibited a p value of 0.014, OR 0.72 (95% CI 0.55-0.93). MYO9B was not associated with UC. MAGI2 or PARD3 was not associated with IBD. A 6-SNP haplotype block in MYO9B demonstrated association with CD and ileal CD (p = 0.0030 and 0.0065, respectively). These data demonstrate an association of MYO9B with ileal CD; however, there was no association of MAGI2 and PARD3 with IBD. Because the direction of association of MYO9B in this Canadian study was not consistent with European studies, further studies are needed to elucidate the role of MYO9B in IBD.

Nonparametric comparison for panel count data with unequal observation processes.

This article considers nonparametric comparison of several treatment groups based on panel count data, which often occur in, among others, medical follow-up studies and reliability experiments concerning recurrent events. For the problem, most of the existing procedures require that observation processes are identical across different treatment groups among other requirements. We propose a new class of nonparametric test procedures that allow different observation processes. The new test statistics are constructed based on the integrated weighted differences between the estimated mean functions of the underlying recurrent event processes. The asymptotic distributions of the proposed test statistics are established and their finite-sample properties are examined through Monte Carlo simulations, which indicate that the proposed approach works well for practical situations. An illustrative example is provided.

Semiparametric transformation models with time-varying coefficients for recurrent and terminal events.

In this article, we propose a family of semiparametric transformation models with time-varying coefficients for recurrent event data in the presence of a terminal event such as death. The new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time. For the inference on the proposed models, a class of estimating equations is developed and asymptotic properties of the resulting estimators are established. In addition, a lack-of-fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is also illustrated.

Goodness-of-fit tests for additive mean residual life model under right censoring.

The mean residual life (MRL) measures the remaining life expectancy and is useful in actuarial studies, biological experiments and clinical trials. To assess the covariate effect, an additive MRL regression model has been proposed in the literature. In this paper, we focus on the topic of model checking. Specifically, we develop two goodness-of-fit tests to test the additive MRL model assumption. We explore the large sample properties of the test statistics and show that both of them are based on asymptotic Gaussian processes so that resampling approaches can be applied to find the rejection regions. Simulation studies indicate that our methods work reasonably well for sample sizes ranging from 50 to 200. Two empirical data sets are analyzed to illustrate the approaches.

Generalized log-rank tests for partly interval-censored failure time data.

In this paper, we consider incomplete survival data: partly interval-censored failure time data where observed data include both exact and interval-censored observations on the survival time of interest. We present a class of generalized log-rank tests for this type of survival data and establish their asymptotic properties. The method is evaluated using simulation studies and illustrated by a set of real data from a diabetes study.