Cox regression model with time-varying coefficients in nested case-control studies

Multistate modeling and structure selection for multitype recurrent events and terminal event data

In cardiovascular disease studies, a large number of risk factors are measured but it often remains unknown whether all of them are relevant variables and whether the impact of these variables is changing with time or remains constant. In addition, more than one kind of cardiovascular disease events can be observed in the same patient and events of different types are possibly correlated. It is expected that different kinds of events are associated with different covariates and the forms of covariate effects also vary between event types. To tackle these problems, we proposed a multistate modeling framework for the joint analysis of multitype recurrent events and terminal event. Model structure selection is performed to identify covariates with time-varying coefficients, time-independent coefficients, and null effects. This helps in understanding the disease process as it can detect relevant covariates and identify the temporal dynamics of the covariate effects. It also provides a more parsimonious model to achieve better risk prediction. The performance of the proposed model and selection method is evaluated in numerical studies and illustrated on a real dataset from the Atherosclerosis Risk in Communities study.

Generalized mean residual life models for case-cohort and nested case-control studies

Mean residual life (MRL) is the remaining life expectancy of a subject who has survived to a certain time point and can be used as an alternative to hazard function for characterizing the distribution of a time-to-event variable. Inference and application of MRL models have primarily focused on full-cohort studies. In practice, case-cohort and nested case-control designs have been commonly used within large cohorts that have long follow-up and study rare diseases, particularly when studying costly molecular biomarkers. They enable prospective inference as the full-cohort design with significant cost-saving benefits. In this paper, we study the modeling and inference of a family of generalized MRL models under case-cohort and nested case-control designs. Built upon the idea of inverse selection probability, the weighted estimating equations are constructed to estimate regression parameters and baseline MRL function. Asymptotic properties of the proposed estimators are established and finite-sample performance is evaluated by extensive numerical simulations. An application to the New York University Women's Health Study is presented to illustrate the proposed models and demonstrate a model diagnostic method to guide practical implementation.

Penalized full likelihood approach to variable selection for Cox's regression model under nested case-control sampling

Assuming Cox's regression model, we consider penalized full likelihood approach to conduct variable selection under nested case-control (NCC) sampling. Penalized non-parametric maximum likelihood estimates (PNPMLEs) are characterized by self-consistency equations derived from score functions. A cross-validation method based on profile likelihood is used to choose the tuning parameter within a family of penalty functions. Simulation studies indicate that the numerical performance of (P)NPMLE is better than weighted partial likelihood in estimating the log-relative risk and in identifying the covariates and the model, under NCC sampling. LASSO performs best when cohort size is small; SCAD performs best when cohort size is large and may eventually perform as well as the oracle estimator. Using the SCAD penalty, we establish the consistency, asymptotic normality, and oracle properties of the PNPMLE, as well as the sparsity property of the penalty. We also propose a consistent estimate of the asymptotic variance using observed profile likelihood. Our method is illustrated to analyze the diagnosis of liver cancer among those in a type 2 diabetic mellitus dataset who were treated with thiazolidinediones in Taiwan.

Tumor Size Has a Time-Varying Effect on Recurrence in Cervical Cancer

OBJECTIVE

This study analyzed the risk factors for their possible association with overall survival and progression-free survival in cervical cancer, with a flexible model that allowed time-varying effects.

METHODS

Information about patients with cervical cancer from 2002 to 2012 was collected in the Kaohsiung Veterans General Hospital. All available biological and clinicopathologic factors were tested for the assumption of the Cox proportional hazard model, that is, whether they had time-varying effect on survival. The factors were also analyzed in univariate and multivariate statistics to identify independent risk factors. The multivariate analysis was performed with an extended Cox model so that those factors that failed the assumption test were allowed to vary with time.

RESULTS

Approximately 797 patients were included in the final analysis. Most factors tested passed the Cox assumption test, except tumor size and body mass index in the event of recurrence and preoperative CA125 values in the event of death (P < 0.05). Univariate and multivariate analysis identified tumor size, stage, and lymph nodal metastasis as independent significant risk factors for both recurrence and death (P < 0.05), with tumor size being a time-varying factor for recurrence.

CONCLUSIONS

Patients with larger tumor size, higher FIGO stage, and lymph nodal metastasis are faced with higher risk of recurrence and death. A larger tumor size poses increasingly higher risk for recurrence initially, and its importance declines as the patient survives longer without disease progression. These findings may be helpful to gynecologists when assessing tumor risk of patients with cervical cancer and in patient consultation.

JOINT STRUCTURE SELECTION AND ESTIMATION IN THE TIME-VARYING COEFFICIENT COX MODEL

Time-varying coefficient Cox model has been widely studied and popularly used in survival data analysis due to its flexibility for modeling covariate effects. It is of great practical interest to accurately identify the structure of covariate effects in a time-varying coefficient Cox model, i.e. covariates with null effect, constant effect and truly time-varying effect, and estimate the corresponding regression coefficients. Combining the ideas of local polynomial smoothing and group nonnegative garrote, we develop a new penalization approach to achieve such goals. Our method is able to identify the underlying true model structure with probability tending to one and simultaneously estimate the time-varying coefficients consistently. The asymptotic normalities of the resulting estimators are also established. We demonstrate the performance of our method using simulations and an application to the primary biliary cirrhosis data.

Assessing incremental value of biomarkers with multi-phase nested case-control studies

Accurate risk prediction models are needed to identify different risk groups for individualized prevention and treatment strategies. In the Nurses' Health Study, to examine the effects of several biomarkers and genetic markers on the risk of rheumatoid arthritis (RA), a three-phase nested case-control (NCC) design was conducted, in which two sequential NCC subcohorts were formed with one nested within the other, and one set of new markers measured on each of the subcohorts. One objective of the study is to evaluate clinical values of novel biomarkers in improving upon existing risk models because of potential cost associated with assaying biomarkers. In this paper, we develop robust statistical procedures for constructing risk prediction models for RA and estimating the incremental value (IncV) of new markers based on three-phase NCC studies. Our method also takes into account possible time-varying effects of biomarkers in risk modeling, which allows us to more robustly assess the biomarker utility and address the question of whether a marker is better suited for short-term or long-term risk prediction. The proposed procedures are shown to perform well in finite samples via simulation studies.