Multivariate Failure Time Research Articles

Improving marginal hazard ratio estimation using quadratic inference functions.

Clustered and multivariate failure time data are commonly encountered in biomedical studies and a marginal regression approach is often employed to identify the potential risk factors of a failure. We consider a semiparametric marginal Cox proportional hazards model for right-censored survival data with potential correlation. We propose to use a quadratic inference function method based on the generalized method of moments to obtain the optimal hazard ratio estimators. The inverse of the working correlation matrix is represented by the linear combination of basis matrices in the context of the estimating equation. We investigate the asymptotic properties of the regression estimators from the proposed method. The optimality of the hazard ratio estimators is discussed. Our simulation study shows that the estimator from the quadratic inference approach is more efficient than those from existing estimating equation methods whether the working correlation structure is correctly specified or not. Finally, we apply the model and the proposed estimation method to analyze a study of tooth loss and have uncovered new insights that were previously inaccessible using existing methods.

On the targets of inference with multivariate failure time data.

There are several different topics that can be addressed with multivariate failure time regression data. Data analysis methods are needed that are suited to each such topic. Specifically, marginal hazard rate models are well suited to the analysis of exposures or treatments in relation to individual failure time outcomes, when failure time dependencies are themselves of little or no interest. On the other hand semiparametric copula models are well suited to analyses where interest focuses primarily on the magnitude of dependencies between failure times. These models overlap with frailty models, that seem best suited to exploring the details of failure time clustering. Recently proposed multivariate marginal hazard methods, on the other hand, are well suited to the exploration of exposures or treatments in relation to single, pairwise, and higher dimensional hazard rates. Here these methods will be briefly described, and the final method will be illustrated using the Women's Health Initiative hormone therapy trial data.

Improving estimation efficiency for multivariate failure time data with auxiliary covariates

For the analysis of multivariate failure time data when the primary covariates are incomplete but the auxiliary covariates for them are available for the whole cohort subjects, an estimated quadratic inference function method is developed to improve the estimation efficiency under the marginal hazard model with common baseline hazard function. Both the auxiliary information and the intra-cluster correlation between the failure times are incorporated in the estimation procedure. The proposed estimator is shown to be consistent and asymptotically normal. Simulation studies demonstrate that when the intra-cluster correlation is strong or moderate, the proposed method gains noticeable efficiency compared to other existing methods.

Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates

Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates

Joint analysis of multivariate failure time data with latent variables.

We propose a joint modeling approach to investigate the observed and latent risk factors of the multivariate failure times of interest. The proposed model comprises two parts. The first part is a distribution-free confirmatory factor analysis model that characterizes the latent factors by correlated multiple observed variables. The second part is a multivariate additive hazards model that assesses the observed and latent risk factors of the failure times. A hybrid procedure that combines the borrow-strength estimation approach and the asymptotically distribution-free generalized least square method is developed to estimate the model parameters. The asymptotic properties of the proposed estimators are derived. Simulation studies demonstrate that the proposed method performs well for practical settings. An application to a study concerning the risk factors of multiple diabetic complications is provided.

Regression estimation of the marginal models with general relative risk form for multivariate failure time data

We develop the quadratic inference function method to the parameter estimation of the marginal models with general relative risk form and common baseline hazard function for multivariate failure time data. The usual exponential relative risk form is relaxed to an non-negative twice differentiable form. The proposed estimator, under some regularity conditions, is shown to be consistent and asymptotically normal with a covariance matrix that can be consistently estimated. In addition, a test statistic based on the quadratic inference function for the parameter inference has been provided. The simulation results show that the proposed method taking the correlation between the failure times into the estimation procedure gains more efficiency than the method using the independent structure when the correlation cannot be ignored, and can easily deal with the situation when the cluster size is large. The proposed method is illustrated by analysis of a real data from the Diabetic Retinopathy Study.

Comparison of variance estimation methods in semiparametric accelerated failure time models for multivariate failure time data

Comparison of variance estimation methods in semiparametric accelerated failure time models for multivariate failure time data

Multivariate failure time distributions derived from shared frailty and copulas

Multivariate failure time distributions derived from shared frailty and copulas

Multivariate survival analysis in big data: A divide-and-combine approach.

Multivariate failure time data are frequently analyzed using the marginal proportional hazards models and the frailty models. When the sample size is extraordinarily large, using either approach could face computational challenges. In this paper, we focus on the marginal model approach and propose a divide-and-combine method to analyze large-scale multivariate failure time data. Our method is motivated by the Myocardial Infarction Data Acquisition System (MIDAS), a New Jersey statewide database that includes 73,725,160 admissions to nonfederal hospitals and emergency rooms (ERs) from 1995 to 2017. We propose to randomly divide the full data into multiple subsets and propose a weighted method to combine these estimators obtained from individual subsets using three weights. Under mild conditions, we show that the combined estimator is asymptotically equivalent to the estimator obtained from the full data as if the data were analyzed all at once. In addition, to screen out risk factors with weak signals, we propose to perform the regularized estimation on the combined estimator using its combined confidence distribution. Theoretical properties, such as consistency, oracle properties, and asymptotic equivalence between the divide-and-combine approach and the full data approach are studied. Performance of the proposed method is investigated using simulation studies. Our method is applied to the MIDAS data to identify risk factors related to multivariate cardiovascular-related health outcomes.

Semiparametric regression based on quadratic inference function for multivariate failure time data with auxiliary information

This paper deals with statistical inference procedure of multivariate failure time data when the primary covariate can be measured only on a subset of the full cohort but the auxiliary information is available. To improve efficiency of statistical inference, we use quadratic inference function approach to incorporate the intra-cluster correlation and use kernel smoothing technique to further utilize the auxiliary information. The proposed method is shown to be more efficient than those ignoring the intra-cluster correlation and auxiliary information and is easy to implement. In addition, we develop a chi-squared test for hypothesis testing of hazard ratio parameters. We evaluate the finite-sample performance of the proposed procedure via extensive simulation studies. The proposed approach is illustrated by analysis of a real data set from the study of left ventricular dysfunction.

Additive Hazard Regression for the Analysis of Clustered Survival Data from Case-Cohort Studies

The case-cohort design is an effective and economical method in large cohort studies, especially when the disease rate is low. Case-cohort design in most of the existing literature is mainly used to analyze the univariate failure time data. But in practice, multivariate failure time data are commonly encountered in biomedical research. In this paper, we will propose methods based on estimating equation method for case-cohort designs for clustered survival data. By introducing the event failure rate, three different weight functions are constructed. Then, three estimating equations and parameter estimators are presented. Furthermore, consistency and asymptotic normality of the proposed estimators are established. Finally, the simulation results show that the proposed estimation procedure has reasonable finite sample behaviors.

Regression Models and Multivariate Life Tables

Semiparametric, multiplicative-form regression models are specified for marginal single and double failure hazard rates for the regression analysis of multivariate failure time data. Cox-type estimating functions are specified for single and double failure hazard ratio parameter estimation, and corresponding Aalen–Breslow estimators are specified for baseline hazard rates. Generalization to allow classification of failure times into a smaller set of failure types, with failures of the same type having common baseline hazard functions, is also included. Asymptotic distribution theory arises by generalization of the marginal single failure hazard rate estimation results of Lin et al. The Péano series representation for the bivariate survival function in terms of corresponding marginal single and double failure hazard rates leads to novel estimators for pairwise bivariate survival functions and pairwise dependency functions, at specified covariate history. Related asymptotic distribution theory follows from that for the marginal single and double failure hazard rates and the continuity, compact differentiability of the Péano series transformation and bootstrap applicability. Simulation evaluation of the proposed estimation procedures is presented, and an application to multiple clinical outcomes in the Women’s Health Initiative Dietary Modification Trial is provided. Higher dimensional marginal hazard rate regression modeling is briefly mentioned. Supplementary materials for this article are available online.

Bayesian semiparametric failure time models for multivariate censored data with latent variables.

In this paper, we propose a semiparametric failure time model to analyze multivariate censored data with latent variables. The proposed model generalizes the conventional accelerated failure time model to accommodate latent risk factors that could be measured by multiple observed variables through a factor analysis and to incorporate additive nonparametric functions of observed and latent risk factors to examine their functional effects on multivariate failure times of interest. A Bayesian approach, along with Bayesian P-splines and Markov chain Monte Carlo techniques, is developed to estimate the unknown parameters and functions. The empirical performance of the proposed methodology is evaluated by a simulation study. An application to a study on the risk factors of two diabetes complications is presented.

AntiEpileptic drug Monitoring in PREgnancy (EMPiRE): a double-blind randomised trial on effectiveness and acceptability of monitoring strategies.

Pregnant women with epilepsy on antiepileptic drugs (AEDs) may experience a reduction in serum AED levels. This has the potential to worsen seizure control. To determine if, in pregnant women with epilepsy on AEDs, additional therapeutic drug monitoring reduces seizure deterioration compared with clinical features monitoring after a reduction in serum AED levels. A double-blind, randomised trial nested within a cohort study was conducted and a qualitative study of acceptability of the two strategies was undertaken. Stratified block randomisation with a 1 : 1 allocation method was carried out. Fifty obstetric and epilepsy clinics in secondary and tertiary care units in the UK. Pregnant women with epilepsy on one or more of the following AEDs: lamotrigine, carbamazepine, phenytoin or levetiracetam. Women with a ≥ 25% decrease in serum AED level from baseline were randomised to therapeutic drug monitoring or clinical features monitoring strategies. In the therapeutic drug monitoring group, clinicians had access to clinical findings and monthly serum AED levels to guide AED dosage adjustment for seizure control. In the clinical features monitoring group, AED dosage adjustment was based only on clinical features. Primary outcome - seizure deterioration, defined as time to first seizure and to all seizures after randomisation per woman until 6 weeks post partum. Secondary outcomes - pregnancy complications in mother and offspring, maternal quality of life, seizure rates in cohorts with stable serum AED level, AED dose exposure and adverse events related to AEDs. Analysis of time to first and to all seizures after randomisation was performed using a Cox proportional hazards model, and multivariate failure time analysis by the Andersen-Gill model. The effects were reported as hazard ratios (HRs) with 95% confidence intervals (CIs). Secondary outcomes were reported as mean differences (MDs) or odds ratios. A total of 130 women were randomised to the therapeutic drug monitoring group and 133 to the clinical features monitoring group; 294 women did not have a reduction in serum AED level. A total of 127 women in the therapeutic drug monitoring group and 130 women in the clinical features monitoring group (98% of complete data) were included in the primary analysis. There were no significant differences in the time to first seizure (HR 0.82, 95% CI 0.55 to 1.2) or timing of all seizures after randomisation (HR 1.3, 95% CI 0.7 to 2.5) between both trial groups. In comparison with the group with stable serum AED levels, there were no significant increases in seizures in the clinical features monitoring (odds ratio 0.93, 95% CI 0.56 to 1.5) or therapeutic drug monitoring group (odds ratio 0.93, 95% CI 0.56 to 1.5) associated with a reduction in serum AED levels. Maternal and neonatal outcomes were similar in both groups, except for higher cord blood levels of lamotrigine (MD 0.55 mg/l, 95% CI 0.11 to 1 mg/l) or levetiracetam (MD 7.8 mg/l, 95% CI 0.86 to 14.8 mg/l) in the therapeutic drug monitoring group than in the clinical features monitoring group. There were no differences between the groups on daily AED exposure or quality of life. An increase in exposure to lamotrigine, levetiracetam and carbamazepine significantly increased the cord blood levels of the AEDs, but not maternal or fetal complications. Women with epilepsy perceived the need for weighing up their increased vulnerability to seizures during pregnancy against the side effects of AEDs. Fewer women than the original target were recruited. There is no evidence to suggest that regular monitoring of serum AED levels in pregnancy improves seizure control or affects maternal or fetal outcomes. Further evaluation of the risks of seizure deterioration for various threshold levels of reduction in AEDs and the long-term neurodevelopment of infants born to mothers in both randomised groups is needed. An individualised prediction model will help to identify those women who need close monitoring in pregnancy. Current Controlled Trials ISRCTN01253916. This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 22, No. 23. See the NIHR Journals Library website for further project information.

Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data.

SummaryInterval-censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval. We investigate the effects of possibly time-dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects, and we study nonparametric maximum likelihood estimation under general interval-censoring schemes. We show that the proposed estimators for the finite-dimensional parameters are consistent and asymptotically normal, with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we develop an EM algorithm that converges stably for arbitrary datasets. Finally, we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the Atherosclerosis Risk in Communities Study.

Variable selection in partially linear hazard regression for multivariate failure time data

The aim of this paper is to explore variable selection approaches in the partially linear proportional hazards model for multivariate failure time data. A new penalised pseudo-partial likelihood method is proposed to select important covariates. Under certain regularity conditions, we establish the rate of convergence and asymptotic normality of the resulting estimates. We further show that the proposed procedure can correctly select the true submodel, as if it was known in advance. Both simulated and real data examples are presented to illustrate the proposed methodology.

Higher Dimensional Clayton-Oakes Models for Multivariate Failure Time Data.

The Clayton-Oakes bivariate failure time model is extended to dimensions m > 2 in a manner that allows unspecified marginal survivor functions for all dimensions less than m. Special cases that allow unspecified marginal survivor functions of dimension q with q < m, while making some provisions for dependencies of dimension greater than q, are also described.

Partially linear transformation models with varying coefficients for multivariate failure time data

This paper studies the estimation and inference of varying coefficients and parameters in the partially linear transformation models for multivariate failure time data. A profile martingale-based estimating method that includes global and local estimating equations is proposed. Asymptotic properties of the estimators are established. Some numerical simulations are given to show the performance of the estimation method in finite-sample situation. In order to reduce the computational burden, a simple and useful one-step estimator method is used. We further suggest a delete-a-group jackknife method to estimate asymptotic variance of estimators. A real data set from the Busselton Population Health Surveys is analyzed to illustrate the proposed methods.

A penalized algorithm for event-specific rate models for recurrent events.

We introduce a covariate-specific total variation penalty in two semiparametric models for the rate function of recurrent event process. The two models are a stratified Cox model, introduced in Prentice and others (1981. On the regression analysis of multivariate failure time data. Biometrika 68: , 373-379.), and a stratified Aalen's additive model. We show the consistency and asymptotic normality of our penalized estimators. We demonstrate, through a simulation study, that our estimators outperform classical estimators for small-to-moderate sample sizes. Finally, an application to the bladder tumor data of Byar (1980. The veterans administration study of chemoprophylaxis for recurrent stage 1 bladder tumors: comparison of placebo, pyridoxine, and topical thiotepa. In Pavone-Macaluso, M. Smith, P. H. and F. Edsmyn (editors), Bladder Tumors and Others Topics in Urological Oncology, pp. 363-370.) is presented.

Weighted Estimator for the Linear Transformation Models with Multivariate Failure Time Data

In this article, a simple and efficient weighted method is proposed to improve the estimation efficiency for the linear transformation models with multivariate failure time data. Asymptotic properties of the estimators with a closed-form variance-covariance matrix are established. In addition, a goodness-of-fit test is developed to evaluate the adequacy of the model. The performance of proposed method and the comparison on the efficiency between the proposed method and the working independence method (Lu, 2005) are conducted in finite-sample situation by simulation studies. Finally a real data set from the Busselton Population Health Surveys is illustrated to validate the proposed methodology. The related proofs of the theorems are given in the Appendix.