A method for analyzing clustered interval-censored data based on Cox's model

A semiparametric joint model for cluster size and subunit-specific interval-censored outcomes

Clustered data frequently arise in biomedical studies, where observations, or subunits, measured within a cluster are associated. The cluster size is said to be informative, if the outcome variable is associated with the number of subunits in a cluster. In most existing work, the informative cluster size issue is handled by marginal approaches based on within-cluster resampling, or cluster-weighted generalized estimating equations. Although these approaches yield consistent estimation of the marginal models, they do not allow estimation of within-cluster associations and are generally inefficient. In this paper, we propose a semiparametric joint model for clustered interval-censored event time data with informative cluster size. We use a random effect to account for the association among event times of the same cluster as well as the association between event times and the cluster size. For estimation, we propose a sieve maximum likelihood approach and devise a computationally-efficient expectation-maximization algorithm for implementation. The estimators are shown to be strongly consistent, with the Euclidean components being asymptotically normal and achieving semiparametric efficiency. Extensive simulation studies are conducted to evaluate the finite-sample performance, efficiency and robustness of the proposed method. We also illustrate our method via application to a motivating periodontal disease dataset.

Marginal proportional hazards models for multivariate interval-censored data

Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We construct the nonparametric pseudolikelihood under the working assumption that all event times are independent, and we provide a simple and stable EM-type algorithm. The resulting nonparametric maximum pseudolikelihood estimators for the regression parameters are shown to be consistent and asymptotically normal, with a limiting covariance matrix that can be consistently estimated by a sandwich estimator under arbitrary dependence structures for the related event times. We evaluate the performance of the proposed methods through extensive simulation studies and present an application to data from the Atherosclerosis Risk in Communities Study.

Marginal proportional hazards models for clustered interval-censored data with time-dependent covariates

The Botswana Combination Prevention Project was a cluster-randomized HIV prevention trial whose follow-up period coincided with Botswana's national adoption of a universal test and treat strategy for HIV management. Of interest is whether, and to what extent, this change in policy modified the preventative effects of the study intervention. To address such questions, we adopt a stratified proportional hazards model for clustered interval-censored data with time-dependent covariates and develop a composite expectation maximization algorithm that facilitates estimation of model parameters without placing parametric assumptions on either the baseline hazard functions or the within-cluster dependence structure. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal. We also propose and provide theoretical justification for the use of the profile composite likelihood function to construct a robust sandwich estimator for the variance. We characterize the finite-sample performance and robustness of these estimators through extensive simulation studies. Finally, we conclude by applying this stratified proportional hazards model to a re-analysis of the Botswana Combination Prevention Project, with the national adoption of a universal test and treat strategy now modeled as a time-dependent covariate.

Randomization-based confidence intervals for cluster randomized trials

In a cluster randomized trial (CRT), groups of people are randomly assigned to different interventions. Existing parametric and semiparametric methods for CRTs rely on distributional assumptions or a large number of clusters to maintain nominal confidence interval (CI) coverage. Randomization-based inference is an alternative approach that is distribution-free and does not require a large number of clusters to be valid. Although it is well-known that a CI can be obtained by inverting a randomization test, this requires testing a non-zero null hypothesis, which is challenging with non-continuous and survival outcomes. In this article, we propose a general method for randomization-based CIs using individual-level data from a CRT. This approach accommodates various outcome types, can account for design features such as matching or stratification, and employs a computationally efficient algorithm. We evaluate this method's performance through simulations and apply it to the Botswana Combination Prevention Project, a large HIV prevention trial with an interval-censored time-to-event outcome.

Semiparametric regression analysis of clustered interval-censored failure time data with a cured subgroup

This article discusses regression analysis of clustered interval-censored failure time data in the presence of a cured fraction or subgroup. Such data often occur in many areas, including epidemiological studies, medical studies, and social sciences. For the problem, a class of semiparametric transformation nonmixture cure models is presented and for estimation, the maximum likelihood estimation procedure is derived. For the implementation of the proposed method, we develop a novel EM algorithm based on a Poisson variable-based augmentation. An extensive simulation study is conducted and suggests that the proposed approach works well in practical situations. Finally the method is applied to an example that motivated this study.

Marginal analysis of current status data with informative cluster size using a class of semiparametric transformation cure models

This research is motivated by a periodontal disease dataset that possesses certain special features. The dataset consists of clustered current status time-to-event observations with large and varying cluster sizes, where the cluster size is associated with the disease outcome. Also, heavy censoring is present in the data even with long follow-up time, suggesting the presence of a cured subpopulation. In this paper, we propose a computationally efficient marginal approach, namely the cluster-weighted generalized estimating equation approach, to analyze the data based on a class of semiparametric transformation cure models. The parametric and nonparametric components of the model are estimated using a Bernstein-polynomial based sieve maximum pseudo-likelihood approach. The asymptotic properties of the proposed estimators are studied. Simulation studies are conducted to evaluate the performance of the proposed estimators in scenarios with different degree of informative clustering and within-cluster dependence. The proposed method is applied to the motivating periodontal disease data for illustration.

Copula-based semiparametric regression method for bivariate data under general interval censoring

This research is motivated by discovering and underpinning genetic causes for the progression of a bilateral eye disease, age-related macular degeneration (AMD), of which the primary outcomes, progression times to late-AMD, are bivariate and interval-censored due to intermittent assessment times. We propose a novel class of copula-based semiparametric transformation models for bivariate data under general interval censoring, which includes the case 1 interval censoring (current status data) and case 2 interval censoring. Specifically, the joint likelihood is modeled through a two-parameter Archimedean copula, which can flexibly characterize the dependence between the two margins in both tails. The marginal distributions are modeled through semiparametric transformation models using sieves, with the proportional hazards or odds model being a special case. We develop a computationally efficient sieve maximum likelihood estimation procedure for the unknown parameters, together with a generalized score test for the regression parameter(s). For the proposed sieve estimators of finite-dimensional parameters, we establish their asymptotic normality and efficiency. Extensive simulations are conducted to evaluate the performance of the proposed method in finite samples. Finally, we apply our method to a genome-wide analysis of AMD progression using the Age-Related Eye Disease Study data, to successfully identify novel risk variants associated with the disease progression. We also produce predicted joint and conditional progression-free probabilities, for patients with different genetic characteristics.

Normal frailty probit model for clustered interval-censored failure time data

Clustered interval-censored data commonly arise in many studies of biomedical research where the failure time of interest is subject to interval-censoring and subjects are correlated for being in the same cluster. A new semiparametric frailty probit regression model is proposed to study covariate effects on the failure time by accounting for the intracluster dependence. Under the proposed normal frailty probit model, the marginal distribution of the failure time is a semiparametric probit model, the regression parameters can be interpreted as both the conditional covariate effects given frailty and the marginal covariate effects up to a multiplicative constant, and the intracluster association can be summarized by two nonparametric measures in simple and explicit form. A fully Bayesian estimation approach is developed based on the use of monotone splines for the unknown nondecreasing function and a data augmentation using normal latent variables. The proposed Gibbs sampler is straightforward to implement since all unknowns have standard form in their full conditional distributions. The proposed method performs very well in estimating the regression parameters as well as the intracluster association, and the method is robust to frailty distribution misspecifications as shown in our simulation studies. Two real-life data sets are analyzed for illustration.

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

Interval-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.

Semi-parametric frailty model for clustered interval-censored data

Abstract:

The shared frailty model is a popular tool to analyze correlated right-censored time-to-event data. In the shared frailty model, the latent frailty is assumed to be shared by the members of a cluster and is assigned a parametric distribution, typically a gamma distribution due to its conjugacy. In the case of interval-censored time-to-event data, the inclusion of frailties results in complicated intractable likelihoods. Here, we propose a flexible frailty model for analyzing such data by assuming a smooth semi-parametric form for the conditional time-to-event distribution and a parametric or a flexible form for the frailty distribution. The results of a simulation study suggest that the estimation of regression parameters is robust to misspecification of the frailty distribution (even when the frailty distribution is multimodal or skewed). Given sufficiently large sample sizes and number of clusters, the flexible approach produces smooth and accurate posterior estimates for the baseline survival function and for the frailty density, and it can correctly detect and identify unusual frailty density forms. The methodology is illustrated using dental data from the Signal Tandmobiel[Formula: see text] study.

Dynamic prediction models for clustered and interval-censored outcomes: Investigating the intra-couple correlation in the risk of dementia

The use of settings such as cohorts or clinical trials with interval-censored data and clustered event times are increasingly popular designs. First, the observed outcomes cannot be considered as independent and random effects survival models were introduced. Second, the failure time is not known exactly but it is only known to have occurred within a certain interval. We propose here an extension of shared frailty models to handle simultaneously the interval censoring, the clustering and also left truncation due to delayed entry in the cohort. A simulation study to evaluate the proposed method was conducted. The estimated results are used to obtain dynamic predictions for clustered patients, with interval-censored failure times and with a given history. We apply our method to the Three-City study, a prospective cohort with periodic follow-up in order to study prognostic factors of dementia. In this application scheme, couples are natural clusters and an intra-couple correlation might be present with a possible increased risk for dementia for subjects whose partner already developed incident dementia. No significant intra-couple correlation for the risk of dementia was observed before and after adjustments for covariates. We also present individual predictions of dementia underlining the usefulness of dynamic prognostic tools that can take into account the clustering. The consideration of frailty models for interval-censoring data and left-truncated data permits useful analysis of very complex clustered data. It could help to improve estimation of the impact of proposed prognostic features in a study with clustering. We proposed here a tractable model and a dynamic prediction tool that can easily be implemented using the R package Frailtypack.

Sample size and robust marginal methods for cluster-randomized trials with censored event times

In cluster-randomized trials, intervention effects are often formulated by specifying marginal models, fitting them under a working independence assumption, and using robust variance estimates to address the association in the responses within clusters. We develop sample size criteria within this framework, with analyses based on semiparametric Cox regression models fitted with event times subject to right censoring. At the design stage, copula models are specified to enable derivation of the asymptotic variance of estimators from a marginal Cox regression model and to compute the number of clusters necessary to satisfy power requirements. Simulation studies demonstrate the validity of the sample size formula in finite samples for a range of cluster sizes, censoring rates, and degrees of within-cluster association among event times. The power and relative efficiency implications of copula misspecification is studied, as well as the effect of within-cluster dependence in the censoring times. Sample size criteria and other design issues are also addressed for the setting where the event status is only ascertained at periodic assessments and times are interval censored.

Mathematical modeling of infectious disease dynamics

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.