Bayesian Models for Multivariate Current Status Data with Informative Censoring

In studies involving subclinical events, times of events are often subject to interval censoring since their occurrence is only detected at inspection times. When individuals are event-free at an initial time and a single follow-up inspection is made, current status data are obtained. In many settings, however, the population comprised a susceptible and a nonsusceptible subpopulation, where only susceptible individuals will go on to experience the event. Then interest often lies primarily in identifying prognostic variables for susceptibility, and secondarily in the event time distribution among the susceptible individuals. We give a simple mixture model that facilitates estimation of the proportion of susceptible individuals, covariate effects on the odds of susceptibility, and the event time distribution under a current status observation scheme. Asymptotic relative efficiency of maximum likelihood estimators is considered based on the Fisher information for a variety of settings. EM algorithms are proposed for parametric, weakly parametric, and nonparametric estimation of the event time distribution. The methods are applied to motivating studies examining an immunological response to low molecular weight heparin in patients undergoing orthopedic surgery.

Spatial Poisson models for areal count data use nonstationary “intrinsic autoregressions,” also often referred to as “conditionally autoregressive” (CAR) models. Bayesian inference for these models has generally involved using single parameter updating Markov chain Monte Carlo algorithms, which often exhibit slow mixing (i.e., poor convergence) properties. These spatial models are richly parameterized and lend themselves to the structured Markov chain Monte Carlo (SMCMC) algorithms. SMCMC provides a simple, general, and flexible framework for accelerating convergence in an MCMC sampler by providing a systematic way to block groups of similar parameters while taking full advantage of the posterior correlation structure induced by the model and data. Among the SMCMC strategies considered here are blocking using different size blocks (grouping by geographical region), reparameterization, updating jointly with and without model hyperparameters, “oversampling” some of the model parameters, and “pilot adaptation” versus continuous tuning techniques for the proposal density. We apply the techniques presented here to datasets on cancer mortality and late detection in the state of Minnesota. We find that, compared to univariate sampling procedures, our techniques will typically lead to more accurate posterior estimates, and they are sometimes also far more efficient in terms of the number of effective samples generated per second.

In an effort to build seismic models that are the most consistent with multiple data sets we have applied a new probabilistic inverse technique. This method uses a Markov chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude‐longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data‐rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting.

Semiparametric methods were proposed by Wei et al. (1989) to analyse recurring event-time data. They modelled the marginal distribution of each event time with a Cox proportional hazards model without imposing any constraint on the joint distribution of different event times. Therefore, it is unclear whether or not event times can simultaneously satisfy their respective marginal proportional hazards assumptions, while having continuous joint distribution. Often this leads to a difficulty of conducting simulation studies. In this note we construct parametric marginal proportional hazards models for recurring event times with proper joint density functions.

Properties of Prior and Posterior Distributions for Multivariate Categorical Response Data Models

Covariate measurement error problems have been recently studied for current status failure time data but not yet for multivariate current status data. Motivated by the three-hypers dataset from a health survey study, where the failure times for three-hypers (hyperglycemia, hypertension, hyperlipidemia) are subject to current status censoring and the covariate self-reported body mass index may be subject to measurement error, we propose a functional inference method under the proportional odds model for multivariate current status data with mismeasured covariates. The new proposal utilizes the working independence strategy to handle correlated current status observations from the same subject, as well as the conditional score approach to handle mismeasured covariate without specifying the covariate distribution. The asymptotic theory, together with a stable computation procedure combining the Newton-Raphson and self-consistency algorithms, is established for the proposed estimation method. We evaluate the method through simulation studies and illustrate it with three-hypers data.

The analysis of time‐to‐event data typically makes the censoring at random assumption, ie, that—conditional on covariates in the model—the distribution of event times is the same, whether they are observed or unobserved (ie, right censored). When patients who remain in follow‐up stay on their assigned treatment, then analysis under this assumption broadly addresses the de jure, or “while on treatment strategy” estimand. In such cases, we may well wish to explore the robustness of our inference to more pragmatic, de facto or “treatment policy strategy,” assumptions about the behaviour of patients post‐censoring.This is particularly the case when censoring occurs because patients change, or revert, to the usual (ie, reference) standard of care. Recent work has shown how such questions can be addressed for trials with continuous outcome data and longitudinal follow‐up, using reference‐based multiple imputation. For example, patients in the active arm may have their missing data imputed assuming they reverted to the control (ie, reference) intervention on withdrawal. Reference‐based imputation has two advantages: (a) it avoids the user specifying numerous parameters describing the distribution of patients' postwithdrawal data and (b) it is, to a good approximation, information anchored, so that the proportion of information lost due to missing data under the primary analysis is held constant across the sensitivity analyses. In this article, we build on recent work in the survival context, proposing a class of reference‐based assumptions appropriate for time‐to‐event data. We report a simulation study exploring the extent to which the multiple imputation estimator (using Rubin's variance formula) is information anchored in this setting and then illustrate the approach by reanalysing data from a randomized trial, which compared medical therapy with angioplasty for patients presenting with angina.

Discharge formation in the A–K space of transient hollow cathode discharge (THCD) is causally linked with the emission of high energy electron beams originating in the hollow cathode region (HCR). Ionization in the A–K gap proceeds through the formation of a moving virtual anode, whose time evolution is strongly correlated with different periods in the electron beam activity. Here, we report on time and space resolved observations of different ionization events inside the HCR, which are time correlated with ionization processes inside the A–K gap. The experiments have been performed in Hydrogen, at pressures between 50 and 400 mTorr. A statistical study of the characteristic times associated with the different ionization events, based on von Laue plots, shows that the time distribution of events is well described by a single Gaussian distribution.

Multivariate current-status failure time data consist of several possibly related event times of interest, in which the status of each event is determined at a single examination time. If the examination time is intrinsically related to the event times, the examination is referred to as dependent censoring and needs to be taken into account. Such data often occur in clinical studies and animal carcinogenicity experiments. To accommodate for possible dependent censoring, this paper proposes a joint frailty model for event times and dependent censoring time. We develop a likelihood approach using Gaussian quadrature techniques for obtaining maximum likelihood estimates. We conduct extensive simulation studies for investigating finite-sample properties of the proposed method. We illustrate the proposed method with an analysis of patients with ankylosing spondylitis, where the examination time may be dependent on the event times of interest.

Multivariate binary data are widely collected in many disciplines, including in finance, psychometrics, and ecology. Often, many binary responses are driven by only a subset of predictors, and groups of binary responses may exhibit similar effects to a predictor. Motivated by a survey containing presence-absence records of 22 demersal fish species recorded across the U.S. Northeast shelf, we propose a novel method for simultaneous coefficient clustering and variable selection in multivariate binary data using a penalized Ising regression model. The Ising regression model formulates an explicit joint distribution for a binary response vector via main and pairwise interaction coefficients, where the former is modeled as a function of covariates and the latter captures conditional dependence relationships between responses. To cluster coefficients within each covariate, and encourage sparsity across both covariates and pairwise interaction coefficients, we propose to augment the Ising regression model with adaptive fused lasso and adaptive lasso penalties. Such a structured penalty to encourage simultaneous sparsity and groupings is aligned with goals of achieving sparse species-covariate relationships, and homogeneity of environmental responses across species, in the motivating demersal fish survey. Through a reparametrization, we show that the proposed estimator can be efficiently obtained by fitting a single, adaptive lasso logistic regression model. Simulation studies and an application to the demersal fish survey demonstrate competitive performance of the proposed method relative to several existing Ising regression models for multivariate binary data, and leads to an interpretable and parsimonious set of response-covariate relationships.

Transformation latent variable models are proposed in this study to analyze multivariate censored data. The proposed models generalize conventional linear transformation models to semiparametric transformation models that accommodate latent variables. The characteristics of the latent variables were assessed based on several correlated observed indicators through measurement equations. A Bayesian approach was developed with Bayesian P-splines technique and the Markov chain Monte Carlo algorithm to estimate the unknown parameters and transformation functions. Simulation shows that the performance of the proposed methodology is satisfactory. The proposed method was applied to analyze a cardiovascular disease data set.

We propose some multivariate reliability models with emphasis on quantitative risk assessment. We give a brief description of different exponential and Weibull models used for multicomponent systems and frailty models for multivariate survival data. We give some applications of frailty models for the multivariate survival data.

In various applications one encounters samples of objects, where each object consists of a small number of repeated event times observed over a fixed time interval. For such rare event data there are no flexible methods available that can be applied when the shapes of the intensity functions that generate the observed event times are not known, or vary substantially between objects. We model the underlying intensity functions as nonparametric object-specific random functions. Applying a novel functional method to obtain the covariance structure of the associated random densities, we reconstruct object-specific density functions that reflect the distribution of event times. We demonstrate in simulations that the proposed functional approach is superior to conventional nonparametric methods, as it borrows strength from the entire sample of objects rather than aiming at the estimation of each object's density separately. Our method is based on a key relationship that allows one to reduce the covariance estimation problem for random densities to the simpler problem of estimating a non-random joint density from pooled event times. We describe an application to model bid arrivals for a sample of online auctions, and also include asymptotic justifications of the methodology.

Methodologic issues and statistical approaches to the analysis of multiple cycle data from couples undergoing in vitro fertilization (IVF)

Although there are many methods for functional data analysis, less emphasis is put on characterizing variability among volatilities of individual functions. In particular, certain individuals exhibit erratic swings in their trajectory while other individuals have more stable trajectories. There is evidence of such volatility heterogeneity in blood pressure trajectories during pregnancy, for example, and reason to suspect that volatility is a biologically important feature. Most functional data analysis models implicitly assume similar or identical smoothness of the individual functions, and hence can lead to misleading inferences on volatility and an inadequate representation of the functions. We propose a novel class of functional data analysis models characterized using hierarchical stochastic differential equations. We model the derivatives of a mean function and deviation functions using Gaussian processes, while also allowing covariate dependence including on the volatilities of the deviation functions. Following a Bayesian approach to inference, a Markov chain Monte Carlo algorithm is used for posterior computation. The methods are tested on simulated data and applied to blood pressure trajectories during pregnancy.