A semiparametric likelihood-based method for regression analysis of mixed panel-count data.

Panel count data typically refer to data arising from studies with recurrent events, in which subjects are observed only at discrete time points rather than under continuous observations. We investigate a general situation where a recurrent event process is eventually truncated by an informative terminal event and we are particularly interested in behaviors of the recurrent event process near the terminal event. We propose a reversed mean model for estimating the mean function of the recurrent event process. We develop a two-stage sieve likelihood-based method to estimate the mean function, which overcomes the computational difficulties arising from a nuisance functional parameter involved in the likelihood. The consistency and the convergence rate of the two-stage estimator are established. Allowing for the convergence rate slower than the standard rate, we develop the general weak convergence theory of M-estimators with a nuisance functional parameter, and then apply it to the proposed estimator for deriving the asymptotic normality. Furthermore, a class of two-sample tests is developed. The proposed methods are evaluated with extensive simulation studies and illustrated with panel count data from the Chinese Longitudinal Healthy Longevity Study.

Marginal structural models (MSMs) are a general class of causal models for specifying the average effect of treatment on an outcome. These models can accommodate discrete or continuous treatments, as well as treatment effect heterogeneity (causal effect modification). The literature on estimation of MSM parameters has been dominated by semiparametric estimation methods, such as inverse probability of treatment weighted (IPTW). Likelihood-based methods have received little development, probably in part due to the need to integrate out confounders from the likelihood and due to reluctance to make parametric modeling assumptions. In this article we develop a fully Bayesian MSM for continuous and survival outcomes. In particular, we take a Bayesian nonparametric (BNP) approach, using a combination of a dependent Dirichlet process and Gaussian process to model the observed data. The BNP approach, like semiparametric methods such as IPTW, does not require specifying a parametric outcome distribution. Moreover, by using a likelihood-based method, there are potential gains in efficiency over semiparametric methods. An additional advantage of taking a fully Bayesian approach is the ability to account for uncertainty in our (uncheckable) identifying assumption. To this end, we propose informative prior distributions that can be used to capture uncertainty about the identifying "no unmeasured confounders" assumption. Thus, posterior inference about the causal effect parameters can reflect the degree of uncertainty about this assumption. The performance of the methodology is evaluated in several simulation studies. The results show substantial efficiency gains over semiparametric methods, and very little efficiency loss over correctly specified maximum likelihood estimates. The method is also applied to data from a study on neurocognitive performance in HIV-infected women and a study of the comparative effectiveness of antihypertensive drug classes.

Current status data arise when each study subject is observed only once and the survival time of interest is known only to be either less or greater than the observation time. Such data often occur in, for example, cross-sectional studies, demographical investigations and tumorigenicity experiments and several semi-parametric and non-parametric methods for their analysis have been proposed. However, most of these methods deal only with the situation where observation time is independent of the underlying survival time completely or given covariates. This paper discusses regression analysis of current status data when the observation time may be related to the underlying survival time and inference procedures are presented for estimation of regression parameters under the additive hazards regression model. The procedures can be easily implemented and are applied to two motivating examples.

In modern biomedical datasets, it is common for recurrent outcomes data to be collected in an incomplete manner. More specifically, information on recurrent events is routinely recorded as a mixture of recurrent event data, panel count data, and panel binary data; we refer to this structure as general mixed recurrent event data. Although the aforementioned data types are individually well-studied, there does not appear to exist an established approach for regression analysis of the three component combination. Often, ad-hoc measures such as imputation or discarding of data are used to homogenize records prior to the analysis, but such measures lead to obvious concerns regarding robustness, loss of efficiency, and other issues. This work proposes a maximum likelihood regression estimation procedure for the combination of general mixed recurrent event data and establishes the asymptotic properties of the proposed estimators. In addition, we generalize the approach to allow for the existence of terminal events, a common complicating feature in recurrent event analysis. Numerical studies and application to the Childhood Cancer Survivor Study suggest that the proposed procedures work well in practical situations.

Panel count data occur in studies that concern recurrent events, or event history studies, when study subjects are observed only at discrete time points. By recurrent events, we mean the event that ca

Panel count data occur in many fields including clinical, demographical and industrial studies and an extensive literature has been established for their regression analysis. However, most of the existing methods apply only to the situations where both covariates and their effects are constant or one of them may be time-dependent. In the first part of this dissertation, we consider a situation where both covariates and their effects may be time-dependent and an estimating equation-based approach is developed for estimating those time-varying effects. In the method, B-spline functions are employed to approximate time-dependent coefficients and the asymptotic properties of the proposed estimators are established. To assess the performance of the proposed approach, an extensive simulation study is conducted and suggests that it works well in practical situations. An application to the China Health and Nutrition Survey (CHNS) study is provided. In practice, there could exist more than one type of event of interest, such as two types of tumor recurrence, leading to multivariate panel count data. The second part of this dissertation considers marginal mean model for multivariate panel count data with time-dependent coefficient and covariate effects, which has limited previous research. Based on the conditional estimating equation method developed for time-dependent covariates, we approximate the coefficients by B-splines, hence allow both coefficients and covariates to be time-dependent. Simulation studies show that the proposed estimation procedures work well for practical situations. The methodology is again applied to the China Health and Nutrition Survey (CHNS) study. When we consider time-varying covariates and coefficients effects, most of the previous study focused on the proportional mean model because the likelihood function under the rate model involves intractable integration. However, the rate model is more realistic and efficient. Hence, in the third part of this dissertation, we propose a semi-parametric MLE method under the rate model for panel count data with time-dependent covariates and time-varying effects. B-spline functions are employed again to approximate time-dependent coefficients and an efficient Expectation-Maximization-type algorithm is developed to overcome the computational difficulty. The resulting estimators are shown to be consistent and asymptotically efficient. Monte Carlo simulation studies demonstrate that the proposed method enjoys desirable finite-sample properties. An application to The Young Women's Project (YWP) is provided.

Panel count data often occur in a long-term recurrent event study, where the exact occurrence time of the recurrent events is unknown, but only the occurrence count between any two adjacent observation time points is recorded. Most traditional methods only handle panel count data for a single type of event. In this paper, we propose a Bayesian semiparameteric approach to analyze panel count data for multiple types of events. For each type of recurrent event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by monotone I-splines. The correlation between multiple types of events is modeled by common frailty terms and scale parameters. Unlike many frequentist estimating equation methods, our approach is based on the observed likelihood and makes no assumption on the relationship between the recurrent process and the observation process. Under the Poisson counting process assumption, we develop an efficient Gibbs sampler based on novel data augmentation for the Markov chain Monte Carlo sampling. Simulation studies show good estimation performance of the baseline mean functions and the regression coefficients; meanwhile, the importance of including the scale parameter to flexibly accommodate the correlation between events is also demonstrated. Finally, a skin cancer data example is fully analyzed to illustrate the proposed methods.

A nonparametric test for the equality of counting processes with panel count data

The brain is exposed to continuous sensory input from the environment (and the body). How does the brain encode such continuous sensory input and translate it into neural activity, e.g., stimulus-induced activity? Results from cellular recordings show that single neurons and a population of neurons represent the stimulus in a rather sparse way so that many stimuli are represented in one neuron’s (or one population of neurons’) activity. This amounts to a many-to-one relationship between stimuli and neurons entailing sparse coding. As such, sparse coding must be distinguished from other coding strategies like dense and local coding that propose a one-to-many and one-to-one relationship between stimuli and neurons. How is such sparse coding possible? The neurons’ (and population of neurons’) activity seems to encode the statistical frequency distribution of stimuli across their different discrete points in physical time and space; that is, their natural statistics. However, this is possible only when presupposing that differences between the stimuli’s different discrete points in physical space and time are encoded into neural activity. In other words, spatial and temporal differences (between the different discrete points in physical time and space) must be encoded into neural activity in order for sparse coding as a many-to-one relationship between stimuli and neurons to be possible.

Integrating Mobile Health Technology for Symptom Management in Acute Pediatric Blood and Marrow Transplant Patients

In patient follow‐up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as “bounded” or “interval‐censored.” Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood‐based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log‐normal regression with postimputation back‐transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.

Space-tethered robot system is a new kind of space robot, which consists of a robot platform, space tether, and operation robot. This paper presents the coordinated control method in order to save thruster fuel of operation robot in the process of tracking the optimal approach trajectory. First, the optimal approach trajectory of an operation robot is designed using the Gauss pseudospectral method, which resulted in continuous optimal control force using the Lagrange interpolation scheme. The optimal control force is optimized and distributed to space tether and thrusters through simulated annealing algorithm in discrete points, which minimized fuel consumption of thrusters. The distributive continuous force is obtained via cubic polynomial fitting of optimal distributive force in 0.1s discrete time point. To tracking the optimal trajectory, Fuzzy Proportional-Derivative controller is designed with the help of optimal distribution force which come from optimization model. Simultaneously, the relative attitude of the operation robot is stabilized using attitude time-delay algorithm through the reaction wheels. Numerical results are presented, demonstrating the validity of saving thruster fuel and well performance in tracking the optimal trajectory.

In this article, we extend the joint frailty models proposed by Zhao and Tong (2011) to panel count data with the time-dependent covariates and informative observation and censoring times. A novel estimating equation approach that does not depend on the distribution of frailty variables and the link function is proposed for estimation of parameters, and the asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The analysis of a bladder tumor data is presented to illustrate the method.

This paper discusses regression analysis of current status data, a type of failure time data where each study subject is observed only once, in the presence of dependent censoring. Furthermore, there may exist a cured subgroup, meaning that a proportion of study subjects are not susceptible to the failure event of interest. For the problem, we develop a sieve maximum likelihood estimation approach with the use of latent variables and Bernstein polynomials. For the determination of the proposed estimators, an EM algorithm is developed and the asymptotic properties of the estimators are established. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. A motivating application from a tumorigenicity experiment is also provided.

We develop a theoretical framework for defining and identifying flows of information in computational systems. Here, a computational system is assumed to be a directed graph, with “clocked” nodes that send transmissions to each other along the edges of the graph at discrete points in time. We are interested in a definition that captures the dynamic flow of information about a specific message, and which guarantees an unbroken “information path” between appropriately defined inputs and outputs in the directed graph. Prior measures, including those based on Granger Causality and Directed Information, fail to provide clear assumptions and guarantees about when they correctly reflect information flow about a message. We take a systematic approach-iterating through candidate definitions and counterexamples-to arrive at a definition for information flow that is based on conditional mutual information, and which satisfies desirable properties, including the existence of information paths. Finally, we describe how information flow might be detected in a noiseless setting, and provide an algorithm to identify information paths on the time-unrolled graph of a computational system.