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Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same event. Most regression models with recurrent events tacitly assume constant effects of covariates over time, which may not be realistic in practice. To address time-varying effects, we develop a dynamic regression model to target the mean frequency of recurrent events. We propose an estimation procedure which fully exploits observed data. Consistency and weak convergence of the proposed estimator are established. Simulation studies demonstrate that the proposed method works well, and two real data analyses are presented for illustration., (© 2019 The International Biometric Society.)

In longitudinal studies, individual subject may experience recurrent events of the same type over a relatively long period of time. The longitudinal pattern of gaps between successive recurrent events is often of great research interest. In this article, the probability structure of the recurrent gap times is first explored in the presence of censoring. According to the discovered structure, we introduce the stratified proportional reverse-time hazards models with unspecified baseline functions to accommodate individual heterogeneity, when the longitudinal pattern parameter is of main interest. Inference procedures are proposed and studied by way of proper riskset construction. The proposed methodology is demonstrated by the Monte Carlo simulations and an application to a well-known Denmark schizophrenia cohort study data set.

We consider regression analysis of a disease outcome in relation to longitudinal data which are observations from a random effects model. The covariate variables of interest are the values of the underlying trajectory at some time points, which may be fixed or subject-specific. Because the underlying random coefficients are unknown, the covariates to the primary model are generally unobserved. In addition, measurements are often not observed at the time points of interest. A motivating example to our model is the effects of age at adiposity rebound and the associated body mass index on the risk of adult obesity. The adiposity rebound is a time point at which the trajectory of a child's body fatness declines to a minimum. This general error in timing problem may be applied to an analysis when time-dependent marker variables follow a polynomial model in which the effect of a local maximum or minimum point may be of interest. It can be seen that directly applying estimated covariates, possibly obtained from estimated time points, may lead to bias. Estimation procedures based on expected estimating equations, regression calibration and simulation extrapolation are applied to this problem., (Copyright 2003 John Wiley & Sons, Ltd.)

Background: Automatic and continuous recording of vaginal temperature (TV) using wearable sensors causes minimal disruptions to animal behavior and can generate data that enable the evaluation of temporal body temperature variation under heat stress (HS) conditions. However, the genetic basis of TV in lactating sows from a longitudinal perspective is still unknown. The objectives of this study were to define statistical models and estimate genetic parameters for TV in lactating sows using random regression models, and identify genomic regions and candidate genes associated with HS indicators derived from automatically-recorded TV. Results: Heritability estimates for TV ranged from 0.14 to 0.20 over time (throughout the day and measurement period) and from 0.09 to 0.18 along environmental gradients (EG, − 3.5 to 2.2, which correspond to dew point values from 14.87 to 28.19 ˚C). Repeatability estimates of TV over time and along EG ranged from 0.57 to 0.66 and from 0.54 to 0.77, respectively. TV measured from 12h00 to 16h00 had moderately high estimates of heritability (0.20) and repeatability (0.64), indicating that this period might be the most suitable for recording TV for genetic selection purposes. Significant genotype-by-environment interactions (GxE) were observed and the moderately high estimates of genetic correlations between pairs of extreme EG indicate potential re-ranking of selection candidates across EG. Two important genomic regions on chromosomes 10 (59.370–59.998 Mb) and16 (21.548–21.966 Mb) were identified. These regions harbor the genes CDC123, CAMK1d, SEC61A2, and NUDT5 that are associated with immunity, protein transport, and energy metabolism. Across the four time-periods, respectively 12, 13, 16, and 10 associated genomic regions across 14 chromosomes were identified for TV. For the three EG classes, respectively 18, 15, and 14 associated genomic windows were identified for TV, respectively. Each time-period and EG class had uniquely enriched genes with identified specific biological functions, including regulation of the nervous system, metabolism and hormone production. Conclusions: TV is a heritable trait with substantial additive genetic variation and represents a promising indicator trait to select pigs for improved heat tolerance. Moderate GxE for TV exist, indicating potential re-ranking of selection candidates across EG. TV is a highly polygenic trait regulated by a complex interplay of physiological, cellular and behavioral mechanisms. [ABSTRACT FROM AUTHOR]

Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however, gap times between recurrent events are of natural interest and moreover the effects may actually vary over time. In this article, we propose a marginal varying-coefficient model for gap times between recurrent events that allows for the intra-individual correlation between events. Estimation and inference procedures are developed for the varying coefficients. Consistency and weak convergence of the proposed estimator are established. Monte Carlo simulation studies demonstrate that the proposed method works well with practical sample sizes. The proposed method is illustrated with an analysis of bladder tumor clinical data. [ABSTRACT FROM AUTHOR]

Dynamic regression models, including the quantile regression model and Aalen’s additive hazards model, are widely adopted to investigate evolving covariate effects. Yet lack of monotonicity respecting with standard estimation procedures remains an outstanding issue. Advances have recently been made, but none provides a complete resolution. In this article, we propose a novel adaptive interpolation method to restore monotonicity respecting, by successively identifying and then interpolating nearest monotonicity-respecting points of an original estimator. Under mild regularity conditions, the resulting regression coefficient estimator is shown to be asymptotically equivalent to the original. Our numerical studies have demonstrated that the proposed estimator is much more smooth and may have better finite-sample efficiency than the original as well as, when available as only in special cases, other competing monotonicity-respecting estimators. Illustration with a clinical study is provided. [ABSTRACT FROM AUTHOR]

ABSTRACT Weighted log-rank estimating function has become a standard estimation method for the censored linear regression model, or the accelerated failure time model. Well established statistically, the estimator defined as a consistent root has, however, rather poor computational properties because the estimating function is neither continuous nor, in general, monotone. We propose a computationally efficient estimator through an asymptotics-guided Newton algorithm, in which censored quantile regression methods are tailored to yield an initial consistent estimate and a consistent derivative estimate of the limiting estimating function. We also develop fast interval estimation with a new proposal for sandwich variance estimation. The proposed estimator is asymptotically equivalent to the consistent root estimator and barely distinguishable in samples of practical size. However, computation time is typically reduced by two to three orders of magnitude for point estimation alone. Illustrations with clinical applications are provided. [ABSTRACT FROM AUTHOR]

The accelerated failure time (AFT) model is an important regression tool to study the association between survival time and covariates. Semiparametric inference procedures have been proposed extensively in the literature. Recently, Zhou (2005a) proposed to use a model-based empirical likelihood approach to interval estimation for the AFT model. However, comparison was not made with more standard approaches based on score test and Wald-type test. In this article, we conduct extensive simulation studies to evaluate their relative performance in small samples. In addition to these methods, we also devise and consider model-free empirical likelihood approach for the comparisons. Our simulation results suggest that these empirical likelihood-based methods are not better than the standard approach based on the score test. [ABSTRACT FROM AUTHOR]

Recurrent event data typically exhibit the phenomenon of intra-individual correlation, owing to not only observed covariates but also random effects. In many applications, the population may be reasonably postulated as a heterogeneous mixture of individual renewal processes, and the inference of interest is the effect of individual-level covariates. In this article, we suggest and investigate a marginal proportional hazards model for gaps between recurrent events. A connection is established between observed gap times and clustered survival data with informative cluster size. We subsequently construct a novel and general inference procedure for the latter, based on a functional formulation of standard Cox regression. Large-sample theory is established for the proposed estimators. Numerical studies demonstrate that the procedure performs well with practical sample sizes. Application to the well-known bladder tumor data is given as an illustration. [ABSTRACT FROM AUTHOR]

Many disease processes are characterized by two or more successive health states, and it is often of interest and importance to assess state-specific covariate effects. However, with incomplete follow-up data such inference has not been satisfactorily addressed in the literature. We model the logarithm-transformed sojourn time in each state as linearly related to the covariates; however, neither the distributional form of the error term nor the dependence structure of the states needs to be specified. We propose a regression procedure to accommodate incomplete follow-up data. Asymptotic theory is presented, along with some tools for goodness-of-fit diagnostics. Simulation studies show that the proposal is reliable for practical use. We illustrate it by application to a cancer clinical trial. [ABSTRACT FROM AUTHOR]