Bayesian Analysis of Coefficient Instability in Dynamic Regressions

Objective: To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time (AFT), Cox proportional hazards (PH), and Cox PH with time-varying coefficient (TVC) models. Methods: A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah, Kedah and Hospital Tuanku Fauziah, Perlis in Northern Malaysia due to confirmed-cultured melioidosis. The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis, and Cox’s models and the findings were compared by using the goodness of fit methods. The analyses were done by using Stata SE version 14.0. Results: A total of 242 patients (53.4%) survived. In this study, the median survival time of melioidosis patients was 30.0 days (95% CI 0.0-60.9). Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model. In AFT survival analysis, a total of seven significant prognostic factors were identified. The results were found to be only a slight difference between the identified prognostic factors among the models. AFT survival showed better results compared to Cox’s models, with the lowest Akaike information criteria and best fitted Cox-snell residuals. Conclusions: AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

Bayesian Bandwidth Selection in Nonparametric Time-Varying Coefficient Models

Specification tests for time-varying coefficient models

In this paper, we discuss wavelet estimation of time-varying coefficient models based on censored data where the survival and the censoring times are from a stationary α-mixing sequence. Under the appropriate conditions, the Berry-Esseen bouds of wavelet estimators are established. For the purpose of statistical inference, a random weighted wavelet estimator of the time-varying coefficient is also constructed, and some approximation rates are given.

We investigated the association between traumatic brain injury (TBI) and incidence of early-onset dementia (EOD) versus late-onset dementia (LOD). We included 501,710 UK Biobank participants (average age 56.5). Over a median 13.6 years of follow-up, 836 developed EOD (before 65) and 8947 developed LOD (after 65). We estimated hazard ratios (HRs) for TBI's association with EOD and LOD using Cox proportional hazard models with TBI as a time-varying exposure and coefficient. TBI was associated with higher risk of both EOD (HR: 4.06 [95% confidence interval: 3.13, 5.26]) and LOD (HR: 2.51 [2.31, 2.72]. Among participants included in both EOD and LOD analyses, the effect estimate was higher for EOD (3.41 vs. 2.80), but the difference was not statistically significant. The association of TBI with EOD was stronger in those with more severe TBIs. TBI is associated with an increased risk of EOD, with a higher risk observed in more severe injuries. Traumatic brain injury (TBI) is a significant risk factor for early-onset dementia (EOD). TBI was analyzed as a time-varying exposure and time-varying coefficient. Moderate/severe/penetrating TBIs have a heightened risk of developing EOD. TBI is more strongly associated with an earlier age cut-off for dementia.

In the analysis of censored failure time observations, the standard Cox proportional hazards model assumes that the regression coefficients are time invariant. Often, these parameters vary over time, and the temporal covariate effects on the failure time are of great interest. In this article, following previous work of Cai and Sun, we propose a simple estimation procedure for the Cox model with time-varying coefficients based on a kernel-weighted partial likelihood approach. We construct pointwise and simultaneous confidence intervals for the regression parameters over a properly chosen time interval via a simple resampling technique. We derive a prediction method for future patients' survival with any specific set of covariates. Building on the estimates for the time-varying coefficients, we also consider the mixed case and present an estimation procedure for time-independent parameters in the model. Furthermore, we show how to use an integrated function of the estimate for a specific regression coefficient to examine the adequacy of proportional hazards assumption for the corresponding covariate graphically and numerically. All of the proposals are illustrated extensively with a well-known study from the Mayo Clinic.

This article proposes a Bayesian time-varying coefficient model to evaluate the temporal profile of intensity for multitype recurrent events. The model obtains smooth estimates for both time-varying coefficients and the baseline intensity using Bayesian penalized splines. One major challenge in Bayesian penalized splines is that the smoothness of a spline fit is sensitive to the subjective choice of hyperparameters. We establish a procedure to objectively determine the hyperparameters through robust prior specification. To effectively update the high-dimensional spline parameters, we develop a Markov chain Monte Carlo procedure based on the Metropolis-adjusted Langevin algorithms. A joint sampling scheme is used to achieve better convergence and mixing properties. A simulation study confirms satisfactory model performance in estimating time-varying coefficients under different curvature and event rate scenarios. Application to a commercial truck driver naturalistic driving data reveals that drivers with 7-hours-or-less sleep time have a significantly higher safety-critical event intensity after 8 hr of driving and the intensity remains high after taking a break. The findings provide crucial information for the truck driver hours-of-service regulation and fatigue management. The proposed model provides a flexible and robust tool to evaluate the temporal profile of intensity for multitype recurrent events. Supplemental materials for this article are available online.

In longitudinal studies, subjects are repeatedly observed at a set of distinct time points until the terminal event time. The time-varying coefficient model extends the parametric method and captures the dynamic trajectories of time-dependent covariate effects, thus enabling it to describe the potential relationship between the longitudinal variable and the observed time points. In this study, we propose a novel approach to the estimation of medical costs using a symmetric kernel smoothing method in the time-varying coefficient joint model. A smooth function of medical costs is derived by weighting the values of longitudinal data at all distinct observed time points via the combination of the kernel method and the inverse probability weighting method. For the simulation study, we first set up the true functions of time-varying coefficients; we then generated random samples for covariates and censored survival times. Subsequently, the longitudinal data of response variables could be produced. Further, numerical simulation experiments were conducted by using the proposed method and applying R code to the generated data. The estimated results for the parameters and non-parametric functions were compared with different settings. The numerical results illustrate that as the sample size increases, the bias and model-based standard errors decrease, and the performance improves with larger sample sizes. The estimates of functions in the model almost coincide with the true functions, as shown in the figures of the simulation study. Furthermore, the consistency of the obtained estimator is demonstrated via theoretical analysis, and a numerical simulation is performed to illustrate the performance of the proposed estimators. The proposed model is applied to a real-world data set acquired from a multicenter automatic defibrillator implantation trial (MADIT).

The research deals with the study of the varying coefficient model as well as the Time-Varying Coefficient Model because of their remarkable interest in recent years. Methods Two methods were used, local polynomial kernal method and the cubic spline method. The simulation method was used for comparison. Compared to three mathematical functions that represented the variable coefficients, different sample sizes, and different levels of the model's standard deviation, the cubic spline method was best.

This paper provides a general procedure to estimate structural vector autoregressions. The algorithm can be used in constant or time-varying coefficient models, and in the latter case, the law of motion of the coefficients can be linear or nonlinear. It can deal in a unified way with just-identified (recursive or nonrecursive) or overidentified systems where identification restrictions are of linear or of nonlinear form. We study the transmission of monetary policy shocks in models with time-varying and time-invariant parameters.

In this paper, we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions involving a bandwidth, centered around a given set of time points. In addition, we study different alternatives of estimation and inference including a Frequentist approach using weighted least squares along with bootstrap methods, and a Bayesian approach through both Markov chain Monte Carlo and variational methods. We compare the estimation strategies mention above with each other, and our radial kernel functions proposal with an expansion based on regression spline, by means of an extensive simulation study considering multiples scenarios in terms of sample size, number of repeated measurements, and subject-specific correlation. Our experiments show that the capabilities of our proposal based on radial kernel functions are indeed comparable with or even better than those obtained from regression splines. We illustrate our methodology by analyzing data from two AIDS clinical studies.

Leverage and Alpha: The Case of Funds of Hedge Funds

This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions. To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages. The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods. The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality. The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

Time-varying coefficient regression is commonly used in the modeling of nonstationary stochastic processes. In this paper, we consider a time-varying coefficient convolution-type smoothed quantile regression (conquer). The covariates and errors are assumed to belong to a general class of locally stationary processes. We propose a local linear conquer estimator for the varying-coefficient function, and obtain the global Bahadur–Kiefer representation, which yields the asymptotic normality. Furthermore, statistical inference on simultaneous confidence bands is also studied. We investigate the finite-sample performance of the conquer estimator and confirm the validity of our asymptotic theory by conducting extensive simulation studies. We also consider financial volatility data as an example of a real-world application.

Traditional performance evaluation assumes that investment styles and economic states remain constant. Conditional performance evaluation, however, compares a fund's returns with the returns of a dynamic strategy that matches the fund's time-varying risk exposures. In this Research Foundation monograph, the authors revisit the main empirical results of the conditional performance evaluation literature using a large, updated sample of mutual funds and expand and refine the treatment of conditioning information. Because conditional performance evaluation uses more information than traditional methods, it has the potential to provide more accurate performance measures—an attractive feature for anyone trying to assess whether a fund's performance arises from manager skill or from chance.