Time-varying coefficients models for recurrent event data when different varying coefficients admit different degrees of smoothness: application to heart disease modeling

2016 ◽  
Vol 35 (23) ◽  
pp. 4166-4182
Author(s):  
Ehsan Eshaghi ◽  
Hossein Baghishani ◽  
Davood Shahsavani
Keyword(s):  
Heart Disease ◽  
Disease Modeling ◽  
Recurrent Event ◽  
Time Varying ◽  
Event Data ◽  
Recurrent Event Data ◽  
Varying Coefficients ◽  
Time Varying Coefficients

scholarly journals Recurrent event data analysis with intermittently observed time-varying covariates

2016 ◽  
Vol 35 (18) ◽  
pp. 3049-3065 ◽  
Author(s):  
Shanshan Li ◽  
Yifei Sun ◽  
Chiung-Yu Huang ◽  
Dean A. Follmann ◽  
Richard Krause
Keyword(s):  
Data Analysis ◽  
Recurrent Event ◽  
Time Varying ◽  
Event Data ◽  
Recurrent Event Data ◽  
Time Varying Covariates ◽  
Event Data Analysis

scholarly journals Mixture cure models with time-varying and multilevel frailties for recurrent event data

2019 ◽  
Vol 29 (5) ◽  
pp. 1368-1385 ◽  
Author(s):  
Richard Tawiah ◽  
Geoffrey J McLachlan ◽  
Shu Kay Ng
Keyword(s):  
Recurrent Events ◽  
General Setting ◽  
Efficient Estimation ◽  
Recurrent Event ◽  
Time Varying ◽  
Event Data ◽  
Recurrent Event Data ◽  
Mixture Cure Model ◽  
Generalised Linear Mixed Model ◽  
Gap Times

Many medical studies yield data on recurrent clinical events from populations which consist of a proportion of cured patients in the presence of those who experience the event at several times (uncured). A frailty mixture cure model has recently been postulated for such data, with an assumption that the random subject effect (frailty) of each uncured patient is constant across successive gap times between recurrent events. We propose two new models in a more general setting, assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data originated from multi-institutional (multi-centre) clinical trials, using extra random effect terms to adjust for institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, we develop an efficient estimation procedure via an EM-type algorithm based on residual maximum likelihood (REML) through the generalised linear mixed model (GLMM) methodology. Simulation studies are presented to assess the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trial were analyzed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed.

scholarly journals Semiparametric estimation of time-varying intervention effects using recurrent event data

2017 ◽  
Vol 36 (17) ◽  
pp. 2682-2696 ◽  
Author(s):  
Jiajun Xu ◽  
K. F. Lam ◽  
Feng Chen ◽  
Paul Milligan ◽  
Yin Bun Cheung
Keyword(s):  
Semiparametric Estimation ◽  
Recurrent Event ◽  
Time Varying ◽  
Event Data ◽  
Recurrent Event Data ◽  
Intervention Effects ◽  
Estimation Of Time

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

scholarly journals Estimating latent group structure in time-varying coefficient panel data models

2019 ◽  
Author(s):  
Jia Chen
Keyword(s):  
Panel Data ◽  
Data Models ◽  
Panel Data Models ◽  
Time Varying ◽  
Clustering Method ◽  
Varying Coefficient ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Latent Group ◽  
Group Structures

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.

scholarly journals Penalized survival models for the analysis of alternating recurrent event data

Biometrics ◽  
2019 ◽  
Vol 76 (2) ◽  
pp. 448-459 ◽  
Author(s):  
Lili Wang ◽  
Kevin He ◽  
Douglas E. Schaubel
Keyword(s):  
Recurrent Event ◽  
Survival Models ◽  
Event Data ◽  
Recurrent Event Data
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