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This paper proposes a novel generalized partial linear mixed models (GPLMMs) with the random effects distribution distributed as a multivariate skew-normal distribution for discrete longitudinal data over time. Under the Bayesian framework, we extended the Bayesian version of adaptive lasso (least absolute shrinkage and selection operator) for linear regression to the Bayesian adaptive lasso with the least squares approximation (LSA) method for generalized partial linear mixed models. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm in conjunction with the Bayesian adaptive lasso with LSA is used to simultaneously obtain the Bayesian estimates of unknown parameters, smoothing function and random effects, as well as select important covariates in GPLMMs. Several simulation studies and a real example are presented to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

Under the Bayesian framework, this study proposes a Tweedie compound Poisson partial linear mixed model on the basis of Bayesian P-spline approximation to nonparametric function for longitudinal semicontinuous data in the presence of nonignorable missing covariates and responses. The logistic regression model is simultaneously used to specify the missing response and covariate mechanisms. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings algorithm is employed to produce the joint Bayesian estimates of unknown parameters and random effects as well as nonparametric function. Several simulation studies and a real example relating to the osteoarthritis initiative data are presented to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

The time-varying reproduction number (Rt) can change rapidly over the course of a pandemic due to changing restrictions, behaviours, and levels of population immunity. Many methods exist that allow the estimation of Rtfrom case data. However, these are not easily adapted to point prevalence data nor can they infer Rtacross periods of missing data. We developed a Bayesian P-spline model suitable for fitting to a wide range of epidemic time-series, including point-prevalence data. We demonstrate the utility of the model by fitting to periodic daily SARS-CoV-2 swab-positivity data in England from the first 7 rounds (May 2020–December 2020) of the REal-time Assessment of Community Transmission-1 (REACT-1) study. Estimates of Rtover the period of two subsequent rounds (6–8 weeks) and single rounds (2–3 weeks) inferred using the Bayesian P-spline model were broadly consistent with estimates from a simple exponential model, with overlapping credible intervals. However, there were sometimes substantial differences in point estimates. The Bayesian P-spline model was further able to infer changes in Rtover shorter periods tracking a temporary increase above one during late-May 2020, a gradual increase in Rtover the summer of 2020 as restrictions were eased, and a reduction in Rtduring England’s second national lockdown followed by an increase as the Alpha variant surged. The model is robust against both under-fitting and over-fitting and is able to interpolate between periods of available data; it is a particularly versatile model when growth rate can change over small timescales, as in the current SARS-CoV-2 pandemic. This work highlights the importance of pairing robust methods with representative samples to track pandemics.

Semiparametric reproductive dispersion mixed model (SPRDMM) is a natural extension of the reproductive dispersion model and the semiparametric mixed model. In this paper, we relax the normality assumption of random effects in SPRDMM and use a truncated and centred Dirichlet process prior to specify random effects, and present the Bayesian P-spline to approximate the smoothing unknown function. A hybrid algorithm combining the block Gibbs sampler and the Metropolis–Hastings algorithm is implemented to sample observations from the posterior distribution. Also, we develop Bayesian case deletion influence measure for SPRDMM based on theφ-divergence and present those computationally feasible formulas. Several simulation studies and a real example are presented to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

The time-varying reproduction number (R t) can change rapidly over the course of a pandemic due to changing restrictions, behaviours, and levels of population immunity. Many methods exist that allow the estimation of R t from case data. However, these are not easily adapted to point prevalence data nor can they infer R t across periods of missing data. We developed a Bayesian P-spline model suitable for fitting to a wide range of epidemic time-series, including point-prevalence data. We demonstrate the utility of the model by fitting to periodic daily SARS-CoV-2 swab-positivity data in England from the first 7 rounds (May 2020–December 2020) of the REal-time Assessment of Community Transmission-1 (REACT-1) study. Estimates of R t over the period of two subsequent rounds (6–8 weeks) and single rounds (2–3 weeks) inferred using the Bayesian P-spline model were broadly consistent with estimates from a simple exponential model, with overlapping credible intervals. However, there were sometimes substantial differences in point estimates. The Bayesian P-spline model was further able to infer changes in R t over shorter periods tracking a temporary increase above one during late-May 2020, a gradual increase in R t over the summer of 2020 as restrictions were eased, and a reduction in R t during England's second national lockdown followed by an increase as the Alpha variant surged. The model is robust against both under-fitting and over-fitting and is able to interpolate between periods of available data; it is a particularly versatile model when growth rate can change over small timescales, as in the current SARS-CoV-2 pandemic. This work highlights the importance of pairing robust methods with representative samples to track pandemics. • Real-time Assessment of Community Transmission-1 (REACT-1) study May–December 2020. • Randomly selected community samples measure SARS-CoV-2 prevalence in England. • Trends in prevalence over time inferred using a Bayesian Penalised-spline (P-spline). • Trends over time in the reproduction number and instantaneous growth rate quantified. [ABSTRACT FROM AUTHOR]