Quantile regression without the curse of unsmoothness

We consider quantile regression models and investigate the induced smoothing method for obtaining the covariance matrix of the regression parameter estimates. We show that the difference between the smoothed and unsmoothed estimating functions in quantile regression is negligible. The detailed and simple computational algorithms for calculating the asymptotic covariance are provided. Intensive simulation studies indicate that the proposed method performs very well. We also illustrate the algorithm by analyzing the rainfall–runoff data from Murray Upland, Australia.

Calculate excess mortality during heatwaves using Hilbert-Huang transform algorithm

Background Heatwaves could cause the population excess death numbers to be ranged from tens to thousands within a couple of weeks in a local area. An excess mortality due to a special event (e.g., a heatwave or an epidemic outbreak) is estimated by subtracting the mortality figure under ‘normal’ conditions from the historical daily mortality records. The calculation of the excess mortality is a scientific challenge because of the stochastic temporal pattern of the daily mortality data which is characterised by (a) the long-term changing mean levels (i.e., non-stationarity); (b) the non-linear temperature-mortality association. The Hilbert-Huang Transform (HHT) algorithm is a novel method originally developed for analysing the non-linear and non-stationary time series data in the field of signal processing, however, it has not been applied in public health research. This paper aimed to demonstrate the applicability and strength of the HHT algorithm in analysing health data. Methods Special R functions were developed to implement the HHT algorithm to decompose the daily mortality time series into trend and non-trend components in terms of the underlying physical mechanism. The excess mortality is calculated directly from the resulting non-trend component series. Results The Brisbane (Queensland, Australia) and the Chicago (United States) daily mortality time series data were utilized for calculating the excess mortality associated with heatwaves. The HHT algorithm estimated 62 excess deaths related to the February 2004 Brisbane heatwave. To calculate the excess mortality associated with the July 1995 Chicago heatwave, the HHT algorithm needed to handle the mode mixing issue. The HHT algorithm estimated 510 excess deaths for the 1995 Chicago heatwave event. To exemplify potential applications, the HHT decomposition results were used as the input data for a subsequent regression analysis, using the Brisbane data, to investigate the association between excess mortality and different risk factors. Conclusions The HHT algorithm is a novel and powerful analytical tool in time series data analysis. It has a real potential to have a wide range of applications in public health research because of its ability to decompose a nonlinear and non-stationary time series into trend and non-trend components consistently and efficiently.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.