Generalized Estimating Equations for Survival Data With Dependent Censoring

Independent censoring is usually assumed in survival data analysis. However, dependent censoring, where the survival time is dependent on the censoring time, is often seen in real data applications. In this project, we model the vector of survival time and censoring time marginally through semiparametric heteroscedastic accelerated failure time models and model their association by the vector of errors in the model. We show that this semiparametric model is identified, and the generalized estimating equation approach is extended to estimate the parameters in this model. It is shown that the estimators of the model parameters are consistent and asymptotically normal. Simulation studies are conducted to compare it with the estimation method under a parametric model. A real dataset from a prostate cancer study is used for illustration of the new proposed method.

Continuous time recurrent neural networks: Overview and benchmarking at forecasting blood glucose in the intensive care unit

OBJECTIVE

Blood glucose measurements in the intensive care unit (ICU) are typically made at irregular intervals. This presents a challenge in choice of forecasting model. This article gives an overview of continuous time autoregressive recurrent neural networks (CTRNNs) and evaluates how they compare to autoregressive gradient boosted trees (GBT) in forecasting blood glucose in the ICU.

METHODS

Continuous time autoregressive recurrent neural networks (CTRNNs) are a deep learning model that account for irregular observations through incorporating continuous evolution of the hidden states between observations. This is achieved using a neural ordinary differential equation (ODE) or neural flow layer. In this manuscript, we give an overview of these models, including the varying architectures that have been proposed to account for issues such as ongoing medical interventions. Further, we demonstrate the application of these models to probabilistic forecasting of blood glucose in a critical care setting using electronic medical record and simulated data and compare with GBT and linear models.

RESULTS

The experiments confirm that addition of a neural ODE or neural flow layer generally improves the performance of autoregressive recurrent neural networks in the irregular measurement setting. However, several CTRNN architecture are outperformed by a GBT model (Catboost), with only a long short-term memory (LSTM) and neural ODE based architecture (ODE-LSTM) achieving comparable performance on probabilistic forecasting metrics such as the continuous ranked probability score (ODE-LSTM: 0.118 ± 0.001; Catboost: 0.118 ± 0.001), ignorance score (0.152 ± 0.008; 0.149 ± 0.002) and interval score (175 ± 1; 176 ± 1).

CONCLUSION

The application of deep learning methods for forecasting in situations with irregularly measured time series such as blood glucose shows promise. However, appropriate benchmarking by methods such as GBT approaches (plus feature transformation) are key in highlighting whether novel methodologies are truly state of the art in tabular data settings.

Roles of ambient temperature and relative humidity on the relationship between fine particulate matter and gaseous pollutants in the largest industrial city of Ulsan, South Korea

Although meteorological conditions play a significant role in air pollution, research on their effects on the relationship between air pollutants is limited. In this study, trends of six criteria air pollutants were investigated from 15 air quality monitoring stations (AQMSs) in Ulsan, a multi-industrial city in South Korea, during 2015-2019. Unlike CO and O3, SO2, NO2, PM10, and PM2.5 showed statistically significant decreasing trends over the period. The companion relationship between PM2.5 and gaseous pollutants was evaluated by their correlations [R (PM2.5-GPs)]. R (PM2.5-NO2) was relatively high at almost all AQMSs, whereas high R (PM2.5-SO2) was observed near the petrochemical industrial complex, suggesting a great influence of local emissions (vehicles and industries). R (PM2.5-CO) and the standardized regression coefficients of CO obtained from the multiple linear regression model were the highest, indicating that combustion processes may significantly contribute to PM2.5. The effect of temperature (T) was more apparent on R (PM2.5-GPs) than that of relative humidity, with significant values under T > 15 °C. Moreover, R (PM2.5-O3) was positive at the T range of 12-18 °C, suggesting that reducing GPs emitted by industrial facilities during May-June may control PM2.5 and O3 in Ulsan. The methodology demonstrated in this study can be further used for a better understanding of the influences of environmental factors on the secondary PM2.5 formation from gaseous precursors and the R (PM2.5-O3).

A new method for estimating Sharpe ratio function via local maximum likelihood

The Sharpe ratio function is a commonly used risk/return measure in financial econometrics. To estimate this function, most existing methods take a two-step procedure that first estimates the mean and volatility functions separately and then applies the plug-in method. In this paper, we propose a direct method via local maximum likelihood to simultaneously estimate the Sharpe ratio function and the negative log-volatility function as well as their derivatives. We establish the joint limiting distribution of the proposed estimators, and moreover extend the proposed method to estimate the multivariate Sharpe ratio function. We also evaluate the numerical performance of the proposed estimators through simulation studies, and compare them with existing methods. Finally, we apply the proposed method to the three-month US Treasury bill data and that captures a well-known covariate-dependent effect on the Sharpe ratio.

Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models

This work is concerned with multivariate conditional heteroscedastic autoregressive nonlinear (CHARN) models with an unknown conditional mean function, conditional variance matrix function and density function of the distribution of noise. We study the kernel estimator of the latter function when the former are either parametric or nonparametric. The consistency, bias and asymptotic normality of the estimator are investigated. Confidence bound curves are given. A simulation experiment is performed to evaluate the performance of the results.

Bootstrapping Nonparametric Prediction Intervals for Conditional Value-at-Risk with Heteroscedasticity

Using bootstrap method, we have constructed nonparametric prediction intervals for Conditional Value-at-Risk for returns that admit a heteroscedastic location-scale model where the location and scale functions are smooth, and the function of the error term is unknown and is assumed to be uncorrelated to the independent variable. The prediction interval performs well for large sample sizes and is relatively small, which is consistent with what is obtainable in the literature.

Age-dynamic networks and functional correlation for early white matter myelination

The maturation of the myelinated white matter throughout childhood is a critical developmental process that underlies emerging connectivity and brain function. In response to genetic influences and neuronal activities, myelination helps establish the mature neural networks that support cognitive and behavioral skills. The emergence and refinement of brain networks, traditionally investigated using functional imaging data, can also be interrogated using longitudinal structural imaging data. However, few studies of structural network development throughout infancy and early childhood have been presented, likely owing to the sparse and irregular nature of most longitudinal neuroimaging data, which complicates dynamic analysis. Here, we overcome this limitation and investigate through concurrent correlation the co-development of white matter myelination and volume, and structural network development of white matter myelination between brain regions as a function of age, using statistically well-supported methods. We show that the concurrent correlation of white matter myelination and volume is overall positive and reaches a peak at 580 days. Brain regions are found to differ in overall magnitudes and patterns of time-varying association throughout early childhood. We introduce time-dynamic developmental networks based on temporal similarity of association patterns in the levels of myelination across brain regions. These networks reflect groups of brain regions that share similar patterns of evolving intra-regional connectivity, as evidenced by levels of myelination, are biologically interpretable and provide novel visualizations of brain development. Comparing the constructed networks between different maternal education groups, we found that children with higher and lower maternal education differ significantly in the overall magnitude of the time-dynamic correlations.

A Functional Varying-Coefficient Single-Index Model for Functional Response Data

Motivated by the analysis of imaging data, we propose a novel functional varying-coefficient single index model (FVCSIM) to carry out the regression analysis of functional response data on a set of covariates of interest. FVCSIM represents a new extension of varying-coefficient single index models for scalar responses collected from cross-sectional and longitudinal studies. An efficient estimation procedure is developed to iteratively estimate varying coefficient functions, link functions, index parameter vectors, and the covariance function of individual functions. We systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions, the asymptotic distribution of the estimated index parameter vectors, and the uniform convergence rate of the estimated covariance function and their spectrum. Simulation studies are carried out to assess the finite-sample performance of the proposed procedure. We apply FVCSIM to investigating the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

Identification of Nonlinear Spatiotemporal Dynamical Systems With Nonuniform Observations Using Reproducing-Kernel-Based Integral Least Square Regulation

The identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades. Several methods, such as searching principle-based algorithms, partially linear kernel methods, and coupled lattice methods, have been developed to address the identification problems. However, most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains. These are actually not applicable for some practical applications. In this paper, to tackle this issue, a novel kernel-based learning algorithm named integral least square regularization regression (ILSRR) is proposed, which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain. With this technique, a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified. Thereafter, with this novel inverse meshless collocation model, the ILSRR, and a multiple-kernel-based learning algorithm, a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations. Numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method.

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory.