Semi-parametric time-to-event modelling of lengths of hospital stays

Length of stay (LOS) is an essential metric for the quality of hospital care. Published works on LOS analysis have primarily focused on skewed LOS distributions and the influences of patient diagnostic characteristics. Few authors have considered the events that terminate a hospital stay: Both successful discharge and death could end a hospital stay but with completely different implications. Modelling the time to the first occurrence of discharge or death obscures the true nature of LOS. In this research, we propose a structure that simultaneously models the probabilities of discharge and death. The model has a flexible formulation that accounts for both additive and multiplicative effects of factors influencing the occurrence of death and discharge. We present asymptotic properties of the parameter estimates so that valid inference can be performed for the parametric as well as nonparametric model components. Simulation studies confirmed the good finite-sample performance of the proposed method. As the research is motivated by practical issues encountered in LOS analysis, we analysed data from two real clinical studies to showcase the general applicability of the proposed model.

Semiparametric efficient estimation for additive hazards regression with case II interval-censored survival data

Interval-censored data often arise naturally in medical, biological, and demographical studies. As a matter of routine, the Cox proportional hazards regression is employed to fit such censored data. The related work in the framework of additive hazards regression, which is always considered as a promising alternative, remains to be investigated. We propose a sieve maximum likelihood method for estimating regression parameters in the additive hazards regression with case II interval-censored data, which consists of right-, left- and interval-censored observations. We establish the consistency and the asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The finite-sample performance of the proposed method is assessed via comprehensive simulation studies, which is further illustrated by a real clinical example for patients with hemophilia.

On computation of semiparametric maximum likelihood estimators with shape constraints

Large sample theory of semiparametric models based on maximum likelihood estimation (MLE) with shape constraint on the nonparametric component is well studied. Relatively less attention has been paid to the computational aspect of semiparametric MLE. The computation of semiparametric MLE based on existing approaches such as the expectation-maximization (EM) algorithm can be computationally prohibitive when the missing rate is high. In this paper, we propose a computational framework for semiparametric MLE based on an inexact block coordinate ascent (BCA) algorithm. We show theoretically that the proposed algorithm converges. This computational framework can be applied to a wide range of data with different structures, such as panel count data, interval-censored data, and degradation data, among others. Simulation studies demonstrate favorable performance compared with existing algorithms in terms of accuracy and speed. Two data sets are used to illustrate the proposed computational method. We further implement the proposed computational method in R package BCA1SG, available at CRAN.

Semiparametric probit models with univariate and bivariate current-status data

Multivariate current-status data are frequently encountered in biomedical and public health studies. Semiparametric regression models have been extensively studied for univariate current-status data, but most existing estimation procedures are computationally intensive, involving either penalization or smoothing techniques. It becomes more challenging for the analysis of multivariate current-status data. In this article, we study the maximum likelihood estimations for univariate and bivariate current-status data under the semiparametric probit regression models. We present a simple computational procedure combining the expectation-maximization algorithm with the pool-adjacent-violators algorithm for solving the monotone constraint on the baseline function. Asymptotic properties of the maximum likelihood estimators are investigated, including the calculation of the explicit information bound for univariate current-status data, as well as the asymptotic consistency and convergence rate for bivariate current-status data. Extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes. We demonstrate the estimation procedure with two real data examples in the areas of diabetic and HIV research.