On a Shape-Invariant Hazard Regression Model with application to an HIV Prevention Study of Mother-to-Child Transmission

In survival analysis, Cox model is widely used for most clinical trial data. Alternatives include the additive hazard model, the accelerated failure time (AFT) model and a more general transformation model. All these models assume that the effects for all covariates are on the same scale. However, it is possible that for different covariates, the effects are on different scales. In this paper, we propose a shape-invariant hazard regression model that allows us to estimate the multiplicative treatment effect with adjustment of covariates that have non-multiplicative effects. We propose moment-based inference procedures for the regression parameters. We also discuss the risk prediction and the goodness of fit test for our proposed model. Numerical studies show good finite sample performance of our proposed estimator. We applied our method to the HIVNET 012 study, a milestone trial of single-dose nevirapine in prevention of mother-to-child transmission of HIV. From the HIVNET 012 data analysis, single-dose nevirapine treatment is shown to improve 18-month infant survival significantly with appropriate adjustment of the maternal CD4 counts and the virus load.

Methods for Contrasting Gap Time Hazard Functions: Application to Repeat Liver Transplantation

In studies featuring a sequence of ordered events, gap times between successive events are often of interest. Despite the rich literature in this area, very few methods for comparing gap times have been developed. We propose methods for estimating a hazard ratio connecting the first and second gap times. Specifically, a two-stage procedure is developed based on estimating equations. At the first stage, a proportional hazards model is fitted for the first gap time. Weighted estimating equations are then solved at the second stage to estimate the hazard ratio between the first and second gap times. The proposed estimator has a closed form and, being analogous to a standardized mortality ratio, is easy to interpret. Large sample properties of the proposed estimators are derived, with simulation studies used to evaluate finite sample characteristics. Extension of the approach to accommodate a piecewise constant hazard ratio is considered. The proposed methods are applied to contrast repeat (second) versus primary (first) liver transplants with respect to graft failure, based on national registry data.

Joint scale-change models for recurrent events and failure time

Recurrent event data arise frequently in various fields such as biomedical sciences, public health, engineering, and social sciences. In many instances, the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event, such as treatment failure and death. In this article, we propose a joint scale-change model for the recurrent event process and the failure time, where a shared frailty variable is used to model the association between the two types of outcomes. In contrast to the popular Cox-type joint modeling approaches, the regression parameters in the proposed joint scale-change model have marginal interpretations. The proposed approach is robust in the sense that no parametric assumption is imposed on the distribution of the unobserved frailty and that we do not need the strong Poisson-type assumption for the recurrent event process. We establish consistency and asymptotic normality of the proposed semiparametric estimators under suitable regularity conditions. To estimate the corresponding variances of the estimators, we develop a computationally efficient resampling-based procedure. Simulation studies and an analysis of hospitalization data from the Danish Psychiatric Central Register illustrate the performance of the proposed method.

Semiparametric time-to-event modeling in the presence of a latent progression event

In cancer research, interest frequently centers on factors influencing a latent event that must precede a terminal event. In practice it is often impossible to observe the latent event precisely, making inference about this process difficult. To address this problem, we propose a joint model for the unobserved time to the latent and terminal events, with the two events linked by the baseline hazard. Covariates enter the model parametrically as linear combinations that multiply, respectively, the hazard for the latent event and the hazard for the terminal event conditional on the latent one. We derive the partial likelihood estimators for this problem assuming the latent event is observed, and propose a profile likelihood-based method for estimation when the latent event is unobserved. The baseline hazard in this case is estimated nonparametrically using the EM algorithm, which allows for closed-form Breslow-type estimators at each iteration, bringing improved computational efficiency and stability compared with maximizing the marginal likelihood directly. We present simulation studies to illustrate the finite-sample properties of the method; its use in practice is demonstrated in the analysis of a prostate cancer data set.

Flexible Bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects

Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide modifiable, user-friendly software that allows the use of these methods in a variety of settings. To accomplish this aim, we use a novel model formulation for the log-hazard based on a low-rank thin plate linear spline that readily facilitates adjustment for covariates with time-dependent and proportional hazards effects, possibly subject to shape restrictions. We investigate the performance of our model choices via simulation. We then analyze colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care for overall survival. We estimate a time-dependent hazard ratio for each novel regime relative to the standard of care while adjusting for the effect of aspartate transaminase, a biomarker of liver function, that is subject to a non-decreasing shape restriction.

A semiparametric graphical modelling approach for large-scale equity selection

We propose a new stock selection strategy that exploits rebalancing returns and improves portfolio performance. To effectively harvest rebalancing gains, we apply ideas from elliptical-copula graphical modelling and stability inference to select stocks that are as independent as possible. The proposed elliptical-copula graphical model has a latent Gaussian representation; its structure can be effectively inferred using the regularized rank-based estimators. The resulting algorithm is computationally efficient and scales to large data-sets. To show the efficacy of the proposed method, we apply it to conduct equity selection based on a 16-year health care stock data-set and a large 34-year stock data-set. Empirical tests show that the proposed method is superior to alternative strategies including a principal component analysis-based approach and the classical Markowitz strategy based on the traditional buy-and-hold assumption.

The efficiency of the second-order nonlinear least squares estimator and its extension

We revisit the second-order nonlinear least square estimator proposed in Wang and Leblanc (Anne Inst Stat Math 60:883-900, 2008) and show that the estimator reaches the asymptotic optimality concerning the estimation variability. Using a fully semiparametric approach, we further modify and extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimator.

A Semiparametric Approach to Dimension Reduction

We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension reduction techniques as special cases in this class. The semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact, the common assumption of linearity and/or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression. The semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example. This article has online supplementary material.