Inference on semi-parametric transformation model with a pairwise likelihood based on left-truncated and interval-censored data

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study.</p

A new approach for semi-parametric regression analysis of bivariate interval-censored outcomes from case-cohort studies

Interval-censored failure time data frequently occur in many areas and a great deal of literature on their analyses has been established. In this article, we discuss the situation where one faces bivariate interval-censored data arising from case-cohort studies, which are commonly used as a tool to save costs when disease incidence is low and covariates are difficult to obtain. For this problem, a class of copula-based semi-parametric models is presented and for estimation, a sieve weighted maximum likelihood estimation procedure is developed. The resulting estimators of regression parameters are shown to be strongly consistent and asymptotically normal. Furthermore, the proposed method is generalized to the situation of non rare diseases. A simulation study is conducted to assess the finite sample performance of the proposed method and suggests that it performs well in practice.</p

A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data

<p>Interval-censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis. However, most of the existing methods are for univariate data and there exists only limited research on bivariate data, especially on regression analysis of bivariate interval-censored data. We present a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed. The strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore, the estimators are shown to be asymptotically efficient. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. Supplementary materials for this article are available online.</p

Additional file 1 of A pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

Additional file 1

S1 Data -

The panel data of 50 new energy vehicle enterprises in Shanghai and Shenzhen A-shares from 2012 to 2021 are selected to empirically analyze the impact of government subsidies on the innovation of new energy vehicle enterprises and to further discuss the differences between such an impact in different forms and regions. The study finds that, first, government subsidies have a certain promotion effect on the innovation of new energy vehicle enterprises, and an inverted U-shaped relationship exists thereof. Second, at the enterprise level, government subsidies have a significant effect on the innovation of non-state enterprises, downstream vehicle enterprises, and enterprises with lower establishment years, and the inverted-U trend is evident. Third, at the regional level, government subsidies have a more significant effect on the innovation of enterprises in non-eastern regions and low-environmental regulation regions, and the inverted-U-shaped relationship trend is more apparent. The study establishes the nonlinear relationship between government subsidies and the innovation of new energy vehicle enterprises through empirical research, which expands the theory of enterprise innovation and has a certain guiding significance for improving the innovation capability of new energy vehicle enterprises in the future.</div

Basic regression.

The panel data of 50 new energy vehicle enterprises in Shanghai and Shenzhen A-shares from 2012 to 2021 are selected to empirically analyze the impact of government subsidies on the innovation of new energy vehicle enterprises and to further discuss the differences between such an impact in different forms and regions. The study finds that, first, government subsidies have a certain promotion effect on the innovation of new energy vehicle enterprises, and an inverted U-shaped relationship exists thereof. Second, at the enterprise level, government subsidies have a significant effect on the innovation of non-state enterprises, downstream vehicle enterprises, and enterprises with lower establishment years, and the inverted-U trend is evident. Third, at the regional level, government subsidies have a more significant effect on the innovation of enterprises in non-eastern regions and low-environmental regulation regions, and the inverted-U-shaped relationship trend is more apparent. The study establishes the nonlinear relationship between government subsidies and the innovation of new energy vehicle enterprises through empirical research, which expands the theory of enterprise innovation and has a certain guiding significance for improving the innovation capability of new energy vehicle enterprises in the future.</div

Enterprise heterogeneity.

The panel data of 50 new energy vehicle enterprises in Shanghai and Shenzhen A-shares from 2012 to 2021 are selected to empirically analyze the impact of government subsidies on the innovation of new energy vehicle enterprises and to further discuss the differences between such an impact in different forms and regions. The study finds that, first, government subsidies have a certain promotion effect on the innovation of new energy vehicle enterprises, and an inverted U-shaped relationship exists thereof. Second, at the enterprise level, government subsidies have a significant effect on the innovation of non-state enterprises, downstream vehicle enterprises, and enterprises with lower establishment years, and the inverted-U trend is evident. Third, at the regional level, government subsidies have a more significant effect on the innovation of enterprises in non-eastern regions and low-environmental regulation regions, and the inverted-U-shaped relationship trend is more apparent. The study establishes the nonlinear relationship between government subsidies and the innovation of new energy vehicle enterprises through empirical research, which expands the theory of enterprise innovation and has a certain guiding significance for improving the innovation capability of new energy vehicle enterprises in the future.</div

Variable descriptions.

The panel data of 50 new energy vehicle enterprises in Shanghai and Shenzhen A-shares from 2012 to 2021 are selected to empirically analyze the impact of government subsidies on the innovation of new energy vehicle enterprises and to further discuss the differences between such an impact in different forms and regions. The study finds that, first, government subsidies have a certain promotion effect on the innovation of new energy vehicle enterprises, and an inverted U-shaped relationship exists thereof. Second, at the enterprise level, government subsidies have a significant effect on the innovation of non-state enterprises, downstream vehicle enterprises, and enterprises with lower establishment years, and the inverted-U trend is evident. Third, at the regional level, government subsidies have a more significant effect on the innovation of enterprises in non-eastern regions and low-environmental regulation regions, and the inverted-U-shaped relationship trend is more apparent. The study establishes the nonlinear relationship between government subsidies and the innovation of new energy vehicle enterprises through empirical research, which expands the theory of enterprise innovation and has a certain guiding significance for improving the innovation capability of new energy vehicle enterprises in the future.</div

Descriptive statistics.

The panel data of 50 new energy vehicle enterprises in Shanghai and Shenzhen A-shares from 2012 to 2021 are selected to empirically analyze the impact of government subsidies on the innovation of new energy vehicle enterprises and to further discuss the differences between such an impact in different forms and regions. The study finds that, first, government subsidies have a certain promotion effect on the innovation of new energy vehicle enterprises, and an inverted U-shaped relationship exists thereof. Second, at the enterprise level, government subsidies have a significant effect on the innovation of non-state enterprises, downstream vehicle enterprises, and enterprises with lower establishment years, and the inverted-U trend is evident. Third, at the regional level, government subsidies have a more significant effect on the innovation of enterprises in non-eastern regions and low-environmental regulation regions, and the inverted-U-shaped relationship trend is more apparent. The study establishes the nonlinear relationship between government subsidies and the innovation of new energy vehicle enterprises through empirical research, which expands the theory of enterprise innovation and has a certain guiding significance for improving the innovation capability of new energy vehicle enterprises in the future.</div

Sample enterprises of new energy vehicles.

The panel data of 50 new energy vehicle enterprises in Shanghai and Shenzhen A-shares from 2012 to 2021 are selected to empirically analyze the impact of government subsidies on the innovation of new energy vehicle enterprises and to further discuss the differences between such an impact in different forms and regions. The study finds that, first, government subsidies have a certain promotion effect on the innovation of new energy vehicle enterprises, and an inverted U-shaped relationship exists thereof. Second, at the enterprise level, government subsidies have a significant effect on the innovation of non-state enterprises, downstream vehicle enterprises, and enterprises with lower establishment years, and the inverted-U trend is evident. Third, at the regional level, government subsidies have a more significant effect on the innovation of enterprises in non-eastern regions and low-environmental regulation regions, and the inverted-U-shaped relationship trend is more apparent. The study establishes the nonlinear relationship between government subsidies and the innovation of new energy vehicle enterprises through empirical research, which expands the theory of enterprise innovation and has a certain guiding significance for improving the innovation capability of new energy vehicle enterprises in the future.</div